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Evapotranspiration

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Title:
Evapotranspiration
Series Title:
Evapotranspiration
Creator:
Heimburg, Klaus
Publisher:
Klaus Heimburg
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Language:
English

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Subjects / Keywords:
Dew point ( jstor )
Estimation methods ( jstor )
Evapotranspiration ( jstor )
Heat ( jstor )
Heat flux ( jstor )
Sensors ( jstor )
Surface temperature ( jstor )
Temperature gradients ( jstor )
Temperature measurement ( jstor )
Vapor pressure ( jstor )

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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028900424 ( AlephBibNum )
09617030 ( OCLC )

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EVAPOTRANSPIRATION: AN AUTOMATIC MEASUREMENT SYSTEM
AND A REMOTE-SENSING METHOD FOR
REGIONAL ESTIMATES




BY

KLAUS HEIMBURG


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF ACTOR R OF PHILOSOPHY


UNIVERSITY OF FLORIDA


1982














ACKNOWLEDGMENTS


The work reported in this dissertation grew out of National Aero-

nautics and Space Administration (NASA) sponsored water resources re-

search. It was primarily supported by a grant from the Office of Water

Resources Technology in the U.S. Department of the Interior and Agri-

culture and Resources Inventory Surveys Through Aerospace Remote Sens-

ing (AgRISTARS) program funds administered through the U.S. Department

of Agriculture (USDA). Some support was also received in the form of an

assistantship from the Agronomy Department at the University of

Florida. All these sources of support.are gratefully acknowledged.

I would especially like to thank Dr. Wayne C. Huber and Dr. L.

Hartwell Allen, Jr. for signing the original research proposal as prin-

ciple investigators and seeing this project through to its completion.

Without their initial confidence in me and the day-to-day administra-

tive efforts of Dr. Allen none of the work would have been possible. I

would also like to thank them and the rest of my supervisory committee,

Dr. Howard T. Odum, Dr. Ralph W. Swain, and Dr. James P. Heaney for

improvements they made possible with their comments on the manuscript.

The research reported in this dissertation stretched over four

years and required the help and cooperation of many people. Sensors and

other equipment were borrowed from USDA, NASA, Center for Wetlands,

Fruit Crops Department, and Environmental Engineering Sciences Depart-

ment of the University of Florida. The Animal Science Department per-

mitted ET measurements in part of one of its pastures and the Agronomy









Department provided space for an instrument room. The people I owe spe-

cial thanks to are Bill Ocumpaugh and Fred McGraw for patiently working

around the measurement equipment and giving up some space; Johnny

Weldon for allowing me the use of the Agricultural Engineering Depart-

ment machine shop; Jim Hales for use of his tools and advice in fabri-

cating apparatus in the machine shop; Mark Lester for his fine machin-

ing; my brother Stephan Heimburg for conscientiously checking and ad-

justing the thermopile time constants; Mike Baker for designing and

helping build the scanning valve control electronics, and repairing the

dewpoint analyzer after a lightning strike; Wayne Wynn for help in

maintaining the measurement system; Dan Ekdahl at the Digital Design

Facility for .electronics repairs--especially a lightning-damaged compu-

ter-controlled voltmeter and similarly damaged computer interface

-.boards; and finally, Beth Chandler for expeditiously inking most of the

figures in this dissertation.

I also wish to thank Dr. Tom R. Sinclair for finally revealing why

Real Scientists don't do micrometeorology in a neat five-minute sermon-

ette.

I owe a debt of gratitude beyond words to three people who went

miles out of their way to help me. Gene Hannah was invaluable in the

original field installation and helped with problems throughout the

course of the project. I'm thankful to Ferris Johnson for his tireless

assistance in use of the computer system and trouble-shooting computer

hardware problems. Finally, I enthusiastically acknowledge the work of

Pattie Everett, who spared no effort and sacrificed evenings, weekends

and holidays in moving this manuscript through countless drafts toward

perfection.








The post-defense party thrown in my honor made the frustrations

encountered in this work seem tolerable--even worthwhile. I have Pattie

Everett, Bill Campbell, Pierce Jones, and Lisa Lucille Biles to thank

for this totally awesome affair, not to mention that Wild and Crazy

Guy, Terry Spires, and the overwhelming Special Guest Appearance of

The Sublime Ms. Shavonne Rhodes. Get down, tiny dancers!















TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS . . . . . . . . ... ....... ii

LIST OF FIGURES . . . . . . . . ... ....... vii

LIST OF TABLES . ... ... . . . . . . . . ix

ABSTRACT . . . . . . . . ... . . . . x

CHAPTER 1: INTRODUCTION . . . . . . . .... ... 1

Potential for Remote Evapotranspiration Estimates .. . 1
Scope of Research . . . . . . . . . '3
Research Approach . . . . . . . . . . 5
Experimental Site and Data Collection .......... 7
Organization of Dissertation . . . . . . ... 11

...CHAPTER 2: EVAPOTRANSPIRATION AND SATELLITE DATA .. .. .. 12

Overview . . . . . . . . . . . . 12
The Evapotranspiration Process . . . . . . .. 12
The Energy Balance Approach to ET Estimation . . . .. 17
The Energy Budget Equation . . .. ...... 17
Transport Similarity and Wind Models ........ 20
Latent and Sensible Heat Flux Expressions ... .. 23
Energy Budget ET Estimation Strategies . . ... 26
Remote ET Estimation Methods . . . . . . .... 29
Surface Temperature and Net Radiation . . . ... 29
Simulation Methods . . . . . . . ... .30
Steady-State Methods . . . . . . .... 33
Temperature Gradient Response Methods . . . ... 35

CHAPTER 3: A SYSTEM FOR AUTOMATIC COLLECTION OF ET DATA . 37

Overview . . . . . . . .. . ... . .37
Energy Budget/Profile Bowen Ratio Theory . . . ... 37
Sensor and Time Constant Considerations . . . ... 40
Data Collection Equipment . . . . . . .... 44
Data Collection Programs . . . . . . . ... 51
Operational Considerations. .... . . . . .58









CHAPTER 4: THEORETICAL BASIS OF THE TEMPERATURE GRADIENT RESPONSE
ET ESTIMATION METHODS . . . . . . .... 62

Overview . . . . . . . ... ..... .62
Temperature Gradient Model . . . . . . .... 63
Strict Temperature Gradient Response Method . . ... 69
Average Temperature Gradient Response Method . . . .. 70
System Stationarity and Average Temperature Gradient
Response . . . . . . . . . . . 70
Use of Temperature Gradient/Net Radiation Correlation 73
Extension to Totally Remote ET Estimation Method . 77
Review of Assumptions . . . . . . . .... .79

CHAPTER 5: VERIFICATION OF THE TEMPERATURE GRADIENT RESPONSE
ET ESTIMATION METHODS . . . . . . ... 82

Overview ............... ... . . . . 82
Validity of Assumptions . . . . . . . . 83
Radiation Temperature and Sensible Heat Transport . 83
Constancy of Parameters . . . . . . .... 86
Strict Temperature Gradient Response Method . . .. 95
Average Temperature Gradient Response Method . . . .. 97
Graphical Representation of the Average TGR Method .97
ET Estimates with the Average TGR Method ...... 103
Effects of Individual Parameter Variations . . .. 105
Generality of ATGR Latent/Sensible Partition .... .112
Tests of the ATGR Method .. ... ...... . ..114

CHAPTER 6: CONCLUSION . . . . . . . . ... ... 123

Summary of Results . . . . . . . . . . 123
The Average Temperature Gradient Response Method . 123
Method Limitations and Strengths . . . . .. 125
Recommendations for Future Research . . . . .... 128

REFERENCES . . . . . . . ... .... . . 131

APPENDIX A: LIST OF SYMBOLS . . . . . . . .. . 136

APPENDIX B: PROGRAM LISTING AND DEFINITION OF NAMES USED . . 138

Program SET . . . . . . . . ... ...... 139
Program MEASR . . . . . . . . ... ... . 141
Program REPRT . . . . . . . . ... .... . 146
Program ANALZ . . . . . . . . ... .... . 149
Definition of Names . . . . . . . .... 152

APPENDIX C: SUMMARY OF ENERGY BUDGET DATA . . . . .. 157

APPENDIX D: SUPPLEMENTARY FIGURES . . . . . .... 178

BIOGRAPHICAL SKETCH . . . . . . . . ... .... . 211









LIST OF FIGURES


Page


Figure 1-1.


Figure

Figure


Figure

Figure


Figure

Figure

Figure

Figure

Figure

'Figure

Figure

Figure


1-2.

2-1.


2-2.

3-1.


3-2.

3-3.

3-4.

3-5.

3-6.

4-1.

4-2.

5-1.


Figure 5-2.


Figure

Figure

Figure

Figure

Figure


5-3.

5-4.

5-5.

5-6.

5-7.


Figure 5-8.


Figure 5-9.


Location of the University of Florida Beef Re-
search Unit . . . . . . . . . . .

Field Apparatus and Sensor Locations . . . .

System Diagram of Generalized Evapotranspiring
Surface . . . . . . . . . . . .

Rough Calculation of Heat Storage in Pasture Canopy

Bowen Ratio Calculation from Measurements of Vapor
Pressure and Temperature . . . . . . .

Schematic of ET Measurement System . . . . .

Detail of Profile Measurement Mast Arm . . . .

Detail of Air Sampling Equipment . . . . .

Example of Intermediate Program Output . . . .

Example of Half-Hourly Data Report . . . .

Definition Sketch for Transport Properties

Components of Vapor Pressure Gradient . . . .

Total vs. Turbulent Temperature Gradients for a
Clear Day . . . . . . . . . . .

Total vs. Turbulent Temperature Gradients for a
Cloudy Day . . . . . . . . . . .

Heat Transport Coefficient Data . . . . ..

Moisture Availability Data . . . . . . .

Vapor Pressure Parameter Data . . . . . .

Soil Heat Flux Parameter Data . . . . . .

Clear Day Temperature Gradient/Net Radiation Corre-
lation . . . . . . . . . . .

Graphical Interpretation of Temperature Gradient/Net
Radiation Correlation . . . . . . . .

Cumulative ET Estimates . . . . . . .


S8

* 10


. 14

. 19


. 41

. 45

* 48

. 50

* 53

* 56

* 64

* 67


. 87

. 89

. 91

S92

. 94


S98


100

102









Figure 5-10. Effect of Moisture Availability and Vapor Pressure
Parameters on Temperature Gradients . . . .

Figure 5-11. Effect of Heat Transport Coefficient and Soil Heat
Flux Parameter on Temperature Gradients . . .

Figure 5-12. Temperature Gradient Response of a Clear Day with
Constant Moisture Availability . . . . .

Figure 5-13. Temperature Gradient Response of a Partly Cloudy
Day . . . . . . . . . . . .

Figure 5-14. Generalized Clear Day H/E and E/R Patterns . .

Figure 5-15. Comparison of Measured and Estimated Bowen Ratios

Figure 5-16. Cumulative ET Estimates by the ATGR and Residual
Methods . . . . . . . . . . .


Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.


Figure 8.

Figure 9.

Figure 10.

Figure 11.

Figure 12.


Appendix D: Supplementary Figures

Hypothetical Daytime Temperature Profile . . .

Simplified Temperature Profile . . . . . .

Simplified Temperature Profiles for a Clear Day . .

Simplified Temperature Profiles for an Overcast Day

Air Transport Coefficient for Average Conditions .

Soil Heat Flux Parameter for Average Conditions . .

Variation of the Daily Average Heat Transport
Coefficient with the Daily Average Windspeed . .

Data and ET Estimates for Oct. 17, 1981 . . . .

Data and ET Estimates for Oct. 18, 1981 . . . .

Data and ET Estimates for Oct. 21, 1981 . . . .

Data and ET Estimates for Oct. 22, 1981 . . . .

Data and ET Estimates for Oct. 23, 1981 . . . .


viii


106


107


110


111

113

115


122








LIST OF TABLES


Table 1-1.

Table 3-1.

Table 3-2.

Table 3-3.

Table 4-1.

Table 5-1.

Table 5-2.


Table 5-3.


Page

Spatial and Temporal Resolution in Satellites . 3

Data Acquisition System Identification . . .. 46

Sensor Identification . . . . . . . . 49

Variable Names and Units for Half-Hourly Reports . 57

Evapotranspiration Formulae for Average TGR Method . 74

Example Calculations with the Strict TGR Method . 96

Comparison of Average and Correlation Estimated
A and B . . . . . . . .... ... . 116

Quality of ET Estimates made with the ATGR Method .119














Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


EVAPOTRANSPIRATION: AN AUTOMATIC MEASUREMENT SYSTEM
AND A REMOTE-SENSING METHOD FOR
REGIONAL ESTIMATES

By

Klaus Heimburg

December 1982

Chairman: Wayne C. Huber
Major Department: Environmental Engineering Sciences

A generalized physical method is developed for making evapotran-

spiration (ET) estimates based on directly measured air temperature and

remotely sensed surface temperature and net radiation data. The method

is based on the correlation of surface-to-air temperature gradients and

varying net radiation loads; the slope and intercept of this correla-

tion are shown to be composite values of two groups of surface parame-

ters. Five equations are developed to calculate ET from these composite

values plus net radiation and some combination of two of the four sur-

face parameters (bulk air transport, moisture availability, saturation

deficit, and soil heat flux).

The method is validated using ET measurements made over a pasture

surface using the energy budget/profile Bowen ratio technique. An auto-

matic measurement system consisting of a computer-controlled data ac-

quisition system and air sampling arrangement, time-constant-matched

humidity, temperature, and radiation sensors, and four interacting








programs was developed to measure and calculate half-hour average sur-

face energy budgets and statistics. Data from 42 days in the spring and

fall of 1981 are reported.

It was found that the radiation surface temperature is in general

not the same as the effective heat transport surface temperature--it

may be necessary to correct remote surface temperature measurements

before using them with conventionally evaluated heat transport coeffi-

cients. Because parameters are assumed constant, instantaneous ET esti-

mates made with the developed method are at times systematically high

or low, but these errors tend to cancel in cumulative estimates.

The method is shown to be well-suited for use with 1- to 3-hour

time resolution satellite data. In effect it evaluates surface parame-

ters such as moisture availability, requires no interpolation for ET

.estimates between data sets, is adapted to the inevitable cloud-caused

loss of satellite surface temperature data, and reduces calculation of

cumulative ET to estimating total positive net radiation and duration

of positive net radiation in a particular estimation period. The meth-

od's ET estimates are shown to be as accurate as the state-of-the-art

simple residual method, which does not have these advantages.














CHAPTER 1

INTRODUCTION

Potential for Remote Evapotranspiration Estimates

The loss of water from the earth's surface by either evaporation

from soil and plant surfaces or transpiration by plants is called evapo-

transpiration (ET). Along with rainfall and runoff, it plays a very sig-

nificant role in determining the availability of water at the earth's

surface and the recharge to deep aquifers. Because water is critically

important to man's existence, ET estimation methods are important in

solving problems of water supply.

Water supply problems in relatively dry areas have long included

the estimation of crop water requirements, evaporation from reservoirs,

and evapotranspiration over aquifer recharge areas. As population has

grown, the demand for water has increased and interest in estimation

methods has become more widespread. Today, there is a growing need for

evapotranspiration estimates even in relatively wet areas, such as

Florida.

Present methods of measuring and estimating ET are diverse, depend-

ing upon the specific purposes of the estimates and available data. On

the one hand are physically-based measurement techniques developed by

scientists. They provide accurate instantaneous ET rates for a specific

location, but require continuous measurements of such variables as air

temperature and vapor pressure, net radiation, and soil heat flux. Exam-

ples of these techniques are the eddy flux correlation, energy








budget/profile Bowen ratio and Penman methods (American Society of Agri-

cultural Engineers, 1966; Brutsaert, 1982).

On the other hand, water use planners and water supply engineers

have developed methods which produce daily to monthly estimates for

larger areas. In locations where such records are kept, these methods

are based on climatologic data. They are generally founded on some phys-

ical correlation, but all involve empirical adjusting factors for vege-

tation type, air humidity, altitude and the like. Examples are the

Blaney-Criddle method, the radiation method, the Penman method, and the

pan evaporation methods (Doorenbos and Pruitt, 1977).

The weather stations which provide the base information for these

methods are widely scattered. On the average, each station in the United

States represents an area on the order of 100 mi square (Price, 1982).

Regional estimates of evapotranspiration are thus difficult to make and

of dubious accuracy. They are limited by insufficient data on highly

variable surface parameters such as soil moisture conditions and vegeta-

tion types.

By comparison to the weather station network, today's satellites

return remotely sensed information about the earth's surface with an

unprecedented level of detail. The surface area element or pixel sizes

and the time intervals between coverage of some of the satellites appro-

priate to regional scale studies are shown in Table 1-1. As a result of

the availability of this type of data and modern high-speed computers,

the potential exists to systematically monitor evapotranspiration on a

regional scale.

Development of this potential could benefit a variety of research.

areas. If remote-sensing methods are also developed to estimate rainfall










Table 1-1. Spatial and Temporal Resolution in Satellites

Satellite Orbit Pixel Time
Acronym Type Size Intervals

Landsat polar 80 x 80 m 18 da
HCMM polar .6 x .6 km 12 hr each 5 da
TIROS polar 1 x 1 km 12 hr.
GOES geostationary 8 x 4 km 30 min


on a regional basis and if streamflow is gaged, aquifer recharge over

wide areas can be estimated (Allen et al., 1980). The information on

surface energy fluxes gained by an ET estimation technique could also be

useful as boundary conditions for models of the atmosphere. It is also

possible that large-scale changes on the earth's surface such as defor-

estation and desertification could be monitored by observing longer-term

changes in ET patterns. Finally, the correlation of evapotranspiration

and yield in agronomic crops may lead to large-scale yield predictions

(Doorenbos and Pruitt, 1977; Chang, 1968).

The purpose of this research is to develop and test a generally

applicable method for estimating evapotranspiration based as much as

possible on remotely sensed data. Since it is ultimately intended for

use with satellite data from large diverse areas, criteria for this

method include that it be strictly physical, relatively easy to apply,

and compatible with the format and limitations of satellite data. The

research is also intended to identify factors critical to the accuracy

of the estimates which require more research, and factors which may im-

prove future satellite measurement for use in ET estimation.

Scope of the Research

Data returned from a satellite consist of the energy flux in a par-

ticular band of wavelengths coming from a particular surface area








element at a particular time. For environmental applications, the elec-

tromagnetic spectrum is usually resolved into visible and thermal bands.

With a clear sky and proper consideration of atmospheric transmission

properties, these measurements can be used to calculate the surface tem-

perature and the net radiation absorbed by the surface.

Net radiation and surface temperature estimates should lead to good

evapotranspiration estimates because they are very prominent variables

in the heat exchange processes that take place at the earth's surface.

Net radiation is the primary energy source used in changing water from

liquid to vapor at the surface, while surface temperature--because it is

a result of surface variables and energy exchange processes--is a com-

posite measurement of the effects of these variables.

However, it is a long step from measurements of net radiation and

surface temperature to an operational ET estimating system using satel-

lite data. The following questions illustrate the range of problems

faced in developing a method for such a system.

1. What is the best way to estimate net radiation from satellite
pixel information? How does one treat clouds or haze?

2. How is the radiation temperature of a complex surface like that
of vegetation interpreted? Does angle of view and height of
vegetation make a difference? How does one handle a canopy
underlain by a cool surface like a marsh or swamp? How does
one treat mountainous topography?

3. Is an interpolation technique required to compensate for the
temporal resolution of satellite data?

4. What level of detail is required in a practical ET estimation
method? How does one get the most acceptably accurate estimate
for the least effort in data collection and processing?

5. How are the effects of water availability, vegetation type,
cloudiness, and wind related? And how do they influence ET?
What is the minimum amount of data needed from ground-based
observations?









6. Can estimates made with area average data be of reasonable
accuracy when there are various vegetation types or net ra-
diation regimes in the same pixel?

7. Ultimately, what factor most limits the accuracy of a given
remote estimation scheme?

The work described in this dissertation addresses many of these

questions. The emphasis is on how to most efficiently account for all

the factors affecting evapotranspiration, and how to extract as much

information as possible about the surface and its environment from re-

mote data. Practical limitations such as the fact that satellite data

are available only at discrete time intervals and sometimes incomplete

because clouds prevent a surface temperature measurement are considered.

All ground-based measurements except air temperature were avoided; meth-

ods to eliminate this measurement are suggested, but their investigation

was considered beyond the scope of this research.

It is assumed that estimates of net radiation and surface tempera-

ture are, barring clouds, available at regular time intervals. The ques-

tion of complex radiation temperatures is side-stepped by considering a

relatively simple pasture grass surface. Although a parameter that in-

cludes the effect of wind on evapotranspiration is used, its functional

dependence on windspeed is not explored.

Research Approach

The overall approach to developing a remote evapotranspiration es-

timation scheme was to compare estimates made with trial methods to ac-

tual ET rates measured over a test surface. Accordingly, there were

three main areas of effort: the collection of a base of accurate ET

data, the theoretical development of an estimation method based on re-

motely sensed data, and the testing of that method against the actual ET

measurements.








As suggested in the previous section, the enormous variety of ter-

rain and vegetation types present on the earth's surface introduce a

large number of complicating factors into ET estimation formulations. In

order to clearly assess the potential of a general method, as many of

these complicating factors as possible were avoided by choosing a rela-

tively homogeneous flat area of pasture as a test surface. The approach

was to develop a basic method which would work for simple surfaces; once

it is proven successful can be modified if necessary to deal with

more complex situations like mountainous terrain or swamp.

A micrometeorologic measurement technique was used to measure ac-

tual ET so that surface processes were left as undisturbed as possible.

The radiation surface temperature as well as net radiation was measured

for later use in method-testing. A great deal of effort went into devel-

oping a data collection system to assure the reliability of the ET mea-

surements. Special efforts were made to match the time constants of the

sensors involved and to reduce electrical signal noise. Control of the

measuring system, scheduling of the measurements, and calculations were

all performed by computer to minimize human error.

The fundamental assumption in method development was that satellite

data would be available in time intervals on the order of 1-3 hours.

After this assumption, the emphasis was on operational criteria--a prac-

tical method must have general applicability, computational simplicity,

and low data requirements. With these objectives in mind, an analytical

approach, rather than a simulation approach, was chosen. In order to

keep data requirements low yet take advantage of satellite data, the

level of detail was chosen to be somewhat intermediate between the

strictly physical ET measurement methods and the empirical estimation









methods. This required a set of assumptions, all of which are explicitly

identified in the derivation of the method.

The general objective of the method-testing was to validate the

general framework of the method and to assess the error contributions of

various parts of the method on instantaneous and cumulative ET esti-

mates. The assumptions made during the development of the method were

individually examined; in this way, the relative importance of ground-

gathered ancillary data such as air temperature, saturation water vapor

deficit, windspeed, and soil temperature could be judged. The testing

was done with ideally accurate on-site measurements of net radiation,

surface temperature, air temperature, and evapotranspiration.

Experimental Site and Data Collection

An area of pasture at the University of Florida's Beef Research

Unit was used as the research surface. The s-ite is loc-ated northeast of

Gainesville, Florida, as shown in Figure 1-1. It was chosen because it

is typical of northern Florida pasture areas, and was amenable to micro-

meteorologic measurement of a surface energy budget. The area was flat

with relatively uniform grass cover, and was large enough to ensure

well-developed temperature and vapor pressure profiles. The test surface

was a mixture of grasses: roughly 60-70% was bahiagrass (Paspalum

notatum), about 20-40% was smutgrass (Sporobolus poiretii), and 5-10%

was white clover (Trifolium repens).

Evapotranspiration was computed by an energy budget/profile Bowen

ratio method from measurements of net radiation, soil heat flux, and

gradients of temperature and water vapor pressure over the pasture sur-

face. A Hewlett-Packard 2100 computer and low-speed data acquisition

subsystem was used to automatically scan and measure the sensors,














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RESEARCH SITE


0 1 2 3

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RESEARCH
0 UNIT -/


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Location of the University of Florida Beef Research Unit.


_ I ,


Figure 1-1.









convert the measurements to proper units, and compute averages. Average

energy budget components and temperature and vapor pressure gradients

were calculated and reported for half-hour periods.

The arrangement of sensors in the field is shown in Figure 1-2.

Aspirated thermopiles and air sampling ports were mounted on arms of a

2.5-m mast. The area within a 10-m radius of this mast was completely

unobstructed to meet the fetch requirements of the measurement method.

Radiometers were attached to the end of a guyed boom about 2 m over the

surface. The precision radiation thermometer was bolted to a camera tri-

pod atop an antenna tower 9.5 m above the grass surface; the windspeed

and direction sensors were mounted on the same tower at 7 m. A 14-m

tower served as lightning protection for the entire group of in-

struments.

Shielded buried signal cable connected the sensors- to the data ac-

quisition system which was housed in a building about 90 m away from the

sensors. For vapor pressure measurements, air samples from five separate

levels in the field were pumped continuously back to the building

through heated insulated tubing and mixing chambers to a dewpoint ana-

lyzer. Air samples were switched sequentially to this instrument by a

scanning valve controlled by the measuring computer program. The dew-

point was measured after a half-minute delay to allow time for the ana-

lyzer to settle on the dewpoint of the sample from the new level.

Altogether, ET data from 42 days were used in verifying the remote

ET estimation method developed. These data were collected in the spring

and fall of 1981.










FIELD APPARATUS

AND SENSOR

LOCATIONS


LIGHTNING
PROTECTION
TOWER


RADIATION
THERMOMETER


WIND SPEED V,,-
AND DIRECTION
"SENSORS I


FENCE


FIELD
CONNECTOR BOX


SENSOR
SIGNAL


RADIATION SENSOR
STAND


TUBING BUNDLE


UNDERGROUND\
SIGNAL CABLE \
TO INSTRUMENT
ROOM \


Figure 1-2. Field Apparatus and Sensor Locations. This diagram is not
to scale.









Organization of Dissertation

Basic concepts underlying current understanding of the evapotran-

spiration process are reviewed in Chapter 2. These concepts are funda-

mental to both the evapotranspiration measurement and method develop-

ment portions of the study. Chapter 3 describes the computer-based evap-

otranspiration measurement system that was developed to collect a base

of accurate ET data. This chapter contains the theory of the meas-

urement technique, considerations made in designing the profile sensing

systems, brief descriptions of the programs that operate the system, and

an assessment of the strengths and weaknesses of the measurement sys-

tem. Two methods of calculating ET based on remotely sensed data are

derived in Chapter 4, one relatively rigorous with a minimum of added

assumptions, and a grosser less detailed one with extensive approxima-

tions. Both methods are based on a temperature gradient model which uses

net radiation and surface temperature data to determine surface parame-

ters. The performance of this model and these methods is compared to

actual ET measurements in Chapter 5. The method most suitable for use

with satellite data is tested component by component to clearly evaluate

its strengths and weaknesses. A summary of conclusions and suggestions

for further research are contained in Chapter 6.

Repeatedly used symbols are defined in Appendix A. (All symbols are

defined in the text where they are introduced.) Appendix B is a listing

of the programs developed for the automatic ET measurement system, along

with definitions of names for subroutines, functions, data arrays, and

indexes. Appendix C is a summary listing of the data collected, and sup-

plementary figures are presented in Appendix D.















CHAPTER 2

EVAPOTRANSPIRATION AND SATELLITE DATA

Overview

The availability of satellite images of the earth's surface and the

resources to investigate their usefulness has resulted in a variety of

remote-sensing research projects. In recent years, there have been pro-

grams in which evapotranspiration estimation procedures were the objec-

tive, notably a joint effort among the National Aeronautics and Space

Administration (NASA), the Institute of Food and Agricultural Sciences

at the University of Florida, the Florida Water Management Districts

(Allen et al., 1980), and NASA's Heat Capacity Mapping Mission, or HCMM

(Goddard Space Flight Center, 1978).

Since the estimation techniques need to be applicable to many dif-

ferent surfaces, physical rather than empirical approaches are.required.

The physical methods that have been developed, including the one pre-

sented in this work, are all based on the energy budget concept of the

surface and on the similarity of transport among quantities in turbulent

flow. These ideas and various approaches to solving the energy budget

equation are developed in the first part of this chapter. Remote ET es-

timation techniques are reviewed in the second part, which concludes

with an introduction to the new method.

The Evapotranspiration Process

At the interface between a liquid and a gas, molecules are continu-

ally breaking and reforming the intermolecular bonds which hold them at









the surface as a liquid. The energy of the random molecular collisions

which cause the bonds to break is carried with the freed molecule; this

thermal (heat) energy is lost by either liquid or gas molecules near the

interface. Since this energy contributes only to the molecule's conver-

sion to the vapor state and not its temperature, it is called the latent

heat of vaporization. It is released to the molecules at the surface

should a free molecule collide with and be captured by molecules in the

liquid state.

When the concentration of vapor molecules is higher at the surface

than at some distance away from it, there is a net flow of molecules and

energy (in the form of latent heat) away from the surface. This process

is evaporation.

Evapotranspiration is the evaporation of water from soil or plant

surfaces together with transpiration by plants. In transpiration, water

evaporates from internal plant surfaces and diffuses into the air around

the plant through openings in the leaves stomataa). Like the process of

evaporation, evapotranspiration consists of three fundamental elements:

the absorption of thermal energy at a water-air interface, the change of

state of water from liquid to vapor, and the resulting net loss of vapor

molecules and their heat of vaporization from the surface due to a fa-

vorable vapor concentration gradient.

The heat energy consumed in the evapotranspiration process is lost

from the vegetation biomass. Therefore, all the energy fluxes to and

from the plant canopy and the factors influencing them play a part in

determining the evapotranspiration rate. Figure 2-1 is a simplified dia-

gram of the surface and its primary energy and water fluxes. It is pre-

sented in the diagramming language of Odum (1982), and embodies many of












AIR
LAYER


Figure 2-1. System Diagram of Generalized Evapotranspiring Surface.
Symbols are from Odum (1982).


PLANT
ANOPY









the concepts and simplifications conventionally applied in evapotranspi-

ration theory.

The heat energy stored in the plant canopy is represented by its

temperature (Ts). The bulk of this energy comes into the vegetation in

the form of direct or scattered solar short wavelength (0.3 to 3 um)

radiation (Qs); it also intercepts thermal or long wavelength (3 to

50 pm) radiation emitted by the atmosphere (Qa). A substantial fraction

of the shortwave radiation received by the surface is reflected (Qr), a

very small part is used to drive photosynthetic reactions in the plants,

and the remainder becomes heat energy absorbed and stored temporarily in

the biomass. Part of this energy is reradiated to the atmosphere (Q ).

The difference between the downwelling radiation (direct and atmo-

spheric) and the upwelling radiation (reflected and emitted) is referred

to as net radiation (R).

Besides these radiant energy fluxes, the vegetation exchanges en-

ergy with its environment in several other ways. Thermal energy ex-

changed with the air by the process of molecular conduction and turbu-

lent diffusion is referred to as sensible heat flux (H); energy ex-

changed with the soil is soil heat flux (G). Energy used in the change

of state from water to water vapor is transported with water vapor and

is referred to as latent heat flux (E).

In this generalized view of the surface system, the plant canopy is

considered to have a uniform temperature representative of its heat con-

tent. There are complex energy exchange processes that occur within the

canopy because of differences in temperature. For example, radiation is

exchanged between plant surfaces, and sensible heat released from one

leaf may be reabsorbed and released from another as latent heat.








However, when the purpose is to make total evapotranspiration estimates,

these exchanges are ignored, and only the energy fluxes entering or

leaving its boundaries are considered.

Besides the radiant energy pathways (R) and heat energy stored in

the plant canopy, Fig. 2-1 shows the dependence of the surface energy

balance, and thus evapotranspiration, on factors in the environment of

the surface. Heat that is lost to (or gained from) the air as sensible

heat is not (is) available for evapotranspiration. This flux is depen-

dent on the air temperature (Ta) and the thermal transport properties of

the air, represented by the eddy thermal diffusivity (KH) in the figure.

When the air temperature is cooler than the surface temperature of the

canopy, sensible heat moves from the canopy into the air. When the can-

opy is cooler than the air, it absorbs heat energy from the air. There

is an analogous heat flux pathway to the soil, dependent on soil temper-

ature (T ) relative to the canopy temperature (T ), and the thermal con-

ductivity of the soil (X).

The right half of Fig. 2-1 shows the pathway of water through the

surface system. It originates in the soil and moves through plant tis-

sues into the leaves, where it evaporates. Depending on the vapor pres-

sure inside the leaves (ei), the vapor pressure in the surface air layer

outside the leaf (es), and the stomatal conductivity (C ), water vapor

then diffuses through stomata into the air around the leaves. From the

surface layer water vapor diffuses into the air, depending on the rela-

tive vapor pressures of the surface layer and air (es and ea) and the

eddy water vapor diffusivity (KW).








The Energy Balance Approach to ET Estimation

The Energy Budget Equation

The three elements of evapotranspiration (the absorption of water

from the soil or plant surfaces, the absorption of thermal energy from

the plant canopy, and the flux of water vapor through the air over the

surface) provide at least three fundamental approaches to evapotranspi-

ration measurement. These have been referred to as the water budget,

energy budget, and aerodynamic approach, respectively. All previously

developed remote ET estimation methods, the remote technique developed

in this study, and the ground truth measurement technique used in this

study are founded on the energy budget equation.

The energy balance of a vegetation and air layer can be written

R E -'H G P S = 0 2-1

where R is the net radiation flux absorbed (from p.15, R Q +Q -Q -Q )
E is the latent heat flux, a r
H is the sensible heat flux,
G is the soil 'heat flux,
P is the photosynthetic heat flux, and
S is the time rate of heat flux storage in the vegetation/air
layer.

Here energy "flux" is used to describe energy "flux density," i.e., the

energy flow per unit time through a unit area. All terms are in these

units.

Because of inherent measurement difficulty and sensor limitations,

the energy budget components can only be measured to within about 10% of

their actual values (Sinclair et al., 1975). Since some of the smaller

components are actually indistinguishable from measurement error, they

need not be considered.





18


Usually the smallest component is photosynthetic heat flux. It can

be considered negligible because only 1 to 5% of the net radiation im-

pinging on vegetation is absorbed in this way (Allen et al., 1964).

It can be shown by a "worst case" calculation that the storage term

is also in the negligible range. Heat in the vegetation/air layer can be

stored as sensible heat in the air, latent heat in the air, sensible

heat in the biomass, and sensible heat in the litter surface layer. In a

strict sense, these are evaluated as follows:

a1 Ta(Z) 1 CaT ea(z)
S = c() dz + -- dz +
Sa t J at
2-2
1 aTb(z) Id T-(z)
Sb(z) dz + cd ()T z dz
b abt dz 9 at


where ca(z), cb(Z), and g (z) are volumetric heat capacities ( c) of
canopy air, plant biomass, and surface soil, respectively,
Ta(z), Tb(z) and Tg(z) are the temperatures of canopy air,
canopy biomass, and surface soil, respectively,
ea(z) is the vapor pressure of canopy air,
y is the psychrometric constant,
1 is the vegetation height,
d is the depth of the surface litter layer, and
z is the vertical space coordinate.

Using averages for the spatial variables, Eq. 2-2 can be rewritten:

AT (pCp ) ae
S = (pCp) h a + -- a h a +
Sa At y At
2-3
AT AT
(Vc) b + (p) d
b At g At
where a, b, and g are subscripts referring to air, biomass, and soil
specific heats, densities, and temperatures, and
V is the mass of vegetation per unit area.











total sensible heat latent heat heat stored heat stored
heat = stored in + stored in + in + in top
storage canopy air canopy air vegetation soil layer


Ae AT AT
S= (P ) h ATa + (p)h a + (Vc) b + () d
pa pa t + (VC)b t +16gd Tf


S = .0012 x 0.24 x 20 cm x24 C + .0012 -g x 0.24 ca x 20 cm x 1.5 x 3mb +
cm cm


10,000 x 1.0 al 24 + 1.5 x 0.2 alx 1 cm x
ha gC 4 hr 3
cm



S = .0006 al + .0004 cal + .01 al + .006 cal
cm min cm min cm min cm min


cal
S .02 cal
cm min


Figure 2-2. Rough Calculation of Heat Storage in Pasture Canopy.








This expression is evaluated in Fig. 2-2 using values typical for

pasture grass. Heat storage in pasture biomass and the top litter layer

is approximately two orders of magnitude less than peak net radiation

loads; latent and sensible heat storage in the canopy air is about three

orders of magnitude less.

Since the values of the photosynthetic heat flux and the time rate

of canopy heat storage are negligibly small, the energy budget equation

may be written

R E H G = 0 2-4

The ET measurement method and the remote estimation method are based on

this simplified form of the equation. It is also the basis for all but

the empirical remote-sensing ET estimation methods. The following sub-

sections briefly review the fundamental analytical concepts and evalua-

tion techniques which are common to previously developed evapotranspira-

tion estimation methods based on the energy budget equation.

Transport Similarity and Wind Models

After the surface energy balance, the most important concept to ET

estimation techniques is that of transport similarity among momentum,

heat, and mass fluxes in the turbulent layer near the surface. This idea

is used in all forms of the energy budget approach to ET estimation,

both to evaluate transport properties and to avoid evaluating transport

properties.

The fundamental equations for the one-dimensional transport of mo-

mentum, heat, and water vapor are (Eagleson, 1970)

= pK 2au
T = pK t_. 2-5


BT
H = pc KHDT 2-6
p H 3z









E = cLe K 2-7
p W a2

where T is momentum flux,
H is sensible heat flux,
E is latent heat flux,
KM, K, KW are the eddy diffusivities of momentum, heat, and water
vapor,
u is the average horizontal windspeed,
T is temperature,
e is vapor pressure,
p is the air density,
c is the air specific heat at constant pressure,
Lp is the latent heat of evaporation,
P is the atmospheric pressure, and
e is the ratio of molecular weights of water and dry air.

The similarity hypothesis, which was developed in the last half of the

nineteenth and early twentieth centuries (reviewed by Brutsaert, 1982),

proposes that the eddy diffusivities of momentum, heat, and water vapor

are all the same:

KM = KH=K 2-8

It was not until Prandtl's (1932) development of the mixing length

concept that general analytical treatment of eddy diffusivity began.

According to mixing length theory, it is argued that

2 du
KM(z) = d 2-9

where a is the mixing length and
Ui is the average windspeed perpendicular to z (horizontal).

By postulating that the mixing length increased with distance from a

surface (k = KZ, where K is the von Karman constant), Prandtl went on to

derive an expression that accurately describes the variation of wind-

speed near a surface, the simple log wind profile. With parameters for

displacement height (D--with dense vegetation, that height above the

surface where the windspeed vanishes) and roughness height (z0--a








parameter included so that the windspeed is defined as zero when

z D = 0), the equation for the log profile can be written
ST z D + z2
u(z) p In 2-10


where TO is the shear stress at the surface. With this wind profile, the

eddy diffusivity can be evaluated between the surface and any level in

the air with average windspeed ua:

2-
K u (z D + z
KM(z) z D + z0 2-11
In
0

With the assumption of transport similarity (Eq. 2-8), this expression

can be used to evaluate KH and KW. Similar treatments of eddy diffusiv-

ity can be found in many texts (e.g., Brutsaert, 1982).

With very precise experimental work it has been determined that the

turbulent transport of momentum, heat, and water vapor is strictly simi-

lar only under neutral stability conditions, e.g., Swinbank and Dyer

(1967). To describe eddy diffusivities under other conditions, diabetic

influence functions (tM' ,H' pW) have been developed. They are defined

such that

KH = KM and 2-12


KW KM 2-13
W M M


These are experimentally determined and expressed in terms of dimension-

less variables such as the Monin-Obukhov length or Richardson number

(Morgan et al., 1971; Businger, 1973).








A number of wind profiles and corresponding eddy diffusivity treat-

ments both with and without stability corrections have been developed.

(These are referred to as wind models.) None are used in this study, but

the fact that bulk air transport is theoretically and experimentally

adequately understood is important in supporting the remote-sensing

method developed. All remote-sensing methods involve a wind model of

some kind to help evaluate sensible and latent heat fluxes.

Latent and Sensible Heat Flux Expressions

In application, the flux between two specific points (z1 and z2)

that have a gradient between them must be evaluated. Since eddy diffu-

sivity in general varies with the distance from a surface (Eq. 2-11),

the latent and sensible heat transport equations (Eqs. 2-5, 2-6 and 2-7)

must be integrated along the direction of transport and between the

points of application (Monteith, 1973). Assuming that all parameters

except diffusivity are constant between the two levels and that the flux

in question is steady (or that flux storage in the layer between levels

is negligible),
PC (T1 T)
H = 1- 2 and 2-14
f z2 dz
z K

pLE (el e2
E p Jz2 dz 2-15



The integral in the denominator of these equations, when evaluated, rep-

resents the lumped transport properties between points z1 and z2 away

from the surface. From the preceding subsection, it is understood that

these integrals can be evaluated with various wind models for K (z).








The expressions for latent and sensible heat flux that are commonly

used are simplified versions of Eqs. 2-14 and 2-15. For sensible heat

flux from the surface to a reference level above the surface, the inte-

gral expression is abbreviated either as a bulk thermal conductivity or

as a bulk air resistance:
PCp(T Ta)
H = pCpK(T T ) p ,r 2-16
p s a r a
a

where T is the surface temperature,
Ta is the air temperature at a reference level above the surface,
K is the bulk thermal conductivity for the slab of air between
the surface and the reference level, and
r is the bulk resistance to heat transport of the slab of air
between the surface and the reference level.

In this study, the sensible heat flux expression is condensed even fur-

ther to

H = h(T Ta) 2-17

Where h is referred to as the bulk heat transport coefficient. Since the

fundamental definition of h is

PC
h =-- 2-18
za dz
JzKHz


use of a wind model (to evaluate KH) is implied any time the bulk heat

transport coefficient or bulk air resistance is used (Monteith, 1973,

1975; Thom and Oliver, 1977).

Applying the similarity concept to a description of latent heat

flux is complicated because it is impossible to measure the vapor pres-

sure at the vegetation surface. The air inside the leaves is usually

assumed to be at the saturation vapor pressure corresponding to the sur-
face temperature [es = e (T)] A unitless parameter M, which varies
face temperature [e = e (T )]. A unitless parameter M, which varies









from 0 to 1, can be introduced to account for subsaturation of the sur-

face air:

M(e e,) = es ea 2-19

This formulation was suggested by Tanner and Pelton (1960) and applied

by Outcalt (1972), Pandolfo and Jacobs (1973), Nappo (1975), and Carlson

and Boland (1978), and in a slightly different form by Barton (1979).

The equation for latent heat flux can then be written in terms of the

heat transport coefficient and moisture availability parameter:
h *
E = h M(es ea) 2-20
y s a
*
where es is the saturation vapor pressure at the surface temperature,
e is the vapor pressure at the reference level a,
Ma is a unitless parameter interpreted as moisture availability,
h is the bulk heat transport coefficient, and
y is the psychrometric.constant (y = c P/Le).

The resistance formulation (Monteith, 1973) includes an additional re-

sistance term, rs, the bulk stomatal diffusion resistance (sometimes

referred to as the canopy resistance, r ) to account for the subsatura-

tion of air at the surface:

PCp (es e )
E = p (es a 2-21
Y(ra + r s)

Both of the transport coefficient resistance formulations are used

in the ET literature; analytic evaluation of either type of expression

is based on diffusivity integrals like those in Eqs. 2-14 and 2-15.

These formulations can be substituted for one another with the following

identities:
PC
h -
r, and 2-22


M = 2-23
r +- r
a s
This study uses the conductivity formulation.









Energy Budget ET Estimation Strategies

There are two major ways in which the energy budget and gradient

equations can be solved. The physically more realistic method is based

on dynamic simulation of the heat transfer processes; the other method

is based on a cruder description of the surface and steady-state analy-

sis of the surface heat exchange processes.

Gradient expressions like those in Eqs. 2-5, 2-6 and 2-7 are used

in both approaches. The difference is that in simulations the expres-

sions are applied over arbitrarily short distances and time steps ac-

cording to the level of detail required in the application. When trans-

port is in one direction, as it is considered to be in most of the prob-

lems encountered in ET measurement or prediction, the medium through

which the flux is transported is thought of as consisting of layers per-

' pendicular to the direction of transport. Fluxes through each layer can

then be computed individually for each time step, allowing the treatment

of flux transients as well as the treatment of differing transport prop-

erties of the layers. In the steady-state approaches the gradient ex-

pressions are applied over the entire distance between measurements, and

transients are ignored.

Simulation models consist of an interdependent system of equations

which describe the exchange of latent, sensible, and soil heat flux with

the vegetation layer and the air or soil, and also the transport of la-

tent, sensible and soil heat between layers. This system of equations is

solved iteratively using solar and atmospheric radiation data as a forc-

ing function and quantities such as air temperature, vapor pressure, and

soil temperature as boundary conditions. Generally, unknown surface pa-

rameters are chosen such that simulated surface temperatures match








observed surface temperatures. The simulated ET flux is then assumed to

be the actual ET flux. Examples of evapotranspiration simulations are

Waggoner et al. (1969), Stewart and Lemon (1969), Sinclair et al.

(1971), Murphy and Knoerr (1970, 1972), Goudriaan and Waggoner (1972),

Lemon et al. (1973), and Sinclair et al. (1976). Dynamic.models of the

surface heat transfer processes are computationally orders of magnitude

more complex than the steady-state approaches, and were developed only

after the introduction of the electronic computer.

The earliest physical models of the surface energy exchange process

were based on steady-state analysis and the similarity of latent and

sensible heat transport. Three steady-state strategies for solving the

energy budget equation for evapotranspiration have been developed; they

are referred to as the simple residual, Penman, and Bowen ratio methods.

To more easily compare these methods, their equations have been written

in the same notation. Soil heat flux is included even though this compo-

nent is often assumed too small to be included for vegetated surfaces.

In the residual approach, the energy budget equation is solved for

latent heat flux, and a simple gradient expression is used to evaluate

sensible heat flux:

E = (R G) h(Ts Ta) .2-24

The transport coefficient for air conductivity is estimated from empiri-

cally derived wind functions or physical wind models as described previ-

ously. The biggest advantage of this method is that it requires no in-

formation on the surface moisture status. Its disadvantage is that it is

very sensitive to an accurate transport coefficient estimate. When the

sensible heat flux term is written in terms of a resistance, this method

is also called the resistance energy balance method (Rosenberg, 1974)








The Penman (1948) approach is very closely related to the residual

approach. In addition to the wind function, it includes an expression

that relates the temperature gradient to the vapor pressure gradient via

the linearized saturation vapor pressure curve,

es ea = s(T Ta) + 6ea. 2-25

where s is the slope of the saturation vapor pressure curve, and
6ea is the saturation deficit of the air.

This approach has since been generalized to include subsaturated sur-

faces (Barton, 1978), which allows ET to be expressed as a function of

net radiation, the moisture availability parameter (M), and the satura-

tion deficit (6ea):


E = Ms+ [s(R G) + h6ea] 2-26

.(See Chapter 4 for the full derivation.) Historically, Penman's method

was the first to combine the energy budget equation with a wind model to

evaluate ET. Although the residual approach also employs a wind model,

in common usage it is the Penman method that is referred to as the com-

bination method. The Penman method's main advantage is that it is not

explicitly dependent on measurement of a temperature gradient; its prin-

cipal disadvantage is that it requires information on moisture availa-

bility of the surface.

The Bowen ratio approach (Bowen, 1926) assumes that in the fully

turbulent layer over the surface, transport of heat and water vapor are

similar (i.e., KH = K). This allows eddy diffusivities to be avoided

altogether, and latent and sensible heat flux to be apportioned accord-

ing to the relative strength of the temperature and water vapor pressure

gradients:








(R G)
E = 2-27
E y(T2 TI
1+
(e2 e1)

where subscripts 1 and 2 refer to two levels in the fully turbulent air

layer. This approach is free of a wind model, but it requires very accu-

rate measurement of temperature and vapor pressure gradients. It is dis-

cussed in detail in Chapter 3.

Remote ET Estimation Methods

Surface Temperature and Net Radiation

Satellite-borne sensors can measure the amount of radiant energy

coming from a particular surface area element in a particular wavelength

interval. For environmental applications, the wavelength intervals mea-

sured are divided into the visible, thermal, and microwave regions of

the electromagnetic spectrum, yielding measurements of reflected solar,

emitted thermal, and microwave radiation. .So far, all ET estimation

methods designed for use with satellite data only employ the visible and

thermal wavelength ranges.

Net radiation is the largest component of the surface energy bud-

get, and surface temperature plays a role in determining all the energy

budget components. Usually, measurements of reflected solar and emitted

thermal radiation measurements are used to estimate net radiation and

surface temperature. Methods to estimate ET are then based on these net

radiation and surface temperature estimates.

With a clear sky and proper consideration of the atmosphere's

transmission properties, surface temperature can be determined directly

from emitted thermal radiation:

Qe = eT 2-28
e s








where e is the emissivity of the surface,
o is the Stefan-Boltzmann constant, and
T is the surface temperature.

Solving for Ts,
44-
Ts = e 2-29
Y o
In principle, net radiation is calculated according to the equation

R = Qs + Q r Qr Qe 2-30

The upwelling components, reflected (Qr) and emitted (Q ) radiation, are

directly measurable by satellite given atmospheric transmission proper-

ties. The solar radiation incident at the surface (Qs) is known as a

function of date, time of day, location, and atmospheric absorption

(Tennessee Valley Authority, 1972). Atmospheric radiation (Qa) can be

similarly estimated.

Some of the ET estimation methods discussed in.-the following sec-

tions are designed for use with satellites that provide only thermal

data from the surface. These methods express the net shortwave radiation

as a function of estimated incident solar radiation (Rs) and albedo (a):

Qs Qr = (1 a)Qs 2-31
Simulation Methods

In 1978, NASA launched the Heat Capacity Mapping Mission (HCMM).

The polar orbit of the HCMM satellite was designed to collect maximum

and minimum temperatures of the earth's surface, and groups worldwide

were funded to study the maximum-minimum temperature data. Several

groups adapted or developed simulation methods to bridge the long time

intervals (12 hours) between data sets. Examples of models used are

Carlson and Boland (1978), Soer (1977), and Rosema et al. (1978).








The Carlson model is very general, having been developed for study

of urban and rural surfaces. It is based on the energy budget equation

and gradient transport equations for latent, sensible, and soil heat

flux. Soil thermal conductivity and heat capacitance are combined into a

thermal inertia parameter which is evaluated with an empirical relation-

ship to thermal conductivity. The model does not describe soil and plant

water transport. It introduces a moisture availability parameter as

shown in Eq. 2-19 to account for the subsaturation of the surface air.

Eddy diffusivities for latent and sensible heat are iteratively computed

using empirical stability corrections; there are, in fact, different

atmospheric models for daytime and nighttime.

Use of the Carlson model to determine daily heat budget components

is discussed in Carlson et al. (1980). Computed solar radiation is used

to force the model; measured windspeed, air temperature and.humidity,

and soil temperature are used as boundary conditions. By varying two

model parameters (thermal inertia and moisture availability) on succes-

sive model runs, sets of corresponding cumulative heat budget components

and 24-hour maximum and minimum temperatures are generated. Then a re-

gression equation expressing daily ET as a function of maximum and mini-

mum temperatures is developed. Given the ground-measured data for the

simulation and two extreme temperature maps from the HCMM satellite, a

map of daily ET is produced.

The Soer model (named TERGRA) is much the same as the Carlson

model, providing for stability conditions in the surface air layer and

requiring temperature, vapor pressure, and windspeed as boundary condi-

tions at a reference level. However, rather than a moisture availability

parameter, soil and plant water transport is modelled in detail. (The








TERGRA model was designed for grasslands, making this more detailed ap-

proach feasible.) It uses pseudo-empirical expressions for soil water

transport resistance and stomatal resistance, and requires a reference

soil moisture pressure as well as a soil temperature as a boundary con-

dition.

Use of the TERGRA model in obtaining cumulative ET estimates is

explained in Soer (1980). The procedure requires data on the boundary

conditions and radiation falling on the surface for the duration of the

simulation periods, and values of various parameters like soil hydraulic

conductivity and surface roughness. First, windspeed, roughness height,

air temperature, and remotely measured surface temperature are used to

compute the instantaneous ET rate for the time at which satellite data

are available. This is done with the simple residual method (see previ-

pus subsection), which requires no knowledge of surface moi-sture. Then

the TERGRA model is run with various soil moisture pressures to match

the ET rate at the time of the satellite overflight. The modelled cumu-

lative daily ET rates are then assigned to areas with matching instanta-

neous ET rates at the time of the overflight.

The Rosema et al. (1978) model (named TELL-US) is also constructed

around the surface energy budget, and similarly computes latent, sensi-

ble, and soil fluxes based on measured gradients and calculated trans-

port properties. It is more detailed in describing the surface; surface

slope and slope direction must be specified. Its parameters are soil

thermal inertia and surface relative humidity.

Given the daily course of boundary conditions and incident radia-

tion, the model is used to compute daily maximum and minimum tempera-

tures and cumulative daily evapotranspiration for various combinations








of thermal inertia and surface relative humidity. This procedure must be

repeated for each combination of surface roughness, slope, and slope

direction. Then satellite-measured maximum and minimum temperatures for

specific areas are matched to the modelled values to determine daily ET

for those areas.

Steady-State Methods

Most efforts to use remote-sensing data to estimate ET rates were

made with the simple residual method (Eq. 2-24). Remotely sensed data

were used to estimate net radiation, and sensible heat flux from the sur-

face was evaluated with a remotely-sensed surface temperature and a

ground-measured air temperature. Evapotranspiration was then calculated

as the net radiation less the estimated sensible and soil heat flux.

Studies that fall into this category are Allen et al. (1980), Seguin

(1980), Soer (1980), and Price (1982). Soer and Price extend their meth-

ods to cumulative daily ET estimates with the help of simulation models

described in the preceding subsection.

These methods differ primarily in how they treat the bulk heat

transport coefficient or transport resistance of the surface air layer.

Two methods of computing sensible heat flux were used in the Allen et

al. (1980) approach. For short vegetation (mostly pasture), a stability-

corrected thermal conductivity was computed using the log law wind model

and dimensionless empirical relationships developed by a group at the

University of California at Davis (Morgan et al., 1971). An empirical

resistance equation based on leaf length, windspeed, shelter factor, and

leaf area index (Monteith, 1965) was used for transport over areas

covered with trees. By using measured windspeed and air temperature, the

estimated tree resistances and a surface temperature map, it was








possible to construct a map of instantaneous evapotranspiration rates.

For regional estimates, the rates computed for subareas were weighted by

the total area with that particular ET rate and summed.

The Seguin (1980) approach to thermal conductivity in the surface

air layer was formulated in terms of a resistance. It used the simple

log law wind function with surface roughness to evaluate the resistance

to sensible heat flux; no stability corrections were made. Measured

windspeed, air and soil temperature, remotely measured surface tempera-

ture, and estimated albedo and soil conductivity were required to esti-

mate instantaneous ET rates. Regional ET rates were estimated by multi-

plying areas with different surface temperature and surface roughness

combinations by their individual ET rates.

Soer (1980) also used a resistance formulation of the sensible heat

flux. It included stability corrections based on the Monin-Obukhov

length and the Businger-Dyer semi-empirical mass and heat transport

equations. In other particulars it is practically identical to the

Seguin approach.

Price (1977, 1980) has developed the energy budget equation in

terms of time averages in an effort to determine surface thermal inertia

using remotely sensed maximum and minimum surface temperatures. He has

since (Price, 1982) used this approach in conjunction with the TELL-US

model to estimate daily ET rates. First a preliminary estimate is made

with a residual equation like Eq. 2-24, except that time average air and

surface temperatures and windspeed are used. The daily ET value obtained

is then corrected with a regression equation developed from a set of

corresponding Price method estimates and TELL-US simulation estimates.









A different approach to solving the residual equation was taken by

Menenti (1980). In his approach, the simple residual equation is simpli-

fied by Taylor series expansion around some central ET rate at a given

shortwave radiation level. All terms except those containing surface

temperature and albedo are eliminated, leaving the ET rate for a partic-

ular surface a function of the central ET rate, its surface temperature,

and its albedo. No means to make cumulative daily ET estimates were sug-

gested.

Temperature Gradient Response Methods

The two ET estimation methods developed in this study are steady-

state methods. They are based on the response of surface-to-air temper-

ature gradients to varying levels of net radiation. One of these meth-

ods, the average temperature gradient response method, is suitable for

use with satellite data.

The primary difference between this method and the simple residual

method is that it expresses the vapor pressure gradient in terms of the

temperature gradient, the slope of the saturation vapor pressure curve,

and saturation deficit--an innovation first made in Penman's (1948) pio-

neering work. This addition gives the method some protection against

"residual errors." For example, if the measured temperature gradient is

erroneously high, both the latent and sensible heat fluxes will be af-

fected; there will not just be an increase in sensible heat and an equal

decrease in latent heat flux. Also, the method allows ET to be expressed

as a function of net radiation and parameters only (without explicit

mention of surface and air temperature). This feature makes ET calcula-

ble when surface temperatures cannot be measured remotely but net









radiation can be estimated, as when there is cloud cover or in between

sets of satellite data.

A significant advantage of the estimation method developed is that

it, in effect, determines surface parameters like moisture conditions

almost completely from remote-sensing data. This is donewith an equa-

tion (hereafter referred to as the temperature gradient model) that re-

lates the surface-to-air temperature gradient to net radiation and pa-

rameters that describe the surface. By assuming that the parameters are

constant, two of them (e.g., moisture availability and saturation defi-

cit) can be determined from the correlation of the surface-to-air tem-

perature gradient and net radiation. Although surface temperatures are

required (implying clear skies) to determine parameters, they can be

used with cloudy condition net radiation estimates for cloudy condition

ET estimates.

The need for a.surface-to-air temperature net radiation correlation

calculation requires several daytime satellite data sets. Unlike the

HCMM methods, the remote ET estimation method developed in this study is

designed for use with satellite data that is available at least every 2

or 3 hours. At this time resolution, the average temperature gradient

response method can make reasonably accurate cumulative daily ET esti-

mates without the need for simulation. Because the parameters are con-

sidered constant, no interpolation scheme is needed to make cumulative

ET estimates; only an estimate of the cumulative daytime net radiation

is required.














CHAPTER 3

A SYSTEM FOR AUTOMATIC COLLECTION OF ET DATA

Overview

The energy budget/profile Bowen ratio technique was used to make

the evapotranspiration measurements needed for a data base in this re-

search. It was selected because it is one of the methods that least dis-

turbs the surface being measured, and when correctly applied, permits

measurements with an error on the order of 10% (Sinclair et al., 1975).

The profile Bowen ratio method has been successfully applied to a vari-

ety of surfaces (Sinclair et al., 1975; Stewart and Thom, 1973; Black

and McNaughton, 1972, 1971).

The theoretical basis of this method is developed first, followed

by a discussion of considerations going into the choice and use of the

sensors and other apparatus. Next, the automatic data collection system

that is assembled to make and report energy budget measurements is de-

scribed. It consists of a computer-controlled scanner, voltmeter, gas

sampling arrangement, and a set of four interacting programs. The chap-

ter concludes with a discussion of practical considerations that are

important in maintaining a high level of accuracy in the measurements

and the limitations of the data collection system.

Energy Budget/Profile Bowen Ratio Theory

As described in Chapter 2, the energy balance of a vegetated sur-

face can be written:

R = E + H + G 3-1








where R is net radiation absorbed by the surface,
E is the evapotranspirative or latent heat flux,
H is sensible heat flux, and
G is the soil heat flux.

It has already been shown that the rate of heat storage in the vegeta-

tion layer and the rate of photosynthetic assimilation are negligible in

comparison to these terms.

The Bowen ratio is defined as the ratio of sensible heat flux to

latent heat flux:
6 3-2
E

In the energy budget/profile Bowen ratio measurement technique, net ra-

diation and soil heat flux are measured directly. Latent and sensible

heat fluxes are determined indirectly by first measuring the Bowen ra-

tio, and then computing the fluxes:

E (R G) and 3-3
S+1


H (R G) 3-4
S+ 1

The Bowen ratio can be calculated from air temperature and water

vapor pressure measurements at various heights over the surface, pro-

vided a number of experimental conditions are met. Over a uniform sur-

face with adequate fetch, latent and sensible heat fluxes may be consid-

ered to exist in the vertical direction only (no flux divergence). In

the turbulent boundary layer the fluxes at any instant can be described

as follows:
aT
H = -pc K 3-5
p H 9z

S-EL e
E -L K 3-6
P W3Z '
where p is air density,
c is specific heat capacity at constant pressure,
E is the ratio of molecular weights of water and dry air,
L is the latent heat of evaporation of water,
P is the atmospheric pressure,









KH is the eddy thermal diffusivity,
K is the eddy vapor diffusivity,
T is the air temperature,
e is the vapor pressure, and
z is the vertical coordinate.

The Bowen ratio can then be written:

aT
c PK
H = pH 3-7
E cLKw
W It
If temperature and vapor pressure measurements are made at the same

heights, the az terms may be cancelled. If the measurements are made at

the same instant, it can be assumed that the eddy diffusivity for water

vapor and heat are the same (KH = KW). This in effect states that turbu-

lent mixing is the dominant transport mechanism in the turbulent bound-

ary layer, and that bouyancy and stability effects cause no significant

differences in the transport of heat or.water vapor (Dyer, -1967;

Swinbank and Dyer, 1967; Webb, 1970; Dyer and Hicks, 1970; Garratt and

Hicks, 1973). Incorporating these conditions into the expression for the

Bowen ratio,

B j I. 3-8
L= e ae 3-8

Since the terms in brackets are physical "constants" (abbreviated as the

psychrometric constant, y), only aT/e needs evaluation. This can be

done with air temperature and vapor pressure measurements.

In this application of the energy budget/profile Bowen ratio con-

cept, air and dewpoint temperatures were measured at five heights--35,

60, 85, 135, and 225 cm over the surface. Vapor pressure was calculated

from the dewpoint temperature according to the Magnus-Tetens formula

(Tennessee Valley Authority, 1972). The ratio aT/;e was the slope of a

two-independent-variable linear regression (Kendall, 1968) calculated









using temperature data as the ordinate and vapor pressure as the ab-

scissa (see Fig. 3-1). In calculating the Bowen ratio, the specific heat

of the air, the atmospheric pressure, and the ratio of molecular weights

was considered constant; the latent heat of vaporization was a function

of the average air temperature.

Sensor and Time Constant Considerations

Although simple in principle, a great deal of care is required in

choosing sensors and collecting data for the calculation of the Bowen

ratio. Temperature and vapor pressure vary randomly from instant-to-in-

stant and level-to-level in the turbulent boundary layer, and the total

temperature and dewpoint differences across the air layer to be measured

are only 1 or 20C. In order to calculate the relative strengths of the

gradients, very precise measurements at several levels are required.

Sensors were chosen to eliminate, as much as possible, the error

introduced by sensor-to-sensor variability. This was avoided entirely in

the case of the vapor pressure profile; the same dewpoint analyzer was

used to measure the dewpoint at each level by use of a gas sampling ar-

rangement. In the case of the temperature profile, the effect of thermo-

couple-to-thermocouple differences was minimized by measuring tempera-

ture differences with thermopiles. Twenty-junction copper constantan

thermopiles, arranged with 10 junctions at each level, were used to mea-

sure temperature differences between levels. The temperature at the low-

est level was measured with a thermocouple using an Omega Engineering

MCJ-T electronic icepoint reference. Temperatures at the other levels

were obtained by adding the appropriate thermopile-measured temperature

differences to the one reference temperature measurement.






A VAPOR PRESSURE (MB)
11.2 11.4 11.6 1.8 12.0


~225
U


135


5
0
5
0


0

LU
Q-
D

F-
LJ


H-


Figure 3-1.


19 20 21
a TEMPERATURE (OC)


0/
-. e4


57T5
I I


I I 11


e T
;1o'I


o T

0,
,0 -",e
T 2
,-' T


- 3' 3
'4 BOWEN_ cT
RATIO e-
=1.75
I I- I


11.2 11.4 11.6 11.8 12.0
VAPOR PRESSURE (MB)
Bowen Ratio Calculation from Measurements of Vapor
Pressure and Temperature. Note that the scale used
to plot vapor pressure profile in upper graph is the
same as the vapor pressure scale in the lower graph.
Data are from October 20, 1981, 9:30 TST (see Fig. 3-6).


2


- A LEVEL NO. 5-


SA 4-


21



20



19


83


o








The apparatus used to collect temperature measurements and air sam-

ples was designed so that the sensors returned signals accurately repre-

sentative of the air layers being sensed. The thermopiles were nested

inside three aspirated radiation shields, with each shield wrapped in

highly reflective aluminum foil. Air samples were pumped continuously

from sampling ports near the thermopiles through about 100 m of 6-mm ID

polypropylene tubing and 11.3-L mixing chambers in the instrument room.

To prevent any danger of condensation, the air sampling system was

heated from sampling mast to dewpoint analyzer. The bundle of five tubes

from the mast was taped around a heater cable (3 W/ft) and packed inside

a 1.3-cm-thick foam rubber insulation tube. The mixing chambers and the

sampling valve were also heated.

The travel time of air samples from mast to instrument room was

approximately 1 min. Therefore, the dewpoint measurement corresponding

to a temperature measurement at a specific level was made 1 min later.

Also, the dewpoint temperature measurements were pressure-corrected be-

cause the arrangement of the air sampling system caused the pressure

rate at the dewpoint sensor to be %30 mb less than atmospheric pressure.

To ensure clean electrical signals, shielded signal cable with a

single common ground was used. In spite of these precautions, the Beef

Research Unit fence charger managed to induce significant voltage spikes

on the low level signals (e.g., the 0-200 microvolt thermopile signals).

This problem was solved with a filtering routine in the data collection

program.

In addition to reducing the error sources from the sensors in every

practicable way, the temperature and vapor pressure signals were

physically smoothed. Smoothing was required because the measurement rate








was limited to one measurement every 2.5 min for the vapor pressure

profile measurements.

Vapor pressure in the Bowen ratio data collection system was com-

puted from a measurement of the dewpoint temperature. Since the same

dewpoint sensor was used for all five levels and a delay had to be

scheduled between measurements to allow the analyzer to settle on new

dewpoints, the response of the dewpoint analyzer was the factor limiting

the sampling rate. The analyzer, an EG&G Model 880 Dewpoint Hygrometer,

was tuned so that it could "lock on" to small dewpoint temperature

changes within about 15 sec. However, 30 sec per measurement were sched-

uled to allow the analyzer to stabilize on a given dewpoint under less

than ideal conditions. Since there were five levels to measure, the time

interval between measurements at the same level was 2.5 min.

The variability of temperature and vapor pressure in the turbulent

air layer is well documented; at any point in this layer, instantaneous

temperatures and dewpoints vary randomly (Desjardins et al., 1978). The

higher-frequency temperature and dewpoint fluctuations were smoothed in

order to get representative measurements with a sampling rate of one

measurement every 2.5 min.

In the case of an air-sampling system, this smoothing is conveni-

ently done by inserting a mixing chamber into the sample stream ahead of

the analyzer. An abrupt (or step) change in an air sample is translated

into a gradual, approximately exponential change by mixing in a chamber.

The exponential change is characterized by a time constant, which is

determined by the volume of the mixing chamber divided by the flow rate.

By harmonic analysis, it was determined that a time constant of 4 min.

would damp random signal variations occurring more often than every 2.5








min to 10% or less of their amplitude. In the case of the dewpoint sys-

tem, 11.5-L mixing chambers with a flow rate of 3 L/min were used.

To maintain the proper correlation between dewpoint and temperature

readings, it was necessary to introduce the same time constant into the

temperature-sensing system. The appropriate time constant was determined

experimentally by varying the air flow rate over the aspirated thermo-

piles and subjecting them to different temperature differences. It was

found that at a set air flow rate, measured time constants varied with

the temperature difference applied to the thermopiles. As a result, the

air flow rates were adjusted so that a 4-min time constant resulted for

temperature differences in the average operating range--temperature dif-

ferences in the range of 0.2 to 0.30C.

The 4-min time constant was also introduced into the surface tem-

perature and net radiation measurements. Sensor response was slowed dig-

itally by using weighted averages of the most recent 25 sensor readings.

Each time a complete temperature and vapor pressure profile was

measured (every 2.5 min), the correlation coefficient between tempera-

ture and dewpoint measurements was calculated. This provided a running

check on the quality of the measurements and the current similarity of

the profiles.

Data Collection Equipment

The overall schematic for the thermopile/air sampling system is

shown in Fig. 3-2. The major parts are the data acquisition system, the

air sampling mast, the mixing box, and the signal cables and tubing

which connect them.

A computer-controlled data acquisition system was used because of

the large number of measurements and extensive calculations that this









SIGNALS
NET RADIATION
SOIL FLUX
REFERENCE TEMPERATURE
4 TEMPERATURE DIFFERENCES
DEW POINT
VALVE CONTROL
VALVE POSITION


Flow Meters
Mixing Bottle


AIR SAMPLING SYSTEM


SOIL FLUX
DISK


PROFILE MEASUREMENT MAST


Figure 3-2.


Schematic of ET Measurement System. Details of profile measurement and air
sampling equipment are shown in Figs. 3-3 and 3-4.








technique requires. The central piece of equipment was a Hewlett-Packard

2100S Minicomputer with a disk resident Real Time Executive-2 operating

system. The system allowed editing and compilation of programs, swapping

programs between core and disk memory, scheduling programs for relative

or absolute start times, and "simultaneous" running of programs accord-

ing to priority. Input and output were by means of a HP-2126P terminal.

The peripheral equipment used in making the measurements and con-

trolling the gas sampling valve is listed in Table 3-1. The controlling

computer, disk drive, data acquisition equipment, and terminal were all

housed in an air-conditioned room.


Table 3-1 Data Acquisition System Identification (All components
are manufactured by Hewlett-Packard)

Component Model No. Serial No.

Minicomputer (32K Memory) HP-2100S 1420A05546
Scanner HP-2911A 737-00476
Scanner Controller HP-2911B 832-00412
Integrating Digital Voltmeter HP-2402A 1027A01060
Disk Drive HP-7901A 1321A-00255
Terminal HP-2621P 2102W03475


The field apparatus on the pasture site consisted of an air-sam-

pling mast, a radiation sensor boom, and a 9.5-m tower supporting a

precision radiation thermometer at its top, and windspeed and direc-

tion sensors at 7 m. Another taller tower was erected and equipped to

protect all instrumentation from lightning.

The 2-m radiation sensor boom was supported by an aluminum tripod

stand and guy wires about 1.8 m over the ground surface. Two Epply pyra-

nometers, oriented to measure incomin: and reflected radiation, and a

Swissteco net radiometer were mounted at its end. An aspirating pump and








dessicant container for the net radiometer were held in a weatherproof

box at the base of the tripod.

The air sampling mast consisted of a 2.5-m steel channel to which

five sensor arms (see Fig. 3-3) were attached at various levels. At one

end of each arm, teflon spacers centered two clusters of 10 thermocouple

junctions inside the smallest of three radiation shields. Individual

junctions were kept in thermal contact with a metal oxide conducting

paste. Air was drawn over the thermopiles, between radiation shields,

and through the length of the arm by a small fan at the opposite end.

Air samples were drawn from the air flowing through the arm. All wiring

(four 20-junction thermopiles and one thermocouple) and tubing (5 sample

lines) were contained inside the 3x3 cm channel down to its base, where

they ended in wire and tubing connectors. The mast and sensor arms as

well as the radiation, shields were wrapped in highly reflective aluminum

foil.

The sensors were connected to the scanner in the instrument room

with shielded signal and thermocouple wire. In the field, leads from the

sensors ran aboveground in wire harnesses to a junction box, where they

were connected to a signal cable via screw connectors. This cable ran

100 m underground to another junction box in the instrument room. From

this panel the signal lines were connected to one of two 50-pin connec-

tors, which plugged into a short piece of cable tied directly into the

scanner. The "quick-disconnect" plugs were included to rapidly isolate

the data acquisition system from possible lightning strikes in severe

weather; the junction boxes allowed signal problems to be quickly traced

to sensors, underground cabling, or the data acquisition system. The

sensors used are identified in Table 3-2.









STEEL
CHANNEL--


PVC PI


ASPIRATING
FAN


AIR SAMPLE PORTj
'POLYPROPYLENE
TUBING
RADIATION SHIELDS
THERMOCOUPLE
JUNCTIONS


Detail of Profile Measurement Mast Arm.


Figure 3-3.










Table 3-2 Sensor Identification

Measurement Sensor Make & Model No. Ser. No.

Net Radiation Swissteco Net Radiometer 6990
Incoming Shortwave Radiation Epply Pyranometer 8-48 12876
Reflected Shortwave Radiation Epply Pyranometer 8-48 10000
Surface Temperature Barnes IT-5 (Spring 1981) --
Barnes IT-3 (Fall 1981) 521
Dewpoint Temperature EG&G 880-C1 1409
Windspeed and Direction R.M. Young 6101 and 6301
Air Temperatures Custom-made Thermopiles
Reference Temperature Omega Engineering MCJ-T
Soil Heat Flux Micromet Heat Flow Disk 282


Air was pumped continuously from each sample port on the mast

through .100 m of heated insulated polypropylene tubing and the gas sam-

pling apparatus in the instrument room. In the "mixing box," air first

passed through flowmeters, then the mixing chambers, the scanning valve,

and the air pump. Samples from each level were drawn sequentially

through a sampling port, a separate sample flowmeter, and the dewpoint

analyzer. All equipment except the pump and analyzer were contained in-

side a heated, insulated plywood box (see Fig. 3-4) to prevent condensa-

tion problems.

The scanning valve was controlled from the data acquisition compu-

ter. The sampling port was turned from one air source port to the next

by an electric motor powered for a precise fraction of a second. This

was done by a relay control circuit that was designed to sense scanner

closure. Thus a program statement calling for a measurement of the scan-

ning valve control channel resulted in changing the position of the

valve. After each change, the valve position was checked to ensure that

the programs and valve were synchronized.







,Valve Control Electronics
- Sampling Valve


Analyzer Sample
Flowmeter


Air to Analyzer
Air to Pump




5 Sample
Tubes from
Mast


Polypropylene

-Foam Rubber
Insulation


Figure 3-4. Detail of Air Sampling Equipment.


Tubing
Bundle








Data Collection Programs

A system of four programs was developed to collect, report, and

analyze the data required for the test surface energy budget. Program

MEASR makes the measurements and calculations, REPRT produces the half-

hourly summary reports, ANALZ does some analysis of data and performs

additional calculations, and SET schedules the other programs. Listings

of these programs appear in Appendix B; brief descriptions of their

functions and interactions follow.

Basically, all sensors are scanned in a computer program loop. De-

pending on the status of various indexes in this loop or the system

clock, control is passed to specific calculation and/or reporting rou-

tines. This fundamental loop is in program MEASR; it is repeated approx-

imately every 30 sec, the measuring rate determined by the dewpoint ana-

lyzer.

When a program calls for a measurement [i.e., CALL EXEC (1, 9,

DATA, CHANNEL NUMBER, VOLTMETER PROGRAM WORD)] the channel number in the

measurement program statement is passed to the scanner controller, and

the program word indicating type of measurement, voltage range, and de-

lay time is passed to the voltmeter. After the scanner has closed on the

proper signal lines, the voltmeter has been set for the type of measure-

ment, and a programmed delay is complete, the voltmeter integrates the

signal for 1/60 second and passes the average back to the measuring pro-

gram. It resumes execution with the next program step.

During each execution of the measurement loop, one air temperature,

one dewpoint temperature, and all other sensors except soil thermocou-

ples are scanned. Immediately after the dewpoint measurement, the scan-

ning valve position is changed (Subroutine STEP) so that the dewpoint








instrument can begin to stabilize on a new dewpoint. A programmed delay

makes up the balance of the 30 sec required between measurements. At the

end of five scans (2.5 min), a complete temperature and dewpoint profile

is available to compute a Bowen ratio. A report on that profile is

printed at the option of the system operator (see Fig. 3-5).

To compensate for the approximately one-minute air sample travel

time from field to mixing chamber, temperature and dewpoint measurements

are offset by two levels. For example, the dewpoint at level 1 is mea-

sured in the same sensor scan as the temperature at level 3. This ac-

counts for extra statements at the beginning of the program which ensure

proper initialization, and for extra branching after sensor scans which

deal with the offset completion times of the temperature and dewpoint

profiles.

To guarantee that the dewpoint analyzer is receiving the air sample

from the level called for in the program, a mark voltage channel is mea-

sured and checked in each scan of the sensors. In one particular posi-

tion of the scanning valve, 12 volts are expected on this channel. If

the voltage measured is low or 12 volts are measured when not expected,

the data for the profile being collected are discarded and a message to

the operator is printed. The program makes one attempt to reposition the

valve and restart data collection. If this fails, another message is

printed and the programs are terminated.

When temperature and dewpoint measurements at all five levels are

complete, the data are passed to subroutine RATIO, which calculates a

linear temperature versus dewpoint regression relationship. Its slope is

multiplied by the appropriate constants (Eq. 3-8) to give the Bowen








PROF# 6
9: 16:27
B =1.723

PROF# 7
9:18:56
B =1.813

PROF# 8
9:21:26
B -1.612

PROF# 9
9:23:55
B -1.590

PROF< 10
9:26:24
P1 =1.904

PROF# 1 I
9:28:54
B =1.679

PROF# 12
9:31:23
B =1.618


RAD.T.
NET R.
N..SPD.

RfD. T.
NET R.
N.SPD.

RAwD.T.
NET R.
N.SPD.

RAD.T.
NET R.
W.SPD.

RAD.T.
NET R.
IN.SPD.

RfD.T.
NET R.
N.SPD.

RAD.T.
NET R.
1N.SPD.


23.27
,45
2.86

23.77
.45
2. 18


24,

3.


24.30
.47
11. z79
3.54

24.49
.47
3.36

24.90
.4 8
2.85


2.


TEMP
DPT.
V.P.

TEMP
DPT.
V.P.

TE1MP
DPT
V.P.

TEMP
DPT.
V.P.

TEMPF
DP T.
V.P.

TEMP
DPT.
V. P.

TEIMP
DPT.
V. P,


21.1
9 .5


21.2
9.6
I 1 .


21 .4
9.8
12.1

21.7
9.8
12 .

21 .8
. 9.9
12,2
12.2
22.2
10 .1
12.4


10.3
12.5


20.4
9.2
1 .6


9.3
11,7

20.7
9.5
11.8

21 .0
9.6
1 .
21.1
9. 9

11.9
9.5


21 .5
9.8
2.1

21.7
9.9
12.2


20.0
9.0
11.5

20.2
9.1
11 .5


20.6
9.2
11 .7

20.8
9.5
11.9

21.1
9. 9
12.0

21.3
9.7
12.0


19.5
8.7
11.3

19.7
8.9
11,4

20.0
9.0
11.5

20. 1
9.0
11.5

20.4
9.3
11.7

20.6
9.4
11.8

20.8
9.5
11.8


19 .1
8.5
11.1


8.7
11.2


8. 8
1 1.
11.3

19.8
8.8
11.4


20.
9.1


1120.5
20.3
9.2


9.3
11.7


R = ,9y/



R =. .99b


R = .988


R .999


R =1 .000


Figure 3-5.


Example of Intermediate Program Output


This report is printed if switch #3


on face of HP 2100 computer is on. Data are from the 15 min preceding half-
hour report shown in Fig. 3-6.








ratio. The ratio and corresponding correlation coefficient are returned

to the calling program.

Function FILT was added to MEASR after it was discovered that the

shielding system did not prevent the Beef Research Unit electric fence

charging system from inducing noticeable spikes on the signal lines.

These 10-50 microvolt spikes were shorter than the voltmeter measurement

cycle, and thus lent themselves to being filtered digitally. FILT takes

10 measurements, looks for three in a row that are the same within a

tolerance, and compares the rest of the measurements to one of them. Any

measurement varying more than a specified tolerance is dropped, and the

average of the "good" measurements is passed back to MEASR. If more than

half of the measurements are noisy (out of tolerance), a warning is

printed to notify the operator.

Subroutine TMTCH is included to match the time constants of the net

radiation and precision radiation thermometer to that of the temperature

and dewpoint measurements. This matching is done by using the weighted

average of the 25 most recent (collected in the last 12.5 min) measure-

ments to calculate a matched measurement. The weights assigned to older

measurements decrease exponentially with a time constant of 4 min. The

same weighting scheme is used for the net radiation and surface tempera-

ture because their sensor response time constants are 8 and 2 seconds,

respectively. At a sampling rate of one measurement every 30 sec, their

responses are, in effect, instantaneous.

Program REPRT produces a half-hourly data summary report. It calcu-

lates half-hourly average profiles of the heat budget components, wind-

speed and direction, Bowen ratio, and profiles of soil and air tempera-

ture, air vapor pressure and relative humidity. Most of this program is








concerned with formating and printing the summary report. An example

report is shown in Fig. 3-6, and Table 3-3 lists the variable names

used.

Program ANALZ makes ancillary calculations and produces the last

five lines of the half-hourly report. It has a search routine which com-

putes the displacement height of the temperature and vapor pressure pro-

files. With an assumed value of the roughness parameter (z0) and trial

values of the displacement height (D), it computes the correlation of

temperature or vapor pressure and height over the surface with

z D + z0
T, e = B ln + A 3-9
0

The assumed roughness height, the displacement height producing the best

correlation, and other profile parameters are printed out.

ANALZ also computes a variety of other quantities which may be of

use in data analysis or operation of the system. Among these are atmo-

spheric and stomatal resistances, albedo, optical air mass and atmo-

spheric transmission coefficient, zenith and hour angle of the sun, and

the equation of time.

The fourth program, SET, is the executive program. It is used to

properly start the acquisition of data and determine whether and when

the other programs should be run. In a "cold" start, SET positions the

scanning valve, initializes counters and statistics, and schedules MEASR

to start so that profile collection is completed at specified times. On

occasions other than a "cold" start, it determines whether the other

programs should be run, depending on flags in MEASR or operator input

via switches on the face of the HP-2100. Its most valuable function i.s

to schedule MEASR to begin at an absolute clock time at the beginning of










BEEF RESEARCH UNIT ET PROJECT DATA


V IWERlGES ANiD ( PERCENT VARIATION ) FOR HALF HOUR ENDING
TULSD-AY, OCTOBER 2G, 1981 (JIJL.I N DAY 293) TIME 09:31:27 TST


NET RAD. SOIL H.F. SENS. H.F. LATF.H.F. N INDS
.45 LY/M .02 LY/M .28 LY/M- .I- LY/M- 3.06 M/S
*16 LY/M .02 LY/M .28 LY/11 1 LY/ 11 33.06 M/S


.NET
IS1
RSI
ALW I
iLW N
I l '


RADIATION AIR TEMP VAP PRESS
(LY/H) (CM) (-C) (CM) (M1B)

.451 (5.0) 225 19.2 (4,2) 225 11.2 (3.0)
.802 (14.1) 135 19.6 (4.1) 135 11. 3 (2.9)
.177 (3.7) 85 20.0 (4. 1) 85 11.5 (2.8)
.109 (16.) 60 20.4 (4.0) 60 I 1 .G (3.1
.61G (5.5) 35 21 .1 (3.9) :35 11 .9 (3.1)
162 MM/H1R 0 23.4/ (5.5) .- .95+ BR =1.760,


TO
23.0
22.6
22.3


DH
22 .-0
22.0
22.0


UH
33.4

31.9


RCH
-I .000
-1. 000
-1 .000


EO
12.8
12.6
12.5
."I.S


RSQ.>.95 B.R. -~VG.R.

12 OF 12 1.753 .999

REL HMDTY SOIL TEMP
(CM) (.) (CM) (-C)

225 50.2 0 16.8
135 49.8 -2 11.6
85 4,9.2 -S 18.2
60 48.6 -10 19.2
35 47.6 -25 20.1
+OR-.11-** -50 21.7


DE
17.0
18.0
19.0


U*E
12.8
12.4
12.2


RCE
999
999
999


iN I R S, R TM(S/M)

A[EDO S110
.22 1.09


.238,4.350 .311,4353 .348,4,350 .397,4.358 ,436,4.365


OA11
0 II


ATC
.85


ZNIGL
57.3


HRNGL
-41 :2


EOT E.S.T. T.S.T.
.2579 9.48 9.25


Figure 3-6. Example of Half-Hourly Data Report.. .Variable names and units are listed in Table 3-3.


DAY
293









Table 3-3. Variable Names and Units for Half-Hour Reports

RSQ.>.95 Number of temperature and vapor pressure profiles with
correlation coefficient better than .95
B.R. Bowen Ratio
AVG.R. Correlation coefficient of half-hour average profiles
NET Net radiation (ly/min)
ISW Incoming shortwave radiation (ly/min)
RSW Reflected shortwave radiation (ly/min)
ALW Atmospheric longwave radiation (ly/min)
ELW Emitted longwave radiation (ly/min)
ET Evapotranspiration rate (mm/h)
.95+BR Average and standard deviation of individual profile Bowen
ratios with greater than .95 correlation coefficient
ZO Roughness height (cm)
TO Temperature at ZO by temperature profile extrapolation (oC)
DH Displacement height for heat (cm)
U*H Friction velocity as determined by fit of profile (m/min)
RCH Correlation coefficient for temperature profile
EO Vapor pressure at ZO by vapor pressure profile extrapo-
lation (mb)
DE Displacement height for vapor pressure (cm)
U*E Friction velocity as determined by fit of vapor pressure
profile (m/min)
RCE Correlation coefficient for vapor pressure'profile
RAIR Air diffusion resistance (s/m)
RSTM Stomatal diffusion resistance (s/m)
ABDO Albedo (fraction)
SWIO Shortwave insolation without atmosphere (ly/min)
OAM Optical air mass (atmospheric diameters)
ATC Atmospheric transmission coefficient
ISW = SWIO (ATC OAM)
[absorption coefficient = -ln(ATC)]
ZNGL Zenith angle of sun (degrees)
HRNGL Hour angle of sun (degrees)
EOT Equation of time (h)
E.S.T. Eastern standard time
T.S.T. True solar time
DAY Day of year









each half hour. This prevents the data reports from processing out of

synchronization with the system clock.

SET also enables REPRT and ANALZ to be swapped between core and

disk so as not to interfere with the measurement schedule. At the end of

a typical half hour (1.5 min past the clock hour or half hour, when mea-

surement of the twelfth profile has just been completed) MEASR calls for

SET to run immediately and ends. SET schedules MEASR to start again at

an absolute clock time, 2 min into the new half hour, or roughly 30 sec-

onds after the last measurement made. It then loads and runs REPRT and

ANALZ. When it is time for MEASR to start, whichever program is in core

is moved back to disk, and MEASR is loaded. MEASR makes its first scan,

and during the usual delay between scans, REPRT and/or ANALZ are re-

loaded and run to completion. MEASR is then swapped back to core to be

continued at the end of the programmed delay;

The programs can be halted from the computer terminal or with

switches on the face of the computer. When switches 1 and 2 are on,

MEASR ends with the next profile and REPRT computes averages for all the

data collected in that half hour. When only switch 2 is on, MEASR ends

at the next normal half-hour reporting time.

Operational Considerations

The thermopile/air sampling system required a great deal of care in

setting up and maintaining the instrumentation involved. It also re-

quired an awareness of the theoretical and practical limitations of the

measurement method. Proper calibration and tuning of the dewpoint analy-

zer were most critical for good measurements. Sensor cleaning and output

calibration procedures are well documented in the EG&G Model 880 Dew-

point Hygrometer Manual (1977). However, to achieve optimum response









times, it was necessary to tune the instrument slightly differently than

Manual specifications. It was made more sensitive by setting the THK

potentiometer so that voltage on the test points was 200-260 mV, and

made faster by setting the GAIN potentiometer so that the test voltage

was 150-210 mV. The new settings sacrificed dewpoint analyzer response

time in large step changes in order to improve response time in the

smaller step changes normally encountered in the profiles. To ensure

that the dewpoint analyzer actually had time to settle on readings be-

fore being read by the voltmeter, its output was spot-monitored on a

millivolt recorder.

The most difficult problem was the individual and cross-correlation

of the dewpoint analyzer, the thermocouple/thermopile air temperature

sensors, and the precision radiation thermometer. The dewpoint analyzer

S-output was calibrated according to the EG&G manual. Temperatures at the

bottom and top of the scale were simulated by substituting precision

resistances for the mirror-temperature sensing thermistor; the analyzer

output at these simulated temperatures was matched to the factory stan-

dard instrument output. The radiation thermometer was calibrated by mea-

suring its output for known surface temperatures produced with a stirred

constant-temperature bath. A regression equation for the temperature vs.

output correlation was calculated and used in the programs.

It was not possible to cross-calibrate these temperature sensors

until the system was run in a light drizzle on Nov. 5, 1981. This situa-

tion resulted in the same temperatures at all measured levels, near-zero

net radiation, and air that was near saturation, so the dewpoint, air,

and surface temperatures were approximately the same. The temperature

differences between sensors were used to correct the rest of the data.








(It should be noted that this correction did not affect the Bowen ratio

calculation, since it used only relative changes. The correction did

affect surface temperatures, which were not used in computing the energy

budget.)

The radiation sensors were calibrated against a recently purchased

(and calibrated) Epply Pyranometer.

On the whole, the thermopile/air sampling system developed worked

very well and produced excellent data. However, there were some situa-

tions in which it could not function well. The system was protected from

almost all of these situations because calculation of a complete energy

budget was made conditional on temperature and dewpoint profile similar-

ity. Latent and sensible heat fluxes were not calculated when the pro-

file correlation coefficient was less than 0.95.

Profiles were regularly dissimilar for a few time-periods in the

early.morning and late afternoon, while temperature and dewpoint pro-

files were reversing in direction. This dissimilarity occurred because

changes in the temperature profile generally preceded changes in the

dewpoint profile.

Sensible heat generated at the surface of the outermost radiation

shields was usually carried away by the air flowing over them. At very

low windspeeds, however, the warm air produced at the outer surface of

the lowest radiation shields could become entrained in the aspiration

air of mast arms above. This problem showed in profile correlation coef-

ficients but was usually not so bad that energy budgets could not be

calculated. Under clear skies this effect was not as marked, presumably

because the radiation shields could more effectively radiate heat away.








When the system was run at night, some condensation took place in

the air sample lines because the air sampling mast was not heated. Water

accumulated in the tubing in proportion to the length of the tubing sec-

tion in the mast. As a result, the fifth level produced obviously high

dewpoint temperatures until the tubing had dried. The temperature dew-

point correlation made it obvious at what time all condensation had been

evaporated from the sample lines.

The situation most hazardous to data quality occurred on very

sunny, dry days. At these times, the air temperature of the instrument

room (21-240C) was quite a bit higher than the dewpoint temperature of

the outside air. At some point the analyzer would no longer be able to

cool its sensor mirror low enough to get dew formation. Since air sam-

ples from different levels have different temperatures, the coolest mir-

ror temperatures possible varied also. A false dewpoint profile, which

correlated very well with air temperatures, would be measured and thus

passed through the correlation coefficient screen. Evidence for this

condition was the brightly-lit cooling circuit lamp on the dewpoint ana-

lyzer. With experience this condition could be anticipated, and its ef-

fects minimized by unplugging the heater cables to the sampling lines

and mixing box.

In spite of precautions taken, susceptibility to lightning damage

was the system's greatest weakness. The system was damaged twice by

lightning. In both cases, instrumentation and computer equipment was

damaged by current surges in the AC power system, in spite of power-

surge arrestors. The only solution was the most fundamental--unplugging

all sensor cabling and all AC power cords.














CHAPTER 4

THEORETICAL BASIS OF THE TEMPERATURE GRADIENT RESPONSE
ET ESTIMATION METHOD

Overview

The key problem in developing a remote ET estimation method is de-

scribing the vegetation and air layer at the surface so as much informa-

tion as possible about its energy budget can be gained from the surface

temperature and net radiation. In addition, there is the question of how

much ancillary data is necessary for acceptable levels of accuracy in

the estimates. Previous approaches to these problems were outlined in

Chapter 2.

The methods developed in this chapter are based on the response of

surface-to-air temperatures to varying net radiation loads. First, a

functional relationship that describes the dependence of the surface-to-

air temperature gradient on net radiation and other factors is derived.

This temperature gradient response (TGR) model is used with surface tem-

perature, air temperature and net radiation data to evaluate surface

parameters, which are then used in an adapted version of the combination

equation to estimate evapotranspiration. Two methods of making estimates

are developed. The first is physically strict, with a minimum of assump-

tions; the second is more approximate with correspondingly fewer data

requirements.

For the sake of simplicity, the derivations that follow are in

terms of surface temperature (Ts) and net radiation (R) rather than the

direct remote measurements, reflected (Qr) and emitted (Q ) radiation.








Also, in application, temperature differences are used to evaluate tem-

perature gradients. For that reason, differences are used in the equa-

tions developed and are referred to interchangeably as differences and

gradients.

Temperature Gradient Model

The simplified energy balance of a vegetated surface was developed

in Chapter 2:

R = E + H + G 4-1

The purpose of this section is to express the components of the surface

energy budget as much as possible in terms of net radiation and surface

temperature, so that a useful relationship between the two can be de-

rived.

Because of heat storage in the surface air layer, surface tempera-

tures lag net radiation. This lag is complicated by the fact that the

passage of clouds usually makes the net radiation absorbed by the system

vary randomly. For this reason, a method containing time as a variable

has been avoided. This was done by modeling the response of surface-to-

air temperature gradients to changes in net radiation.

In describing heat flux using a surface temperature (i.e., between

the surface and some plane above the surface), at least two layers with

different transport properties must be considered (see Fig. 4-1). The

first is the surface layer, in which molecular diffusion is the primary

transport mechanism. It is the thin layer of air immediately next to the

plant surfaces, represented by the layer between zs and z0 in the dia-

gram. The second is the fully turbulent layer between z0 and za, where

turbulent eddies are the primary transport mechanism. Following the de-

velopment shown in Chapter 2, the heat flux between the surface (at




64








Za ---- T- -- --


Z--




Air KH h Turbulent
(3 Layer
LLJ


KH
S,.. Surface-.
'Zo.- - ;~-t : |Layer I-"
S "'. -* y I'-
ZT P, lant gpDQ;,e tcS 1I;

Soil


Figure 4-1. Definition Sketch for Transport Properties. The
surface layer which is dominated by laminar air
flow (molecular thermal diffusivity, kH) is repre-
sented by the layer between zs and za. The heat
transport coefficient is used to represent the
combined transport properties of both layers.








temperature Ts) and some level in the air above the surface (at Ta) is

described by
(pCp )a (Ts Ta)
H= ,p 4-2
f zO dz Za dz
zk H z H

where p is air density,
c is the specific heat of air at constant pressure,
kP is the molecular thermal diffusivity of air, and
KH is the eddy thermal diffusivity of air.

(The first term in the denominator is equivalent to the resistance of

the laminar surface air layer, and the second term in the denominator is

equivalent to the resistance of the surface turbulent boundary layer.)

Treating latent heat flux analogously,

(pCp)a (es ea)
E = 4-3
fZO lz fza dz)
z W k z
s 0 -

where e is the water vapor pressure,
y is the'psychrometric constant (- = c P/Le),
kw is the molecular water vapor diffusivity, and
K is the eddy water vapor diffusivity.

It has been shown that for a wide range of stability conditions normally

found (Dyer, 1967; Swinbank and Dyer, 1967; Webb, 1970; Dyer and Hicks,

1970; Garratt and Hicks, 1973):

KW KH
Z a dz z a dz 44
z W z H
z0 0
For simplicity, it is also assumed that
zI0 dz z dz
.4-5
z W z H
s s
This assumption is unvalidated, but shared by the majority of theoreti-

cal treatments. Literature values for the molecular water vapor and

thermal diffusivities are in fact at least approximately equal [e.g.,

Eagleson (1970) quotes values of 0.1 and 0.13 cm2/sec, respectively].









With the above assumption, transport of latent and sensible heat

can be considered similar from the surface to a reference level in the

air. The simple expressions developed in Chapter 2 (Eqs. 2-17 and 2-20)

can then be used to describe these fluxes:

H = h(Ts Ta) and 4-6

h *
E = M(e e ) 4-7
y s a

The moisture availability parameter (M) is included to account for the

subsaturation of the surface air layer. However, use of Eq. 4-7 as a

hard equality will force M to include minor differences due to inequali-

ty of molecular diffusivities of latent and sensible heat (Jarvis et

al., 1971), any differences due to stability effects, and any differ-

ences due to dissimilar sources and sinks of latent and sensible heat

within the vegetation system.

The dependence of the vapor pressure gradient on the surface-to-air

temperature gradient is shown in Fig. 4-2. It shows that the vapor pres-
*
sure difference (e ea) is in part due to the greater temperature of
s
the surface relative to the air, and in part due to the saturation defi-

cit of the air. Considering the saturation vapor pressure curve linear

in the neighborhood of the surface and air temperatures,

e ea = s(Ts T ) + ea 4-8

where s is the slope of the saturation vapor pressure curve between
Ts and Ta, and
6ea is the saturation deficit of the air.

Substituting this expression into the latent heat flux equation (Eq.

4-7) gives the latent heat flux in terms of the temperature gradient:

E = M [s(T T ) + 6e] 4-9
Y s a a







S60

LU
D40

20
CL20


0
CL
>


Figure 4-2.


,ea
*'


T e
a
O -
o0 20 30 40
TEMPERATURE (C)

es'-ea a+b
es*-eas(Ts-Ta) +ea


Components of Vapor Pressure Gradient. Component (a)
can be calculated from the surface-to-air temperature
difference (Ts T,) and the slope (s) of the saturation
water vapor pressure curve [e*(T)]. Component (b) is
the saturation deficit (6ea) of the air.


(?(T)








The advantage of this substitution is that whatever error occurs in the

temperature gradient measurement affects both latent and sensible heat

fluxes, not just the sensible heat flux, as in the simple residual ap-

proach. Substituting Eqs. 4-6 and 4-9 into Eq. 4-1,

R = G + h(T T ) + hM [s(Ts Ta) + 6ea] 4-10

Rearranging terms and dividing by constants,


T Ta = h(Ms + ) [y(R G) hMea] 4-11

Equation 4-11 explicitly states the dependence of the surface-to-

air temperature gradient (difference) on other variables--net radiation

(R), soil heat flux (G), saturation deficit (6ea), bulk air conductivity

(h), and moisture availability (M). The equation is generally applica-

ble; the psychrometric "constant" can be adjusted to various atmospheric

pressures (altitudes) and the slope of the saturation vapor pressure

curve can be adjusted for various temperature ranges. The resistance

formulation of this equation has been used by Jackson et al. (1980).

In the strictest sense Eq. 4-11 is true only instantaneously. How-

ever, with the assumption of some degree of system stationarity, various

approaches to remote ET estimates can be made. Two are developed here.

The first makes a minimum of additional assumptions and uses ground-mea-

sured air temperature, saturation deficit, and soil heat flux measure-

ments. The second assumes that only surface and air temperatures change

in response to changes in radiation, and uses only remote measurements.

Both use the response of temperature gradients to varying net radiation

loads to evaluate surface parameters; these are then used in calculating

ET.








Strict Temperature Gradient Response Method

From Eq. 4-11, one recognizes that

H = h(Ts Ta) = y [y(R G) hM6ea] 4-12

Substituting into the energy budget equation (Eq. 4-1),

E=R-G Ms+y
E = R G Ms + [y(R G) -hM6e a] 4-13

E = Ms [s(R G) + hea] 4-14

This is a version of the combination equation for evapotranspiration

(Penman, 1948). When the surface is saturated (M = 1), this equation

reduces to the potential evapotranspiration equation of Tanner and

Fuchs (1968).

The slope of the saturation vapor pressure curve (s) is a known

function of temperature, and the psychrometric constant is a known func-

tion of atmospheric pressure. Net radiation (R), soil heat flux (G), and

saturation deficit (6ea) are measurable. Only the parameters for bulk

heat transport (h) and moisture availability (M) are unknown. These can

be evaluated with Eq. 4-11, assuming that they can be considered con-

stant for some period of time.

Supposing that measurements of Ts, Ta, 6ea, G, and R are available

for two different radiation loads,

y(R G)1 hM6e
(Ts Ta h(Ms + ) and 4-15

y(R G)2 hMse
(T T2 h(Ms ) a2 4-16
.s a 2 h(Ms+y)

The numerical subscripts identify the two sets of data corresponding to

the two differing radiation regimes. If the measurements are made close

enough in time so that moisture availability and the bulk thermal








conductivity can be considered constant, this pair of equations can be

solved for the two unknowns M and h,

RieI RiAe2
h = R -Ae1- e2 4-17
6elAT2 6e2AT1


y=(R2AT1 + RAT2)
M = 4-18
RjAe2 + R2Ae1

where R1 = (R G). 4-19

ATi = (Ts Ta)i and 4-20

Aei =(es e )i = SAT + 6e 4-21
1 s a i i a .

Equations 4-17 and 4-18 can be substituted into Eq. 4-14 to yield:

R2?AT RIAT2 R2Ael R1Ae2
R = R6ej 2 Reel] s(R G) + 6ea 6e lT2 6e2AT1 4-22
Rfse2 R^6e1 a 6e1ATT RetA2]]

Now any evapotranspiration rate between the two measured radiation re-

gimes can be calculated by substituting intermediate values of R, G, and

6ea. As a practical consideration, the measured radiation regimes must

be near enough in time such that the constant M and h assumption is

valid, but far enough apart in radiation load so that reasonably accu-

rate calculation of the parameters is possible.

Average Temperature Gradient Response Method

System Stationarity and Average Temperature Gradient Response

The most restrictive problem faced in estimating ET from above the

atmosphere is that very often clouds make surface temperatures unobserv-

able. As shown in Eqs. 4-17 and 4-18, surface temperatures are necessary

to estimate surface moisture availability and bulk air conductivity.

This fact requires that remote ET estimates be made in two stages. The

first stage consists of using clear sky net radiation and surface








temperature data to evaluate the surface parameters. The second stage

consists of using those parameters and measured or estimated net radia-

tion data alone to make ET estimates. It is assumed that through a com-

bination of cloud-reflected radiation and cloud-top temperatures, a net

radiation estimate for the surface is still possible.

The success of this scheme is limited by the period over which the

parameters can or must be considered constant. They do vary; moisture

availability changes as dew evaporates and the bulk air conductivity

changes with the windspeed. But for the strict temperature response

method to work, the parameters must be considered constant for the time

interval between clear sky data sets, which is limited by the time reso-

lution of the data collection system and cloud cover.

This unavoidable necessity motivates viewing the surface as a sys-

tem with approximately stationary parameters for the duration of a lon-

ger measurement period (i.e., assuming that the surface-to-air tempera-

ture gradients in Eq. 4-11 are a function of net radiation and con-

stants). Information on the average parameters can then be extracted

from the correlation of clear sky surface-to-air temperature gradients

and net radiation, and used to estimate ET for clear or cloudy skies.

A soil heat flux parameter is required in order to fully parameter-

ize the temperature gradient model. Soil heat flux is the smallest of

the energy budget components, usually accounting for less than 10% of

net radiation under a vegetated surface. It lags net radiation in time,

but because its magnitude is in the range of error expected in the esti-

mates, it can be safely and conveniently treated as a constant fraction

of net radiation:

= g 4-23








The quantity used in calculations is (R G), which for convenience can

be written

R G = (1 g)R = fR 4-24

Typical daytime values of "g" in the literature range from approximately

0.0 to 0.2, so for a vegetated surface "f" will have values between 1.0

and 0.8.

Substituting Eq. 4-24 into Eq. 4-11,
1
T T hMs (YfR hMea) 4-25

Formalizing the approximation of system stationarity,

h, M, f, s, 6ea i f(t) 4-26

Eq. 4-25 reduces to the form

Ts T = AR B 4-27

where A and B are constants:

A f 4-28
h(Ms + y) and

M6e
B 4-29
(Ms + ) ,

and the parameter values are averages for the time period over which the

surface system is considered stationary. The constants A and B can be

evaluated by correlating the temperature differences (T, Ta) and net

radiation (R) data. Simple linear regression equations can be used:

E RtAT nRAT
A = and 4-30
E (Rt)2 nR2

B = AT AR 4-31

where the summations are done with clear sky data only,
AT = (Ts Ta), and
t is a subscript denoting the time of the measurement.









As a practical matter, the time period for which A and B are calcu-

lated (and the parameters are considered constant) needs to be at least

a day. This period must be extended if enough clear sky data are not

available for a reasonable estimate of A and B. It should also be noted

that for normal daytime conditions, A and B must be positive for physi-

cally real parameters. This implies that the intercept of the surface-

to-air temperature gradient/net radiation correlation must always be

negative (zero at most), and the slope must always be positive (see Eq.

4-27).

Use of the Average Temperature Gradient/Net Radiation Correlation

Incorporating the definition of the soil heat flux parameter (Eq.

2-24) into the equation for evapotranspiration (Eq. 4-14),
M
E =Ms (sfR + h6ea) 4-32

The slope of the saturation vapor pressure curve (s) is a known function

of temperature, the psychrometric constant (y) is relatively constant at

a given altitude, and net radiation (R) can be estimated directly from

satellite data. There are four unknown parameters: moisture availability

(M), the soil heat flux parameter (f), the bulk transport coefficient

(h), and the saturation deficit (6ea).

The equations for A and B, Eqs. 4-28 and 29, are in these four un-

knowns. Since all four are required to estimate ET, two must be approxi-

mated from average conditions or a rough daily measurement. Equations

4-28 and 29 can then be solved for the other two and substituted into

Eq. 4-32. Table 4-1 shows the ET formulae derived for the possible com-

binations of known and unknown parameters and the correlation constants

A and B.










Evapotranspiration Formulae for Average TGR Method. Conditions listed are necessary to
physically real solutions and prevent numerical problems. It is understood that A must


positive and unless otherwise noted, B must be
appear at right.


greater than or equal to zero.


maintain
always be


Equation numbers


Known Unknown Substitutions Special Evapotranspiration Equation
Parameters Parameters Constraints Formulae Number

M6e
--- M,f,h,6e A=- a 0 M < 1 E M (sfR + h6e) 4-32
a h(Ms +y) B Ms + .8 f < 1 Ms + a


Ah5e 6e
h,6e M,f M= yBf a 0 < B < a E = Bh sAR + 4-33
aa afa Bea Bs ea Bs s- Bs



a a a
M f(6ea Bs) 6e
f6 Mh h = 0 < B < a E = Ba (AsR + 6e, Bs) 4-34


h,f M,6ea M = (f hA) Bsf A < f E = (f hA)R + hB 4-35
a hAs ea (f hA) h


Mf h,= yf a = B(Ms + none E Mf sR +B 4-36
a A(Ms + y) a M Ms + y MA


_Ah(Ms + ) B(Ms + _)Ms
M,h f,6e, f = Ah(Ms e M none E = h MsAR + B] 4-37


M,6ea h,f --- -- --- no solution
a


Table 4-1.








All of the equations in Table 4-1 have the same basic form because

A, B and the parameters are considered constant for the measurement per-

iod:

E = CR + D 4-38

With A and B determined from clear sky data (requires surface tempera-

ture, air temperature, and net radiation), and two independently esti-

mated parameters, all that is needed in any of the formulae is a net

radiation estimate. If net radiation can be estimated for partly cloudy

or cloudy skies, ET rates for these conditions can also be calculated.

A significant advantage of considering the parameters approximately con-

stant arises in computing cumulative evapotranspiration. Using the gen-

eralized version of the equations in Table 4-1 (Eq. 4-38), the cumula-

tive ET rate for some period (p) can be calculated as follows:

Ep = Edt =. (CR + D)dt

= Cfp Rdt + DJp dt

Ep = CR + Dtp 4-39

where E is the cumulative ET over the estimating period,
Rp is the cumulative positive net radiation over the period,
tp is the duration of positive net radiation during the
P estimating period, and
C and D are constants calculated from A, B, and estimates of two
parameters as shown in Eqs. 4-33 through 37.

Since the parameters are approximated as constant, no interpolation is

necessary for cumulative ET estimates. Use of an interpolation scheme

may be required to more accurately determine R depending on the time

interval between satellite data sets.

Use of particular versions of the ET equation listed in Table 4-1

is discussed in the remainder of this section. It is difficult to pre-

dict particular applications or weaknesses of these equations; they








depend both on the accuracy with which A and B can be determined, and

which of the parameters are most conveniently supplied from other mea-

surements.

In general, the most difficult parameter to estimate independently

is moisture availability. Equations 4-33, 4-34, and 4-35 assume that it

and one of the other parameters are unknown. It can be anticipated that

the first two of these equations will have difficulties with low satura-

tion deficits; Eq. 4-34 predicts infinite ET as the saturation deficit

nears zero. This is a result of having to express the parameters in

terms of the saturation deficit. From the substitutions, it is clear

that 6ea must remain larger than Bs in order for physically real (posi-

tive) parameter values to result. Equation 4-33 seems to be the most

sensitive to low saturation deficits since it is meaningless even when

6ea is equal to Bs; Eq. 4-34 reduces to E = fR with this condition (no

sensible heat is generated; all available net radiation is consumed in

evapotranspiration).

Equations 4-33 and 4-34 are also very sensitive to the value of B

obtained from the temperature gradient net radiation correlation. This

presents another potential problem in their use because the clear sky

data collected in a given estimation period may not be able to estimate

B at an accuracy level commensurate with its influence on the ET esti-

mate. Once the behavior of B is better known, however, these equations

may become useful in areas where the least is known about the surface.

Saturation deficit is probably the parameter with the least spatial var-

iability, and since it is directly measurable it can be estimated for

large areas. Equation 4-33 might be useful over a large grassland area

or large area of short crops since the transport coefficient of this









type of area may also be approximated. For large forested areas, where

it can be assumed that f=l, Eq. 3-34 might work well. In both equations,

the only other estimate required is the slope of the saturation vapor

pressure curve, which is a known function of temperature.

Equation 4-35 assumes that moisture availability and saturation

deficit are unknown. The evapotranspiration equation generated has the

advantage that neither the psychrometric constant nor the slope of the

saturation vapor pressure curve needs to be evaluated. This makes the

equation easier to use, and since no division is involved, it is compu-

tationally safe. The additional parameters required are the bulk trans-

fer coefficient and the soil heat flux parameter. The former may be cal-

culable from measurements of windspeed and estimates of surface rough-

ness. This approach has a long history in the literature (see Chapter

.2), but its adaptability for use with a surface temperature has not been

demonstrated. The soil heat flux parameter only varies %20%, and might

possibly be estimated from near-infrared remotely sensed data, which

gives a good idea of vegetative cover. Because of its potential, simpli-

city, and easy graphical interpretation, Eq. 4-35 is used in the method

verification part of this study.

The last two equations, Eq. 4-36 and 4-37, assume that moisture

availability and either the soil heat flux parameter or the bulk tran-

sport coefficient are known. Since M is a normalized parameter, it can

be assumed to have various values in a constrained range. It is conceiv-

able that these equations might then be of some use.

Extension to Totally Remote ET Estimation Method

The final step in making a method depend only on remotely sensed

data is to generate air temperature measurements from surface








temperature measurements. Air temperatures are determined by the mixing

of air from higher in the atmosphere with near-surface air that has been

warmed (or cooled) by the surface. Therefore, one would expect air tem-

peratures, particularly those near the surface, to be primarily a func-

tion of the surface temperature. There is precedent for this approach.

In an effort to meet the boundary condition requirements of numerical

weather models, mesoscale climate modelers have begun developing "tem-

perature response functions" (Idso, 1982).

There are practical reasons for this approach as well. A network of

ground stations to supply this measurement would be very expensive, and

calibrating the ground-based sensors against a satellite sensor is in-

herently difficult. In addition to requiring knowledge of the atmo-

sphere's transmission properties, temperature measurements made by a

contact sensor (e.g., a thermocouple or thermistor) must be matched to

measurements made by a thermal radiation sensor. Since temperature dif-

ferences are required, a system based completely on remotely measured

surface temperatures would not be as sensitive to such absolute error

sources.

There are several ways in which air temperature measurements might

be generated. The simplest way is to choose a vegetation surface like

forest, whose surface temperature is closer to air temperature because

of the large fraction of surface elements visible to a satellite in

shade. The surface temperature of some reference pixel could then be

used as the air temperature for all pixels. In effect, the reference

pixel would never see a temperature gradient; its evapotranspiration

would exactly equal its available net energy (fR) since there could be

no sensible heat flux.








Another approach would be to simulate air temperature with a linear

combination of particular pixel temperatures. This involves empirically

choosing a set of reference pixels and determining coefficients for an

equation of the form:

Ta= a0 + alT+ a2 T + . 4-40

Both the length of time these coefficients are accurate and the extent

of the pixels for which they can be used to generate air temperature

measurements are important considerations in this approach. It should be

noted that similar considerations are involved in generating air temper-

ature measurements for all pixels from a limited number of ground sta-

tions.

The approaches suggested above are not developed any further in

this study.

Review of Assumptions

At the outset, the surface was conceived as a radiation-absorbing

(vegetation) layer, in contact with an air layer above and a soil layer

below. Energy fluxes inside the absorbing layer were considered irrele-

vant, and energy fluxes to and from the surface were considered one-di-

mensional and normal to the surface. It was assumed that the sensible

heat flux could be calculated from the surface-to-air temperature dif-

ference (i.e., that the radiation surface temperature is representative

of the effective heat transfer surface temperature). It was also assumed

that the vapor pressure gradient could be represented in terms of this

temperature difference and the saturation deficit of the air by way of

the linearized saturation vapor pressure curve. The time derivative term

and the photosynthetic heat flux term were considered negligible in the

energy budget equation.








These assumptions are typical in the evapotranspiration literature.

However, they amount to assuming a uniform surface with adequate fetch

and close to steady-state heat transfer. Realistically, the system is

always transient and there is some energy storage in both the surface

and air layer. Remotely sensed surface information in general does not

come from flat homogeneous surfaces.

Both the strict and totally remote temperature gradient response

methods are dependent on some degree of system stationarity. The former

assumes that only moisture availability and bulk air conductivity are

constant between data sets. It requires surface and air temperature, net

radiation, soil heat flux, and saturation deficit measurements.

To lessen the data requirements, these assumptions are extended and

a new parameter is introduced in the totally remote method. Moisture

availability, bulk air conductivity, and air saturation deficit are con-

sidered constant for a day or more, and soil heat flux is treated as a

constant fraction of net radiation. The surface is assumed to be a sta-

tionary system with four unknown parameters (M, h, 6ea, and f), and one

known parameter (s), the slope of the saturation vapor pressure curve.

To make up for data that cannot be collected, it is assumed that two of

the unknown parameters can be estimated from some prior knowledge of the

surface; the other two can be determined from the temperature gradient

response to various radiation loads. Once the parameters are determined,

evapotranspiration for any net radiation load is calculable.

Several elements of these methods were considered beyond the scope

of this study, but assumed possible. It is taken for granted that rea-

sonably accurate remote measurements of surface temperature and net ra-

diation can be made, further, that estimates of surface net radiation





81


are possible even with cloudy conditions. The pivotal assumptions are

that the surface temperature can be used as the effective heat transfer

temperature, and that air temperature measurements can be generated from

surface temperatures.














CHAPTER 5

VERIFICATION OF THE TEMPERATURE GRADIENT RESPONSE
ET ESTIMATION METHOD

Overview

The central idea of the temperature gradient response (TGR) ap-

proach is to use the changes in the surface-to-air temperature differ-

ence relative to corresponding changes in net radiation in lieu of sur-

face parameters to estimate ET. A temperature gradient model is used to

determine the surface parameters from the temperature gradient re-

sponse; these are then used in calculating ET rates.

Use of the temperature gradient model, which expresses the func-

tional relationship between temperature gradients, net radiation, and

surface parameters,'involves a number of assumptions and approxima-

tions. Since the accuracy of the eventual ET estimate is limited by

this model and ancillary approximations, verification of the TGR meth-

ods is carried out in stages. Initially, the assumptions required are

individually examined. Then the implication for both the strict and

daily average TGR methods is demonstrated. For the most part, this is

done with data from a clear fall day, October 17, 1981.

The daily average TGR method is most suited for use with satellite

data. It is tested with practically all data collected. First, measured

temperature gradient/net radiation correlations are compared to those

predicted with independently measured constant parameters. Then the ET

estimates made with the correlations are compared to measured ET rates.








Validity of Assumptions

Radiation Temperature and Sensible Heat Transport

A simple expression involving a temperature difference and a bulk

heat transport coefficient (Eq. 4-6) was proposed to describe sensible

heat flux. It considers the sensible heat transport to and from the veg-

etation layer to be the same as that across a relatively thick layer of

air above the surface. This layer is at the average grass surface tem-

perature on one side, and at the average temperature of the air at a

specific reference level (a) above the surface on the other side. It is

assumed that the heat capacitance of air is very small and therefore

that the heat transport across the layer is close to steady. All the

properties of the air relevant to heat transport through this layer are

accounted for in the heat transport coefficient (h).

The most critical assumption in this formulation is that.the aver-

age radiation temperature of surfaces visible to an overhead sensor

(referred to as the surface temperature) and the effective heat trans-

fer temperature are the same, or related in some predictable way. In a

vegetation canopy, many small areas at different levels in the canopy

contribute toward a radiation surface temperature measured from above.

These represent only a small fraction of the total plant surfaces. All

surfaces, including those not seen by a radiation sensor, contribute

sensible heat to the air. These contributions depend on how well venti-

lated the canopy is at various levels.

Since radiation and sensible heat transfer are completely differ-

ent and a vegetation surface is so complex, the radiation surface tem-

perature and the effective heat transfer surface temperature may be dif-

ferent. The only way to compare these two temperatures is to infer









their relationship from observations of the temperature profiles over

the grass surface. Sensible heat flux was calculated using five temper-

ature measurements from the turbulent layer via the profile Bowen ratio

technique. One would therefore expect the heat flux to be proportional

to the temperature difference between the lowest and highest air tem-

perature measurements. The heat transport coefficient of this fully

turbulent layer can be calculated by solving Eq. 4-6 for the heat

transport coefficient

ht T T 5-
0 a
where TO is the lowest temperature measurement (35 cm) and Ta is the

highest (235 cm). If heat transport through the total air layer (between

the surface and highest air temperature measurement) is steady, the same

heat flux passes through it as the turbulent layer. Then the heat trans-

port coefficient of the total air layer can be calculated:
H
h = 5-2
s a
If the radiation surface temperature is the same as the effective heat

transfer surface temperature, one would expect the ratio of h/ht to re-

main constant over the course of a day. This ratio,


h T0 Ta
5-3
ht T Ta

can be most easily examined by plotting T Ta vs. TO Ta (see Fig.

5-1).

The points in this figure would lie on a straight line intersect-

ing the origin if the relationship between the turbulent temperature

gradients (or effective heat transfer gradient) and the total surface-

to-air temperature gradients was constant. However, relative to a given










10.0


8.0

C-)
6.0-

H-
4.0
r--


2.0



0.0


Figure 5-1.


1.0
To-Ta (0C)


2.0


Total vs. Turbulent Temperature Gradients for a Clear
Day. The total surface-to-air temperature difference
was calculated by subtracting the temperature measured
at 235 cm from the surface temperature. The turbulent
temperature difference was calculated by subtracting the
235-cm temperature from the 35-cm temperature. Data ar.e
from October 17, 1982; numbers indicate true solar time
at end of half-hour averaging period. Individual temper-
ature profiles for this day are plotted in Fig. 3 of
Appendix D.








effective heat transfer gradient, surface-to-air gradients are larger

in the afternoon than they are in the morning. This is because in the

afternoon, radiating surfaces lower in the canopy have also become

warm. Apparently, these surfaces make a relatively greater contribution

to the radiation surface temperature than they do to the sensible heat

flux via the effective heat transfer surface temperature. Although it

is not as extreme, this pattern is also observed on cloudy days, under

a diffuse radiation regime (Fig. 5-2).

One could reasonably expect radiation geometry to play a role in

creating differences between the radiation temperature and the effec-

tive heat transfer temperature. At high sun angles, when direct sun-

light is coming from angles close to the viewing angle of the radiation

sensor, less shaded area is visible to the sensor. The radiation tem-

peratures should peak relative to effective heat transfer temperatures

when the angle of incidence of direct sunlight coincides with the angle

of view of the sensor. The slight upward curvature in the total/turbu-

lent gradient correlation (Fig. 5-1) seems to confirm this effect, but

it is small in comparison to the morning/afternoon radiation tempera-

ture hysteresis.

The apparent difference in the effective heat transfer surface

temperature and radiation surface temperature must be viewed as a poten-

tial problem which may require modification of the equation used to com-

pute surface temperature. A time-varying factor may be required, espe-

cially in cases where the radiation geometry is further complicated by

surface slopes, as in mountainous areas.

Constancy of Parameters

The heat transport coefficient (h) and moisture availability (M)

are considered parameters in the strict TGR method, and they are




























.4 .6
To-Ta (0C)


Figure 5-2.


Total vs. Turbulent Temperature Gradients for a Cloudy
Day. Temperature differences were calculated as in
Fig. 5-1; data are from October 30, 1981. Note that
compared to Fig. 5-1 the temperature scale is expanded
by a factor of five. Temperature profiles for this day
are plotted in Fig. 4 of Appendix D.


4.0


3.0



2.0


0
0
0
H
I
C,)
H


1.0 -



7
.0


.2


.8


1.0








required to remain constant between sets of data. In the average TGR

method, the slope of the saturation water vapor pressure curve (s),

the saturation deficit (6ea), and the fraction of net radiation conduc-

ted into the soil (f) are also required to be approximately constant

for periods of a day or more. Though some of these variables are known

functions of measurable variables (e.g., s is a known function of tem-

perature), they must be considered parameters. This section shows how

these parameters vary over the course of a day.

The sensible heat flux is plotted as a function of the surface-

to-air temperature difference in Fig. 5-3a. The average heat transport

coefficient is represented by the slope of a line passing through the

origin and the center of gravity of the plotted points. The bulk air

conductivity for any half-hour period is computed as in Eq. 5-2 and has

been plotted in Fig. .5-3b.

It was shown in Figs. 5-1 and 5-2 that radiation surface tempera-

tures in the morning appeared cool relative to the effective heat trans-

fer surface temperature. Barring other factors, the resulting lower tem-

perature gradients would lead to higher calculated thermal conductivi-

ties for morning time periods. This does not show in Fig. 5-3b, how-

ever. The only apparent effect seems to be lowered conductivities

around noon resulting from apparently higher surface temperatures while

relatively less shaded areas are visible to the sensor.

It is difficult to say anything conclusive about the heat trans-

port coefficient in the early morning or late afternoon. Temperature

gradients are in the process of changing direction, making the calcula-

tion of h somewhat unreliable.





.6


> 4-
10
2-
(a)

0 2 4 6 8 10

.06 Ts-Ta (oC)
0
,04



.02 h=.034 LY/MC

(b)

8 10 12 14 16
TIME (TST OCT. 17, 1981)


Figure 5-3. Heat Transport Coefficient Data.




Full Text
174
Day
Time
Net
Soil
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
FI ux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
305
1400
0.25
0.00
0.13
0.02
5.14
20.9
22.9
22.4
.992
1430
0.14
-0.00
0.07
0.07
5.44
20.5
21.8
22.2
.978
1500
0.11
-0.00
0.05
0.06
5.49
19.8
20.6
22.3
.981
1530
0.12
-0.00
0.04
0.08
4.62
19.3
20.4
22.5
.994
1600
0.12
-0.00
0.04
0.09
5.12
19.2
20.3
22.2
.994
1630
0.07
-0.01
0.03
0.05
4.40
19.0
19.9
22.2
.978
1700
0.04
-0.01
0.01
0.03
3.69
19.0
19.7
22.0
.993
1730
0.01
-0.01
0.00
0.02
3.43
18.7
19.2
20.4
.916
306
730
0.02
-0.01
0.00
0.02
2.91
18.0
18.4
19.9
.976
800
0.08
-0.01
0.02
0.07
2.78
18.3
19.3
20.1
.988
830
0.17
-0.00
0.05
0.12
3.12
18.9
20.3
20.2
.994
900
0.29
0.00
0.10
0.19
3.23
20.1
22.3
20.3
.997
930
0.40
0.01
0.15
0.24
3.19
21.4
24.7
20.5
.998
1000
0.50
0.01
0.19
0.30
3.82
22.7
26.3
20.3
.996
1030
0.57
0.01
0.23
0.32
4.45
23.8
28.5
19.9
.996
1100
0.63
0.02
0.28
0.34
4.41
24.8
30.2
20.2
.999
1130
0.64
0.02
0.29
0.33
6.26
25.3
30.8
20.0
.998
1200
0.36
0.01
0.15
0.20
5.44
23.8
26.7
20.7 .
.998
1230
0.67
0.02
.0.27
0.38
4.. 27
24.5
32.2
21.6.
1.000
1300
0.63
0.02
0.29
0.32
5.74
25.8
32.3
20.5
.996
1330
0.53
0.02
0.26
0.25
5.47
25.7
31.1
20.4
.994
1400
0.26
0.01
0.12
0.12
5.07
25.0
27.6
20.7
.997
1430
0.25
0.00
-0.02
0.26
3.84
23.3
23.7
21.1
-.948
1500
0.30
0.00
0.06
0.23
5.72
23.4
24.4
21.1
.999
1530
0.10
-0.01
0.01
0.10
3.32
19.9
21.0
21.0
.987
1600
0.14
0.00
0.02
0.11
2.73
20.7
22.2
22.0
.988
1630
0.08
-0.01
--

4.75
20.8
21.0
20.7
-.879
1700
0.02
-0.01
-0.01
0.04
2.66
20.9
20.6
19.9
-.982
307
730
0.03
-0.01

....
2.38
17.9
18.2
-.921
800
0.08
-0.00


2.46
18.1
19.1

-.329
830
0.19
0.00

--
2.43
19.0
20.6

-.731
900
0.29
0.01


3.14
20.9
22.9

-.979
930
0.39
0.01
--

4.10
23.0
25.1
-.407
1000
0.50
0.02
0.17
0.31
4.19
24.1
27.1
20.1
.999
1030
0.58
0.02
0.22
0.34
5.71
24.9
28.9
19.1
.996
1100
0.48
0.01
0.18
0.29
5.60
25.0
27.9
17.7
.995
1130
0.57
0.02
0.23
0.32
4.80
25.7
30.4
17.3
.998
1200
0.63
0.02
0.27
0.34
5.06
26.2
32.4
17.4
.998
1230
0.51
0.02
0.21
0.28
5.12
26.4
31.2
18.0
.996
1300
0.44
0.02
0.18
0.25
4.80
26.2
30.5
18.2
.997
1330
0.48
0.02
0.20
0.26
3.90
26.4
31.6
18.5
.999
1400
0.38
0.02
0.19
0.17
4.74
25.8
29.9
19.5
.999
1430
0.18
0.01
0.07
0.10
3.34
25.0
27.1
19.8
.995
1500
0.13
0.01
0.05
0.07
2.44
24.5
26.4
19.5
.997


13
the surface as a liquid. The energy of the random molecular collisions
which cause the bonds to break is carried with the freed molecule; this
thermal (heat) energy is lost by either liquid or gas molecules near the
interface. Since this energy contributes only to the molecule's conver
sion to the vapor state and not its temperature, it is called the latent
heat of vaporization. It is released to the molecules at the surface
should a free molecule collide with and be captured by molecules in the
liquid state.
When the concentration of vapor molecules is higher at the surface
than at some distance away from it, there is a net flow of molecules and
energy (in the form of latent heat) away from the surface. This process
is evaporation.
Evapotranspiration is the evaporation of water from soil or plant
surfaces together with transpiration by plants. In transpiration, water
evaporates from internal plant surfaces and diffuses into the air around
the plant through openings in the leaves (stomata). Like the process of
evaporation, evapotranspiration consists of three fundamental elements:
the absorption of thermal energy at a water-air interface, the change of
state of water from liquid to vapor, and the resulting net loss of vapor
molecules and their heat of vaporization from the surface due to a fa
vorable vapor concentration gradient.
The heat energy consumed in the evapotranspiration process is lost
from the vegetation biomass. Therefore, all the energy fluxes to and
from the plant canopy and the factors influencing them play a part in
determining the evapotranspiration rate. Figure 2-1 is a simplified dia
gram of the surface and its primary energy and water fluxes. It is pre
sented in the diagramming language of Odum (1982), and embodies many of


159
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
141
1300
0.86
0.09
0.31
0.46
3.82
23.3
41.8
20.4
.998
1330
0.83
0.09
0.30
0.44
3.74
23.8
41.5
19.7
.999
1400
0.86
0.09
0.30
0.46
4.18
24.4
41.9
19.5
.998
1430
0.85
0.09
0.31
0.45
4.25
25.2
42.1
19.7
.998
1500
0.80
0.09
0.28
0.43
3.53
25.4
41.8
19.1
.999
1530
0.76
0.09
0.27
0.41
4.17
25.8
41.4
19.8
.999
1600
0.69
0.07
0.23
0.38
4.54
25.8
40.1
18.9
998
1630
0.60
0.06
0.22
0.32
3.88
25.9
39.2
18.4
.998
1700
0.49
0.04
0.18
0.27
4.65
25.9
36.4
19.0
.997
1730
0.41
0.03
0.14
0.24
4.27
25.4
34.2
18.7
.996
1800
0.31
0.02
0.11
0.18
4.60
25.3
31.3
18.5
.995
1830
0.20
0.02
0.07
0.12
4.76
24.8
28.8
18.4
.994
1900
0.10
0.01
0.02
0.07
4.12
24.0
26.5
18.6
.987
142
730
0.03
-0.02
-
...
-0.00
7.1
10.1
.740
800
0.09
-0.01

--
0.47
10.5
14.5

.913
830
0.20
0.00


1.08
13.8
19.3
--
.706
900
0.30
0.01

2.04
16.6
23.8

-.458
930
0.38
0.02

--
1.52
19.7
28.9

.845
1000
0.47
0.03

.
2.33
21.8
32.6

-.762
1030
0.56
0.05
0.19
0.32
2.63
23.2
36.0
16.5
.948
1100
0.63
0.06
0.24
0.33
3.03
23.9
38.1
15.9
.996
1130
0.70
0.07
0.23
0.39
3.04
24.6
39.5
14.3
.997
1200
0.73
0.09
0.26
0.38
2.99
25.4
40.8
14.2
.991
1230
0.76
0.08
0.29
0.38
3.15
25.5
41.1
14.2
.997
1300
0.84
0.11
0.30
0.44
4.13
26.5
42.4
14.4
.992
1330
0.85
0.11
0.29
0.44
3.28
26.9
43.2
14.2
.996
1400
0.83
0.12
0.27
0.45
3.29
27.4
43.5
14.9
.994
1430
0.82
0.11
0.28
0.43
3.50
27.8
43.1
14.7
.996
1500
0.78
0.11
0.27
0.41
3.37
28.4
42.6
13.9
.991
1530
0.73
0.10
0.23
0.40
2.94
28.6
42.4
13.7
.992
1600
0.67
0.09
0.22
0.35
3.48
29.0
41.2
14.2
.987
1630
0.59
0.08
0.19
0.32
3.62
29.0
39.9
14.1
.988
1700
0.50
0.06
0.17
0.28
4.25
28.7
38.1
14.1
.989
1730
0.41
0.05
0.13
0.23
3.63
28.5
36.7
14.2
.985
1800
0.30
0.03
0.09
0.19
4.28
28.2
33.2
14.5
.981
1830
0.20
0.03
0.05
0.12
4.17
27.7
30.4
14.5
.964
1900
0.09
0.01
--

3.51
26.9
27.7
14.0
-.618
143
730
0.04
-0.02
-0.00
9.3
11.2
..
.896
800
0.11
-0.00

--
-0.00
12.3
15.8
--
.854
830
0.18
0.01
0.17
0.00
-0.00
16.8
21.2
--
.949
900
0.28
0.02
--
0.44
20.8
26.8

-.128
930
0.35
0.03

--
2.35
23.1
29.8
.848
1000
0.49
0.04
0.21
0.24
3.64
23.9
32.9
23.1
.975
1030
0.59
0.06
0.23
0.30
2.98
24.9
36.6
22.3
.976


65
temperature T ) and some'level in the air above the surface (at T ) is
$ Q
described by
4-2
where p is air density,
c is the specific heat of air at constant pressure,
kR is the molecular thermal diffusivity of air, and
K^J is the eddy thermal diffusivity of air.
(The first term in the denominator is equivalent to the resistance of
the laminar surface air layer, and the second term in the denominator is
equivalent to the resistance of the surface turbulent boundary layer.)
Treating latent heat flux analogously,
4-3
where e is the water vapor pressure,
y is the psychrometric constant (y = c P/Le),
is the molecular water vapor diffusivity, and
is the eddy water vapor diffusivity.
It has been shown that for a wide range of stability conditions normally
found (Dyer, 1967; Swinbank and Dyer, 1967; Webb, 1970; Dyer and Hicks,
1970; Garratt and Hicks, 1973):
Za dz [Za jjz
4-4
For simplicity, it is also assumed that
Z dz. ~ [Z0 dz
k k
JZs KW JZs kH
4-5
This assumption is unvalidated, but shared by the majority of theoreti
cal treatments. Literature values for the molecular water vapor and
thermal diffusivities are in fact at least approximately equal [e.g.,
Eagleso'n (1970) quotes values of 0.1 and 0.13 cm^/sec, respectively].


(LY/min) ec-en (MB)
207
Figure 12. (cont.)


148
DO 120 K=1,5
AE (K, I) = 0.0
AT(K ,1) = 0.0
120 CONTINUE
AWSPD = 0.0
DO 125 K=l,8
ND(K) = 0
125 CONTINUE
BR(1) = 0.0
BR(2) =0.0
NBR = 0
END
SUBROUTINE RATIO(E,T,B,C)
C*****RATIO COMPUTES DT/DE BY DIAGONAL REGRESSION
DIMENSION E(5),T(5),SUM(5)
DO 210 Ll=l,5
SUM(Ll) = 0.0
210 CONTINUE
DO 220 L2=l,5
SUM(1) = SUM(1)+T(L2)
SUM(2) = SUM(2)+E(L2)
SUM(3) = SUM(3)+T(L2)**2
SUM(4) = SUM(4)+E(L2)**2
SUM(5) = SUM(5)+E(L2)*T(L2)
220 CONTINUE
ST = SUM(3)-(SUM(1)**2)/5.
SE = SUM(4)-(SUM(2)**2)/5. .
SET = SUM(5)-(SUM(1)*SUM(2))/5.
B = (ST-SE)/(2.*SET)
IF(SET)225,230,230
225 B = B-SQRT(1.+B**2)
GO TO 235
230 B = B+SQRT(1.+B**2)
235 C = SET/SQRT(SE*ST)
RETURN
END
ENDS


114
correctly reproduces the complex Bowen ratio patterns of partly cloudy
days, as shown in the middle section of Fig. 5-15 (same day as shown in
Fig. 5-13).
The relative magnitudes of sensible and latent heat flux vary with
the amount of net radiation received by the surface because of the sat
uration deficit term in the equation for evapotranspiration. If there
were no saturation deficit, the intercept (B) of the temperature gradi
ent/net radiation correlation would be zero, reducing the expressions
for the dimensionless ratios (Eqs. 5-13 and 5-14) to constants:
| = f hA 5-18
The greater the role of the saturation deficit in driving ET, the
greater the variations in the dimensionless ratios.
The fact that the average temperature gradient/net radiation cor
relation coefficients A and B explain general patterns and can be con
sidered roughly constant suggest they may be useful in some form of
climate index. They are more representative of the surface and surface
environment than the Bowen ratio or other ratios, which are representa
tive only of the particular time at which they were measured.
Tests of the ATGR Method
The purpose of this section is to show that the temperature gradi
ent/net radiation correlation does reflect the average values of the
parameters during the time of the measurements, and that the ATGR meth
od produces reasonably accurate ET estimates. This is done with data
collected in the fall of 1981.


250
200
150
G
N
100
50
0
'SAAAAA' vv^AvnaMa /wtviVM/ +\J,A
Turbulent
Layer
Ns-
UMiA/tJv
Surfacfe-.r-----
Layer
T5 t4 t3t2 1¡
Figure 1. Hypothetical Daytime Temperature
Profile. The various levels at
which temperature measurements
for the Bowen ratio calculation
were made is also shown, as sur-
fact temperature is plotted at
an arbitrary height within the
canopy.
200
100
ZA
Figure 2. Simplified Temperature Profile.
T^ is the air temperature mea
sured at level 5 in the profile,
Tg is the temperature at the
surface/turbulent layer inter
face and Ts is the radiation
temperature. The displacement
height (D) is 35 cm, and the
roughness height (Rg) is 1 cm.
lO


-D (cm) Z-D fcm)
Figure 3. Simplified Temperature Profiles for a Clear Day. Temperature gradients are rep
resented as in Fig. 2. The heavy lines are the average surface-to-air tempera
ture gradients measured on October 17, 1981. They are labeled with the true
solar time at the end of the half-hour period in which they were collected. The
turbulent and surface segments are shown in light lines.


LIST OF TABLES
Page
Table 1-1. Spatial and Temporal Resolution in Satellites .... 3
Table 3-1. Data Acquisition System Identification 46
Table 3-2. Sensor Identification 49
Table 3-3. Variable Names and Units for Half-Hourly Reports ... 57
Table 4-1. Evapotranspiration Formulae for Average TGR Method . 74
Table 5-1. Example Calculations with the Strict TGR Method ... 96
Table 5-2. Comparison of Average and Correlation Estimated
A and B 116
Table 5-3. Quality of ET Estimates made with the ATGR Method . 119
ix


109
The hysteresis caused by changes in the slope of the saturation
vapor pressure curve and saturation deficit is often masked by rela
tively large changes in moisture availability. When there is heavy dew,
as on Oct. 17, 1981, more evaporation takes place in the morning, caus
ing temperature gradients to remain small relative to afternoon gradi
ents at equivalent radiation loads. In the afternoon, moisture availa
bility has decreased and temperature gradients are pushed higher. The
extreme changes in M in the early morning are what cause the belly in
the graph.
Figure 5-12 shows data from a clear day in spring which had a much
smaller range of moisture availabilities. Very little dew accumulated
during the previous night because of a steady post-cold front northeast
breeze. In this case, morning temperature gradients are higher than
corresponding afternoon gradients because the variations in the slope
of the saturation vapor pressure curve and saturation deficit out
weighed changes in moisture availability.
The morning-afternoon hysteresis in Figs. 5-7 and 5-12 is most
extreme on clear days which have the temperature extremes to cause rel
atively large variations in s. Variations in the parameters are less
ened on partly cloudy days; Fig. 5-13 shows the parameters and tempera
ture gradient/net radiation correlation for a partly cloudy day. Clouds
narrow the range of surface and air temperatures and concurrent s, thus
lessening the variation between morning and afternoon temperature gra
dients .
Variations in the fraction of net radiation going into soil heat
flux have a negligible effect on the surface-to-air temperature gradi
ents because soil heat flux is a very small component of the heat


101
E = fR H = (f- hA)R + hB 5-12
This equation is identical to Eq. 4-35, the expression developed for
the case in which the heat transfer coefficient (h) and the soil heat
flux parameter (f) were known.
Like all the equations for evapotranspiration (Table 4-1), this
equation has the general form of Eq. 4-38. There is a component propor
tional to net radiation which varies over the course of a day, and a
constant component, referred to as advected energy because it is a
function of the saturation deficit (a result of dry air advection onto
the evapotranspiring surface) and the transport coefficient. In this
case (Eq. 5-12), the time-varying component is a function of Athe
greater the slope of the temperature gradient/net radiation correla
tion, the smaller the fraction of net radiation that contributes to
£Tand vice versa. The constant component is a function of Bthe low
er the intercept of the correlation, the greater the role of advected
energy in driving ET. The average TGR method in effect considers the
advected energy constant throughout the day, added to a component pro
portional to the varying net radiation.
Figure 5-9 shows evapotranspiration estimated using the tempera
ture gradient/net radiation correlation and actual ET rates plotted
against time. The area under the lines connecting the estimates and
measurements corresponds to the total daily estimated and actual evapo
transpiration. The dashed line in this graph separates the components
of estimated ET due to the "constant" advected energy term and the net
radiation term. The constancy of the parameters over the estimating
period is what makes cumulative ET rates easy to calculate;
P
Ep = (f hA)Rp + hBt
5-13


ESTIMATED ET (LY/min) BOWEN RATIO
204
Figure 11. (cont.)


99
If one changes the temperature scale by multiplying it by h, the
average air thermal conductivity (.035 ly/minC), an approximate plot
of sensible heat flux vs. net radiation results (see Fig. 5-8). This
graph can be interpreted with the help of the surface energy balance,
E+H = R- G ~ fR .
Since soil heat flux is very small (i.e. f = 1), the 45 line approxi
mately represents this equation. The distance from the R axis to the
solid line connecting the data points approximates (depending on the
constancy of h) the sensible heat flux at that radiation load and time.
Therefore the distance from the solid line connecting the data points
to the 45 line represents the approximate latent heat flux for partic
ular radiation loads and times. This is true even when the solid line
is below the R axis; at these times sensible heat flux is toward the
surface (T T < 0) and helping to drive evapotranspiration*
$ d
The heavy dashed line shows the approximate relationship between
the surface-to-air temperature gradient (or sensible heat flux, with
the vertical axis scaled by h) and net radiation. The average TGR meth
od amounts to using the dashed line to partition the latent and sensi
ble heat fluxes. Physically, the dashed line represents the temperature
gradient response of the surface that would occur if the parameters
were nonvarying.
In terms of the equations developed in Chapter 4, the dashed line
is described by
H = h(T T ) = h(AR B) 5-11
S a
using the surface-to-air temperature gradient/net radiation correlation
(Eq. 4-27). The distance from it to the 45 or fR line can be described
with the help of the energy balance:


Table 4-1.
Evapotranspiration Formulae for Average TGR Method. Conditions listed are necessary to maintain
physically real solutions and prevent numerical problems. It is understood that A must always be
positive and unless otherwise noted, B must be greater than or equal to zero. Equation numbers
appear at right.
Known Unknown Substitutions
Parameters Parameters
Special Evapotranspiration Equation
Constraints Formulae Number
Yf
, B =
M6e
a
0 < M
< 1
E =
h(Ms + y )
Ms + y
.8 < f
< 1
yB
, f =
Ah<5e
a
0 < B <
6ea
E =
6e, Bs
a
6e, Bs
a
s
yB
, h =
f(6e^ Bs)
a
0 < B <
6ea
E =
Se, Bs
a
A5ea .
a
s
y (f hA)
5 ea
Bsf
A < 1
A < h
E =
hAs
(f hA)
Yf
" A(Ms + y)
5ea
B(Ms + Y)
M
none
E =
HrW 4'32
h,Se, M,f
f ,e M, h
h,f M,<$e.
M,f h,6e.
sAR
<5e, Bs
a
+ l
4-33
75F- (AsR 6ea Bs) 4'34
E = (f hA)R + hB
Mf
Ms + y
MA,
4-35
4-36
M.h f ,5 e.
r Ah(Ms + y ) B(Ms + y )
f y Sea = H
none
E = h
MsAR n '
+ B
V
4-37
M, 6e, h,f
a
no solution
42*


57
Table 3-3. Variable Names and Units for Half-Hour Reports
RSQ.>.95
B.R.
AVG.R.
NET
ISW
RSW
ALW
ELW
ET
.95+BR
ZO
TO
DH
U*H
RCH
EO
DE
U*E
RCE
RAIR
RSTM
ABDO
SWIO
OAM
ATC
ZNGL
HRNGL
EOT
E.S.T.
T.S.T.
DAY
Number of temperature and vapor pressure profiles with
correlation coefficient better than .95
Bowen Ratio
Correlation coefficient of half-hour average profiles
Net radiation (ly/min
Incoming shortwave radiation (ly/min)
Reflected shortwave radiation (ly/min)
Atmospheric longwave radiation (ly/min)
Emitted longwave radiation (ly/min)
Evapotranspiration rate (mm/h)
Average and standard deviation of individual profile Bowen
ratios with greater than .95 correlation coefficient
Roughness height (cm)
Temperature at ZO by temperature profile extrapolation (C)
Displacement height for heat (cm)
Friction velocity as determined by fit of profile (m/min)
Correlation coefficient for temperature profile
Vapor pressure at ZO by vapor pressure profile extrapo
lation (mb)
Displacement height for vapor pressure (cm)
Friction velocity as determined by fit of vapor pressure
profile (m/min)
Correlation coefficient for vapor pressure'profile
Air diffusion resistance (s/m)
Stomatal diffusion resistance (s/m)
Albedo (fraction)
Shortwave insolation without atmosphere (ly/min)
Optical air mass (atmospheric diameters)
Atmospheric transmission coefficient
ISW = SWIO (ATC 0AM)
[absorption coefficient = -ln(ATC)]
Zenith angle of sun (degrees)
Hour angle of sun (degrees)
Equation of time (h)
Eastern standard time
True solar time
Day of year


83
Validity of Assumptions
Radiation Temperature and Sensible Heat Transport
A simple expression involving a temperature difference and a bulk
heat transport coefficient (Eq. 4-6) was proposed to describe sensible
heat flux. It considers the sensible heat transport to and from the veg
etation layer to be the same as that across a relatively thick layer of
air above the surface. This layer is at the average grass surface tem
perature on one side, and at the average temperature of the air at a
specific reference level (a) above the surface on the other side. It is
assumed that the heat capacitance of air is very small and therefore
that the heat transport across the layer is close to steady. All the
properties of.the air relevant to heat transport through this layer are
accounted for in the heat transport coefficient (h).
The most critical assumption in this formulation is that.the aver
age radiation temperature of surfaces visible to an overhead sensor
(referred to as the surface temperature) and the effective heat trans
fer temperature are the same, or related in some predictable way. In a
vegetation canopy, many small areas at different levels in the canopy
contribute toward a radiation surface temperature measured from above.
These represent only a small fraction of the total plant surfaces. All
surfaces, including those not seen by a radiation sensor, contribute
sensible heat to the air. These contributions depend on how well venti
lated the canopy is at various levels.
Since radiation and sensible heat transfer are completely differ
ent and a vegetation surface is so complex, the radiation surface tem
perature and the effective heat transfer surface temperature may be dif
ferent. The only way to compare these two temperatures is to infer


Figure 12. (cont.)
PO
O


ET (LY/min)
Figure 9. (cont.)


162
Day
Time
Net
Soi 1
. Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
150
800
0.37
0.03
0.08
0.26
0.58
25.7
32.3
34.6
.947
830
0.44
0.04
0.09
0.31
0.68
27.1
34.6
35.0
.966
900
0.54
0.05
0.09
0.39
0.72
28.7
36.1
33.6
.968
930
0.63
0.06

--
0.42
29.8
37.4
30.4
.889
1000
0.70
0.07
0.11
0.52
0.53
30.6
38.5
28.1
.940
1030
0.77
0.08
0.14
0.55
0.97
31.4
39.5
28.4
.967
1100
0.68
0.08
0.13
0.47
1.20
31.3
38.7
27.4
.989
1130
0.80
0.10
0.15
0.64
1.88
32.3
40.6
27.2
.988
1200
0.90
0.12
0.15
0.63
1.04
32.7
41.4
25.7
.989
1230
0.87
0.12
0.15
0.60
1.87
33.3
40.9
24.8
.941
1300
0.85
0.12
0.16
0.57
1.23
33.3
41.1
24.3
.978
1330
0.84
0.12
0.15
0.56
1.44
34.1
41.1
24.0
.957
1400
0.71
0.10
0.13
0.48
1.71
33.8
39.4
25.1
.979
1430
0.69
0.09
0.12
0.48
2.01
33.8
39.0
25.1
.986
1500
0.26
0.05
-
--
1.42
33.2
33.7
24.4
.691
1530
0.32
0.06

--
1.31
33.5
34.4
25.1
.719
1600
0.39
0.06

0.79
33.8
35.1
25.0
.212
1630
0.28
0.04


2.26
33.8
33.7
26.0
.739
1700
0.18
0.03

--
1.71
33.3
32.3
26.3
-.383
1730
0.10
0.03
--
1.37
33.1
30.7 -
26.3 -
-.837
1800
0.03
0.02
-0.00
0.02.
0.91
32.3
28.3
27.5
-.992
151
730
0.27
0.03
_
1.25
25.1
28.6
36.0
.796
800
0.36
0.03


1.01
26.5
31.7
35.8
.908
830
0.46
0.04
0.10
0.32
1.35
27.9
34.0
36.1
.936
900
0.56
0.05
0.11
0.39
1.55
29.0
35.7
36.5
.970
930
0.64
0.07
0.12
0.45
1.68
29.9
36.9
35.3
.982
1000
0.71
0.08
0.14
0.50
1.45
30.9
38.4
35.2
.962
1030
0.77
0.09
0.14
0.53
1.40
31.9
39.7
34.2
.959
1100
0.78
0.09
0.18
0.51
1.39
32.4
40.0
33.9
.967
1130
0.82
0.10
0.19
0.52
1.70
33.2
40.5
32.7
.966
1200
0.67
0.11
0.15
0.42
1.55
33.2
39.4
33.1
.971
1230
0.59
0.08
0.13
0.38
2.10
33.1
37.5
34.0
.943
1300
0.61
0.09
0.11
0.41
2.35
33.5
38.2
33.2
.962
1330
0.49
0.07
0.09
0.32
2.46
33.5
36.4
31.4
.953
1400
0.45
0.07
0.07
0.31
2.03
33.7
36.0
31.0
.900
1430
0.37
0.06
0.08
0.24
2.27
33.5
35.3
32.2
.912
1500
0.49
0.06

--
1.74
33.9
36.4
32.8
.842
1530
0.56
0.08
0.15
0.34
2.89
34.5
37.4
33.7
.949
1600
0.45
0.07
0.13
0.26
2.37
34.4
36.1
33.9
.943
1630
0.28
0.04
0.07
0.16
2.81
33.8
34.1
34.2
.940
1700
0.15
0.03
--
--
2.27
33.2
32.5
34.1
.574
1730
0.11
0.03

--
2.24
32.9
31.6
32.4
.602
1800
0.03
0.01
--
--
2.91
31.9
29.4
28.5
-.925


32
TERGR model was designed for grasslands, making this more detailed ap
proach feasible.) It uses pseudo-empirical expressions for soil water
transport resistance and stomatal resistance, and requires a reference
soil moisture pressure as well as a soil temperature as a boundary con
dition.
Use of the TERGRA model in obtaining cumulative ET estimates is
explained in Soer (1980). The procedure requires data on the boundary
conditions and radiation falling on the surface for the duration of the
simulation periods, and values of various parameters like soil hydraulic
conductivity and surface roughness. First, windspeed, roughness height,
air temperature, and remotely measured surface temperature are used to
compute the instantaneous ET rate for the time at which satellite data
are available. This is done with the simple residual method (see previ
ous subsection), which requires no. knowledge of surface moisture. Then
the TERGRA model is run with various soil moisture pressures to match
the ET rate at the time of the satellite overflight. The modelled cumu
lative daily ET rates are then assigned to areas with matching instanta
neous ET rates at the time of the overflight.
The Rosema et aQ_. (1978) model (named TELL-US) is also constructed
around the surface energy budget, and similarly computes latent, sensi
ble, and soil fluxes based on measured gradients and calculated trans
port properties. It is more detailed in describing the surface; surface
slope and slope direction must be specified. Its parameters are soil
thermal inertia and surface relative humidity.
Given the daily course of boundary conditions and incident radia
tion, the model is used to compute daily maximum and minimum tempera-
tures and cumulative daily evapotranspiration for various combinations


40
using temperature data as the ordinate and vapor pressure as the ab
scissa (see Fig. 3-1). In calculating the Bowen ratio, the specific heat
of the air, the atmospheric pressure, and the ratio of molecular weights
was considered constant; the latent heat of vaporization was a function
of the average air temperature.
Sensor and Time Constant Considerations
Although simple in principle, a great deal of care is required in
choosing sensors and collecting data for the calculation of the Bowen
ratio. Temperature and vapor pressure vary randomly from instant-to-in-
stant and level-to-level in the turbulent boundary layer, and the total
temperature and dewpoint differences across the air layer to be measured
are only 1 or 2C. In order to calculate the relative strengths of the
gradients, very precise measurements at several levels are required.
Sensors were chosen to eliminate, as much as possible, the error
introduced by sensor-to-sensor variability. This was avoided entirely in
the case of the vapor pressure profile; the same dewpoint analyzer was
used to measure the dewpoint at each level by use of a gas sampling ar
rangement. In the case of the temperature profile, the effect of thermo-
couple-to-thermocouple differences was minimized by measuring tempera
ture differences with thermopiles. Twenty-junction copper constantan
thermopiles, arranged with 10 junctions at each level, were used to mea
sure temperature differences between levels. The temperature at the low
est level was measured with a thermocouple using an Omega Engineering
MCJ-T electronic icepoint reference. Temperatures at the other levels
were obtained by adding the appropriate thermopile-measured temperature
differences to the one reference temperature measurement.


63
Also, in application, temperature differences are used to evaluate tem
perature gradients. For that reason, differences are used in the equa
tions developed and are referred to interchangeably as differences and
gradients.
Temperature Gradient Model
The simplified energy balance of a vegetated surface was developed
in Chapter 2:
R = E + H + G 4-1
The purpose of this section is to express the components of the surface
energy budget as much as possible in terms of net radiation and surface
temperature, so that a useful relationship between the two can be de
rived.
Because of heat storage in the surface air layer, surface tempera
tures lag net radiation. This lag is complicated by the fact that the
passage of clouds usually makes the net radiation absorbed by the system
vary randomly. For this reason, a method containing time as a variable
has been avoided. This was done by modeling the response of surface-to-
air temperature gradients to changes in net radiation.
In describing heat flux using a surface temperature (i.e., between
the surface and some plane above the surface), at least two layers with
different transport properties must be considered (see Fig. 4-1). The
first is the surface layer, in which molecular diffusion is the primary
transport mechanism. It is the thin layer of air immediately next to the
plant surfaces, represented by the layer between z$ and Zq in the dia
gram. The second is the fully turbulent layer between zn and z where
turbulent eddies are the primary transport mechanism. Following the de
velopment shown in Chapter 2, the heat flux between the surface (at


EVAPOTRANSPIRATION: AN AUTOMATIC MEASUREMENT SYSTEM
AND A REMOTE-SENSING METHOD FOR
REGIONAL ESTIMATES
BY
KLAUS HEIMBURG
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1982


CHAPTER 6
CONCLUSIONS
Summary of Results
The Average Temperature Gradient Response Method
The challenge in developing a general ET estimation method for use
with satellite data is to find the method that delivers the most accept
ably accurate ET estimate for the least in data collection and data pro
cessing costs. The average temperature gradient response (ATGR) method,
the primary result of this research, is directed at these practical con
siderations.
The ATGR method is based on a steady-state model of the surface
developed to describe the relationship of temperature gradients and net
radiation over a surface. This model,
1
T- Ta = hTHT+TT WfR Mhse.) ,
4-25
s a rums + y) a
characterizes the surface with parameters for heat transport through the
near-surface air layer (h), surface moisture availability (M), the tem
perature dependent slope of the saturation vapor pressure curve (s), the
fraction of net radiation available to be converted into latent or sen
sible heat (f), and the saturation deficit (6eJ. By considering the
a
parameters (and the psychrometric constant, y) stationary over some time
period, the average temperature gradient/net radiation correlation
T T = AR B
5 a
4-27
can be used to obtain a composite measurement of the average parameters:
123


U (M/S)
Figure 7. Variation of the Daily Average Heat Transport Coefficient with the Daily
Average Windspeed.


78
temperature measurements. Air temperatures are determined by the mixing
of air from higher in the atmosphere with near-surface air that has been
warmed (or cooled) by the surface. Therefore, one would expect air tem
peratures, particularly those near the surface, to be primarily a func
tion of the surface temperature. There is precedent for this approach.
In an effort to meet the boundary condition requirements of numerical
weather models, mesoscale climate modelers have begun developing "tem
perature response functions" (Idso, 1982).
There are practical reasons for this approach as well. A network of
ground stations to supply this measurement would be very expensive, and
calibrating the ground-based sensors against a satellite sensor is in
herently difficult. In addition to requiring knowledge of the atmo
sphere's transmission properties, temperature measurements made by a
contact sensor (e.g., a thermocouple or thermistor) must be matched to
measurements made by a thermal radiation sensor. Since temperature dif
ferences are required, a system based completely on remotely measured
surface temperatures would not be as sensitive to such absolute error
sources.
There are several ways in which air temperature measurements might
be generated. The simplest way is to choose a vegetation surface like
forest, whose surface temperature is closer to air temperature because
of the large fraction of surface elements visible to a satellite in
shade. The surface temperature of some reference pixel could then be
used as the air temperature for all pixels. In effect, the reference
pixel would never see a temperature gradient; its evapotranspiration
would exactly equal its available net energy (fR) since there could be
no sensible heat flux.


70
conductivity can be considered constant, this pair of equations can be
solved for the two unknowns M and h,
'k k
RAAe, RiAe^,
h = 4-17
se^AT2 6e2AT1
yCRoAT, + R'iATp)
M = ~~ ^r- 4-18
R^Aeg + R^Ae-|
where R:j = (R 6)^ 4-19
AT, = (T TJ, and 4-20
1 b Q 1
4ei s i = $ATi + 5ea. 4-21
Equations 4-17 and 4-18 can be substituted into Eq. 4-14 to yield:
~ RaTj RJAT2~
-
* V
R^Ae-j ^lAe2
R =
Rj6e2 R^Aej
s(R G) + 6e
a
6e^AT2 6e2AT^
, j
Now any evapotranspiration rate between the two measured radiation re
gimes can be calculated by substituting intermediate values of R, G, and
be near enough in time such that the constant M and h assumption is
valid, but far enough apart in radiation load so that reasonably accu
rate calculation of the parameters is possible.
Average Temperature Gradient Response Method
System Stationarity and Average Temperature Gradient Response
The most restrictive problem faced in estimating ET from above the
atmosphere is that very often clouds make surface temperatures unobserv
able. As shown in Eqs. 4-17 and 4-18, surface temperatures are necessary
to estimate surface moisture availability and bulk air conductivity.
This fact requires that remote ET estimates be made in two stages. The
first stage consists of using clear sky net radiation and surface


130
except in areas where the surface moisture in parts of the same pixel
are radically different, as in irrigated fields surrounded by very dry
areas.
Besides building the method one step at a time for more complex
estimating problems, the remote ET estimation problem might also be ap
proached by applying the ATGR method as is. The ATGR method's ET esti
mates for research watersheds can be compared to ET estimates made by
other methods. It would also be productive to examine the stationarity
and distribution of the temperature/net radiation correlation coeffi
cients, A and B. An idea of the behavior of these coefficients and the
problems associated with their calculation would help in developing op
erational data processing methods. If A and B can be legitimately con
strained to reasonable values, use of the more numerically sensitive
equations for ET might prove feasible.
Clearly there are many potential problem areas that remain to be
investigated before the general applicability of the ATGR method is
proven. The ATGR method is reasonably simple and theoretically sound,
and in this study is shown to work for a simple pasture surface. The
number of parameters needed to describe a vegetated surface has been
reduced to a minimum, and the temperature gradient model correctly de
scribes their interrelationship and relationship to remotely sensed
data. On that basis, the method can definitely be used as a framework
for further research toward a practical regional ET estimation method.


171
Day
Time
Net
Soil
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
295
700
0.02
-0.00
....
0.50
17.7
16.9
_ _
.893
730
0.08
0.00


1.19
18.8
19.7

-.016
800
0.17
0.01

--
2.03
20.3
21.4
--
-.469
830
0.17
0.01


1.54
21.7
22.5
--
-.684
900
0.16
0.01


1.45
22.8
23.6

.226
930
0.28
0.02
0.07
0.19
1.87
24.2
26.5
22.8
.984
1000
0.46
0.03
0.17
0.27
2.37
25.8
30.6
22.3
.992
1030
0.55
0.03
0.25
0.28
3.24
26.8
33.4
21.2
.997
1100
0.51
0.03
0.23
0.25
2.65
27.1
34.3
20.8
.998
1130
0.23
0.02
0.07
0.14
2.13
26.7
29.7
20.4
.991
1200
0.74
0.04
0.31
0.38
2.79
28.0
38.3
20.2
.997
1230
0.67
0.04
0.29
0.34
3.17
28.4
38.6
20.3
.998
1300
0.71
0.04
0.30
0.36
3.63
28.7
38.9
19.8
.997
1330
0.65
0.04
0.26
0.35
3.00
29.1
38.4
19.1
.996
1400
0.57
0.04
0.23
0.30
3.50
29.0
36.6
19.4
.996
1430
0.54
0.03
0.22
0.29
3.38
29.2
36.4
19.4
.995
1500
0.45
0.03
0.18
0.24
4.08
29.1
34.8
18.7
.993
1530
0.33
0.02
0.13
0.18
3.89
28.9
32.7
18.1
.993
1600
0.23
0.02
0.06
0.14
3.51
28.7 '
31.0
18.1
.978
1630
0.11
0.02
0.02
0.08
4.01
27.9'
28.6-
17.9
.913
1700
0.02
0.01
-0.00
0.00
3.00
27.2
26.4
17.9
-.969
296
700
0.01
-0.02
...
- -
0.00
14.1
13.1
~
.890
730
0.05
-0.01

--
0.00
15.1
15.2
--
-.034
800
0.13
0.00
--

0.51
17.5
18.3

-.691
830
0.24
0.01


0.26
19.4
21.6

-.844
900
0.34
0.02


0.26
21.2
25.3
-.946
930
0.43
0.03


0.83
23.9
29.3
...
-.610
1000
0.51
0.03
0.22
0.26
1.28
25.7
32.0
21.7
.953
1030
0.56
0.04
0.24
0.29
1.07
26.9
34.8
20.6
.994
1100
0.63
0.04
0.26
0.32
1.06
27.8
36.4
20.2
.990
1130
0.48
0.04
0.18
0.27
0.87
28.3
35.4
19.4
.993
1200
0.65
0.04
0.23
0.38
1.31
28.9
38.2
18.7
.994
1230
0.75
0.05
0.28
0.42
0.84
29.5
40.7
18.2
.996
1300
0.55
0.04
0.19
0.32
2.27
29.6
37.8
17.0
.996
1330
0.72
0.05
0.27
0.40
1.95
30.4
40.7
16.9
.998
1400
0.62
0.04
0.22
0.35
2.61
30.6
39.5
16.9
.997
1430
0.30
0.03
0.07
0.20
1.11
29.5
34.0
17.6
.991
1500
0.21
0.03
0.03
0.15
1.17
29.0
31.8
17.4
.976
1530
0.17
0.03
0.01
0.13
1.27
29.1
31.1
17.5
.947
1600
0.19
0.03
0.02
0.15
1.39
29.1
31.1
18.1
.924
1630
0.06
0.02
-0.01
0.04
1.42
28.5
28.4
18.0
-.979
1700
0.00
0.01
-0.01
0.02
0.15
27.4
16.1
19.4
-.998


Figure 5-10. Effect of Moisture Availability and Vapor Pressure
Parameters on Temperature Gradients 106
Figure 5-11. Effect of Heat Transport Coefficient and Soil Heat
Flux Parameter on Temperature Gradients 107
Figure 5-12. Temperature Gradient Response of a Clear Day with
Constant Moisture Availability 110
Figure 5-13. Temperature Gradient Response of a Partly Cloudy
Day Ill
Figure 5-14. Generalized Clear Day H/E and E/R Patterns 113
Figure 5-15. Comparison of Measured and Estimated Bowen Ratios . 115
Figure 5-16. Cumulative ET Estimates by the ATGR and Residual
Methods 122
Appendix D: Supplementary Figures
Figure 1. Hypothetical Daytime Temperature Profile ...... 179
Figure 2. Simplified Temperature Profile 179
Figure 3. Simplified Temperature Profi1es .for a Clear Day . 180
Figure 4. Simplified Temperature Profiles for an Overcast Day 181
Figure 5. Air Transport Coefficient for Average Conditions . 182
Figure 6. Soil Heat Flux Parameter for Average Conditions . 183
Figure 7. Variation of the Daily Average Heat Transport
Coefficient with the Daily Average Windspeed .... 184
Figure 8. Data and ET Estimates for Oct. 17, 1981 186
Figure 9. Data and ET Estimates for Oct. 18, 1981 191
Figure 10. Data and ET Estimates for Oct. 21, 1981 196
Figure 11. Data and ET Estimates for Oct. 22, 1981 201
Figure 12. Data and ET Estimates for Oct. 23, 1981 206
vi i i


175
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
307
1530
0.09
0.01
0.03
0.06
2.62
24.1
25.5
19.8
.991
1600
0.06
-0.00
0.02
0.04
3.04
23.4
24.2
18.3
.988
1630
0.03
-0.00
0.00
0.03
2.00
23.2
23.7
18.4
.954
1700
0.02
-0.00
-0.00
0.02
2.64
23.1
23.2
18.6
-1.022
308
730
0.01
-0.00
1.92
19.8
20.0
22.5
-.359
800
0.06
-0.00


2.34
20.0
20.7
22.9
.846
830
0.14
0.00
0.04
0.10
3.19
20.4
21.6
23.1
.999
900
0.28
0.01
0.07
0.20
2.58
21.4
23.6
23.6
.996
930
0.43
0.02
0.13
0.28
2.96
22.8
25.9
24.1
.997
1000
0.40
0.02
0.13
0.25
2.45
23.6
26.8
24.1
.989
1030
0.57
0.02
0.19
0.35
3.69
25.5
29.7
23.4
.992
1100
0.55
0.02
0.21
0.32
4.37
25.6
29.3
22.0
.996
1130
0.51
0.02
0.21
0.29
3.70
26.0
30.0
21.8
.996
1200
0.44
0.02
0.16
0.26
3.15
26.2
30.0
21.4
.996
1230
0.46
0.02
0.17
0.27
3.01
26.6
31.4
20.9
.993
1300
0.31
0.02
0.11
0.19
3.40
26.4
29.0
20.3
.994
1330
0.34
0.02
0.12
0.20
2.73
26.7
29.9
20.9
.996
1400
0.28
0.02
0.11
0.15
3.68
26.3 '
29.3
21.9
.998
1430
0.22
0.01
0.09
0.12
3.57
25.8
28.4
22.5
.994
. 1500
0.11
0.01
0.04
0.06
4.30
24.8
26.3
22.7
.985
1530
0.10
0.01
0.04
0.05
4.22
24.1
25.6
23.4
.992
1600
0.05
0.00
0.02
0.03
3.61
23.5
24.8
23.7
.967
1630
0.03
0.00
0.01
0.02
3.88
22.8
23.7
23.5
1.000
309
800
0.03
-0.00
0.01
0.02
2.67
20.3
20.7
23.2
1.039
830
0.02
-0.00
0.01
0.02
2.51
20.6
21.0
23.6
1.024
900
0.03
-0.00
0.01
0.03
2.16
20.8
21.2
23.7
.940
930
0.05
-0.00
0.01
0.03
2.61
20.9
21.3
23.9
.983
1000
0.05
0.00
0.01
0.04
2.62
21.1
21.5
24.2
.993
1030
0.02
-0.00
0.00
0.01
2.96
21.1
21.2
24.0
.860
1100
0.02
-0.00
0.00
0.02
2.50
20.8
20.9
23.6
.870
1130
0.01
-0.00


2.36
20.7
20.7
23.5
.594
1200
0.02
-0.00
0.00
0.02
2.16
20.8
20.8
23.5
.957
1230
0.03
-0.00
0.01
0.03
2.63
20.8
20.9
23.6
.900
1300
0.02
-0.00
0.00
0.02
3.29
20.9
21.1
23.9
1.010
1330
0.03
-0.00
0.01
0.03
3.57
21.0
21.1
23.9
.926
1400
0.02
-0.00
0.00
0.02
2.70
20.9
21.2
23.8
.899
1430
0.02
-0.00
0.00
0.02
3.63
20.8
21.0
23.7
1.161
1500
0.07
-0.00
0.02
0.05
3.62
20.7
21.2
23.5
.995
1530
0.07
-0.00
0.01
0.06
4.06
20.5
21.1
23.3
.985
1600
0.05
-0.00
0.01
0.04
3.31
20.3
20.9
22.8
1.013
1630
0.10
-0.00
0.02
0.08
2.95
20.5
21.2
22.9
1.003
1700
0.03
-0.00
0.01
0.03
3.11
20.3
20.7
22.7
.979


BIOGRAPHICAL SKETCH
Klaus Heimburg was born in El Paso, Texas, in 1949, and grew up
in Huntsville, Alabama. He received a Bachelor of Science degree in
physics from Southwestern at Memphis in 1971. After a few years work
ing at a variety of jobs, he returned to school to continue his edu
cation. He completed an M.S. degree (1976) and a Ph.D. degree (1982)
in environmental engineering sciences at the University of Florida.
211


Figure 8. (cont.)
<£>
o


129
method. The level of detail of other parts of the method does not need
to be greater than can be justified by this potential accuracy.
There are also a number of questions directly related to the ATGR
method which need to be addressed. The surface-to-air temperature gradi
ent/net radiation correlation needs to be observed over other surfaces
to determine whether the ATGR method can be applied in the same way. For
a more complex vegetation canopy, the influence of the sun to surface to
remote sensor radiation geometry needs to be investigated. If the radia
tion temperature of complex surfaces like swamp or mountains is signifi
cantly different than the effective heat transfer surface temperature, a
correcting technique will need to be developed for surface temperature
measurements.
Further research is required to determine a general method of esti
mating the bulk heat transport coefficient. The primary question to be
investigated is whether complication of obtaining average surface rough
ness and windspeed data is justified with the accuracy levels antici
pated in the raw data, or whether an "average conditions" value is ade
quate.
Making the ATGR method depend as much as possible on remote data is
another area that needs investigation. How to obtain surface-to-air tem
perature gradients from surface temperatures alone is the most impor
tant area, but the possibility of estimating the other parameters from
remote data should also be investigated.
Eventually a study must be made to determine the magnitude of er
rors introduced when average net radiation and surface temperature val
ues from nonhomogeneous pixels are used to compute ET. From the
equations it would appear that this would not be too great a problem


I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
^ 'J'j'L i'i'$L?\
W/C/ Tiubr
Professgr, Environmental Engineering
Sciences
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
L.H. Allen, Or.
Associate Professor, Agronomy
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
H.T. Odum
Graduate Research Professor,
Environmental Engineering Sciences
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
R.W. ^waii
Professor, Industrial and Systems
Engineering


18
Usually the smallest component is photosynthetic heat flux. It can
be considered negligible because only 1 to 5% of the net radiation im
pinging on vegetation is absorbed in this way (Allen _et al_., 1964).
It can be shown by a "worst case" calculation that the storage term
is also in the negligible range. Heat in the vegetation/air layer can be
stored as sensible heat in the air, latent heat in the air, sensible
heat in the biomass, and sensible heat in the litter surface layer. In a
strict sense, these are evaluated as follows:
S =
c (z)
a
STa(z)
3 t
dz +
1 ca 3ea(z)
0
y 31
dz +
3 T h (z)
cj!) i! +
rd 3T (z)
C (z) ^
0 9
2-2
where c (z), c,(z), and c (z) are volumetric heat capacities ( c) of
a o g
canopy air, plant biomass, and surface soil, respectively,
T (z), T, (z) and T (z) are the temperatures of canopy air,
a d g
canopy biomass, and surface soil, respectively,
e (z) is the vapor pressure of canopy air,
a
Y is the psychrometric constant,
1 is the vegetation height,
d is the depth of the surface litter layer, and
z is the vertical space coordinate.
Using averages for the spatial variables, Eq. 2-2 can be rewritten:
S = (Pcp}a h
ATa (pCn Aea
£ + ELi h
At Y At
(Vc)
^b
b At
AT,
(pc) d Z9-
At
2-3
where a, b, and g are subscripts referring to air, biomass, and soil
specific heats, densities, and temperatures, and
V is the mass of vegetation per unit area.


95
Clearly none of the parameters are constant. However, the strict
and average temperature gradient response methods have different de
grees of sensitivity to the variations in parameters, and must be
judged accordingly.
Strict Temperature Gradient Response Method
An example calculation of bulk air conductivity and moisture
availability according to the strict TGR method equations (Eqs. 4-17
and 4-18) is presented in the first column of Table 5-1. Measured val
ues of these parameters are listed in the third column of the table.
The example calculation shows poor agreement with measured values,
particularly before noon, when Eqs. 4-17 and 4-18 produce negative val
ues. Apparently, this is due to the numerical sensitivity of the equa
tions. This sensitivity is most apparent while dew is evaporating. Rela
tive changes in temperature and vapor pressure are large enough while
moisture availability is changing rapidly to produce physically nonmean
ingful negative bulk conductivities and moisture availabilities. How
ever, even in the afternoon, when h and M are relatively much .more sta
ble, the values obtained by the strict TGR equations match independent
measurements of h and M in order of magnitude at best.
The poor match is partially due to the equation's susceptibility
to round-off error. This can be demonstrated by calculating temperature
gradients assuming constant values of h and M. Using vapor pressure def
icit, air temperature, net radiation, and soil heat flux measurements
and assuming a value of .035 ly/minC for h and 0.12 for M, temperature
gradients were calculated with the temperature gradient equation (Eq.
4-11). These simulated gradients and raw data were then used in the '
strict TGR equations to calculate h and M. Results of the calculations


n
Organization of Dissertation
Basic concepts underlying current understanding of the evapotran-
spiration process are reviewed in Chapter 2. These concepts are funda
mental to both the evapotranspiration measurement and method develop
ment portions of the study. Chapter 3 describes the computer-based evap
otranspiration measurement system that was developed to collect a base
of accurate ET data. This chapter contains the theory of the meas
urement technique, considerations made in designing the profile sensing
systems, brief descriptions of the programs that operate the system, and
an assessment of the strengths and weaknesses of the measurement sys
tem. Two methods of calculating ET based on remotely sensed data are
derived in Chapter 4, one relatively rigorous with a minimum of added
assumptions, and a grosser less detailed one with extensive approxima
tions. Both methods are based on a temperature gradient model which uses
net radiation and surface temperature data to determine surface parame
ters. The performance of this model and these methods is compared to
actual ET measurements in Chapter 5. The method most suitable for use
with satellite data is tested component by component to clearly evaluate
its strengths and weaknesses. A summary of conclusions and suggestions
for further research are contained in Chapter 6.
Repeatedly used symbols are defined in Appendix A. (All symbols are
defined in the text where they are introduced.) Appendix B is a listing
of the programs developed for the automatic ET measurement system, along
with definitions of names for subroutines, functions, data arrays, and
indexes. Appendix C is a summary listing of the data collected, and sup
plementary figures are presented in Appendix D.


100
Figure 5-8. Graphical Interpretation of Temperature Gradient/Net
Radiation Correlation. The temperature gradient data
from Fig. 5-7 (October 17, 1981) were multiplied by
.035 cal/cm2secC to produce this graph of sensible
heat flux vs. net radiation. The soil heat flux
parameter is .93.


Z-D (cm) Z-D (cm)
Figure 4. Simplified Temperature Profiles for an Overcast Day. These gradients were
measured on October 30, 1981. Note the difference in temperature scale when
comparing to Figure 3. The rapid afternoon cooling was caused by intermittent
drizzle.


132
Chang, J. 1968. Climate-and Agriculture. Aldine Publishing Co.,
Chicago, IL. 303 pp.
Desjardins, R.L., L.H. Allen, Jr. and E.R. Lemon. 1978. Variations of
carbon dioxide, air temperature, and horizontal wind within and
above a maize crop. Boundary-Layer Met. 14:369-380
Doorenbos, J. and W.D. Pruitt. 1977. Guidelines for predicting crop
water requirements. Food and Agriculture Organization of the
United Nations, Irrigation and Drainage Paper No. 24. 144 pp.
Dyer, A.J. 1967. The turbulent transport of heat and water vapor in an
unstable atmosphere. Quart. J. Roy. Met. Soc. 93:501-508.
Dyer, A.J. and B.B. Hicks. 1970. Flux-gradient relationships in the
constant flux layer. Quart. J. Roy. Met. Soc. 96:715-721.
Eagleson, P.S. 1970. Dynamic Hydrology. McGraw-Hill Book Co., New York,
NY. 462 pp.
EG&G International, Inc. 1977. The Dew Point Hygrometer Model 880 In
struction Manual TM 71-174. Waltham, MA.
Garratt, J.R. and B.B. Hicks. 1973. Momentum, heat and water vapor
transfer to and from natural and artificial surfaces. Quart. J.
Roy. Met. Soc. 99:680-687.
Goddard Space Flight Center. 1980. Heat Capacity Mapping Mission (HCMM)
Data User's Handbook for Applications Explorer Mission-A (AEM).
National Aeronautics and Space Administration (NASA), Greenbelt,
MD. 120 pp.
Goudriaan, J. and Waggoner, P.E. 1972. Simulating both aerial micro
climate and soil temperature from observations above the foliar
canopy. Neth. J. Agrie. Sci. 20:104-124.
Idso, S.B. 1982. A surface air temperature response function for
earth's atmosphere. Boundary-Layer Met. 22:227-232.
Jackson, R.D., S.B. Idso, R.J. Reginato and P.J. Pinter, Jr. 1980.
Remotely sensed crop temperatures and reflectances as inputs to
irrigation scheduling. Proc. Spec. Conf. on Irrig. and Drain.
ASCE, Boise, Idaho, July 23-25, 1980.
Jarvis, P.G. 1971. The estimation of resistances to carbon dioxide
transfer. _In Plant Photosynthetic Production, Sestak, Z.,
J. Catsky, and Jarvis, P.G., eds, Dr. W. Junk N.V., The Hague,
Netherlands. 818 pp.
Kendall, M.G. 1968. A course in multivariate analysis. In Statistical-
Monographs and Courses. Charles Griffin & Co. LTD, London, UK.


55
concerned with formating and printing the summary report. An example
report is shown in Fig. 3-6, and Table 3-3 lists the variable names
used.
Program ANALZ makes ancillary calculations and produces the last
five lines of the half-hourly report. It has a search routine which com
putes the displacement height of the temperature and vapor pressure pro
files. With an assumed value of the roughness parameter (Zq) and trial
values of the displacement height (D), it computes the correlation of
temperature or vapor pressure and height over the surface with
rz D + z/
T, e = B In
O
'0
+ A
3-9
The assumed roughness height, the displacement height producing the best
correlation, and other profile parameters are printed out.
ANALZ also computes a variety of other quantities which may be of
use in data analysis or operation of the system. Among these are atmo
spheric and stomata! resistances, albedo, optical air mass and atmo
spheric transmission coefficient, zenith and hour angle of the sun, and
the equation of time.
The fourth program, SET, is the executive program. It is used to
properly start the acquisition of data and determine whether and when
the other programs should be run. In a "cold" start, SET positions the
scanning valve, initializes counters and statistics, and schedules MEASR
to start so that profile collection is completed at specified times. On
occasions other than a "cold" start, it determines whether the other
programs should be run, depending on flags in MEASR or operator input
via switches on the face of the HP-2100. Its most valuable function is
to schedule MEASR to begin at an absolute clock time at the beginning of


160
Day
Time
Net
Soi 1
. Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
143
1100
0.66
0.07
0.26
0.32
2.79
25.7
38.3
20.9
.985
1130
0.65
0.08
0.26
0.32
2.47
26.0
38.7
20.7
.977
1200
0.59
0.08
0.18
0.33
2.16
26.4
38.5
20.6
.992
1230
0.82
0.11
0.28
0.44
2.41
27.2
41.8
19.9
.983
1300
0.90
0.13
0.25
0.52
1.80
28.3
43.7
18.7
.946
1330
0.92
0.14
0.30
0.48
1.95
28.8
44.3
19.6
.990
1400
0.65
0.11
0.25
0.29
2.62
28.9
40.8
19.0
.962
1430
0.43
0.06
0.15
0.22
2.91
28.4
36.6
18.8
.934
1500
0.87
0.11
0.34
0.43
2.42
29.6
43.4
18.3
.967
1530
0.77
0.11
0.29
0.38
2.51
30.1
42.7
17.5
.980
1600
0.39
0.07
0.12
0.21
2.19
29.4
37.8
16.2
.991
1630
0.21
0.04
0.05
0.13
1.65
29.0
34.1
16.9
.916
1700
0.26
0.04


1.42
29.1
33.9
17.9
.680
1730
0.29
0.05


2.11
29.5
34.8
18.6
.899
1800
0.20
0.03
.

0.77
29.2
32.9
18.7
.669
1830
0.10
0.02


0.79
28.4
29.7
19.3
.307
1900
0.06
0.02


0.66
27.9
27.9
20.5
-.939
145
800
0.31
0.03
0.10
0.18
3.13
25.1
28.1
28.3
.989
830
0.36
0.03
0.12
0.21
3.85
25.7
31.8-
27.3
.967
900
0.50
0.05
0.16
0.30
3.67
26.5
35.6
26.9
.980
930
0.62
0.06
0.21
0.35
3.42
27.4
37.6
24.8
.982
1000
0.64
0.07
0.21
0.37
3.19
28.1
38.9
25.5
.977
1030
0.77
0.09
0.21
0.47
2.68
29.2
41.7
25.6
.995
1100
0.62
0.10
0.16
0.36
2.33
29.6
40.2
26.1
.975
1130
0.83
0.10
0.21
0.52
2.84
30.1
42.4
24.1
.975
1200
0.92
0.13
0.27
0.52
2.98
30.8
44.3
22.9
.991
1230
0.61
0.11
0.17
0.33
3.15
30.8
40.6
22.7
.984
1300
0.84
0.12
0.27
0.46
3.41
31.3
42.9
22.8
.970
1330
0.85
0.12
0.26
0.47
2.36
31.7
43.6
22.8
.975
1400
0.50
0.08
0.14
0.29
2.23
31.2
39.1
22.0
.960
1430
0.62
0.09
0.19
0.33
3.02
31.6
40.6
22.8
.981
1500
0.42
0.05
0.10
0.26
3.59
30.8
36.8
23.8
.987
1530
0.32
0.05
0.07
0.21
3.02
31.0
35.3
23.9
.975
1600
0.40
0.05
0.10
0.25
3.34
31.9
36.8
22.9
.953
1630
0.26
0.03
0.10
0.15
3.59
31.6
34.5
22.4
.940
1700
0.20
0.03


3.56
31.4
33.1
22.1
.785
147
830
0.53
0.03
0.09
0.40
2.78
25.3
28.1
36.4
.949
900
0.58
0.04
0.11
0.44
3.12
26.2
30.1
37.2
.968
930
0.60
0.04
0.11
0.44
3.25
27.1
32.1
37.2
.987
1000
0.66
0.05
0.13
0.48
3.26
28.3
34.2
37.7
.991
1030
0.71
0.05
0.14
0.52
4.48
28.8
34.8
37.9
.997
1100
0.53
0.06
0.13
0.34
4.05
27.9
34.8
38.3
.942
1130
0.44
0.08


4.70
24.2
37.0
37.8
.913
1200
0.32
0.07
--
4.99
25.8
36.2
36.3
.819


80
These assumptions are typical in the evapotranspiration literature.
However, they amount to assuming a uniform surface with adequate fetch
and close to steady-state heat transfer. Realistically, the system is
always transient and there is some energy storage in both the surface
and air layer. Remotely sensed surface information in general does not
come from flat homogeneous surfaces.
Both the strict and totally remote temperature gradient response
methods are dependent on some degree of system stationarity. The former
assumes that only moisture availability and bulk air conductivity are
constant between data sets. It requires surface and air temperature, net
radiation, soil heat flux, and saturation deficit measurements.
To lessen the data requirements, these assumptions are extended and
a new parameter is introduced in the totally remote method. Moisture
availability, bulk air conductivity, and air saturation deficit are con
sidered constant for a day or more, and soil heat flux is treated as a
constant fraction of net radiation. The surface is assumed to be a sta
tionary system with four unknown parameters (M, h, e and f), and one
a
known parameter (s), the slope of the saturation vapor pressure curve.
To make up for data that cannot be collected, it is assumed that two of
the unknown parameters can be estimated from some prior knowledge of the
surface; the other two can be determined from the temperature gradient
response to various radiation loads. Once the parameters are determined,
evapotranspiration for any net radiation load is calculable.
Several elements of these methods were considered beyond the scope
of this study, but assumed possible. It is taken for granted that rea
sonably accurate remote measurements of surface temperature and net ra
diation can be made, further, that estimates of surface net radiation


69
Strict Temperature Gradient Response Method
From Eq. 4-11, one recognizes that
4-12
Substituting into the energy budget equation (Eq. 4-1),
E = R G -flsVr [y(R G) hMfea]
4-13
4-14
This is a version of the combination equation for evapotranspiration
(Penman, 1948). When the surface is saturated (M = 1), this equation
reduces to the potential evapotranspiration equation of Tanner and
Fuchs (1968).
The slope of the saturation vapor pressure curve (s) is a known
function of temperature, and the psychrometric constant is a known func
tion of atmospheric pressure. Net radiation (R), soil heat flux (G), and
saturation deficit (fie ) are measurable. Only the parameters for bulk
a
heat transport (h) and moisture availability (M) are unknown. These can
be evaluated with Eq. 4-11, assuming that they can be considered con
stant for some period of time.
Supposing that measurements of T T fie G, and R are available
S a d
for two different radiation loads,
y(R G), hMSe,
1 a
4-15
(Ts Ta}2 = h(Ms + y) 2
4-16
The numerical subscripts identify the two sets of data corresponding to
the two differing radiation regimes. If the measurements are made close
enough in time so that moisture availability and the bulk thermal


NET RAD. (LY/min)
198


(C) NET RAD.
Temperature Gradient Response of a Clear Day with Constant
Moisture Availability. The temperature gradient hysteresis
is the opposite of that for October 17, 1981 (Fig. 5-7)
which had decreasing moisture availability.
Fioure 5-12.


163
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
152
730
0.30
0.02

-
0.06
24.4
29.7
.884
800
0.40
0.03


0.56
26.4
32.9

.828
830
0.46
0.04
0.11
0.31
1.73
27.5
33.9
37.1
.965
900
0.57
0.05
0.14
0.38
1.55
28.0
35.5
37.1
.974
930
0.66
0.07
0.15
0.43
1.84
29.1
36.9
36.5
.979
1000
0.72
0.08
0.17
0.48
1.64
29.7
38.2
36.0
.979
1030
0.75
0.08
0.17
0.50
2.07
30.5
39.0
35.9
.992
1100
0.60
0.09
0.11
0.41
1.08
31.0
37.9
35.4
.955
1130
0.70
0.08
0.14
0.47
1.14
31.3
38.5
34.9
.968
1200
0.81
0.11
0.16
0.53
1.55
32.4
40.7
34.0
.989
1230
0.71
0.10
0.13
0.48
1.63
32.9
39.5
34.0
.975
1300
0.60
0.09
0.12
0.39
1.38
33.0
38.5
33.7
.978
1330
0.65
0.09
0.13
0.44
1.61
33.5
38.7
34.1
.948
1400
0.47
0.09
0.10
0.28
1.50
33.5
37.3
34.4
.974
1430
0.10
-0.02


3.46
28.4
25.7
37.9
.536
1500
0.16
-0.05

--
4.54
24.0
22.5
36.0
-.897
1530
0.10
-0.01
-0.02
0.14
3.02
23.7
23.0
36.8
-.955
153
700
0.22
0.01

1.41
23.7
24.4
.007
730
0.31
0.02
--
2.14 .
25.0
25.6
.
.824
800
0.42
0.03

--
2.05
26.1
27.5

.919
830
0.53
0.04
0.10
0.39
2.20
27.2
30.0
41.0
.959
900
0.61
0.05
0.12
0.44
2.62
27.8
31.9
41.0
.984
930
0.63
0.05
0.12
0.46
2.73
28.4
32.7
40.7
.975
1000
0.76
0.05
0.14
0.57
2.61
29.1
34.4
40.3
.981
1030
0.81
0.06
0.15
0.60
2.84
29.8
35.5
39.0
.989
1100
0.89
0.07
0.16
0.67
2.77
30.6
36.8
38.2
.984
1130
0.89
0.07
0.16
0.65
2.81
30.8
37.2
37.4
.986
1200
0.91
0.09
0.16
0.66
2.37
31.5
38.0
36.1
.988
1230
0.91
0.09
0.20
0.62
2.85
31.9
37.9
36.2
.980
1300
0.88
0.07
0.24
0.57
3.10
32.3
37.8
36.3
.987
1330
0.86
0.07
0.22
0.57
2.92
32.8
37.7
35.9
.980
1400
0.79
0.06
0.20
0.53
3.10
33.1
37.0
36.0
.977
1430
0.72
0.06
0.18
0.49
2.76
33.7
36.5
36.1
.969
1500
0.58
0.04
0.16
0.38
3.03
33.5
35.0
37.0
.943
1530
0.47
0.03
--

2.60
33.5
34.1
38.8
.917
1600
0.26
0.02
--
--
2.20
33.1
32.1
39.4
.742
1630
0.04
0.00
--

1.44
31.9
28.4
39.4
-.821
1700
0.04
0.00
--

0.93
31.4
28.0
40.6
-.900


118
The accuracy of ET estimates made using the ATGR method is evalu
ated in Table 5-3. This is done by calculating the correlation between
measured ET rates and ATGR method estimates (Eq. 4-35). The first three
numbers after the date indicate the slope, intercept, and correlation
coefficient of a simple regression line fit to the measurements and
estimates. If the correlation was perfect, the slope would be 1, the
intercept would be 0, and the correlation coefficient would be 1. The
latter is a measure of the scatter between measured and estimated ET
rates; the departure of the slope and intercept from 1 and 0 is an in
dication of systematic differences between measured and estimated ET
rates. These systematic differences probably occur because of the lack
of data at low net radiation levels. Morning ET data were generally
missing because of condensation in the air sampling mast, so tempera
ture gradient/net radiation correlations are biased toward afternoon
conditions.
The comparison of ET estimates to measurements is presented graph
ically for five days in graphs (g), (h), and (i) in Figs. 8, 9, 10, 11,
and 12 of Appendix D. Estimates made with the simple residual method
(Eq. 2-24) are also shown for comparison. This method represents the
state-of-the-art in remote ET estimation methods.
Graph (g) in each of the figures compares the daily course of mea
sured Bowen ratios, ratios calculated via the ATGR method (Eq. 5-14)
and ratios calculated by the simple residual method. The latter was
calculated according to:
h(T, Tj
5-19
" fR h(T T ) '
b a
In both cases, the average heat transfer coefficient of the particular
day graphed was used in computations. The ATGR method Bowen ratio is


133
Lemon, E.R., D.W. Stewart, R.W. Shawcroft and S.E. Jensen. 1973. Exper
iments in predicting evapotranspiration by simulation with a soil-
plant-atmosphere model (SPAM). _In Field Soil Water Regime, Soil
Sci. Soc. Amer., Madison, WI.
Menenti, M. 1980. Defining relationships between surface character
istics and actual evaporation rate. NTIS #E80-10335, U.S. Dept.
Commerce, Springfield, VA.
Monteith, J.L. 1965. Evaporation and environment. Symp. Soc. Exp. Biol.
19:205-234.
Monteith, J.L. 1973. Principles of Environmental Physics. Edward
Arnold, London. 241 pp.
Monteith, J.L. 1975. Vegetation and the Atmosphere. Vol. 1. Academic
Press, London, UK. 273 pp.
Morgan, D.L., W.O. Pruitt and F.J. Lourence. 1971. Analysis of energy
and mass transfers above vegetative surfaces. Res. & Devel. Tech.
Rept. ECOM 68-G10-F by Univ. of Calif.-Davis for U.S. Army Elec
tronics Command, Atmos. Sciences Lab., Ft. Huachuca, AZ. AD 721-
301. 128 pp.
Murphy, C.E., Or. and K.R. Knoerr. 1970. A general model for the energy
exchange and microclimate of plant communities. Proc. Summer Com
puter Simul. Conf., Simul. Council, Inc.., La Jolla, CA. pp. 786-
797.
Murphy, C.E., Jr. and K.R. Knoerr. 1972. Modeling the energy balance
processes of natural ecosystems. E. Decid. Forest Biome. Memo
Rept. No. 72-10. Oak Ridge Natl. Lab., Oak Ridge, TN.
Nappo, C.J. 1975. Parameterization of surface moisture and evaporation
rate in a planetary boundary layer model. J. Appl. Met. 14:289-
296.
Odum, H.T. 1982. Systems Ecology: An Introduction. John Wiley & Sons,
NY. 614 pp.
Outcalt, S.I. 1972. The development and application of a simple digital
surface-climate simulator. J. Appl. Met. 11:629-636.
Pandolfo, J.P. and C.A. Jacobs. 1973. Test of an urban meteorological
pollutant model using CO validation data in the Los Angeles metro
politan area. Vol. I, CEM-4121-490A, The Ctr. for the Environ, and
Man, Hartford, CT. 176 pp.
Penman, H.L. 1948. Natural evaporation from open water, bare soil and
grass. Proc. Roy. Soc. A. 199:120-145.
Prandtl, L. 1932. Meteorologische Anwendungen der Stromungslehre.
Beitr. Phys. Fr. Atmosph. 19:188-202.


96
Table 5-1. Example Calculations with the Strict TGR Method. Data
used are from Oct. 17, 1981.
Calculated
with strict
TGR equations1
Calculated
with corrected
surface temps.2
Calculated
directly
from data3
t
h
M
h
M
h
M
(TST)
ly/min
C ly/minC
ly/min C
1000
.041
.14
1030
-.051
-.26
.020
.31
.033
.16
1100
-.092
-.14
.028
.19
.032
.15
1130
-.001
5.69
.024
.24
.034
.14
1200
-.133
-.15
.115
.65
.034
.12
1230


.041
.08
.033
.12
1300
.031
.14
.030
.16
.035
.11
1330
.016
.37
.033
.14
.036
.10
1400
.017
.24
.048
.06
.038
.10
1430
.037
.09
.031
.15
.035
.12
1500
- .044
.06
.036
.11
.038
.10 .
1530
.062
.02
.038
.10
.032
.12
1600
.051
.05
--

.022

1 heat
transport
coefficient and moisture availability calculated
with Eqs
. 4-17 and
4-18.
2 heat
transport
coefficient and moisture availability calculated
with corrected surface temperatures. Surface temperature was
calculated with Eq. 4-11 using h
=.035 ly/min C and M=0.12,
and then
h and M were recalculated as in
1.
3 heat
transport
coefficient calculated
using Eq. 5-2, and
moisture
availability calculated using Eq. 5-5.


151
123 IF(ABS(RCOEF)-ROLD)130,130,125
125 ROLD = ABS(RCOEF)
VO = A
DV = D
BV = ABS(B)
RV = RCOEF
IF(RK )135,135,100
130 ROLD = ABS(RCOEF)
IF(RK )100,100,140
135 CONTINUE
140 RETURN
END
ENDS


LIST OF FIGURES
Page
Figure 1-1. Location of the University of Florida Beef Re
search Unit 8
Figure 1-2. Field Apparatus and Sensor Locations 10
Figure 2-1. System Diagram of Generalized Evapotranspiring
Surface 14
Figure 2-2. Rough Calculation of Heat Storage in Pasture Canopy . 19
Figure 3-1. Bowen Ratio Calculation from Measurements of Vapor
Pressure and Temperature 41
Figure 3-2. Schematic of ET Measurement System 45
Figure 3-3. Detail of Profile Measurement Mast Arm .48
Figure 3-4. Detail of Air Sampling Equipment 50
Figure 3-5. Example of Intermediate Program Output 53
Figure 3-6. Example of Half-Hourly Data Report . 56
Figure 4-1. Definition Sketch for Transport Properties . . .64
Figure 4-2. Components of Vapor Pressure Gradient 67
Figure 5-1. Total vs. Turbulent Temperature Gradients for a
Clear Day 85
Figure 5-2. Total vs. Turbulent Temperature Gradients for a
Cloudy Day 87
Figure 5-3. Heat Transport Coefficient Data 89
Figure 5-4. Moisture Availability Data 91
Figure 5-5. Vapor Pressure Parameter Data 92
Figure 5-6. Soil Heat Flux Parameter Data 94
Figure 5-7. Clear Day Temperature Gradient/Net Radiation Corre
lation 98
Figure 5-8. Graphical Interpretation of Temperature Gradient/Net
Radiation Correlation 100
Figure 5-9. Cumulative ET Estimates 102
vii


42
The apparatus used to collect temperature measurements and air sam
ples was designed so that the sensors returned signals accurately repre
sentative of the air layers being sensed. The thermopiles were nested
inside three aspirated radiation shields, with each shield wrapped in
highly reflective aluminum foil. Air samples were pumped continuously
from sampling ports near the thermopiles through about 100 m of 6-mm ID
polypropylene tubing and 11.3-L mixing chambers in the instrument room.
To prevent any danger of condensation, the air sampling system was
heated from sampling mast to dewpoint analyzer. The bundle of five tubes
from the mast was taped around a heater cable (3 W/ft) and packed inside
a 1.3-cm-thick foam rubber insulation tube. The mixing chambers and the
sampling valve were also heated.
The travel time of air samples from mast to instrument room was
approximately 1 min. Therefore, the dewpoint measurement corresponding
to a temperature measurement at a specific level was made 1 min later.
Also, the dewpoint temperature measurements were pressure-corrected be
cause the arrangement of the air sampling system caused the pressure
rate at the dewpoint sensor to be ^30 mb less than atmospheric pressure.
To ensure clean electrical signals, shielded signal cable with a
single common ground was used. In spite of these precautions, the Beef
Research Unit fence charger managed to induce significant voltage spikes
on the low level signals (e.g., the 0-200 microvolt thermopile signals).
This problem was solved with a filtering routine in the data collection
program.
In addition to reducing the error sources from the sensors in every
practicable way, the temperature and vapor pressure signals were
physically smoothed. Smoothing was required because the measurement rate


170
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
293
700
0.02
-0.04
- _
1.10
6.0
3.8
.919
730
0.11
-0.02


2.42
9.6
9.6

.808
800
0.17
-0.01


2.36
11.5
11.7

-.767
830
0.27
-0.00


2.76
14.0
15.6

-.557
900
0.37
0.01
0.22
0.13
2.60
16.8
20.6
10.3
.999
930
0.45
0.02
0.28
0.16
3.06
19.2
24.9
11.2
.999
1000
0.53
0.03
0.30
0.20
3.59
21.3
27.9
12.2
1.000
1030
0.59
0.03
0.31
0.25
3.69
22.5
30.2
12.9
.997
1100
0.65
0.04
0.33
0.28
4.45
23.5
31.9
12.9
.998
1130
0.70
0.04
0.39
0.27
5.38
24.0
32.9
12.8
.998
1200
0.45
0.03
0.22
0.20
4.61
23.9
30.6
13.0
.998
1230
0.37
0.03
0.15
0.19
4.68
23.8
28.4
13.0
.997
1300
0.51
0.03
0.24
0.24
4.99
24.6
31.1
13.3
.999
1330
0.63
0.04
0.29
0.31
3.75
25.3
33.5
13.0
.994
1400
0.48
0.03
0.24
0.21
4.43
25.2
31.8
12.9
.995
1430
0.43
0.02
0.19
0.22
5.33
24.8
29.4
13.4
.995
1500
0.15
0.02
0.04
0.09
4.91
23.8
25.6
13.7
.996
1530
0.24
0.02
0.09
0.14
5.23
24.3
26.9
13.6
.993
1600
0.15
0.01
0.03
0.11
4.22
23.8
25.1
13.6
.941
1630
0.08
0,01
--

3.59,
23.3
24.0 .
13.9
.916
1700
0.02
0.01
--

4,20
22.8
22.8
13.8
-.861
294
700
-0.01
-0.02
_ _
1.31
12.1
10.5
_ __
.855
730
0.08
-0.01

--
1.67
13.4
14.0

-.415
800
0.11
-0.00

--
1.42
14.8
15.9

-.704
830
0.29
0.01

--
2.00
17.2
19.4

-.769
900
0.35
0.01


2.53
19.5
22.6

-.796
930
0.44
0.02


2.52
21.9
26.9
19.6
-.168
1000
0.52
0.03
0.24
0.25
2.82
23.8
30.1
17.3
.995
1030
0.58
0.03
0.28
0.27
3.79
24.9
32.2
17.3
.999
1100
0.55
0.03
0.24
0.27
4.28
25.8
32.5
16.7
.999
1130
0.55
0.03
0.23
0.29
4.29
26.3
33.3
16.2
.999
1200
0.57
0.04
0.26
0.28
4.60
26.4
34.5
16.2
.999
1230
0.50
0.03
0.22
0.26
4.40
26.3
32.9
16.5
.999
1300
0.51
0.03
0.20
0.27
4.71
26.7
33.2
17.1
.998
1330
0.51
0.03
0.21
0.26
4.64
27.1
33.3
17.5
.999
1400
0.30
0.03
0.10
0.18
3.95
26.8
30.8
17.4
.995
1430
0.47
0.03
0.17
0.27
4.57
27.2
32.3
17.4
.992
1500
0.32
0.03
0.12
0.18
4.97
27.1
30.6
17.3
.995
1530
0.32
0.02
0.12
0.18
5.11
27.1
30.3
17.4
.993
1600
0.27
0.02
0.09
0.16
4.99
27.1
29.7
17.4
.991
1630
0.10
0.02
0.02
0.06
4.43
26.1
26.8
17.3
.961
1700
0.01
0.01
0.00
0.00
3.99
25.1
24.8
17.2
-.970


166
Day
Time
Net
Soil
. Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
279
1030
0.65
0.03
0.19
0.42
1.12
25.8
35.0
18.5
.985
1100
0.70
0.04
0.22
0.45
1.58
26.2
37.5
18.4
.997
1130
0.77
0.04
0.24
0.49
1.97
26.9
39.6
18.1
.998
1200
0.81
0.05
0.26
0.50
2.10
27.4
40.6
17.9
.998
1230
0.83
0.05
0.27
0.52
1.96
27.7
41.1
18.0
.997
1300
0.78
0.05
0.23
0.51
1.60
27.9
40.4
18.0
.993
1330
0.73
0.04
0.21
0.48
2.32
28.3
40.0
17.5
.993
1400
0.66
0.04
0.19
0.44
2.02
28.7
38.8
16.9
.984
1430
0.58
0.03
0.14
0.41
1.47
28.9
37.8
17.1
.973
1500
0.49
0.03
0.11
0.35
1.64
29.1
36.1
17.5
.966
1530
0.39
0.03
0.06
0.31
1.10
28.9
34.5
17.0
.937
1600
0.28
0.02


1.33
29.4
32.7
16.9
.873
1630
0.16
0.02

--
1.01
29.4
30.6
17.1
-.373
1700
0.04
0.01
-0.01
0.04
0.95
28.9
27.6
17.0
-.974
280
700
0.03
-0.00
__
. -
0.06
17.8
17.3
_ _
.766
1000
0.55
0.03
0.19
0.33
3.16
26.1
33.9
23.6
.996
1030
0.63
0.03
0.24
0.36
3.37
26.9
35.7
23.2
.993
1100
0.70
0.04
0.23
0.43
2.89
27.6 -
38.6
23.3
.996
1130
0.69
0.04
0.21
0.44
3.22
28.1-
38.8.
22.8 .
. 997
1200
0.77
0.04
0.23
0.49
2.99
28.8
40.9
22.2
.996
1230
0.60
0.04
0.15
0.40
2.55
29.1
38.6
21.9
.996
1300
0.65
0.04
0.18
0.44
2.81
29.5
39.8
21.1
.997
1330
0.68
0.04
0.18
0.46
2.72
29.9
39.9
21.0
.998
1400
0.48
0.03
0.09
0.35
1.80
29.8
37.1
20.9
.988
1430
0.41
0.03
0.08
0.30
2.70
30.2
36.3
21.0
.994
1500
0.34
0.03
0.04
0.27
1.96
29.9
34.9
21.6
.974
1530
0.37
0.03
0.05
0.29
2.43
29.8
34.8
21.7
.975
1600
0.28
0.03
0.03
0.22
2.19
30.0
33.9
21.8
.936
1630
0.12
0.02


2.22
29.7
31.2
21.7
-.919
1700
0.01
0.01
-0.00
0.01
0.65
28.5
28.0
22.3
-.996
285
830
0.30
-0.01
0.11
0.19
3.55
18.8
....
18.4
.989
900
0.38
-0.00
0.16
0.22
4.30
19.8
30.1
18.4
.996
930
0.47
0.00
0.22
0.25
3.93
20.9
26.2
18.7
.996
1000
0.57
0.01
0.25
0.30
4.23
22.1
28.6
18.6
.996
1030
0.64
0.01
0.30
0.33
3.57
22.5
30.2
18.9
.999
1100
0.55
0.01
0.24
0.30
3.93
22.5
29.7
18.8
.996
1130
0.73
0.02
0.32
0.40
3.95
23.3
33.0
18.4
.998
1200
0.81
0.02
0.35
0.43
4.02
23.8
34.6
18.3
.998
1230
0.61
0.01
0.25
0.34
4.00
23.6
32.8
17.8
.997
1300
0.61
0.01
0.24
0.36
3.53
23.6
32.0
17.0
.996
1330
0.62
0.01
0.25
0.36
3.69
24.1
32.8
16.9
.999
1400
0.55
0.01
0.22
0.32
4.07
23.9
31.8
16.6
.995
1430
0.58
0.01
0.24
0.33
3.72
23.7
31.6
16.4
.996
1500
0.42
0.00
0.18
0.24
4.06
23.5
29.5
16.4
.994


22
parameter included so that the windspeed is defined as zero when
z D = 0), the equation for the log profile can be written
u(z) =ln
z D + z
2-10
where is the shear stress at the surface. With this wind profile, the
eddy diffusivity can be evaluated between the surface and any level in
the air with average windspeed ufl:
K(z)
K Ua(z D + z0)
In
z D + z.
2-11
With the assumption of transport similarity (Eq. 2-8), this expression
can be used to evaluate and K^. Similar treatments of eddy diffusiv
ity can be found in many texts (e.g., Brutsaert, 1982).
With very precise experimental work it has been determined that the.
turbulent transport of momentum, heat, and water vapor is strictly simi
lar only under neutral stability conditions, e.g., Swinbank and Dyer
(1967). To describe eddy diffusivities under other conditions, diabatic
influence functions w) have been developed. They are defined
such that
kh * km a"d
Kw = t~
W M
2-12
2-13
These are experimentally determined and expressed in terms of dimension
less variables such as the Monin-Obukhov length or Richardson number
(Morgan et al_., 1971; Businger, 1973).


4
element at a particular time. For environmental applications, the elec
tromagnetic spectrum is usually resolved into visible and thermal bands.
With a clear sky and proper consideration of atmospheric transmission
properties, these measurements can be used to calculate the surface tem
perature and the net radiation absorbed by the surface.
Net radiation and surface temperature estimates should lead to good
evapotranspiration estimates because they are very prominent variables
in the heat exchange processes that take place at the earth's surface.
Net radiation is the primary energy source used in changing water from
liquid to vapor at the surface, while surface temperaturebecause it is
a result of surface variables and energy exchange processes--is a com
posite measurement of the effects of these variables.
However, it is a long step from measurements of net radiation and
surface temperature to an operational ET estimating'system-using satel-
lite data. The following questions illustrate the range of problems
faced in developing a method for such a system.
1. What is the best way to estimate net radiation from satellite
pixel information? How does one treat clouds or haze?
2. How is the radiation temperature of a complex surface like that
of vegetation interpreted? Does angle of view and height of
vegetation make a difference? How does one handle a canopy
underlain by a cool surface like a marsh or swamp? How does
one treat mountainous topography?
3. Is an interpolation technique required to compensate for the
temporal resolution of satellite data?
4. What level of detail is required in a practical ET estimation
method? How does one get the most acceptably accurate estimate
for the least effort in data collection and processing?
5. How are the effects of water availability, vegetation type,
cloudiness, and wind related? And how do they influence ET?
What is the minimum amount of data needed from ground-based
observations?


120
better at following the general pattern of the measured Bowen ratio.
The residual method Bowen ratio is noisy by comparison because it is
very responsive to small variations in temperature gradients; whenever
the numerator in Eq. 5-19 is reduced, the denominator is increased by
an equal amount, and vice versa.
Instantaneous ET estimates made by the ATGR and residual methods
are compared in graph (h) of each of the figures. In these calculations
an average conditions value is used for the heat transport coefficient
(.035 ly/minC). Both methods produce estimates of the same quality,
since they use essentially the same information to produce estimates.
Both appear to have the same sensitivity to the heat transport coeffi
cient value. Figure 11(h) shows a day (Oct. 22, 1981) on which the heat
transport coefficient averaged about 15% less than the average condi
tions value, causing both.methods to underestimate ET. Graph (i) in
Figs. 8, 9, 10, 11 and 12 shows the same data as graph (h) plotted
against time. This presentation of the data more clearly shows the sys
tematic departure of ATGR estimates from measured ET rates.
Finally, the accuracy of cumulative ATGR method ET estimates are
compared to measurements. The simplest comparison is shown in the
fourth column of Table 5-3. It is the slope of a line passing through
the origin and the center of the measured vs. estimated ET points, as
shown in graph (h) of Figs. 8, 9, 10, 11, and 12 in Appendix D. If the
slope is 1.11, for example, the cumulative ET estimate is 11% too high.
The second set of numbers in Table 5-3 was calculated under more real
istic estimating constraints "average conditions" values for the air
heat transfer coefficient (.035 ly/minC) and the soil heat flux


126
attention is called to the fact that the radiation surface temperature
may not be the same as the effective heat transfer surface temperature.
Caution should be exercised in adapting a wind model from the litera
ture; the need for a surface temperature correction procedure for more
complex surfaces than pasture, like swamp or mountainous terrain, cannot
be ruled out.
The primary advantage in using the ATGR method is that it can ob
tain a measure of the surface moisture availability from the temperature
gradient/net radiation correlation. In fact, with an average measure of
the saturation deficit (6e_) or bulk transfer coefficient (h) and the
a
correlation parameters (A and B), both moisture availability and bulk
stomata! diffusion resistance should be calculable:
M = y B (f hA)
6ea Bs lifts
a
pc Ae (6e - Bs By)
r P a a
s Byf(6e Bs)
and
4-28,29
6-1
(Equation 6-1 was obtained by simultaneous solution of Eqs. 2-23, 4-28
and 4-29.)
The data presented in Chapter 5 make a good case in favor of using
daily average data in the Penman equation. The reason this approach
works is that the factors which affect the ET rate (h, M, s, f, and 6e )
ct
are constant enough to allow good cumulative ET estimates. The ATGR
method has an additional advantage: the process of fitting a line to the
temperature gradient/net radiation correlation minimizes the errors
caused by considering the parameters constant. With several sets of data
per day, it is likely that the ATGR method will be more accurately rep
resentative of a particular day than the Penman method, and produce bet
ter ET estimates. Usually, daily maximum and minimum temperatures and an


BOWEN RATIO (UNITLESS)
)CT. 17, 1981 OCT 22, 1981 MAY
115
Figure 5-15. Comparison of Measured and Estimated Bowen Ratios. Bowen
ratios were estimated with Eq. 5-14. Mote the increasing
curvature in the pattern with increasing saturation defi
cits, and the change in Bowen ratio with clouds on Oct.' 22,
1981. (The temperature gradient responses of these days
were shown in Figs. 5-7, 5-12, and 5-13.)


145
SUBROUTINE TMTCH(DATA,L,NMEAS,SVAL, DAT)
C*****TMATCH SLOWS SENSOR RESPONSE TO MATCH TEMPERATURE AND DEW
C*****POINT MEASUREMENTS BY WEIGHTED AVERAGES
DIMENSION DAT(26,2),W(25)
DATA W/.137,.119,.104,.090,.077,.067,.058,.050,.044,.038,
*.033,.028,.025,.021,.018,.016,.014,.012,.010,.009,
*.008,.007,.006,.005,.004/
IF(NMEAS .LT. 25)190,195
190 K = 26 NMEAS
DAT(K,L) = DATA
GO TO 200
195 DAT(1,L) = DATA
SVAL = 0.0
DO 200 1=25,1,-1
SVAL = SVAL + DAT(I,L)*W (I)
DAT(I+1,L) = DAT(I,L)
200 CONTINUE
RETURN
END
SUBROUTINE RATIO(E,T,B,C)
C*****ratio COMPUTES SLOPE OF T(LEVEL)VS.E(LEVEL) BY DIAGONAL REGRESSION
DIMENSION E(5),T(5),SUM(5)
DO 210 K=l,5
SUM(K) = 0.0
210 CONTINUE
DO 220 K=l,5
SUM(l) = SUM(1)+T(K)
SUM(2) = SUM(2)+E(K)
SUM(3) = SUM(3)+T(K)**2
SUM(4) = SUM(4)+E(K)**2
SUM(5) = SUM(5)+T(K)*E(K)
220 CONTINUE
ST = SUM(3)-(SUM(l)** 2)/5. .
SE = SUM(4)-(SUM(2)**2)/5.
SET = SUM(5)-(SUM(l)*SUM(2))/5.
B = (ST-SE)/(2.*SET)
IF(SET)225,230,230
225 B = B-SQRT(1.+B**2)
GO TO 235
230 B = B+SQRT(1.+B**2)
235 C = SET/SQRT(SE*ST)
RETURN
END
ENDS


168
Day
Time
Net
Soi 1
. Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
FI ux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
287
1600
0.22
0.01
0.12
0.10
5.88
22.3
25.6
20.3
.994
1630
0.11
0.00
0.05
0.05
4.87
21.0
23.2
20.0
.995
1700
0.06
-0.00
0.03
0.03
4.23
20.3
22.3
19.9
.993
1730
0.01
-0.00
0.01
0.01
4.09
19.6
21.2
19.6
1.000
288
700
0.02
-0.02
_ -
2.05
13.2
13.5
17.0
.937
730
0.09
-0.01
--

2.87
14.1
15.0
18.0
.502
800
0.17
-0.01

3.02
15.3
16.6
18.5
.824
830
0.26
-0.00
0.06
0.21
3.03
17.2
18.9
18.8
.991
900
0.37
0.00
0.13
0.23
2.85
18.8
21.8
19.5
.997
930
0.47
0.01
0.21
0.25
3.33
20.2
25.0
19.7
.997
1000
0.55
0.02
0.27
0.26
3.11
21.6
28.5
20.0
.998
1030
0.63
0.02
0.32
0.29
3.71
22.7
31.0
20.1
.999
1100
0.67
0.02
0.36
0.29
3.44
23.2
33.5
20.1
.999
1130
0.55
0.02
0.27
0.26
3.09
23.5
32.5
20.1
.999
1200
0.75
0.03
0.36
0.36
3.14
24.4
36.0
20.0
.998
1230
0.54
0.03
0.25
0.27
2.74
24.2
33.6
19.6
.997
1300
0.65
0.03
0.31
0.31
2.90
24.7
35.0
19.4
.996
1330
0.43
0.03
0.19
0.22
2.88
24.6
31.8
19.7
.996
1400
0.51
0.02
0.21
0.27
3.36
24.9-
32.4.
18.7-
.997
1430
0.41
0.02
0.15
0.24
3.28
24.8
31.2
17.7
.992
1500
0.39
0.02
0.14
0.23
3.30
25.0
30.5
16.8
.991
1530
0.35
0.02
0.13
0.21
2.93
25.0
30.2
16.1
.989
1600
0.25
0.01
0.08
0.16
2.76
24.8
28.4
16.0
.987
1630
0.12
0.01


2.89
24.3
26.0
15.7
.906
1700
0.02
0.00
--

2.24
23.7
23.8
15.6
-.915
289
730
0.06
-0.02
_ _
0.31
11.8
11.7
-.789
800
0.16
-0.01

--
1.65
14.2
14.8
--
-.508
830
0.26
0.00


1.26
16.3
17.9

-.670
900
0.36
0.01
--
--
1.52
18.9
21.8
--
-.917
930
0.45
0.01
--
--
2.43
20.9
25.7

-.353
1200
0.69
0.04
0.29
0.36
1.84
25.6
36.6
13.2
.996
1230
0.69
0.04
0.28
0.36
1.06
25.8
36.7
13.2
.999
1300
0.67
0.04
0.26
0.37
1.45
26.3
36.8
13.0
.996
1330
0.64
0.04
0.24
0.35
1.33
26.8
36.4
12.9
.993
1400
0.58
0.04
0.24
0.31
1.45
27.3
35.6
13.2
.994
1430
0.51
0.03
0.20
0.28
1.66
27.5
34.6
13.5
.991
1500
0.42
0.03
0.18
0.22
0.92
27.5
32.9
13.6
.977
1530
0.33
' 0.02
0.13
0.18
0.91
27.7
31.5
13.9
.932
1600
0.23
0.02
--
1.13
27.5
29.6
13.8
.895
1630
0.11
0.02
--

0.40
27.3
27.2
13.7
-.149
1700
0.02
0.01
-0.01
0.01
0.99
26.5
24.4
14.2
-.975


172
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
301
900
0.19
-0.01
0.08
0.11
1.87
16.8
19.1
14.6
.999
930
0.25
0.00
0.11
0.14
2.11
17.7
20.9
14.8
.997
1000
0.29
0.00
0.14
0.15
1.82
18.8
22.9
15.1
.996
1030
0.37
0.01
0.18
0.18
1.58
20.2
25.5
15.8
.994
1100
0.51
0.02
0.25
0.24
1.88
21.9
28.6
16.8
.995
1130
0.61
0.02
0.33
0.26
1.95
23.2
32.3
18.2
.998
1200
0.67
0.03
0.34
0.30
1.66
24.2
34.7
19.7
.996
1230
0.67
0.03
0.35
0.29
2.24
24.6
34.6
19.7
.997
1300
0.67
0.03
0.34
0.30
2.23
25.3
35.1
20.2
.997
1330
0.60
0.02
0.30
0.28
1.89
25.3
34.3
19.9
.996
1400
0.56
0.02
0.28
0.26
2.23
25.7
33.9
19.8
.996
1430
0.48
0.01
0.24
0.23
2.25
25.9
33.0
19.8
.994
1500
0.40
0.01
0.19
0.20
1.72
25.9
31.7
19.6
.987
1530
0.30
0.01
0.14
0.15
2.03
26.1
30.3
19.8
.986
1600
0.19
0.01
0.08
0.11
2.22
25.8
28.4
19.8
.976
1630
0.09
0.00
0.02
0.06
2.01
25.3
26.3
20.0
.947
1700
-0.01
-0.00
-0.00
0.01
1.32
24.6
23.8
19.9
-.890
302
730
0.05
-0.01
_
1.99
16.1
16.7
_ _
.024
800
0.06
-0.01

1 .'89.
16.6
17.4.
-- .
-.921
830
0.18
-0.00

--
2.35
17.8
19.5
--
-.704
900
0.20
0.00
--
--
2.59
18.6
20.3
--
-.682
930
0.25
0.01
--
--
2.32
19.8
21.9
--
-.898
1000
0.31
0.01
--
--
2.47
21.2
24.0

-.868
1030
0.49
0.02
--
--
3.09
22.9
28.2

-.607
1100
0.48
0.02
--

3.47
24.2
29.9

.897
1130
0.33
0.02
0.15
0.17
3.30
24.4
28.4
21.3
.991
1200
0.47
0.02
0.22
0.23
3.41
25.1
30.9
21.6
.997
1230
0.67
0.03
0.32
0.31
3.52
26.0
35.3
21.4
.998
1300
0.67
0.03
0.32
0.32
3.64
26.8
35.7
21.1
.996
1330
0.42
0.02
0.19
0.22
3.70
26.6
32.2
20.6
.995
1400
0.23
0.01
0.09
0.13
3.69
26.2
29.3
20.4
.997
1430
0.22
0.01
0.07
0.14
3.50
26.0
28.6
20.3
.991
1500
0.18
0.01
0.06
0.12
3.33
26.1
28.5
20.3
.992
1530
0.19
0.01
0.07
0.11
4.44
25.8
28.1
20.5
.998
1600
0.08
0.00
0.03
0.05
4.75
24.9
26.0
20.7
.991
1630
0.10
0.00
0.03
0.07
4.58
24.7
25.8
20.3
.964
1700
-0.01
-0.00
-- '
--
4.85
23.8
23.8
20.1
-.898
303
730
0.02
-0.00
0.01
0.02
4.78
20.4
20.9
21.8
.995
800
0.02
-0.00
0.01
0.01
4.36
20.4
21.0
22.0
1.029
830
0.04
-0.00

--
3.62
20.6
21.4
22.3
-.749
900
0.09
0.00
0.04
0.04
4.41
21.0
22.2
22.6
1.009
930
0.11
0.00
0.06
0.05
4.03
21.3
23.0
22.8
.971
1000
0.10
0.00
0.06
0.04
3.94
21.4
23.0
22.9
.991
1030
0.20
0.01
0.11
0.09
4.29
22.1
24.6
23.2
.988
1100
0.29
0.01
--
--
4.64
22.9
26.4
23.4
-.047


88
required to remain constant between sets of data. In the average TGR
method, the slope of the saturation water vapor pressure curve (s),
the saturation deficit (Se ), and the fraction of net radiation conduc-
Q
ted into the soil (f) are also required to be approximately constant
for periods of a day or more. Though some of these variables are known
functions of measurable variables (e.g., s is a known function of tem
perature), they must be considered parameters. This section shows how
these parameters vary over the course of a day.
The sensible heat flux is plotted as a function of the surface-
to-air temperature difference in Fig. 5-3a. The average heat transport
coefficient is represented by the slope of a line passing through the
origin and the center of gravity of the plotted points. The bulk air
conductivity for any half-hour period is computed as in Eq. 5-2 and has
been plotted in Fig. 5-3b
It was shown in Figs. 5-1 and 5-2 that radiation surface tempera
tures in the morning appeared cool relative to the effective heat trans
fer surface temperature. Barring other factors, the resulting lower tem
perature gradients would lead to higher calculated thermal conductivi
ties for morning time periods. This does not show in Fig. 5-3b, how
ever. The only apparent effect seems to be lowered conductivities
around noon resulting from apparently higher surface temperatures while
relatively less shaded areas are visible to the sensor.
It is difficult to say anything conclusive about the heat trans
port coefficient in the early morning or late afternoon. Temperature
gradients are in the process of changing direction, making the calcula
tion of h somewhat unreliable.


total
sensible heat
latent heat
heat stored
heat
stored
heat
=
stored in
+
stored in
+
in
+
in
top
storage
canopy air
canopy air
vegetation
soi 1
layer
(pc ) h ATa
p a At
(pc) h
1 Aea
pa y At
(Vc)
ilb
b At
AT
+ .0012 x 0.24 SIx20cXt + -0012 -K x 0.24 j20oul.s5l3
cm y cm-3 y
mb +
10000 Tia x 1,0 g^ x Tr + 1,5 ~S x '2 g* x 1 cm x 1 W
3 cm 3
.0006
cal
2
cm min
.0004
cal
cm mm
.01
cal
2 .
cm min
.006
cal
cm mm
.02
crrr min
Figure 2-2. Rough Calculation of Heat Storage in Pasture Canopy.


43
was limited to one measurement every 2.5 min for the vapor pressure
profile measurements.
Vapor pressure in the Bowen ratio data collection system was com
puted from a measurement' of the dewpoint temperature. Since the same
dewpoint sensor was used for all five levels and a delay had to be
scheduled between measurements to allow the analyzer to settle on new
dewpoints, the response of the dewpoint analyzer was the factor limiting
the sampling rate. The analyzer, an EG&G Model 880 Dewpoint Hygrometer,
was tuned so that it could "lock on" to small dewpoint temperature
changes within about 15 sec. However, 30 sec per measurement were sched
uled to allow the analyzer to stabilize on a given dewpoint under less
than ideal conditions. Since there were five levels to measure, the time
interval between measurements at the same level was 2.5 min.
The variability of temperature and vapor pressure in the turbulent
air layer is well documented; at any point in this layer, instantaneous
temperatures and dewpoints vary randomly (Desjardins et al_., 1978). The
higher-frequency temperature and dewpoint fluctuations were smoothed in
order to get representative measurements with a sampling rate of one
measurement every 2.5 min.
In the case of an air-sampling system, this smoothing is conveni
ently done by inserting a mixing chamber into the sample stream ahead of
the analyzer. An abrupt (or step) change in an air sample is translated
into a gradual, approximately exponential change by mixing in a chamber.
The exponential change is characterized by a time constant, which is
determined by the volume of the mixing chamber divided by the flow rate.
By harmonic analysis, it was determined that a time constant of 4 min .
would damp random signal variations occurring more often than every 2.5


PROF" 6
RAD.T.
23.27
TEMP
21 1
9:18:27
MET R.
.45
DPT.
9.5
B -1.723
W.SPD.
2.86
V.P.
11.9
PROF" 7
ROD.T.
23.7 7
TEMP
2 1.2
9:18:58
NET R.
.45
DPT.
9.6
B =1.813
W.SPD.
2.18
V.P.
T1 .9
PROF" 8
RAD.T.
24.25
TEMP
21.4
9:21:26
NET R.
.46
DPT.
9.8
B =1.812
W.SPD.
3.73
V. P.
12. 1
PROF" 9
RftD.T.
24.30
TEMP
21.7
9:23:55
MET R.
.47
DPT.
9.8
B 1.590
W.SPD.
3.54
V.P.
1 2.2
PROF" 10
RAD.T.
24.49
TEMP
21.8
9:26:24
NET R.
.47
DPT.
. 9.9
R =1.904
W.SPD.
3.36
V.P.
12.2
PROF" 11
RAD.T.
24.90
TEMP
22.2
9:28:54
MET R.
.48
DPT.
10.1
B =1.679
W.SPD.
2.85
V.P.
12.4
PROF" 12
RAD.T.
25.28
TEMP
22.5
9:31:23
NET R.'
.49
DPT.
10.3
B =1 .818
W.SPD.
2.94
V.P.
12.5
Figure 3-5. Example of Intermediate Program Output,
on face of HP 2100 computer is on.
hour report shown in Fig. 3-6.
20.4
20.0
19.5
9.2
9.0
8.7
1 1 .6
1 1 .5
1 1 .3
20.5
20.2
19.7
9.3
9.1
8.9
11.7
1 1 .5
1 1.4
20.7
20.4
20.0
9.5
9.2
9.0
11.0
11.7
1 1 .5
21.0
20.6
20.1
9.6
9.2
9.0
11.9
11.7
11.5
21.1
20.8
20.4
9.5
9.5
9.3
1 1 .9
1 1 .9
11.7
21 .5
21 1
20.6
9.8
9.6
9.4
12.1
12.0
1 1 .8
21.7
21.3 .
20.8
9.9
9.7
9.5
12.2
12.0
11.8
19.1 R = .999
8.5
19.3 R .99/
8.7
11.2
19.6 R = .997
8.8
11.3
19.8 R =. .998
8.8
11.4
0.1 K = 988
9. 1
11.5
20.3 R .999
9.2
11.8
20.4 R = I .000
9.3
11.7
This report is printed if switch #3
are from the 15 min preceding half-
U1
CO


EVAPOTRANSPIRATION
TIME (TST)
Figure 5-9. Cumulative ET Estimates. Evapotranspiration estimates
made with the ATGR method and ET measured by the profile
Bowen ratio method are plotted against time. Data used
are the same as those in Fig. 5-8 (October 17, 1981);
the dotted line is for unavailable ET data. The sub
script D in the equation stands for a daily estimation
period.


6
As suggested in the previous section, the enormous variety of ter
rain and vegetation types present on the earth's surface introduce a
large number of complicating factors into ET estimation formulations. In
order to clearly assess the potential of a general method, as many of
these complicating factors as possible were avoided by choosing a rela
tively homogeneous flat area of pasture as a test surface. The approach
was to develop a basic method which would work for simple surfaces; once
it is proven successfult can be modified if necessary to deal with
more complex situations like mountainous terrain or swamp.
A micrometeorologic measurement technique was used to measure ac
tual ET so that surface processes were left as undisturbed as possible.
The radiation surface temperature as well as net radiation was measured
for later use in method-testing. A great deal of effort went into devel
oping a data collection system to assure the reliability of the ET mea
surements. Special efforts were made to match the time constants of the
sensors involved and to reduce electrical signal noise. Control of the
measuring system, scheduling of the measurements, and calculations were
all performed by computer to minimize human error.
The fundamental assumption in method development was that satellite
data would be available in time intervals on the order of 1-3 hours.
After this assumption, the emphasis was on operational criteriaa prac
tical method must have general applicability, computational simplicity,
and low data requirements. With these objectives in mind, an analytical
approach, rather than a simulation approach, was chosen. In order to
keep data requirements low yet take advantage of satellite data, the
level of detail was chosen to be somewhat intermediate between the
strictly physical ET measurement methods and the empirical estimation


165
Time
Net
Soil
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
730
0.41
0.04
_ -
...
3.45
28.7
30.5
_
-.651
800
0.54
0.05
--
--
3.21
29.8
31.6
--
-.270
830
0.51
0.05
0.17
0.29
2.72
30.2
32.1
32.2
.992
900
0.56
0.05
0.17
0.34
3.22
31.0
32.9
30.8
.965
930
0.63
0.06
0.15
0.42
2.74
31.6
34.0
29.1
.977
1000
0.58
0.06
0.11
0.42
2.49
31.8
33.9
27.8
.982
1030
0.91
0.09
0.17
0.65
2.54
33.0
36.9
26.7
.974
1100
0.80
0.10
0.15
0.56
2.73
33.2
36.5
25.8
.987
1130
0.89
0.11
0.16
0.61
2.49
34.0
37.5
25.4
.981
1200
0.74
0.11
0.14
0.49
2.33
34.1
36.5
25.3
.989
1230
0.46
0.08
0.07
0.30
2.84
33.9
33.7
25.8
.966


125
The two-stage method solves the problem of cloudy skies and the
problem of interpolating between data sets. Although there may be some
cost in the form of reduced accuracy for instantaneous ET estimates,
the considerable data collected over Florida pasture (including net
radiation and surface-to-air temperature gradient measurements under
partly cloudy and cloudy skies) indicate that the ATGR approach is a
good approximation. Cumulative ET estimates were as good as estimates
made by the simple residual method (Chapter 2), which requires the same
amount of data but has no physically based method of dealing with
clouds and the time resolution of satellite data.
Method Limitations and Strengths
In principle, the ATGR method is a descendant of the Penman method
and many of the criticisms of the Penman method are relevant to it. The
Penman equation has been faulted for including a heat transport coeffi
cient which is an empirical function of wind (Thom and Oliver, 1977). In
its generalized form (for unsaturated surfaces) the Penman equation is
difficult to use because it requires knowledge of the dryness of the
surface in the form of a moisture availability parameter (Barton, 1979)
or a bulk stomatal diffusion resistance (Monteith, 1973). Methods of
predicting these parameters are all empirical, ranging from an air tem
perature weighting factor (Doorenbos and Pruitt, 1977) to resistance
functions for various plant species (e.g., American Society of Agricul
tural Engineers, 1966). Finally, the Penman method has been criticized
for its use with average daily data; the Penman equation is considered
strictly correct only instantaneously (Van Bavel, 1966).
The issue of the correct wind model to use in evaluating the heat
transport coefficient is not addressed in this research, although


47
dessicant container for the net radiometer were held in a weatherproof
box at the base of the tripod.
The air sampling mast consisted of a 2.5-m steel channel to which
five sensor arms (see Fig. 3-3) were attached at various levels. At one
end of each arm, teflon spacers centered two clusters of 10 thermocouple
junctions inside the smallest of three radiation shields. Individual
junctions were kept in thermal contact with a metal oxide conducting
paste. Air was drawn over the thermopiles, between radiation shields,
and through the length of the arm by a small fan at the opposite end.
Air samples were drawn from the air flowing through the arm. All wiring
(four 20-junction thermopiles and one thermocouple) and tubing (5 sample
lines) were contained inside the 3x3 cm channel down to its base, where
they ended in wire and tubing connectors. The mast and sensor arms as
well as the radiation, shields were wrapped in highly reflective aluminum
foi 1.
The sensors were connected to the scanner in the instrument room
with shielded signal and thermocouple wire. In the field, leads from the
sensors ran aboveground in wire harnesses to a junction box, where they
were connected to a signal cable via screw connectors. This cable ran
100 m underground to another junction box in the instrument room. From
this panel the signal lines were connected to one of two 50-pin connec
tors, which plugged into a short piece of cable tied directly into the
scanner. The "quick-disconnect" plugs were included to rapidly isolate
the data acquisition system from possible lightning strikes in severe
weather; the junction boxes allowed signal problems to be quickly traced
to sensors, underground cabling, or the data acquisition system. The
sensors used are identified in Table 3-2.


27
observed surface temperatures. The simulated ET flux is then assumed to
be the actual ET flux. Examples of evapotranspiration simulations are
Waggoner et _al_. (1969), Stewart and Lemon (1969), Sinclair et al.
(1971), Murphy and Knoerr (1970, 1972), Goudriaan and Waggoner (1972),
Lemon _et _al_. (1973), and Sinclair et. _al_. (1976). Dynamic models of the
surface heat transfer processes are computationally orders of magnitude
more complex than the steady-state approaches, and were developed only
after the introduction of the electronic computer.
The earliest physical models of the surface energy exchange process
were based on steady-state analysis and the similarity of latent and
sensible heat transport. Three steady-state strategies for solving the
energy budget equation for evapotranspiration have been developed; they
are referred.to as the simple residual, Penman, and Bowen ratio methods.
To more easily compare these methods, their equations have been written
in the same notation. Soil heat flux is included even though this compo
nent is often assumed too small to be included for vegetated surfaces.
In the residual approach, the energy budget equation is solved for
latent heat flux, and a simple gradient expression is used to evaluate
sensible heat flux:
E = (R G) h(Tc T ) 2-24
The transport coefficient for air conductivity is estimated from empiri
cally derived wind functions or physical wind models as described previ
ously. The biggest advantage of this method is that it requires no in
formation on the surface moisture status. Its disadvantage is that it is
very sensitive to an accurate transport coefficient estimate. When the
sensible heat flux term is written in terms of a resistance, this method
is also called the resistance energy balance method (Rosenberg, 1974) .


97
are shown in the second column of Table 5-1. They do not reproduce the
constant values of h and M, but are positive and correct in order of
magnitude.
The numerical hypersensitivity of the.strict TGR equations pre
vents good estimates of the bulk air conductivity and moisture availa
bility using data of realistic accuracy (two significant figures).
These equations are made up of compound differences; for example, the
numerator in Eq. 4-17 contains the product of a saturation deficit

[e (T ) ej and a temperature difference (T T ), which is
subtracted from a similar product. For this reason, the strict TGR
method does not lend itself to a practical ET estimation method.
Average Temperature Gradient Response Method
Graphical Representation of the Average TGR Method
Because of the number of parameters and complexity of'the equa
tions relating them to the temperature gradients (Eq. 4-25) and evapo-
transpiration (Eq. 4-32), it is difficult to get a feel for how param
eter variations affect ET estimates. However, some idea of their effect
on estimates of instantaneous ET rates can be gained directly from the
surface-to-air temperature gradient/net radiation relationship.
Figure 5-7 shows the measured surface-to-air temperature gradient
as a function of net radiation for the example day, October 17, 1981.
The relationship is not exactly linear, but it is a smooth non-noisy
relationship. The characteristic features are that the morning limb
does not coincide with the afternoon limb, and that the morning limb
has a distinct droop, or "belly." These features result from variations
in the parameters.


APPENDIX B
PROGRAM LISTING AND DEFINITION OF NAMES USED
Programs SET, MEASR, REPRT, and ANALZ are listed in the following
pages. They are written in Fortran IV and run under Hewlett-Packard's
Real Time Executive (RTE-2) operating system. Calls to RTE-2 (CALL
EXEC) were used to schedule programs, delay program execution between
program statements, make measurements, and determine the system time.
Names of subroutines, functions, data arrays, and indexes are defined
in the pages following the programs.
138


73
As a practical matter, the time period for which A and B are calcu
lated (and the parameters are considered constant) needs to be at least
a day. This period must be extended if enough clear sky data are not
available for a reasonable estimate of A and B. It should also be noted
that for normal daytime conditions, A and B must be positive for physi
cally real parameters. This implies that the intercept of the surface-
to-air temperature gradient/net radiation correlation must always be
negative (zero at most), and the slope must always be positive (see Eq.
4-27).
Use of the Average Temperature Gradient/Net Radiation Correlation
Incorporating the definition of the soil heat flux parameter (Eq.
2-24) into the equation for evapotranspiration (Eq. 4-14),
E > T5T7
4-32
The slope of the saturation vapor pressure curve (s) is a known function
of temperature, the psychrometric constant (y) is relatively constant at
a given altitude, and net radiation (R) can be estimated directly from
satellite data. There are four unknown parameters: moisture availability
(M), the soil heat flux parameter (f), the bulk transport coefficient
(h), and the saturation deficit (<5e ).
a
The equations for A and B, Eqs. 4-28 and 29, are in these four un
knowns. Since all four are required to estimate ET, two must be approxi
mated from average conditions or a rough daily measurement. Equations
4-28 and 29 can then be solved for the other two and substituted into
Eq. 4-32. Table 4-1 shows the ET formulae derived for the possible com
binations of known and unknown parameters and the correlation constants
A and B.


CHAPTER 2
EVAPOTRANSP¡RATION AND SATELLITE DATA
Overview
The availability of satellite images of the earth's surface and the
resources to investigate their usefulness has resulted in a variety of
remote-sensing research projects. In recent years, there have been pro
grams in which evapotranspiration estimation procedures were the objec
tive, notably a joint effort among the National Aeronautics and Space
Administration (NASA), the Institute of Food and Agricultural Sciences
at the University of Florida, the Florida Water Management Districts
(Allen 'jet ai_., 1980), and NASA's Heat Capacity Mapping Mission, or HCMM
(Goddard Space Flight Center, 1978).
Since the estimation techniques need to be applicable to many dif
ferent surfaces, physical rather than empirical approaches are. required.
The physical methods that have been developed, including the one pre
sented in this work, are all based on the energy budget concept of the
surface and on the similarity of transport among quantities in turbulent
flow. These ideas and various approaches to solving the energy budget
equation are developed in the first part of this chapter. Remote ET es
timation techniques are reviewed in the second part, which concludes
with an introduction to the new method.
The Evapotranspiration Process
At the interface between a liquid and a gas, molecules are continu
ally breaking and reforming the intermolecular bonds which hold them at
12


G (LY/min) ef-en(MB)
187
Figure 8. (cont.)


ESTIMATED ET (LY/min) BOWEN RATIO
199
Figure 10. (cont.)


O .2 .4 .6
R (LY/MIN)
Figure 5-14. Generalized Clear Day H/E and E/R Patterns. The patterns in (b) were generated with
the average temperature gradient response in (a) and a sinusoidal net radiation
pattern. When the intercept in (a) is zero (negligible saturation deficit), E/R and
H/E are constant (see Fig. 5-12). The curvature in the patterns of these ratios
increases as the intercept becomes more negative (saturation deficit increases).


52
instrument can begin to stabilize on a new dewpoint. A programmed delay
makes up the balance of the 30 sec required between measurements. At the
end of five scans (2.5 min), a complete temperature and dewpoint profile
is available to compute a Bowen ratio. A report on that profile is
printed at the option of the system operator (see Fig. 3-5).
To compensate for the approximately one-minute air sample travel
time from field to mixing chamber, temperature and dewpoint measurements
are offset by two levels. For example, the dewpoint at level 1 is mea
sured in the same sensor scan as the temperature at level 3. This ac
counts for extra statements at the beginning of the program which ensure
proper initialization, and for extra branching after sensor scans which
deal with the offset completion times of the temperature and dewpoint
profiles.
To guarantee that the dewpoint analyzer is- receiving the air. sample
from the level called for in the program, a mark voltage channel is mea
sured and checked in each scan of the sensors. In one particular posi
tion of the scanning valve, 12 volts are expected on this channel. If
the voltage measured is low or 12 volts are measured when not expected,
the data for the profile being collected are discarded and a message to
the operator is printed. The program makes one attempt to reposition the
valve and restart data collection. If this fails, another message is
printed and the programs are terminated.
When temperature and dewpoint measurements at all five levels are
complete, the data are passed to subroutine RATIO, which calculates a
linear temperature versus dewpoint regression relationship. Its slope is
multiplied by the appropriate constants (Eq. 3-8) to give the Bowen


60
(It should be noted that this correction did not affect the Bowen ratio
calculation, since it used only relative changes. The correction did
affect surface temperatures, which were not used in computing the energy
budget.)
The radiation sensors were calibrated against a recently purchased
(and calibrated) Epply Pyranometer.
On the whole, the thermopile/air sampling system developed worked
very well and produced excellent data. However, there were some situa
tions in which it could not function well. The system was protected from
almost all of these situations because calculation of a complete energy
budget was made conditional on temperature and dewpoint profile similar
ity. Latent and sensible heat fluxes were not calculated when the pro
file correlation coefficient was less than 0.95.
Profiles were, regularly dissimilar for a few time-periods in the
early morning and late afternoon, while temperature and dewpoint pro
files were reversing in direction. This dissimilarity occurred because
changes in the temperature profile generally preceded changes in the
dewpoint profile.
Sensible heat generated at the surface of the outermost radiation
shields was usually carried away by the air flowing over them. At very
low windspeeds, however, the warm air produced at the outer surface of
the lowest radiation shields could become entrained in the aspiration
air of mast arms above. This problem showed in profile correlation coef
ficients but was usually not so bad that energy budgets could not be
calculated. Under clear skies this effect was not as marked, presumably
because the radiation shields could more effectively radiate heat away.


STEEL
CHANNEL
ASPIRATING
FAN
Figure 3-3. Detail of Profile Measurement Mast Arm.


f (UNITLESS) G (LY/MIN)
94
TIME (TST,OCT 17, 1981)
Figure 5-6. Soil Heat Flux Parameter Data.


UNIVERSITY of
FLORIDA
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AUTHOR: Heimburg, Klaus
TITLE: Evapotranspiration : (record number: 339630)
PUBLICATION DATE: 1982
I
i
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specific and limited archive and distribution rights to the Board of Trustees of the
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Can I interest you in an excellent masters thesis? Hydrology of Some North-Central
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93
saturation vapor pressure curve, and the intercept as the average day
time saturation deficit.
The slope of the saturation vapor pressure curve and the satura
tion deficit are plotted for individual half-hour periods in Fig. 5-5b.
They are computed using the equation
T + T
s = 2.00 [(0.00738
+ 0.8072)7 0.00116] 5-6
from Bosen (1960), and
6ea = e*(Ta) ea 5-7
where the saturation vapor pressure at the air temperature is calculated
with the Magnus-Tetens formula (Tennessee Valley Authority, 1972)
7,5 Ta 1
e (T ) = exp
a
2.3026
T + 237.3 + 0,7858
Ia
The steady increase in the slope of the saturation vapor pressure curve
and the growth of the saturation deficit over the course of the day is
clearly evident.
Soil heat flux is graphed against net radiation in Fig. 5-6a. The
relationship is not smooth because the heat flux measurements were
rounded off to one significant figure (hundredths of ly/min). The aver
age daytime fraction of net radiation absorbed by the soil (1 f) is
represented by the slope of the line through the origin and the center
of the plotted data. The soil heat flux parameter is computed for half-
hour periods by
f 1 £ 5-9
and plotted in Fig. 5-6b. Even though soil heat flux (G) is low in the
morning relative to the afternoon, the soil heat flux parameter (f) is
very constant relative to the other parameters, because G/R is so small.


154
CA (7)
CB(7)
D
DAT(12)
DAT(25,2)
DATA
DPTCOR
DTEMP
EGG
EOT
GD
.HLTNT
HRNGL
HSENS
HV(T)
IPGM2(6)
ISSW(N)
ISSW(O)
ISSW(l)
ISSW(2)
ISSW(3)
ISSW(5)
ITIME(5)
Sensor calibration factor-slope for the 6 sensors in
RAD(6,2) and the windspeed sensor
Sensor calibration factor-intercept for the 6 sensors in
RAD(6,2) and the windspeed sensor
Pressure correction for dewpoint measurement (in Hg)
Array of sensor readings checked for voltage spikes in FILT
Array of last 25 surface temperature and net radiation
readings in TMTCH
Temporary name for measurements returned by voltmeter
Pressure correction for dewpoint temperature reading
Temperature difference calculated from the vapor pressure
profile (m/min)
Voltage from EG&G Dewpoint Analyzer
Equation of time (hrs)
Number of good measurements made by FILT
Latent; heat flux (ly/min) '
Hour angle of the sun (degrees)
Sensible heat flux (ly/min)
A function that calculates heat of vaporization as a
function of temperature
Voltmeter program word for the 6 measurements in RAD(6,2).
Each is coded for type of measurement, delay time, and
range of measurement
Sense switch number N on face of HP-2100 Minicomputer:
When on, causes Program MEASR to print the time, all
measurements and indexes for each measurement cycle
When on, causes MEASR to produce full half-hour report
with all data collected since last half-hour report
When on, causes MEASR to stop at end of next half-hour
report
When on, causes MEASR to print data from each set of
profiles collected
When on, causes Program ANALZ to print complete profile
fitting search
Time: ITIME(5), Day of year; ITIME(4), hour; ITIME(3),
minute; ITIME(2), second; ITIME(1), centisecond


103
ET Estimates with the Average TGR Method
Satellite data have two practical limitations that must be ad
dressed by any ET estimation method: they are only available at dis
crete sensing-system-determined time intervals, and they are intermit
tently incomplete because of cloud cover. Dealing with these situations
requires a method which can bridge the gaps between data sets.
The average T6R method does this by assuming that there is an ap
proximately linear correlation between temperature gradients and the
net radiation loads that cause them. As shown in the previous chapter,
this is the equivalent of assuming that the surface parametersthe
bulk air thermal conductivity, moisture availability, saturation defi
cit, slope of.the saturation vapor pressure curve, and the fraction of
net radiation warming the soilare constant. This assumption both de
fines an ET rate for any given net radiation load and reduces the prob
lem of computing cumulative ET to estimating the cumulative net ra
diation.
The convenience of this assumption has a cost in the accuracy of
the estimated instantaneous ET rates. As can be seen in Fig. 5-8, when
the solid data line lies higher than the dashed constant parameter
line, estimates by the average TGR method generally overestimate ET,
and vice versa. There is a pattern in the direction of these errors
(see Fig. 5-9). In general, it is not possible to predict the error
direction on a given day at a given time because the direction is a
function of the variation in parameters. However, the errors that re
sult from using the average TGR method to estimate instantaneous ET
rates are minimized in the process of fitting a line to the temperature
gradient/net radiation data points. Some error remains because use of


5
6. Can estimates made with area average data be of reasonable
accuracy when there are various vegetation types or net ra
diation regimes in the same pixel?
7. Ultimately, what factor most limits the accuracy of a given
remote estimation scheme?
The work described in this dissertation addresses many of these
questions. The emphasis is on how to most efficiently account for all
the factors affecting evapotranspiration, and how to extract as much
information as possible about the surface and its environment from re
mote data. Practical limitations such as the fact that satellite data
are available only at discrete time intervals and sometimes incomplete
because clouds prevent a surface temperature measurement are considered.
All ground-based measurements except air temperature were avoided; meth
ods to eliminate this measurement are suggested, but their investigation
was considered beyond the scope of this research.
It is assumed that estimates of net radiation and surface tempera
ture are, barring clouds, available at regular time intervals. The ques
tion of complex radiation temperatures is side-stepped by considering a
relatively simple pasture grass surface. Although a parameter that in
cludes the effect of wind on evapotranspiration is used, its functional
dependence on windspeed is not explored.
Research Approach
The overall approach to developing a remote evapotranspiration es
timation scheme was to compare estimates made with trial methods to ac
tual ET rates measured over a test surface. Accordingly, there were
three main areas of effort: the collection of a base of accurate ET
data, the theoretical development of an estimation method based on re
motely sensed data, and the testing of that method against the actual ET
measurements.


155
IWAIT(5)
LAG
LEVEL
LEVT
KFLAG
NADV
NBR
NCHAN
NDA(8)
NDE
NDL
NGD
NMEAS
NPROF
NTOT
NVALV
OAM
P
Delay between measurements: IWAIT(l) is delay between
levels 5 and 1, IWAIT(2) delay between levels 1 and 2,
IWAIK3) delay between levels 2 and 3, etc.
Delay time (in seconds) used to schedule MEASR when
ISSW(l) is on.
Level at which dewpoint is currently being measured
Level at which temperature is currently being measured
Flags for program SET:
0 default value
1 to prepare system for "cold" start
2 to recover when sampling valve is out of sync with
program
3 to run REPRT and ANALZ immediately, restart MEASR
after a delay when ISSW(l) is on
4 to run REPRT and ANALZ immediately, and schedule MEASR
for absolute start time at beginning of half-hour per
iod. Usual half-hour transition KFLAG
Number of levels temperature is measured in advance of
vapor pressure to compensate for air sample travel time
Number of Bowen ratios with greater than .95 correlation
coefficient
Channel number to be measured by FILT
Array containing letter abbreviations for wind direction
octants: NDA(l), N; NDA(2), E; NDA(3), S; NDA(4), W;
NDA(5), NE; NDA(6), SE; NDA(7), SW; NDA(8), NW
Wind direction octant with greatest number of occurrences
Wind direction octant with number of occurrences less than
or equal to NDE
Number of bad (noisy) measurements made by FILT
Number of measurements in subroutine TMTCH data array.
When 25 or over, TMTCH returns weighted averages.
Chronological number of profile being collected, starting
at beginning of half-hour period
Name used to save NPROF in COMMON
Current scanning valve position (ranges from 1 through 10)
Optical air mass (unitless)
Atmospheric pressure (in Hg)


92
60
CD
5 40
o
0)
^'o)20
I
I
(U
Q
0
o
o
o
CD
ms
' o
CO a>
60
i r
i r
(a)
J 1 L
J L
4 6 8 10
TIME (TST,OCT. 17, 198!)
Figure 5-5. Vapor Pressure Parameter Data.


176
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
310
730
0.02
-0.01

1.93
18.1
18.3
19.5
.791
800
0.05
-0.01
0.01
0.05
1.50
18.4
18.9
19.7
.981
830
0.11
-0.00
0.02
0.10
2.61
18.9
19.6
19.8
1.000
900
0.18
-0.00
0.03
0.15
3.46
19.3
20.1
19.4
1.001
930
0.37
-0.00
0.09
0.28
4.00
20.0
22.0
18.9
.997
1000
0.46
0.00
0.14
0.31
3.29
20.8
23.6
18.5
.999
1030
0.55
0.01
0.19
0.35
3.38
21.6
25.9
18.2
.998
1100
0.63
0.01
0.24
0.38
3.36
22.3
27.0
17.4
.997
1130
0.66
0.01
0.26
0.39
3.78
23.0
28.9
16.6
.998
1200
0.68
0.01
0.29
0.38
3.73
23.4
30.0
15.8
.998
1230
0.68
0.01
0.30
0.37
4.22
23.5
30.3
15.0
.997
1300
0.66
0.01
0.29
0.36
4.16
24.0
31.0
14.8
.996
1330
0.59
0.01
0.26
0.32
4.14
24.0
30.0
13.2
.993
1400
0.56
0.00
0.26
0.30
4.05
24.0
29.8
12.4
.996
1430
0.48
-0.00
0.22
0.26
4.04
23.9
28.9
11.6
.995
1500
0.39
-0.01
0.17
0.23
4.47
23.7
27.4
10.5
.994
1530
0.29
-0.01
0.12
0.17
3.59
23.5
26.0
10.6
.997
1600
0.17
-0.01
0.06
0.12
3.33
23.1
24.2
11.1
.992
1630
0.06
-0.01

2.34
22.6
22.2
11.1 .
.150
311
730
0.05
-0.04
_ _
0.02 '
6.1
'6.2
-.913
800
0.14
-0.03


0.61
9.1
9.4

.249
830
0.19
-0.02

--
2.31
11.7
11.6

.782
900
0.31
-0.02
0.07
0.26
3.83
12.8
13.5
8.2
.971
930
0.40
-0.01
0.18
0.23
3.65
13.9
16.7
7.7
.998
1000
0.48
-0.01
0.30
0.18
3.44
15.0
19.5
7.5
.999
1030
0.53
-0.00
0.37
0.17
2.68
15.8
23.1
7.5
.999
1100
0.59
0.00
0.39
0.20
1.66
16.6
24.6
7.6
.999
1130
0.62
0.01
0.40
0.22
2.03
17.5
26.9
7.6
.999
1200
0.64
0.01
0.41
0.21
1.35
17.9
28.5
7.5
.999
1230
0.63
0.01
0.41
0.21
1.18
18.6
29.2
7.5
.998
1300
0.62
0.01
0.39
0.22
1.62
19.3
29.3
7.6
.999
1330
0.58
0.01
0.35
0.22
1.61
19.7
29.0
7.7
.999
1400
0.52
0.00
0.31
0.21
1.88
20.6
28.5
7.8
.999
1430
0.45
0.00
0.25
0.19
1.93
21.1
27.6
7.8
.999
1500
0.36
-0.00
0.20
0.16
2.07
21.3
26.3
7.6
.997
1530
0.26
-0.00
0.14
0.13
1.75
21.4
24.7
7.6
.992
1600
0.15
-0.00
0.07
0.09
1.44
21.2
22.6
7.6
.973
1630
0.04
-0.01


1.58
20.5
20.0
7.6
.617
312
730
0.06
-0.03
_ _
0.00
3.9
4.5
~
.549
800
0.15
-0.02

--
0.00
7.2
7.9

-.648
830
0.20
-0.00
--
--
0.04
11.1
12.1
--
-.611
900
0.30
0.01

--
1.37
14.7
16.0

-.593
930
0.39
0.02


1.16
17.5
19.8

-.669
1000
0.45
0.02


1.37
19.1
23.2

-.837


The post-defense party thrown in my honor made the frustrations
encountered in this work seem tolerableeven worthwhile. I have Pattie
Everett, Bill Campbell, Pierce Jones, and Lisa Lucille Biles to thank
for this totally awesome affair, not to mention that Wild and Crazy
Guy, Terry Spires, and the overwhelming Special Guest Appearance of
The Sublime Ms. Shavonne Rhodes. Get down, tiny dancers!
TV


(C) NET RAD. (LY/min)
208
Figure 12. (cont.)


153
Main Data Arrays
E(5)*
ND(8)
DPT(5)
RAD(1,1)*
RAD(2,1)
RAD(3,1)
RAD(4,1)
RAD(5,1)
RAD(6,1)
ST (6)
T(10 )*
WSP
Air vapor pressure for 5 levels (mb)
Number of occurrences per wind direction octant: ND(1), N;
ND(2), E; ND(3), S; ND(4), W; ND(5), NE; ND(6), SE; ND(7),
SW; ND(8), NW
Dewpoint temperature for 5 levels (C)
Net radiation (ly/min)
Solar shortwave radiation (ly/min)
Reflected shortwave radiation (ly/min)
Atmospheric longwave radiation (ly/min)
Emitted longwave radiation (ly/min)
Soil heat flux (ly/min)
Soil temperature for 6 levels (C)
Air temperature for 5 levels (C). Completed temperature
profiles are stored in T(6) through T(10) until corre
sponding vapor pressure profile is completely measured.
Prefixed versions of this array (see below) have only 5
values.
Windspeed (m/s)
These array names may be prefixed by A, C, or T. Measurements are
first loaded into the nonprefixed array. Arrays that are prefixed by T
are "temporary" and'hold values used in the intermediate data reports.
Half-hour "average" values are summed in arrays prefixed with A, and
these values are stored for analysis in the following half hour in
"common" arrays prefixed with a C. The A-prefixed version of the
asterisked arrays has a second column for squared measurements, like
RAD does. These statistics are used to compute percent variations for
the half-hour report.
Other Names and Indexes
ABDO
ABR
ATC
AVG
B
BR(2)
C
Albedo
Average of Bowen ratios with greater than .95 correlation
coefficient
Atmospheric transmission coefficient
Filtered average voltage of reference thermocouple at
level 1 on profile measurement mast
Bowen ratio returned by RATIO
Bowen ratio statistics summations
Correlation coefficient returned by RATIO


152
Definition of Names
Subroutines and Functions
CUC0N(V0LTS,-1) Hewlett-Packard library function which converts volt
age from a copper-constantan thermocouple with ice point
reference temperature into degrees Centrigrade
FILT(NCHAN,IPGM,TOL) Function used to filter fence charger voltage
spikes out of low level signals. Argument requires chan
nel number (NCHAN), voltmeter program word (IPGM), and
noise tolerance (TOL).
FIND(VMARK) Subroutine used in Program SET to position air sampling
valve for first vapor pressure measurement. It returns
mark voltage to SET.
HV(T) Function that calculates heat of vaporization as a func
tion of temperature.
PR0FT(V,V0,Z0,DV,BV,RV) Subroutine in Program ANALZ which fits 5-level
profile (V) and calculates displacement height (DV) given
roughness height (ZO). Other arguments: VO is V at Z=0,
BV is the slope of the profile, and RV is the correlation
coefficient.
.RATIO(E,T,B,C) Subroutine in Programs MEASR and REPRT which computes
Bowen ratio (B) with diagonal regression of vapor pressure
(E) and temperature (T) profiles. Also returns correlation
coefficient (C).
STEP(VMARK) Subroutine used in Program MEASR to change position of
sampling valve and return mark voltage from air sampling
valve.
TMTCH(DATA,L,NMEAS,SVAL,DAT) Subroutine which imposes a 4 min time
constant on surface temperature and net radiation measure
ments by calculating a weighted average of past 25 mea
surements. The last measurement (DATA) and sensor identi
fication (L) are sent to the subroutine, and it returns a
"slowed" value (SVAL) to the main program. In order that
measurements made in the preceding half hour survive the
program swapping that takes place during the half-hour re
porting sequence (see Chapter 3), they are placed in
COMMON via DAT(25,2). When the system is started, NMEAS is
used to monitor the past data array to see if it has been
fi1led--after NMEAS=25 weighted averages are reported.
ZERO(AST,ARAD,AE,AT,AWSPD,ND,BR,NBR) Subroutine in Program SET that
initializes all surrmations used in calculating half-hour
averages.


CHAPTER 1
INTRODUCTION
Potential for Remote Evapotranspiration Estimates
The loss of water from the earth's surface by either evaporation
from soil and plant surfaces or transpiration by plants is called evapo
transpiration (ET). Along with rainfall and runoff, it plays a very sig
nificant role in determining the availability of water at the earth's
surface and the recharge to deep aquifers. Because water is critically
important to man's existence, ET estimation methods are important in
solving problems of water supply.
Water supply problems in relatively dry -areas have, long included
the estimation of crop water requirements, evaporation from reservoirs,
and evapotranspiration over aquifer recharge areas. As population has
grown, the demand for water has increased and interest in estimation
methods has become more widespread. Today, there is a growing need for
evapotranspiration estimates even in relatively wet areas, such as
Florida.
Present methods of measuring and estimating ET are diverse, depend
ing upon the specific purposes of the estimates and available data. On
the one hand are physically-based measurement techniques developed by
scientists. They provide accurate instantaneous ET rates for a specific
location, but require continuous measurements of such variables as air
temperature and vapor pressure, net radiation, and soil heat flux. Exam
ples of these techniques are the eddy flux correlation, energy
1


35
A different approach to solving the residual equation was taken by
Menenti (1980). In his approach, the simple residual equation is simpli
fied by Taylor series expansion around some central ET rate at a given
shortwave radiation level. All terms except those containing surface
temperature and albedo are eliminated, leaving the ET rate for a partic
ular surface a function of the central ET rate, its surface temperature,
and its albedo. No means to make cumulative daily ET estimates were sug
gested.
Temperature Gradient Response Methods
The two ET estimation methods developed in this study are steady-
state methods. They are based on the response of surface-to-air temper
ature gradients to varying levels of net radiation. One of these meth
ods, the average temperature gradient response method, is suitable for
use with satellite data.
The primary difference between this method and the simple residual
method is that it expresses the vapor pressure gradient in terms of the
temperature gradient, the slope of the saturation vapor pressure curve,
and saturation deficitan innovation first made in Penman's (1948) pio
neering work. This addition gives the method some protection against
"residual errors." For example, if the measured temperature gradient is
erroneously high, both the latent and sensible heat fluxes will be af
fected; there will not just be an increase in sensible heat and an equal
decrease in latent heat flux. Also, the method allows ET to be expressed
as a function of net radiation and parameters only (without explicit
mention of surface and air temperature). This feature makes ET calcula
ble when surface temperatures cannot be measured remotely but net


E (LY/min) H (LY/min)
196
Figure 10. Data and ET Estimates for Oct. 21, 1981. See p. 185 for
brief explanation of individual graphs.


7
methods. This required a set of assumptions, all of which are explicitly
identified in the derivation of the method.
The general objective of the method-testing was to validate the
general framework of the method and to assess the error contributions of
various parts of the method on instantaneous and cumulative ET esti
mates. The assumptions made during the development of the method were
individually examined; in this way, the relative importance of ground-
gathered ancillary data such as air temperature, saturation water vapor
deficit, windspeed, and soil temperature could be judged. The testing
was done with ideally accurate on-site measurements of net radiation,
surface temperature, air temperature, and evapotranspiration.
Experimental Site and Data Collection
An area of pasture at the University of Florida's Beef Research
Unit was used as the research surface. The site is located northeast of
Gainesville, Florida, as shown in Figure 1-1. It was chosen because it
is typical of northern Florida pasture areas, and was amenable to micro-
meteorologic measurement of a surface energy budget. The area was flat
with relatively uniform grass cover, and was large enough to ensure
well-developed temperature and vapor pressure profiles. The test surface
was a mixture of grasses: roughly 60-70% was bahiagrass (Paspa!urn
notatum), about 20-40% was smutgrass (Sporobolus polretii), and 5-10%
was white clover (Trifolium repens).
Evapotranspiration was computed by an energy budget/profile Bowen
ratio method from measurements of net radiation, soil heat flux, and
gradients of temperature and water vapor pressure over the pasture sur
face. A Hewlett-Packard 2100 computer and low-speed data acquisition
subsystem was used to automatically scan and measure the sensors,


127
estimate of wind run are the basis for a daily ET estimate with the
Penman method. The ATGR method uses several sets of net radiation and
corresponding surface-to-air temperature gradients, in effect evaluating
surface moisture conditions. As with the Penman method, the ATGR method
estimates should improve as they are applied to longer time periods.
The principal limitation of the ATGR method is that it is not yet
dependent on remote data alone; it still requires ground-measured air
temperatures and independent estimates of two surface parameters. How
ever, air temperatures are dependent on surface temperatures, so at
least pseudoempirical methods of estimating air temperature with surface
temperatures can be developed (Idso, 1981). Soil heat flux is quite
small for areas with closed vegetation canopies and thus does not pre
sent a significant problem with regard to the accuracy of the estimate.
Potential problems with the heat transport coefficient -have been identi
fied, and it can probably be evaluated with one of the wind models in
the literature (Thom and Oliver, 1977), possibly with a preliminary sur
face temperature correction.
The ATGR approach and the approaches developed for the HCMM pro
gram suggest a tradeoff between the amount of satellite and ground data
collected and the amount of data processing required in producing ET
estimates. The simulation approaches require only one or two sets of
remote data per day, but require a lot of ground-measured data to force
and provide boundary conditions for dynamic models. They also require a
good deal of computation to match ancillary data, trial values of sur
face conditions, and model results to observed surface temperatures.
The ATGR approach requires roughly ten times as much remote data, but


38
where R is net radiation absorbed by the surface,
E is the evapotranspirative or latent heat flux,
H is sensible heat flux, and
G is the soil heat flux.
It has already been shown that the rate of heat storage in the vegeta
tion layer and the rate of photosynthetic assimilation are negligible in
comparison to these terms.
The Bowen ratio is defined as the ratio of sensible heat flux to
latent heat flux: u
' 3 = f 3-2
In the energy budget/profile Bowen ratio measurement technique, net ra
diation and soil heat flux are measured directly. Latent and sensible
heat fluxes are determined indirectly by first measuring the Bowen ra
tio, and then computing the fluxes:
E = (R G) and 3-3
H=^t(R-G)
3-4
The Bowen ratio can be calculated from air temperature and water
vapor pressure measurements at various heights over the surface, pro
vided a number of experimental conditions are met. Over a uniform sur
face with adequate fetch, latent and sensible heat fluxes may be consid
ered to exist in the vertical direction only (no flux divergence). In
the turbulent boundary layer the fluxes at any instant can be described
as follows:
H =
E =
r v 3T
"pCPKH 3 Z
-epL l
P w3z
3-5
3-6
where p is air density,
c is specific heat capacity at constant pressure,
eH is the ratio of molecular weights of water and dry air,
L is the latent heat of evaporation of water,
P is the atmospheric pressure,


59
times, it was necessary to tune the instrument slightly differently than
Manual specifications. It was made more sensitive by setting the THK
potentiometer so that voltage on the test points was 200-260 mV, and
made faster by setting the GAIN potentiometer so that the test voltage
was 150-210 mV. The new settings sacrificed dewpoint analyzer response
time in large step changes in order to improve response time in the
smaller step changes normally encountered in the profiles. To ensure
that the dewpoint analyzer actually had time to settle on readings be
fore being read by the voltmeter, its output was spot-monitored on a
millivolt recorder.
The most difficult problem was the individual and cross-correlation
of the dewpoint analyzer, the thermocouple/thermopile air temperature
sensors, and the precision radiation thermometer. The dewpoint analyzer
output was calibrated according to the EG&G manual. Temperatures'at the
bottom and top of the scale were simulated by substituting precision
resistances for the mirror-temperature sensing thermistor; the analyzer
output at these simulated temperatures was matched to the factory stan
dard instrument output. The radiation thermometer was calibrated by mea
suring its output for known surface temperatures produced with a stirred
constant-temperature bath. A regression equation for the temperature vs.
output correlation was calculated and used in the programs.
It was not possible to cross-calibrate these temperature sensors
until the system was run in a light drizzle on Nov. 5, 1981. This situa
tion resulted in the same temperatures at all measured levels, near-zero
net radiation, and air that was near saturation, so the dewpoint, air,
and surface temperatures were approximately the same. The temperature
differences between sensors were used to correct the rest of the data.


86
effective heat transfer gradient, surface-to-air gradients are larger
in the afternoon than they are in the morning. This is because in the
afternoon, radiating surfaces lower in the canopy have also become
warm. Apparently, these surfaces make a relatively greater contribution
to the radiation surface temperature than they do to the sensible heat
flux via the effective heat transfer surface temperature. Although it
is not as extreme, this pattern is also observed on cloudy days, under
a diffuse radiation regime (Fig. 5-2).
One could reasonably expect radiation geometry to play a role in
creating differences between the radiation temperature and the effec
tive heat transfer temperature. At high sun angles, when direct sun
light is coming from angles close to the viewing angle of the radiation
sensor, less shaded area is visible to the sensor. The radiation tem
peratures should peak relative to effective heat transfer temperatures
when the angle of incidence of direct sunlight coincides with the angle
of view of the sensor. The slight upward curvature in the total/turbu
lent gradient correlation (Fig. 5-1) seems to confirm this effect, but
it is small in comparison to the morning/afternoon radiation tempera
ture hysteresis.
The apparent difference in the effective heat transfer surface
temperature and radiation surface temperature must be viewed as a poten
tial problem which may require modification of the equation used to com
pute surface temperature. A time-varying factor may be required, espe
cially in cases where the radiation geometry is further complicated by
surface slopes, as in mountainous areas.
Constancy of Parameters
The heat transport coefficient (h) and moisture availability (M)
are considered parameters in the strict TGR method, and they are


21
E =
dc w ae
p az
2-7
where t is momentum flux,
H is sensible heat flux,
E is latent heat flux,
Km, Kn, Kw are the eddy diffusivities of momentum, heat, and water
M vapor.
u
T
e
p
&
P
e
s the average horizontal windspeed,
s temperature,
s vapor pressure,
s the air density,
s the air specific heat at constant pressure,
s the latent heat of evaporation,
s the atmospheric pressure, and
is the ratio of molecular weights of water and dry air.
The similarity hypothesis, which was developed in the last half of the
nineteenth and early twentieth centuries (reviewed by Brutsaert, 1982),
proposes that the eddy diffusivities of momentum, heat, and water vapor
are all the same:
km = kh -fw
2-8
It was not until Prandtl's (1932) development of the mixing length
concept that general analytical treatment of eddy diffusivity began.
According to mixing length theory, it is argued that
,2 du
V2) = 1 Si
2-9
where l is the mixing length and
IT is the average windspeed perpendicular to z (horizontal).
By postulating that the mixing length increased with distance from a
surface (i = kz, where k is the von Karman constant), Prandtl went on to
derive an expression that accurately describes the variation of wind-
speed near a surface, the simple log wind profile. With parameters for
displacement height (Dwith dense vegetation, that height above the
surface where the windspeed vanishes) and roughness height (ZQ--a


77
type of area may also be approximated. For large forested areas, where
it can be assumed that f=l, Eq. 3-34 might work well. In both equations,
the only other estimate required is the slope of the saturation vapor
pressure curve, which is a known function of temperature.
Equation 4-35 assumes that moisture availability and saturation
deficit are unknown. The evapotranspiration equation generated has the
advantage that neither the psychrometric constant nor the slope of the
saturation vapor pressure curve needs to be evaluated. This makes the
equation easier to use, and since no division is involved, it is compu
tationally safe. The additional parameters required are the bulk trans
fer coefficient and the soil heat flux parameter. The former may be cal
culable from measurements of windspeed and estimates of surface rough
ness. This approach has a long history in the literature (see Chapter
2), but its adaptability for use with a surface temperature has not been
demonstrated. The soil heat flux parameter only varies ^20%, and might
possibly be estimated from near-infrared remotely sensed data, which
gives a good idea of vegetative cover. Because of its potential, simpli
city, and easy graphical interpretation, Eq. 4-35 is used in the method
verification part of this study.
The last two equations, Eq. 4-36 and 4-37, assume that moisture
availability and either the soil heat flux parameter or the bulk tran
sport coefficient are known. Since M is a normalized parameter, it can
be assumed to have various values in a constrained range. It is conceiv
able that these equations might then be of some use.
Extension to Totally Remote ET Estimation Method
The final step in making a method depend only on remotely sensed
data is to generate air temperature measurements from surface


28
The Penman (1948) approach is very closely related to the residual
approach. In addition to the wind function, it includes an expression
that relates the temperature gradient to the vapor pressure gradient via
the linearized saturation vapor pressure curve,
cs ea = s(Ts V + Sea 2-26
where s is the slope of the saturation vapor pressure curve, and
6e is the saturation deficit of the air.
cl
This approach has since been generalized to include subsaturated sur
faces (Barton, 1978), which allows ET to be expressed as a function of
net radiation, the moisture availability parameter (M), and the satura
tion deficit (e ):
a
E [S + hg 2.26
(See Chapter 4 for the full derivation.) Historically, Penman's method
was the first to combine the energy budget equation with a wind model to
evaluate ET. Although the residual approach also employs a wind model,
in common usage it is the Penman method that is referred to as the com
bination method. The Penman method's main advantage is that it is not
explicitly dependent on measurement of a temperature gradient; its prin
cipal disadvantage is that it requires information on moisture availa
bility of the surface.
The Bowen ratio approach (Bowen, 1926) assumes that in the fully
turbulent layer over the surface, transport of heat and water vapor are
similar (i.e., = K^). This allows eddy diffusivities to be avoided
altogether, and latent and sensible heat flux to be apportioned accord
ing to the relative strength of the temperature and water vapor pressure
gradients:


TEMPERATURE (C) HEIGHT (CM)
a VAPOR PRESSURE (MB)
11.2 11.4 11.6 11.8 12.0
VAPOR PRESSURE (MB)
Figure 3-1. Bowen Ratio Calculation from Measurements of Vapor
Pressure and Temperature. Note that the scale used
to plot vapor pressure profile in upper graph is the
same as the vapor pressure scale in the lower graph.
Data are from October 20, 1981, 9:30 TST (see Fig. 3-6).


CHAPTER 3
A SYSTEM FOR AUTOMATIC COLLECTION OF ET DATA
Overview
The energy budget/profile Bowen ratio technique was used to make
the evapotranspiration measurements needed for a data base in this re
search. It was selected because it is one of the methods that least dis
turbs the surface being measured, and when correctly applied, permits
measurements with an error on the order of 10% (Sinclair et al_., 1975).
The profile Bowen ratio method has been successfully applied to a vari
ety of surfaces (Sinclair et al_., 1975; Stewart and Thom, 1973; Black
and McNaughton, 1972, 1971). .
The theoretical basis of this method is developed first, followed
by a discussion of considerations going into the choice and use of the
sensors and other apparatus. Next, the automatic data collection system
that is assembled to make and report energy budget measurements is de
scribed. It consists of a computer-controlled scanner, voltmeter, gas
sampling arrangement, and a set of four interacting programs. The chap
ter concludes with a discussion of practical considerations that are
important in maintaining a high level of accuracy in the measurements
and the limitations of the data collection system.
Energy Budget/Profile Bowen Ratio Theory
As described in Chapter 2, the energy balance of a vegetated sur
face can be written:
R = E + H + G 3-1
37


8
Figure 1-1. Location of the University of Florida Beef Research Unit


117
The parameters were calculated for each time period (according to
Eqs. 5-2, 5-5, 5-6, 5-7, and 5-9) and then averaged. This calculation
is equivalent to the line-fitting procedure used in Figs. 5-3, 5-4,
5-5, and 5-6. The parameter data and temperature gradient/net radiation
correlation for five of the days listed in Table 5-2 are graphed in the
(a), (b), (c), (d), and (f) parts of Figs. 8, 9, 10, 11, and 12 in
Appendix D.
The calculated and observed values of A show a better degree of
agreement than do the values of B. This can be traced to the cross-cal
ibration of the surface and air temperature sensors. If they are not in
agreement, the temperature difference due to lack of cross-calibration
becomes part of the surface-to-air temperature difference. This system
atic error directly affects the intercept (B) of the temperature gradi
ent/net radiation correlation. Indirectly, it also affects the value of
A calculated using an average value of the air transport coefficient.
For example, if the surface temperature is slightly high relative to
the air temperature, temperature gradients will be overestimated, and
the value of B obtained from the temperature gradient/net radiation
correlation will be high. This means that B will be less negative than
it ought to be, or too small in absolute value. Indirectly, a high sur
face temperature measurement will result in a low air transport coeffi
cient, which will produce a correspondingly high calculated value of A
(Eq. 4-28). The surface and air temperature cross-calibration used in
this analysis was obtained from time periods in which there was little
net radiation and immeasurably small temperature gradients, as de
scribed on p. 59.


44
min to 10% or less of their amplitude. In the case of the dewpoint sys
tem, 11.5-L mixing chambers with a flow rate of 3 L/min were used.
To maintain the proper correlation between dewpoint and temperature
readings, it was necessary to introduce the same time constant into the
temperature-sensing system. The appropriate time constant was determined
experimentally by varying the air flow rate over the aspirated thermo
piles and subjecting them to different temperature differences. It was
found that at a set air flow rate, measured time constants varied with
the temperature difference applied to the thermopiles. As a result, the
air flow rates were adjusted so that a 4-min time constant resulted for
temperature differences in the average operating rangetemperature dif
ferences in the range of 0.2 to 0.3C.
The 4-min time constant was also introduced into the surface tem
perature and net radiation measurements. Sensor response was slowed dig
itally by using weighted averages of the most recent 25 sensor readings.
Each time a complete temperature and vapor pressure profile was
measured (every 2.5 min), the correlation coefficient between tempera
ture and dewpoint measurements was calculated. This provided a running
check on the quality of the measurements and the current similarity of
the profiles.
Data Collection Equipment
The overall schematic for the thermopile/air sampling system is
shown in Fig. 3-2. The major parts are the data acquisition system, the
air sampling mast, the mixing box, and the signal cables and tubing
which connect them.
A computer-controlled data acquisition system was used because of
the large number of measurements and extensive calculations that this


E (LY/min) H(LY/mm)
191
Figure 9. Data and ET Estimates for Oct. 18, 1981. See p. 185 for
brief explanation of individual graphs.


104
the correlation (Eq. 4-27) physically corresponds to using average val
ues of the parameters.
The process of fitting a line to the temperature gradient/net ra
diation relationship ensures good cumulative ET estimates. As can be
seen in Fig. 5-8, fitting balances the deviations of the data around
the dashed regression line used to estimate ET. Errors in estimates in
one direction at a particular time of day are thus balanced by errors
in the other direction at other times, as shown in Fig. 5-9. Good cumu
lative ET estimates result because errors in instantaneous ET estimates
made in the same measurement period tend to cancel each other as they
are summed over the period.
There are some potential sources of unbalanced errors. The "belly"
in the temperature gradient/net radiation relationship may introduce a
bias on the side of underpredicting ET, because there is no compensat
ing bulge on the other side of the straight line. However, since the
belly lowers the intercept of the temperature gradient/net radiation
correlation, a compensating bias is introduced. The lowered intercept
causes ET to be overestimated at all levels of net radiation by in
creasing the constant "advected" component of ET. The method is obvi
ously very sensitive to B and the daylength used in cumulative esti
mates.
It is possible to intentionally bias the average TGR method with
specific measurement schedules. For example, the purpose of the mea
surements might be to estimate net daily ET (total ET less the amount
of dew evaporated). By using only afternoon surface temperatures and
net radiation, the influence of the low morning temperature gradients
is avoided. This results in overestimating morning sensible heat flux


23
A number of wind profiles and corresponding eddy diffusivity treat
ments both with and without stability corrections have been developed.
(These are referred to as wind models.) None are used in this study, but
the fact that bulk air transport is theoretically and experimentally
adequately understood is important in supporting the remote-sensing
method developed. All remote-sensing methods involve a wind model of
some kind to help evaluate sensible and latent heat fluxes.
Latent and Sensible Heat Flux Expressions
In application, the flux between two specific points (z^ and z^)
that have a gradient between them must be evaluated. Since eddy diffu
sivity in general varies with the distance from a surface (Eq. 2-11),
the latent and sensible heat transport equations (Eqs. 2-5, 2-6 and 2-7)
must be integrated along the direction of transport and between the
points of application (Monteith, 1973). Assuming that .all parameters
except diffusivity are constant between the two levels and that the flux
in question is steady (or that flux storage in the layer between levels
is negligible),
H (T1 T2>
'2 dz
and
pLe (el e2}
E = p
dz
2-14
2-15
z, y77
The integral in the denominator of these equations, when evaluated, rep
resents the lumped transport properties between points z^ and z^ away
from the surface. From the preceding subsection, it is understood that
these integrals can be evaluated with various wind models for K2(z).


76
depend both on the accuracy with which A and B can be determined, and
which of the parameters are most conveniently supplied from other mea
surements .
In general, the most difficult parameter to estimate independently
is moisture availability. Equations 4-33, 4-34, and 4-35 assume that it
and one of the other parameters are unknown. It can be anticipated that
the first two of these equations will have difficulties with low satura
tion deficits; Eq. 4-34 predicts infinite ET as the saturation deficit
nears zero. This is a result of having to express the parameters in
terms of the saturation deficit. From the substitutions, it is clear
that 6e must remain larger than Bs in order for physically real (posi-
a
tive) parameter values to result. Equation 4-33 seems to be the most
sensitive to low saturation deficits since it is meaningless even when
Se= is equal to Bs; Eq. 4-34 reduces to E ='fR with this condition (no
a
sensible heat is generated; all available net radiation is consumed in
evapotranspiration).
Equations 4-33 and 4-34 are also very sensitive to the value of B
obtained from the temperature gradient net radiation correlation. This
presents another potential problem in their use because the clear sky
data collected in a given estimation period may not be able to estimate
B at an accuracy level commensurate with its influence on the ET esti
mate. Once the behavior of B is better known, however, these equations
may become useful in areas where the least is known about the surface.
Saturation deficit is probably the parameter with the least spatial var
iability, and since it is directly measurable it can be estimated for
large areas. Equation 4-33 might be useful over a large grassland area
or large area of short crops since the transport coefficient of this


CHAPTER 5
VERIFICATION OF THE TEMPERATURE GRADIENT RESPONSE
ET ESTIMATION METHOD
Overview
The central idea of the temperature gradient response (TGR) ap
proach is to use the changes in the surface-to-air temperature differ
ence relative to corresponding changes in net radiation in lieu of sur
face parameters to estimate ET. A temperature gradient model is used to
determine the surface parameters from the temperature gradient re
sponse; these are then used in calculating ET rates.
Use of the temperature gradient model, which expresses the funcr
tional relationship between temperature gradients, net radiation, and
surface parameters, 'involves a number of assumptions and approxima
tions. Since the accuracy of the eventual ET estimate is limited by
this model and ancillary approximations, verification of the TGR meth
ods is carried out in stages. Initially, the assumptions required are
individually examined. Then the implication for both the strict and
daily average TGR methods is demonstrated. For the most part, this is
done with data from a clear fall day, October 17, 1981.
The daily average TGR method is most suited for use with satellite
data. It is tested with practically all data collected. First, measured
temperature gradient/net radiation correlations are compared to those
predicted with independently measured constant parameters. Then the ET
estimates made with the correlations are compared to measured ET rates.
82


REFERENCES
Allen, L.H. Jr., C.S. Yocum, and E.R. Lemon. 1964. Photosynthesis Under
Field Conditions. VII. Radiant Energy Exchanges Within a Corn Crop
Canopy and Implications in Water Use Efficiency. Agron. 0. 56:
253-259.
Allen, L.H. Jr., J.F. Bartholic, R.G. Bill, Jr., A.F. Cook,
H.E. Hannah, K.F. Heimburg, W.H. Henry, K. Hokkanen, F.G. Johnson
and J.W. Jones. 1980. Chapter 5.6, Evapotranspiration Measure
ments. _In^ Florida Water Resources, NAS10-9348 Final Report, IFAS,
University of Florida, in cooperation with NASA and the South
Florida Water Management District, pp. 5.6-1-88. (Technical Re
search Report).
American Society of Agricultural Engineers. 1966. Evapotranspiration
and its role in water resources management. Proceedings, Chicago,
IL, Dec. 5-6, 1966. ASAE, St. Joseph, MI.
Barton, I.J. 1979. A parameterization of the evaporation from non-
saturated surfaces. J. Appl. Met. 18:43-47.
Black, T.A. and K.G. McNaughton. 1971. Psychrometric apparatus for
Bowen-ratio determination over forests. Bound. Layer Met.
2:246-254.
Black, T.A. and K.G. McNaughton. 1972. Average Bowen-ratio methods of
calculating evapotranspiration applied to a Douglas fir forest.
Bound. Layer Met. 3:466:475.
Bosen, J.F. 1960. A formula for approximation of saturation vapor
pressure over water. Monthly Weather Rev. 88:275-276.
Bowen, I.S. 1926. The ratio of heat losses by conduction and by
evaporation from any water surface. Phys. Rev. 27:779-87.
Brutsaert, W. 1982. Evaporation into the Atmosphere. Theory, History
and Applications. D. Reidel Publ. Co. Boston. 283 pp.
Businger, J.A. 1973. Aerodynamics of vegetated surfaces. _In Heat and
Mass Transfer in the Biosphere, De Vries, D.A. and Afgan, N.H.,
eds., Scripts Book Co., Washington, D.C. 594 pp.
Carlson, T.N. and F.E. Boland. 1978. Analysis of urban-rural canopy
using a surface heat flux/temperature model. J. Appl. Met.
17:998-1013.
Carlson, T.N., J.K. Dodd, S.G. Benjamin and J.N. Cooper. 1981. Satel
lite estimation of the surface energy balance, moisture avail
ability and thermal inertia. J. Appl. Met. 20:67-87.
131


26
Energy Budget ET Estimation Strategies
There are two major ways in which the energy budget and gradient
equations can be solved. The physically more realistic method is based
on dynamic simulation of the heat transfer processes; the other method
is based on a cruder description of the surface and steady-state analy
sis of the surface heat exchange processes.
Gradient expressions like those in Eqs. 2-5, 2-6 and 2-7 are used
in both approaches. The difference is that in simulations the expres
sions are applied over arbitrarily short distances and time steps ac
cording to the level of detail required in the application. When trans
port is in one direction, as it is considered to be in most of the prob
lems encountered in ET measurement or prediction, the medium through
which the flux is transported is thought of as consisting of layers per
pendicular to the direction of transport. Fluxes through each layer can
then be computed individually for each time step, allowing the treatment
of flux transients as well as the treatment of differing transport prop
erties of the layers. In the steady-state approaches the gradient ex
pressions are applied over the entire distance between measurements, and
transients are ignored.
Simulation models consist of an interdependent system of equations
which describe the exchange of latent, sensible, and soil heat flux with
the vegetation layer and the air or soil, and also the transport of la
tent, sensible and soil heat between layers. This system of equations is
solved iteratively using solar and atmospheric radiation data as a forc
ing function and quantities such as air temperature, vapor pressure, and
soil temperature as boundary conditions. Generally, unknown surface pa
rameters are chosen such that simulated surface temperatures match


108
gradient/net radiation relationship. Note that Eq. 4-25 is non-linear;
the effects shown in Figs. 5-10 and 5-11 are not additive.
The parameter apparently causing the most short-term variations is
bulk thermal conductivity. Part of this variation is expected; it is
dependent on changes in radiation temperature relative to effective
heat transfer temperature, as well as windspeed. However, it can be
argued that some of the variation is numerical in origin. Temperatures
were rounded to the nearest tenth of a degree, and sensible heat flux
to hundredths of ly/min. This introduced some "artificial" variations
into the calculated thermal conductivities, particularly early in the
morning and late in the afternoon when temperature gradients are small.
The fact that considering h constant leads to smoother, more reasonable
moisture availability estimates (see Fig. 5-4b) also supports this ar
gument.
The change in slope of the saturation vapor pressure curve varies
with the increase and decrease in air and surface temperatures; as
shown in Fig. 5-10, it leads to higher gradients in the morning than in
the afternoons. Saturation deficit has the same effect. Changes in
these parameters impose a general hysteresis in the temperature gradi
ent/net radiation relationship. All other parameters being constant,
near-surface temperature gradients would be stronger in the mornings
than in the afternoons because a reservoir of cold air builds up over
night. As the surface and the cool air increase in temperature, the
vapor pressure gradient (both components) becomes stronger relative to
the temperature gradient. This favors latent to sensible heat loss,
thereby causing relatively weaker temperature gradients in the after
noon .


CHAPTER 4
THEORETICAL BASIS OF THE TEMPERATURE GRADIENT RESPONSE
ET ESTIMATION METHOD
Overview
The key problem in developing a remote ET estimation method is de
scribing the vegetation and air layer at the surface so as much informa
tion as possible about its energy budget can be gained from the surface
temperature and net radiation. In addition, there is the question of how
much ancillary data is necessary for acceptable levels of accuracy in
the estimates. Previous approaches to these problems were outlined in
Chapter 2.
The methods developed in this chapter are based on the response of
surface-to-air temperatures to varying net radiation loads. First, a
functional relationship that describes the dependence of the surface-to-
air temperature gradient on net radiation and other factors is derived.
This temperature gradient response (TGR) model is used with surface tem
perature, air temperature and net radiation data to evaluate surface
parameters, which are then used in an adapted version of the combination
equation to estimate evapotranspiration. Two methods of making estimates
are developed. The first is physically strict, with a minimum of assump
tions; the second is more approximate with correspondingly fewer data
requirements.
For the sake of simplicity, the derivations that follow are in
terms of surface temperature (T ) and net radiation (R) rather than the
direct remote measurements, reflected (Qr) and emitted (Q ) radiation.
62


119
Table 5-3. Quality of ET Estimates made with' the ATGR Method. The table
below gives two measures of the quality of ET estimates for
each of two methods of calculating instantaneous ET. The
first measure of quality is the slope intercept and regres
sion coefficient of a line fit to the relationship between
ET estimates and measured ET rates. The second is the slope
of a line describing the same relationship, except forced
through the origin.
Date
Oct.
Calculated
average
with daily
h and f
Calculated with average
conditions h and f
Slope
2
Intercept R
Cum.
Err.
Slope
2
Intercept R
Cum.
Err.
17
.88
.03
.96
.99
.84
.03
.96
.97
18
.52
.04
.97
.68
.86
.04
.97
.99
20
.98
.01
.92
1.02
1.09
.00
.92
1.11
21
.94
.01
.98
.98
.90
.01
.98
.95
22
.93
.02
.99
.99
.77
.03
.99
.88
' 23
1.14
-.03
.98
1.05" .
.79
-.01
.98
' .74
28
1.14
-.02
1.00
1.06
1.07
-.02
1.00
1.00
29
1.23
-.03
1.00
1.09
1.11
-.03
1.00
.99


192
Figure 9. (cont.)


116
It can be shown that the temperature gradient/rtet radiation corre
lation is a result of the average parameters by comparing estimates of
A and B computed using independently estimated values of the parameters
to A and B computed by regression equations. Table 5-2 lists average
parameter values for most of the fall days on which data were collected
and corresponding A's and B's calculated by Eqs. 4-28 and 4-29 (using
averaged parameters) and by Eqs. 4-30 and 4-31 (using measured net ra
diation and surface-to-air temperature gradients).
Table 5-2. Comparison of Average and Correlation Estimated A and B.
Numbers in parentheses are the coefficients of variation
of the parameters expressed as percentages.
Oct
h
M
f
s
6ea
^avg
a
corr
Bavg
^corr
17
.034
.13
.92
2.6
21
18.2
17.5
2.6
2.2
(13)
(17)
(2)
(7)
(9)
18
.037
.13 '
.92
2.6
20
16.7
12.8
2.6
0.8
(16)
(28) .
(4)
(7)
(10)
20
.038
.13
.94
2.0
16
17.7
14.0
2.2
0.6
(23)
(14)
(2)
(13)
(18)
21
.033
.15
.92
2.3
17
18.2
14.5
2.6
1.0
(11)
(18)
(4)
(6)
(ID
22
.031
.18
.94
2.6
18
18.2
16.5
2.8
1.7
(12)
(32)
(1)
(12)
(25)
23
.026
.24
.91
2.8
21
20.2
14.9
3.8
0.4
(36)
(52)
(4)
(10)
(21)
28
.033
.18
.98
2.1
11
19.0
15.7
1.8
0.6
(ID
(26)
(3)
(18)
(28)
29
.031
.15
.96
2.2
12
20.3
13.7
1.9
0.2
(14)
(16)
(2)
(10)
(13)
31
.041
.33
1.05
1.4
2
15.0
8.9
0.5
-0.3
(32)
(87)
(12)
(5)
(65)


79
Another approach would be to simulate air temperature with a linear
combination of particular pixel temperatures. This involves empirically
choosing a set of reference pixels and determining coefficients for an
equation of the form:
T = an + a,T + a0T + . .
ci 0 1 s ^ 2 s ^
4-40
Both the length of time these coefficients are accurate and the extent
of the pixels for which they can be used to generate air temperature
measurements are important considerations in this approach. It should be
noted that similar considerations are involved in generating air temper
ature measurements for all pixels from a limited number of ground sta
tions.
The approaches suggested above are not developed any further in
this study.
Review of Assumptions
At the outset, the surface was conceived as a radiation-absorbing
(vegetation) layer, in contact with an air layer above and a soil layer
below. Energy fluxes inside the absorbing layer were considered irrele
vant, and energy fluxes to and from the surface were considered one-di
mensional and normal to the surface. It was assumed that the sensible
heat flux could be calculated from the surface-to-air temperature dif
ference (i.e., that the radiation surface temperature is representative
of the effective heat transfer surface temperature). It was also assumed
that the vapor pressure gradient could be represented in terms of this
temperature difference and the saturation deficit of the air by way of
the linearized saturation vapor pressure curve. The time derivative term
and the photosynthetic heat flux term were considered negligible in the
energy budget equation.


ET (LY/m¡n)
Figure 11. (cont.)


34
possible to construct a map of instantaneous evapotranspiration rates.
For regional estimates, the rates computed for subareas were weighted by
the total area with that particular ET rate and summed.
The Seguin (1980) approach to thermal conductivity in the surface
air layer was formulated in terms of a resistance. It used the simple
log law wind function with surface roughness to evaluate the resistance
to sensible heat flux; no stability corrections were made. Measured
windspeed, air and soil temperature, remotely measured surface tempera
ture, and estimated albedo and soil conductivity were required to esti
mate instantaneous ET rates. Regional ET rates were estimated by multi
plying areas with different surface temperature and surface roughness
combinations by their individual ET rates.
Soer (1980) also used a resistance formulation of the sensible heat
flux. It included stability corrections based on the Monin-Obukhov
length and the Businger-Dyer semi-empirical mass and heat transport
equations. In other particulars it is practically identical to the
Seguin approach.
Price (1977, 1980) has developed the energy budget equation in
terms of time averages in an effort to determine surface thermal inertia
using remotely sensed maximum and minimum surface temperatures. He has
since (Price, 1982) used this approach in conjunction with the TELL-US
model to estimate daily ET rates. First a preliminary estimate is made
with a residual equation like Eq. 2-24, except that time average air and
surface temperatures and windspeed are used. The daily ET value obtained
is then corrected with a regression equation developed from a set of
corresponding Price method estimates and TELL-US simulation estimates.


141
Program MEASR
PROGRAM MEASR(3,90)
C*****MEASR CONTROLS AIR SAMPLE FLOW TO DEWPOINT ANALYZER, SCHEDULES
C*****AND MAKES ALL MEASUREMENTS AND PERFORMS PRELIMINARY CALCULATIONS
COMMON CST(6),CAT(5),CAE(5),CRAD(6),TSURF,HSENS,HLTNT,CWSP,R
*AST(6),AT(5,2),AE(5,2),ARAD(6,2),AWSPD,ND(8),NBR,NTOT,BR(2),
*KFLAG,NVALV,LEVEL,VMARK,RAD(6,2),DPTC0R,NADV,WSPD,T(10),
*NMEAS,DAT(26,2)
DIMENSION E(5),ITIME(5),DPT(5),
*TRAD(6),CB(7),CA(7),IPGM2(6),IWAIT(5)
INTEGER CHAN1(4),CHAN2(6),ANALZ(3)REPRT(3),SET(3)
DATA CHAN1/111,112,113,115/,CHAN2/14,101,102,100,104,109/,
*REPRT/2HRE,2HPR,2HT /,ANALZ/2HAN,2HAL,2HZ /,SET/2HSE,2HT ,2H /
DATA CA/29.40,127.88,142.04,35.4,3210.,104.5,9.37/,
*CB/0.,0.,0.,0.,59.5,0.,0./,IPGM2/3042B,3042B,3042B,3042B,
*3043B,3042B/,IWAIT/-30,-15,-14,-12,-16/
HV(T) = 597.3-.566*T
GO TO 30
25 CALL EXECU2,0,2,0,-23)
C*****VALVE POSITION CHECK(USUAL RETURN, START OF EACH MEAS. SEQUENCE)
30 IF(VMARK .GT. 6.)35,45
35 WRITE(6,40 )
40 FORMAT(IX,"VALVE POSITION NOT IN SYNC WITH PROGRAM.WILL TRY ",
*"RESTART")
KFLAG =2
GO TO 140
45 NVALV = NVALV+1
LEVEL = LEVEL+1
LEVT = LEVEL+NADV
C*****SUSPEND PROGRAM EXECUTION BETWEEN MEASUREMENTS
IF((NPROF .EQ. 0) .AND. (LEVEL .EQ. 1))55,50
50 CALL EXEC(12,0,2,0,IWAIT(LEVEL))
55 TBASE =0.0
DTEMP = 0.0
C*****MEASURE TEMPERATURE AT PROFILE BASE
AVG = FILT(108,3042B,.000002)
TBASE = CUC0N(AVG,-1)
IF((LEVT .EQ. 1) .OR. (LEVT .EQ. 6))68,60
C*****LOOP TO DETERMINE TEMPERATURE AT LEVT VIA THERMOPILES
60 NDT = LEVT-1
IF(LEVT .GT. 6) NDT = LEVT-6
DO 64 K=1,NDT
DTEMP = DTEMP+2451.* FILT(CHAN1(K),3042B,.000002)
64 CONTINUE
68 T(LEVT) = TBASE-DTEMP
C*****LOOP TO MAKE OTHER MEASUREMENTS
NMEAS = NMEAS + 1
DO 72 1=1,6
DATA = FILT(CHAN2(I),IPGM2(I),.000002)
DATA = (CA(I)*DATA+CB(I))


17
The Energy Balance Approach to ET Estimation
The Energy Budget Equation
The three elements of evapotranspiration (the absorption of water
from the soil or plant surfaces, the absorption of thermal energy from
the plant canopy, and the flux of water vapor through the air over the
surface) provide at least three fundamental approaches to evapotranspi
ration measurement. These have been referred to as the water budget,
energy budget, and aerodynamic approach, respectively. All previously
developed remote ET estimation methods, the remote technique developed
in this study, and the ground truth measurement technique used in this
study are founded on the energy budget equation.
The energy balance of a vegetation and air layer can be written
R-E-H-G-P-S = 0, 2-1
where R is the net radiation flux absorbed '(from p.15, R = Q +Q -Q -Q )
E is the latent heat flux, are
H is the sensible heat flux,
G is the soi1 'heat flux,
P is the photosynthetic heat flux, and
S is the time rate of heat flux storage in the vegetation/air
layer.
Here energy "flux" is used to describe energy "flux density," i.e., the
energy flow per unit time through a unit area. All terms are in these
units.
Because of inherent measurement difficulty and sensor limitations,
the energy budget components can only be measured to within about 10% of
their actual values (Sinclair et _al_., 1975). Since some of the smaller
components are actually indistinguishable from measurement error, they
need not be considered.


I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Heaney~
Professor, Environmer
Sciences
Engineering
This dissertation was submitted to the Graduate Faculty of the College
of Engineering and to the Graduate Council, and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
December 1982
Dean, College of Engineering
Dean, Graduate School


29
2-27
where subscripts 1 and 2 refer to two levels in the fully turbulent air
layer. This approach is free of a wind model, but it requires very accu
rate measurement of temperature and vapor pressure gradients. It is dis
cussed in detail in Chapter 3.
Remote ET Estimation Methods
Surface Temperature and Net Radiation
Satellite-borne sensors can measure the amount of radiant energy
coming from a particular surface area element in a particular wavelength
interval. For environmental applications, the wavelength intervals mea
sured are divided into the visible, thermal, and microwave regions of
the electromagnetic spectrum, yielding measurements of reflected solar,
emitted thermal, and microwave radiation. So' far, all £T estimation
methods designed for use with satellite data only employ the visible and
thermal wavelength ranges.
Net radiation is the largest component of the surface energy bud
get, and surface temperature plays a role in determining all the energy
budget components. Usually, measurements of reflected solar and emitted
thermal radiation measurements are used to estimate net radiation and
surface temperature. Methods to estimate ET are then based on these net
radiation and surface temperature estimates.
With a clear sky and proper consideration of the atmosphere's
transmission properties, surface temperature can be determined directly
from emitted thermal radiation:
Q
e
2-28


49
Table 3-2 Sensor Identification
Measurement
Sensor Make & Model No.
Ser. No.
Net Radiation
Swissteco Net Radiometer
6990
Incoming Shortwave Radiation
Epply Pyranometer 8-48
12876
Reflected Shortwave Radiation
Epply Pyranometer 8-48
10000
Surface Temperature
Barnes IT-5 (Spring 1981)

Barnes IT-3 (Fall 1981)
521
Dewpoint Temperature
EG&G 880-Cl
1409
Windspeed and Direction
R.M. Young 6101 and 6301

Air Temperatures
Custom-made Thermopiles

Reference Temperature
Omega Engineering MCJ-T

Soil Heat Flux
Micromet Heat Flow Disk
282
Air was pumped continuously from each sample port on the mast
through ^100 m of heated insulated polypropylene tubing and the gas sam
pling apparatus in the instrument room. In the "mixing box," air first
passed through flowmeters, then the mixing chambers, the scanning valve,
and the air pump. Samples from each level were drawn sequentially
through a sampling port, a separate sample flowmeter, and the dewpoint
analyzer. All equipment except the pump and analyzer were contained in
side a heated, insulated plywood box (see Fig. 3-4) to prevent condensa
tion problems.
The scanning valve was controlled from the data acquisition compu
ter. The sampling port was turned from one air source port to the next
by an electric motor powered for a precise fraction of a second. This
was done by a relay control circuit that was designed to sense scanner
closure. Thus a program statement calling for a measurement of the scan
ning valve control channel resulted in changing the position of the
valve. After each change, the valve position was checked to ensure that
the programs and valve were synchronized.


NET RAD. (LY/nnih)
203
Figure 11. (cont.)


30
where e is the emissivity of the surface,
a is the Stefan-BoTtzmann constant, and
T is the surface temperature.
Solving for T ,
T
s
2-29
In principle, net radiation is calculated according to the equation
2-30
The upwelling components, reflected (Qr) and emitted (Qg) radiation, are
directly measurable by satellite given atmospheric transmission proper
ties. The solar radiation incident at the surface (Qs) is known as a
function of date, time of day, location, and atmospheric absorption
(Tennessee Valley Authority, 1972). Atmospheric radiation (Q,) can be
a
similarly estimated.
Some of the ET estimation methods discussed in. the following sec
tions are designed for use with satellites that provide only thermal
data from the surface. These methods express the net shortwave radiation
as a function of estimated incident solar radiation (Rs) and albedo (a):
Qs Qr = a a)Qs
2-31
Simulation Methods
In 1978, NASA launched the Heat Capacity Mapping Mission (HCMM).
The polar orbit of the HCMM satellite was designed to collect maximum
and minimum temperatures of the earth's surface, and groups worldwide
were funded to study the maximum-minimum temperature data. Several
groups adapted or developed simulation methods to bridge the long time
intervals (12 hours) between data sets. Examples of models used are
Carlson and Boland (1978), Soer (1977), and Rosema et al. (1978).


16
However, when the purpose is to make total evapotranspiration estimates,
these exchanges are ignored, and only the energy fluxes entering or
leaving its boundaries are considered.
Besides the radiant energy pathways (R) and heat energy stored in
the plant canopy, Fig. 2-1 shows the dependence of the surface energy
balance, and thus evapotranspiration, on factors in the environment of
the surface. Heat that is lost to (or gained from) the air as sensible
heat is not (is) available for evapotranspiration. This flux is depen
dent on the air temperature (T ) and the thermal transport properties of
a
the air, represented by the eddy thermal diffusivity (K^) in the figure.
When the air temperature is cooler than the surface temperature of the
canopy, sensible heat moves from the canopy into the air. When the can
opy is cooler than the air, it absorbs heat energy from the air. There
is an analogous heat flux pathway to. the soil, dependent on soil temper
ature (T ) relative to the canopy temperature (T ), and the thermal con-
9 s
ductivity of the soil (X).
The right half of Fig. 2-1 shows the pathway of water through the
surface system. It originates in the soil and moves through plant tis
sues into the leaves, where it evaporates. Depending on the vapor pres
sure inside the leaves (e^), the vapor pressure in the surface air layer
outside the leaf (e$), and the stomatal conductivity (Cs), water vapor
then diffuses through stomata into the air around the leaves. From the
surface layer water vapor diffuses into the air, depending on the rela
tive vapor pressures of the surface layer and air (e,. and e ) and the
eddy water vapor diffusivity (K^).


2
budget/profile Bowen ratio and Penman methods (American Society of Agri
cultural Engineers, 1966; Brutsaert, 1982).
On the other hand, water use planners and water supply engineers
have developed methods which produce daily to monthly estimates for
larger areas. In locations where such records are kept, these methods
are based on climatologic data. They are generally founded on some phys
ical correlation, but all involve empirical adjusting factors for vege
tation type, air humidity, altitude and the like. Examples are the
Blaney-Criddle method, the radiation method, the Penman method, and the
pan evaporation methods (Doorenbos and Pruitt, 1977).
The weather stations which provide the base information for these
methods are widely scattered. On the average, each station in the United
States represents an area on the order of 100 mi square (Price, 1982).
Regional estimates of evapotranspira.tion are thus difficult to make and
of dubious accuracy. They are limited by insufficient data on highly
variable surface parameters such as soil moisture conditions and vegeta
tion types.
By comparison to the weather station network, today's satellites
return remotely sensed information about the earth's surface with an
unprecedented level of detail. The surface area element or pixel sizes
and the time intervals between coverage of some of the satellites appro
priate to regional scale studies are shown in Table 1-1. As a result of
the availability of this type of data and modern high-speed computers,
the potential exists to systematically monitor evapotranspiration on a
regional scale.
Development of this potential could benefit a variety of research-
areas. If remote-sensing methods are also developed to estimate rainfall


157
APPENDIX C
SUMMARY OF ENERGY BUDGET DATA
This appendix contains most of the energy budget data collected in
the spring and fall of 1981. The table below is a catalog of the data.
It should be noted that different radiation thermometers were used
in spring and fall (see Table 2-2), and that only the fall surface
temperatures have been cross-calibrated to the air temperatures (1.5C
was added to surface temperature measurements). Subroutine TMTCH, which
imposed a 4 min time constant on the radiation sensors, was in use only
in the fall. Windspeed was measured 7 m over the pasture surface in
both measuring periods.
The number at the far right on the data tables is the correlation
coefficient for the temperature and vapor pressure gradients for each
half hour period. On some occasions correlation coefficients greater
than 1 are reported; these are for time periods when gradients were
very small, causing numerical problems in computing the coefficient.
Spring 1981
Fall 1981
Day
Date
No. of
Day
Date
No. of
Periods
Periods
139
May 19
. 20
279
Oct 6
14
140
20
14
280
7
16
141
21
23
285
12
18
142
22
24
286
13
21
143
23
24
287
14
21
145
25
19
288
15
21
147
27
8
289
16
16
148
28
18
290
17
21
149
29
23
291
18
20
150
30
21
293
20
21
151
31
22
294
21
21
152
Jun 1
17
295
22
21
153
2
21
296
23
21
155
4
11
301
28
16
160
9
11
302
29
20
161
10
21
303
30
20
162
11
11
304
31
20
305
Nov 1
21
306
2
20
307
3
20
308
4
19
309
5
19
310
6
19
311
7
19
312
8
19


66
With the above assumption, transport of latent and sensible heat
can be considered similar from the surface to a reference level in the
air. The simple expressions developed in Chapter 2 (Eqs. 2-17 and 2-20)
can then be used to describe these fluxes:
H = h(T T ) and 4-6
S a
E = ^ M(e* ej 4-7
y S a
The moisture availability parameter (M) is included to account for the
subsaturation of the surface air layer. However, use of Eq. 4-7 as a
hard equality will force M to include minor differences due to inequali
ty of molecular diffusivities of latent and sensible heat (Jarvis et
al., 1971), any differences due to stability effects, and any differ
ences due to dissimilar sources and sinks of latent and sensible heat
within the vegetation system.
The dependence of the vapor pressure gradient on the surface-to-air
temperature gradient is shown in Fig. 4-2. It shows that the vapor pres-
*
sure difference (e efi) is in part due to the greater temperature of
the surface relative to the air, and in part due to the saturation defi
cit of the air. Considering the saturation vapor pressure curve linear
in the neighborhood of the surface and air temperatures,
*
e e = s(T T ) + se
S a S a a
4-8
where s is the slope of the saturation vapor pressure curve between
T and T and
S a
6ea is the saturation deficit of the air.
a
Substituting this expression into the latent heat flux equation (Eq.
4-7) gives the latent heat flux in terms of the temperature gradient:
E = £ M [s(T T ) + 6e ] .
i b a a
4-9


167
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
285
1530
0.35
-0.00
0.15
0.20
4.58
23.1
27.9
16.2
.993
1600
0.27
-0.01
0.11
0.17
3.88
22.8
26.7
15.8
.990
1630
0.12
-0.01
0.04
0.09
3.82
22.2
24.4
15.8
.987
1700
0.03
-0.01


3.74
21.2
22.3
16.2
.787
286
730
0.05
-0.02
- _
2.63
14.8
15.2
.029
800
0.16
-0.01
0.04
0.12
3.29
16.1
17.0
16.0
.982
830
0.27
-0.01
0.10
0.18
4.83
17.5
19.2
16.6
.994
900
0.35
-0.00
0.16
0.19
6.03
18.3
21.0
16.7
.996
930
0.40
-0.00
0.19
0.20
5.51
19.0
22.6
16.7
.999
1000
0.53
0.01
0.28
. 0.25
5.03
19.8
25.8
16.6
.996
1030
0.45
0.00
0.24
0.21
5.37
19.8
25.0
16.1
.998
1100
0.38
0.00
0.20
0.18
4.70
19.6
24.4
15.9
.998
1130
0.37
0.00
0.19
0.17
4.54
19.5
24.5
15.7
.997
1200
0.42
0.00
0.22
0.20
4.20
19.7
25.8
15.6
.997
1230
0.64
0.01
0.34
0.29
5.36
20.4
28.8
15.8
.998
1300
0.70
0.01
0.39
0.30
4.95
20.7
30.8
15.8
.999
1330
0.74
0.01
0.41
0.32
4.92
21.2
31.4
15.8
.998
1400
0.54
0.01
0.29
0.24
4.28
21.2
29.3
15.8-
.998
1430
0.52
0.01
0.28
0.23
4.91
21.1
28.5
15.7.
.997
1500
0.32
0.00
0.17
0.15
5.02
20.7
25.6
15.6
.996
1530
0.21
-0.00
0.10
0.11
4.34
20.1
23.8
15.5
.995
1600
0.19
-0.00
0.10
0.09
4.70
19.8
23.3
15.6
1.000
1630
0.08
-0.00
0.04
0.05
3.97
19.2
21.5
15.6
.999
1700
0.02
-0.01
0.01
0.02
3.95
18.5
20.0
15.3
.994
1730
0.02
-0.01
0.01
0.02
3.65
18.0
19.5
15.3
.992
287
730
0.06
-0.01
0.01
0.06
2.45
16.0
16.8
18.3
.956
800
0.16
-0.00
0.05
0.11
2.66
17.5
18.8
19.4
.998
830
0.26
0.00
0.10
0.16
3.32
19.3
21.4
20.7
.993
900
0.26
0.01
0.11
0.15
3.85
20.7
23.1
21.6
.996
930
0.31
0.01
0.14
0.16
3.96
21.4
25.0
21.9
.996
1000
0.29
0.01
0.11
0.16
4.07
.22.1
25.5
21.9
.997
1030
0.47
0.02
0.21
0.24
4.77
22.5
27.2
22.2
.999
1100
0.70
0.02
0.30
0.38
4.13
22.8
31.8
22.9
.999
1130
0.41
0.01
0.17
0.22
4.78
22.9
28.2
21.8
1.000
1200
0.55
0.02
0.23
0.31
4.20
24.0
30.9
21.5
.997
1230
0.37
0.01
0.13
0.23
4.84
22.8
26.9
22.0
.997
1300
0.72
0.02
0.37
0.34
5.28
23.8
33.0
22.1
.999
1330
0.35
0.01
0.16
0.18
5.09
22.3
26.9
22.0
.998
1400
0.27
0.01
0.10
0.16
4.50
22.2
26.4
21.7
.995
1430
0.18
0.01
0.05
0.13
3.42
21.4
24.2
21.9
.987
1500
0.23
0.01
0.09
0.13
4.53
22.6
26.3
21.3
.998
1530
0.37
0.01
0.18
0.17
5.48
22.9
27.5
20.8
.996


31
The Carlson model is very general, having been developed for study
of urban and rural surfaces. It is based on the energy budget equation
and gradient transport equations for latent, sensible, and soil heat
flux. Soil thermal conductivity and heat capacitance are combined into a
thermal inertia parameter which is evaluated with an empirical relation
ship to thermal conductivity. The model does not describe soil and plant
water transport. It introduces a moisture availability parameter as
shown in Eq. 2-19 to account for the subsaturation of the surface air.
Eddy diffusivities for latent and sensible heat are iteratively computed
using empirical stability corrections; there are, in fact, different
atmospheric models for daytime and nighttime.
Use of the Carlson model to determine daily heat budget components
is discussed in Carlson et _al_'. (1980). Computed solar radiation is used
to force the model; measured windspeed, air temperature and. humidity,
and soil temperature are used as boundary conditions. By varying two
model parameters (thermal inertia and moisture availability) on succes
sive model runs, sets of corresponding cumulative heat budget components
and 24-hour maximum and minimum temperatures are generated. Then a re
gression equation expressing daily ET as a function of maximum and mini
mum temperatures is developed. Given the ground-measured data for the
simulation and two extreme temperature maps from the HCMM satellite, a
map of daily ET is produced.
The Soer model (named TERGRA) is much the same as the Carlson
model, providing for stability conditions in the surface air layer and
requiring temperature, vapor pressure, and windspeed as boundary condi
tions at a reference level. However, rather than a moisture availability
parameter, soil and plant water transport is modelled in detail. (The


124
A =
yf
h(Ms + y)
and
4-28
MSe
B = (Ms +\)
With independent evaluation of two of the parameters,
4-29
for example,
the heat transfer coefficient (h) and the fraction of net radiation
available for latent or sensible heat (f), the composite parameters can
be used to estimate evapotranspiration:
E = (f hA)R + hB
4-35
This is one of five equations for latent heat flux developed, each for a
different combination of unknown parameters (see Table 4-1).
Making an ET estimate with the ATGR method is a two-stage process.
First, individual remote net radiation and surface temperature measure
ments and ground-gathered air temperature data are used to calculate
the. temperature gradient/net radiation correlation (i.e., A and B).
This requires data from clear time periods when surface temperatures
are observable. The second stage consists of making the ET estimates.
With A and B determined, only a net radiation estimate and the two in
dependently estimated parameters are required. For instantaneous ET
estimates, these values are simply substituted into Eqs. 4-33, 4-34,
4-35, 4-36, or 4-37.
Since the parameters are considered constant, making cumulative ET
estimates is also relatively convenient. Only an estimate of the total
positive net radiation during the estimating period (R ) and the dura
tion of positive net radiation during the estimation period (t ) are
required. For the particular parameter combination in Eq. 4-35, the
cumulative ET over the estimating period is
P
E = (f hA)Rp + hBt
5-13


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14
Figure 2-1. System Diagram of Generalized Evapotranspiring Surface.
Symbols are from Odum (1982).


158
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
139
900
0.30
0.03
_
0.00
22.5
30.9
33.3
.513
930
0.37
0.03
0.08
0.26
3.48
26.1
32.8
34.1
.983
1000
0.30
0.04
0.08
0.19
3.91
26.9
32.7
32.1
.979
1030
0.47
0.04
0.11
0.31
4.09
27.4
35.8
32.9
.986
1100
0.44
0.05
0.13
0.25
5.12
27.9
36.2
32.4
.990
1130
0.51
0.06
0.12
0.34
5.62
27.8
36.7
32.4
.986
1200
0.54
0.06
0.14
0.34
4.82
28.1
38.2
32.2
.999
1230
0.55
0.08
0.12
0.36
4.26
29.1
39.6
31.6
.991
1300
0.50
0.06
0.10
0.34
4.68
29.5
38.2
29.4
.969
1330
0.93
0.12
0.23
0.58
5.10
30.9
45.4
29.2
.998
1400
0.67
0.10
0.17
0.40
5.86
31.1
42.0
27.9
.984
1430
0.84
0.12
0.23
0.48
6.59
31.8
44.4
25.2
.985
1500
0.69
0.10
0.17
0.41
6.62
31.8
42.7
19.8
.987
1530
0.62
0.09
0.17
0.39
5.64
31.9
42.1
20.1
.985
1600
0.52
0.08
0.13
0.30
5.79
31.7
40.2
20.2
.978
1630
0.35
0.05
0.08
0.22
6.25
31.1
36.3
19.9
.963
1700
0.29
0.04
0.08
0.17
5.51
30.9
35.2
22.2
.953
1730
0.18
0.03
0.03
0.12
5.68
30.0
32.2
25.3
.977
1800
0.12
0.02
0.02
0.08
5.38
28.9
30.4
26.9
.950
1830
0.06
0.01
.

4.78
28.2-
28.8-
26.4 -
.787
140
1130
0.45
0.07
0.14
0.24
6.37
29.5
_ _
31.5
.994
1200
0.77
0.09
0.21
0.48
5.41
30.1

31.1
.999
1230
0.75
0.11
0.23
0.41
6.75
31.1
22.6
29.4
.996
1300
0.65
0.09
0.21
0.36
6.65
30.7
39.7
28.6
.992
1330
0.50
0.07
0.14
0.29
6.47
30.6
38.0
28.0
.990
1400
0.56
0.07
0.15
0.33
5.60
30.5
38.4
29.2
.983
1430
0.68
0.09
0.21
0.38
6.96
30.8
40.3
29.7
.989
1500
0.59
0.09
0.19
0.31
6.70
30.9
38.9
29.9
.998
1530
0.73
0.09
0.24
0.40
7.59
30.9
39.6
28.4
.990
1600
0.63
0.09
0.20
0.34
7.30
30.9
39.0
29.3
.993
1630
0.55
0.08
0.20
0.28
7.56
30.6
37.8
27.8
.996
1700
0.43
0.06
0.14
0.23
6.45
30.1
35.8
28.1
.984
1730
0.37
0.05
0.11
0.21
6.42
29.8
34.5
27.5
.989
1800
0.28
0.03
0.10
0.15
6.33
29.2
32.2
27.1
.975
141
800
0.06
-0.01
3.87
15.8
17.8
21.6
-.714
830
0.15
-0.00
0.03
0.12
4.03
16.4
19.9
21.3
.990
900
0.17
-0.00
0.06
0.12
4.37
16.7
21.2
20.9
.994
930
0.31
0.01
0.12
0.18
4.13
17.4
25.1
20.7
.997
1000
0.40
0.01
0.18
0.20
3.71
17.4
27.1
20.4
.996
1030
0.52
0.03
0.24
0.26
3.61
18.6
30.9
20.6
.998
1100
0.55
0.03
0.25
0.27
3.91
18.9
31.7
20.3
.999
1130
0.56
0.04
0.24
0.28
3.24
19.8
34.5
20.4
.998
1200
0.70
0.05
0.28
0.37
3.28
20.8
37.1
20.5
.997
1230
0.82
0.08
0.31
0.44
3.14
22.1
40.8
20.7
.997


Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
EVAPOTRANSP¡RATION: AN AUTOMATIC MEASUREMENT SYSTEM
AND A REMOTE-SENSING METHOD FOR
REGIONAL ESTIMATES
By
Klaus Heimburg
December 1982
Chairman: Wayne C. Huber
Major Department: Environmental Engineering Sciences
A generalized physical method is developed for making evapotran-
spiration (ET) estimates based on directly measured air temperature and
remotely sensed surface temperature and net radiation data. The method
is based on the correlation of surface-to-air temperature gradients and
varying net radiation loads; the slope and intercept of this correla
tion are shown to be composite values of two groups of surface parame
ters. Five equations are developed to calculate ET from these composite
values plus net radiation and some combination of two of the four sur
face parameters (bulk air transport, moisture availability, saturation
deficit, and soil heat flux).
The method is validated using ET measurements made over a pasture
surface using the energy budget/profile Bowen ratio technique. An auto
matic measurement system consisting of a computer-controlled data ac
quisition system and air sampling arrangement, time-constant-matched
humidity, temperature, and radiation sensors, and four interacting
x


ESTIMATED ET (LY/min) BOWEN RATIO
194
Figure 9. (cont.)


54
ratio. The ratio and corresponding correlation coefficient are returned
to the calling program.
Function FILT was added to MEASR after it was discovered that the
shielding system did not prevent the Beef Research Unit electric fence
charging system from inducing noticeable spikes on the signal lines.
These 10-50 microvolt spikes were shorter than the voltmeter measurement
cycle, and thus lent themselves to being filtered digitally. FILT takes
10 measurements, looks for three in a row that are the same within a
tolerance, and compares the rest of the measurements to one of them. Any
measurement varying more than a specified tolerance is dropped, and the
average of the "good" measurements is passed back to MEASR. If more than
half of the measurements are noisy (out of tolerance), a warning is
printed to notify the operator.
Subroutine TMTCH is included to match the time constants of the net
radiation and precision radiation thermometer to that of the temperature
and dewpoint measurements. This matching is done by using the weighted
average of the 25 most recent (collected in the last 12.5 min) measure
ments to calculate a matched measurement. The weights assigned to older
measurements decrease exponentially with a time constant of 4 min. The
same weighting scheme is used for the net radiation and surface tempera
ture because their sensor response time constants are 8 and 2 seconds,
respectively. At a sampling rate of one measurement every 30 sec, their
responses are, in effect, instantaneous.
Program REPRT produces a half-hourly data summary report. It calcu
lates half-hourly average profiles of the heat budget components, wind-
speed and direction, Bowen ratio, and profiles of soil and air tempera
ture, air vapor pressure and relative humidity. Most of this program is


144
FUNCTION FILT(NCHAN,I PGM,TOL)
C*****FUNCTION FILT THROWS OUT MEASUREMENTS CONTAINING NOISE
C*****CAUSED BY ELECTRIC CATTLE FENCE CHARGER.
DIMENSION DAT(12)
DO 145 Ml=1,10
CALL EXEC(1,9,DAT(Ml),2,NCHAN,IPGM)
DAT(Ml) = C0NV(DAT(M1))
145 CONTINUE
DAT(11) = DAT(1)
DAT(12) = DAT(2)
DIF1 = ABS(DAT(1)-DAT(2))
DO 155 M2=l,10
DIF2 = ABS(DAT(M2+1)-DAT(M2+2))
IF (DIF1 .LT. TOL) .AND. (DIF2 .LT. T0L))160,150
150 DIF1 = DIF2
155 CONTINUE
160 TOT = DAT(M2)
NGD = 1
GD = DAT(M2+1)
DO 170 M3=M2,10
DIF2 = ABS(GD-DAT(M3+2))
IF(DIF2 .LT. TOL)165,170
165 TOT = TOT+GD
GD = DAT(M3+2)
NGD = NGD+1
170 CONTINUE
RGD = NGD '
RMEAS = NMEAS
DQ = RGD/RMEAS
FILT = TOT/RGD
IF(DQ .LT. .5) 175,185
175 WRITE(6,180) NCHAN
180 FORMAT!IX,"CHANNEL ",I3," IS SUSPICIOUSLY NOISY CHECK IT OUT")
185 RETURN
END
SUBROUTINE STEP(VMARK)
C*****STEP TURNS SELECTOR VALVE ONE PORT AND RETURNS MARK VOLTAGE
CALL EXEC(1,9,DATA,2,19,4043B)
CALL EXEC(1,9,DATA,2,0,4043B)
CALL EXEC(12,0,2,0,-2)
CALL EXEC(1,9,DATA,2,110,4045B)
VMARK = CONV(DATA)
RETURN
END


202


ESTIMATED ET (LY/min) BOWEN RATIO
Figure 8. (cont.)


3
Table 1-1.
Spatial and Temporal
Resolution in
Satelli tes
Satellite
Orbit
Pixel
Time
Acronym
Type
Size
Intervals
Landsat
polar
80 x 80 m
18 da
HCMM
pol ar
.6 x .6 km
12 hr each 5 da
TIROS
pol ar
1 x 1 km
12 hr.
GOES
geostationary
8 x 4 km
30 min
on a regional basis and if streamflow is gaged, aquifer recharge over
wide areas can be estimated (Allen et jfL, 1980). The information on
surface energy fluxes gained by an ET estimation technique could also be
useful as boundary conditions for models of the atmosphere. It is also
possible that large-scale changes on the earth's surface such as defor
estation and desertification could be monitored by observing longer-term
changes in ET patterns. Finally, the correlation of evapotranspiration
and yield in agronomic crops may lead to large-scale yield predictions
(Doorenbos and Pruitt, 1977; Chang, 1968).
The purpose of this research is to develop and test a generally
applicable method for estimating evapotranspiration based as much as
possible on remotely sensed data. Since it is ultimately intended for
use with satellite data from large diverse areas, criteria for this
method include that it be strictly physical, relatively easy to apply,
and compatible with the format and limitations of satellite data. The
research is also intended to identify factors critical to the accuracy
of the estimates which require more research, and factors which may im
prove future satellite measurement for use in ET estimation.
Scope of the Research
Data returned from a satellite consist of the energy flux in a par
ticular band of wavelengths coming from a particular surface area


m
2 i.o
6 8 10 12 14 1618
TIME (TST, OCT. 22, 1981)
Figure 5-13. Temperature Gradient Response of a Partly Cloudy Day.


164
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
155
930
0.90
0.07
0.19
0.63
3.73
30.6
37.0
40.1
.987
1000
0.77
0.06
0.18
0.53
3.12
30.5
36.6
40.1
.990
1030
0.79
0.07
0.16
0.56
4.12
31.0
36.4
39.8
.987
1100
0.89
0.09
0.16
0.63
3.50
31.5
37.7
40.0
.983
1130
0.92
0.10
0.16
0.66
4.00
32.0
38.2
38.9
.979
1200
0.96
0.12
0.18
0.66
4.05
32.6
39.1
38.3
.992
1230
1.00
0.14
0.16
0.70
3.39
33.2
39.8
38.7
.982
1300
0.88
0.13
0.16
0.60
2.33
33.5
38.7
38.1
.950
1330
0.88
0.12
0.15
0.61
2.43
33.9
38.6
37.7
.970
1400
0.81
0.11
0.17
0.53
2.34
34.2
38.0
38.4
.956
1430
0.72
0.10
0.18
0.44
2.28
34.3
37.1
39.9
.964
160
800
0.45
0.04

_ _
3.78
29.1
30.0
_ _
-.190
830
0.52
0.05
0.19
0.28
4.34
29.7
31.2
31.3
.957
900
0.53
0.05
0.16
0.32
3.96
30.5
32.2
30.5
.972
930
0.57
0.05
0.17
0.35
3.58
31.0
32.7
29.4
.967
1000
0.54
0.05
0.15
0.34
3.89
31.4
32.8
28.8
.992
1030
0.82
0.06
0.21
0.54
3.18
29.9
34.3
26.3
.985
1100
0.70
0.08
0.16
0.46
3.11
31.2
34.5
29.4
.994
1130
1.00
0.12
0.26
0.61
4.88
32.3-
36.7.
30.1
.985
1200
0.97
0.14
0.27
0.56
5.53
32.7
36.6
29.9
.981
1230
0.85
0.15
0.27
0.43
5.13
33.3
36.0
30.6
.991
1300
0.53
0.09
--

4.73
32.9
33.3
31.9
.925
161
730
0.36
0.03
--
_ -
3.33
28.5
28.8
...
.117
800
0.42
0.04

--
4.09
29.1
30.1

-.263
830
0.47
0.04
0.14
0.29
4.42
29.7
31.0
30.7
.967
900
0.37
0.03
0.09
0.24
3.70
29.9
30.9
29.9
.985
930
0.73
0.06
0.20
0.47
4.36
31.1
33.7
28.9
.982
1000
0.65
0.06
0.15
0.43
3.95
31.2
33.3
28.9
.980
1030
0.62
0.07
0.15
0.40
4.46
31.4
33.5
28.3
.995
1100
0.90
0.10
0.21
0.59
4.49
32.3
36.2
29.0
.983
1130
0.69
0.10
0.14
0.46
4.21
32.8
34.8
28.0
.985
1200
0.50
0.08
0.09
0.33
4.95
32.4
33.1
27.7
.982
1230
0.90
0.13
0.17
0.60
5.82
33.7
36.4
26.4
.984
1300
0.89
0.14
0.19
0.56
5.50
34.7
36.8
26.4
.988
1330
0.62
0.10
0.12
0.40
5.41
34.0
34.4
25.6
.991
1400
0.75
0.11
0.13
0.51
5.31
34.4
35.4
25.3
.983
1430
0.70
0.11
0.14
0.45
5.59
34.7
35.3
25.2
.990
1500
0.50
0.08
0.10
0.32
5.43
34.3
33.6
25.0
.985
1530
0.55
0.07
0.07
0.40
5.11
34.1
33.4
25.9
.966
1600
0.31
0.05
0.07
0.19
5.57
33.4
31.6
25.6
.991
1630
0.23
0.03
0.05
0.16
3.57
30.2
29.9
25.8
.971
1700
0.11
0.02


2.23
29.2
28.8
26.3
.133
1730
0.03
0.01
--
--
2.58
28.2
26.5
25.6
-.886


APPENDIX A
LIST OF SYMBOLS
The following is a list of the most frequently used symbols.
A Slope of the line fit to the surface-to-air temperature
gradient/net radiation correlation
B Intercept of the line fit to the surface-to-air temperature
gradient/net radiation correlation
C Generalized coefficient of net radiation in evapotranspiration
formulae. Computed from A, B, and estimates of two parameters,
as shown in Table 4-1
Cp Specific heat of air at constant pressure
D Generalized constant term in evapotranspiration formulae. Com
puted from A, B, and estimates of two parameters, as shown in
Table 4-1
E Latent heat flux, evapotranspiration rate, or ET
Ep Cumulative ET over an estimating period
eQ Water vapor pressure at a reference level in the air above the
surface
e$ Vapor pressure at plant surfaces corresponding to the surface
temperature; not measurable
k
e$ Saturation vapor pressure at the surface temperature
f Unitless soil heat flux parameter (f = 1 G/R)
G Soil heat flux
H Sensible heat flux
h Bulk heat transport coefficient
L Latent heat of evaporation
k
M Unitless parameter for moisture availability M(e e ) =
es ea "
P Atmospheric pressure
136


CHAPTER 4: THEORETICAL BASIS OF THE TEMPERATURE GRADIENT RESPONSE
ET ESTIMATION METHODS 62
Overview 62
Temperature Gradient Model 63
Strict Temperature Gradient Response Method 69
Average Temperature Gradient Response Method 70
System Stationarity and Average Temperature Gradient
Response 70
Use of Temperature Gradient/Net Radiation Correlation 73
Extension to Totally Remote ET Estimation Method ... 77
Review of Assumptions 79
CHAPTER 5: VERIFICATION OF THE TEMPERATURE GRADIENT RESPONSE
ET ESTIMATION METHODS 82
Overview 82
Validity of Assumptions 83
Radiation Temperature and Sensible Heat Transport ... 83
Constancy of Parameters 86
Strict Temperature Gradient Response Method 95
Average Temperature Gradient Response Method 97
Graphical Representation of the Average TGR Method . 97
ET Estimates with the Average TGR Method 103
Effects of Individual Parameter Variations 105
Generality of ATGR Latent/Sensible Partition 112
Tests of the ATGR Method /. . . . ... . .114
CHAPTER 6: CONCLUSION 123
Summary of Results 123
The Average Temperature Gradient Response Method . 123
Method Limitations and Strengths 125
Recommendations for Future Research 128
REFERENCES 131
APPENDIX A: LIST OF SYMBOLS 136
APPENDIX B: PROGRAM LISTING AND DEFINITION OF NAMES USED .... 138
Program SET 139
Program MEASR 141
Program REPRT 146
Program ANALZ 149
Definition of Names 152
APPENDIX C: SUMMARY OF ENERGY BUDGET DATA 157
APPENDIX D: SUPPLEMENTARY FIGURES 178
BIOGRAPHICAL SKETCH 211
VI


112
budget--here less than 10% of net radiation. The noisy character of air
bulk thermal conductivity also does not seem to show in the temperature
gradient/net radiation correlation. This and the fact that considering
h constant leads to more reasonable moisture availability estimates
suggests that variations in thermal conductivity have an insignificant
effect on temperature gradients. For the most part, the pattern in the
temperature gradient/net radiation correlation is a result of the in
teraction of moisture availability and the vapor pressure parameters.
Generality of the ATGR Latent/Sensible Partition
Another argument in favor of the ATGR method is that it correctly
reproduces the general pattern of change in latent and sensible heat
fluxes. Even though instantaneous ET rates are sometimes slightly over-
and underestimated because the parameters are considered constant, the
ATGR partition matches the daily pattern of other partition measures,
such as the Bowen ratio.
Figure 5-14 shows an idealized ATGR latent/sensible heat flux par
tition and the resulting idealized daily time course of the Bowen ratio
and E/R, another widely used dimensionless partition ratio. The ratios
were computed according to
H hAR hB
E (f hA)R + hB
and
5-14
E (f hA)R + hB
R ~ R
wi th
5-15
R = Rq cos
2ir
[2T
TST tt
5-16
where TST is true solar time (6 < TST < 18), and
Rq is an arbitrary maximum net radiation load.
These patterns have been observed and reported for clear days by other
researchers (e.g., Pruitt, 1964). The gradient response partition also


105
approximately to the levels that would have occurred had it not been
for the dew.
This section has shown that due to the pattern of changes in the
parameters, use of their average values leads to systematic over- and
underestimates of instantaneous ET rates. It has also been shown that
in cases where interpolation capability is necessary and cumulative
accuracy is sufficient (in applications where daily or longer ET esti
mates are the goal), assuming that the parameters are constant is a
very useful approximation. Figures 8, 9, 10, 11, and 12 in Appendix D
graphically demonstrate these points for five days in October of 1981.
Effects of Individual Parameter Variations
With the.graphic representation of the ATGR method shown in Fig.
5-8, it is relatively easy to directly see how patterns in the tempera-
.ture gradient/net radiation relationship influence instantaneous ET
estimates. This subsection shows how individual parameter variations
cause the patterns in the temperature gradient/net radiation relation
ship.
The most convenient way to demonstrate the effects of variations
in individual parameters is to compare temperature gradients predicted
with only one parameter varying to temperature gradients predicted with
constant parameters (see Figs. 5-10, 5-11). It is possible to calculate
each parameter for each time period with the available measurements.
When the average value of each parameter is used to calculate tempera
ture gradients (only net radiation varies in Eq. 4-25), the gradients
fall on the ideal straight line postulated in the average TGR method.
Recalculating the temperature gradient with only one parameter varying-
qualitatively shows the effect of that parameter on the temperature


BEEF RESEARCH UNIT ET PROJECT DATA
AVERAGES AND ( PERCENT VARIATION ) FOR HALF HOUR ENDING
TUESDAY, OCTOBER 2C, 1981 (JULIAN DAY 293) TINE 09:31:2? TS'I
NET
RAD.
SOIL
H. F.
SENS.
H.F.
EAT. H.F. N
WINDS
RSQ.>.95 B.R.
AVG.R
. 45
LY/H
.02
LY/M
.28 LY/H
.16 LY/H 3.
06 M/S
12.OF 12 1,753
.999
RADIATION
AIR
TEMP
VAP PRESS
REL HMDTY SOIL
TEMP
(LY/H)
(CM)
(*C >
(CM) (MB)
(CM) (7.) (CM)
(*C)
NET
.451
(5.0)
22S
T9.2
(4.2)
225 11.2
(3.0)
225 50.2 0
16.8
ISW
.802
(4.1)
135
1 9.6
(4.1)
135 11.3
(2.9)
135 49.8 -2
1 7.6
RSH
. 17 7
(3.7)
85
20.0
(4.1)
85 11.5
(2.8)
85 49.2 -5
18.2
Al m
. 1 09
(IS.)
GO
20.4
(4.0)
GO 11.6
(3.1)
GO 48. 6 1 0
I 9.2
El. W
GIG
(5.5)
35
21 1
(3.9)
35 11.9
(3.1)
35 47.6 -25
20. 1
F
. 1 62
11 If/HR
0
23.4
(5.5)
.*.*.95+' BR
-1.760.+PR-.115** -50
21.7
ZO
TO
H
U*H
. RCH
EO
DE U*E
RCE
I .
23.0
22.
0
33.4
- 1.000
12.8
17.0 12.8
-.999
22. G
22.
0
32.6
-1.000
1 2. G
18.0 12.4
- .999
o
o
22.3
22.
0
31.9
-1.000
12.5
19.0 12.2
- .999
r\ AIR
,RSTM(
S/H)
.238,
4.350
.31 I
,4.353 .348,
4,350
.397,4.358 .436,
4.365
A EDO
SHIO
OAH
ATC
ZNG'L HRNGL
EOT
E.S.T. T.S.T.
DAY

1.09 1
.84
.85
57.
3 -41 :2
.2579
9,46 9.25
293
Figure 3-6. Example of Half-Hourly Data Report.. Variable names and units are listed in Table 3-3.


75
All of the equations in Table 4-1 have the same basic form because
A, B and the parameters are considered constant for the measurement per
iod :
E = CR + D .. 4-38
With A and B determined from clear sky data (requires surface tempera
ture, air temperature, and net radiation), and two independently esti
mated parameters, all that is needed in any of the formulae is a net
radiation estimate. If net radiation can be estimated for partly cloudy
or cloudy skies, ET rates for these conditions can also be calculated.
A significant advantage of considering the parameters approximately con
stant arises in computing cumulative evapotranspiration. Using the gen
eralized version of the equations in Table 4-1 (Eq. 4-38), the cumula
tive ET rate for some period (p) can be calculated as follows:
Ep = Jp Edt = Jp (CR + D)dt
= C/p Rdt + D/p dt
En = CR + Dt 4-39
P P P
where E is the cumulative ET over the estimating period,
R^ is the cumulative positive net radiation over the period,
tj" is the duration of positive net radiation during the
P estimating period, and
C and D are constants calculated from A, B, and estimates of two
parameters as shown in Eqs. 4-33 through 37.
Since the parameters are approximated as constant, no interpolation is
necessary for cumulative ET estimates. Use of an interpolation scheme
may be required to more accurately determine Rp, depending on the time
interval between satellite data sets.
Use of particular versions of the ET equation listed in Table 4-1
is discussed in the remainder of this section. It is difficult to pre
dict particular applications or weaknesses of these equations; they


programs was developed to measure and calculate half-hour average sur
face energy budgets and statistics. Data from 42 days in the spring and
fall of 1981 are reported.
It was found that the radiation surface temperature is in general
not the same as the effective heat transport surface temperatureit
may be necessary to correct remote surface temperature measurements
before using them with conventionally evaluated heat transport coeffi
cients. Because parameters are assumed constant, instantaneous ET esti
mates made with the developed method are at times systematically high
or low, but these errors tend to cancel in cumulative estimates.
The method is shown to be well-suited for use with 1- to 3-hour
time resolution satellite data. In effect it evaluates surface parame
ters such as moisture availability, requires no interpolation for ET
estimates between data sets, is adapted.to the inevitable cloud-caused
loss of satellite surface temperature data, and reduces calculation of
cumulative ET to estimating total positive net radiation and duration
of positive net radiation in a particular estimation period. The meth
od's ET estimates are shown to be as accurate as the state-of-the-art
simple residual method, which does not have these advantages.
XI


10
Figure 1-2. Field Apparatus and Sensor Locations. This diagram is not
to scale.


20
This expression is evaluated in Fig. 2-2 using values typical for
pasture grass. Heat storage in pasture biomass and the top litter layer
is approximately two orders of magnitude less than peak net radiation
loads; latent and sensible heat storage in the canopy air is about three
orders of magnitude less.
Since the values of the photosynthetic heat flux and the time rate
of canopy heat storage are negligibly small, the energy budget equation
may be written
R-E-H-G=0 2-4
The ET measurement method and the remote estimation method are based on
this simplified form of the equation. It is also the basis for all but
the empirical remote-sensing ET estimation methods. The following sub
sections briefly review the fundamental analytical concepts and evalua
tion techniques which .are common to previously developed evapotranspira-
tion estimation methods based on the energy budget equation.
Transport Similarity and Wind Models
After the surface energy balance, the most important concept to ET
estimation techniques is that of transport similarity among momentum,
heat, and mass fluxes in the turbulent layer near the surface. This idea
is used in all forms of the energy budget approach to ET estimation,
both to evaluate transport properties and to avoid evaluating transport
properties.
The fundamental equations for the one-dimensional transport of mo
mentum, heat, and water vapor are (Eagleson, 1970)
H = pcpK
3JT
H 3 z
2-6


135
Stewart, J.B. and A.S. Thom. 1973. Energy budgets in pine forest.
Quart. 0. Roy. Met. Soc. 99:154-170.
Swinbank, W.C. and A.J. Dyer. 1967. An experimental study in micro
meteorology. Quart. J. Roy. Met. Soc. 93:494-500.
Tanner, C.B. and M. Fuchs. 1968. Evaporation from unsaturated surfaces:
a generalized combination method. J. Geophys. Res. 73:1299-1304.
Tanner, C.B. and W.L. Pelton. 1960. Potential evapotranspiration es
timates by the approximate energy balance method of Penman. J.
Geophys. Res. 65:3391-3413.
Tennessee Valley Authority. 1972. Heat and mass transfer between a
water surface and the atmosphere. Water Resources Res. Lab. Rept.
#14 (TVA Rept. #0-6803), Norris, TN.
Thom, A.S. and H.R. Oliver. 1977. On Penman's equation for estimating
regional evaporation. Quart. J. Roy. Met. Soc. 103:345-357.
van Bavel, C.H.M. 1966. Potential evaporation: the combination concept
and its experimental verification. Water Resources Res. 2:455-467.
Waggoner, P.E., G.M. FurnivaT and W.E. Reifsnyder. 1969. Simulation of
the microclimate in a forest. Forest Sci. 15:37-45.
Webb, E.K. 1970. Profile relationships: the log-linear extension to
strong stability. Quart. J. Roy. Met. Soc. 96:67-90.


46
technique requires. The central piece of equipment was a Hewlett-Packard
2100S Minicomputer with a disk resident Real Time Executive-2 operating
system. The system allowed editing and compilation of programs, swapping
programs between core and disk memory, scheduling programs for relative
or absolute start times, and "simultaneous" running of programs accord
ing to priority. Input and output were by means of a HP-2126P terminal.
The peripheral equipment used in making the measurements and con
trolling the gas sampling valve is listed in Table 3-1. The controlling
computer, disk drive, data acquisition equipment, and terminal were all
housed in an air-conditioned room.
Table 3-1 Data Acquisition
are manufactured
System Identification
by Hewlett-Packard)
(All components
Component
Model No.
Serial No.
Minicomputer (32K Memory)
HP-2100S '
1420A05546
Scanner
HP-2911A
737-00476
Scanner Controller
HP-2911B
832-00412
Integrating Digital Voltmeter
HP-2402A
1027A01060
Disk Drive
HP-7901A
1321A-00255
Terminal
HP-2621P
2102W03475
The field apparatus on the pasture site consisted of an air-sam
pling mast, a radiation sensor boom, and a 9.5-m tower supporting a
precision radiation thermometer at its top, and windspeed and direc
tion sensors at 7 m. Another taller tower was erected and equipped to
protect all instrumentation from lightning.
The 2-m radiation sensor boom was supported by an aluminum tripod
stand and guy wires about 1.8 m over the ground surface. Two Epply pyra-
nometers, oriented to measure incoming and reflected radiation, and a
Swissteco net radiometer were mounted at its end. An aspirating pump and


84
their relationship from observations of the temperature profiles over
the grass surface. Sensible heat flux was calculated using five temper
ature measurements from the turbulent layer via the profile Bowen ratio
technique. One would therefore expect the heat flux to be proportional
to the temperature difference between the lowest and highest air tem
perature measurements. The heat transport coefficient of this fully
turbulent layer can be calculated by solving Eq. 4-6 for the heat
transport coefficient
where Tg is the lowest temperature measurement (35 cm) and is the
highest (235 cm). If heat transport through the total air layer (between
the surface and highest air temperature measurement) is steady, the same
heat flux passes through it as the turbulent layer. Then the heat trans
port coefficient of the total air layer can be calculated:
If the radiation surface temperature is the same as the effective heat
transfer surface temperature, one would expect the ratio of h/h^. to re
main constant over the course of a day. This ratio,
h T0 Ta c 0
hT = T "~r 5-3
t s a
can be most easily examined by plotting T T vs. Tn T (see Fig.
S d U d
5-1).
The points in this figure would lie on a straight line intersect
ing the origin if the relationship between the turbulent temperature
gradients (or effective heat transfer gradient) and the total surface-
to-air temperature gradients was constant. However, relative to a given


VAPOR PRESSURE
e^-eQ = a + b
e8*-ea8(Ts-Ta)+8ea
Figure 4-2. Components of Vapor Pressure Gradient. Component (a)
can be calculated from the surface-to-air temperature
difference (Ts Ta) and the slope (s) of the saturation
water vapor pressure curve [e*(T)]. Component (b) is
the saturation deficit (6ea) of the air.


61
When the system was run at night, some condensation took place in
the air sample lines because the air sampling mast was not heated. Water
accumulated in the tubing in proportion to the length of the tubing sec
tion in the mast. As a result, the fifth level produced obviously high
dewpoint temperatures until the tubing had dried. The temperature dew
point correlation made it obvious at what time all condensation had been
evaporated from the sample lines.
The situation most hazardous to data quality occurred on very
sunny, dry days. At these times, the air temperature of the instrument
room (21-24C) was quite a bit higher than the dewpoint temperature of
the outside air. At some point the analyzer would no longer be able to
cool its sensor mirror low enough to get dew formation. Since air sam
ples from different levels have different temperatures, the coolest mir
ror temperatures possible varied also. A .false-dewpoint profile, which
correlated very well with air temperatures, would be measured and thus
passed through the correlation coefficient screen. Evidence for this
condition was the brightly-lit cooling circuit lamp on the dewpoint ana
lyzer. With experience this condition could be anticipated, and its ef
fects minimized by unplugging the heater cables to the sampling lines
and mixing box.
In spite of precautions taken, susceptibility to lightning damage
was the system's greatest weakness. The system was damaged twice by
lightning. In both cases, instrumentation and computer equipment was
damaged by current surges in the AC power system, in spite of power-
surge arrestors. The only solution was the most fundamental unplugging
all sensor cabling and all AC power cords.


NET RAD. (LY/min)
188
Figure 8. (cont.)


NET RAD. (LY/m¡n)
193
Figure 9. (cont.)


139
Program SET
PROGRAM SET(3,90)
C*****SET SCHEDULES PROGRAM MEASR FOR UNIFORM MEASUREMENT TIMING AND
C*****RUNS PROGRAMS REPRT AND ANALZ AT 12 PROFILE (HALF HOUR) INTERVALS
COMMON DUMMY (27),AST(6),AT(5,2),AE(5,2),ARAD(6,2),AWSPD,ND(8),
*NBR,NPROF, BR(2),KFLAG,NVALV,LEVEL, VMARK,RAD(6,2),DPTCOR,NADV,
*WSPD,T(10),NMEAS
DIMENSION ITIME(5),MEASR(3)
INTEGER ANALZ(3),REPRT(3)
DATA MEASR/2HME,2HAS,2HR /,
*REPRT/2HRE,2HPR,2HT /,ANALZ/2HAN,2HAL,2HZ /
IF(ISSW(2))40,1
1 LAG = 29
GO T0(2,5,30,35)KFLAG
2 NADV = 2
NMEAS = 0
D = .85
P = 29.92
DPTCOR = P/CP-D)
WRITEd, 3)
3 FORMAT!IX,"SENSOR PLUGS IN ? PUMP, DEW POINT",
*" INSTRUMENT, MIXING BOX, MAST FANS ON?")
READ(1,4)IANS
IF(IANS .EQ. 2HYE)5,1
4 FORMAT(A2)
C*****CHECK POSITION OF ROTARY VALVE
5 CALL EXEC(1,9,DATA,2,110,4045B)
VMARK = CONV(DATA)
IF(VMARK .GT. 6.)20,10
10 CALL FIND(VMARK)
C*****INITIALIZE COUNTERS AND PROFILE AVERAGES FOR COLD START
20 NVALV = -NADV
LEVEL = -NADV
VMARK = 0.0
NPROF =0
CALL ZERO (AST, ARAD, AE, AT, AWSPD, ND, BR,NBR)
DO 25 K=l,6
RAD(K,1) = 0.0
RAD(K,2) = 0.0
25 CONTINUE
WSPD = 0.0
C*****DE|_AY PROGRAM MEASR START FOR UNIFORM REPORT TIMING
CALL EXECdl,ITIME)
K = ITIME(3)*60+ITIME(2)
LAG = 150-M0D(K,150)+62
IF(LAG .GT. 150) LAG = LAG-150
30 CALL EXEC(12,MEASR,2,0,-LAG)
IF(KFLAG .LT. 3)45,40
35 CALL EXECdl,ITIME)
MIN = 2


E (LY/min) H(LY/mln)
186
Ts-Ta (C)
Figure 8. Data and ET Estimates for Oct. 17, 1981. See p. 185 for
brief explanation of individual graphs.


149
Program ANALZ
PROGRAM ANALZ(3,99)
C*****ANALZ TAKES DATA COLLECTED BY SET AND COMPUTES OTHER
C*****PARAMETERS THAT MAY BE OF INTEREST
COMMON CST(6),T(5),E(5),RNET,SWI,RSW,ALW,ELW,SFLX,
*TSURF,HSENS,HLTNT,CWSP,R
DIMENSION ITIME(5),RSTM(5),RATM(5)
HV = 597.3-.566*TSURF
WRITE(6,2)
2 FORMAT(IX,"ZO",10X,"TO",6X,"DH",6X,"U*H",5X,"RCH",
*9X," EO", 6X," DE", 6X," U*E", 5X, "RCE")
RHO = .0012832-.00000389*T(3)
DO 5 I=L,3
ZO = I
CALL PR0FT(T,T0,Z0,DH,BH,RH)
UH = HSENS/C.24*RH0*.4*BH*100.)
CALL PROFT(E,EO,ZO,DE,BE,RE)
UE = HLTNT*1013./(RH0*.622*HV*.4*BH*100.)
WRITE(6,4) ZO,TO,DH,UH,RH,EO,DE,UE,RE
4 FORMAT(F3.0,1X,2(F12.1,2F8.1,F8.3))
5 CONTINUE
IF((RH .LT. -.95) .AND. (TSURF .GT. T(l)))10,15
10 SVP = 10,**((7.5*TSURF)/(TSURF+237.3)+.7858)
DO 12 1=1,5
RHO = .0012832-.00000389*((TSURF+T(I))/2.)
RTOT = 100 .*.622*RH0*HV*(SVP-E(I))/(1013.* HLTNT) '
RATM(I) = 100.*.240*RH0*(TSURF-T(I))/HSENS
RSTM(I) = RTOT- RATM(I)
12 CONTINUE
WRITE(6,14)(RATMCI),RSTM(I), 1=1
14 FORMATS," RAIR,RSTM(S/M) ", 5(F6.3, ", ", F5.3))
15 CALL EXECdl,ITIME)
D = ITIME(5)
TST = ITIME(4)+.25
IF(ITIME(3) .LT. 10)TST = TST-.5
c*****tva REPORT, APPENDIX B
YA = .017 2028* CD-I.)
SYA = SIN(YA)
CYA = COS(YA)
S2Y = SIN(2.*YA)
C2Y = C0S(2.*YA)
SIG = 4.885784+D+.03342*SYA-.001388*CYA+.000348*S2Y-.000028*C2Y
SIND = .3978686*SIN(SIG)
EOT = .004289*CYA-.12357*SYA-.153809*S2Y-.060783*C2Y
C*****TVA REPORT 5.5
EST = TST+.48467-EOT
COST = COS(.2618*(TST-12.))
SIND = SIN(.40928*(COS(.017214*(172.-D))))
COSD = SQRT(1.-SIND**2)
SINA = .49606*SIND+.86794*C0SD*C0ST


197
Figure 10. (cont.)


Figure 10. (cont.)


71
temperature data to evaluate the surface parameters. The second stage
consists of using those parameters and measured or estimated net radia
tion data alone to make ET estimates. It is assumed that through a com
bination of cloud-reflected radiation and cloud-top temperatures, a net
radiation estimate for the surface is still possible.
The success of this scheme is limited by the period over which the
parameters can or must be considered constant. They do vary; moisture
availability changes as dew evaporates and the bulk air conductivity
changes with the windspeed. But for the strict temperature response
method to work, the parameters must be considered constant for the time
interval between clear sky data sets, which is limited by the time reso
lution of the data collection system and cloud cover.
, This unavoidable necessity motivates viewing the surface as a sys
tem with approximately stationary parameters for the duration of a lon
ger measurement period (i.e., assuming that the surface-to-air tempera
ture gradients in Eq. 4-11 are a function of net radiation and con
stants). Information on the average parameters can then be extracted
from the correlation of clear sky surface-to-air temperature gradients
and net radiation, and used to estimate ET for clear or cloudy skies.
A soil heat flux parameter is required in order to fully parameter
ize the temperature gradient model. Soil heat flux is the smallest of
the energy budget components, usually accounting for less than 10£ of
net radiation under a vegetated surface. It lags net radiation in time,
but because its magnitude is in the range of error expected in the esti
mates, it can be safely and conveniently treated as a constant fraction
of net radiation:
G
R = 9 *
4-23


137
Q_ Radiation emitted by the atmosphere
a
Qg Radiation emitted by the surface
Qr Radiation reflected by the surface
Q$ Solar radiation incident on the surface (direct and scattered)
R Net radiation absorbed by the surface (R = Qg + Qq Qr Qg)
Rp Cumulative positive net radiation over an estimating period
Rq Arbitrary maximum net radiation load
rQ Bulk resistance to heat transport of the slab of air between
the surface and a reference level
rs Bulk stomata! diffusion resistance
s Slope of the saturation vapor pressure curve (a known function of
temperature, e.g., Eq. 5-6)
T Temperature
T Air temperature at a reference level above the surface
a
T Radiation surface temperature
Tq Temperature at the hypothetical boundary between the laminar
layer next to the vegetation and the turbulent layer above.
Arbitrarily taken to be the lowest temperature measurement
(35 cm) for calculations
TST True solar time
tp Duration of positive net radiation during the estimating period
z Vertical space coordinate
B Bowen ratio
y Psychrometric constant (y = CpP/Le)
6e, Saturation deficit of the air
a
e Ratio of molecular weights of water and dry air
p Air density
a Stefan-Boltzmann constant


39
K is the eddy thermal diffusivity,
is the eddy vapor diffusivity,
Tw is the air temperature,
e is the vapor pressure, and
2 is the vertical coordinate.
The Bowen ratio can then be written:
H
E
Vkh t?
eLK,
3_e
W 3Z
3-7
If temperature and vapor pressure measurements are made at the same
heights, the 32 terms may be cancelled. If the measurements are made at
the same instant, it can be assumed that the eddy diffusivity for water
vapor and heat are the same (K^ = K^). This in effect states that turbu
lent mixing is the dominant transport mechanism in the turbulent bound
ary layer, and that bouyancy and stability effects cause no significant
differences in the transport of heat. or.water vapor (Dyer,-1967;
Swinbank and Dyer, 1967; Webb, 1970; Dyer and Hicks, 1970; Garratt and
Hicks, 1973). Incorporating these conditions into the expression for the
Bowen ratio,
e =
eL
3 T
3 T
3e y3 e
3-8
Since the terms in brackets are physical "constants" (abbreviated as the
psychrometric constant, y), only 3T/^e needs evaluation. This can be
done with air temperature and vapor pressure measurements.
In this application of the energy budget/profile Bowen ratio con
cept, air and dewpoint temperatures were measured at five heights35,
60, 85, 135, and 225 cm over the surface. Vapor pressure was calculated
from the dewpoint temperature according to the Magnus-Tetens formula
(Tennessee Valley Authority, 1972). The ratio 3T/3e was the slope of a
two-independent-variable linear regression (Kendall, 1968) calculated


i i i i-i-j j i I i
0 2 4 6 8 10
Ts-Ta PC)
Figure 5. Air Transport Coefficient for Average Conditions. Data are from
days 290-310 inclusive except days 297-300 inclusive, on which no
data were collected.
CO
ro


ESTIMATED ET ( LY/DA)
122
MEASURED ET (LY/DA)
Figure 5-16. Cumulative ET Estimates by the Residual and ATGR Methods.
Only the periods for which measured ET was available were
used in comparing estimated daily ET with measured daily
ET. Data from 15 days between October 17 and November 6,
1981, are shown.


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Rad Heat Heat Heat Temp Temp Pres Corr
Flux Flux Flux


146
Program REPRT
PROGRAM REPRT(3,94)
C*****REPRT COMPUTES AND REPORTS HALF HOUR AVERAGE HEAT BUDGET AND
C*****PROFILES
COMMON CST(6),CAT(5),CAE(5),CRAD(6),TSURF,HSENS,HLTNT,CWSP,
*RCOEF,AST(6),AT(5,2),AE(5,2) ,ARAD(6,2),AWSPD,ND(8),NBR,NPROF
*BR(2)
DIMENSION RH(5),NS(6),NA(6),NAM(12),NDA(8),-VCE(5),VCT(5),VCR(6)
INTEGER DTIME(3),DIR(2)
DATA NS/O,-2,-5,-10,-25,-50/,NA/225,135,85,60,35,0/,
*NAM/2H N,2H I,2H R,2H A,2H E,2H ,2HET,2HSW,2HSW,2HLW,2HLW,
*2H /,NDA/2H N,2H E,2H S,2H W,2HNE,2HSE,2HSW,2HNW/
DATA DTIME/2HDT,2HIM,2HE /
VC(SS,AVG,RN) = 100.*(SQRT(SS/RN-AVG**2))/AVG
PROF = NPROF
DO 5 K=l,6
ARAD(K,2) = ARAD(K,2)/5.
CRAD(K) = ARAD(K,D/PROF
VCR(K) = VC(ARADK,2),CRAD(K),PROF)
CST(K) = AST(K)/PROF
5 CONTINUE
HV = 597.3-.566*CRAD(5)
DO 10 K=l,5
CAE(K) = AE(K, D/PROF
VCE(K) = VC(AE(K,2),CAE(K),PROF)
CAT(K) = AT(K,1)/PR0F
VCT(K) = VC(AT(K,2),CAT(K),PROF)
RH(K) = 100.*CAE(K)/(10.**(7.5*CAT(K)/(CAT(K)+237.3)+.7858))
10 CONTINUE
CWSP = AWSPD/PROF
NDL = 1
NDE = 1
DIR(l) = 2H
DO 30 K=2 8
IF(ND(NDL) .LE. ND(K))15,30
15 IF(ND(NDL) .EQ. ND(K))20,25
20 NDE = NDL
25 NDL = K
30 CONTINUE
IF((ND(NDE) .EQ. ND(NDL)) .AND. (NDE .NE. NDL)) DIR(1)=NDA(NDE)
DIR(2) = NDA(NDL)
RNET = CRAD(l)
SFLX = CRADC6)
IF(NBR .EQ. 0)35,38
35 R = 0.0
BR = 0.0
GO TO 40
38 ABR = BR(1)/NBR
R = SQRT(BR(2)/NBR-ABR** 2)
40 CALL RATIO(CAE,CAT,BNR,RCOEF)


134
Price, J.C.
Geophy.
1977. Thermal inertia mapping: a new view of the earth. J.
Res. 82:2582-2590.
Price, J.C. 1980. The potential of remotely sensed thermal infrared
data to infer surface soil moisture and evaporation. Water Re
sources Res. 16:787-795.
Price, J.C. 1982. Estimation of regional scale evapotranspiration
through analysis of satellite thermal infrared data. IEE Trans
actions of Geoscience & Remote Sens. GE-20 #3, July 1982.
Pruitt, W.O. 1964. Cyclic relations between evapotranspiration and
radiation. Paper No. 61-716, presented at Am. Soc. Agr. Eng.
Winter Mtg., Chicago, IL, Dec. 1961.
Rosema, A., J.H. Bijleveld, P. Reiniger, G. Tassone, K. Blyth and
J. Gurney. 1978. TELL-US, a combined surface temperature, soil
moisture and evaporation mapping approach. Presented at 12th Int.
Symp. on Remote Sens, of Environ., Environ. Res. Inst, of MI,
Manila, Philippines, 1978.
Rosenberg, N.J. 1974. Micro-climate, the Biological Environment. John
Wiley & Sons, NY. 315 pp.
Seguin, B. 1980. Determination de 11 evaporation reelle dans les bilans
hydrologiques par la tldetection en thermographie infra-rouge.
Bull. -Sci Hydro]. 25:143-153.
Sinclair, T.R., L.H. Allen, Jr. and E.R. Lemon. 1975. An analysis of
errors in the calculation of energy flux densities above vegeta
tion by a Bowen-ratio profile method. Boundary-Layer Met. 8:129-
139.
Sinclair, T.R., L.H. Allen, Jr. and D.W. Stewart. 1971. A simulation
model for crop-environmental interactions and its use in improving
crop productivity. Proc. Summer Computer Simul. Conf., Simul.
Council, Inc., La Jolla, CA. pp. 784-794.
Sinclair, T.R., C.E. Murphey, Jr. and K.R. Knoerr. 1976. Development
and evaluation of simplified models for simulating canopy photo
synthesis and transpiration. J. Appl. Ecol. 13:813-829.
Soer, G.J.R. 1977. The Tergra model, a mathematical model for the
simulation of the daily behaviour of crop surface temperature and
actual evapotranspiration. NIWARS publ. 46, Delft, Netherlands.
Soer, G.J.R. 1980. Estimation of regional evapotranspiration and soil
moisture conditions using remotely sensed crop surface temp
eratures. Remote Sensing Environ. 9:27-45.
Stewart, D.W. and E.R. Lemon. 1969. The energy budget at the earth's
surface: a simulation of net photosynthesis of field. U.S. Army
ECOM Tech. Rept. 2-68-1-6. U.S. Army Electronics Command, Ft.
Huachuca, AZ. 132 pp.


90
Figure 5-4a shows latent heat flux plotted against the surface-to-
air vapor pressure gradient, considering the surface to be saturated at
the surface temperature. The slope of a line passing through the origin
and the plotted points is
The moisture availability for individual half-hour periods is computed
according to
M = 5-5
h(es ea>
where h has been calculated using Eq. 5-2. Moisture availability is
plotted as a function of time in Fig. 5-4b.
Since moisture availability is calculated with the help of the
heat transport coefficient, it responds to all the factors that influ
ence h. The dotted-line in Fig. 5-4b is a plot of moisture availability
calculated assuming.that h is a constant .035 ly/minC (its average
value, as shown in Fig. 5-3b). It shows the exponentially decreasing
pattern one would expect with an originally dew-laden surface. It
should be noted that 1981 was an exceptionally dry year for the
Gainesville area and that, by mid-October, about 50% of the grass was
dead. This accounts for the extremely low moisture availability data.
The relationship between the surface-to-air vapor pressure and
temperature gradients is plotted in Fig. 5-5a. It is determined by two
of the vapor pressure parameters which help determine the temperature
gradient response--the slope of the saturation vapor pressure curve,
and the saturation deficit. If a straight line is fit to this relation
ship, the slope can be interpreted as the average daytime slope of the


9
convert the measurements to proper units, and compute averages. Average
energy budget components and temperature and vapor pressure gradients
were calculated and reported for half-hour periods.
The arrangement of sensors in the field is shown in Figure 1-2.
Aspirated thermopiles and air sampling ports were mounted on arms of a
2.5-m mast. The area within a 10-m radius of this mast was completely
unobstructed to meet the fetch requirements of the measurement method.
Radiometers were attached to the end of a guyed boom about 2 m over the
surface. The precision radiation thermometer was bolted to a camera tri
pod atop an antenna tower 9.5 m above the grass surface; the windspeed
and direction sensors were mounted on the same tower at 7 m. A 14-m
tower served as lightning protection for the entire group of in
struments.
Shielded buried signal cable connected the sensors- to the data ac
quisition system which was housed in a building about 90 m away from the
sensors. For vapor pressure measurements, air samples from five separate
levels in the field were pumped continuously back to the building
through heated insulated tubing and mixing chambers to a dewpoint ana
lyzer. Air samples were switched sequentially to this instrument by a
scanning valve controlled by the measuring computer program. The dew
point was measured after a half-minute delay to allow time for the ana
lyzer to settle on the dewpoint of the sample from the new level.
Altogether, ET data from 42 days were used in verifying the remote
ET estimation method developed. These data were collected in the spring
and fall of 1981.


M (UNITLESS) E (LY/MIN)
.6
91
hM/Y=.006
J L
(a)
J L
0 10 20 30 40 50
Figure 5-4. Moisture Availability Data.


89
riME (TST OCT. 17, 1981)
Figure 5-3. Heat Transport Coefficient Data.


EVAPOTRANSPIRATION: AN AUTOMATIC MEASUREMENT SYSTEM
AND A REMOTE-SENSING METHOD FOR
REGIONAL ESTIMATES
BY
KLAUS HEIMBURG
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1982

ACKNOWLEDGMENTS
The work reported in this dissertation grew out of National Aero
nautics and Space Administration (NASA) sponsored water resources re
search. It was primarily supported by a grant from the Office of Water
Resources Technology in the U.S. Department of the Interior and Agri
culture and Resources Inventory Surveys Through Aerospace Remote Sens
ing (AgRISTARS) program funds administered through the U.S. Department
of Agriculture (USDA). Some support was also received in the form of an
assistantship from the Agronomy Department at the University of
Florida. All these sources of support.are gratefully acknowledged.
I would especially like to thank Dr. Wayne C. Huber and Dr. L.
Hartwell Allen, Jr. for signing the original research proposal as prin
ciple investigators and seeing this project through to its completion.
Without their initial confidence in me and the day-to-day administra
tive efforts of Dr. Allen none of the work would have been possible. I
would also like to thank them and the rest of my supervisory committee,
Dr. Howard T. Odum, Dr. Ralph W. Swain, and Dr. James P. Heaney for
improvements they made possible with their comments on the manuscript.
The research reported in this dissertation stretched over four
years and required the help and cooperation of many people. Sensors and
other equipment were borrowed from USDA, NASA, Center for Wetlands,
Fruit Crops Department, and Environmental Engineering Sciences Depart
ment of the University of Florida. The Animal Science Department per
mitted ET measurements in part of one of its pastures and the Agronomy

Department provided space for an instrument room. The people I owe spe
cial thanks to are Bill Ocumpaugh and Fred McGraw for patiently working
around the measurement equipment and giving up some space; Johnny
Weldon for allowing me the use of the Agricultural Engineering Depart
ment machine shop; Jim Hales for use of his tools and advice in fabri
cating apparatus in the machine shop; Mark Lester for his fine machin
ing; my brother Stephan Heimburg for conscientiously checking and ad
justing the thermopile time constants; Mike Baker for designing and
helping build the scanning valve control electronics, and repairing the
dewpoint analyzer after a lightning strike; Wayne Wynn for help in
maintaining the measurement system; Dan Ekdahl at the Digital Design
Facility for electronics repairsespecially a lightning-damaged compu
ter-controlled voltmeter and similarly damaged computer interface
boards; and finally, Beth Chandler for expeditiously inking most of the
figures in this dissertation.
I also wish to thank Dr. Tom R. Sinclair for finally revealing why
Real Scientists don't do micrometeorology in a neat five-minute sermon-
ette.
I owe a debt of gratitude beyond words to three people who went
miles out of their way to help me. Gene Hannah was invaluable in the
original field installation and helped with problems throughout the
course of the project. I'm thankful to Ferris Johnson for his tireless
assistance in use of the computer system and trouble-shooting computer
hardware problems. Finally, I enthusiastically acknowledge the work of
Pattie Everett, who spared no effort and sacrificed evenings, weekends
and holidays in moving this manuscript through countless drafts toward
perfection.

The post-defense party thrown in my honor made the frustrations
encountered in this work seem tolerableeven worthwhile. I have Pattie
Everett, Bill Campbell, Pierce Jones, and Lisa Lucille Biles to thank
for this totally awesome affair, not to mention that Wild and Crazy
Guy, Terry Spires, and the overwhelming Special Guest Appearance of
The Sublime Ms. Shavonne Rhodes. Get down, tiny dancers!
TV

TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ii
LIST OF FIGURES vii
LIST OF TABLES ix
ABSTRACT x
CHAPTER 1: INTRODUCTION 1
Potential for Remote Evapotranspiration Estimates 1
Scope of Research '3
Research Approach 5
Experimental Site and Data Collection 7
Organization of Dissertation 11
.CHAPTER 2: EVAPOTRANSPIRATION AND SATELLITE DATA'.". '. ... .12
Overview 12
The Evapotranspiration Process 12
The Energy Balance Approach to ET Estimation 17
The Energy Budget Equation 17
Transport Similarity and Wind Models 20
Latent and Sensible Heat Flux Expressions . 23
Energy Budget ET Estimation Strategies 26
Remote ET Estimation Methods 29
Surface Temperature and Net Radiation 29
Simulation Methods 30
Steady-State Methods 33
Temperature Gradient Response Methods 35
CHAPTER 3: A SYSTEM FOR AUTOMATIC COLLECTION OF ET DATA .... 37
Overview 37
Energy Budget/Profile Bowen Ratio Theory 37
Sensor and Time Constant Considerations 40
Data Collection Equipment 44
Data Collection Programs 51
Operational Considerations 58
v

CHAPTER 4: THEORETICAL BASIS OF THE TEMPERATURE GRADIENT RESPONSE
ET ESTIMATION METHODS 62
Overview 62
Temperature Gradient Model 63
Strict Temperature Gradient Response Method 69
Average Temperature Gradient Response Method 70
System Stationarity and Average Temperature Gradient
Response 70
Use of Temperature Gradient/Net Radiation Correlation 73
Extension to Totally Remote ET Estimation Method ... 77
Review of Assumptions 79
CHAPTER 5: VERIFICATION OF THE TEMPERATURE GRADIENT RESPONSE
ET ESTIMATION METHODS 82
Overview 82
Validity of Assumptions 83
Radiation Temperature and Sensible Heat Transport ... 83
Constancy of Parameters 86
Strict Temperature Gradient Response Method 95
Average Temperature Gradient Response Method 97
Graphical Representation of the Average TGR Method . 97
ET Estimates with the Average TGR Method 103
Effects of Individual Parameter Variations 105
Generality of ATGR Latent/Sensible Partition 112
Tests of the ATGR Method /. . . . ... . .114
CHAPTER 6: CONCLUSION 123
Summary of Results 123
The Average Temperature Gradient Response Method . 123
Method Limitations and Strengths 125
Recommendations for Future Research 128
REFERENCES 131
APPENDIX A: LIST OF SYMBOLS 136
APPENDIX B: PROGRAM LISTING AND DEFINITION OF NAMES USED .... 138
Program SET 139
Program MEASR 141
Program REPRT 146
Program ANALZ 149
Definition of Names 152
APPENDIX C: SUMMARY OF ENERGY BUDGET DATA 157
APPENDIX D: SUPPLEMENTARY FIGURES 178
BIOGRAPHICAL SKETCH 211
VI

LIST OF FIGURES
Page
Figure 1-1. Location of the University of Florida Beef Re
search Unit 8
Figure 1-2. Field Apparatus and Sensor Locations 10
Figure 2-1. System Diagram of Generalized Evapotranspiring
Surface 14
Figure 2-2. Rough Calculation of Heat Storage in Pasture Canopy . 19
Figure 3-1. Bowen Ratio Calculation from Measurements of Vapor
Pressure and Temperature 41
Figure 3-2. Schematic of ET Measurement System 45
Figure 3-3. Detail of Profile Measurement Mast Arm .48
Figure 3-4. Detail of Air Sampling Equipment 50
Figure 3-5. Example of Intermediate Program Output 53
Figure 3-6. Example of Half-Hourly Data Report . 56
Figure 4-1. Definition Sketch for Transport Properties . . .64
Figure 4-2. Components of Vapor Pressure Gradient 67
Figure 5-1. Total vs. Turbulent Temperature Gradients for a
Clear Day 85
Figure 5-2. Total vs. Turbulent Temperature Gradients for a
Cloudy Day 87
Figure 5-3. Heat Transport Coefficient Data 89
Figure 5-4. Moisture Availability Data 91
Figure 5-5. Vapor Pressure Parameter Data 92
Figure 5-6. Soil Heat Flux Parameter Data 94
Figure 5-7. Clear Day Temperature Gradient/Net Radiation Corre
lation 98
Figure 5-8. Graphical Interpretation of Temperature Gradient/Net
Radiation Correlation 100
Figure 5-9. Cumulative ET Estimates 102
vii

Figure 5-10. Effect of Moisture Availability and Vapor Pressure
Parameters on Temperature Gradients 106
Figure 5-11. Effect of Heat Transport Coefficient and Soil Heat
Flux Parameter on Temperature Gradients 107
Figure 5-12. Temperature Gradient Response of a Clear Day with
Constant Moisture Availability 110
Figure 5-13. Temperature Gradient Response of a Partly Cloudy
Day Ill
Figure 5-14. Generalized Clear Day H/E and E/R Patterns 113
Figure 5-15. Comparison of Measured and Estimated Bowen Ratios . 115
Figure 5-16. Cumulative ET Estimates by the ATGR and Residual
Methods 122
Appendix D: Supplementary Figures
Figure 1. Hypothetical Daytime Temperature Profile ...... 179
Figure 2. Simplified Temperature Profile 179
Figure 3. Simplified Temperature Profi1es .for a Clear Day . 180
Figure 4. Simplified Temperature Profiles for an Overcast Day 181
Figure 5. Air Transport Coefficient for Average Conditions . 182
Figure 6. Soil Heat Flux Parameter for Average Conditions . 183
Figure 7. Variation of the Daily Average Heat Transport
Coefficient with the Daily Average Windspeed .... 184
Figure 8. Data and ET Estimates for Oct. 17, 1981 186
Figure 9. Data and ET Estimates for Oct. 18, 1981 191
Figure 10. Data and ET Estimates for Oct. 21, 1981 196
Figure 11. Data and ET Estimates for Oct. 22, 1981 201
Figure 12. Data and ET Estimates for Oct. 23, 1981 206
vi i i

LIST OF TABLES
Page
Table 1-1. Spatial and Temporal Resolution in Satellites .... 3
Table 3-1. Data Acquisition System Identification 46
Table 3-2. Sensor Identification 49
Table 3-3. Variable Names and Units for Half-Hourly Reports ... 57
Table 4-1. Evapotranspiration Formulae for Average TGR Method . 74
Table 5-1. Example Calculations with the Strict TGR Method ... 96
Table 5-2. Comparison of Average and Correlation Estimated
A and B 116
Table 5-3. Quality of ET Estimates made with the ATGR Method . 119
ix

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
EVAPOTRANSP¡RATION: AN AUTOMATIC MEASUREMENT SYSTEM
AND A REMOTE-SENSING METHOD FOR
REGIONAL ESTIMATES
By
Klaus Heimburg
December 1982
Chairman: Wayne C. Huber
Major Department: Environmental Engineering Sciences
A generalized physical method is developed for making evapotran-
spiration (ET) estimates based on directly measured air temperature and
remotely sensed surface temperature and net radiation data. The method
is based on the correlation of surface-to-air temperature gradients and
varying net radiation loads; the slope and intercept of this correla
tion are shown to be composite values of two groups of surface parame
ters. Five equations are developed to calculate ET from these composite
values plus net radiation and some combination of two of the four sur
face parameters (bulk air transport, moisture availability, saturation
deficit, and soil heat flux).
The method is validated using ET measurements made over a pasture
surface using the energy budget/profile Bowen ratio technique. An auto
matic measurement system consisting of a computer-controlled data ac
quisition system and air sampling arrangement, time-constant-matched
humidity, temperature, and radiation sensors, and four interacting
x

programs was developed to measure and calculate half-hour average sur
face energy budgets and statistics. Data from 42 days in the spring and
fall of 1981 are reported.
It was found that the radiation surface temperature is in general
not the same as the effective heat transport surface temperatureit
may be necessary to correct remote surface temperature measurements
before using them with conventionally evaluated heat transport coeffi
cients. Because parameters are assumed constant, instantaneous ET esti
mates made with the developed method are at times systematically high
or low, but these errors tend to cancel in cumulative estimates.
The method is shown to be well-suited for use with 1- to 3-hour
time resolution satellite data. In effect it evaluates surface parame
ters such as moisture availability, requires no interpolation for ET
estimates between data sets, is adapted.to the inevitable cloud-caused
loss of satellite surface temperature data, and reduces calculation of
cumulative ET to estimating total positive net radiation and duration
of positive net radiation in a particular estimation period. The meth
od's ET estimates are shown to be as accurate as the state-of-the-art
simple residual method, which does not have these advantages.
XI

CHAPTER 1
INTRODUCTION
Potential for Remote Evapotranspiration Estimates
The loss of water from the earth's surface by either evaporation
from soil and plant surfaces or transpiration by plants is called evapo
transpiration (ET). Along with rainfall and runoff, it plays a very sig
nificant role in determining the availability of water at the earth's
surface and the recharge to deep aquifers. Because water is critically
important to man's existence, ET estimation methods are important in
solving problems of water supply.
Water supply problems in relatively dry -areas have, long included
the estimation of crop water requirements, evaporation from reservoirs,
and evapotranspiration over aquifer recharge areas. As population has
grown, the demand for water has increased and interest in estimation
methods has become more widespread. Today, there is a growing need for
evapotranspiration estimates even in relatively wet areas, such as
Florida.
Present methods of measuring and estimating ET are diverse, depend
ing upon the specific purposes of the estimates and available data. On
the one hand are physically-based measurement techniques developed by
scientists. They provide accurate instantaneous ET rates for a specific
location, but require continuous measurements of such variables as air
temperature and vapor pressure, net radiation, and soil heat flux. Exam
ples of these techniques are the eddy flux correlation, energy
1

2
budget/profile Bowen ratio and Penman methods (American Society of Agri
cultural Engineers, 1966; Brutsaert, 1982).
On the other hand, water use planners and water supply engineers
have developed methods which produce daily to monthly estimates for
larger areas. In locations where such records are kept, these methods
are based on climatologic data. They are generally founded on some phys
ical correlation, but all involve empirical adjusting factors for vege
tation type, air humidity, altitude and the like. Examples are the
Blaney-Criddle method, the radiation method, the Penman method, and the
pan evaporation methods (Doorenbos and Pruitt, 1977).
The weather stations which provide the base information for these
methods are widely scattered. On the average, each station in the United
States represents an area on the order of 100 mi square (Price, 1982).
Regional estimates of evapotranspira.tion are thus difficult to make and
of dubious accuracy. They are limited by insufficient data on highly
variable surface parameters such as soil moisture conditions and vegeta
tion types.
By comparison to the weather station network, today's satellites
return remotely sensed information about the earth's surface with an
unprecedented level of detail. The surface area element or pixel sizes
and the time intervals between coverage of some of the satellites appro
priate to regional scale studies are shown in Table 1-1. As a result of
the availability of this type of data and modern high-speed computers,
the potential exists to systematically monitor evapotranspiration on a
regional scale.
Development of this potential could benefit a variety of research-
areas. If remote-sensing methods are also developed to estimate rainfall

3
Table 1-1.
Spatial and Temporal
Resolution in
Satelli tes
Satellite
Orbit
Pixel
Time
Acronym
Type
Size
Intervals
Landsat
polar
80 x 80 m
18 da
HCMM
pol ar
.6 x .6 km
12 hr each 5 da
TIROS
pol ar
1 x 1 km
12 hr.
GOES
geostationary
8 x 4 km
30 min
on a regional basis and if streamflow is gaged, aquifer recharge over
wide areas can be estimated (Allen et jfL, 1980). The information on
surface energy fluxes gained by an ET estimation technique could also be
useful as boundary conditions for models of the atmosphere. It is also
possible that large-scale changes on the earth's surface such as defor
estation and desertification could be monitored by observing longer-term
changes in ET patterns. Finally, the correlation of evapotranspiration
and yield in agronomic crops may lead to large-scale yield predictions
(Doorenbos and Pruitt, 1977; Chang, 1968).
The purpose of this research is to develop and test a generally
applicable method for estimating evapotranspiration based as much as
possible on remotely sensed data. Since it is ultimately intended for
use with satellite data from large diverse areas, criteria for this
method include that it be strictly physical, relatively easy to apply,
and compatible with the format and limitations of satellite data. The
research is also intended to identify factors critical to the accuracy
of the estimates which require more research, and factors which may im
prove future satellite measurement for use in ET estimation.
Scope of the Research
Data returned from a satellite consist of the energy flux in a par
ticular band of wavelengths coming from a particular surface area

4
element at a particular time. For environmental applications, the elec
tromagnetic spectrum is usually resolved into visible and thermal bands.
With a clear sky and proper consideration of atmospheric transmission
properties, these measurements can be used to calculate the surface tem
perature and the net radiation absorbed by the surface.
Net radiation and surface temperature estimates should lead to good
evapotranspiration estimates because they are very prominent variables
in the heat exchange processes that take place at the earth's surface.
Net radiation is the primary energy source used in changing water from
liquid to vapor at the surface, while surface temperaturebecause it is
a result of surface variables and energy exchange processes--is a com
posite measurement of the effects of these variables.
However, it is a long step from measurements of net radiation and
surface temperature to an operational ET estimating'system-using satel-
lite data. The following questions illustrate the range of problems
faced in developing a method for such a system.
1. What is the best way to estimate net radiation from satellite
pixel information? How does one treat clouds or haze?
2. How is the radiation temperature of a complex surface like that
of vegetation interpreted? Does angle of view and height of
vegetation make a difference? How does one handle a canopy
underlain by a cool surface like a marsh or swamp? How does
one treat mountainous topography?
3. Is an interpolation technique required to compensate for the
temporal resolution of satellite data?
4. What level of detail is required in a practical ET estimation
method? How does one get the most acceptably accurate estimate
for the least effort in data collection and processing?
5. How are the effects of water availability, vegetation type,
cloudiness, and wind related? And how do they influence ET?
What is the minimum amount of data needed from ground-based
observations?

5
6. Can estimates made with area average data be of reasonable
accuracy when there are various vegetation types or net ra
diation regimes in the same pixel?
7. Ultimately, what factor most limits the accuracy of a given
remote estimation scheme?
The work described in this dissertation addresses many of these
questions. The emphasis is on how to most efficiently account for all
the factors affecting evapotranspiration, and how to extract as much
information as possible about the surface and its environment from re
mote data. Practical limitations such as the fact that satellite data
are available only at discrete time intervals and sometimes incomplete
because clouds prevent a surface temperature measurement are considered.
All ground-based measurements except air temperature were avoided; meth
ods to eliminate this measurement are suggested, but their investigation
was considered beyond the scope of this research.
It is assumed that estimates of net radiation and surface tempera
ture are, barring clouds, available at regular time intervals. The ques
tion of complex radiation temperatures is side-stepped by considering a
relatively simple pasture grass surface. Although a parameter that in
cludes the effect of wind on evapotranspiration is used, its functional
dependence on windspeed is not explored.
Research Approach
The overall approach to developing a remote evapotranspiration es
timation scheme was to compare estimates made with trial methods to ac
tual ET rates measured over a test surface. Accordingly, there were
three main areas of effort: the collection of a base of accurate ET
data, the theoretical development of an estimation method based on re
motely sensed data, and the testing of that method against the actual ET
measurements.

6
As suggested in the previous section, the enormous variety of ter
rain and vegetation types present on the earth's surface introduce a
large number of complicating factors into ET estimation formulations. In
order to clearly assess the potential of a general method, as many of
these complicating factors as possible were avoided by choosing a rela
tively homogeneous flat area of pasture as a test surface. The approach
was to develop a basic method which would work for simple surfaces; once
it is proven successfult can be modified if necessary to deal with
more complex situations like mountainous terrain or swamp.
A micrometeorologic measurement technique was used to measure ac
tual ET so that surface processes were left as undisturbed as possible.
The radiation surface temperature as well as net radiation was measured
for later use in method-testing. A great deal of effort went into devel
oping a data collection system to assure the reliability of the ET mea
surements. Special efforts were made to match the time constants of the
sensors involved and to reduce electrical signal noise. Control of the
measuring system, scheduling of the measurements, and calculations were
all performed by computer to minimize human error.
The fundamental assumption in method development was that satellite
data would be available in time intervals on the order of 1-3 hours.
After this assumption, the emphasis was on operational criteriaa prac
tical method must have general applicability, computational simplicity,
and low data requirements. With these objectives in mind, an analytical
approach, rather than a simulation approach, was chosen. In order to
keep data requirements low yet take advantage of satellite data, the
level of detail was chosen to be somewhat intermediate between the
strictly physical ET measurement methods and the empirical estimation

7
methods. This required a set of assumptions, all of which are explicitly
identified in the derivation of the method.
The general objective of the method-testing was to validate the
general framework of the method and to assess the error contributions of
various parts of the method on instantaneous and cumulative ET esti
mates. The assumptions made during the development of the method were
individually examined; in this way, the relative importance of ground-
gathered ancillary data such as air temperature, saturation water vapor
deficit, windspeed, and soil temperature could be judged. The testing
was done with ideally accurate on-site measurements of net radiation,
surface temperature, air temperature, and evapotranspiration.
Experimental Site and Data Collection
An area of pasture at the University of Florida's Beef Research
Unit was used as the research surface. The site is located northeast of
Gainesville, Florida, as shown in Figure 1-1. It was chosen because it
is typical of northern Florida pasture areas, and was amenable to micro-
meteorologic measurement of a surface energy budget. The area was flat
with relatively uniform grass cover, and was large enough to ensure
well-developed temperature and vapor pressure profiles. The test surface
was a mixture of grasses: roughly 60-70% was bahiagrass (Paspa!urn
notatum), about 20-40% was smutgrass (Sporobolus polretii), and 5-10%
was white clover (Trifolium repens).
Evapotranspiration was computed by an energy budget/profile Bowen
ratio method from measurements of net radiation, soil heat flux, and
gradients of temperature and water vapor pressure over the pasture sur
face. A Hewlett-Packard 2100 computer and low-speed data acquisition
subsystem was used to automatically scan and measure the sensors,

8
Figure 1-1. Location of the University of Florida Beef Research Unit

9
convert the measurements to proper units, and compute averages. Average
energy budget components and temperature and vapor pressure gradients
were calculated and reported for half-hour periods.
The arrangement of sensors in the field is shown in Figure 1-2.
Aspirated thermopiles and air sampling ports were mounted on arms of a
2.5-m mast. The area within a 10-m radius of this mast was completely
unobstructed to meet the fetch requirements of the measurement method.
Radiometers were attached to the end of a guyed boom about 2 m over the
surface. The precision radiation thermometer was bolted to a camera tri
pod atop an antenna tower 9.5 m above the grass surface; the windspeed
and direction sensors were mounted on the same tower at 7 m. A 14-m
tower served as lightning protection for the entire group of in
struments.
Shielded buried signal cable connected the sensors- to the data ac
quisition system which was housed in a building about 90 m away from the
sensors. For vapor pressure measurements, air samples from five separate
levels in the field were pumped continuously back to the building
through heated insulated tubing and mixing chambers to a dewpoint ana
lyzer. Air samples were switched sequentially to this instrument by a
scanning valve controlled by the measuring computer program. The dew
point was measured after a half-minute delay to allow time for the ana
lyzer to settle on the dewpoint of the sample from the new level.
Altogether, ET data from 42 days were used in verifying the remote
ET estimation method developed. These data were collected in the spring
and fall of 1981.

10
Figure 1-2. Field Apparatus and Sensor Locations. This diagram is not
to scale.

n
Organization of Dissertation
Basic concepts underlying current understanding of the evapotran-
spiration process are reviewed in Chapter 2. These concepts are funda
mental to both the evapotranspiration measurement and method develop
ment portions of the study. Chapter 3 describes the computer-based evap
otranspiration measurement system that was developed to collect a base
of accurate ET data. This chapter contains the theory of the meas
urement technique, considerations made in designing the profile sensing
systems, brief descriptions of the programs that operate the system, and
an assessment of the strengths and weaknesses of the measurement sys
tem. Two methods of calculating ET based on remotely sensed data are
derived in Chapter 4, one relatively rigorous with a minimum of added
assumptions, and a grosser less detailed one with extensive approxima
tions. Both methods are based on a temperature gradient model which uses
net radiation and surface temperature data to determine surface parame
ters. The performance of this model and these methods is compared to
actual ET measurements in Chapter 5. The method most suitable for use
with satellite data is tested component by component to clearly evaluate
its strengths and weaknesses. A summary of conclusions and suggestions
for further research are contained in Chapter 6.
Repeatedly used symbols are defined in Appendix A. (All symbols are
defined in the text where they are introduced.) Appendix B is a listing
of the programs developed for the automatic ET measurement system, along
with definitions of names for subroutines, functions, data arrays, and
indexes. Appendix C is a summary listing of the data collected, and sup
plementary figures are presented in Appendix D.

CHAPTER 2
EVAPOTRANSP¡RATION AND SATELLITE DATA
Overview
The availability of satellite images of the earth's surface and the
resources to investigate their usefulness has resulted in a variety of
remote-sensing research projects. In recent years, there have been pro
grams in which evapotranspiration estimation procedures were the objec
tive, notably a joint effort among the National Aeronautics and Space
Administration (NASA), the Institute of Food and Agricultural Sciences
at the University of Florida, the Florida Water Management Districts
(Allen 'jet ai_., 1980), and NASA's Heat Capacity Mapping Mission, or HCMM
(Goddard Space Flight Center, 1978).
Since the estimation techniques need to be applicable to many dif
ferent surfaces, physical rather than empirical approaches are. required.
The physical methods that have been developed, including the one pre
sented in this work, are all based on the energy budget concept of the
surface and on the similarity of transport among quantities in turbulent
flow. These ideas and various approaches to solving the energy budget
equation are developed in the first part of this chapter. Remote ET es
timation techniques are reviewed in the second part, which concludes
with an introduction to the new method.
The Evapotranspiration Process
At the interface between a liquid and a gas, molecules are continu
ally breaking and reforming the intermolecular bonds which hold them at
12

13
the surface as a liquid. The energy of the random molecular collisions
which cause the bonds to break is carried with the freed molecule; this
thermal (heat) energy is lost by either liquid or gas molecules near the
interface. Since this energy contributes only to the molecule's conver
sion to the vapor state and not its temperature, it is called the latent
heat of vaporization. It is released to the molecules at the surface
should a free molecule collide with and be captured by molecules in the
liquid state.
When the concentration of vapor molecules is higher at the surface
than at some distance away from it, there is a net flow of molecules and
energy (in the form of latent heat) away from the surface. This process
is evaporation.
Evapotranspiration is the evaporation of water from soil or plant
surfaces together with transpiration by plants. In transpiration, water
evaporates from internal plant surfaces and diffuses into the air around
the plant through openings in the leaves (stomata). Like the process of
evaporation, evapotranspiration consists of three fundamental elements:
the absorption of thermal energy at a water-air interface, the change of
state of water from liquid to vapor, and the resulting net loss of vapor
molecules and their heat of vaporization from the surface due to a fa
vorable vapor concentration gradient.
The heat energy consumed in the evapotranspiration process is lost
from the vegetation biomass. Therefore, all the energy fluxes to and
from the plant canopy and the factors influencing them play a part in
determining the evapotranspiration rate. Figure 2-1 is a simplified dia
gram of the surface and its primary energy and water fluxes. It is pre
sented in the diagramming language of Odum (1982), and embodies many of

14
Figure 2-1. System Diagram of Generalized Evapotranspiring Surface.
Symbols are from Odum (1982).

15
the concepts and simplifications conventionally applied in evapotranspi-
ration theory.
The heat energy stored in the plant canopy is represented by its
temperature (T ). The bulk of this energy comes into the vegetation in
the form of direct or scattered solar short wavelength (0.3 to 3 pm)
radiation (Qs); it also intercepts thermal or long wavelength (3 to
50 pm) radiation emitted by the atmosphere (Q ). A substantial fraction
G
of the shortwave radiation received by the surface is reflected (Qr), a
very small part is used to drive photosynthetic reactions in the plants,
and the remainder becomes heat energy absorbed and stored temporarily in
the biomass. Part of this energy is reradiated to the atmosphere (Qg).
The difference between the downwelling radiation (direct and atmo
spheric) and.the upwelling radiation (reflected and emitted) is referred
to as net radiation (R).
Besides these radiant energy fluxes, the vegetation exchanges en
ergy with its environment in several other ways. Thermal energy ex
changed with the air by the process of molecular conduction and turbu
lent diffusion is referred to as sensible heat flux (H); energy ex
changed with the soil is soil heat flux (G). Energy used in the change
of state from water to water vapor is transported with water vapor and
is referred to as latent heat flux (E).
In this generalized view of the surface system, the plant canopy is
considered to have a uniform temperature representative of its heat con
tent. There are complex energy exchange processes that occur within the
canopy because of differences in temperature. For example, radiation is
exchanged between plant surfaces, and sensible heat released from one
leaf may be reabsorbed and released from another as latent heat.

16
However, when the purpose is to make total evapotranspiration estimates,
these exchanges are ignored, and only the energy fluxes entering or
leaving its boundaries are considered.
Besides the radiant energy pathways (R) and heat energy stored in
the plant canopy, Fig. 2-1 shows the dependence of the surface energy
balance, and thus evapotranspiration, on factors in the environment of
the surface. Heat that is lost to (or gained from) the air as sensible
heat is not (is) available for evapotranspiration. This flux is depen
dent on the air temperature (T ) and the thermal transport properties of
a
the air, represented by the eddy thermal diffusivity (K^) in the figure.
When the air temperature is cooler than the surface temperature of the
canopy, sensible heat moves from the canopy into the air. When the can
opy is cooler than the air, it absorbs heat energy from the air. There
is an analogous heat flux pathway to. the soil, dependent on soil temper
ature (T ) relative to the canopy temperature (T ), and the thermal con-
9 s
ductivity of the soil (X).
The right half of Fig. 2-1 shows the pathway of water through the
surface system. It originates in the soil and moves through plant tis
sues into the leaves, where it evaporates. Depending on the vapor pres
sure inside the leaves (e^), the vapor pressure in the surface air layer
outside the leaf (e$), and the stomatal conductivity (Cs), water vapor
then diffuses through stomata into the air around the leaves. From the
surface layer water vapor diffuses into the air, depending on the rela
tive vapor pressures of the surface layer and air (e,. and e ) and the
eddy water vapor diffusivity (K^).

17
The Energy Balance Approach to ET Estimation
The Energy Budget Equation
The three elements of evapotranspiration (the absorption of water
from the soil or plant surfaces, the absorption of thermal energy from
the plant canopy, and the flux of water vapor through the air over the
surface) provide at least three fundamental approaches to evapotranspi
ration measurement. These have been referred to as the water budget,
energy budget, and aerodynamic approach, respectively. All previously
developed remote ET estimation methods, the remote technique developed
in this study, and the ground truth measurement technique used in this
study are founded on the energy budget equation.
The energy balance of a vegetation and air layer can be written
R-E-H-G-P-S = 0, 2-1
where R is the net radiation flux absorbed '(from p.15, R = Q +Q -Q -Q )
E is the latent heat flux, are
H is the sensible heat flux,
G is the soi1 'heat flux,
P is the photosynthetic heat flux, and
S is the time rate of heat flux storage in the vegetation/air
layer.
Here energy "flux" is used to describe energy "flux density," i.e., the
energy flow per unit time through a unit area. All terms are in these
units.
Because of inherent measurement difficulty and sensor limitations,
the energy budget components can only be measured to within about 10% of
their actual values (Sinclair et _al_., 1975). Since some of the smaller
components are actually indistinguishable from measurement error, they
need not be considered.

18
Usually the smallest component is photosynthetic heat flux. It can
be considered negligible because only 1 to 5% of the net radiation im
pinging on vegetation is absorbed in this way (Allen _et al_., 1964).
It can be shown by a "worst case" calculation that the storage term
is also in the negligible range. Heat in the vegetation/air layer can be
stored as sensible heat in the air, latent heat in the air, sensible
heat in the biomass, and sensible heat in the litter surface layer. In a
strict sense, these are evaluated as follows:
S =
c (z)
a
STa(z)
3 t
dz +
1 ca 3ea(z)
0
y 31
dz +
3 T h (z)
cj!) i! +
rd 3T (z)
C (z) ^
0 9
2-2
where c (z), c,(z), and c (z) are volumetric heat capacities ( c) of
a o g
canopy air, plant biomass, and surface soil, respectively,
T (z), T, (z) and T (z) are the temperatures of canopy air,
a d g
canopy biomass, and surface soil, respectively,
e (z) is the vapor pressure of canopy air,
a
Y is the psychrometric constant,
1 is the vegetation height,
d is the depth of the surface litter layer, and
z is the vertical space coordinate.
Using averages for the spatial variables, Eq. 2-2 can be rewritten:
S = (Pcp}a h
ATa (pCn Aea
£ + ELi h
At Y At
(Vc)
^b
b At
AT,
(pc) d Z9-
At
2-3
where a, b, and g are subscripts referring to air, biomass, and soil
specific heats, densities, and temperatures, and
V is the mass of vegetation per unit area.

total
sensible heat
latent heat
heat stored
heat
stored
heat
=
stored in
+
stored in
+
in
+
in
top
storage
canopy air
canopy air
vegetation
soi 1
layer
(pc ) h ATa
p a At
(pc) h
1 Aea
pa y At
(Vc)
ilb
b At
AT
+ .0012 x 0.24 SIx20cXt + -0012 -K x 0.24 j20oul.s5l3
cm y cm-3 y
mb +
10000 Tia x 1,0 g^ x Tr + 1,5 ~S x '2 g* x 1 cm x 1 W
3 cm 3
.0006
cal
2
cm min
.0004
cal
cm mm
.01
cal
2 .
cm min
.006
cal
cm mm
.02
crrr min
Figure 2-2. Rough Calculation of Heat Storage in Pasture Canopy.

20
This expression is evaluated in Fig. 2-2 using values typical for
pasture grass. Heat storage in pasture biomass and the top litter layer
is approximately two orders of magnitude less than peak net radiation
loads; latent and sensible heat storage in the canopy air is about three
orders of magnitude less.
Since the values of the photosynthetic heat flux and the time rate
of canopy heat storage are negligibly small, the energy budget equation
may be written
R-E-H-G=0 2-4
The ET measurement method and the remote estimation method are based on
this simplified form of the equation. It is also the basis for all but
the empirical remote-sensing ET estimation methods. The following sub
sections briefly review the fundamental analytical concepts and evalua
tion techniques which .are common to previously developed evapotranspira-
tion estimation methods based on the energy budget equation.
Transport Similarity and Wind Models
After the surface energy balance, the most important concept to ET
estimation techniques is that of transport similarity among momentum,
heat, and mass fluxes in the turbulent layer near the surface. This idea
is used in all forms of the energy budget approach to ET estimation,
both to evaluate transport properties and to avoid evaluating transport
properties.
The fundamental equations for the one-dimensional transport of mo
mentum, heat, and water vapor are (Eagleson, 1970)
H = pcpK
3JT
H 3 z
2-6

21
E =
dc w ae
p az
2-7
where t is momentum flux,
H is sensible heat flux,
E is latent heat flux,
Km, Kn, Kw are the eddy diffusivities of momentum, heat, and water
M vapor.
u
T
e
p
&
P
e
s the average horizontal windspeed,
s temperature,
s vapor pressure,
s the air density,
s the air specific heat at constant pressure,
s the latent heat of evaporation,
s the atmospheric pressure, and
is the ratio of molecular weights of water and dry air.
The similarity hypothesis, which was developed in the last half of the
nineteenth and early twentieth centuries (reviewed by Brutsaert, 1982),
proposes that the eddy diffusivities of momentum, heat, and water vapor
are all the same:
km = kh -fw
2-8
It was not until Prandtl's (1932) development of the mixing length
concept that general analytical treatment of eddy diffusivity began.
According to mixing length theory, it is argued that
,2 du
V2) = 1 Si
2-9
where l is the mixing length and
IT is the average windspeed perpendicular to z (horizontal).
By postulating that the mixing length increased with distance from a
surface (i = kz, where k is the von Karman constant), Prandtl went on to
derive an expression that accurately describes the variation of wind-
speed near a surface, the simple log wind profile. With parameters for
displacement height (Dwith dense vegetation, that height above the
surface where the windspeed vanishes) and roughness height (ZQ--a

22
parameter included so that the windspeed is defined as zero when
z D = 0), the equation for the log profile can be written
u(z) =ln
z D + z
2-10
where is the shear stress at the surface. With this wind profile, the
eddy diffusivity can be evaluated between the surface and any level in
the air with average windspeed ufl:
K(z)
K Ua(z D + z0)
In
z D + z.
2-11
With the assumption of transport similarity (Eq. 2-8), this expression
can be used to evaluate and K^. Similar treatments of eddy diffusiv
ity can be found in many texts (e.g., Brutsaert, 1982).
With very precise experimental work it has been determined that the.
turbulent transport of momentum, heat, and water vapor is strictly simi
lar only under neutral stability conditions, e.g., Swinbank and Dyer
(1967). To describe eddy diffusivities under other conditions, diabatic
influence functions w) have been developed. They are defined
such that
kh * km a"d
Kw = t~
W M
2-12
2-13
These are experimentally determined and expressed in terms of dimension
less variables such as the Monin-Obukhov length or Richardson number
(Morgan et al_., 1971; Businger, 1973).

23
A number of wind profiles and corresponding eddy diffusivity treat
ments both with and without stability corrections have been developed.
(These are referred to as wind models.) None are used in this study, but
the fact that bulk air transport is theoretically and experimentally
adequately understood is important in supporting the remote-sensing
method developed. All remote-sensing methods involve a wind model of
some kind to help evaluate sensible and latent heat fluxes.
Latent and Sensible Heat Flux Expressions
In application, the flux between two specific points (z^ and z^)
that have a gradient between them must be evaluated. Since eddy diffu
sivity in general varies with the distance from a surface (Eq. 2-11),
the latent and sensible heat transport equations (Eqs. 2-5, 2-6 and 2-7)
must be integrated along the direction of transport and between the
points of application (Monteith, 1973). Assuming that .all parameters
except diffusivity are constant between the two levels and that the flux
in question is steady (or that flux storage in the layer between levels
is negligible),
H (T1 T2>
'2 dz
and
pLe (el e2}
E = p
dz
2-14
2-15
z, y77
The integral in the denominator of these equations, when evaluated, rep
resents the lumped transport properties between points z^ and z^ away
from the surface. From the preceding subsection, it is understood that
these integrals can be evaluated with various wind models for K2(z).

24
The expressions for latent and sensible heat flux that are commonly
used are simplified versions of Eqs. 2-14 and 2-15. For sensible heat
flux from the surface to a reference level above the surface, the inte
gral expression is abbreviated either as a bulk thermal conductivity or
as a bulk air resistance:
pCo(Ts V
H = pc K(T T ) = L s 2-16
p s a ra
where T is the surface temperature,
Ta is the air temperature at a reference level above the surface,
Ka is the bulk thermal conductivity for the slab of air between
the surface and the reference level, and
r is the bulk resistance to heat transport of the slab of air
a between the surface and the reference level.
In this study, the sensible heat flux expression is condensed even fur
ther to
H = h(T T ) 2-17
b a
where h is referred to as the bulk heat transport coefficient. Since the
fundamental definition of h is
PCn
h = 2-18
la dz
use of a wind model (to evaluate K^) is implied any time the bulk heat
transport coefficient or bulk air resistance is used (Monteith, 1973,
1975; Thom and Oliver, 1977).
Applying the similarity concept to a description of latent heat
flux is complicated because it is impossible to measure the vapor pres
sure at the vegetation surface. The air inside the leaves is usually
assumed to be at the saturation vapor pressure corresponding to the sur-
face temperature [e$ = e (Tg)]. A unitless parameter M, which varies

25
from 0 to 1, can be introduced to account for subsaturation of the sur
face air:
M(e* ea) = es ea 2-19
This formulation was suggested by Tanner and Pelton (1960) and applied
by Outcalt (1972), Pandolfo and Jacobs (1973), Nappo (1975), and Carlson
and Boland (1978), and in a slightly different form by Barton (1979).
The equation for latent heat flux can then be written in terms of the
heat transport coefficient and moisture availability parameter:
E = M(e* ej 2-20
y s a
*
where e$ is the saturation vapor pressure at the surface temperature,
e is the vapor pressure at the reference level a,
Ma is a unitless parameter interpreted as moisture availability,
h is the bulk heat transport coefficient, and
Y is the psychrometric.constant (y = cpP/Le).
The resistance formulation (Monteith, 1973) includes an additional' re
sistance term, r the bulk stomatal diffusion resistance (sometimes
referred to as the canopy resistance, r ) to account for the subsatura
tion of air at the surface:
E =
PCD y(r + r )
G o
2-21
Both of the transport coefficient resistance formulations are used
in the ET literature; analytic evaluation of either type of expression
is based on diffusivity integrals like those in Eqs. 2-14 and 2-15.
These formulations can be substituted for one another with the following
identities:
h
a
r
and
2-22
M =
ra + rs
This study uses the conductivity formulation.
2-23

26
Energy Budget ET Estimation Strategies
There are two major ways in which the energy budget and gradient
equations can be solved. The physically more realistic method is based
on dynamic simulation of the heat transfer processes; the other method
is based on a cruder description of the surface and steady-state analy
sis of the surface heat exchange processes.
Gradient expressions like those in Eqs. 2-5, 2-6 and 2-7 are used
in both approaches. The difference is that in simulations the expres
sions are applied over arbitrarily short distances and time steps ac
cording to the level of detail required in the application. When trans
port is in one direction, as it is considered to be in most of the prob
lems encountered in ET measurement or prediction, the medium through
which the flux is transported is thought of as consisting of layers per
pendicular to the direction of transport. Fluxes through each layer can
then be computed individually for each time step, allowing the treatment
of flux transients as well as the treatment of differing transport prop
erties of the layers. In the steady-state approaches the gradient ex
pressions are applied over the entire distance between measurements, and
transients are ignored.
Simulation models consist of an interdependent system of equations
which describe the exchange of latent, sensible, and soil heat flux with
the vegetation layer and the air or soil, and also the transport of la
tent, sensible and soil heat between layers. This system of equations is
solved iteratively using solar and atmospheric radiation data as a forc
ing function and quantities such as air temperature, vapor pressure, and
soil temperature as boundary conditions. Generally, unknown surface pa
rameters are chosen such that simulated surface temperatures match

27
observed surface temperatures. The simulated ET flux is then assumed to
be the actual ET flux. Examples of evapotranspiration simulations are
Waggoner et _al_. (1969), Stewart and Lemon (1969), Sinclair et al.
(1971), Murphy and Knoerr (1970, 1972), Goudriaan and Waggoner (1972),
Lemon _et _al_. (1973), and Sinclair et. _al_. (1976). Dynamic models of the
surface heat transfer processes are computationally orders of magnitude
more complex than the steady-state approaches, and were developed only
after the introduction of the electronic computer.
The earliest physical models of the surface energy exchange process
were based on steady-state analysis and the similarity of latent and
sensible heat transport. Three steady-state strategies for solving the
energy budget equation for evapotranspiration have been developed; they
are referred.to as the simple residual, Penman, and Bowen ratio methods.
To more easily compare these methods, their equations have been written
in the same notation. Soil heat flux is included even though this compo
nent is often assumed too small to be included for vegetated surfaces.
In the residual approach, the energy budget equation is solved for
latent heat flux, and a simple gradient expression is used to evaluate
sensible heat flux:
E = (R G) h(Tc T ) 2-24
The transport coefficient for air conductivity is estimated from empiri
cally derived wind functions or physical wind models as described previ
ously. The biggest advantage of this method is that it requires no in
formation on the surface moisture status. Its disadvantage is that it is
very sensitive to an accurate transport coefficient estimate. When the
sensible heat flux term is written in terms of a resistance, this method
is also called the resistance energy balance method (Rosenberg, 1974) .

28
The Penman (1948) approach is very closely related to the residual
approach. In addition to the wind function, it includes an expression
that relates the temperature gradient to the vapor pressure gradient via
the linearized saturation vapor pressure curve,
cs ea = s(Ts V + Sea 2-26
where s is the slope of the saturation vapor pressure curve, and
6e is the saturation deficit of the air.
cl
This approach has since been generalized to include subsaturated sur
faces (Barton, 1978), which allows ET to be expressed as a function of
net radiation, the moisture availability parameter (M), and the satura
tion deficit (e ):
a
E [S + hg 2.26
(See Chapter 4 for the full derivation.) Historically, Penman's method
was the first to combine the energy budget equation with a wind model to
evaluate ET. Although the residual approach also employs a wind model,
in common usage it is the Penman method that is referred to as the com
bination method. The Penman method's main advantage is that it is not
explicitly dependent on measurement of a temperature gradient; its prin
cipal disadvantage is that it requires information on moisture availa
bility of the surface.
The Bowen ratio approach (Bowen, 1926) assumes that in the fully
turbulent layer over the surface, transport of heat and water vapor are
similar (i.e., = K^). This allows eddy diffusivities to be avoided
altogether, and latent and sensible heat flux to be apportioned accord
ing to the relative strength of the temperature and water vapor pressure
gradients:

29
2-27
where subscripts 1 and 2 refer to two levels in the fully turbulent air
layer. This approach is free of a wind model, but it requires very accu
rate measurement of temperature and vapor pressure gradients. It is dis
cussed in detail in Chapter 3.
Remote ET Estimation Methods
Surface Temperature and Net Radiation
Satellite-borne sensors can measure the amount of radiant energy
coming from a particular surface area element in a particular wavelength
interval. For environmental applications, the wavelength intervals mea
sured are divided into the visible, thermal, and microwave regions of
the electromagnetic spectrum, yielding measurements of reflected solar,
emitted thermal, and microwave radiation. So' far, all £T estimation
methods designed for use with satellite data only employ the visible and
thermal wavelength ranges.
Net radiation is the largest component of the surface energy bud
get, and surface temperature plays a role in determining all the energy
budget components. Usually, measurements of reflected solar and emitted
thermal radiation measurements are used to estimate net radiation and
surface temperature. Methods to estimate ET are then based on these net
radiation and surface temperature estimates.
With a clear sky and proper consideration of the atmosphere's
transmission properties, surface temperature can be determined directly
from emitted thermal radiation:
Q
e
2-28

30
where e is the emissivity of the surface,
a is the Stefan-BoTtzmann constant, and
T is the surface temperature.
Solving for T ,
T
s
2-29
In principle, net radiation is calculated according to the equation
2-30
The upwelling components, reflected (Qr) and emitted (Qg) radiation, are
directly measurable by satellite given atmospheric transmission proper
ties. The solar radiation incident at the surface (Qs) is known as a
function of date, time of day, location, and atmospheric absorption
(Tennessee Valley Authority, 1972). Atmospheric radiation (Q,) can be
a
similarly estimated.
Some of the ET estimation methods discussed in. the following sec
tions are designed for use with satellites that provide only thermal
data from the surface. These methods express the net shortwave radiation
as a function of estimated incident solar radiation (Rs) and albedo (a):
Qs Qr = a a)Qs
2-31
Simulation Methods
In 1978, NASA launched the Heat Capacity Mapping Mission (HCMM).
The polar orbit of the HCMM satellite was designed to collect maximum
and minimum temperatures of the earth's surface, and groups worldwide
were funded to study the maximum-minimum temperature data. Several
groups adapted or developed simulation methods to bridge the long time
intervals (12 hours) between data sets. Examples of models used are
Carlson and Boland (1978), Soer (1977), and Rosema et al. (1978).

31
The Carlson model is very general, having been developed for study
of urban and rural surfaces. It is based on the energy budget equation
and gradient transport equations for latent, sensible, and soil heat
flux. Soil thermal conductivity and heat capacitance are combined into a
thermal inertia parameter which is evaluated with an empirical relation
ship to thermal conductivity. The model does not describe soil and plant
water transport. It introduces a moisture availability parameter as
shown in Eq. 2-19 to account for the subsaturation of the surface air.
Eddy diffusivities for latent and sensible heat are iteratively computed
using empirical stability corrections; there are, in fact, different
atmospheric models for daytime and nighttime.
Use of the Carlson model to determine daily heat budget components
is discussed in Carlson et _al_'. (1980). Computed solar radiation is used
to force the model; measured windspeed, air temperature and. humidity,
and soil temperature are used as boundary conditions. By varying two
model parameters (thermal inertia and moisture availability) on succes
sive model runs, sets of corresponding cumulative heat budget components
and 24-hour maximum and minimum temperatures are generated. Then a re
gression equation expressing daily ET as a function of maximum and mini
mum temperatures is developed. Given the ground-measured data for the
simulation and two extreme temperature maps from the HCMM satellite, a
map of daily ET is produced.
The Soer model (named TERGRA) is much the same as the Carlson
model, providing for stability conditions in the surface air layer and
requiring temperature, vapor pressure, and windspeed as boundary condi
tions at a reference level. However, rather than a moisture availability
parameter, soil and plant water transport is modelled in detail. (The

32
TERGR model was designed for grasslands, making this more detailed ap
proach feasible.) It uses pseudo-empirical expressions for soil water
transport resistance and stomatal resistance, and requires a reference
soil moisture pressure as well as a soil temperature as a boundary con
dition.
Use of the TERGRA model in obtaining cumulative ET estimates is
explained in Soer (1980). The procedure requires data on the boundary
conditions and radiation falling on the surface for the duration of the
simulation periods, and values of various parameters like soil hydraulic
conductivity and surface roughness. First, windspeed, roughness height,
air temperature, and remotely measured surface temperature are used to
compute the instantaneous ET rate for the time at which satellite data
are available. This is done with the simple residual method (see previ
ous subsection), which requires no. knowledge of surface moisture. Then
the TERGRA model is run with various soil moisture pressures to match
the ET rate at the time of the satellite overflight. The modelled cumu
lative daily ET rates are then assigned to areas with matching instanta
neous ET rates at the time of the overflight.
The Rosema et aQ_. (1978) model (named TELL-US) is also constructed
around the surface energy budget, and similarly computes latent, sensi
ble, and soil fluxes based on measured gradients and calculated trans
port properties. It is more detailed in describing the surface; surface
slope and slope direction must be specified. Its parameters are soil
thermal inertia and surface relative humidity.
Given the daily course of boundary conditions and incident radia
tion, the model is used to compute daily maximum and minimum tempera-
tures and cumulative daily evapotranspiration for various combinations

33
of thrmal inertia and surface relative humidity. This procedure must be
repeated for each combination of surface roughness, slope, and slope
direction. Then satellite-measured maximum and minimum temperatures for
specific areas are matched to the modelled values to determine daily ET
for those areas.
Steady-State Methods
Most efforts to use remote-sensing data to estimate ET rates were
made with the simple residual method (Eq. 2-24). Remotely sensed data
were used to estimate net radiation, and sensible heat flux from the sur
face was evaluated with a remotely-sensed surface temperature and a
ground-measured air temperature. Evapotranspiration was then calculated
as the net radiation less the estimated sensible and soil heat flux.
Studies that fall into this category are Allen et _al_. (1980), Seguin
(1980), Soer (1980), and Price (1982). Soer and Price extend their- meth
ods to cumulative daily ET estimates with the help of simulation models
described in the preceding subsection.
These methods differ primarily in how they treat the bulk heat
transport coefficient or transport resistance of the surface air layer.
Two methods of computing sensible heat flux were used in the Allen et
al. (1980) approach. For short vegetation (mostly pasture), a stability-
corrected thermal conductivity was computed using the log law wind model
and dimensionless empirical relationships developed by a group at the
University of California at Davis (Morgan £t _al_., 1971). An empirical
resistance equation based on leaf length, windspeed, shelter factor, and
leaf area index (Monteith, 1965) was used for transport over areas
covered with trees. By using measured windspeed and air temperature, the
estimated tree resistances and a surface temperature map, it was

34
possible to construct a map of instantaneous evapotranspiration rates.
For regional estimates, the rates computed for subareas were weighted by
the total area with that particular ET rate and summed.
The Seguin (1980) approach to thermal conductivity in the surface
air layer was formulated in terms of a resistance. It used the simple
log law wind function with surface roughness to evaluate the resistance
to sensible heat flux; no stability corrections were made. Measured
windspeed, air and soil temperature, remotely measured surface tempera
ture, and estimated albedo and soil conductivity were required to esti
mate instantaneous ET rates. Regional ET rates were estimated by multi
plying areas with different surface temperature and surface roughness
combinations by their individual ET rates.
Soer (1980) also used a resistance formulation of the sensible heat
flux. It included stability corrections based on the Monin-Obukhov
length and the Businger-Dyer semi-empirical mass and heat transport
equations. In other particulars it is practically identical to the
Seguin approach.
Price (1977, 1980) has developed the energy budget equation in
terms of time averages in an effort to determine surface thermal inertia
using remotely sensed maximum and minimum surface temperatures. He has
since (Price, 1982) used this approach in conjunction with the TELL-US
model to estimate daily ET rates. First a preliminary estimate is made
with a residual equation like Eq. 2-24, except that time average air and
surface temperatures and windspeed are used. The daily ET value obtained
is then corrected with a regression equation developed from a set of
corresponding Price method estimates and TELL-US simulation estimates.

35
A different approach to solving the residual equation was taken by
Menenti (1980). In his approach, the simple residual equation is simpli
fied by Taylor series expansion around some central ET rate at a given
shortwave radiation level. All terms except those containing surface
temperature and albedo are eliminated, leaving the ET rate for a partic
ular surface a function of the central ET rate, its surface temperature,
and its albedo. No means to make cumulative daily ET estimates were sug
gested.
Temperature Gradient Response Methods
The two ET estimation methods developed in this study are steady-
state methods. They are based on the response of surface-to-air temper
ature gradients to varying levels of net radiation. One of these meth
ods, the average temperature gradient response method, is suitable for
use with satellite data.
The primary difference between this method and the simple residual
method is that it expresses the vapor pressure gradient in terms of the
temperature gradient, the slope of the saturation vapor pressure curve,
and saturation deficitan innovation first made in Penman's (1948) pio
neering work. This addition gives the method some protection against
"residual errors." For example, if the measured temperature gradient is
erroneously high, both the latent and sensible heat fluxes will be af
fected; there will not just be an increase in sensible heat and an equal
decrease in latent heat flux. Also, the method allows ET to be expressed
as a function of net radiation and parameters only (without explicit
mention of surface and air temperature). This feature makes ET calcula
ble when surface temperatures cannot be measured remotely but net

36
radiation can be estimated, as when there is cloud cover or in between
sets of satellite data.
A significant advantage of the estimation method developed is that
it, in effect, determines surface parameters like moisture conditions
almost completely from remote-sensing data. This is done with an equa
tion (hereafter referred to as the temperature gradient model) that re
lates the surface-to-air temperature gradient to net radiation and pa
rameters that describe the surface. By assuming that the parameters are
constant, two of them (e.g., moisture availability and saturation defi
cit) can be determined from the correlation of the surface-to-air tem
perature gradient and net radiation. Although surface temperatures are
required (implying clear skies) to determine parameters, they can be
used with cloudy condition net radiation estimates for cloudy condition
ET estimates.
The need for a .surface-to-air temperature net radiation correlation
calculation requires several daytime satellite data sets. Unlike the
HCMM methods, the remote ET estimation method developed in this study is
designed for use with satellite data that is available at least every 2
or 3 hours. At this time resolution, the average temperature gradient
response method can make reasonably accurate cumulative daily ET esti
mates without the need for simulation. Because the parameters are con
sidered constant, no interpolation scheme is needed to make cumulative
ET estimates; only an estimate of the cumulative daytime net radiation
is required.

CHAPTER 3
A SYSTEM FOR AUTOMATIC COLLECTION OF ET DATA
Overview
The energy budget/profile Bowen ratio technique was used to make
the evapotranspiration measurements needed for a data base in this re
search. It was selected because it is one of the methods that least dis
turbs the surface being measured, and when correctly applied, permits
measurements with an error on the order of 10% (Sinclair et al_., 1975).
The profile Bowen ratio method has been successfully applied to a vari
ety of surfaces (Sinclair et al_., 1975; Stewart and Thom, 1973; Black
and McNaughton, 1972, 1971). .
The theoretical basis of this method is developed first, followed
by a discussion of considerations going into the choice and use of the
sensors and other apparatus. Next, the automatic data collection system
that is assembled to make and report energy budget measurements is de
scribed. It consists of a computer-controlled scanner, voltmeter, gas
sampling arrangement, and a set of four interacting programs. The chap
ter concludes with a discussion of practical considerations that are
important in maintaining a high level of accuracy in the measurements
and the limitations of the data collection system.
Energy Budget/Profile Bowen Ratio Theory
As described in Chapter 2, the energy balance of a vegetated sur
face can be written:
R = E + H + G 3-1
37

38
where R is net radiation absorbed by the surface,
E is the evapotranspirative or latent heat flux,
H is sensible heat flux, and
G is the soil heat flux.
It has already been shown that the rate of heat storage in the vegeta
tion layer and the rate of photosynthetic assimilation are negligible in
comparison to these terms.
The Bowen ratio is defined as the ratio of sensible heat flux to
latent heat flux: u
' 3 = f 3-2
In the energy budget/profile Bowen ratio measurement technique, net ra
diation and soil heat flux are measured directly. Latent and sensible
heat fluxes are determined indirectly by first measuring the Bowen ra
tio, and then computing the fluxes:
E = (R G) and 3-3
H=^t(R-G)
3-4
The Bowen ratio can be calculated from air temperature and water
vapor pressure measurements at various heights over the surface, pro
vided a number of experimental conditions are met. Over a uniform sur
face with adequate fetch, latent and sensible heat fluxes may be consid
ered to exist in the vertical direction only (no flux divergence). In
the turbulent boundary layer the fluxes at any instant can be described
as follows:
H =
E =
r v 3T
"pCPKH 3 Z
-epL l
P w3z
3-5
3-6
where p is air density,
c is specific heat capacity at constant pressure,
eH is the ratio of molecular weights of water and dry air,
L is the latent heat of evaporation of water,
P is the atmospheric pressure,

39
K is the eddy thermal diffusivity,
is the eddy vapor diffusivity,
Tw is the air temperature,
e is the vapor pressure, and
2 is the vertical coordinate.
The Bowen ratio can then be written:
H
E
Vkh t?
eLK,
3_e
W 3Z
3-7
If temperature and vapor pressure measurements are made at the same
heights, the 32 terms may be cancelled. If the measurements are made at
the same instant, it can be assumed that the eddy diffusivity for water
vapor and heat are the same (K^ = K^). This in effect states that turbu
lent mixing is the dominant transport mechanism in the turbulent bound
ary layer, and that bouyancy and stability effects cause no significant
differences in the transport of heat. or.water vapor (Dyer,-1967;
Swinbank and Dyer, 1967; Webb, 1970; Dyer and Hicks, 1970; Garratt and
Hicks, 1973). Incorporating these conditions into the expression for the
Bowen ratio,
e =
eL
3 T
3 T
3e y3 e
3-8
Since the terms in brackets are physical "constants" (abbreviated as the
psychrometric constant, y), only 3T/^e needs evaluation. This can be
done with air temperature and vapor pressure measurements.
In this application of the energy budget/profile Bowen ratio con
cept, air and dewpoint temperatures were measured at five heights35,
60, 85, 135, and 225 cm over the surface. Vapor pressure was calculated
from the dewpoint temperature according to the Magnus-Tetens formula
(Tennessee Valley Authority, 1972). The ratio 3T/3e was the slope of a
two-independent-variable linear regression (Kendall, 1968) calculated

40
using temperature data as the ordinate and vapor pressure as the ab
scissa (see Fig. 3-1). In calculating the Bowen ratio, the specific heat
of the air, the atmospheric pressure, and the ratio of molecular weights
was considered constant; the latent heat of vaporization was a function
of the average air temperature.
Sensor and Time Constant Considerations
Although simple in principle, a great deal of care is required in
choosing sensors and collecting data for the calculation of the Bowen
ratio. Temperature and vapor pressure vary randomly from instant-to-in-
stant and level-to-level in the turbulent boundary layer, and the total
temperature and dewpoint differences across the air layer to be measured
are only 1 or 2C. In order to calculate the relative strengths of the
gradients, very precise measurements at several levels are required.
Sensors were chosen to eliminate, as much as possible, the error
introduced by sensor-to-sensor variability. This was avoided entirely in
the case of the vapor pressure profile; the same dewpoint analyzer was
used to measure the dewpoint at each level by use of a gas sampling ar
rangement. In the case of the temperature profile, the effect of thermo-
couple-to-thermocouple differences was minimized by measuring tempera
ture differences with thermopiles. Twenty-junction copper constantan
thermopiles, arranged with 10 junctions at each level, were used to mea
sure temperature differences between levels. The temperature at the low
est level was measured with a thermocouple using an Omega Engineering
MCJ-T electronic icepoint reference. Temperatures at the other levels
were obtained by adding the appropriate thermopile-measured temperature
differences to the one reference temperature measurement.

TEMPERATURE (C) HEIGHT (CM)
a VAPOR PRESSURE (MB)
11.2 11.4 11.6 11.8 12.0
VAPOR PRESSURE (MB)
Figure 3-1. Bowen Ratio Calculation from Measurements of Vapor
Pressure and Temperature. Note that the scale used
to plot vapor pressure profile in upper graph is the
same as the vapor pressure scale in the lower graph.
Data are from October 20, 1981, 9:30 TST (see Fig. 3-6).

42
The apparatus used to collect temperature measurements and air sam
ples was designed so that the sensors returned signals accurately repre
sentative of the air layers being sensed. The thermopiles were nested
inside three aspirated radiation shields, with each shield wrapped in
highly reflective aluminum foil. Air samples were pumped continuously
from sampling ports near the thermopiles through about 100 m of 6-mm ID
polypropylene tubing and 11.3-L mixing chambers in the instrument room.
To prevent any danger of condensation, the air sampling system was
heated from sampling mast to dewpoint analyzer. The bundle of five tubes
from the mast was taped around a heater cable (3 W/ft) and packed inside
a 1.3-cm-thick foam rubber insulation tube. The mixing chambers and the
sampling valve were also heated.
The travel time of air samples from mast to instrument room was
approximately 1 min. Therefore, the dewpoint measurement corresponding
to a temperature measurement at a specific level was made 1 min later.
Also, the dewpoint temperature measurements were pressure-corrected be
cause the arrangement of the air sampling system caused the pressure
rate at the dewpoint sensor to be ^30 mb less than atmospheric pressure.
To ensure clean electrical signals, shielded signal cable with a
single common ground was used. In spite of these precautions, the Beef
Research Unit fence charger managed to induce significant voltage spikes
on the low level signals (e.g., the 0-200 microvolt thermopile signals).
This problem was solved with a filtering routine in the data collection
program.
In addition to reducing the error sources from the sensors in every
practicable way, the temperature and vapor pressure signals were
physically smoothed. Smoothing was required because the measurement rate

43
was limited to one measurement every 2.5 min for the vapor pressure
profile measurements.
Vapor pressure in the Bowen ratio data collection system was com
puted from a measurement' of the dewpoint temperature. Since the same
dewpoint sensor was used for all five levels and a delay had to be
scheduled between measurements to allow the analyzer to settle on new
dewpoints, the response of the dewpoint analyzer was the factor limiting
the sampling rate. The analyzer, an EG&G Model 880 Dewpoint Hygrometer,
was tuned so that it could "lock on" to small dewpoint temperature
changes within about 15 sec. However, 30 sec per measurement were sched
uled to allow the analyzer to stabilize on a given dewpoint under less
than ideal conditions. Since there were five levels to measure, the time
interval between measurements at the same level was 2.5 min.
The variability of temperature and vapor pressure in the turbulent
air layer is well documented; at any point in this layer, instantaneous
temperatures and dewpoints vary randomly (Desjardins et al_., 1978). The
higher-frequency temperature and dewpoint fluctuations were smoothed in
order to get representative measurements with a sampling rate of one
measurement every 2.5 min.
In the case of an air-sampling system, this smoothing is conveni
ently done by inserting a mixing chamber into the sample stream ahead of
the analyzer. An abrupt (or step) change in an air sample is translated
into a gradual, approximately exponential change by mixing in a chamber.
The exponential change is characterized by a time constant, which is
determined by the volume of the mixing chamber divided by the flow rate.
By harmonic analysis, it was determined that a time constant of 4 min .
would damp random signal variations occurring more often than every 2.5

44
min to 10% or less of their amplitude. In the case of the dewpoint sys
tem, 11.5-L mixing chambers with a flow rate of 3 L/min were used.
To maintain the proper correlation between dewpoint and temperature
readings, it was necessary to introduce the same time constant into the
temperature-sensing system. The appropriate time constant was determined
experimentally by varying the air flow rate over the aspirated thermo
piles and subjecting them to different temperature differences. It was
found that at a set air flow rate, measured time constants varied with
the temperature difference applied to the thermopiles. As a result, the
air flow rates were adjusted so that a 4-min time constant resulted for
temperature differences in the average operating rangetemperature dif
ferences in the range of 0.2 to 0.3C.
The 4-min time constant was also introduced into the surface tem
perature and net radiation measurements. Sensor response was slowed dig
itally by using weighted averages of the most recent 25 sensor readings.
Each time a complete temperature and vapor pressure profile was
measured (every 2.5 min), the correlation coefficient between tempera
ture and dewpoint measurements was calculated. This provided a running
check on the quality of the measurements and the current similarity of
the profiles.
Data Collection Equipment
The overall schematic for the thermopile/air sampling system is
shown in Fig. 3-2. The major parts are the data acquisition system, the
air sampling mast, the mixing box, and the signal cables and tubing
which connect them.
A computer-controlled data acquisition system was used because of
the large number of measurements and extensive calculations that this

DATA AQUISITION
TTE1
.M
TERMINAL
COMPUTER
SYSTEM
Flow Meters
Mixing Bottles-
SIGNALS
SENSORS
NET RADIATION
SOIL FLUX
REFERENCE TEMPERATURE
4 TEMPERATURE DIFFERENCES
DEW POINT
VALVE CONTROL
VALVE POSITION
-0
NET RADIOMETER
SOIL FLUX
DISK
AIR SAMPLE
PORT
RADIATION \]
SHIELDING'
'ASPIRATING
FAN
THERMOPILE
SENSOR ARM
AIR SAMPLING SYSTEM
Heated Tubing Bundle
PROFILE MEASUREMENT MAST
Figure 3-2. Schematic of ET Measurement System. Details of profile measurement and air
sampling equipment are shown in Figs. 3-3 and 3-4.
45*
CTJ

46
technique requires. The central piece of equipment was a Hewlett-Packard
2100S Minicomputer with a disk resident Real Time Executive-2 operating
system. The system allowed editing and compilation of programs, swapping
programs between core and disk memory, scheduling programs for relative
or absolute start times, and "simultaneous" running of programs accord
ing to priority. Input and output were by means of a HP-2126P terminal.
The peripheral equipment used in making the measurements and con
trolling the gas sampling valve is listed in Table 3-1. The controlling
computer, disk drive, data acquisition equipment, and terminal were all
housed in an air-conditioned room.
Table 3-1 Data Acquisition
are manufactured
System Identification
by Hewlett-Packard)
(All components
Component
Model No.
Serial No.
Minicomputer (32K Memory)
HP-2100S '
1420A05546
Scanner
HP-2911A
737-00476
Scanner Controller
HP-2911B
832-00412
Integrating Digital Voltmeter
HP-2402A
1027A01060
Disk Drive
HP-7901A
1321A-00255
Terminal
HP-2621P
2102W03475
The field apparatus on the pasture site consisted of an air-sam
pling mast, a radiation sensor boom, and a 9.5-m tower supporting a
precision radiation thermometer at its top, and windspeed and direc
tion sensors at 7 m. Another taller tower was erected and equipped to
protect all instrumentation from lightning.
The 2-m radiation sensor boom was supported by an aluminum tripod
stand and guy wires about 1.8 m over the ground surface. Two Epply pyra-
nometers, oriented to measure incoming and reflected radiation, and a
Swissteco net radiometer were mounted at its end. An aspirating pump and

47
dessicant container for the net radiometer were held in a weatherproof
box at the base of the tripod.
The air sampling mast consisted of a 2.5-m steel channel to which
five sensor arms (see Fig. 3-3) were attached at various levels. At one
end of each arm, teflon spacers centered two clusters of 10 thermocouple
junctions inside the smallest of three radiation shields. Individual
junctions were kept in thermal contact with a metal oxide conducting
paste. Air was drawn over the thermopiles, between radiation shields,
and through the length of the arm by a small fan at the opposite end.
Air samples were drawn from the air flowing through the arm. All wiring
(four 20-junction thermopiles and one thermocouple) and tubing (5 sample
lines) were contained inside the 3x3 cm channel down to its base, where
they ended in wire and tubing connectors. The mast and sensor arms as
well as the radiation, shields were wrapped in highly reflective aluminum
foi 1.
The sensors were connected to the scanner in the instrument room
with shielded signal and thermocouple wire. In the field, leads from the
sensors ran aboveground in wire harnesses to a junction box, where they
were connected to a signal cable via screw connectors. This cable ran
100 m underground to another junction box in the instrument room. From
this panel the signal lines were connected to one of two 50-pin connec
tors, which plugged into a short piece of cable tied directly into the
scanner. The "quick-disconnect" plugs were included to rapidly isolate
the data acquisition system from possible lightning strikes in severe
weather; the junction boxes allowed signal problems to be quickly traced
to sensors, underground cabling, or the data acquisition system. The
sensors used are identified in Table 3-2.

STEEL
CHANNEL
ASPIRATING
FAN
Figure 3-3. Detail of Profile Measurement Mast Arm.

49
Table 3-2 Sensor Identification
Measurement
Sensor Make & Model No.
Ser. No.
Net Radiation
Swissteco Net Radiometer
6990
Incoming Shortwave Radiation
Epply Pyranometer 8-48
12876
Reflected Shortwave Radiation
Epply Pyranometer 8-48
10000
Surface Temperature
Barnes IT-5 (Spring 1981)

Barnes IT-3 (Fall 1981)
521
Dewpoint Temperature
EG&G 880-Cl
1409
Windspeed and Direction
R.M. Young 6101 and 6301

Air Temperatures
Custom-made Thermopiles

Reference Temperature
Omega Engineering MCJ-T

Soil Heat Flux
Micromet Heat Flow Disk
282
Air was pumped continuously from each sample port on the mast
through ^100 m of heated insulated polypropylene tubing and the gas sam
pling apparatus in the instrument room. In the "mixing box," air first
passed through flowmeters, then the mixing chambers, the scanning valve,
and the air pump. Samples from each level were drawn sequentially
through a sampling port, a separate sample flowmeter, and the dewpoint
analyzer. All equipment except the pump and analyzer were contained in
side a heated, insulated plywood box (see Fig. 3-4) to prevent condensa
tion problems.
The scanning valve was controlled from the data acquisition compu
ter. The sampling port was turned from one air source port to the next
by an electric motor powered for a precise fraction of a second. This
was done by a relay control circuit that was designed to sense scanner
closure. Thus a program statement calling for a measurement of the scan
ning valve control channel resulted in changing the position of the
valve. After each change, the valve position was checked to ensure that
the programs and valve were synchronized.

Mixing
Chambers
Analyzer Sample
Flowmeter
Styrofoam Insulation
1/4" Plywood
Figure 3-4. Detail of Air Sampling Equipment.
-Valve Control Electronics
Sampling Valve
Air to Analyzer
Air to Pump
5 Sample
Tubes from
Mast
Polypropylene
Foam Rubber
Insulation
Heater Cable
Tubing
Bundle
CT
o

51
Data Collection Programs
A system of four programs was developed to collect, report, and
analyze the data required for the test surface energy budget. Program
MEASR makes the measurements and calculations, REPRT produces the half-
hourly summary reports, ANALZ does some analysis of data and performs
additional calculations, and SET schedules the other programs. Listings
of these programs appear in Appendix B; brief descriptions of their
functions and interactions follow.
Basically, all sensors are scanned in a computer program loop. De
pending on the status of various indexes in this loop or the system
clock, control is passed to specific calculation and/or reporting rou
tines. This fundamental loop is in program MEASR; it is repeated approx
imately every 30 sec, the measuring rate determined by the dewpoint ana-
. lyzer.
When a program calls for a measurement [i.e., CALL EXEC (1, 9,
DATA, CHANNEL NUMBER, VOLTMETER PROGRAM WORD)] the channel number in the
measurement program statement is passed to the scanner controller, and
the program word indicating type of measurement, voltage range, and de
lay time is passed to the voltmeter. After the scanner has closed on the
proper signal lines, the voltmeter has been set for the type of measure
ment, and a programmed delay is complete, the voltmeter integrates the
signal for 1/60 second and passes the average back to the measuring pro
gram. It resumes execution with the next program step.
During each execution of the measurement loop, one air temperature,
one dewpoint temperature, and all other sensors except soil thermocou
ples are scanned. Immediately after the dewpoint measurement, the scan
ning valve position is changed (Subroutine STEP) so that the dewpoint

52
instrument can begin to stabilize on a new dewpoint. A programmed delay
makes up the balance of the 30 sec required between measurements. At the
end of five scans (2.5 min), a complete temperature and dewpoint profile
is available to compute a Bowen ratio. A report on that profile is
printed at the option of the system operator (see Fig. 3-5).
To compensate for the approximately one-minute air sample travel
time from field to mixing chamber, temperature and dewpoint measurements
are offset by two levels. For example, the dewpoint at level 1 is mea
sured in the same sensor scan as the temperature at level 3. This ac
counts for extra statements at the beginning of the program which ensure
proper initialization, and for extra branching after sensor scans which
deal with the offset completion times of the temperature and dewpoint
profiles.
To guarantee that the dewpoint analyzer is- receiving the air. sample
from the level called for in the program, a mark voltage channel is mea
sured and checked in each scan of the sensors. In one particular posi
tion of the scanning valve, 12 volts are expected on this channel. If
the voltage measured is low or 12 volts are measured when not expected,
the data for the profile being collected are discarded and a message to
the operator is printed. The program makes one attempt to reposition the
valve and restart data collection. If this fails, another message is
printed and the programs are terminated.
When temperature and dewpoint measurements at all five levels are
complete, the data are passed to subroutine RATIO, which calculates a
linear temperature versus dewpoint regression relationship. Its slope is
multiplied by the appropriate constants (Eq. 3-8) to give the Bowen

PROF" 6
RAD.T.
23.27
TEMP
21 1
9:18:27
MET R.
.45
DPT.
9.5
B -1.723
W.SPD.
2.86
V.P.
11.9
PROF" 7
ROD.T.
23.7 7
TEMP
2 1.2
9:18:58
NET R.
.45
DPT.
9.6
B =1.813
W.SPD.
2.18
V.P.
T1 .9
PROF" 8
RAD.T.
24.25
TEMP
21.4
9:21:26
NET R.
.46
DPT.
9.8
B =1.812
W.SPD.
3.73
V. P.
12. 1
PROF" 9
RftD.T.
24.30
TEMP
21.7
9:23:55
MET R.
.47
DPT.
9.8
B 1.590
W.SPD.
3.54
V.P.
1 2.2
PROF" 10
RAD.T.
24.49
TEMP
21.8
9:26:24
NET R.
.47
DPT.
. 9.9
R =1.904
W.SPD.
3.36
V.P.
12.2
PROF" 11
RAD.T.
24.90
TEMP
22.2
9:28:54
MET R.
.48
DPT.
10.1
B =1.679
W.SPD.
2.85
V.P.
12.4
PROF" 12
RAD.T.
25.28
TEMP
22.5
9:31:23
NET R.'
.49
DPT.
10.3
B =1 .818
W.SPD.
2.94
V.P.
12.5
Figure 3-5. Example of Intermediate Program Output,
on face of HP 2100 computer is on.
hour report shown in Fig. 3-6.
20.4
20.0
19.5
9.2
9.0
8.7
1 1 .6
1 1 .5
1 1 .3
20.5
20.2
19.7
9.3
9.1
8.9
11.7
1 1 .5
1 1.4
20.7
20.4
20.0
9.5
9.2
9.0
11.0
11.7
1 1 .5
21.0
20.6
20.1
9.6
9.2
9.0
11.9
11.7
11.5
21.1
20.8
20.4
9.5
9.5
9.3
1 1 .9
1 1 .9
11.7
21 .5
21 1
20.6
9.8
9.6
9.4
12.1
12.0
1 1 .8
21.7
21.3 .
20.8
9.9
9.7
9.5
12.2
12.0
11.8
19.1 R = .999
8.5
19.3 R .99/
8.7
11.2
19.6 R = .997
8.8
11.3
19.8 R =. .998
8.8
11.4
0.1 K = 988
9. 1
11.5
20.3 R .999
9.2
11.8
20.4 R = I .000
9.3
11.7
This report is printed if switch #3
are from the 15 min preceding half-
U1
CO

54
ratio. The ratio and corresponding correlation coefficient are returned
to the calling program.
Function FILT was added to MEASR after it was discovered that the
shielding system did not prevent the Beef Research Unit electric fence
charging system from inducing noticeable spikes on the signal lines.
These 10-50 microvolt spikes were shorter than the voltmeter measurement
cycle, and thus lent themselves to being filtered digitally. FILT takes
10 measurements, looks for three in a row that are the same within a
tolerance, and compares the rest of the measurements to one of them. Any
measurement varying more than a specified tolerance is dropped, and the
average of the "good" measurements is passed back to MEASR. If more than
half of the measurements are noisy (out of tolerance), a warning is
printed to notify the operator.
Subroutine TMTCH is included to match the time constants of the net
radiation and precision radiation thermometer to that of the temperature
and dewpoint measurements. This matching is done by using the weighted
average of the 25 most recent (collected in the last 12.5 min) measure
ments to calculate a matched measurement. The weights assigned to older
measurements decrease exponentially with a time constant of 4 min. The
same weighting scheme is used for the net radiation and surface tempera
ture because their sensor response time constants are 8 and 2 seconds,
respectively. At a sampling rate of one measurement every 30 sec, their
responses are, in effect, instantaneous.
Program REPRT produces a half-hourly data summary report. It calcu
lates half-hourly average profiles of the heat budget components, wind-
speed and direction, Bowen ratio, and profiles of soil and air tempera
ture, air vapor pressure and relative humidity. Most of this program is

55
concerned with formating and printing the summary report. An example
report is shown in Fig. 3-6, and Table 3-3 lists the variable names
used.
Program ANALZ makes ancillary calculations and produces the last
five lines of the half-hourly report. It has a search routine which com
putes the displacement height of the temperature and vapor pressure pro
files. With an assumed value of the roughness parameter (Zq) and trial
values of the displacement height (D), it computes the correlation of
temperature or vapor pressure and height over the surface with
rz D + z/
T, e = B In
O
'0
+ A
3-9
The assumed roughness height, the displacement height producing the best
correlation, and other profile parameters are printed out.
ANALZ also computes a variety of other quantities which may be of
use in data analysis or operation of the system. Among these are atmo
spheric and stomata! resistances, albedo, optical air mass and atmo
spheric transmission coefficient, zenith and hour angle of the sun, and
the equation of time.
The fourth program, SET, is the executive program. It is used to
properly start the acquisition of data and determine whether and when
the other programs should be run. In a "cold" start, SET positions the
scanning valve, initializes counters and statistics, and schedules MEASR
to start so that profile collection is completed at specified times. On
occasions other than a "cold" start, it determines whether the other
programs should be run, depending on flags in MEASR or operator input
via switches on the face of the HP-2100. Its most valuable function is
to schedule MEASR to begin at an absolute clock time at the beginning of

BEEF RESEARCH UNIT ET PROJECT DATA
AVERAGES AND ( PERCENT VARIATION ) FOR HALF HOUR ENDING
TUESDAY, OCTOBER 2C, 1981 (JULIAN DAY 293) TINE 09:31:2? TS'I
NET
RAD.
SOIL
H. F.
SENS.
H.F.
EAT. H.F. N
WINDS
RSQ.>.95 B.R.
AVG.R
. 45
LY/H
.02
LY/M
.28 LY/H
.16 LY/H 3.
06 M/S
12.OF 12 1,753
.999
RADIATION
AIR
TEMP
VAP PRESS
REL HMDTY SOIL
TEMP
(LY/H)
(CM)
(*C >
(CM) (MB)
(CM) (7.) (CM)
(*C)
NET
.451
(5.0)
22S
T9.2
(4.2)
225 11.2
(3.0)
225 50.2 0
16.8
ISW
.802
(4.1)
135
1 9.6
(4.1)
135 11.3
(2.9)
135 49.8 -2
1 7.6
RSH
. 17 7
(3.7)
85
20.0
(4.1)
85 11.5
(2.8)
85 49.2 -5
18.2
Al m
. 1 09
(IS.)
GO
20.4
(4.0)
GO 11.6
(3.1)
GO 48. 6 1 0
I 9.2
El. W
GIG
(5.5)
35
21 1
(3.9)
35 11.9
(3.1)
35 47.6 -25
20. 1
F
. 1 62
11 If/HR
0
23.4
(5.5)
.*.*.95+' BR
-1.760.+PR-.115** -50
21.7
ZO
TO
H
U*H
. RCH
EO
DE U*E
RCE
I .
23.0
22.
0
33.4
- 1.000
12.8
17.0 12.8
-.999
22. G
22.
0
32.6
-1.000
1 2. G
18.0 12.4
- .999
o
o
22.3
22.
0
31.9
-1.000
12.5
19.0 12.2
- .999
r\ AIR
,RSTM(
S/H)
.238,
4.350
.31 I
,4.353 .348,
4,350
.397,4.358 .436,
4.365
A EDO
SHIO
OAH
ATC
ZNG'L HRNGL
EOT
E.S.T. T.S.T.
DAY

1.09 1
.84
.85
57.
3 -41 :2
.2579
9,46 9.25
293
Figure 3-6. Example of Half-Hourly Data Report.. Variable names and units are listed in Table 3-3.

57
Table 3-3. Variable Names and Units for Half-Hour Reports
RSQ.>.95
B.R.
AVG.R.
NET
ISW
RSW
ALW
ELW
ET
.95+BR
ZO
TO
DH
U*H
RCH
EO
DE
U*E
RCE
RAIR
RSTM
ABDO
SWIO
OAM
ATC
ZNGL
HRNGL
EOT
E.S.T.
T.S.T.
DAY
Number of temperature and vapor pressure profiles with
correlation coefficient better than .95
Bowen Ratio
Correlation coefficient of half-hour average profiles
Net radiation (ly/min
Incoming shortwave radiation (ly/min)
Reflected shortwave radiation (ly/min)
Atmospheric longwave radiation (ly/min)
Emitted longwave radiation (ly/min)
Evapotranspiration rate (mm/h)
Average and standard deviation of individual profile Bowen
ratios with greater than .95 correlation coefficient
Roughness height (cm)
Temperature at ZO by temperature profile extrapolation (C)
Displacement height for heat (cm)
Friction velocity as determined by fit of profile (m/min)
Correlation coefficient for temperature profile
Vapor pressure at ZO by vapor pressure profile extrapo
lation (mb)
Displacement height for vapor pressure (cm)
Friction velocity as determined by fit of vapor pressure
profile (m/min)
Correlation coefficient for vapor pressure'profile
Air diffusion resistance (s/m)
Stomatal diffusion resistance (s/m)
Albedo (fraction)
Shortwave insolation without atmosphere (ly/min)
Optical air mass (atmospheric diameters)
Atmospheric transmission coefficient
ISW = SWIO (ATC 0AM)
[absorption coefficient = -ln(ATC)]
Zenith angle of sun (degrees)
Hour angle of sun (degrees)
Equation of time (h)
Eastern standard time
True solar time
Day of year

58
each half hour. This prevents the data reports from precessing out of
synchronization with the system clock.
SET also enables REPRT and ANALZ to be swapped between core and
disk so as not to interfere with the measurement schedule. At the end of
a typical half hour (1.5 min past the clock hour or half hour, when mea
surement of the twelfth profile has just been completed) MEASR calls for
SET to run immediately and ends. SET schedules MEASR to start again at
an absolute clock time, 2 min into the new half hour, or roughly 30 sec
onds after the last measurement made. It then loads and runs REPRT and
ANALZ. When it is time for MEASR to start, whichever program is in core
is moved back to disk, and MEASR is loaded. MEASR makes its first scan,
and during the usual delay between scans, REPRT and/or ANALZ are re
loaded and run to completion. MEASR is then swapped back to core to be
continued at the end of the programmed delay;
The programs can be halted from the computer terminal or with
switches on the face of the computer. When switches 1 and 2 are on,
MEASR ends with the next profile and REPRT computes averages for all the
data collected in that half hour. When only switch 2 is on, MEASR ends
at the next normal half-hour reporting time.
Operational Considerations
The thermopile/air sampling system required a great deal of care in
setting up and maintaining the instrumentation involved. It also re
quired an awareness of the theoretical and practical limitations of the
measurement method. Proper calibration and tuning of the dewpoint analy
zer were most critical for good measurements. Sensor cleaning and output
calibration procedures are well documented in the EG&G Model 880 Dew
point Hygrometer Manual (1977). However, to achieve optimum response

59
times, it was necessary to tune the instrument slightly differently than
Manual specifications. It was made more sensitive by setting the THK
potentiometer so that voltage on the test points was 200-260 mV, and
made faster by setting the GAIN potentiometer so that the test voltage
was 150-210 mV. The new settings sacrificed dewpoint analyzer response
time in large step changes in order to improve response time in the
smaller step changes normally encountered in the profiles. To ensure
that the dewpoint analyzer actually had time to settle on readings be
fore being read by the voltmeter, its output was spot-monitored on a
millivolt recorder.
The most difficult problem was the individual and cross-correlation
of the dewpoint analyzer, the thermocouple/thermopile air temperature
sensors, and the precision radiation thermometer. The dewpoint analyzer
output was calibrated according to the EG&G manual. Temperatures'at the
bottom and top of the scale were simulated by substituting precision
resistances for the mirror-temperature sensing thermistor; the analyzer
output at these simulated temperatures was matched to the factory stan
dard instrument output. The radiation thermometer was calibrated by mea
suring its output for known surface temperatures produced with a stirred
constant-temperature bath. A regression equation for the temperature vs.
output correlation was calculated and used in the programs.
It was not possible to cross-calibrate these temperature sensors
until the system was run in a light drizzle on Nov. 5, 1981. This situa
tion resulted in the same temperatures at all measured levels, near-zero
net radiation, and air that was near saturation, so the dewpoint, air,
and surface temperatures were approximately the same. The temperature
differences between sensors were used to correct the rest of the data.

60
(It should be noted that this correction did not affect the Bowen ratio
calculation, since it used only relative changes. The correction did
affect surface temperatures, which were not used in computing the energy
budget.)
The radiation sensors were calibrated against a recently purchased
(and calibrated) Epply Pyranometer.
On the whole, the thermopile/air sampling system developed worked
very well and produced excellent data. However, there were some situa
tions in which it could not function well. The system was protected from
almost all of these situations because calculation of a complete energy
budget was made conditional on temperature and dewpoint profile similar
ity. Latent and sensible heat fluxes were not calculated when the pro
file correlation coefficient was less than 0.95.
Profiles were, regularly dissimilar for a few time-periods in the
early morning and late afternoon, while temperature and dewpoint pro
files were reversing in direction. This dissimilarity occurred because
changes in the temperature profile generally preceded changes in the
dewpoint profile.
Sensible heat generated at the surface of the outermost radiation
shields was usually carried away by the air flowing over them. At very
low windspeeds, however, the warm air produced at the outer surface of
the lowest radiation shields could become entrained in the aspiration
air of mast arms above. This problem showed in profile correlation coef
ficients but was usually not so bad that energy budgets could not be
calculated. Under clear skies this effect was not as marked, presumably
because the radiation shields could more effectively radiate heat away.

61
When the system was run at night, some condensation took place in
the air sample lines because the air sampling mast was not heated. Water
accumulated in the tubing in proportion to the length of the tubing sec
tion in the mast. As a result, the fifth level produced obviously high
dewpoint temperatures until the tubing had dried. The temperature dew
point correlation made it obvious at what time all condensation had been
evaporated from the sample lines.
The situation most hazardous to data quality occurred on very
sunny, dry days. At these times, the air temperature of the instrument
room (21-24C) was quite a bit higher than the dewpoint temperature of
the outside air. At some point the analyzer would no longer be able to
cool its sensor mirror low enough to get dew formation. Since air sam
ples from different levels have different temperatures, the coolest mir
ror temperatures possible varied also. A .false-dewpoint profile, which
correlated very well with air temperatures, would be measured and thus
passed through the correlation coefficient screen. Evidence for this
condition was the brightly-lit cooling circuit lamp on the dewpoint ana
lyzer. With experience this condition could be anticipated, and its ef
fects minimized by unplugging the heater cables to the sampling lines
and mixing box.
In spite of precautions taken, susceptibility to lightning damage
was the system's greatest weakness. The system was damaged twice by
lightning. In both cases, instrumentation and computer equipment was
damaged by current surges in the AC power system, in spite of power-
surge arrestors. The only solution was the most fundamental unplugging
all sensor cabling and all AC power cords.

CHAPTER 4
THEORETICAL BASIS OF THE TEMPERATURE GRADIENT RESPONSE
ET ESTIMATION METHOD
Overview
The key problem in developing a remote ET estimation method is de
scribing the vegetation and air layer at the surface so as much informa
tion as possible about its energy budget can be gained from the surface
temperature and net radiation. In addition, there is the question of how
much ancillary data is necessary for acceptable levels of accuracy in
the estimates. Previous approaches to these problems were outlined in
Chapter 2.
The methods developed in this chapter are based on the response of
surface-to-air temperatures to varying net radiation loads. First, a
functional relationship that describes the dependence of the surface-to-
air temperature gradient on net radiation and other factors is derived.
This temperature gradient response (TGR) model is used with surface tem
perature, air temperature and net radiation data to evaluate surface
parameters, which are then used in an adapted version of the combination
equation to estimate evapotranspiration. Two methods of making estimates
are developed. The first is physically strict, with a minimum of assump
tions; the second is more approximate with correspondingly fewer data
requirements.
For the sake of simplicity, the derivations that follow are in
terms of surface temperature (T ) and net radiation (R) rather than the
direct remote measurements, reflected (Qr) and emitted (Q ) radiation.
62

63
Also, in application, temperature differences are used to evaluate tem
perature gradients. For that reason, differences are used in the equa
tions developed and are referred to interchangeably as differences and
gradients.
Temperature Gradient Model
The simplified energy balance of a vegetated surface was developed
in Chapter 2:
R = E + H + G 4-1
The purpose of this section is to express the components of the surface
energy budget as much as possible in terms of net radiation and surface
temperature, so that a useful relationship between the two can be de
rived.
Because of heat storage in the surface air layer, surface tempera
tures lag net radiation. This lag is complicated by the fact that the
passage of clouds usually makes the net radiation absorbed by the system
vary randomly. For this reason, a method containing time as a variable
has been avoided. This was done by modeling the response of surface-to-
air temperature gradients to changes in net radiation.
In describing heat flux using a surface temperature (i.e., between
the surface and some plane above the surface), at least two layers with
different transport properties must be considered (see Fig. 4-1). The
first is the surface layer, in which molecular diffusion is the primary
transport mechanism. It is the thin layer of air immediately next to the
plant surfaces, represented by the layer between z$ and Zq in the dia
gram. The second is the fully turbulent layer between zn and z where
turbulent eddies are the primary transport mechanism. Following the de
velopment shown in Chapter 2, the heat flux between the surface (at

HEIGHT
64
a
Air
A
K
H
K,
Jr
h
a
Turbulent
Layer
Surface.^-
Soil
Figure 4-1. Definition Sketch for Transport Properties. The
surface layer which is dominated by laminar air
flow (molecular thermal diffusivity, k^) is repre
sented by the layer between zs and za. The heat
transport coefficient is used to represent the
combined transport properties of both layers.

65
temperature T ) and some'level in the air above the surface (at T ) is
$ Q
described by
4-2
where p is air density,
c is the specific heat of air at constant pressure,
kR is the molecular thermal diffusivity of air, and
K^J is the eddy thermal diffusivity of air.
(The first term in the denominator is equivalent to the resistance of
the laminar surface air layer, and the second term in the denominator is
equivalent to the resistance of the surface turbulent boundary layer.)
Treating latent heat flux analogously,
4-3
where e is the water vapor pressure,
y is the psychrometric constant (y = c P/Le),
is the molecular water vapor diffusivity, and
is the eddy water vapor diffusivity.
It has been shown that for a wide range of stability conditions normally
found (Dyer, 1967; Swinbank and Dyer, 1967; Webb, 1970; Dyer and Hicks,
1970; Garratt and Hicks, 1973):
Za dz [Za jjz
4-4
For simplicity, it is also assumed that
Z dz. ~ [Z0 dz
k k
JZs KW JZs kH
4-5
This assumption is unvalidated, but shared by the majority of theoreti
cal treatments. Literature values for the molecular water vapor and
thermal diffusivities are in fact at least approximately equal [e.g.,
Eagleso'n (1970) quotes values of 0.1 and 0.13 cm^/sec, respectively].

66
With the above assumption, transport of latent and sensible heat
can be considered similar from the surface to a reference level in the
air. The simple expressions developed in Chapter 2 (Eqs. 2-17 and 2-20)
can then be used to describe these fluxes:
H = h(T T ) and 4-6
S a
E = ^ M(e* ej 4-7
y S a
The moisture availability parameter (M) is included to account for the
subsaturation of the surface air layer. However, use of Eq. 4-7 as a
hard equality will force M to include minor differences due to inequali
ty of molecular diffusivities of latent and sensible heat (Jarvis et
al., 1971), any differences due to stability effects, and any differ
ences due to dissimilar sources and sinks of latent and sensible heat
within the vegetation system.
The dependence of the vapor pressure gradient on the surface-to-air
temperature gradient is shown in Fig. 4-2. It shows that the vapor pres-
*
sure difference (e efi) is in part due to the greater temperature of
the surface relative to the air, and in part due to the saturation defi
cit of the air. Considering the saturation vapor pressure curve linear
in the neighborhood of the surface and air temperatures,
*
e e = s(T T ) + se
S a S a a
4-8
where s is the slope of the saturation vapor pressure curve between
T and T and
S a
6ea is the saturation deficit of the air.
a
Substituting this expression into the latent heat flux equation (Eq.
4-7) gives the latent heat flux in terms of the temperature gradient:
E = £ M [s(T T ) + 6e ] .
i b a a
4-9

VAPOR PRESSURE
e^-eQ = a + b
e8*-ea8(Ts-Ta)+8ea
Figure 4-2. Components of Vapor Pressure Gradient. Component (a)
can be calculated from the surface-to-air temperature
difference (Ts Ta) and the slope (s) of the saturation
water vapor pressure curve [e*(T)]. Component (b) is
the saturation deficit (6ea) of the air.

68
The advantage of this substitution is that whatever error occurs in the
temperature gradient measurement affects both latent and sensible heat
fluxes, not just the sensible heat flux, as in the simple residual ap
proach. Substituting Eqs. 4-6 and 4-9 into Eq. 4-1,
R = G + h(T TJ + [s(T T ) + 6eJ 4-10
S a y S cl a
Rearranging terms and dividing by constants,
Ts Ta h(KsV-Y-) [v(R G) hnsea] 4-11
Equation 4-11 explicitly states the dependence of the surface-to-
air temperature gradient (difference) on other variables--net radiation
(R), soil heat flux (G), saturation deficit (6e ), bulk air conductivity
a
(h), and moisture availability (M). The equation is generally applica
ble; the psychrometric "constant" can be adjusted to various atmospheric
pressures (altitudes) and the slope of the saturation vapor pressure
curve can be adjusted for various temperature ranges. The resistance
formulation of this equation has been used by Jackson et jfL (1980).
In the strictest sense Eq. 4-11 is true only instantaneously. How
ever, with the assumption of some degree of system stationarity, various
approaches to remote ET estimates can be made. Two are developed here.
The first makes a minimum of additional assumptions and uses ground-mea
sured air temperature, saturation deficit, and soil heat flux measure
ments. The second assumes that only surface and air temperatures change
in response to changes in radiation, and uses only remote measurements.
Both use the response of temperature gradients to varying net radiation
loads to evaluate surface parameters; these are then used in calculating
ET.

69
Strict Temperature Gradient Response Method
From Eq. 4-11, one recognizes that
4-12
Substituting into the energy budget equation (Eq. 4-1),
E = R G -flsVr [y(R G) hMfea]
4-13
4-14
This is a version of the combination equation for evapotranspiration
(Penman, 1948). When the surface is saturated (M = 1), this equation
reduces to the potential evapotranspiration equation of Tanner and
Fuchs (1968).
The slope of the saturation vapor pressure curve (s) is a known
function of temperature, and the psychrometric constant is a known func
tion of atmospheric pressure. Net radiation (R), soil heat flux (G), and
saturation deficit (fie ) are measurable. Only the parameters for bulk
a
heat transport (h) and moisture availability (M) are unknown. These can
be evaluated with Eq. 4-11, assuming that they can be considered con
stant for some period of time.
Supposing that measurements of T T fie G, and R are available
S a d
for two different radiation loads,
y(R G), hMSe,
1 a
4-15
(Ts Ta}2 = h(Ms + y) 2
4-16
The numerical subscripts identify the two sets of data corresponding to
the two differing radiation regimes. If the measurements are made close
enough in time so that moisture availability and the bulk thermal

70
conductivity can be considered constant, this pair of equations can be
solved for the two unknowns M and h,
'k k
RAAe, RiAe^,
h = 4-17
se^AT2 6e2AT1
yCRoAT, + R'iATp)
M = ~~ ^r- 4-18
R^Aeg + R^Ae-|
where R:j = (R 6)^ 4-19
AT, = (T TJ, and 4-20
1 b Q 1
4ei s i = $ATi + 5ea. 4-21
Equations 4-17 and 4-18 can be substituted into Eq. 4-14 to yield:
~ RaTj RJAT2~
-
* V
R^Ae-j ^lAe2
R =
Rj6e2 R^Aej
s(R G) + 6e
a
6e^AT2 6e2AT^
, j
Now any evapotranspiration rate between the two measured radiation re
gimes can be calculated by substituting intermediate values of R, G, and
be near enough in time such that the constant M and h assumption is
valid, but far enough apart in radiation load so that reasonably accu
rate calculation of the parameters is possible.
Average Temperature Gradient Response Method
System Stationarity and Average Temperature Gradient Response
The most restrictive problem faced in estimating ET from above the
atmosphere is that very often clouds make surface temperatures unobserv
able. As shown in Eqs. 4-17 and 4-18, surface temperatures are necessary
to estimate surface moisture availability and bulk air conductivity.
This fact requires that remote ET estimates be made in two stages. The
first stage consists of using clear sky net radiation and surface

71
temperature data to evaluate the surface parameters. The second stage
consists of using those parameters and measured or estimated net radia
tion data alone to make ET estimates. It is assumed that through a com
bination of cloud-reflected radiation and cloud-top temperatures, a net
radiation estimate for the surface is still possible.
The success of this scheme is limited by the period over which the
parameters can or must be considered constant. They do vary; moisture
availability changes as dew evaporates and the bulk air conductivity
changes with the windspeed. But for the strict temperature response
method to work, the parameters must be considered constant for the time
interval between clear sky data sets, which is limited by the time reso
lution of the data collection system and cloud cover.
, This unavoidable necessity motivates viewing the surface as a sys
tem with approximately stationary parameters for the duration of a lon
ger measurement period (i.e., assuming that the surface-to-air tempera
ture gradients in Eq. 4-11 are a function of net radiation and con
stants). Information on the average parameters can then be extracted
from the correlation of clear sky surface-to-air temperature gradients
and net radiation, and used to estimate ET for clear or cloudy skies.
A soil heat flux parameter is required in order to fully parameter
ize the temperature gradient model. Soil heat flux is the smallest of
the energy budget components, usually accounting for less than 10£ of
net radiation under a vegetated surface. It lags net radiation in time,
but because its magnitude is in the range of error expected in the esti
mates, it can be safely and conveniently treated as a constant fraction
of net radiation:
G
R = 9 *
4-23

72
The quantity used in calculations is (R G), which for convenience can
be written
R G = (1 g)R = fR 4-24
Typical daytime values of "g" in the literature range from approximately
0.0 to 0.2, so for a vegetated surface "f" will have values between 1.0
and 0.8.
Substituting Eq. 4-24 into Eq. 4-11,
Ts Ta hOCTT)'^ hM5ea>
Formalizing the approximation of system stationarity,
4-25
h, M, f, s, Se, f f(t) 4-26
a
Eq. 4-25 reduces to the form
T, T = AR B
s a
where A and B are constants:
a = ri_ '
h(Ms + y) and
4-27
4-28
M6e
B =
4-29
(Ms + y) ,
and the parameter values are averages for the time period over which the
surface system is considered stationary. The constants A and B can be
evaluated by correlating the temperature differences (T T ) and net
radiation (R) data. Simple linear regression equations can be used:
E R.AT. nRAT
A = and 4-30
? 2
E (Rt) nR
B = AT AR 4-31
where the summations are done with clear sky data only,
AT = (T T ), and
b a
t is a subscript denoting the time of the measurement.

73
As a practical matter, the time period for which A and B are calcu
lated (and the parameters are considered constant) needs to be at least
a day. This period must be extended if enough clear sky data are not
available for a reasonable estimate of A and B. It should also be noted
that for normal daytime conditions, A and B must be positive for physi
cally real parameters. This implies that the intercept of the surface-
to-air temperature gradient/net radiation correlation must always be
negative (zero at most), and the slope must always be positive (see Eq.
4-27).
Use of the Average Temperature Gradient/Net Radiation Correlation
Incorporating the definition of the soil heat flux parameter (Eq.
2-24) into the equation for evapotranspiration (Eq. 4-14),
E > T5T7
4-32
The slope of the saturation vapor pressure curve (s) is a known function
of temperature, the psychrometric constant (y) is relatively constant at
a given altitude, and net radiation (R) can be estimated directly from
satellite data. There are four unknown parameters: moisture availability
(M), the soil heat flux parameter (f), the bulk transport coefficient
(h), and the saturation deficit (<5e ).
a
The equations for A and B, Eqs. 4-28 and 29, are in these four un
knowns. Since all four are required to estimate ET, two must be approxi
mated from average conditions or a rough daily measurement. Equations
4-28 and 29 can then be solved for the other two and substituted into
Eq. 4-32. Table 4-1 shows the ET formulae derived for the possible com
binations of known and unknown parameters and the correlation constants
A and B.

Table 4-1.
Evapotranspiration Formulae for Average TGR Method. Conditions listed are necessary to maintain
physically real solutions and prevent numerical problems. It is understood that A must always be
positive and unless otherwise noted, B must be greater than or equal to zero. Equation numbers
appear at right.
Known Unknown Substitutions
Parameters Parameters
Special Evapotranspiration Equation
Constraints Formulae Number
Yf
, B =
M6e
a
0 < M
< 1
E =
h(Ms + y )
Ms + y
.8 < f
< 1
yB
, f =
Ah<5e
a
0 < B <
6ea
E =
6e, Bs
a
6e, Bs
a
s
yB
, h =
f(6e^ Bs)
a
0 < B <
6ea
E =
Se, Bs
a
A5ea .
a
s
y (f hA)
5 ea
Bsf
A < 1
A < h
E =
hAs
(f hA)
Yf
" A(Ms + y)
5ea
B(Ms + Y)
M
none
E =
HrW 4'32
h,Se, M,f
f ,e M, h
h,f M,<$e.
M,f h,6e.
sAR
<5e, Bs
a
+ l
4-33
75F- (AsR 6ea Bs) 4'34
E = (f hA)R + hB
Mf
Ms + y
MA,
4-35
4-36
M.h f ,5 e.
r Ah(Ms + y ) B(Ms + y )
f y Sea = H
none
E = h
MsAR n '
+ B
V
4-37
M, 6e, h,f
a
no solution
42*

75
All of the equations in Table 4-1 have the same basic form because
A, B and the parameters are considered constant for the measurement per
iod :
E = CR + D .. 4-38
With A and B determined from clear sky data (requires surface tempera
ture, air temperature, and net radiation), and two independently esti
mated parameters, all that is needed in any of the formulae is a net
radiation estimate. If net radiation can be estimated for partly cloudy
or cloudy skies, ET rates for these conditions can also be calculated.
A significant advantage of considering the parameters approximately con
stant arises in computing cumulative evapotranspiration. Using the gen
eralized version of the equations in Table 4-1 (Eq. 4-38), the cumula
tive ET rate for some period (p) can be calculated as follows:
Ep = Jp Edt = Jp (CR + D)dt
= C/p Rdt + D/p dt
En = CR + Dt 4-39
P P P
where E is the cumulative ET over the estimating period,
R^ is the cumulative positive net radiation over the period,
tj" is the duration of positive net radiation during the
P estimating period, and
C and D are constants calculated from A, B, and estimates of two
parameters as shown in Eqs. 4-33 through 37.
Since the parameters are approximated as constant, no interpolation is
necessary for cumulative ET estimates. Use of an interpolation scheme
may be required to more accurately determine Rp, depending on the time
interval between satellite data sets.
Use of particular versions of the ET equation listed in Table 4-1
is discussed in the remainder of this section. It is difficult to pre
dict particular applications or weaknesses of these equations; they

76
depend both on the accuracy with which A and B can be determined, and
which of the parameters are most conveniently supplied from other mea
surements .
In general, the most difficult parameter to estimate independently
is moisture availability. Equations 4-33, 4-34, and 4-35 assume that it
and one of the other parameters are unknown. It can be anticipated that
the first two of these equations will have difficulties with low satura
tion deficits; Eq. 4-34 predicts infinite ET as the saturation deficit
nears zero. This is a result of having to express the parameters in
terms of the saturation deficit. From the substitutions, it is clear
that 6e must remain larger than Bs in order for physically real (posi-
a
tive) parameter values to result. Equation 4-33 seems to be the most
sensitive to low saturation deficits since it is meaningless even when
Se= is equal to Bs; Eq. 4-34 reduces to E ='fR with this condition (no
a
sensible heat is generated; all available net radiation is consumed in
evapotranspiration).
Equations 4-33 and 4-34 are also very sensitive to the value of B
obtained from the temperature gradient net radiation correlation. This
presents another potential problem in their use because the clear sky
data collected in a given estimation period may not be able to estimate
B at an accuracy level commensurate with its influence on the ET esti
mate. Once the behavior of B is better known, however, these equations
may become useful in areas where the least is known about the surface.
Saturation deficit is probably the parameter with the least spatial var
iability, and since it is directly measurable it can be estimated for
large areas. Equation 4-33 might be useful over a large grassland area
or large area of short crops since the transport coefficient of this

77
type of area may also be approximated. For large forested areas, where
it can be assumed that f=l, Eq. 3-34 might work well. In both equations,
the only other estimate required is the slope of the saturation vapor
pressure curve, which is a known function of temperature.
Equation 4-35 assumes that moisture availability and saturation
deficit are unknown. The evapotranspiration equation generated has the
advantage that neither the psychrometric constant nor the slope of the
saturation vapor pressure curve needs to be evaluated. This makes the
equation easier to use, and since no division is involved, it is compu
tationally safe. The additional parameters required are the bulk trans
fer coefficient and the soil heat flux parameter. The former may be cal
culable from measurements of windspeed and estimates of surface rough
ness. This approach has a long history in the literature (see Chapter
2), but its adaptability for use with a surface temperature has not been
demonstrated. The soil heat flux parameter only varies ^20%, and might
possibly be estimated from near-infrared remotely sensed data, which
gives a good idea of vegetative cover. Because of its potential, simpli
city, and easy graphical interpretation, Eq. 4-35 is used in the method
verification part of this study.
The last two equations, Eq. 4-36 and 4-37, assume that moisture
availability and either the soil heat flux parameter or the bulk tran
sport coefficient are known. Since M is a normalized parameter, it can
be assumed to have various values in a constrained range. It is conceiv
able that these equations might then be of some use.
Extension to Totally Remote ET Estimation Method
The final step in making a method depend only on remotely sensed
data is to generate air temperature measurements from surface

78
temperature measurements. Air temperatures are determined by the mixing
of air from higher in the atmosphere with near-surface air that has been
warmed (or cooled) by the surface. Therefore, one would expect air tem
peratures, particularly those near the surface, to be primarily a func
tion of the surface temperature. There is precedent for this approach.
In an effort to meet the boundary condition requirements of numerical
weather models, mesoscale climate modelers have begun developing "tem
perature response functions" (Idso, 1982).
There are practical reasons for this approach as well. A network of
ground stations to supply this measurement would be very expensive, and
calibrating the ground-based sensors against a satellite sensor is in
herently difficult. In addition to requiring knowledge of the atmo
sphere's transmission properties, temperature measurements made by a
contact sensor (e.g., a thermocouple or thermistor) must be matched to
measurements made by a thermal radiation sensor. Since temperature dif
ferences are required, a system based completely on remotely measured
surface temperatures would not be as sensitive to such absolute error
sources.
There are several ways in which air temperature measurements might
be generated. The simplest way is to choose a vegetation surface like
forest, whose surface temperature is closer to air temperature because
of the large fraction of surface elements visible to a satellite in
shade. The surface temperature of some reference pixel could then be
used as the air temperature for all pixels. In effect, the reference
pixel would never see a temperature gradient; its evapotranspiration
would exactly equal its available net energy (fR) since there could be
no sensible heat flux.

79
Another approach would be to simulate air temperature with a linear
combination of particular pixel temperatures. This involves empirically
choosing a set of reference pixels and determining coefficients for an
equation of the form:
T = an + a,T + a0T + . .
ci 0 1 s ^ 2 s ^
4-40
Both the length of time these coefficients are accurate and the extent
of the pixels for which they can be used to generate air temperature
measurements are important considerations in this approach. It should be
noted that similar considerations are involved in generating air temper
ature measurements for all pixels from a limited number of ground sta
tions.
The approaches suggested above are not developed any further in
this study.
Review of Assumptions
At the outset, the surface was conceived as a radiation-absorbing
(vegetation) layer, in contact with an air layer above and a soil layer
below. Energy fluxes inside the absorbing layer were considered irrele
vant, and energy fluxes to and from the surface were considered one-di
mensional and normal to the surface. It was assumed that the sensible
heat flux could be calculated from the surface-to-air temperature dif
ference (i.e., that the radiation surface temperature is representative
of the effective heat transfer surface temperature). It was also assumed
that the vapor pressure gradient could be represented in terms of this
temperature difference and the saturation deficit of the air by way of
the linearized saturation vapor pressure curve. The time derivative term
and the photosynthetic heat flux term were considered negligible in the
energy budget equation.

80
These assumptions are typical in the evapotranspiration literature.
However, they amount to assuming a uniform surface with adequate fetch
and close to steady-state heat transfer. Realistically, the system is
always transient and there is some energy storage in both the surface
and air layer. Remotely sensed surface information in general does not
come from flat homogeneous surfaces.
Both the strict and totally remote temperature gradient response
methods are dependent on some degree of system stationarity. The former
assumes that only moisture availability and bulk air conductivity are
constant between data sets. It requires surface and air temperature, net
radiation, soil heat flux, and saturation deficit measurements.
To lessen the data requirements, these assumptions are extended and
a new parameter is introduced in the totally remote method. Moisture
availability, bulk air conductivity, and air saturation deficit are con
sidered constant for a day or more, and soil heat flux is treated as a
constant fraction of net radiation. The surface is assumed to be a sta
tionary system with four unknown parameters (M, h, e and f), and one
a
known parameter (s), the slope of the saturation vapor pressure curve.
To make up for data that cannot be collected, it is assumed that two of
the unknown parameters can be estimated from some prior knowledge of the
surface; the other two can be determined from the temperature gradient
response to various radiation loads. Once the parameters are determined,
evapotranspiration for any net radiation load is calculable.
Several elements of these methods were considered beyond the scope
of this study, but assumed possible. It is taken for granted that rea
sonably accurate remote measurements of surface temperature and net ra
diation can be made, further, that estimates of surface net radiation

81
are possible even with cloudy conditions. The pivotal assumptions are
that the surface temperature can be used as the effective heat transfer
temperature, and that air temperature measurements can be generated from
surface temperatures.

CHAPTER 5
VERIFICATION OF THE TEMPERATURE GRADIENT RESPONSE
ET ESTIMATION METHOD
Overview
The central idea of the temperature gradient response (TGR) ap
proach is to use the changes in the surface-to-air temperature differ
ence relative to corresponding changes in net radiation in lieu of sur
face parameters to estimate ET. A temperature gradient model is used to
determine the surface parameters from the temperature gradient re
sponse; these are then used in calculating ET rates.
Use of the temperature gradient model, which expresses the funcr
tional relationship between temperature gradients, net radiation, and
surface parameters, 'involves a number of assumptions and approxima
tions. Since the accuracy of the eventual ET estimate is limited by
this model and ancillary approximations, verification of the TGR meth
ods is carried out in stages. Initially, the assumptions required are
individually examined. Then the implication for both the strict and
daily average TGR methods is demonstrated. For the most part, this is
done with data from a clear fall day, October 17, 1981.
The daily average TGR method is most suited for use with satellite
data. It is tested with practically all data collected. First, measured
temperature gradient/net radiation correlations are compared to those
predicted with independently measured constant parameters. Then the ET
estimates made with the correlations are compared to measured ET rates.
82

83
Validity of Assumptions
Radiation Temperature and Sensible Heat Transport
A simple expression involving a temperature difference and a bulk
heat transport coefficient (Eq. 4-6) was proposed to describe sensible
heat flux. It considers the sensible heat transport to and from the veg
etation layer to be the same as that across a relatively thick layer of
air above the surface. This layer is at the average grass surface tem
perature on one side, and at the average temperature of the air at a
specific reference level (a) above the surface on the other side. It is
assumed that the heat capacitance of air is very small and therefore
that the heat transport across the layer is close to steady. All the
properties of.the air relevant to heat transport through this layer are
accounted for in the heat transport coefficient (h).
The most critical assumption in this formulation is that.the aver
age radiation temperature of surfaces visible to an overhead sensor
(referred to as the surface temperature) and the effective heat trans
fer temperature are the same, or related in some predictable way. In a
vegetation canopy, many small areas at different levels in the canopy
contribute toward a radiation surface temperature measured from above.
These represent only a small fraction of the total plant surfaces. All
surfaces, including those not seen by a radiation sensor, contribute
sensible heat to the air. These contributions depend on how well venti
lated the canopy is at various levels.
Since radiation and sensible heat transfer are completely differ
ent and a vegetation surface is so complex, the radiation surface tem
perature and the effective heat transfer surface temperature may be dif
ferent. The only way to compare these two temperatures is to infer

84
their relationship from observations of the temperature profiles over
the grass surface. Sensible heat flux was calculated using five temper
ature measurements from the turbulent layer via the profile Bowen ratio
technique. One would therefore expect the heat flux to be proportional
to the temperature difference between the lowest and highest air tem
perature measurements. The heat transport coefficient of this fully
turbulent layer can be calculated by solving Eq. 4-6 for the heat
transport coefficient
where Tg is the lowest temperature measurement (35 cm) and is the
highest (235 cm). If heat transport through the total air layer (between
the surface and highest air temperature measurement) is steady, the same
heat flux passes through it as the turbulent layer. Then the heat trans
port coefficient of the total air layer can be calculated:
If the radiation surface temperature is the same as the effective heat
transfer surface temperature, one would expect the ratio of h/h^. to re
main constant over the course of a day. This ratio,
h T0 Ta c 0
hT = T "~r 5-3
t s a
can be most easily examined by plotting T T vs. Tn T (see Fig.
S d U d
5-1).
The points in this figure would lie on a straight line intersect
ing the origin if the relationship between the turbulent temperature
gradients (or effective heat transfer gradient) and the total surface-
to-air temperature gradients was constant. However, relative to a given

(3o)
85
0.0 1.0 2.0
T0-Ta CC)
Figure 5-1. Total vs. Turbulent Temperature Gradients for a Clear
Day'. The total surface-to-air temperature difference
was calculated by subtracting the temperature measured
at 235 cm from the surface temperature. The turbulent
temperature difference was calculated by subtracting the
235-cm temperature from the 35-cm temperature. Data ar.e
from October 17, 1982; numbers indicate true solar time
at end of half-hour averaging period. Individual temper
ature profiles for this day are plotted in Fig. 3 of
Appendix D.

86
effective heat transfer gradient, surface-to-air gradients are larger
in the afternoon than they are in the morning. This is because in the
afternoon, radiating surfaces lower in the canopy have also become
warm. Apparently, these surfaces make a relatively greater contribution
to the radiation surface temperature than they do to the sensible heat
flux via the effective heat transfer surface temperature. Although it
is not as extreme, this pattern is also observed on cloudy days, under
a diffuse radiation regime (Fig. 5-2).
One could reasonably expect radiation geometry to play a role in
creating differences between the radiation temperature and the effec
tive heat transfer temperature. At high sun angles, when direct sun
light is coming from angles close to the viewing angle of the radiation
sensor, less shaded area is visible to the sensor. The radiation tem
peratures should peak relative to effective heat transfer temperatures
when the angle of incidence of direct sunlight coincides with the angle
of view of the sensor. The slight upward curvature in the total/turbu
lent gradient correlation (Fig. 5-1) seems to confirm this effect, but
it is small in comparison to the morning/afternoon radiation tempera
ture hysteresis.
The apparent difference in the effective heat transfer surface
temperature and radiation surface temperature must be viewed as a poten
tial problem which may require modification of the equation used to com
pute surface temperature. A time-varying factor may be required, espe
cially in cases where the radiation geometry is further complicated by
surface slopes, as in mountainous areas.
Constancy of Parameters
The heat transport coefficient (h) and moisture availability (M)
are considered parameters in the strict TGR method, and they are

87
Figure 5-2. Total vs. Turbulent Temperature Gradients for a Cloudy
Day. Temperature differences were calculated as in
Fig. 5-1; data are from October 30, 1981. Note that
compared to Fig. 5-1 the temperature scale is expanded
by a factor of five. Temperature profiles for this day
are plotted in Fig. 4 of Appendix D.

88
required to remain constant between sets of data. In the average TGR
method, the slope of the saturation water vapor pressure curve (s),
the saturation deficit (Se ), and the fraction of net radiation conduc-
Q
ted into the soil (f) are also required to be approximately constant
for periods of a day or more. Though some of these variables are known
functions of measurable variables (e.g., s is a known function of tem
perature), they must be considered parameters. This section shows how
these parameters vary over the course of a day.
The sensible heat flux is plotted as a function of the surface-
to-air temperature difference in Fig. 5-3a. The average heat transport
coefficient is represented by the slope of a line passing through the
origin and the center of gravity of the plotted points. The bulk air
conductivity for any half-hour period is computed as in Eq. 5-2 and has
been plotted in Fig. 5-3b
It was shown in Figs. 5-1 and 5-2 that radiation surface tempera
tures in the morning appeared cool relative to the effective heat trans
fer surface temperature. Barring other factors, the resulting lower tem
perature gradients would lead to higher calculated thermal conductivi
ties for morning time periods. This does not show in Fig. 5-3b, how
ever. The only apparent effect seems to be lowered conductivities
around noon resulting from apparently higher surface temperatures while
relatively less shaded areas are visible to the sensor.
It is difficult to say anything conclusive about the heat trans
port coefficient in the early morning or late afternoon. Temperature
gradients are in the process of changing direction, making the calcula
tion of h somewhat unreliable.

89
riME (TST OCT. 17, 1981)
Figure 5-3. Heat Transport Coefficient Data.

90
Figure 5-4a shows latent heat flux plotted against the surface-to-
air vapor pressure gradient, considering the surface to be saturated at
the surface temperature. The slope of a line passing through the origin
and the plotted points is
The moisture availability for individual half-hour periods is computed
according to
M = 5-5
h(es ea>
where h has been calculated using Eq. 5-2. Moisture availability is
plotted as a function of time in Fig. 5-4b.
Since moisture availability is calculated with the help of the
heat transport coefficient, it responds to all the factors that influ
ence h. The dotted-line in Fig. 5-4b is a plot of moisture availability
calculated assuming.that h is a constant .035 ly/minC (its average
value, as shown in Fig. 5-3b). It shows the exponentially decreasing
pattern one would expect with an originally dew-laden surface. It
should be noted that 1981 was an exceptionally dry year for the
Gainesville area and that, by mid-October, about 50% of the grass was
dead. This accounts for the extremely low moisture availability data.
The relationship between the surface-to-air vapor pressure and
temperature gradients is plotted in Fig. 5-5a. It is determined by two
of the vapor pressure parameters which help determine the temperature
gradient response--the slope of the saturation vapor pressure curve,
and the saturation deficit. If a straight line is fit to this relation
ship, the slope can be interpreted as the average daytime slope of the

M (UNITLESS) E (LY/MIN)
.6
91
hM/Y=.006
J L
(a)
J L
0 10 20 30 40 50
Figure 5-4. Moisture Availability Data.

92
60
CD
5 40
o
0)
^'o)20
I
I
(U
Q
0
o
o
o
CD
ms
' o
CO a>
60
i r
i r
(a)
J 1 L
J L
4 6 8 10
TIME (TST,OCT. 17, 198!)
Figure 5-5. Vapor Pressure Parameter Data.

93
saturation vapor pressure curve, and the intercept as the average day
time saturation deficit.
The slope of the saturation vapor pressure curve and the satura
tion deficit are plotted for individual half-hour periods in Fig. 5-5b.
They are computed using the equation
T + T
s = 2.00 [(0.00738
+ 0.8072)7 0.00116] 5-6
from Bosen (1960), and
6ea = e*(Ta) ea 5-7
where the saturation vapor pressure at the air temperature is calculated
with the Magnus-Tetens formula (Tennessee Valley Authority, 1972)
7,5 Ta 1
e (T ) = exp
a
2.3026
T + 237.3 + 0,7858
Ia
The steady increase in the slope of the saturation vapor pressure curve
and the growth of the saturation deficit over the course of the day is
clearly evident.
Soil heat flux is graphed against net radiation in Fig. 5-6a. The
relationship is not smooth because the heat flux measurements were
rounded off to one significant figure (hundredths of ly/min). The aver
age daytime fraction of net radiation absorbed by the soil (1 f) is
represented by the slope of the line through the origin and the center
of the plotted data. The soil heat flux parameter is computed for half-
hour periods by
f 1 £ 5-9
and plotted in Fig. 5-6b. Even though soil heat flux (G) is low in the
morning relative to the afternoon, the soil heat flux parameter (f) is
very constant relative to the other parameters, because G/R is so small.

f (UNITLESS) G (LY/MIN)
94
TIME (TST,OCT 17, 1981)
Figure 5-6. Soil Heat Flux Parameter Data.

95
Clearly none of the parameters are constant. However, the strict
and average temperature gradient response methods have different de
grees of sensitivity to the variations in parameters, and must be
judged accordingly.
Strict Temperature Gradient Response Method
An example calculation of bulk air conductivity and moisture
availability according to the strict TGR method equations (Eqs. 4-17
and 4-18) is presented in the first column of Table 5-1. Measured val
ues of these parameters are listed in the third column of the table.
The example calculation shows poor agreement with measured values,
particularly before noon, when Eqs. 4-17 and 4-18 produce negative val
ues. Apparently, this is due to the numerical sensitivity of the equa
tions. This sensitivity is most apparent while dew is evaporating. Rela
tive changes in temperature and vapor pressure are large enough while
moisture availability is changing rapidly to produce physically nonmean
ingful negative bulk conductivities and moisture availabilities. How
ever, even in the afternoon, when h and M are relatively much .more sta
ble, the values obtained by the strict TGR equations match independent
measurements of h and M in order of magnitude at best.
The poor match is partially due to the equation's susceptibility
to round-off error. This can be demonstrated by calculating temperature
gradients assuming constant values of h and M. Using vapor pressure def
icit, air temperature, net radiation, and soil heat flux measurements
and assuming a value of .035 ly/minC for h and 0.12 for M, temperature
gradients were calculated with the temperature gradient equation (Eq.
4-11). These simulated gradients and raw data were then used in the '
strict TGR equations to calculate h and M. Results of the calculations

96
Table 5-1. Example Calculations with the Strict TGR Method. Data
used are from Oct. 17, 1981.
Calculated
with strict
TGR equations1
Calculated
with corrected
surface temps.2
Calculated
directly
from data3
t
h
M
h
M
h
M
(TST)
ly/min
C ly/minC
ly/min C
1000
.041
.14
1030
-.051
-.26
.020
.31
.033
.16
1100
-.092
-.14
.028
.19
.032
.15
1130
-.001
5.69
.024
.24
.034
.14
1200
-.133
-.15
.115
.65
.034
.12
1230


.041
.08
.033
.12
1300
.031
.14
.030
.16
.035
.11
1330
.016
.37
.033
.14
.036
.10
1400
.017
.24
.048
.06
.038
.10
1430
.037
.09
.031
.15
.035
.12
1500
- .044
.06
.036
.11
.038
.10 .
1530
.062
.02
.038
.10
.032
.12
1600
.051
.05
--

.022

1 heat
transport
coefficient and moisture availability calculated
with Eqs
. 4-17 and
4-18.
2 heat
transport
coefficient and moisture availability calculated
with corrected surface temperatures. Surface temperature was
calculated with Eq. 4-11 using h
=.035 ly/min C and M=0.12,
and then
h and M were recalculated as in
1.
3 heat
transport
coefficient calculated
using Eq. 5-2, and
moisture
availability calculated using Eq. 5-5.

97
are shown in the second column of Table 5-1. They do not reproduce the
constant values of h and M, but are positive and correct in order of
magnitude.
The numerical hypersensitivity of the.strict TGR equations pre
vents good estimates of the bulk air conductivity and moisture availa
bility using data of realistic accuracy (two significant figures).
These equations are made up of compound differences; for example, the
numerator in Eq. 4-17 contains the product of a saturation deficit

[e (T ) ej and a temperature difference (T T ), which is
subtracted from a similar product. For this reason, the strict TGR
method does not lend itself to a practical ET estimation method.
Average Temperature Gradient Response Method
Graphical Representation of the Average TGR Method
Because of the number of parameters and complexity of'the equa
tions relating them to the temperature gradients (Eq. 4-25) and evapo-
transpiration (Eq. 4-32), it is difficult to get a feel for how param
eter variations affect ET estimates. However, some idea of their effect
on estimates of instantaneous ET rates can be gained directly from the
surface-to-air temperature gradient/net radiation relationship.
Figure 5-7 shows the measured surface-to-air temperature gradient
as a function of net radiation for the example day, October 17, 1981.
The relationship is not exactly linear, but it is a smooth non-noisy
relationship. The characteristic features are that the morning limb
does not coincide with the afternoon limb, and that the morning limb
has a distinct droop, or "belly." These features result from variations
in the parameters.

NET RAD.
TIME (TST, OCT. 17, 1981)
Figure 5-7. Clear Day Temperature Gradient/Net Radiation
Correlation. Data are from October 17, 1981;
numbers indicate true solar time at end of
half-hour averaging period.

99
If one changes the temperature scale by multiplying it by h, the
average air thermal conductivity (.035 ly/minC), an approximate plot
of sensible heat flux vs. net radiation results (see Fig. 5-8). This
graph can be interpreted with the help of the surface energy balance,
E+H = R- G ~ fR .
Since soil heat flux is very small (i.e. f = 1), the 45 line approxi
mately represents this equation. The distance from the R axis to the
solid line connecting the data points approximates (depending on the
constancy of h) the sensible heat flux at that radiation load and time.
Therefore the distance from the solid line connecting the data points
to the 45 line represents the approximate latent heat flux for partic
ular radiation loads and times. This is true even when the solid line
is below the R axis; at these times sensible heat flux is toward the
surface (T T < 0) and helping to drive evapotranspiration*
$ d
The heavy dashed line shows the approximate relationship between
the surface-to-air temperature gradient (or sensible heat flux, with
the vertical axis scaled by h) and net radiation. The average TGR meth
od amounts to using the dashed line to partition the latent and sensi
ble heat fluxes. Physically, the dashed line represents the temperature
gradient response of the surface that would occur if the parameters
were nonvarying.
In terms of the equations developed in Chapter 4, the dashed line
is described by
H = h(T T ) = h(AR B) 5-11
S a
using the surface-to-air temperature gradient/net radiation correlation
(Eq. 4-27). The distance from it to the 45 or fR line can be described
with the help of the energy balance:

100
Figure 5-8. Graphical Interpretation of Temperature Gradient/Net
Radiation Correlation. The temperature gradient data
from Fig. 5-7 (October 17, 1981) were multiplied by
.035 cal/cm2secC to produce this graph of sensible
heat flux vs. net radiation. The soil heat flux
parameter is .93.

101
E = fR H = (f- hA)R + hB 5-12
This equation is identical to Eq. 4-35, the expression developed for
the case in which the heat transfer coefficient (h) and the soil heat
flux parameter (f) were known.
Like all the equations for evapotranspiration (Table 4-1), this
equation has the general form of Eq. 4-38. There is a component propor
tional to net radiation which varies over the course of a day, and a
constant component, referred to as advected energy because it is a
function of the saturation deficit (a result of dry air advection onto
the evapotranspiring surface) and the transport coefficient. In this
case (Eq. 5-12), the time-varying component is a function of Athe
greater the slope of the temperature gradient/net radiation correla
tion, the smaller the fraction of net radiation that contributes to
£Tand vice versa. The constant component is a function of Bthe low
er the intercept of the correlation, the greater the role of advected
energy in driving ET. The average TGR method in effect considers the
advected energy constant throughout the day, added to a component pro
portional to the varying net radiation.
Figure 5-9 shows evapotranspiration estimated using the tempera
ture gradient/net radiation correlation and actual ET rates plotted
against time. The area under the lines connecting the estimates and
measurements corresponds to the total daily estimated and actual evapo
transpiration. The dashed line in this graph separates the components
of estimated ET due to the "constant" advected energy term and the net
radiation term. The constancy of the parameters over the estimating
period is what makes cumulative ET rates easy to calculate;
P
Ep = (f hA)Rp + hBt
5-13

EVAPOTRANSPIRATION
TIME (TST)
Figure 5-9. Cumulative ET Estimates. Evapotranspiration estimates
made with the ATGR method and ET measured by the profile
Bowen ratio method are plotted against time. Data used
are the same as those in Fig. 5-8 (October 17, 1981);
the dotted line is for unavailable ET data. The sub
script D in the equation stands for a daily estimation
period.

103
ET Estimates with the Average TGR Method
Satellite data have two practical limitations that must be ad
dressed by any ET estimation method: they are only available at dis
crete sensing-system-determined time intervals, and they are intermit
tently incomplete because of cloud cover. Dealing with these situations
requires a method which can bridge the gaps between data sets.
The average T6R method does this by assuming that there is an ap
proximately linear correlation between temperature gradients and the
net radiation loads that cause them. As shown in the previous chapter,
this is the equivalent of assuming that the surface parametersthe
bulk air thermal conductivity, moisture availability, saturation defi
cit, slope of.the saturation vapor pressure curve, and the fraction of
net radiation warming the soilare constant. This assumption both de
fines an ET rate for any given net radiation load and reduces the prob
lem of computing cumulative ET to estimating the cumulative net ra
diation.
The convenience of this assumption has a cost in the accuracy of
the estimated instantaneous ET rates. As can be seen in Fig. 5-8, when
the solid data line lies higher than the dashed constant parameter
line, estimates by the average TGR method generally overestimate ET,
and vice versa. There is a pattern in the direction of these errors
(see Fig. 5-9). In general, it is not possible to predict the error
direction on a given day at a given time because the direction is a
function of the variation in parameters. However, the errors that re
sult from using the average TGR method to estimate instantaneous ET
rates are minimized in the process of fitting a line to the temperature
gradient/net radiation data points. Some error remains because use of

104
the correlation (Eq. 4-27) physically corresponds to using average val
ues of the parameters.
The process of fitting a line to the temperature gradient/net ra
diation relationship ensures good cumulative ET estimates. As can be
seen in Fig. 5-8, fitting balances the deviations of the data around
the dashed regression line used to estimate ET. Errors in estimates in
one direction at a particular time of day are thus balanced by errors
in the other direction at other times, as shown in Fig. 5-9. Good cumu
lative ET estimates result because errors in instantaneous ET estimates
made in the same measurement period tend to cancel each other as they
are summed over the period.
There are some potential sources of unbalanced errors. The "belly"
in the temperature gradient/net radiation relationship may introduce a
bias on the side of underpredicting ET, because there is no compensat
ing bulge on the other side of the straight line. However, since the
belly lowers the intercept of the temperature gradient/net radiation
correlation, a compensating bias is introduced. The lowered intercept
causes ET to be overestimated at all levels of net radiation by in
creasing the constant "advected" component of ET. The method is obvi
ously very sensitive to B and the daylength used in cumulative esti
mates.
It is possible to intentionally bias the average TGR method with
specific measurement schedules. For example, the purpose of the mea
surements might be to estimate net daily ET (total ET less the amount
of dew evaporated). By using only afternoon surface temperatures and
net radiation, the influence of the low morning temperature gradients
is avoided. This results in overestimating morning sensible heat flux

105
approximately to the levels that would have occurred had it not been
for the dew.
This section has shown that due to the pattern of changes in the
parameters, use of their average values leads to systematic over- and
underestimates of instantaneous ET rates. It has also been shown that
in cases where interpolation capability is necessary and cumulative
accuracy is sufficient (in applications where daily or longer ET esti
mates are the goal), assuming that the parameters are constant is a
very useful approximation. Figures 8, 9, 10, 11, and 12 in Appendix D
graphically demonstrate these points for five days in October of 1981.
Effects of Individual Parameter Variations
With the.graphic representation of the ATGR method shown in Fig.
5-8, it is relatively easy to directly see how patterns in the tempera-
.ture gradient/net radiation relationship influence instantaneous ET
estimates. This subsection shows how individual parameter variations
cause the patterns in the temperature gradient/net radiation relation
ship.
The most convenient way to demonstrate the effects of variations
in individual parameters is to compare temperature gradients predicted
with only one parameter varying to temperature gradients predicted with
constant parameters (see Figs. 5-10, 5-11). It is possible to calculate
each parameter for each time period with the available measurements.
When the average value of each parameter is used to calculate tempera
ture gradients (only net radiation varies in Eq. 4-25), the gradients
fall on the ideal straight line postulated in the average TGR method.
Recalculating the temperature gradient with only one parameter varying-
qualitatively shows the effect of that parameter on the temperature

106
Figure 5-10. Effect of Moisture Availability and Vapor Pressure Param
eters on Temperature Gradients. The solid straight lines
represent the temperature gradient response that would be
observed if all parameters remained constant at their av
erage value. They represent the same temperature gradients;
they have been offset to show the pattern of variations.

107
Figure 5-11.
Effect of Heat Transport Coefficient and Soil Heat Flux
Parameter on Temperature Gradients.

108
gradient/net radiation relationship. Note that Eq. 4-25 is non-linear;
the effects shown in Figs. 5-10 and 5-11 are not additive.
The parameter apparently causing the most short-term variations is
bulk thermal conductivity. Part of this variation is expected; it is
dependent on changes in radiation temperature relative to effective
heat transfer temperature, as well as windspeed. However, it can be
argued that some of the variation is numerical in origin. Temperatures
were rounded to the nearest tenth of a degree, and sensible heat flux
to hundredths of ly/min. This introduced some "artificial" variations
into the calculated thermal conductivities, particularly early in the
morning and late in the afternoon when temperature gradients are small.
The fact that considering h constant leads to smoother, more reasonable
moisture availability estimates (see Fig. 5-4b) also supports this ar
gument.
The change in slope of the saturation vapor pressure curve varies
with the increase and decrease in air and surface temperatures; as
shown in Fig. 5-10, it leads to higher gradients in the morning than in
the afternoons. Saturation deficit has the same effect. Changes in
these parameters impose a general hysteresis in the temperature gradi
ent/net radiation relationship. All other parameters being constant,
near-surface temperature gradients would be stronger in the mornings
than in the afternoons because a reservoir of cold air builds up over
night. As the surface and the cool air increase in temperature, the
vapor pressure gradient (both components) becomes stronger relative to
the temperature gradient. This favors latent to sensible heat loss,
thereby causing relatively weaker temperature gradients in the after
noon .

109
The hysteresis caused by changes in the slope of the saturation
vapor pressure curve and saturation deficit is often masked by rela
tively large changes in moisture availability. When there is heavy dew,
as on Oct. 17, 1981, more evaporation takes place in the morning, caus
ing temperature gradients to remain small relative to afternoon gradi
ents at equivalent radiation loads. In the afternoon, moisture availa
bility has decreased and temperature gradients are pushed higher. The
extreme changes in M in the early morning are what cause the belly in
the graph.
Figure 5-12 shows data from a clear day in spring which had a much
smaller range of moisture availabilities. Very little dew accumulated
during the previous night because of a steady post-cold front northeast
breeze. In this case, morning temperature gradients are higher than
corresponding afternoon gradients because the variations in the slope
of the saturation vapor pressure curve and saturation deficit out
weighed changes in moisture availability.
The morning-afternoon hysteresis in Figs. 5-7 and 5-12 is most
extreme on clear days which have the temperature extremes to cause rel
atively large variations in s. Variations in the parameters are less
ened on partly cloudy days; Fig. 5-13 shows the parameters and tempera
ture gradient/net radiation correlation for a partly cloudy day. Clouds
narrow the range of surface and air temperatures and concurrent s, thus
lessening the variation between morning and afternoon temperature gra
dients .
Variations in the fraction of net radiation going into soil heat
flux have a negligible effect on the surface-to-air temperature gradi
ents because soil heat flux is a very small component of the heat

(C) NET RAD.
Temperature Gradient Response of a Clear Day with Constant
Moisture Availability. The temperature gradient hysteresis
is the opposite of that for October 17, 1981 (Fig. 5-7)
which had decreasing moisture availability.
Fioure 5-12.

m
2 i.o
6 8 10 12 14 1618
TIME (TST, OCT. 22, 1981)
Figure 5-13. Temperature Gradient Response of a Partly Cloudy Day.

112
budget--here less than 10% of net radiation. The noisy character of air
bulk thermal conductivity also does not seem to show in the temperature
gradient/net radiation correlation. This and the fact that considering
h constant leads to more reasonable moisture availability estimates
suggests that variations in thermal conductivity have an insignificant
effect on temperature gradients. For the most part, the pattern in the
temperature gradient/net radiation correlation is a result of the in
teraction of moisture availability and the vapor pressure parameters.
Generality of the ATGR Latent/Sensible Partition
Another argument in favor of the ATGR method is that it correctly
reproduces the general pattern of change in latent and sensible heat
fluxes. Even though instantaneous ET rates are sometimes slightly over-
and underestimated because the parameters are considered constant, the
ATGR partition matches the daily pattern of other partition measures,
such as the Bowen ratio.
Figure 5-14 shows an idealized ATGR latent/sensible heat flux par
tition and the resulting idealized daily time course of the Bowen ratio
and E/R, another widely used dimensionless partition ratio. The ratios
were computed according to
H hAR hB
E (f hA)R + hB
and
5-14
E (f hA)R + hB
R ~ R
wi th
5-15
R = Rq cos
2ir
[2T
TST tt
5-16
where TST is true solar time (6 < TST < 18), and
Rq is an arbitrary maximum net radiation load.
These patterns have been observed and reported for clear days by other
researchers (e.g., Pruitt, 1964). The gradient response partition also

O .2 .4 .6
R (LY/MIN)
Figure 5-14. Generalized Clear Day H/E and E/R Patterns. The patterns in (b) were generated with
the average temperature gradient response in (a) and a sinusoidal net radiation
pattern. When the intercept in (a) is zero (negligible saturation deficit), E/R and
H/E are constant (see Fig. 5-12). The curvature in the patterns of these ratios
increases as the intercept becomes more negative (saturation deficit increases).

114
correctly reproduces the complex Bowen ratio patterns of partly cloudy
days, as shown in the middle section of Fig. 5-15 (same day as shown in
Fig. 5-13).
The relative magnitudes of sensible and latent heat flux vary with
the amount of net radiation received by the surface because of the sat
uration deficit term in the equation for evapotranspiration. If there
were no saturation deficit, the intercept (B) of the temperature gradi
ent/net radiation correlation would be zero, reducing the expressions
for the dimensionless ratios (Eqs. 5-13 and 5-14) to constants:
| = f hA 5-18
The greater the role of the saturation deficit in driving ET, the
greater the variations in the dimensionless ratios.
The fact that the average temperature gradient/net radiation cor
relation coefficients A and B explain general patterns and can be con
sidered roughly constant suggest they may be useful in some form of
climate index. They are more representative of the surface and surface
environment than the Bowen ratio or other ratios, which are representa
tive only of the particular time at which they were measured.
Tests of the ATGR Method
The purpose of this section is to show that the temperature gradi
ent/net radiation correlation does reflect the average values of the
parameters during the time of the measurements, and that the ATGR meth
od produces reasonably accurate ET estimates. This is done with data
collected in the fall of 1981.

BOWEN RATIO (UNITLESS)
)CT. 17, 1981 OCT 22, 1981 MAY
115
Figure 5-15. Comparison of Measured and Estimated Bowen Ratios. Bowen
ratios were estimated with Eq. 5-14. Mote the increasing
curvature in the pattern with increasing saturation defi
cits, and the change in Bowen ratio with clouds on Oct.' 22,
1981. (The temperature gradient responses of these days
were shown in Figs. 5-7, 5-12, and 5-13.)

116
It can be shown that the temperature gradient/rtet radiation corre
lation is a result of the average parameters by comparing estimates of
A and B computed using independently estimated values of the parameters
to A and B computed by regression equations. Table 5-2 lists average
parameter values for most of the fall days on which data were collected
and corresponding A's and B's calculated by Eqs. 4-28 and 4-29 (using
averaged parameters) and by Eqs. 4-30 and 4-31 (using measured net ra
diation and surface-to-air temperature gradients).
Table 5-2. Comparison of Average and Correlation Estimated A and B.
Numbers in parentheses are the coefficients of variation
of the parameters expressed as percentages.
Oct
h
M
f
s
6ea
^avg
a
corr
Bavg
^corr
17
.034
.13
.92
2.6
21
18.2
17.5
2.6
2.2
(13)
(17)
(2)
(7)
(9)
18
.037
.13 '
.92
2.6
20
16.7
12.8
2.6
0.8
(16)
(28) .
(4)
(7)
(10)
20
.038
.13
.94
2.0
16
17.7
14.0
2.2
0.6
(23)
(14)
(2)
(13)
(18)
21
.033
.15
.92
2.3
17
18.2
14.5
2.6
1.0
(11)
(18)
(4)
(6)
(ID
22
.031
.18
.94
2.6
18
18.2
16.5
2.8
1.7
(12)
(32)
(1)
(12)
(25)
23
.026
.24
.91
2.8
21
20.2
14.9
3.8
0.4
(36)
(52)
(4)
(10)
(21)
28
.033
.18
.98
2.1
11
19.0
15.7
1.8
0.6
(ID
(26)
(3)
(18)
(28)
29
.031
.15
.96
2.2
12
20.3
13.7
1.9
0.2
(14)
(16)
(2)
(10)
(13)
31
.041
.33
1.05
1.4
2
15.0
8.9
0.5
-0.3
(32)
(87)
(12)
(5)
(65)

117
The parameters were calculated for each time period (according to
Eqs. 5-2, 5-5, 5-6, 5-7, and 5-9) and then averaged. This calculation
is equivalent to the line-fitting procedure used in Figs. 5-3, 5-4,
5-5, and 5-6. The parameter data and temperature gradient/net radiation
correlation for five of the days listed in Table 5-2 are graphed in the
(a), (b), (c), (d), and (f) parts of Figs. 8, 9, 10, 11, and 12 in
Appendix D.
The calculated and observed values of A show a better degree of
agreement than do the values of B. This can be traced to the cross-cal
ibration of the surface and air temperature sensors. If they are not in
agreement, the temperature difference due to lack of cross-calibration
becomes part of the surface-to-air temperature difference. This system
atic error directly affects the intercept (B) of the temperature gradi
ent/net radiation correlation. Indirectly, it also affects the value of
A calculated using an average value of the air transport coefficient.
For example, if the surface temperature is slightly high relative to
the air temperature, temperature gradients will be overestimated, and
the value of B obtained from the temperature gradient/net radiation
correlation will be high. This means that B will be less negative than
it ought to be, or too small in absolute value. Indirectly, a high sur
face temperature measurement will result in a low air transport coeffi
cient, which will produce a correspondingly high calculated value of A
(Eq. 4-28). The surface and air temperature cross-calibration used in
this analysis was obtained from time periods in which there was little
net radiation and immeasurably small temperature gradients, as de
scribed on p. 59.

118
The accuracy of ET estimates made using the ATGR method is evalu
ated in Table 5-3. This is done by calculating the correlation between
measured ET rates and ATGR method estimates (Eq. 4-35). The first three
numbers after the date indicate the slope, intercept, and correlation
coefficient of a simple regression line fit to the measurements and
estimates. If the correlation was perfect, the slope would be 1, the
intercept would be 0, and the correlation coefficient would be 1. The
latter is a measure of the scatter between measured and estimated ET
rates; the departure of the slope and intercept from 1 and 0 is an in
dication of systematic differences between measured and estimated ET
rates. These systematic differences probably occur because of the lack
of data at low net radiation levels. Morning ET data were generally
missing because of condensation in the air sampling mast, so tempera
ture gradient/net radiation correlations are biased toward afternoon
conditions.
The comparison of ET estimates to measurements is presented graph
ically for five days in graphs (g), (h), and (i) in Figs. 8, 9, 10, 11,
and 12 of Appendix D. Estimates made with the simple residual method
(Eq. 2-24) are also shown for comparison. This method represents the
state-of-the-art in remote ET estimation methods.
Graph (g) in each of the figures compares the daily course of mea
sured Bowen ratios, ratios calculated via the ATGR method (Eq. 5-14)
and ratios calculated by the simple residual method. The latter was
calculated according to:
h(T, Tj
5-19
" fR h(T T ) '
b a
In both cases, the average heat transfer coefficient of the particular
day graphed was used in computations. The ATGR method Bowen ratio is

119
Table 5-3. Quality of ET Estimates made with' the ATGR Method. The table
below gives two measures of the quality of ET estimates for
each of two methods of calculating instantaneous ET. The
first measure of quality is the slope intercept and regres
sion coefficient of a line fit to the relationship between
ET estimates and measured ET rates. The second is the slope
of a line describing the same relationship, except forced
through the origin.
Date
Oct.
Calculated
average
with daily
h and f
Calculated with average
conditions h and f
Slope
2
Intercept R
Cum.
Err.
Slope
2
Intercept R
Cum.
Err.
17
.88
.03
.96
.99
.84
.03
.96
.97
18
.52
.04
.97
.68
.86
.04
.97
.99
20
.98
.01
.92
1.02
1.09
.00
.92
1.11
21
.94
.01
.98
.98
.90
.01
.98
.95
22
.93
.02
.99
.99
.77
.03
.99
.88
' 23
1.14
-.03
.98
1.05" .
.79
-.01
.98
' .74
28
1.14
-.02
1.00
1.06
1.07
-.02
1.00
1.00
29
1.23
-.03
1.00
1.09
1.11
-.03
1.00
.99

120
better at following the general pattern of the measured Bowen ratio.
The residual method Bowen ratio is noisy by comparison because it is
very responsive to small variations in temperature gradients; whenever
the numerator in Eq. 5-19 is reduced, the denominator is increased by
an equal amount, and vice versa.
Instantaneous ET estimates made by the ATGR and residual methods
are compared in graph (h) of each of the figures. In these calculations
an average conditions value is used for the heat transport coefficient
(.035 ly/minC). Both methods produce estimates of the same quality,
since they use essentially the same information to produce estimates.
Both appear to have the same sensitivity to the heat transport coeffi
cient value. Figure 11(h) shows a day (Oct. 22, 1981) on which the heat
transport coefficient averaged about 15% less than the average condi
tions value, causing both.methods to underestimate ET. Graph (i) in
Figs. 8, 9, 10, 11 and 12 shows the same data as graph (h) plotted
against time. This presentation of the data more clearly shows the sys
tematic departure of ATGR estimates from measured ET rates.
Finally, the accuracy of cumulative ATGR method ET estimates are
compared to measurements. The simplest comparison is shown in the
fourth column of Table 5-3. It is the slope of a line passing through
the origin and the center of the measured vs. estimated ET points, as
shown in graph (h) of Figs. 8, 9, 10, 11, and 12 in Appendix D. If the
slope is 1.11, for example, the cumulative ET estimate is 11% too high.
The second set of numbers in Table 5-3 was calculated under more real
istic estimating constraints "average conditions" values for the air
heat transfer coefficient (.035 ly/minC) and the soil heat flux

121
parameter (.94) were used for all estimates. Although errors in esti
mates for individual days change, the overall error level does not.
The overall error level of the cumulative ET estimates can most
easily be seen in Fig. 5-16. It graphically compares ET estimates made
with the ATGR method (using "average conditions" h and f) and residual
methods. In general, cumulative estimates are more accurate than in
stantaneous estimates, and days on which the ATGR method performance is
worst are generally overcast days for which it was very difficult to
obtain representative values of A and B.
From the calculations presented in this chapter it can be con
cluded that the average temperature gradient response is a measure of
the average surface parameters, and that the slope and intercept of the
temperature gradient/net radiation correlation can be used to make rea
sonably accurate ET estimates. It must be noted that the cross-calibra
tion of the surface and air temperature sensors is of critical impor
tance in application of the ATGR method. In these calculations it ap
pears that the surface temperature may have been slightly high relative
to the air temperature measurement.
Cumulative ET estimates made with the ATGR method are exactly as
accurate as estimates made with the state-of-the-art simple residual
method. However, unlike the simple residual method, it is useful for
any time period(s) for which a net radiation estimate is available--its
application is thus not limited to clear time periods. Both methods
seem equally susceptible to errors in the value of the heat transport
coefficient used in making estimates; estimates that agree least close
ly with measured ET amounts generally have a heat transfer coefficient-
substantially different from the average conditions value used.

ESTIMATED ET ( LY/DA)
122
MEASURED ET (LY/DA)
Figure 5-16. Cumulative ET Estimates by the Residual and ATGR Methods.
Only the periods for which measured ET was available were
used in comparing estimated daily ET with measured daily
ET. Data from 15 days between October 17 and November 6,
1981, are shown.

CHAPTER 6
CONCLUSIONS
Summary of Results
The Average Temperature Gradient Response Method
The challenge in developing a general ET estimation method for use
with satellite data is to find the method that delivers the most accept
ably accurate ET estimate for the least in data collection and data pro
cessing costs. The average temperature gradient response (ATGR) method,
the primary result of this research, is directed at these practical con
siderations.
The ATGR method is based on a steady-state model of the surface
developed to describe the relationship of temperature gradients and net
radiation over a surface. This model,
1
T- Ta = hTHT+TT WfR Mhse.) ,
4-25
s a rums + y) a
characterizes the surface with parameters for heat transport through the
near-surface air layer (h), surface moisture availability (M), the tem
perature dependent slope of the saturation vapor pressure curve (s), the
fraction of net radiation available to be converted into latent or sen
sible heat (f), and the saturation deficit (6eJ. By considering the
a
parameters (and the psychrometric constant, y) stationary over some time
period, the average temperature gradient/net radiation correlation
T T = AR B
5 a
4-27
can be used to obtain a composite measurement of the average parameters:
123

124
A =
yf
h(Ms + y)
and
4-28
MSe
B = (Ms +\)
With independent evaluation of two of the parameters,
4-29
for example,
the heat transfer coefficient (h) and the fraction of net radiation
available for latent or sensible heat (f), the composite parameters can
be used to estimate evapotranspiration:
E = (f hA)R + hB
4-35
This is one of five equations for latent heat flux developed, each for a
different combination of unknown parameters (see Table 4-1).
Making an ET estimate with the ATGR method is a two-stage process.
First, individual remote net radiation and surface temperature measure
ments and ground-gathered air temperature data are used to calculate
the. temperature gradient/net radiation correlation (i.e., A and B).
This requires data from clear time periods when surface temperatures
are observable. The second stage consists of making the ET estimates.
With A and B determined, only a net radiation estimate and the two in
dependently estimated parameters are required. For instantaneous ET
estimates, these values are simply substituted into Eqs. 4-33, 4-34,
4-35, 4-36, or 4-37.
Since the parameters are considered constant, making cumulative ET
estimates is also relatively convenient. Only an estimate of the total
positive net radiation during the estimating period (R ) and the dura
tion of positive net radiation during the estimation period (t ) are
required. For the particular parameter combination in Eq. 4-35, the
cumulative ET over the estimating period is
P
E = (f hA)Rp + hBt
5-13

125
The two-stage method solves the problem of cloudy skies and the
problem of interpolating between data sets. Although there may be some
cost in the form of reduced accuracy for instantaneous ET estimates,
the considerable data collected over Florida pasture (including net
radiation and surface-to-air temperature gradient measurements under
partly cloudy and cloudy skies) indicate that the ATGR approach is a
good approximation. Cumulative ET estimates were as good as estimates
made by the simple residual method (Chapter 2), which requires the same
amount of data but has no physically based method of dealing with
clouds and the time resolution of satellite data.
Method Limitations and Strengths
In principle, the ATGR method is a descendant of the Penman method
and many of the criticisms of the Penman method are relevant to it. The
Penman equation has been faulted for including a heat transport coeffi
cient which is an empirical function of wind (Thom and Oliver, 1977). In
its generalized form (for unsaturated surfaces) the Penman equation is
difficult to use because it requires knowledge of the dryness of the
surface in the form of a moisture availability parameter (Barton, 1979)
or a bulk stomatal diffusion resistance (Monteith, 1973). Methods of
predicting these parameters are all empirical, ranging from an air tem
perature weighting factor (Doorenbos and Pruitt, 1977) to resistance
functions for various plant species (e.g., American Society of Agricul
tural Engineers, 1966). Finally, the Penman method has been criticized
for its use with average daily data; the Penman equation is considered
strictly correct only instantaneously (Van Bavel, 1966).
The issue of the correct wind model to use in evaluating the heat
transport coefficient is not addressed in this research, although

126
attention is called to the fact that the radiation surface temperature
may not be the same as the effective heat transfer surface temperature.
Caution should be exercised in adapting a wind model from the litera
ture; the need for a surface temperature correction procedure for more
complex surfaces than pasture, like swamp or mountainous terrain, cannot
be ruled out.
The primary advantage in using the ATGR method is that it can ob
tain a measure of the surface moisture availability from the temperature
gradient/net radiation correlation. In fact, with an average measure of
the saturation deficit (6e_) or bulk transfer coefficient (h) and the
a
correlation parameters (A and B), both moisture availability and bulk
stomata! diffusion resistance should be calculable:
M = y B (f hA)
6ea Bs lifts
a
pc Ae (6e - Bs By)
r P a a
s Byf(6e Bs)
and
4-28,29
6-1
(Equation 6-1 was obtained by simultaneous solution of Eqs. 2-23, 4-28
and 4-29.)
The data presented in Chapter 5 make a good case in favor of using
daily average data in the Penman equation. The reason this approach
works is that the factors which affect the ET rate (h, M, s, f, and 6e )
ct
are constant enough to allow good cumulative ET estimates. The ATGR
method has an additional advantage: the process of fitting a line to the
temperature gradient/net radiation correlation minimizes the errors
caused by considering the parameters constant. With several sets of data
per day, it is likely that the ATGR method will be more accurately rep
resentative of a particular day than the Penman method, and produce bet
ter ET estimates. Usually, daily maximum and minimum temperatures and an

127
estimate of wind run are the basis for a daily ET estimate with the
Penman method. The ATGR method uses several sets of net radiation and
corresponding surface-to-air temperature gradients, in effect evaluating
surface moisture conditions. As with the Penman method, the ATGR method
estimates should improve as they are applied to longer time periods.
The principal limitation of the ATGR method is that it is not yet
dependent on remote data alone; it still requires ground-measured air
temperatures and independent estimates of two surface parameters. How
ever, air temperatures are dependent on surface temperatures, so at
least pseudoempirical methods of estimating air temperature with surface
temperatures can be developed (Idso, 1981). Soil heat flux is quite
small for areas with closed vegetation canopies and thus does not pre
sent a significant problem with regard to the accuracy of the estimate.
Potential problems with the heat transport coefficient -have been identi
fied, and it can probably be evaluated with one of the wind models in
the literature (Thom and Oliver, 1977), possibly with a preliminary sur
face temperature correction.
The ATGR approach and the approaches developed for the HCMM pro
gram suggest a tradeoff between the amount of satellite and ground data
collected and the amount of data processing required in producing ET
estimates. The simulation approaches require only one or two sets of
remote data per day, but require a lot of ground-measured data to force
and provide boundary conditions for dynamic models. They also require a
good deal of computation to match ancillary data, trial values of sur
face conditions, and model results to observed surface temperatures.
The ATGR approach requires roughly ten times as much remote data, but

128
needs only concurrent ground-measured air temperatures and the solution
of regression equations to make ET estimates.
Because of the directness and simplicity of the ATGR approach, it
is the opinion of the author that developing the combination of high
time resolution satellite data and relatively simple steady-state meth
ods for ET estimates is preferable to the combination of low time reso
lution satellite data and complex simulation methods. The major advan
tage of the steady-state approach lies in the reduced total effort in
volved in the ET estimates. The cruder surface description of the ATGR
method seems better matched to the strengths and limitations of the
satellite data source. Another practical advantage of the use of higher
time resolution satellite data is that it offers more opportunities to
acquire data under clear sky conditions, which are required in both
approaches.
Recommendations for Future Research
An estimation procedure can be no more accurate than allowed by its
weakest part. From this perspective, the most important area for future
research is development of operational methods to determine surface tem
perature and net radiation from satellite data. This development in
cludes solutions to the problems of image registration and atmospheric
absorption corrections. The ability to accurately overlay visible and
infrared data collected at different times from the same area on the
earth's surface is critical to all remote-sensing methods, as is the
ability to correct temperature and net radiation estimates for atmo
spheric effects. The success with which these "raw" data estimates can
be made under realistic operational conditions (varying levels of cloud
iness) will determine the overall potential accuracy of an estimation

129
method. The level of detail of other parts of the method does not need
to be greater than can be justified by this potential accuracy.
There are also a number of questions directly related to the ATGR
method which need to be addressed. The surface-to-air temperature gradi
ent/net radiation correlation needs to be observed over other surfaces
to determine whether the ATGR method can be applied in the same way. For
a more complex vegetation canopy, the influence of the sun to surface to
remote sensor radiation geometry needs to be investigated. If the radia
tion temperature of complex surfaces like swamp or mountains is signifi
cantly different than the effective heat transfer surface temperature, a
correcting technique will need to be developed for surface temperature
measurements.
Further research is required to determine a general method of esti
mating the bulk heat transport coefficient. The primary question to be
investigated is whether complication of obtaining average surface rough
ness and windspeed data is justified with the accuracy levels antici
pated in the raw data, or whether an "average conditions" value is ade
quate.
Making the ATGR method depend as much as possible on remote data is
another area that needs investigation. How to obtain surface-to-air tem
perature gradients from surface temperatures alone is the most impor
tant area, but the possibility of estimating the other parameters from
remote data should also be investigated.
Eventually a study must be made to determine the magnitude of er
rors introduced when average net radiation and surface temperature val
ues from nonhomogeneous pixels are used to compute ET. From the
equations it would appear that this would not be too great a problem

130
except in areas where the surface moisture in parts of the same pixel
are radically different, as in irrigated fields surrounded by very dry
areas.
Besides building the method one step at a time for more complex
estimating problems, the remote ET estimation problem might also be ap
proached by applying the ATGR method as is. The ATGR method's ET esti
mates for research watersheds can be compared to ET estimates made by
other methods. It would also be productive to examine the stationarity
and distribution of the temperature/net radiation correlation coeffi
cients, A and B. An idea of the behavior of these coefficients and the
problems associated with their calculation would help in developing op
erational data processing methods. If A and B can be legitimately con
strained to reasonable values, use of the more numerically sensitive
equations for ET might prove feasible.
Clearly there are many potential problem areas that remain to be
investigated before the general applicability of the ATGR method is
proven. The ATGR method is reasonably simple and theoretically sound,
and in this study is shown to work for a simple pasture surface. The
number of parameters needed to describe a vegetated surface has been
reduced to a minimum, and the temperature gradient model correctly de
scribes their interrelationship and relationship to remotely sensed
data. On that basis, the method can definitely be used as a framework
for further research toward a practical regional ET estimation method.

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APPENDIX A
LIST OF SYMBOLS
The following is a list of the most frequently used symbols.
A Slope of the line fit to the surface-to-air temperature
gradient/net radiation correlation
B Intercept of the line fit to the surface-to-air temperature
gradient/net radiation correlation
C Generalized coefficient of net radiation in evapotranspiration
formulae. Computed from A, B, and estimates of two parameters,
as shown in Table 4-1
Cp Specific heat of air at constant pressure
D Generalized constant term in evapotranspiration formulae. Com
puted from A, B, and estimates of two parameters, as shown in
Table 4-1
E Latent heat flux, evapotranspiration rate, or ET
Ep Cumulative ET over an estimating period
eQ Water vapor pressure at a reference level in the air above the
surface
e$ Vapor pressure at plant surfaces corresponding to the surface
temperature; not measurable
k
e$ Saturation vapor pressure at the surface temperature
f Unitless soil heat flux parameter (f = 1 G/R)
G Soil heat flux
H Sensible heat flux
h Bulk heat transport coefficient
L Latent heat of evaporation
k
M Unitless parameter for moisture availability M(e e ) =
es ea "
P Atmospheric pressure
136

137
Q_ Radiation emitted by the atmosphere
a
Qg Radiation emitted by the surface
Qr Radiation reflected by the surface
Q$ Solar radiation incident on the surface (direct and scattered)
R Net radiation absorbed by the surface (R = Qg + Qq Qr Qg)
Rp Cumulative positive net radiation over an estimating period
Rq Arbitrary maximum net radiation load
rQ Bulk resistance to heat transport of the slab of air between
the surface and a reference level
rs Bulk stomata! diffusion resistance
s Slope of the saturation vapor pressure curve (a known function of
temperature, e.g., Eq. 5-6)
T Temperature
T Air temperature at a reference level above the surface
a
T Radiation surface temperature
Tq Temperature at the hypothetical boundary between the laminar
layer next to the vegetation and the turbulent layer above.
Arbitrarily taken to be the lowest temperature measurement
(35 cm) for calculations
TST True solar time
tp Duration of positive net radiation during the estimating period
z Vertical space coordinate
B Bowen ratio
y Psychrometric constant (y = CpP/Le)
6e, Saturation deficit of the air
a
e Ratio of molecular weights of water and dry air
p Air density
a Stefan-Boltzmann constant

APPENDIX B
PROGRAM LISTING AND DEFINITION OF NAMES USED
Programs SET, MEASR, REPRT, and ANALZ are listed in the following
pages. They are written in Fortran IV and run under Hewlett-Packard's
Real Time Executive (RTE-2) operating system. Calls to RTE-2 (CALL
EXEC) were used to schedule programs, delay program execution between
program statements, make measurements, and determine the system time.
Names of subroutines, functions, data arrays, and indexes are defined
in the pages following the programs.
138

139
Program SET
PROGRAM SET(3,90)
C*****SET SCHEDULES PROGRAM MEASR FOR UNIFORM MEASUREMENT TIMING AND
C*****RUNS PROGRAMS REPRT AND ANALZ AT 12 PROFILE (HALF HOUR) INTERVALS
COMMON DUMMY (27),AST(6),AT(5,2),AE(5,2),ARAD(6,2),AWSPD,ND(8),
*NBR,NPROF, BR(2),KFLAG,NVALV,LEVEL, VMARK,RAD(6,2),DPTCOR,NADV,
*WSPD,T(10),NMEAS
DIMENSION ITIME(5),MEASR(3)
INTEGER ANALZ(3),REPRT(3)
DATA MEASR/2HME,2HAS,2HR /,
*REPRT/2HRE,2HPR,2HT /,ANALZ/2HAN,2HAL,2HZ /
IF(ISSW(2))40,1
1 LAG = 29
GO T0(2,5,30,35)KFLAG
2 NADV = 2
NMEAS = 0
D = .85
P = 29.92
DPTCOR = P/CP-D)
WRITEd, 3)
3 FORMAT!IX,"SENSOR PLUGS IN ? PUMP, DEW POINT",
*" INSTRUMENT, MIXING BOX, MAST FANS ON?")
READ(1,4)IANS
IF(IANS .EQ. 2HYE)5,1
4 FORMAT(A2)
C*****CHECK POSITION OF ROTARY VALVE
5 CALL EXEC(1,9,DATA,2,110,4045B)
VMARK = CONV(DATA)
IF(VMARK .GT. 6.)20,10
10 CALL FIND(VMARK)
C*****INITIALIZE COUNTERS AND PROFILE AVERAGES FOR COLD START
20 NVALV = -NADV
LEVEL = -NADV
VMARK = 0.0
NPROF =0
CALL ZERO (AST, ARAD, AE, AT, AWSPD, ND, BR,NBR)
DO 25 K=l,6
RAD(K,1) = 0.0
RAD(K,2) = 0.0
25 CONTINUE
WSPD = 0.0
C*****DE|_AY PROGRAM MEASR START FOR UNIFORM REPORT TIMING
CALL EXECdl,ITIME)
K = ITIME(3)*60+ITIME(2)
LAG = 150-M0D(K,150)+62
IF(LAG .GT. 150) LAG = LAG-150
30 CALL EXEC(12,MEASR,2,0,-LAG)
IF(KFLAG .LT. 3)45,40
35 CALL EXECdl,ITIME)
MIN = 2

140
IF(ITIME(3) .GT. 3) MIN = 32
CALL EXEC(12,MEASR,2,0,ITIME(4),MIN,3,0)
40 CALL EXEC(10,REPRT,1)
CALL EXEC(10,ANALZ,1)
45 KFLAG = 0
END
SUBROUTINE ZERO(AST,ARAD,AE,AT,AWSPD,ND,BR,NBR)
C*****ZERO INITIALIZES SUMMATIONS USED IN CALCULATING AVERAGES
DIMENSION AST(6),ARAD(6,2),AE(5,2),AT(5,2),ND(8),BR(2)
DO 50 1=1,2
BR(I) = 0.0
DO 50 K=l,5
AE(K.I) = 0.0
AT(K,I) = 0.0
50 CONTINUE
AWSPD = 0.0
DO 55 K=l,8
ND(K) = 0
55 CONTINUE
DO 60 K=l,6
AST(K) = 0.0
ARAD(K,1) =0.0
ARAD(K,2) = 0.0
60 CONTINUE
NBR = 0
RETURN
END
SUBROUTINE FIND(VMARK)
C*****FIND turns SELECTOR VALVE ONE PORT AND RETURNS MARK VOLTAGE
DO 65 K=l,10
CALL EXEC(1,9,DATA,2,19,4043B)
CALL EXEC(1,9,DATA,2,0,4043B)
CALL EXEC(12,0,2,0,-2)
CALL EXEC(1,9,DATA,2,110,4045B)
VMARK = CONV(DATA)
IF(VMARK .GT. 6.0)RETURN
65 CONTINUE
WRITE(6,70)
70 FORMAT(IX,"NO MARK VOLTAGE. CHECK PANEL PLUGS AND POWER TO BOX.")
STOP 0001
END
ENDS

141
Program MEASR
PROGRAM MEASR(3,90)
C*****MEASR CONTROLS AIR SAMPLE FLOW TO DEWPOINT ANALYZER, SCHEDULES
C*****AND MAKES ALL MEASUREMENTS AND PERFORMS PRELIMINARY CALCULATIONS
COMMON CST(6),CAT(5),CAE(5),CRAD(6),TSURF,HSENS,HLTNT,CWSP,R
*AST(6),AT(5,2),AE(5,2),ARAD(6,2),AWSPD,ND(8),NBR,NTOT,BR(2),
*KFLAG,NVALV,LEVEL,VMARK,RAD(6,2),DPTC0R,NADV,WSPD,T(10),
*NMEAS,DAT(26,2)
DIMENSION E(5),ITIME(5),DPT(5),
*TRAD(6),CB(7),CA(7),IPGM2(6),IWAIT(5)
INTEGER CHAN1(4),CHAN2(6),ANALZ(3)REPRT(3),SET(3)
DATA CHAN1/111,112,113,115/,CHAN2/14,101,102,100,104,109/,
*REPRT/2HRE,2HPR,2HT /,ANALZ/2HAN,2HAL,2HZ /,SET/2HSE,2HT ,2H /
DATA CA/29.40,127.88,142.04,35.4,3210.,104.5,9.37/,
*CB/0.,0.,0.,0.,59.5,0.,0./,IPGM2/3042B,3042B,3042B,3042B,
*3043B,3042B/,IWAIT/-30,-15,-14,-12,-16/
HV(T) = 597.3-.566*T
GO TO 30
25 CALL EXECU2,0,2,0,-23)
C*****VALVE POSITION CHECK(USUAL RETURN, START OF EACH MEAS. SEQUENCE)
30 IF(VMARK .GT. 6.)35,45
35 WRITE(6,40 )
40 FORMAT(IX,"VALVE POSITION NOT IN SYNC WITH PROGRAM.WILL TRY ",
*"RESTART")
KFLAG =2
GO TO 140
45 NVALV = NVALV+1
LEVEL = LEVEL+1
LEVT = LEVEL+NADV
C*****SUSPEND PROGRAM EXECUTION BETWEEN MEASUREMENTS
IF((NPROF .EQ. 0) .AND. (LEVEL .EQ. 1))55,50
50 CALL EXEC(12,0,2,0,IWAIT(LEVEL))
55 TBASE =0.0
DTEMP = 0.0
C*****MEASURE TEMPERATURE AT PROFILE BASE
AVG = FILT(108,3042B,.000002)
TBASE = CUC0N(AVG,-1)
IF((LEVT .EQ. 1) .OR. (LEVT .EQ. 6))68,60
C*****LOOP TO DETERMINE TEMPERATURE AT LEVT VIA THERMOPILES
60 NDT = LEVT-1
IF(LEVT .GT. 6) NDT = LEVT-6
DO 64 K=1,NDT
DTEMP = DTEMP+2451.* FILT(CHAN1(K),3042B,.000002)
64 CONTINUE
68 T(LEVT) = TBASE-DTEMP
C*****LOOP TO MAKE OTHER MEASUREMENTS
NMEAS = NMEAS + 1
DO 72 1=1,6
DATA = FILT(CHAN2(I),IPGM2(I),.000002)
DATA = (CA(I)*DATA+CB(I))

142
SVAL = DATA
IF(I .EQ. 1) CALL TNTCH(DATA,1,NMEAS,SVAL, DAT)
IF(I. EQ. 5) CALL TMTCH(DATA,2,NMEAS,SVAL,DAT)
DATA = SVAL
IF( I. NE. 4) GO TO 70
AVG = FILT(13,3042B,.000002)
AVG = CUC0N(AVG,-1)
DATA = DATA+.00000000008131*AVG**4
70 RAD(1,1) = RAD(1,1)+.2*DATA
RAD(1,2) = RAD(I,2)+DATA**2
72 CONTINUE
CALL EXEC(1,9,DATA,2,106,7044B)
W = CONV(DATA)
IF((W .GE. 9.375) .OR. (W .LT. 0.625)) ND(1)=ND(1)+1
IF((W .GE. 0.625) .AND. (W .LT. 1.875)) ND(5)=ND(5)+1
IF((W .GE. 1.875) .AND.
IF((W .GE. 3.125) .AND.
(W .LT. 3.125)) ND(2)=ND(2)+1
(W .LT.
IF((W .GE. 4.375) .AND. (W .LT.
4.375)) ND(6)=ND(6)+1
5.625)) ND(3)=ND(3)+1
IF((W .GE. 5.625)
IF((W .GE. 6.875)
IF((W .GE. 8.125)
(W .LT. 6.875)) ND(7)=ND(7)+l
(W
(W
.LT. 8.125)) ND(4)=ND(4)+1
.LT. 9.375)) ND(8)=ND(8)+l
CONTINUE
.AND.
.AND.
.AND.
CALL EXEC(1,9,DATA,2,105,7043B)
DATA = CONV(DATA)
WSPD = WSPD+.2*(CA(7)*DATA+CB(7))
C*****IF INITIAL (COLD START) MEASUREMENTS COMPLETE.
IF(LEVEL)25,25,74
C*****MAKE DEW POINT MEASUREMENT AND STEP VALVE TO NEXT LEVEL
74 EGG = FILT(107,4042B,.000002)
CALL EXEC(11,1 TIME)
CALL STEP(VMARK)
DPT(LEVEL) = (1508.*EGG-32.768)*DPTC0R
E(LEVEL) = 10.**((7.5*DPT(LEVEL))/(DPT(LEVEL)+237.3)+.7858)
IF (ISSW(0))76,80
76 WRITE(1,78)ITIME(4),ITIME(3),ITIME(2),VMARK,T(LEVEL),
*DPT(LEVEL),E(LEVEL),TBASE,DTEMP,T(LEVT),NVALV,LEVEL,LEVT,NDT,K
78 FORMAT(IX,12,":12,":",I2,F7.3,6F7.1,514)
C*****IF REAL TIME PROFILE COMPLETE, SAVE AVERAGES FOR PROFILE REPORT
80 IF(LEVT .NE. 5) GO TO 95
C*****aT START OF HALF HOUR, MAKE SURE THAT REPRT HAS ZEROED AVERAGES
IF((NPROF .EQ. 0) .AND. (NBR .NE. 0)) STOP 0002
85 DO 90 K=l,6
DATA = FILT(K,3042B,.000002)
AST(K) = AST(K)+CUCON(DATA,-1)
ARAD(K,1) = ARAD(K,1)+RAD(K,1)
ARAD(K,2) = ARAD(K,2)+RAD(K,2)
TRAD(K) = RAD(K,1)
RAD(K,1) = 0.0
RAD(K,2) = 0.0
90 CONTINUE
AWSPD = AWSPD+WSPD
TWSPD = WSPD
WSPD = 0.0

TEMP",5F6.1,
AW DIR = AWDIR+WDIR
WDIR = 0.0
C*****IF LAGGED DEW POINT PROFILE COMPLETE, COMPUTE BOWEN RATIO,
C*****rEP0RT PROFILE DATA, AND ADD IT TO HALF HOUR SUMS
95 IF(LEVEL .EQ. 5)100,30
100 NPROF = NPROF+1
CALL RATIO(E,T,B,C)
B = (391.7*B)/HV(TRAD(5))
CD = ABS(C)
IF(CD-.95)106,106,104
104 NBR = NBR+1
BR(1) = BR(1)+B
BR(2) = BR(2)+B**2
106 IF(ISSW(3))107,109
107 WRITE(6,108)NPR0F,TRAD(5),T(1),T(2),T(3),T(4),T(5),C,
*ITIME(4),ITIME(3), (2),
*TRAD(1),DPT(1),DPT(2),DPT(3),DPT(4),DPT(5),B,TWSPD,E(1),E(2)
*E(3),E(4),E(5)
108 F0RMAT(/,4X,"PROF#",13," RAD.T.", FT.2,"
*" R = ",F5.3,/,4X,12,":",12,":",12," NET R.",F7.2,
DPT.",5F6.1,/,4X,"B =",F5.3," W.SPD.",F7.2,
V.P.",5F6.1)
C*****TKIMMER DELAY
CALL EXEC(12,0,1,0,-32) .
GO TO 110
.109 CALL EXC2,0,1,0,-49)
C*****$UM PROFILE DATA FOR AVERAGES, ROLL DOWN ADVANCE TEMPERATURE
C*****READINGS
110 DO 115 K=l,5 .
AT (K,1) = AT(K,1)+T(K)
AT(K,2) = AT(K,2)+T(K)**2
T(K) = T(K+5)
AE (K, 1) = AE (K, 1 )+E(K)
AE(K ,2) = AE(K,2)+E(K)**2
115 CONTINUE
LEVEL = 0
IFCNVALV .EQ. 10)120,130
IF(VMARK .GT. 6.)125,35
125 NVALV = 0
VMARK =0.0
130 IF(ISSW(1))132,134
132 KFLAG = 3
GO TO 138
C*****AT END OF HALF HOUR, COMPUTE AVERAGES AND REPORT
134 IF(((ITIME(3) .GE. 0) .AND. (ITIME(3) .LT. 3)) .OR.
*((ITIME(3) .GE. 30) .AND. (ITIME(3) .LT. 33)))136,30
136 KFLAG = 4
138 NTOT = NPROF
IF(NTOT .GT. 5) NMEAS = 25
NPROF = 0
140 CALL EXEC(9,SET,1)
END
120

144
FUNCTION FILT(NCHAN,I PGM,TOL)
C*****FUNCTION FILT THROWS OUT MEASUREMENTS CONTAINING NOISE
C*****CAUSED BY ELECTRIC CATTLE FENCE CHARGER.
DIMENSION DAT(12)
DO 145 Ml=1,10
CALL EXEC(1,9,DAT(Ml),2,NCHAN,IPGM)
DAT(Ml) = C0NV(DAT(M1))
145 CONTINUE
DAT(11) = DAT(1)
DAT(12) = DAT(2)
DIF1 = ABS(DAT(1)-DAT(2))
DO 155 M2=l,10
DIF2 = ABS(DAT(M2+1)-DAT(M2+2))
IF (DIF1 .LT. TOL) .AND. (DIF2 .LT. T0L))160,150
150 DIF1 = DIF2
155 CONTINUE
160 TOT = DAT(M2)
NGD = 1
GD = DAT(M2+1)
DO 170 M3=M2,10
DIF2 = ABS(GD-DAT(M3+2))
IF(DIF2 .LT. TOL)165,170
165 TOT = TOT+GD
GD = DAT(M3+2)
NGD = NGD+1
170 CONTINUE
RGD = NGD '
RMEAS = NMEAS
DQ = RGD/RMEAS
FILT = TOT/RGD
IF(DQ .LT. .5) 175,185
175 WRITE(6,180) NCHAN
180 FORMAT!IX,"CHANNEL ",I3," IS SUSPICIOUSLY NOISY CHECK IT OUT")
185 RETURN
END
SUBROUTINE STEP(VMARK)
C*****STEP TURNS SELECTOR VALVE ONE PORT AND RETURNS MARK VOLTAGE
CALL EXEC(1,9,DATA,2,19,4043B)
CALL EXEC(1,9,DATA,2,0,4043B)
CALL EXEC(12,0,2,0,-2)
CALL EXEC(1,9,DATA,2,110,4045B)
VMARK = CONV(DATA)
RETURN
END

145
SUBROUTINE TMTCH(DATA,L,NMEAS,SVAL, DAT)
C*****TMATCH SLOWS SENSOR RESPONSE TO MATCH TEMPERATURE AND DEW
C*****POINT MEASUREMENTS BY WEIGHTED AVERAGES
DIMENSION DAT(26,2),W(25)
DATA W/.137,.119,.104,.090,.077,.067,.058,.050,.044,.038,
*.033,.028,.025,.021,.018,.016,.014,.012,.010,.009,
*.008,.007,.006,.005,.004/
IF(NMEAS .LT. 25)190,195
190 K = 26 NMEAS
DAT(K,L) = DATA
GO TO 200
195 DAT(1,L) = DATA
SVAL = 0.0
DO 200 1=25,1,-1
SVAL = SVAL + DAT(I,L)*W (I)
DAT(I+1,L) = DAT(I,L)
200 CONTINUE
RETURN
END
SUBROUTINE RATIO(E,T,B,C)
C*****ratio COMPUTES SLOPE OF T(LEVEL)VS.E(LEVEL) BY DIAGONAL REGRESSION
DIMENSION E(5),T(5),SUM(5)
DO 210 K=l,5
SUM(K) = 0.0
210 CONTINUE
DO 220 K=l,5
SUM(l) = SUM(1)+T(K)
SUM(2) = SUM(2)+E(K)
SUM(3) = SUM(3)+T(K)**2
SUM(4) = SUM(4)+E(K)**2
SUM(5) = SUM(5)+T(K)*E(K)
220 CONTINUE
ST = SUM(3)-(SUM(l)** 2)/5. .
SE = SUM(4)-(SUM(2)**2)/5.
SET = SUM(5)-(SUM(l)*SUM(2))/5.
B = (ST-SE)/(2.*SET)
IF(SET)225,230,230
225 B = B-SQRT(1.+B**2)
GO TO 235
230 B = B+SQRT(1.+B**2)
235 C = SET/SQRT(SE*ST)
RETURN
END
ENDS

146
Program REPRT
PROGRAM REPRT(3,94)
C*****REPRT COMPUTES AND REPORTS HALF HOUR AVERAGE HEAT BUDGET AND
C*****PROFILES
COMMON CST(6),CAT(5),CAE(5),CRAD(6),TSURF,HSENS,HLTNT,CWSP,
*RCOEF,AST(6),AT(5,2),AE(5,2) ,ARAD(6,2),AWSPD,ND(8),NBR,NPROF
*BR(2)
DIMENSION RH(5),NS(6),NA(6),NAM(12),NDA(8),-VCE(5),VCT(5),VCR(6)
INTEGER DTIME(3),DIR(2)
DATA NS/O,-2,-5,-10,-25,-50/,NA/225,135,85,60,35,0/,
*NAM/2H N,2H I,2H R,2H A,2H E,2H ,2HET,2HSW,2HSW,2HLW,2HLW,
*2H /,NDA/2H N,2H E,2H S,2H W,2HNE,2HSE,2HSW,2HNW/
DATA DTIME/2HDT,2HIM,2HE /
VC(SS,AVG,RN) = 100.*(SQRT(SS/RN-AVG**2))/AVG
PROF = NPROF
DO 5 K=l,6
ARAD(K,2) = ARAD(K,2)/5.
CRAD(K) = ARAD(K,D/PROF
VCR(K) = VC(ARADK,2),CRAD(K),PROF)
CST(K) = AST(K)/PROF
5 CONTINUE
HV = 597.3-.566*CRAD(5)
DO 10 K=l,5
CAE(K) = AE(K, D/PROF
VCE(K) = VC(AE(K,2),CAE(K),PROF)
CAT(K) = AT(K,1)/PR0F
VCT(K) = VC(AT(K,2),CAT(K),PROF)
RH(K) = 100.*CAE(K)/(10.**(7.5*CAT(K)/(CAT(K)+237.3)+.7858))
10 CONTINUE
CWSP = AWSPD/PROF
NDL = 1
NDE = 1
DIR(l) = 2H
DO 30 K=2 8
IF(ND(NDL) .LE. ND(K))15,30
15 IF(ND(NDL) .EQ. ND(K))20,25
20 NDE = NDL
25 NDL = K
30 CONTINUE
IF((ND(NDE) .EQ. ND(NDL)) .AND. (NDE .NE. NDL)) DIR(1)=NDA(NDE)
DIR(2) = NDA(NDL)
RNET = CRAD(l)
SFLX = CRADC6)
IF(NBR .EQ. 0)35,38
35 R = 0.0
BR = 0.0
GO TO 40
38 ABR = BR(1)/NBR
R = SQRT(BR(2)/NBR-ABR** 2)
40 CALL RATIO(CAE,CAT,BNR,RCOEF)

IF(ABS(RCOEF) .LT. .85)42,44
42 HLTNT = 0.0
HSENS = 0.0
GO TO 75
44 BNR = (391.7*BNR)/HV
HLTNT = (RNET-SFLX)/(1.+BNR)
HSENS = BNR*(RNET-SFLX)/(1.+BNR)
IF(BNR .GE. 0.0)45,60
45 IF(AT(1) .GT. AT(5))75,50
50 HLTNT = -ABS(HLTNT)
HSENS = -ABS(HSENS)
GO TO 75
60 IF(AT(1) .GT. AT(5))65,70
65 HSENS = ABS(HSENS)
HLTNT = -ABSCHLTNT)
GO TO 75
70 HSENS = -ABS(HSENS)
HLTNT = ABS(HLTNT)
75 WRITE(6,95)
ET = 600.*HLTNT/HV
CALL EXEC(9,DTIME,1)
WRITE(6,80)DIR
WRITE(6,85)RNET,SFLX,HSENS,HLTNT,CWSP,NBR,NPROF,BNR,RCOEF
80 FORMAT!/,IX,"NET RAD. SOIL H.F. SENS. H.F. LAT. H.F.",
*2A2," WINDS RSQ. >. 95 B'.R. AVG.R.",/,78("-"))
85 FORMAT(F4.2," LY/M",F6.2," LY/M",F6.2," LY/M",F6.2," LY/M",
*F7.2," M/S ",12," OF ",I2,F6.3,F7.3)
TSURF = CRAD(5)
CRAD(5) = 273.2+CRAD(5)
CRAD(5) = .98*I00000000008131*(CRAD(5)**4)
WRITE(6,100)
DO 90 K=l,5
WRITE(6,105)NAM(K),NAM(K+6),CRAD(K),VCR(K),NA(K),
*CAT(6-K),VCT(6-K),NA(K),CAE(6-K),VCE(6-K),NA(K),RH(6-K),
*NS(K),CST(K)
90 CONTINUE
WRITE(6,110)ET,NA(6),TSURF,VCR(5),ABR,R,NS(6),CST(6)
95 FORMAT(2/,22X,"BEEF RESEARCH UNIT ET PROJECT DATA",2/,2X,
*"AVERAGES AND ( PERCENT VARIATION ) FOR HALF HOUR ENDING")
100 F0RMAT(1/,4X,"RADIATION",6X,"AIR TEMP",9X,"VAP PRESS",9X,
*"REL HMDTY",3X,"SOIL TEMP",/,5X,"(LY/M)",8X,"(CM) (*C)",
*9X,"(CM) (MB)",9X,"(CM) (%)",4X,"(CM) (*C)",/,78("-"))
105 FORMAT(A2,A2,F6.3," (",F3.1,")",2(I6,F6.1," (",F3.1,")"),
*2(16,F6.D)
110 FORMAT(" ET ",F6.3," MM/HR",16,F6.1," (",F3.1,")",2X,
*" **.95+ BR =",F5.3,",+0R-",F4.3,"**",16,F6.1,1/)
DO 115 K=1,6
AST(K) = 0.0
ARAD(K,1) = 0.0
ARAD(K,2) = 0.0
115 CONTINUE
DO 120 1=1,2

148
DO 120 K=1,5
AE (K, I) = 0.0
AT(K ,1) = 0.0
120 CONTINUE
AWSPD = 0.0
DO 125 K=l,8
ND(K) = 0
125 CONTINUE
BR(1) = 0.0
BR(2) =0.0
NBR = 0
END
SUBROUTINE RATIO(E,T,B,C)
C*****RATIO COMPUTES DT/DE BY DIAGONAL REGRESSION
DIMENSION E(5),T(5),SUM(5)
DO 210 Ll=l,5
SUM(Ll) = 0.0
210 CONTINUE
DO 220 L2=l,5
SUM(1) = SUM(1)+T(L2)
SUM(2) = SUM(2)+E(L2)
SUM(3) = SUM(3)+T(L2)**2
SUM(4) = SUM(4)+E(L2)**2
SUM(5) = SUM(5)+E(L2)*T(L2)
220 CONTINUE
ST = SUM(3)-(SUM(1)**2)/5.
SE = SUM(4)-(SUM(2)**2)/5. .
SET = SUM(5)-(SUM(1)*SUM(2))/5.
B = (ST-SE)/(2.*SET)
IF(SET)225,230,230
225 B = B-SQRT(1.+B**2)
GO TO 235
230 B = B+SQRT(1.+B**2)
235 C = SET/SQRT(SE*ST)
RETURN
END
ENDS

149
Program ANALZ
PROGRAM ANALZ(3,99)
C*****ANALZ TAKES DATA COLLECTED BY SET AND COMPUTES OTHER
C*****PARAMETERS THAT MAY BE OF INTEREST
COMMON CST(6),T(5),E(5),RNET,SWI,RSW,ALW,ELW,SFLX,
*TSURF,HSENS,HLTNT,CWSP,R
DIMENSION ITIME(5),RSTM(5),RATM(5)
HV = 597.3-.566*TSURF
WRITE(6,2)
2 FORMAT(IX,"ZO",10X,"TO",6X,"DH",6X,"U*H",5X,"RCH",
*9X," EO", 6X," DE", 6X," U*E", 5X, "RCE")
RHO = .0012832-.00000389*T(3)
DO 5 I=L,3
ZO = I
CALL PR0FT(T,T0,Z0,DH,BH,RH)
UH = HSENS/C.24*RH0*.4*BH*100.)
CALL PROFT(E,EO,ZO,DE,BE,RE)
UE = HLTNT*1013./(RH0*.622*HV*.4*BH*100.)
WRITE(6,4) ZO,TO,DH,UH,RH,EO,DE,UE,RE
4 FORMAT(F3.0,1X,2(F12.1,2F8.1,F8.3))
5 CONTINUE
IF((RH .LT. -.95) .AND. (TSURF .GT. T(l)))10,15
10 SVP = 10,**((7.5*TSURF)/(TSURF+237.3)+.7858)
DO 12 1=1,5
RHO = .0012832-.00000389*((TSURF+T(I))/2.)
RTOT = 100 .*.622*RH0*HV*(SVP-E(I))/(1013.* HLTNT) '
RATM(I) = 100.*.240*RH0*(TSURF-T(I))/HSENS
RSTM(I) = RTOT- RATM(I)
12 CONTINUE
WRITE(6,14)(RATMCI),RSTM(I), 1=1
14 FORMATS," RAIR,RSTM(S/M) ", 5(F6.3, ", ", F5.3))
15 CALL EXECdl,ITIME)
D = ITIME(5)
TST = ITIME(4)+.25
IF(ITIME(3) .LT. 10)TST = TST-.5
c*****tva REPORT, APPENDIX B
YA = .017 2028* CD-I.)
SYA = SIN(YA)
CYA = COS(YA)
S2Y = SIN(2.*YA)
C2Y = C0S(2.*YA)
SIG = 4.885784+D+.03342*SYA-.001388*CYA+.000348*S2Y-.000028*C2Y
SIND = .3978686*SIN(SIG)
EOT = .004289*CYA-.12357*SYA-.153809*S2Y-.060783*C2Y
C*****TVA REPORT 5.5
EST = TST+.48467-EOT
COST = COS(.2618*(TST-12.))
SIND = SIN(.40928*(COS(.017214*(172.-D))))
COSD = SQRT(1.-SIND**2)
SINA = .49606*SIND+.86794*C0SD*C0ST

150
COSA = SQRT(1.-SINA**2)
ZNGL = 90.-57.2958*ATAN(SINA/COSA)
HRNGL = 15.*(TST-12.)
c*****TVA REPORT 2.24
OAM = 1./(SINA+.15*(93.885ZNGL)**(-1.253))
C*****TVA REPORT 2.4
AESR = l.+.017*C0S(.01721*(186.D))
SWIO = (2.*SINA)/(AESR**2)
ATC = (SWI/SWIO)**SINA
ABDO = RSW/SWI
WRITE(6,20)
20 FORMAT!/," ABDO SWIO OAM ATC ZNGL HRNGL EOT "
*" E.S.T. T.S.T. DAY")
WRITE(630 )ABDO,SWIO,OAM, ATC,ZNGL, HRNGL, EOT, EST,TST, ITIME(5)
30 F0RMAT(F4.2,1X,3F7.2,2F9.1,F8.4,2F8.2,I8)
END
SUBROUTINE PR0FT(V,V0,Z0,DV,BV,RV)
C*****PR0FT FITS TEMPERATURE AND VAPOR PRESSURE PROFILES BY LINEAR
REGRESSION. DISPLACEMENT HEIGHTS CHOSEN BY BEST REGRESSION FIT.
DIMENSION SUM(5),V(5),X(5),Z(5)
DATA Z/35.,60.,85.,135.,225./
RP = 5.0
ROLD = 0.0
RK = 0.0
DO 135 J = 2,22,4
BSTEP = J
GO TO 105
100 RK = RK+1.0
105 D = BSTEP RK
IF(D)140,140,108
108 DO 110 L2 = 1,5
SUM(L2) = 0.0
110 CONTINUE
DO 120 L3 = 1,5
IF(Z(L3) .LE. D)118,116
116 X(L3) = ALOG((Z(L3)-D+ZO)/ZO)
SUM(l) = SUM(1)+V(L3)
SUM(2) = SUM(2)+V(L3)**2
SUM(3) = SUM(3)+X(L3)
SUM(4) = SUM(4)+X(L3)**2
SUM(5) = SUM(5)+V(L3)*X(L3)
GO TO 120
118 RP = RP-1
120 CONTINUE
B = (RP*SUM(5)-SUM(1)*SUM(3))/(RP*SUM(4)-SUM(3)**2)
A = (SUM(1)-B*SUM(3))/RP
SDZ = SQRT(SUM(4)-(SUM(3)**2)/RP)
SDV = SQRT(SUM(2)-(SUM(l)**2)/RP)
RCOEF = B*(SDZ/SDV)
IF(ISSW(5))121,123
121 WRITE(6,122)ZO,D,A,B,RCOEF
122 FORMAT(IX,5F12.5)

151
123 IF(ABS(RCOEF)-ROLD)130,130,125
125 ROLD = ABS(RCOEF)
VO = A
DV = D
BV = ABS(B)
RV = RCOEF
IF(RK )135,135,100
130 ROLD = ABS(RCOEF)
IF(RK )100,100,140
135 CONTINUE
140 RETURN
END
ENDS

152
Definition of Names
Subroutines and Functions
CUC0N(V0LTS,-1) Hewlett-Packard library function which converts volt
age from a copper-constantan thermocouple with ice point
reference temperature into degrees Centrigrade
FILT(NCHAN,IPGM,TOL) Function used to filter fence charger voltage
spikes out of low level signals. Argument requires chan
nel number (NCHAN), voltmeter program word (IPGM), and
noise tolerance (TOL).
FIND(VMARK) Subroutine used in Program SET to position air sampling
valve for first vapor pressure measurement. It returns
mark voltage to SET.
HV(T) Function that calculates heat of vaporization as a func
tion of temperature.
PR0FT(V,V0,Z0,DV,BV,RV) Subroutine in Program ANALZ which fits 5-level
profile (V) and calculates displacement height (DV) given
roughness height (ZO). Other arguments: VO is V at Z=0,
BV is the slope of the profile, and RV is the correlation
coefficient.
.RATIO(E,T,B,C) Subroutine in Programs MEASR and REPRT which computes
Bowen ratio (B) with diagonal regression of vapor pressure
(E) and temperature (T) profiles. Also returns correlation
coefficient (C).
STEP(VMARK) Subroutine used in Program MEASR to change position of
sampling valve and return mark voltage from air sampling
valve.
TMTCH(DATA,L,NMEAS,SVAL,DAT) Subroutine which imposes a 4 min time
constant on surface temperature and net radiation measure
ments by calculating a weighted average of past 25 mea
surements. The last measurement (DATA) and sensor identi
fication (L) are sent to the subroutine, and it returns a
"slowed" value (SVAL) to the main program. In order that
measurements made in the preceding half hour survive the
program swapping that takes place during the half-hour re
porting sequence (see Chapter 3), they are placed in
COMMON via DAT(25,2). When the system is started, NMEAS is
used to monitor the past data array to see if it has been
fi1led--after NMEAS=25 weighted averages are reported.
ZERO(AST,ARAD,AE,AT,AWSPD,ND,BR,NBR) Subroutine in Program SET that
initializes all surrmations used in calculating half-hour
averages.

153
Main Data Arrays
E(5)*
ND(8)
DPT(5)
RAD(1,1)*
RAD(2,1)
RAD(3,1)
RAD(4,1)
RAD(5,1)
RAD(6,1)
ST (6)
T(10 )*
WSP
Air vapor pressure for 5 levels (mb)
Number of occurrences per wind direction octant: ND(1), N;
ND(2), E; ND(3), S; ND(4), W; ND(5), NE; ND(6), SE; ND(7),
SW; ND(8), NW
Dewpoint temperature for 5 levels (C)
Net radiation (ly/min)
Solar shortwave radiation (ly/min)
Reflected shortwave radiation (ly/min)
Atmospheric longwave radiation (ly/min)
Emitted longwave radiation (ly/min)
Soil heat flux (ly/min)
Soil temperature for 6 levels (C)
Air temperature for 5 levels (C). Completed temperature
profiles are stored in T(6) through T(10) until corre
sponding vapor pressure profile is completely measured.
Prefixed versions of this array (see below) have only 5
values.
Windspeed (m/s)
These array names may be prefixed by A, C, or T. Measurements are
first loaded into the nonprefixed array. Arrays that are prefixed by T
are "temporary" and'hold values used in the intermediate data reports.
Half-hour "average" values are summed in arrays prefixed with A, and
these values are stored for analysis in the following half hour in
"common" arrays prefixed with a C. The A-prefixed version of the
asterisked arrays has a second column for squared measurements, like
RAD does. These statistics are used to compute percent variations for
the half-hour report.
Other Names and Indexes
ABDO
ABR
ATC
AVG
B
BR(2)
C
Albedo
Average of Bowen ratios with greater than .95 correlation
coefficient
Atmospheric transmission coefficient
Filtered average voltage of reference thermocouple at
level 1 on profile measurement mast
Bowen ratio returned by RATIO
Bowen ratio statistics summations
Correlation coefficient returned by RATIO

154
CA (7)
CB(7)
D
DAT(12)
DAT(25,2)
DATA
DPTCOR
DTEMP
EGG
EOT
GD
.HLTNT
HRNGL
HSENS
HV(T)
IPGM2(6)
ISSW(N)
ISSW(O)
ISSW(l)
ISSW(2)
ISSW(3)
ISSW(5)
ITIME(5)
Sensor calibration factor-slope for the 6 sensors in
RAD(6,2) and the windspeed sensor
Sensor calibration factor-intercept for the 6 sensors in
RAD(6,2) and the windspeed sensor
Pressure correction for dewpoint measurement (in Hg)
Array of sensor readings checked for voltage spikes in FILT
Array of last 25 surface temperature and net radiation
readings in TMTCH
Temporary name for measurements returned by voltmeter
Pressure correction for dewpoint temperature reading
Temperature difference calculated from the vapor pressure
profile (m/min)
Voltage from EG&G Dewpoint Analyzer
Equation of time (hrs)
Number of good measurements made by FILT
Latent; heat flux (ly/min) '
Hour angle of the sun (degrees)
Sensible heat flux (ly/min)
A function that calculates heat of vaporization as a
function of temperature
Voltmeter program word for the 6 measurements in RAD(6,2).
Each is coded for type of measurement, delay time, and
range of measurement
Sense switch number N on face of HP-2100 Minicomputer:
When on, causes Program MEASR to print the time, all
measurements and indexes for each measurement cycle
When on, causes MEASR to produce full half-hour report
with all data collected since last half-hour report
When on, causes MEASR to stop at end of next half-hour
report
When on, causes MEASR to print data from each set of
profiles collected
When on, causes Program ANALZ to print complete profile
fitting search
Time: ITIME(5), Day of year; ITIME(4), hour; ITIME(3),
minute; ITIME(2), second; ITIME(1), centisecond

155
IWAIT(5)
LAG
LEVEL
LEVT
KFLAG
NADV
NBR
NCHAN
NDA(8)
NDE
NDL
NGD
NMEAS
NPROF
NTOT
NVALV
OAM
P
Delay between measurements: IWAIT(l) is delay between
levels 5 and 1, IWAIT(2) delay between levels 1 and 2,
IWAIK3) delay between levels 2 and 3, etc.
Delay time (in seconds) used to schedule MEASR when
ISSW(l) is on.
Level at which dewpoint is currently being measured
Level at which temperature is currently being measured
Flags for program SET:
0 default value
1 to prepare system for "cold" start
2 to recover when sampling valve is out of sync with
program
3 to run REPRT and ANALZ immediately, restart MEASR
after a delay when ISSW(l) is on
4 to run REPRT and ANALZ immediately, and schedule MEASR
for absolute start time at beginning of half-hour per
iod. Usual half-hour transition KFLAG
Number of levels temperature is measured in advance of
vapor pressure to compensate for air sample travel time
Number of Bowen ratios with greater than .95 correlation
coefficient
Channel number to be measured by FILT
Array containing letter abbreviations for wind direction
octants: NDA(l), N; NDA(2), E; NDA(3), S; NDA(4), W;
NDA(5), NE; NDA(6), SE; NDA(7), SW; NDA(8), NW
Wind direction octant with greatest number of occurrences
Wind direction octant with number of occurrences less than
or equal to NDE
Number of bad (noisy) measurements made by FILT
Number of measurements in subroutine TMTCH data array.
When 25 or over, TMTCH returns weighted averages.
Chronological number of profile being collected, starting
at beginning of half-hour period
Name used to save NPROF in COMMON
Current scanning valve position (ranges from 1 through 10)
Optical air mass (unitless)
Atmospheric pressure (in Hg)

156
PROF
R
RATM
RCOEF
RH(5)
RHO
RNET
RSTM
RTOT
SFLX
SUM(5)
SVAL
.SWIO
TBASE
TOT
TST
TSURF
UH
UE
VCE(5)
VCR(6)
VCT (5)
VMARK
W
ZO
ZNGL
Number of profiles collected in last half-hour period
(floating point NPROF)
Average correlation coefficient of profiles collected in
last half hour
Atmospheric diffusion resistance (s/m)
Correlation coefficient of half-hour average profiles
Relative humidity for 5 levels (%)
3
Air density (g/cm )
Half-hour average net radiation (ly/min)
Bulk stomatal diffusion resistance (s/m)
Total resistance to vapor pressure transport (s/m)
Half-hour average soil heat flux (ly/min)
Regression summations in RATIO and PROFT
Weighted average returned by subroutine TMTCH
Intensity of solar shortwave radiationwithout atmosphere
Air temperature at lowest level (1) on profile measurement mast
Used to sum good readings in subroutine FILT
True solar time
Half-hour average surface temperature (C)
Friction velocity calculated from the temperature profile
(m/min)
Friction velocity calculated from the vapor pressure pro
file (m/min)
Variation coefficient for vapor pressure at 5 levels (%)
Variation coefficient for readings in RAD (%)
Variation coefficient for temperature at 5 levels (%)
Mark voltage from scanning valve (0 or 12 volts)
Voltage from wind direction sensor (between 0-10 volts)
Roughness height (cm)
Zenith angle of the sun (degrees)

157
APPENDIX C
SUMMARY OF ENERGY BUDGET DATA
This appendix contains most of the energy budget data collected in
the spring and fall of 1981. The table below is a catalog of the data.
It should be noted that different radiation thermometers were used
in spring and fall (see Table 2-2), and that only the fall surface
temperatures have been cross-calibrated to the air temperatures (1.5C
was added to surface temperature measurements). Subroutine TMTCH, which
imposed a 4 min time constant on the radiation sensors, was in use only
in the fall. Windspeed was measured 7 m over the pasture surface in
both measuring periods.
The number at the far right on the data tables is the correlation
coefficient for the temperature and vapor pressure gradients for each
half hour period. On some occasions correlation coefficients greater
than 1 are reported; these are for time periods when gradients were
very small, causing numerical problems in computing the coefficient.
Spring 1981
Fall 1981
Day
Date
No. of
Day
Date
No. of
Periods
Periods
139
May 19
. 20
279
Oct 6
14
140
20
14
280
7
16
141
21
23
285
12
18
142
22
24
286
13
21
143
23
24
287
14
21
145
25
19
288
15
21
147
27
8
289
16
16
148
28
18
290
17
21
149
29
23
291
18
20
150
30
21
293
20
21
151
31
22
294
21
21
152
Jun 1
17
295
22
21
153
2
21
296
23
21
155
4
11
301
28
16
160
9
11
302
29
20
161
10
21
303
30
20
162
11
11
304
31
20
305
Nov 1
21
306
2
20
307
3
20
308
4
19
309
5
19
310
6
19
311
7
19
312
8
19

158
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
139
900
0.30
0.03
_
0.00
22.5
30.9
33.3
.513
930
0.37
0.03
0.08
0.26
3.48
26.1
32.8
34.1
.983
1000
0.30
0.04
0.08
0.19
3.91
26.9
32.7
32.1
.979
1030
0.47
0.04
0.11
0.31
4.09
27.4
35.8
32.9
.986
1100
0.44
0.05
0.13
0.25
5.12
27.9
36.2
32.4
.990
1130
0.51
0.06
0.12
0.34
5.62
27.8
36.7
32.4
.986
1200
0.54
0.06
0.14
0.34
4.82
28.1
38.2
32.2
.999
1230
0.55
0.08
0.12
0.36
4.26
29.1
39.6
31.6
.991
1300
0.50
0.06
0.10
0.34
4.68
29.5
38.2
29.4
.969
1330
0.93
0.12
0.23
0.58
5.10
30.9
45.4
29.2
.998
1400
0.67
0.10
0.17
0.40
5.86
31.1
42.0
27.9
.984
1430
0.84
0.12
0.23
0.48
6.59
31.8
44.4
25.2
.985
1500
0.69
0.10
0.17
0.41
6.62
31.8
42.7
19.8
.987
1530
0.62
0.09
0.17
0.39
5.64
31.9
42.1
20.1
.985
1600
0.52
0.08
0.13
0.30
5.79
31.7
40.2
20.2
.978
1630
0.35
0.05
0.08
0.22
6.25
31.1
36.3
19.9
.963
1700
0.29
0.04
0.08
0.17
5.51
30.9
35.2
22.2
.953
1730
0.18
0.03
0.03
0.12
5.68
30.0
32.2
25.3
.977
1800
0.12
0.02
0.02
0.08
5.38
28.9
30.4
26.9
.950
1830
0.06
0.01
.

4.78
28.2-
28.8-
26.4 -
.787
140
1130
0.45
0.07
0.14
0.24
6.37
29.5
_ _
31.5
.994
1200
0.77
0.09
0.21
0.48
5.41
30.1

31.1
.999
1230
0.75
0.11
0.23
0.41
6.75
31.1
22.6
29.4
.996
1300
0.65
0.09
0.21
0.36
6.65
30.7
39.7
28.6
.992
1330
0.50
0.07
0.14
0.29
6.47
30.6
38.0
28.0
.990
1400
0.56
0.07
0.15
0.33
5.60
30.5
38.4
29.2
.983
1430
0.68
0.09
0.21
0.38
6.96
30.8
40.3
29.7
.989
1500
0.59
0.09
0.19
0.31
6.70
30.9
38.9
29.9
.998
1530
0.73
0.09
0.24
0.40
7.59
30.9
39.6
28.4
.990
1600
0.63
0.09
0.20
0.34
7.30
30.9
39.0
29.3
.993
1630
0.55
0.08
0.20
0.28
7.56
30.6
37.8
27.8
.996
1700
0.43
0.06
0.14
0.23
6.45
30.1
35.8
28.1
.984
1730
0.37
0.05
0.11
0.21
6.42
29.8
34.5
27.5
.989
1800
0.28
0.03
0.10
0.15
6.33
29.2
32.2
27.1
.975
141
800
0.06
-0.01
3.87
15.8
17.8
21.6
-.714
830
0.15
-0.00
0.03
0.12
4.03
16.4
19.9
21.3
.990
900
0.17
-0.00
0.06
0.12
4.37
16.7
21.2
20.9
.994
930
0.31
0.01
0.12
0.18
4.13
17.4
25.1
20.7
.997
1000
0.40
0.01
0.18
0.20
3.71
17.4
27.1
20.4
.996
1030
0.52
0.03
0.24
0.26
3.61
18.6
30.9
20.6
.998
1100
0.55
0.03
0.25
0.27
3.91
18.9
31.7
20.3
.999
1130
0.56
0.04
0.24
0.28
3.24
19.8
34.5
20.4
.998
1200
0.70
0.05
0.28
0.37
3.28
20.8
37.1
20.5
.997
1230
0.82
0.08
0.31
0.44
3.14
22.1
40.8
20.7
.997

159
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
141
1300
0.86
0.09
0.31
0.46
3.82
23.3
41.8
20.4
.998
1330
0.83
0.09
0.30
0.44
3.74
23.8
41.5
19.7
.999
1400
0.86
0.09
0.30
0.46
4.18
24.4
41.9
19.5
.998
1430
0.85
0.09
0.31
0.45
4.25
25.2
42.1
19.7
.998
1500
0.80
0.09
0.28
0.43
3.53
25.4
41.8
19.1
.999
1530
0.76
0.09
0.27
0.41
4.17
25.8
41.4
19.8
.999
1600
0.69
0.07
0.23
0.38
4.54
25.8
40.1
18.9
998
1630
0.60
0.06
0.22
0.32
3.88
25.9
39.2
18.4
.998
1700
0.49
0.04
0.18
0.27
4.65
25.9
36.4
19.0
.997
1730
0.41
0.03
0.14
0.24
4.27
25.4
34.2
18.7
.996
1800
0.31
0.02
0.11
0.18
4.60
25.3
31.3
18.5
.995
1830
0.20
0.02
0.07
0.12
4.76
24.8
28.8
18.4
.994
1900
0.10
0.01
0.02
0.07
4.12
24.0
26.5
18.6
.987
142
730
0.03
-0.02
-
...
-0.00
7.1
10.1
.740
800
0.09
-0.01

--
0.47
10.5
14.5

.913
830
0.20
0.00


1.08
13.8
19.3
--
.706
900
0.30
0.01

2.04
16.6
23.8

-.458
930
0.38
0.02

--
1.52
19.7
28.9

.845
1000
0.47
0.03

.
2.33
21.8
32.6

-.762
1030
0.56
0.05
0.19
0.32
2.63
23.2
36.0
16.5
.948
1100
0.63
0.06
0.24
0.33
3.03
23.9
38.1
15.9
.996
1130
0.70
0.07
0.23
0.39
3.04
24.6
39.5
14.3
.997
1200
0.73
0.09
0.26
0.38
2.99
25.4
40.8
14.2
.991
1230
0.76
0.08
0.29
0.38
3.15
25.5
41.1
14.2
.997
1300
0.84
0.11
0.30
0.44
4.13
26.5
42.4
14.4
.992
1330
0.85
0.11
0.29
0.44
3.28
26.9
43.2
14.2
.996
1400
0.83
0.12
0.27
0.45
3.29
27.4
43.5
14.9
.994
1430
0.82
0.11
0.28
0.43
3.50
27.8
43.1
14.7
.996
1500
0.78
0.11
0.27
0.41
3.37
28.4
42.6
13.9
.991
1530
0.73
0.10
0.23
0.40
2.94
28.6
42.4
13.7
.992
1600
0.67
0.09
0.22
0.35
3.48
29.0
41.2
14.2
.987
1630
0.59
0.08
0.19
0.32
3.62
29.0
39.9
14.1
.988
1700
0.50
0.06
0.17
0.28
4.25
28.7
38.1
14.1
.989
1730
0.41
0.05
0.13
0.23
3.63
28.5
36.7
14.2
.985
1800
0.30
0.03
0.09
0.19
4.28
28.2
33.2
14.5
.981
1830
0.20
0.03
0.05
0.12
4.17
27.7
30.4
14.5
.964
1900
0.09
0.01
--

3.51
26.9
27.7
14.0
-.618
143
730
0.04
-0.02
-0.00
9.3
11.2
..
.896
800
0.11
-0.00

--
-0.00
12.3
15.8
--
.854
830
0.18
0.01
0.17
0.00
-0.00
16.8
21.2
--
.949
900
0.28
0.02
--
0.44
20.8
26.8

-.128
930
0.35
0.03

--
2.35
23.1
29.8
.848
1000
0.49
0.04
0.21
0.24
3.64
23.9
32.9
23.1
.975
1030
0.59
0.06
0.23
0.30
2.98
24.9
36.6
22.3
.976

160
Day
Time
Net
Soi 1
. Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
143
1100
0.66
0.07
0.26
0.32
2.79
25.7
38.3
20.9
.985
1130
0.65
0.08
0.26
0.32
2.47
26.0
38.7
20.7
.977
1200
0.59
0.08
0.18
0.33
2.16
26.4
38.5
20.6
.992
1230
0.82
0.11
0.28
0.44
2.41
27.2
41.8
19.9
.983
1300
0.90
0.13
0.25
0.52
1.80
28.3
43.7
18.7
.946
1330
0.92
0.14
0.30
0.48
1.95
28.8
44.3
19.6
.990
1400
0.65
0.11
0.25
0.29
2.62
28.9
40.8
19.0
.962
1430
0.43
0.06
0.15
0.22
2.91
28.4
36.6
18.8
.934
1500
0.87
0.11
0.34
0.43
2.42
29.6
43.4
18.3
.967
1530
0.77
0.11
0.29
0.38
2.51
30.1
42.7
17.5
.980
1600
0.39
0.07
0.12
0.21
2.19
29.4
37.8
16.2
.991
1630
0.21
0.04
0.05
0.13
1.65
29.0
34.1
16.9
.916
1700
0.26
0.04


1.42
29.1
33.9
17.9
.680
1730
0.29
0.05


2.11
29.5
34.8
18.6
.899
1800
0.20
0.03
.

0.77
29.2
32.9
18.7
.669
1830
0.10
0.02


0.79
28.4
29.7
19.3
.307
1900
0.06
0.02


0.66
27.9
27.9
20.5
-.939
145
800
0.31
0.03
0.10
0.18
3.13
25.1
28.1
28.3
.989
830
0.36
0.03
0.12
0.21
3.85
25.7
31.8-
27.3
.967
900
0.50
0.05
0.16
0.30
3.67
26.5
35.6
26.9
.980
930
0.62
0.06
0.21
0.35
3.42
27.4
37.6
24.8
.982
1000
0.64
0.07
0.21
0.37
3.19
28.1
38.9
25.5
.977
1030
0.77
0.09
0.21
0.47
2.68
29.2
41.7
25.6
.995
1100
0.62
0.10
0.16
0.36
2.33
29.6
40.2
26.1
.975
1130
0.83
0.10
0.21
0.52
2.84
30.1
42.4
24.1
.975
1200
0.92
0.13
0.27
0.52
2.98
30.8
44.3
22.9
.991
1230
0.61
0.11
0.17
0.33
3.15
30.8
40.6
22.7
.984
1300
0.84
0.12
0.27
0.46
3.41
31.3
42.9
22.8
.970
1330
0.85
0.12
0.26
0.47
2.36
31.7
43.6
22.8
.975
1400
0.50
0.08
0.14
0.29
2.23
31.2
39.1
22.0
.960
1430
0.62
0.09
0.19
0.33
3.02
31.6
40.6
22.8
.981
1500
0.42
0.05
0.10
0.26
3.59
30.8
36.8
23.8
.987
1530
0.32
0.05
0.07
0.21
3.02
31.0
35.3
23.9
.975
1600
0.40
0.05
0.10
0.25
3.34
31.9
36.8
22.9
.953
1630
0.26
0.03
0.10
0.15
3.59
31.6
34.5
22.4
.940
1700
0.20
0.03


3.56
31.4
33.1
22.1
.785
147
830
0.53
0.03
0.09
0.40
2.78
25.3
28.1
36.4
.949
900
0.58
0.04
0.11
0.44
3.12
26.2
30.1
37.2
.968
930
0.60
0.04
0.11
0.44
3.25
27.1
32.1
37.2
.987
1000
0.66
0.05
0.13
0.48
3.26
28.3
34.2
37.7
.991
1030
0.71
0.05
0.14
0.52
4.48
28.8
34.8
37.9
.997
1100
0.53
0.06
0.13
0.34
4.05
27.9
34.8
38.3
.942
1130
0.44
0.08


4.70
24.2
37.0
37.8
.913
1200
0.32
0.07
--
4.99
25.8
36.2
36.3
.819

161
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
FI ux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
148
930
0.62
0.04
0.14
0.43
2.05
27.0
35.4
31.8
.988
1000
0.69
0.05
0.16
0.48
2.35
27.8
36.7
31.3
.990
1030
0.65
0.04
0.15
0.46
2.97
28.1
36.1
30.8
.996
1100
0.82
0.06
0.18
0.57
2.89
28.9
38.6
29.8
.994
1130
0.72
0.07
0.15
0.50
2.97
28.8
37.6
28.2
.996
1200
0.76
0.08
0.16
0.52
2.84
29.4
38.4
27.0
.997
1230
0.66
0.07
0.13
0.46
2.42
29.7
37.7
26.8
.993
1300
0.79
0.08
0.16
0.55
2.95
30.0
38.6
26.1
.991
1330
0.84
0.10
0.19
0.56
2.99
30.4
39.4
26.0
.992
1400
0.86
0.10
0.19
0.57
2.72
31.1
39.9
25.9
.991
1430
0.71
0.09
0.15
0.47
2.89
30.8
38.2
26.1
.994
1500
0.68
0.08
0.15
0.45
2.83
30.8
37.6
26.2
.994
1530
0.44
0.06
0.09
0.29
2.20
30.5
34.9
25.7
.979
1600
0.39
0.05
0.08
0.27
2.24
30.5
34.3
26.5
.984
1630
0.29
0.03
0.05
0.20
1.78
30.2
32.9
26.3
.950
1700
0.22
0.03

--
1.51
30.2
31.6
25.5
.811
1730
0.10
0.02

--
1.01
29.6
28.7
25.3
-.938
1800
0.03
0.01

0.83
29.0
26.3
25.1
-.998
149
630
0.10
0.01
.
...
0.71 .
20.9
22.6

-.418
700
0.17
0.01

--
1.27
21.8
23.3

-.526
730
0.29
0.02

--
1.48
23.5
25.3

.713
800
0.39
0.02
0.06
0.31
1.38
24.8
28.8
30.8
.975
830
0.48
0.03
0.10
0.35
1.21
26.5
33.3
29.6
.984
900
0.57
0.05
0.12
0.41
1.13
27.7
35.6
28.2
.976
930
0.65
0.05
0.15
0.45
1.71
28.5
36.9
26.1
.991
1000
0.73
0.06
0.17
0.50
2.29
29.3
37.9
24.4
.995
1030
0.66
0.07
0.15
0.44
2.46
29.5
37.1
24.2
.994
1100
0.84
0.09
0.17
0.58
1.85
30.3
39.6
22.1
.983
1130
0.79
0.09
0.17
0.54
2.40
30.5
39.0
22.5
.990
1200
0.72
0.10
0.16
0.46
2.82
30.8
38.2
22.8
.992
1230
0.76
0.09
0.15
0.51
2.21
30.9
38.5
22.9
.993
1300
0.85
0.11
0.20
0.54
2.25
31.7
40.1
22.8
.986
1330
0.75
0.10
0.16
0.49
1.96
31.5
39.1
23.2
.990
1400
0.73
0.11
0.15
0.48
1.55
32.2
39.4
23.2
.971
1430
0.66
0.08
0.14
0.44
2.44
31.8
37.9
23.6
.988
1500
0.59
0.07
0.12
0.39
2.41
31.9
37.0
23.9
.985
1530
0.50
0.06
0.10
0.34
2.66
31.8
35.8
23.3
.986
1600
0.40
0.06
0.06
0.28
1.66
32.2
35.3
22.9
.951
1630
0.25
0.03
0.04
0.18
2.00
31.5
33.0
22.9
.925
1700
0.15
0.03

--
1.05
31.2
31.5
23.0
-.317
1730
0.08
0.02
--
--
1.06
30.7
29.3
24.2
-.965

162
Day
Time
Net
Soi 1
. Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
150
800
0.37
0.03
0.08
0.26
0.58
25.7
32.3
34.6
.947
830
0.44
0.04
0.09
0.31
0.68
27.1
34.6
35.0
.966
900
0.54
0.05
0.09
0.39
0.72
28.7
36.1
33.6
.968
930
0.63
0.06

--
0.42
29.8
37.4
30.4
.889
1000
0.70
0.07
0.11
0.52
0.53
30.6
38.5
28.1
.940
1030
0.77
0.08
0.14
0.55
0.97
31.4
39.5
28.4
.967
1100
0.68
0.08
0.13
0.47
1.20
31.3
38.7
27.4
.989
1130
0.80
0.10
0.15
0.64
1.88
32.3
40.6
27.2
.988
1200
0.90
0.12
0.15
0.63
1.04
32.7
41.4
25.7
.989
1230
0.87
0.12
0.15
0.60
1.87
33.3
40.9
24.8
.941
1300
0.85
0.12
0.16
0.57
1.23
33.3
41.1
24.3
.978
1330
0.84
0.12
0.15
0.56
1.44
34.1
41.1
24.0
.957
1400
0.71
0.10
0.13
0.48
1.71
33.8
39.4
25.1
.979
1430
0.69
0.09
0.12
0.48
2.01
33.8
39.0
25.1
.986
1500
0.26
0.05
-
--
1.42
33.2
33.7
24.4
.691
1530
0.32
0.06

--
1.31
33.5
34.4
25.1
.719
1600
0.39
0.06

0.79
33.8
35.1
25.0
.212
1630
0.28
0.04


2.26
33.8
33.7
26.0
.739
1700
0.18
0.03

--
1.71
33.3
32.3
26.3
-.383
1730
0.10
0.03
--
1.37
33.1
30.7 -
26.3 -
-.837
1800
0.03
0.02
-0.00
0.02.
0.91
32.3
28.3
27.5
-.992
151
730
0.27
0.03
_
1.25
25.1
28.6
36.0
.796
800
0.36
0.03


1.01
26.5
31.7
35.8
.908
830
0.46
0.04
0.10
0.32
1.35
27.9
34.0
36.1
.936
900
0.56
0.05
0.11
0.39
1.55
29.0
35.7
36.5
.970
930
0.64
0.07
0.12
0.45
1.68
29.9
36.9
35.3
.982
1000
0.71
0.08
0.14
0.50
1.45
30.9
38.4
35.2
.962
1030
0.77
0.09
0.14
0.53
1.40
31.9
39.7
34.2
.959
1100
0.78
0.09
0.18
0.51
1.39
32.4
40.0
33.9
.967
1130
0.82
0.10
0.19
0.52
1.70
33.2
40.5
32.7
.966
1200
0.67
0.11
0.15
0.42
1.55
33.2
39.4
33.1
.971
1230
0.59
0.08
0.13
0.38
2.10
33.1
37.5
34.0
.943
1300
0.61
0.09
0.11
0.41
2.35
33.5
38.2
33.2
.962
1330
0.49
0.07
0.09
0.32
2.46
33.5
36.4
31.4
.953
1400
0.45
0.07
0.07
0.31
2.03
33.7
36.0
31.0
.900
1430
0.37
0.06
0.08
0.24
2.27
33.5
35.3
32.2
.912
1500
0.49
0.06

--
1.74
33.9
36.4
32.8
.842
1530
0.56
0.08
0.15
0.34
2.89
34.5
37.4
33.7
.949
1600
0.45
0.07
0.13
0.26
2.37
34.4
36.1
33.9
.943
1630
0.28
0.04
0.07
0.16
2.81
33.8
34.1
34.2
.940
1700
0.15
0.03
--
--
2.27
33.2
32.5
34.1
.574
1730
0.11
0.03

--
2.24
32.9
31.6
32.4
.602
1800
0.03
0.01
--
--
2.91
31.9
29.4
28.5
-.925

163
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
152
730
0.30
0.02

-
0.06
24.4
29.7
.884
800
0.40
0.03


0.56
26.4
32.9

.828
830
0.46
0.04
0.11
0.31
1.73
27.5
33.9
37.1
.965
900
0.57
0.05
0.14
0.38
1.55
28.0
35.5
37.1
.974
930
0.66
0.07
0.15
0.43
1.84
29.1
36.9
36.5
.979
1000
0.72
0.08
0.17
0.48
1.64
29.7
38.2
36.0
.979
1030
0.75
0.08
0.17
0.50
2.07
30.5
39.0
35.9
.992
1100
0.60
0.09
0.11
0.41
1.08
31.0
37.9
35.4
.955
1130
0.70
0.08
0.14
0.47
1.14
31.3
38.5
34.9
.968
1200
0.81
0.11
0.16
0.53
1.55
32.4
40.7
34.0
.989
1230
0.71
0.10
0.13
0.48
1.63
32.9
39.5
34.0
.975
1300
0.60
0.09
0.12
0.39
1.38
33.0
38.5
33.7
.978
1330
0.65
0.09
0.13
0.44
1.61
33.5
38.7
34.1
.948
1400
0.47
0.09
0.10
0.28
1.50
33.5
37.3
34.4
.974
1430
0.10
-0.02


3.46
28.4
25.7
37.9
.536
1500
0.16
-0.05

--
4.54
24.0
22.5
36.0
-.897
1530
0.10
-0.01
-0.02
0.14
3.02
23.7
23.0
36.8
-.955
153
700
0.22
0.01

1.41
23.7
24.4
.007
730
0.31
0.02
--
2.14 .
25.0
25.6
.
.824
800
0.42
0.03

--
2.05
26.1
27.5

.919
830
0.53
0.04
0.10
0.39
2.20
27.2
30.0
41.0
.959
900
0.61
0.05
0.12
0.44
2.62
27.8
31.9
41.0
.984
930
0.63
0.05
0.12
0.46
2.73
28.4
32.7
40.7
.975
1000
0.76
0.05
0.14
0.57
2.61
29.1
34.4
40.3
.981
1030
0.81
0.06
0.15
0.60
2.84
29.8
35.5
39.0
.989
1100
0.89
0.07
0.16
0.67
2.77
30.6
36.8
38.2
.984
1130
0.89
0.07
0.16
0.65
2.81
30.8
37.2
37.4
.986
1200
0.91
0.09
0.16
0.66
2.37
31.5
38.0
36.1
.988
1230
0.91
0.09
0.20
0.62
2.85
31.9
37.9
36.2
.980
1300
0.88
0.07
0.24
0.57
3.10
32.3
37.8
36.3
.987
1330
0.86
0.07
0.22
0.57
2.92
32.8
37.7
35.9
.980
1400
0.79
0.06
0.20
0.53
3.10
33.1
37.0
36.0
.977
1430
0.72
0.06
0.18
0.49
2.76
33.7
36.5
36.1
.969
1500
0.58
0.04
0.16
0.38
3.03
33.5
35.0
37.0
.943
1530
0.47
0.03
--

2.60
33.5
34.1
38.8
.917
1600
0.26
0.02
--
--
2.20
33.1
32.1
39.4
.742
1630
0.04
0.00
--

1.44
31.9
28.4
39.4
-.821
1700
0.04
0.00
--

0.93
31.4
28.0
40.6
-.900

164
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
155
930
0.90
0.07
0.19
0.63
3.73
30.6
37.0
40.1
.987
1000
0.77
0.06
0.18
0.53
3.12
30.5
36.6
40.1
.990
1030
0.79
0.07
0.16
0.56
4.12
31.0
36.4
39.8
.987
1100
0.89
0.09
0.16
0.63
3.50
31.5
37.7
40.0
.983
1130
0.92
0.10
0.16
0.66
4.00
32.0
38.2
38.9
.979
1200
0.96
0.12
0.18
0.66
4.05
32.6
39.1
38.3
.992
1230
1.00
0.14
0.16
0.70
3.39
33.2
39.8
38.7
.982
1300
0.88
0.13
0.16
0.60
2.33
33.5
38.7
38.1
.950
1330
0.88
0.12
0.15
0.61
2.43
33.9
38.6
37.7
.970
1400
0.81
0.11
0.17
0.53
2.34
34.2
38.0
38.4
.956
1430
0.72
0.10
0.18
0.44
2.28
34.3
37.1
39.9
.964
160
800
0.45
0.04

_ _
3.78
29.1
30.0
_ _
-.190
830
0.52
0.05
0.19
0.28
4.34
29.7
31.2
31.3
.957
900
0.53
0.05
0.16
0.32
3.96
30.5
32.2
30.5
.972
930
0.57
0.05
0.17
0.35
3.58
31.0
32.7
29.4
.967
1000
0.54
0.05
0.15
0.34
3.89
31.4
32.8
28.8
.992
1030
0.82
0.06
0.21
0.54
3.18
29.9
34.3
26.3
.985
1100
0.70
0.08
0.16
0.46
3.11
31.2
34.5
29.4
.994
1130
1.00
0.12
0.26
0.61
4.88
32.3-
36.7.
30.1
.985
1200
0.97
0.14
0.27
0.56
5.53
32.7
36.6
29.9
.981
1230
0.85
0.15
0.27
0.43
5.13
33.3
36.0
30.6
.991
1300
0.53
0.09
--

4.73
32.9
33.3
31.9
.925
161
730
0.36
0.03
--
_ -
3.33
28.5
28.8
...
.117
800
0.42
0.04

--
4.09
29.1
30.1

-.263
830
0.47
0.04
0.14
0.29
4.42
29.7
31.0
30.7
.967
900
0.37
0.03
0.09
0.24
3.70
29.9
30.9
29.9
.985
930
0.73
0.06
0.20
0.47
4.36
31.1
33.7
28.9
.982
1000
0.65
0.06
0.15
0.43
3.95
31.2
33.3
28.9
.980
1030
0.62
0.07
0.15
0.40
4.46
31.4
33.5
28.3
.995
1100
0.90
0.10
0.21
0.59
4.49
32.3
36.2
29.0
.983
1130
0.69
0.10
0.14
0.46
4.21
32.8
34.8
28.0
.985
1200
0.50
0.08
0.09
0.33
4.95
32.4
33.1
27.7
.982
1230
0.90
0.13
0.17
0.60
5.82
33.7
36.4
26.4
.984
1300
0.89
0.14
0.19
0.56
5.50
34.7
36.8
26.4
.988
1330
0.62
0.10
0.12
0.40
5.41
34.0
34.4
25.6
.991
1400
0.75
0.11
0.13
0.51
5.31
34.4
35.4
25.3
.983
1430
0.70
0.11
0.14
0.45
5.59
34.7
35.3
25.2
.990
1500
0.50
0.08
0.10
0.32
5.43
34.3
33.6
25.0
.985
1530
0.55
0.07
0.07
0.40
5.11
34.1
33.4
25.9
.966
1600
0.31
0.05
0.07
0.19
5.57
33.4
31.6
25.6
.991
1630
0.23
0.03
0.05
0.16
3.57
30.2
29.9
25.8
.971
1700
0.11
0.02


2.23
29.2
28.8
26.3
.133
1730
0.03
0.01
--
--
2.58
28.2
26.5
25.6
-.886

165
Time
Net
Soil
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
730
0.41
0.04
_ -
...
3.45
28.7
30.5
_
-.651
800
0.54
0.05
--
--
3.21
29.8
31.6
--
-.270
830
0.51
0.05
0.17
0.29
2.72
30.2
32.1
32.2
.992
900
0.56
0.05
0.17
0.34
3.22
31.0
32.9
30.8
.965
930
0.63
0.06
0.15
0.42
2.74
31.6
34.0
29.1
.977
1000
0.58
0.06
0.11
0.42
2.49
31.8
33.9
27.8
.982
1030
0.91
0.09
0.17
0.65
2.54
33.0
36.9
26.7
.974
1100
0.80
0.10
0.15
0.56
2.73
33.2
36.5
25.8
.987
1130
0.89
0.11
0.16
0.61
2.49
34.0
37.5
25.4
.981
1200
0.74
0.11
0.14
0.49
2.33
34.1
36.5
25.3
.989
1230
0.46
0.08
0.07
0.30
2.84
33.9
33.7
25.8
.966

166
Day
Time
Net
Soil
. Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
279
1030
0.65
0.03
0.19
0.42
1.12
25.8
35.0
18.5
.985
1100
0.70
0.04
0.22
0.45
1.58
26.2
37.5
18.4
.997
1130
0.77
0.04
0.24
0.49
1.97
26.9
39.6
18.1
.998
1200
0.81
0.05
0.26
0.50
2.10
27.4
40.6
17.9
.998
1230
0.83
0.05
0.27
0.52
1.96
27.7
41.1
18.0
.997
1300
0.78
0.05
0.23
0.51
1.60
27.9
40.4
18.0
.993
1330
0.73
0.04
0.21
0.48
2.32
28.3
40.0
17.5
.993
1400
0.66
0.04
0.19
0.44
2.02
28.7
38.8
16.9
.984
1430
0.58
0.03
0.14
0.41
1.47
28.9
37.8
17.1
.973
1500
0.49
0.03
0.11
0.35
1.64
29.1
36.1
17.5
.966
1530
0.39
0.03
0.06
0.31
1.10
28.9
34.5
17.0
.937
1600
0.28
0.02


1.33
29.4
32.7
16.9
.873
1630
0.16
0.02

--
1.01
29.4
30.6
17.1
-.373
1700
0.04
0.01
-0.01
0.04
0.95
28.9
27.6
17.0
-.974
280
700
0.03
-0.00
__
. -
0.06
17.8
17.3
_ _
.766
1000
0.55
0.03
0.19
0.33
3.16
26.1
33.9
23.6
.996
1030
0.63
0.03
0.24
0.36
3.37
26.9
35.7
23.2
.993
1100
0.70
0.04
0.23
0.43
2.89
27.6 -
38.6
23.3
.996
1130
0.69
0.04
0.21
0.44
3.22
28.1-
38.8.
22.8 .
. 997
1200
0.77
0.04
0.23
0.49
2.99
28.8
40.9
22.2
.996
1230
0.60
0.04
0.15
0.40
2.55
29.1
38.6
21.9
.996
1300
0.65
0.04
0.18
0.44
2.81
29.5
39.8
21.1
.997
1330
0.68
0.04
0.18
0.46
2.72
29.9
39.9
21.0
.998
1400
0.48
0.03
0.09
0.35
1.80
29.8
37.1
20.9
.988
1430
0.41
0.03
0.08
0.30
2.70
30.2
36.3
21.0
.994
1500
0.34
0.03
0.04
0.27
1.96
29.9
34.9
21.6
.974
1530
0.37
0.03
0.05
0.29
2.43
29.8
34.8
21.7
.975
1600
0.28
0.03
0.03
0.22
2.19
30.0
33.9
21.8
.936
1630
0.12
0.02


2.22
29.7
31.2
21.7
-.919
1700
0.01
0.01
-0.00
0.01
0.65
28.5
28.0
22.3
-.996
285
830
0.30
-0.01
0.11
0.19
3.55
18.8
....
18.4
.989
900
0.38
-0.00
0.16
0.22
4.30
19.8
30.1
18.4
.996
930
0.47
0.00
0.22
0.25
3.93
20.9
26.2
18.7
.996
1000
0.57
0.01
0.25
0.30
4.23
22.1
28.6
18.6
.996
1030
0.64
0.01
0.30
0.33
3.57
22.5
30.2
18.9
.999
1100
0.55
0.01
0.24
0.30
3.93
22.5
29.7
18.8
.996
1130
0.73
0.02
0.32
0.40
3.95
23.3
33.0
18.4
.998
1200
0.81
0.02
0.35
0.43
4.02
23.8
34.6
18.3
.998
1230
0.61
0.01
0.25
0.34
4.00
23.6
32.8
17.8
.997
1300
0.61
0.01
0.24
0.36
3.53
23.6
32.0
17.0
.996
1330
0.62
0.01
0.25
0.36
3.69
24.1
32.8
16.9
.999
1400
0.55
0.01
0.22
0.32
4.07
23.9
31.8
16.6
.995
1430
0.58
0.01
0.24
0.33
3.72
23.7
31.6
16.4
.996
1500
0.42
0.00
0.18
0.24
4.06
23.5
29.5
16.4
.994

167
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
285
1530
0.35
-0.00
0.15
0.20
4.58
23.1
27.9
16.2
.993
1600
0.27
-0.01
0.11
0.17
3.88
22.8
26.7
15.8
.990
1630
0.12
-0.01
0.04
0.09
3.82
22.2
24.4
15.8
.987
1700
0.03
-0.01


3.74
21.2
22.3
16.2
.787
286
730
0.05
-0.02
- _
2.63
14.8
15.2
.029
800
0.16
-0.01
0.04
0.12
3.29
16.1
17.0
16.0
.982
830
0.27
-0.01
0.10
0.18
4.83
17.5
19.2
16.6
.994
900
0.35
-0.00
0.16
0.19
6.03
18.3
21.0
16.7
.996
930
0.40
-0.00
0.19
0.20
5.51
19.0
22.6
16.7
.999
1000
0.53
0.01
0.28
. 0.25
5.03
19.8
25.8
16.6
.996
1030
0.45
0.00
0.24
0.21
5.37
19.8
25.0
16.1
.998
1100
0.38
0.00
0.20
0.18
4.70
19.6
24.4
15.9
.998
1130
0.37
0.00
0.19
0.17
4.54
19.5
24.5
15.7
.997
1200
0.42
0.00
0.22
0.20
4.20
19.7
25.8
15.6
.997
1230
0.64
0.01
0.34
0.29
5.36
20.4
28.8
15.8
.998
1300
0.70
0.01
0.39
0.30
4.95
20.7
30.8
15.8
.999
1330
0.74
0.01
0.41
0.32
4.92
21.2
31.4
15.8
.998
1400
0.54
0.01
0.29
0.24
4.28
21.2
29.3
15.8-
.998
1430
0.52
0.01
0.28
0.23
4.91
21.1
28.5
15.7.
.997
1500
0.32
0.00
0.17
0.15
5.02
20.7
25.6
15.6
.996
1530
0.21
-0.00
0.10
0.11
4.34
20.1
23.8
15.5
.995
1600
0.19
-0.00
0.10
0.09
4.70
19.8
23.3
15.6
1.000
1630
0.08
-0.00
0.04
0.05
3.97
19.2
21.5
15.6
.999
1700
0.02
-0.01
0.01
0.02
3.95
18.5
20.0
15.3
.994
1730
0.02
-0.01
0.01
0.02
3.65
18.0
19.5
15.3
.992
287
730
0.06
-0.01
0.01
0.06
2.45
16.0
16.8
18.3
.956
800
0.16
-0.00
0.05
0.11
2.66
17.5
18.8
19.4
.998
830
0.26
0.00
0.10
0.16
3.32
19.3
21.4
20.7
.993
900
0.26
0.01
0.11
0.15
3.85
20.7
23.1
21.6
.996
930
0.31
0.01
0.14
0.16
3.96
21.4
25.0
21.9
.996
1000
0.29
0.01
0.11
0.16
4.07
.22.1
25.5
21.9
.997
1030
0.47
0.02
0.21
0.24
4.77
22.5
27.2
22.2
.999
1100
0.70
0.02
0.30
0.38
4.13
22.8
31.8
22.9
.999
1130
0.41
0.01
0.17
0.22
4.78
22.9
28.2
21.8
1.000
1200
0.55
0.02
0.23
0.31
4.20
24.0
30.9
21.5
.997
1230
0.37
0.01
0.13
0.23
4.84
22.8
26.9
22.0
.997
1300
0.72
0.02
0.37
0.34
5.28
23.8
33.0
22.1
.999
1330
0.35
0.01
0.16
0.18
5.09
22.3
26.9
22.0
.998
1400
0.27
0.01
0.10
0.16
4.50
22.2
26.4
21.7
.995
1430
0.18
0.01
0.05
0.13
3.42
21.4
24.2
21.9
.987
1500
0.23
0.01
0.09
0.13
4.53
22.6
26.3
21.3
.998
1530
0.37
0.01
0.18
0.17
5.48
22.9
27.5
20.8
.996

168
Day
Time
Net
Soi 1
. Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
FI ux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
287
1600
0.22
0.01
0.12
0.10
5.88
22.3
25.6
20.3
.994
1630
0.11
0.00
0.05
0.05
4.87
21.0
23.2
20.0
.995
1700
0.06
-0.00
0.03
0.03
4.23
20.3
22.3
19.9
.993
1730
0.01
-0.00
0.01
0.01
4.09
19.6
21.2
19.6
1.000
288
700
0.02
-0.02
_ -
2.05
13.2
13.5
17.0
.937
730
0.09
-0.01
--

2.87
14.1
15.0
18.0
.502
800
0.17
-0.01

3.02
15.3
16.6
18.5
.824
830
0.26
-0.00
0.06
0.21
3.03
17.2
18.9
18.8
.991
900
0.37
0.00
0.13
0.23
2.85
18.8
21.8
19.5
.997
930
0.47
0.01
0.21
0.25
3.33
20.2
25.0
19.7
.997
1000
0.55
0.02
0.27
0.26
3.11
21.6
28.5
20.0
.998
1030
0.63
0.02
0.32
0.29
3.71
22.7
31.0
20.1
.999
1100
0.67
0.02
0.36
0.29
3.44
23.2
33.5
20.1
.999
1130
0.55
0.02
0.27
0.26
3.09
23.5
32.5
20.1
.999
1200
0.75
0.03
0.36
0.36
3.14
24.4
36.0
20.0
.998
1230
0.54
0.03
0.25
0.27
2.74
24.2
33.6
19.6
.997
1300
0.65
0.03
0.31
0.31
2.90
24.7
35.0
19.4
.996
1330
0.43
0.03
0.19
0.22
2.88
24.6
31.8
19.7
.996
1400
0.51
0.02
0.21
0.27
3.36
24.9-
32.4.
18.7-
.997
1430
0.41
0.02
0.15
0.24
3.28
24.8
31.2
17.7
.992
1500
0.39
0.02
0.14
0.23
3.30
25.0
30.5
16.8
.991
1530
0.35
0.02
0.13
0.21
2.93
25.0
30.2
16.1
.989
1600
0.25
0.01
0.08
0.16
2.76
24.8
28.4
16.0
.987
1630
0.12
0.01


2.89
24.3
26.0
15.7
.906
1700
0.02
0.00
--

2.24
23.7
23.8
15.6
-.915
289
730
0.06
-0.02
_ _
0.31
11.8
11.7
-.789
800
0.16
-0.01

--
1.65
14.2
14.8
--
-.508
830
0.26
0.00


1.26
16.3
17.9

-.670
900
0.36
0.01
--
--
1.52
18.9
21.8
--
-.917
930
0.45
0.01
--
--
2.43
20.9
25.7

-.353
1200
0.69
0.04
0.29
0.36
1.84
25.6
36.6
13.2
.996
1230
0.69
0.04
0.28
0.36
1.06
25.8
36.7
13.2
.999
1300
0.67
0.04
0.26
0.37
1.45
26.3
36.8
13.0
.996
1330
0.64
0.04
0.24
0.35
1.33
26.8
36.4
12.9
.993
1400
0.58
0.04
0.24
0.31
1.45
27.3
35.6
13.2
.994
1430
0.51
0.03
0.20
0.28
1.66
27.5
34.6
13.5
.991
1500
0.42
0.03
0.18
0.22
0.92
27.5
32.9
13.6
.977
1530
0.33
' 0.02
0.13
0.18
0.91
27.7
31.5
13.9
.932
1600
0.23
0.02
--
1.13
27.5
29.6
13.8
.895
1630
0.11
0.02
--

0.40
27.3
27.2
13.7
-.149
1700
0.02
0.01
-0.01
0.01
0.99
26.5
24.4
14.2
-.975

169
Day
Time
Net
Soil
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
290
700
0.01
-0.02

0.00
10.7
9.3
_ _
.937
730
0.07
-0.01

--
0.00
12.5
12.3
--
.150
800
0.15
-0.00

--
0.00
15.3
15.6
--
-.523
830
0.24
0.01


0.35
18.3
19.7

-.826
900
0.34
0.02


1.65
21.9
23.9

-.569
930
0.43
0.02


2.65
23.6
27.5

.595
1000
0.51
0.03
0.24
0.25
2.20
24.6
30.4
13.7
.997
1030
0.58
0.04
0.25
0.29
1.26
25.5
33.0
14.4
.997
1100
0.64
0.04
0.28
0.31
2.25
26.3
35.1
14.5
.998
1130
0.67
0.04
0.32
0.31
2.42
26.5
36.0
15.3
.998
1200
0.69
0.05
0.34
0.30
1.79
27.0
37.4
16.1
.997
1230
0.69
0.05
0.34
0.30
1.56
27.4
37.7
16.3
.997
1300
0.67
0.05
0.34
0.28
1.48
27.7
37.5
16.3
.994
1330
0.63
0.05
0.31
0.27
1.12
28.2
36.9
16.5
.988
1400
0.58
0.04
0.30
0.24
1.66
28.4
36.2
16.5
.990
1430
0.51
0.04
0.23
0.25
1.53
28.6
35.1
16.5
.992
1500
0.43
0.03
0.20
0.20
1.28
28.7
34.0
16.6
.973
1530
0.32
0.03
0.12
0.18
0.70
28.7
32.4
16.6
.956
1600
0.21
0.03
0.04
0.14
1.17
28.6
30.4
16.8
.923
1630
0.11
0.02

-- -
0.59
28.1
28.4
17.0
.457
1700
0.02
0.01
--
0.01
0.79
27.5
26.0
17.2
-.980
291
700
0.02
-0.01
0.00
13.7
13.5
__ _
1.084
730
0.04
-0.00

--
0.00
15.6
15.7

.950
800
0.06
0.00


0.06
17.4
17.5

.699
830
0.20
0.01

--
1.77
19.2
20.5
--
-.759
900
0.31
0.02
--
--
2.95
21.7
24.0

-.877
930
0.43
0.03
--

3.02
24.3
28.3
--
.078
1000
0.52
0.03

--
4.09
25.7
30.7

.602
1030
0.59
0.03
0.28
0.27
3.55
26.8
33.2
19.3
.998
1100
0.62
0.04
0.28
0.30
3.88
27.8
34.9
19.5
.998
1130
0.44
0.03
0.16
0.24
4.11
27.6
32.3
19.3
.997
1200
0.68
0.04
0.27
0.38
4.79
28.7
36.9
18.8
.997
1230
0.50
0.04
0.18
0.28
4.05
28.6
34.5
18.0
.997
1300
0.46
0.04
0.16
0.26
3.81
28.7
34.5
18.8
.999
1330
0.63
0.04
0.24
0.36
4.88
29.1
35.9
18.6
.996
1400
0.49
0.04
0.19
0.26
4.33
29.2
34.8
18.6
.999
1430
0.48
0.03
0.21
0.24
4.72
29.3
34.5
18.7
.992
1500
0.41
0.03
0.18
0.19
4.62
29.4
33.8
18.8
.998
1530
0.29
0.03
0.12
0.15
4.21
28.5
31.1
18.8
.989
1600
0.20
0.02
0.07
0.11
4.62
28.2
29.9
19.1
.995
1630
0.11
0.02
0.02
0.07
3.99
27.6
28.3
19.5
.955
1700
0.02
0.01
""
3.33
26.7
26.2
19.9
-.877

170
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
293
700
0.02
-0.04
- _
1.10
6.0
3.8
.919
730
0.11
-0.02


2.42
9.6
9.6

.808
800
0.17
-0.01


2.36
11.5
11.7

-.767
830
0.27
-0.00


2.76
14.0
15.6

-.557
900
0.37
0.01
0.22
0.13
2.60
16.8
20.6
10.3
.999
930
0.45
0.02
0.28
0.16
3.06
19.2
24.9
11.2
.999
1000
0.53
0.03
0.30
0.20
3.59
21.3
27.9
12.2
1.000
1030
0.59
0.03
0.31
0.25
3.69
22.5
30.2
12.9
.997
1100
0.65
0.04
0.33
0.28
4.45
23.5
31.9
12.9
.998
1130
0.70
0.04
0.39
0.27
5.38
24.0
32.9
12.8
.998
1200
0.45
0.03
0.22
0.20
4.61
23.9
30.6
13.0
.998
1230
0.37
0.03
0.15
0.19
4.68
23.8
28.4
13.0
.997
1300
0.51
0.03
0.24
0.24
4.99
24.6
31.1
13.3
.999
1330
0.63
0.04
0.29
0.31
3.75
25.3
33.5
13.0
.994
1400
0.48
0.03
0.24
0.21
4.43
25.2
31.8
12.9
.995
1430
0.43
0.02
0.19
0.22
5.33
24.8
29.4
13.4
.995
1500
0.15
0.02
0.04
0.09
4.91
23.8
25.6
13.7
.996
1530
0.24
0.02
0.09
0.14
5.23
24.3
26.9
13.6
.993
1600
0.15
0.01
0.03
0.11
4.22
23.8
25.1
13.6
.941
1630
0.08
0,01
--

3.59,
23.3
24.0 .
13.9
.916
1700
0.02
0.01
--

4,20
22.8
22.8
13.8
-.861
294
700
-0.01
-0.02
_ _
1.31
12.1
10.5
_ __
.855
730
0.08
-0.01

--
1.67
13.4
14.0

-.415
800
0.11
-0.00

--
1.42
14.8
15.9

-.704
830
0.29
0.01

--
2.00
17.2
19.4

-.769
900
0.35
0.01


2.53
19.5
22.6

-.796
930
0.44
0.02


2.52
21.9
26.9
19.6
-.168
1000
0.52
0.03
0.24
0.25
2.82
23.8
30.1
17.3
.995
1030
0.58
0.03
0.28
0.27
3.79
24.9
32.2
17.3
.999
1100
0.55
0.03
0.24
0.27
4.28
25.8
32.5
16.7
.999
1130
0.55
0.03
0.23
0.29
4.29
26.3
33.3
16.2
.999
1200
0.57
0.04
0.26
0.28
4.60
26.4
34.5
16.2
.999
1230
0.50
0.03
0.22
0.26
4.40
26.3
32.9
16.5
.999
1300
0.51
0.03
0.20
0.27
4.71
26.7
33.2
17.1
.998
1330
0.51
0.03
0.21
0.26
4.64
27.1
33.3
17.5
.999
1400
0.30
0.03
0.10
0.18
3.95
26.8
30.8
17.4
.995
1430
0.47
0.03
0.17
0.27
4.57
27.2
32.3
17.4
.992
1500
0.32
0.03
0.12
0.18
4.97
27.1
30.6
17.3
.995
1530
0.32
0.02
0.12
0.18
5.11
27.1
30.3
17.4
.993
1600
0.27
0.02
0.09
0.16
4.99
27.1
29.7
17.4
.991
1630
0.10
0.02
0.02
0.06
4.43
26.1
26.8
17.3
.961
1700
0.01
0.01
0.00
0.00
3.99
25.1
24.8
17.2
-.970

171
Day
Time
Net
Soil
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
295
700
0.02
-0.00
....
0.50
17.7
16.9
_ _
.893
730
0.08
0.00


1.19
18.8
19.7

-.016
800
0.17
0.01

--
2.03
20.3
21.4
--
-.469
830
0.17
0.01


1.54
21.7
22.5
--
-.684
900
0.16
0.01


1.45
22.8
23.6

.226
930
0.28
0.02
0.07
0.19
1.87
24.2
26.5
22.8
.984
1000
0.46
0.03
0.17
0.27
2.37
25.8
30.6
22.3
.992
1030
0.55
0.03
0.25
0.28
3.24
26.8
33.4
21.2
.997
1100
0.51
0.03
0.23
0.25
2.65
27.1
34.3
20.8
.998
1130
0.23
0.02
0.07
0.14
2.13
26.7
29.7
20.4
.991
1200
0.74
0.04
0.31
0.38
2.79
28.0
38.3
20.2
.997
1230
0.67
0.04
0.29
0.34
3.17
28.4
38.6
20.3
.998
1300
0.71
0.04
0.30
0.36
3.63
28.7
38.9
19.8
.997
1330
0.65
0.04
0.26
0.35
3.00
29.1
38.4
19.1
.996
1400
0.57
0.04
0.23
0.30
3.50
29.0
36.6
19.4
.996
1430
0.54
0.03
0.22
0.29
3.38
29.2
36.4
19.4
.995
1500
0.45
0.03
0.18
0.24
4.08
29.1
34.8
18.7
.993
1530
0.33
0.02
0.13
0.18
3.89
28.9
32.7
18.1
.993
1600
0.23
0.02
0.06
0.14
3.51
28.7 '
31.0
18.1
.978
1630
0.11
0.02
0.02
0.08
4.01
27.9'
28.6-
17.9
.913
1700
0.02
0.01
-0.00
0.00
3.00
27.2
26.4
17.9
-.969
296
700
0.01
-0.02
...
- -
0.00
14.1
13.1
~
.890
730
0.05
-0.01

--
0.00
15.1
15.2
--
-.034
800
0.13
0.00
--

0.51
17.5
18.3

-.691
830
0.24
0.01


0.26
19.4
21.6

-.844
900
0.34
0.02


0.26
21.2
25.3
-.946
930
0.43
0.03


0.83
23.9
29.3
...
-.610
1000
0.51
0.03
0.22
0.26
1.28
25.7
32.0
21.7
.953
1030
0.56
0.04
0.24
0.29
1.07
26.9
34.8
20.6
.994
1100
0.63
0.04
0.26
0.32
1.06
27.8
36.4
20.2
.990
1130
0.48
0.04
0.18
0.27
0.87
28.3
35.4
19.4
.993
1200
0.65
0.04
0.23
0.38
1.31
28.9
38.2
18.7
.994
1230
0.75
0.05
0.28
0.42
0.84
29.5
40.7
18.2
.996
1300
0.55
0.04
0.19
0.32
2.27
29.6
37.8
17.0
.996
1330
0.72
0.05
0.27
0.40
1.95
30.4
40.7
16.9
.998
1400
0.62
0.04
0.22
0.35
2.61
30.6
39.5
16.9
.997
1430
0.30
0.03
0.07
0.20
1.11
29.5
34.0
17.6
.991
1500
0.21
0.03
0.03
0.15
1.17
29.0
31.8
17.4
.976
1530
0.17
0.03
0.01
0.13
1.27
29.1
31.1
17.5
.947
1600
0.19
0.03
0.02
0.15
1.39
29.1
31.1
18.1
.924
1630
0.06
0.02
-0.01
0.04
1.42
28.5
28.4
18.0
-.979
1700
0.00
0.01
-0.01
0.02
0.15
27.4
16.1
19.4
-.998

172
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
301
900
0.19
-0.01
0.08
0.11
1.87
16.8
19.1
14.6
.999
930
0.25
0.00
0.11
0.14
2.11
17.7
20.9
14.8
.997
1000
0.29
0.00
0.14
0.15
1.82
18.8
22.9
15.1
.996
1030
0.37
0.01
0.18
0.18
1.58
20.2
25.5
15.8
.994
1100
0.51
0.02
0.25
0.24
1.88
21.9
28.6
16.8
.995
1130
0.61
0.02
0.33
0.26
1.95
23.2
32.3
18.2
.998
1200
0.67
0.03
0.34
0.30
1.66
24.2
34.7
19.7
.996
1230
0.67
0.03
0.35
0.29
2.24
24.6
34.6
19.7
.997
1300
0.67
0.03
0.34
0.30
2.23
25.3
35.1
20.2
.997
1330
0.60
0.02
0.30
0.28
1.89
25.3
34.3
19.9
.996
1400
0.56
0.02
0.28
0.26
2.23
25.7
33.9
19.8
.996
1430
0.48
0.01
0.24
0.23
2.25
25.9
33.0
19.8
.994
1500
0.40
0.01
0.19
0.20
1.72
25.9
31.7
19.6
.987
1530
0.30
0.01
0.14
0.15
2.03
26.1
30.3
19.8
.986
1600
0.19
0.01
0.08
0.11
2.22
25.8
28.4
19.8
.976
1630
0.09
0.00
0.02
0.06
2.01
25.3
26.3
20.0
.947
1700
-0.01
-0.00
-0.00
0.01
1.32
24.6
23.8
19.9
-.890
302
730
0.05
-0.01
_
1.99
16.1
16.7
_ _
.024
800
0.06
-0.01

1 .'89.
16.6
17.4.
-- .
-.921
830
0.18
-0.00

--
2.35
17.8
19.5
--
-.704
900
0.20
0.00
--
--
2.59
18.6
20.3
--
-.682
930
0.25
0.01
--
--
2.32
19.8
21.9
--
-.898
1000
0.31
0.01
--
--
2.47
21.2
24.0

-.868
1030
0.49
0.02
--
--
3.09
22.9
28.2

-.607
1100
0.48
0.02
--

3.47
24.2
29.9

.897
1130
0.33
0.02
0.15
0.17
3.30
24.4
28.4
21.3
.991
1200
0.47
0.02
0.22
0.23
3.41
25.1
30.9
21.6
.997
1230
0.67
0.03
0.32
0.31
3.52
26.0
35.3
21.4
.998
1300
0.67
0.03
0.32
0.32
3.64
26.8
35.7
21.1
.996
1330
0.42
0.02
0.19
0.22
3.70
26.6
32.2
20.6
.995
1400
0.23
0.01
0.09
0.13
3.69
26.2
29.3
20.4
.997
1430
0.22
0.01
0.07
0.14
3.50
26.0
28.6
20.3
.991
1500
0.18
0.01
0.06
0.12
3.33
26.1
28.5
20.3
.992
1530
0.19
0.01
0.07
0.11
4.44
25.8
28.1
20.5
.998
1600
0.08
0.00
0.03
0.05
4.75
24.9
26.0
20.7
.991
1630
0.10
0.00
0.03
0.07
4.58
24.7
25.8
20.3
.964
1700
-0.01
-0.00
-- '
--
4.85
23.8
23.8
20.1
-.898
303
730
0.02
-0.00
0.01
0.02
4.78
20.4
20.9
21.8
.995
800
0.02
-0.00
0.01
0.01
4.36
20.4
21.0
22.0
1.029
830
0.04
-0.00

--
3.62
20.6
21.4
22.3
-.749
900
0.09
0.00
0.04
0.04
4.41
21.0
22.2
22.6
1.009
930
0.11
0.00
0.06
0.05
4.03
21.3
23.0
22.8
.971
1000
0.10
0.00
0.06
0.04
3.94
21.4
23.0
22.9
.991
1030
0.20
0.01
0.11
0.09
4.29
22.1
24.6
23.2
.988
1100
0.29
0.01
--
--
4.64
22.9
26.4
23.4
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Day Time Net Soil Sens Lat Wind Air Surf Vap Prof
Rad Heat Heat Heat Temp Temp Pres Corr
Flux Flux Flux

174
Day
Time
Net
Soil
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
FI ux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
305
1400
0.25
0.00
0.13
0.02
5.14
20.9
22.9
22.4
.992
1430
0.14
-0.00
0.07
0.07
5.44
20.5
21.8
22.2
.978
1500
0.11
-0.00
0.05
0.06
5.49
19.8
20.6
22.3
.981
1530
0.12
-0.00
0.04
0.08
4.62
19.3
20.4
22.5
.994
1600
0.12
-0.00
0.04
0.09
5.12
19.2
20.3
22.2
.994
1630
0.07
-0.01
0.03
0.05
4.40
19.0
19.9
22.2
.978
1700
0.04
-0.01
0.01
0.03
3.69
19.0
19.7
22.0
.993
1730
0.01
-0.01
0.00
0.02
3.43
18.7
19.2
20.4
.916
306
730
0.02
-0.01
0.00
0.02
2.91
18.0
18.4
19.9
.976
800
0.08
-0.01
0.02
0.07
2.78
18.3
19.3
20.1
.988
830
0.17
-0.00
0.05
0.12
3.12
18.9
20.3
20.2
.994
900
0.29
0.00
0.10
0.19
3.23
20.1
22.3
20.3
.997
930
0.40
0.01
0.15
0.24
3.19
21.4
24.7
20.5
.998
1000
0.50
0.01
0.19
0.30
3.82
22.7
26.3
20.3
.996
1030
0.57
0.01
0.23
0.32
4.45
23.8
28.5
19.9
.996
1100
0.63
0.02
0.28
0.34
4.41
24.8
30.2
20.2
.999
1130
0.64
0.02
0.29
0.33
6.26
25.3
30.8
20.0
.998
1200
0.36
0.01
0.15
0.20
5.44
23.8
26.7
20.7 .
.998
1230
0.67
0.02
.0.27
0.38
4.. 27
24.5
32.2
21.6.
1.000
1300
0.63
0.02
0.29
0.32
5.74
25.8
32.3
20.5
.996
1330
0.53
0.02
0.26
0.25
5.47
25.7
31.1
20.4
.994
1400
0.26
0.01
0.12
0.12
5.07
25.0
27.6
20.7
.997
1430
0.25
0.00
-0.02
0.26
3.84
23.3
23.7
21.1
-.948
1500
0.30
0.00
0.06
0.23
5.72
23.4
24.4
21.1
.999
1530
0.10
-0.01
0.01
0.10
3.32
19.9
21.0
21.0
.987
1600
0.14
0.00
0.02
0.11
2.73
20.7
22.2
22.0
.988
1630
0.08
-0.01
--

4.75
20.8
21.0
20.7
-.879
1700
0.02
-0.01
-0.01
0.04
2.66
20.9
20.6
19.9
-.982
307
730
0.03
-0.01

....
2.38
17.9
18.2
-.921
800
0.08
-0.00


2.46
18.1
19.1

-.329
830
0.19
0.00

--
2.43
19.0
20.6

-.731
900
0.29
0.01


3.14
20.9
22.9

-.979
930
0.39
0.01
--

4.10
23.0
25.1
-.407
1000
0.50
0.02
0.17
0.31
4.19
24.1
27.1
20.1
.999
1030
0.58
0.02
0.22
0.34
5.71
24.9
28.9
19.1
.996
1100
0.48
0.01
0.18
0.29
5.60
25.0
27.9
17.7
.995
1130
0.57
0.02
0.23
0.32
4.80
25.7
30.4
17.3
.998
1200
0.63
0.02
0.27
0.34
5.06
26.2
32.4
17.4
.998
1230
0.51
0.02
0.21
0.28
5.12
26.4
31.2
18.0
.996
1300
0.44
0.02
0.18
0.25
4.80
26.2
30.5
18.2
.997
1330
0.48
0.02
0.20
0.26
3.90
26.4
31.6
18.5
.999
1400
0.38
0.02
0.19
0.17
4.74
25.8
29.9
19.5
.999
1430
0.18
0.01
0.07
0.10
3.34
25.0
27.1
19.8
.995
1500
0.13
0.01
0.05
0.07
2.44
24.5
26.4
19.5
.997

175
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
307
1530
0.09
0.01
0.03
0.06
2.62
24.1
25.5
19.8
.991
1600
0.06
-0.00
0.02
0.04
3.04
23.4
24.2
18.3
.988
1630
0.03
-0.00
0.00
0.03
2.00
23.2
23.7
18.4
.954
1700
0.02
-0.00
-0.00
0.02
2.64
23.1
23.2
18.6
-1.022
308
730
0.01
-0.00
1.92
19.8
20.0
22.5
-.359
800
0.06
-0.00


2.34
20.0
20.7
22.9
.846
830
0.14
0.00
0.04
0.10
3.19
20.4
21.6
23.1
.999
900
0.28
0.01
0.07
0.20
2.58
21.4
23.6
23.6
.996
930
0.43
0.02
0.13
0.28
2.96
22.8
25.9
24.1
.997
1000
0.40
0.02
0.13
0.25
2.45
23.6
26.8
24.1
.989
1030
0.57
0.02
0.19
0.35
3.69
25.5
29.7
23.4
.992
1100
0.55
0.02
0.21
0.32
4.37
25.6
29.3
22.0
.996
1130
0.51
0.02
0.21
0.29
3.70
26.0
30.0
21.8
.996
1200
0.44
0.02
0.16
0.26
3.15
26.2
30.0
21.4
.996
1230
0.46
0.02
0.17
0.27
3.01
26.6
31.4
20.9
.993
1300
0.31
0.02
0.11
0.19
3.40
26.4
29.0
20.3
.994
1330
0.34
0.02
0.12
0.20
2.73
26.7
29.9
20.9
.996
1400
0.28
0.02
0.11
0.15
3.68
26.3 '
29.3
21.9
.998
1430
0.22
0.01
0.09
0.12
3.57
25.8
28.4
22.5
.994
. 1500
0.11
0.01
0.04
0.06
4.30
24.8
26.3
22.7
.985
1530
0.10
0.01
0.04
0.05
4.22
24.1
25.6
23.4
.992
1600
0.05
0.00
0.02
0.03
3.61
23.5
24.8
23.7
.967
1630
0.03
0.00
0.01
0.02
3.88
22.8
23.7
23.5
1.000
309
800
0.03
-0.00
0.01
0.02
2.67
20.3
20.7
23.2
1.039
830
0.02
-0.00
0.01
0.02
2.51
20.6
21.0
23.6
1.024
900
0.03
-0.00
0.01
0.03
2.16
20.8
21.2
23.7
.940
930
0.05
-0.00
0.01
0.03
2.61
20.9
21.3
23.9
.983
1000
0.05
0.00
0.01
0.04
2.62
21.1
21.5
24.2
.993
1030
0.02
-0.00
0.00
0.01
2.96
21.1
21.2
24.0
.860
1100
0.02
-0.00
0.00
0.02
2.50
20.8
20.9
23.6
.870
1130
0.01
-0.00


2.36
20.7
20.7
23.5
.594
1200
0.02
-0.00
0.00
0.02
2.16
20.8
20.8
23.5
.957
1230
0.03
-0.00
0.01
0.03
2.63
20.8
20.9
23.6
.900
1300
0.02
-0.00
0.00
0.02
3.29
20.9
21.1
23.9
1.010
1330
0.03
-0.00
0.01
0.03
3.57
21.0
21.1
23.9
.926
1400
0.02
-0.00
0.00
0.02
2.70
20.9
21.2
23.8
.899
1430
0.02
-0.00
0.00
0.02
3.63
20.8
21.0
23.7
1.161
1500
0.07
-0.00
0.02
0.05
3.62
20.7
21.2
23.5
.995
1530
0.07
-0.00
0.01
0.06
4.06
20.5
21.1
23.3
.985
1600
0.05
-0.00
0.01
0.04
3.31
20.3
20.9
22.8
1.013
1630
0.10
-0.00
0.02
0.08
2.95
20.5
21.2
22.9
1.003
1700
0.03
-0.00
0.01
0.03
3.11
20.3
20.7
22.7
.979

176
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
310
730
0.02
-0.01

1.93
18.1
18.3
19.5
.791
800
0.05
-0.01
0.01
0.05
1.50
18.4
18.9
19.7
.981
830
0.11
-0.00
0.02
0.10
2.61
18.9
19.6
19.8
1.000
900
0.18
-0.00
0.03
0.15
3.46
19.3
20.1
19.4
1.001
930
0.37
-0.00
0.09
0.28
4.00
20.0
22.0
18.9
.997
1000
0.46
0.00
0.14
0.31
3.29
20.8
23.6
18.5
.999
1030
0.55
0.01
0.19
0.35
3.38
21.6
25.9
18.2
.998
1100
0.63
0.01
0.24
0.38
3.36
22.3
27.0
17.4
.997
1130
0.66
0.01
0.26
0.39
3.78
23.0
28.9
16.6
.998
1200
0.68
0.01
0.29
0.38
3.73
23.4
30.0
15.8
.998
1230
0.68
0.01
0.30
0.37
4.22
23.5
30.3
15.0
.997
1300
0.66
0.01
0.29
0.36
4.16
24.0
31.0
14.8
.996
1330
0.59
0.01
0.26
0.32
4.14
24.0
30.0
13.2
.993
1400
0.56
0.00
0.26
0.30
4.05
24.0
29.8
12.4
.996
1430
0.48
-0.00
0.22
0.26
4.04
23.9
28.9
11.6
.995
1500
0.39
-0.01
0.17
0.23
4.47
23.7
27.4
10.5
.994
1530
0.29
-0.01
0.12
0.17
3.59
23.5
26.0
10.6
.997
1600
0.17
-0.01
0.06
0.12
3.33
23.1
24.2
11.1
.992
1630
0.06
-0.01

2.34
22.6
22.2
11.1 .
.150
311
730
0.05
-0.04
_ _
0.02 '
6.1
'6.2
-.913
800
0.14
-0.03


0.61
9.1
9.4

.249
830
0.19
-0.02

--
2.31
11.7
11.6

.782
900
0.31
-0.02
0.07
0.26
3.83
12.8
13.5
8.2
.971
930
0.40
-0.01
0.18
0.23
3.65
13.9
16.7
7.7
.998
1000
0.48
-0.01
0.30
0.18
3.44
15.0
19.5
7.5
.999
1030
0.53
-0.00
0.37
0.17
2.68
15.8
23.1
7.5
.999
1100
0.59
0.00
0.39
0.20
1.66
16.6
24.6
7.6
.999
1130
0.62
0.01
0.40
0.22
2.03
17.5
26.9
7.6
.999
1200
0.64
0.01
0.41
0.21
1.35
17.9
28.5
7.5
.999
1230
0.63
0.01
0.41
0.21
1.18
18.6
29.2
7.5
.998
1300
0.62
0.01
0.39
0.22
1.62
19.3
29.3
7.6
.999
1330
0.58
0.01
0.35
0.22
1.61
19.7
29.0
7.7
.999
1400
0.52
0.00
0.31
0.21
1.88
20.6
28.5
7.8
.999
1430
0.45
0.00
0.25
0.19
1.93
21.1
27.6
7.8
.999
1500
0.36
-0.00
0.20
0.16
2.07
21.3
26.3
7.6
.997
1530
0.26
-0.00
0.14
0.13
1.75
21.4
24.7
7.6
.992
1600
0.15
-0.00
0.07
0.09
1.44
21.2
22.6
7.6
.973
1630
0.04
-0.01


1.58
20.5
20.0
7.6
.617
312
730
0.06
-0.03
_ _
0.00
3.9
4.5
~
.549
800
0.15
-0.02

--
0.00
7.2
7.9

-.648
830
0.20
-0.00
--
--
0.04
11.1
12.1
--
-.611
900
0.30
0.01

--
1.37
14.7
16.0

-.593
930
0.39
0.02


1.16
17.5
19.8

-.669
1000
0.45
0.02


1.37
19.1
23.2

-.837

177
Day
Time
Net
Soi 1
- Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
312
1030
0.51
0.02

_
2.23
20.1
26.5
-.491
1100
0.58
0.03


1.86
20.7
27.7

.520
1130
0.62
0.03
0.35
0.24
2.22
21.5
30.2
12.1
.999
1200
0.64
0.03
0.36
0.25
2.86
21.9
31.4
11.9
.998
1230
0.64
0.03
0.36
0.25
2.87
22.5
32.2
11.9
.999
1300
0.62
0.03
0.35
0.25
2.80
23.0
32.4
12.2
.996
1330
0.59
0.02
0.32
0.25
2.94
23.5
31.7
11.7
.994
1400
0.53
0.02
0.21
0.29
2.46
23.8
31.2
11.1
.904
1430
0.46
0.01
0.24
0.20
2.33
24.1
23.9
11.9
.991
1500
0.36
0.01
0.19
0.17
2.47
24.3
28.6
12.4
.989
1530
0.27
0.01
0.13
0.13
2.17
24.4
27.0
12.0
.981
1600
0.15
0.01
0.06
0.09
1.66
24.2
24.9
11.8
.969
1630
0.03
0.00


0.83
23.8
22.1
12.3
.300

APPENDIX D
SUPPLEMENTARY FIGURES
178

250
200
150
G
N
100
50
0
'SAAAAA' vv^AvnaMa /wtviVM/ +\J,A
Turbulent
Layer
Ns-
UMiA/tJv
Surfacfe-.r-----
Layer
T5 t4 t3t2 1¡
Figure 1. Hypothetical Daytime Temperature
Profile. The various levels at
which temperature measurements
for the Bowen ratio calculation
were made is also shown, as sur-
fact temperature is plotted at
an arbitrary height within the
canopy.
200
100
ZA
Figure 2. Simplified Temperature Profile.
T^ is the air temperature mea
sured at level 5 in the profile,
Tg is the temperature at the
surface/turbulent layer inter
face and Ts is the radiation
temperature. The displacement
height (D) is 35 cm, and the
roughness height (Rg) is 1 cm.
lO

-D (cm) Z-D fcm)
Figure 3. Simplified Temperature Profiles for a Clear Day. Temperature gradients are rep
resented as in Fig. 2. The heavy lines are the average surface-to-air tempera
ture gradients measured on October 17, 1981. They are labeled with the true
solar time at the end of the half-hour period in which they were collected. The
turbulent and surface segments are shown in light lines.

Z-D (cm) Z-D (cm)
Figure 4. Simplified Temperature Profiles for an Overcast Day. These gradients were
measured on October 30, 1981. Note the difference in temperature scale when
comparing to Figure 3. The rapid afternoon cooling was caused by intermittent
drizzle.

i i i i-i-j j i I i
0 2 4 6 8 10
Ts-Ta PC)
Figure 5. Air Transport Coefficient for Average Conditions. Data are from
days 290-310 inclusive except days 297-300 inclusive, on which no
data were collected.
CO
ro

.05
NET RADIATION (LY/min)
Figure 6. Soil Heat Flux Parameter for Average Conditions. Data are from days 290-310
inclusive except days 297-300 inclusive, on which no data were collected.
Data are grouped because soil heat flux data were recorded in hundredths of
ly/min.
co
CO

U (M/S)
Figure 7. Variation of the Daily Average Heat Transport Coefficient with the Daily
Average Windspeed.

185
Figures 8, 9, 10, 11, and 12. Data and ET Estimates for October 17, 18,
21, 22, and 23, 1981. Each figure presents one day's data in 9
graphs on 5 pages. The numbers on the graphs indicate the true so
lar time at the end of the half hour averaging period that the
corresponding point represents. The graphs are labelled (a)
through (i), and are described below:
(a) Sensible Heat Flux vs. Surface-to-Air Temperature Difference. The
slope of the line passing through the origin and the data points
is the average heat transport coefficient.
(b) Latent Heat Flux vs. Surface-to-Air Vapor Pressure Difference. The
surface vapor pressure is the saturation vapor pressure at the
surface temperature. The slope of the line passing through the
origin and data points is the average vapor pressure transport co
efficient, from which average moisture availability can be com
puted.
(c) Vapor Pressure Gradient vs. Temperature Gradient. The slope of the
line fitted to the points is the slope of the saturation vapor
pressure curve at the average temperature, and the intercept is
the average vapor pressure deficit.
(d) Soil Heat Flux vs. Net Radiation. The slope of the line passing
through the origin and the data points is equal to the average
fraction of net radiation conducted into the soil (G/R). The soil
heat flux parameter (f) is calculated from f =1 G/R.
(e) Daily Course of Net Radiation. This graph shows the general cloud
iness of the day in question.
(f) Surface-to-Air Temperature Gradient/Net Radiation Relationship.
The equation in the lower right corner has been "eye fit" to the data.
(g) Comparison of Bowen Ratios in Time. The solid line ratios were
calculated from half-hour average temperature and vapor pressure
profiles; the data plotted are from periods in which the profile
correlation was at least .95. The dotted ratios were computed by
the simple residual method, and the dashed using the correlation
developed from the temperature gradient/net radiation correlation.
The heat transport coefficient used in the latter two methods was
constant (the same for each time period) but separately determined
for the day in question.
(h) Comparison of Instantaneous ET Estimates. Estimates by the simple
residual method and the ATGR method are compared to actual ET
rates under more realistic estimation conditions. The residual and
ATGR estimates are calculated using an "average conditions" heat
transfer coefficient (h = .035 ly/minC) and soil heat flux param
eter (f = .94); see Figs. 5 and 6 for "average conditions" plots.
(i) Comparison of Instantaneous Measurements and Estimates over Time.

E (LY/min) H(LY/mln)
186
Ts-Ta (C)
Figure 8. Data and ET Estimates for Oct. 17, 1981. See p. 185 for
brief explanation of individual graphs.

G (LY/min) ef-en(MB)
187
Figure 8. (cont.)

NET RAD. (LY/min)
188
Figure 8. (cont.)

ESTIMATED ET (LY/min) BOWEN RATIO
Figure 8. (cont.)

Figure 8. (cont.)
<£>
o

E (LY/min) H(LY/mm)
191
Figure 9. Data and ET Estimates for Oct. 18, 1981. See p. 185 for
brief explanation of individual graphs.

192
Figure 9. (cont.)

NET RAD. (LY/m¡n)
193
Figure 9. (cont.)

ESTIMATED ET (LY/min) BOWEN RATIO
194
Figure 9. (cont.)

ET (LY/min)
Figure 9. (cont.)

E (LY/min) H (LY/min)
196
Figure 10. Data and ET Estimates for Oct. 21, 1981. See p. 185 for
brief explanation of individual graphs.

197
Figure 10. (cont.)

NET RAD. (LY/min)
198

ESTIMATED ET (LY/min) BOWEN RATIO
199
Figure 10. (cont.)

Figure 10. (cont.)

E(LY/min) H(LY/min)
201
e*-ea (MB)
Oct. 22,1981
Figure 11. Data and ET Estimates for Oct. 22, 1981. See p. 185 for
brief explanation of individual graphs.

202

NET RAD. (LY/nnih)
203
Figure 11. (cont.)

ESTIMATED ET (LY/min) BOWEN RATIO
204
Figure 11. (cont.)

ET (LY/m¡n)
Figure 11. (cont.)

E (LY/min) H (LY/min)
206
Oct. 23, 198!
Figure 12. Data and ET Estimates for Oct. 23, 1981. See p. 185
for brief explanation of individual graphs.

(LY/min) ec-en (MB)
207
Figure 12. (cont.)

(C) NET RAD. (LY/min)
208
Figure 12. (cont.)

ESTIMATED ET (LY/min) BOWEN RATIO
Figure 12. (cont.)

Figure 12. (cont.)
PO
O

BIOGRAPHICAL SKETCH
Klaus Heimburg was born in El Paso, Texas, in 1949, and grew up
in Huntsville, Alabama. He received a Bachelor of Science degree in
physics from Southwestern at Memphis in 1971. After a few years work
ing at a variety of jobs, he returned to school to continue his edu
cation. He completed an M.S. degree (1976) and a Ph.D. degree (1982)
in environmental engineering sciences at the University of Florida.
211

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
^ 'J'j'L i'i'$L?\
W/C/ Tiubr
Professgr, Environmental Engineering
Sciences
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
L.H. Allen, Or.
Associate Professor, Agronomy
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
H.T. Odum
Graduate Research Professor,
Environmental Engineering Sciences
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
R.W. ^waii
Professor, Industrial and Systems
Engineering

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Heaney~
Professor, Environmer
Sciences
Engineering
This dissertation was submitted to the Graduate Faculty of the College
of Engineering and to the Graduate Council, and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
December 1982
Dean, College of Engineering
Dean, Graduate School

UNIVERSITY of
FLORIDA
The Fomnlation for The Gator Nation
Internet Distribution Consent Agreement
In reference to the following dissertation:
AUTHOR: Heimburg, Klaus
TITLE: Evapotranspiration : (record number: 339630)
PUBLICATION DATE: 1982
I
i
I, Klaus Heimburg, as copyright holder for the aforementioned dissertation, hereby grant
specific and limited archive and distribution rights to the Board of Trustees of the
University of Florida and its agents. I authorize the University of Florida to digitize and
distribute the dissertation described above for nonprofit, educational purposes via the
Internet or successive technologies: All 'fortKeTjfear Glory, of The Gator Nation!
This is a non-exclusive grant of permissions for specific pff-lini;arid on-line uses for an
indefinite term. Off-line uses shall be limited to thosp specifically, alio wed by "Fair Use"
as prescribed by the terms of-United States copyright legislation (cf, Title 17, U.S. Code)
as well as to the maintenance and preservation of'a digital archive copy. Digitization
allows the University of Florida to generate image and text-based versions as appropriate
and to provide and enhance access using search software.
This grant of permissions prohibits use offthb'idgtized .versions Tor commercial use or
profit
...-UJ&jls iflcu
Signature of Copyright Holder)
Personal information blurred
Can I interest you in an excellent masters thesis? Hydrology of Some North-Central
Florida Cypress Domes. Heimburg, 1976.



128
needs only concurrent ground-measured air temperatures and the solution
of regression equations to make ET estimates.
Because of the directness and simplicity of the ATGR approach, it
is the opinion of the author that developing the combination of high
time resolution satellite data and relatively simple steady-state meth
ods for ET estimates is preferable to the combination of low time reso
lution satellite data and complex simulation methods. The major advan
tage of the steady-state approach lies in the reduced total effort in
volved in the ET estimates. The cruder surface description of the ATGR
method seems better matched to the strengths and limitations of the
satellite data source. Another practical advantage of the use of higher
time resolution satellite data is that it offers more opportunities to
acquire data under clear sky conditions, which are required in both
approaches.
Recommendations for Future Research
An estimation procedure can be no more accurate than allowed by its
weakest part. From this perspective, the most important area for future
research is development of operational methods to determine surface tem
perature and net radiation from satellite data. This development in
cludes solutions to the problems of image registration and atmospheric
absorption corrections. The ability to accurately overlay visible and
infrared data collected at different times from the same area on the
earth's surface is critical to all remote-sensing methods, as is the
ability to correct temperature and net radiation estimates for atmo
spheric effects. The success with which these "raw" data estimates can
be made under realistic operational conditions (varying levels of cloud
iness) will determine the overall potential accuracy of an estimation


NET RAD.
TIME (TST, OCT. 17, 1981)
Figure 5-7. Clear Day Temperature Gradient/Net Radiation
Correlation. Data are from October 17, 1981;
numbers indicate true solar time at end of
half-hour averaging period.


.05
NET RADIATION (LY/min)
Figure 6. Soil Heat Flux Parameter for Average Conditions. Data are from days 290-310
inclusive except days 297-300 inclusive, on which no data were collected.
Data are grouped because soil heat flux data were recorded in hundredths of
ly/min.
co
CO


58
each half hour. This prevents the data reports from precessing out of
synchronization with the system clock.
SET also enables REPRT and ANALZ to be swapped between core and
disk so as not to interfere with the measurement schedule. At the end of
a typical half hour (1.5 min past the clock hour or half hour, when mea
surement of the twelfth profile has just been completed) MEASR calls for
SET to run immediately and ends. SET schedules MEASR to start again at
an absolute clock time, 2 min into the new half hour, or roughly 30 sec
onds after the last measurement made. It then loads and runs REPRT and
ANALZ. When it is time for MEASR to start, whichever program is in core
is moved back to disk, and MEASR is loaded. MEASR makes its first scan,
and during the usual delay between scans, REPRT and/or ANALZ are re
loaded and run to completion. MEASR is then swapped back to core to be
continued at the end of the programmed delay;
The programs can be halted from the computer terminal or with
switches on the face of the computer. When switches 1 and 2 are on,
MEASR ends with the next profile and REPRT computes averages for all the
data collected in that half hour. When only switch 2 is on, MEASR ends
at the next normal half-hour reporting time.
Operational Considerations
The thermopile/air sampling system required a great deal of care in
setting up and maintaining the instrumentation involved. It also re
quired an awareness of the theoretical and practical limitations of the
measurement method. Proper calibration and tuning of the dewpoint analy
zer were most critical for good measurements. Sensor cleaning and output
calibration procedures are well documented in the EG&G Model 880 Dew
point Hygrometer Manual (1977). However, to achieve optimum response


TEMP",5F6.1,
AW DIR = AWDIR+WDIR
WDIR = 0.0
C*****IF LAGGED DEW POINT PROFILE COMPLETE, COMPUTE BOWEN RATIO,
C*****rEP0RT PROFILE DATA, AND ADD IT TO HALF HOUR SUMS
95 IF(LEVEL .EQ. 5)100,30
100 NPROF = NPROF+1
CALL RATIO(E,T,B,C)
B = (391.7*B)/HV(TRAD(5))
CD = ABS(C)
IF(CD-.95)106,106,104
104 NBR = NBR+1
BR(1) = BR(1)+B
BR(2) = BR(2)+B**2
106 IF(ISSW(3))107,109
107 WRITE(6,108)NPR0F,TRAD(5),T(1),T(2),T(3),T(4),T(5),C,
*ITIME(4),ITIME(3), (2),
*TRAD(1),DPT(1),DPT(2),DPT(3),DPT(4),DPT(5),B,TWSPD,E(1),E(2)
*E(3),E(4),E(5)
108 F0RMAT(/,4X,"PROF#",13," RAD.T.", FT.2,"
*" R = ",F5.3,/,4X,12,":",12,":",12," NET R.",F7.2,
DPT.",5F6.1,/,4X,"B =",F5.3," W.SPD.",F7.2,
V.P.",5F6.1)
C*****TKIMMER DELAY
CALL EXEC(12,0,1,0,-32) .
GO TO 110
.109 CALL EXC2,0,1,0,-49)
C*****$UM PROFILE DATA FOR AVERAGES, ROLL DOWN ADVANCE TEMPERATURE
C*****READINGS
110 DO 115 K=l,5 .
AT (K,1) = AT(K,1)+T(K)
AT(K,2) = AT(K,2)+T(K)**2
T(K) = T(K+5)
AE (K, 1) = AE (K, 1 )+E(K)
AE(K ,2) = AE(K,2)+E(K)**2
115 CONTINUE
LEVEL = 0
IFCNVALV .EQ. 10)120,130
IF(VMARK .GT. 6.)125,35
125 NVALV = 0
VMARK =0.0
130 IF(ISSW(1))132,134
132 KFLAG = 3
GO TO 138
C*****AT END OF HALF HOUR, COMPUTE AVERAGES AND REPORT
134 IF(((ITIME(3) .GE. 0) .AND. (ITIME(3) .LT. 3)) .OR.
*((ITIME(3) .GE. 30) .AND. (ITIME(3) .LT. 33)))136,30
136 KFLAG = 4
138 NTOT = NPROF
IF(NTOT .GT. 5) NMEAS = 25
NPROF = 0
140 CALL EXEC(9,SET,1)
END
120


81
are possible even with cloudy conditions. The pivotal assumptions are
that the surface temperature can be used as the effective heat transfer
temperature, and that air temperature measurements can be generated from
surface temperatures.


87
Figure 5-2. Total vs. Turbulent Temperature Gradients for a Cloudy
Day. Temperature differences were calculated as in
Fig. 5-1; data are from October 30, 1981. Note that
compared to Fig. 5-1 the temperature scale is expanded
by a factor of five. Temperature profiles for this day
are plotted in Fig. 4 of Appendix D.


150
COSA = SQRT(1.-SINA**2)
ZNGL = 90.-57.2958*ATAN(SINA/COSA)
HRNGL = 15.*(TST-12.)
c*****TVA REPORT 2.24
OAM = 1./(SINA+.15*(93.885ZNGL)**(-1.253))
C*****TVA REPORT 2.4
AESR = l.+.017*C0S(.01721*(186.D))
SWIO = (2.*SINA)/(AESR**2)
ATC = (SWI/SWIO)**SINA
ABDO = RSW/SWI
WRITE(6,20)
20 FORMAT!/," ABDO SWIO OAM ATC ZNGL HRNGL EOT "
*" E.S.T. T.S.T. DAY")
WRITE(630 )ABDO,SWIO,OAM, ATC,ZNGL, HRNGL, EOT, EST,TST, ITIME(5)
30 F0RMAT(F4.2,1X,3F7.2,2F9.1,F8.4,2F8.2,I8)
END
SUBROUTINE PR0FT(V,V0,Z0,DV,BV,RV)
C*****PR0FT FITS TEMPERATURE AND VAPOR PRESSURE PROFILES BY LINEAR
REGRESSION. DISPLACEMENT HEIGHTS CHOSEN BY BEST REGRESSION FIT.
DIMENSION SUM(5),V(5),X(5),Z(5)
DATA Z/35.,60.,85.,135.,225./
RP = 5.0
ROLD = 0.0
RK = 0.0
DO 135 J = 2,22,4
BSTEP = J
GO TO 105
100 RK = RK+1.0
105 D = BSTEP RK
IF(D)140,140,108
108 DO 110 L2 = 1,5
SUM(L2) = 0.0
110 CONTINUE
DO 120 L3 = 1,5
IF(Z(L3) .LE. D)118,116
116 X(L3) = ALOG((Z(L3)-D+ZO)/ZO)
SUM(l) = SUM(1)+V(L3)
SUM(2) = SUM(2)+V(L3)**2
SUM(3) = SUM(3)+X(L3)
SUM(4) = SUM(4)+X(L3)**2
SUM(5) = SUM(5)+V(L3)*X(L3)
GO TO 120
118 RP = RP-1
120 CONTINUE
B = (RP*SUM(5)-SUM(1)*SUM(3))/(RP*SUM(4)-SUM(3)**2)
A = (SUM(1)-B*SUM(3))/RP
SDZ = SQRT(SUM(4)-(SUM(3)**2)/RP)
SDV = SQRT(SUM(2)-(SUM(l)**2)/RP)
RCOEF = B*(SDZ/SDV)
IF(ISSW(5))121,123
121 WRITE(6,122)ZO,D,A,B,RCOEF
122 FORMAT(IX,5F12.5)


36
radiation can be estimated, as when there is cloud cover or in between
sets of satellite data.
A significant advantage of the estimation method developed is that
it, in effect, determines surface parameters like moisture conditions
almost completely from remote-sensing data. This is done with an equa
tion (hereafter referred to as the temperature gradient model) that re
lates the surface-to-air temperature gradient to net radiation and pa
rameters that describe the surface. By assuming that the parameters are
constant, two of them (e.g., moisture availability and saturation defi
cit) can be determined from the correlation of the surface-to-air tem
perature gradient and net radiation. Although surface temperatures are
required (implying clear skies) to determine parameters, they can be
used with cloudy condition net radiation estimates for cloudy condition
ET estimates.
The need for a .surface-to-air temperature net radiation correlation
calculation requires several daytime satellite data sets. Unlike the
HCMM methods, the remote ET estimation method developed in this study is
designed for use with satellite data that is available at least every 2
or 3 hours. At this time resolution, the average temperature gradient
response method can make reasonably accurate cumulative daily ET esti
mates without the need for simulation. Because the parameters are con
sidered constant, no interpolation scheme is needed to make cumulative
ET estimates; only an estimate of the cumulative daytime net radiation
is required.


121
parameter (.94) were used for all estimates. Although errors in esti
mates for individual days change, the overall error level does not.
The overall error level of the cumulative ET estimates can most
easily be seen in Fig. 5-16. It graphically compares ET estimates made
with the ATGR method (using "average conditions" h and f) and residual
methods. In general, cumulative estimates are more accurate than in
stantaneous estimates, and days on which the ATGR method performance is
worst are generally overcast days for which it was very difficult to
obtain representative values of A and B.
From the calculations presented in this chapter it can be con
cluded that the average temperature gradient response is a measure of
the average surface parameters, and that the slope and intercept of the
temperature gradient/net radiation correlation can be used to make rea
sonably accurate ET estimates. It must be noted that the cross-calibra
tion of the surface and air temperature sensors is of critical impor
tance in application of the ATGR method. In these calculations it ap
pears that the surface temperature may have been slightly high relative
to the air temperature measurement.
Cumulative ET estimates made with the ATGR method are exactly as
accurate as estimates made with the state-of-the-art simple residual
method. However, unlike the simple residual method, it is useful for
any time period(s) for which a net radiation estimate is available--its
application is thus not limited to clear time periods. Both methods
seem equally susceptible to errors in the value of the heat transport
coefficient used in making estimates; estimates that agree least close
ly with measured ET amounts generally have a heat transfer coefficient-
substantially different from the average conditions value used.


25
from 0 to 1, can be introduced to account for subsaturation of the sur
face air:
M(e* ea) = es ea 2-19
This formulation was suggested by Tanner and Pelton (1960) and applied
by Outcalt (1972), Pandolfo and Jacobs (1973), Nappo (1975), and Carlson
and Boland (1978), and in a slightly different form by Barton (1979).
The equation for latent heat flux can then be written in terms of the
heat transport coefficient and moisture availability parameter:
E = M(e* ej 2-20
y s a
*
where e$ is the saturation vapor pressure at the surface temperature,
e is the vapor pressure at the reference level a,
Ma is a unitless parameter interpreted as moisture availability,
h is the bulk heat transport coefficient, and
Y is the psychrometric.constant (y = cpP/Le).
The resistance formulation (Monteith, 1973) includes an additional' re
sistance term, r the bulk stomatal diffusion resistance (sometimes
referred to as the canopy resistance, r ) to account for the subsatura
tion of air at the surface:
E =
PCD y(r + r )
G o
2-21
Both of the transport coefficient resistance formulations are used
in the ET literature; analytic evaluation of either type of expression
is based on diffusivity integrals like those in Eqs. 2-14 and 2-15.
These formulations can be substituted for one another with the following
identities:
h
a
r
and
2-22
M =
ra + rs
This study uses the conductivity formulation.
2-23


33
of thrmal inertia and surface relative humidity. This procedure must be
repeated for each combination of surface roughness, slope, and slope
direction. Then satellite-measured maximum and minimum temperatures for
specific areas are matched to the modelled values to determine daily ET
for those areas.
Steady-State Methods
Most efforts to use remote-sensing data to estimate ET rates were
made with the simple residual method (Eq. 2-24). Remotely sensed data
were used to estimate net radiation, and sensible heat flux from the sur
face was evaluated with a remotely-sensed surface temperature and a
ground-measured air temperature. Evapotranspiration was then calculated
as the net radiation less the estimated sensible and soil heat flux.
Studies that fall into this category are Allen et _al_. (1980), Seguin
(1980), Soer (1980), and Price (1982). Soer and Price extend their- meth
ods to cumulative daily ET estimates with the help of simulation models
described in the preceding subsection.
These methods differ primarily in how they treat the bulk heat
transport coefficient or transport resistance of the surface air layer.
Two methods of computing sensible heat flux were used in the Allen et
al. (1980) approach. For short vegetation (mostly pasture), a stability-
corrected thermal conductivity was computed using the log law wind model
and dimensionless empirical relationships developed by a group at the
University of California at Davis (Morgan £t _al_., 1971). An empirical
resistance equation based on leaf length, windspeed, shelter factor, and
leaf area index (Monteith, 1965) was used for transport over areas
covered with trees. By using measured windspeed and air temperature, the
estimated tree resistances and a surface temperature map, it was


68
The advantage of this substitution is that whatever error occurs in the
temperature gradient measurement affects both latent and sensible heat
fluxes, not just the sensible heat flux, as in the simple residual ap
proach. Substituting Eqs. 4-6 and 4-9 into Eq. 4-1,
R = G + h(T TJ + [s(T T ) + 6eJ 4-10
S a y S cl a
Rearranging terms and dividing by constants,
Ts Ta h(KsV-Y-) [v(R G) hnsea] 4-11
Equation 4-11 explicitly states the dependence of the surface-to-
air temperature gradient (difference) on other variables--net radiation
(R), soil heat flux (G), saturation deficit (6e ), bulk air conductivity
a
(h), and moisture availability (M). The equation is generally applica
ble; the psychrometric "constant" can be adjusted to various atmospheric
pressures (altitudes) and the slope of the saturation vapor pressure
curve can be adjusted for various temperature ranges. The resistance
formulation of this equation has been used by Jackson et jfL (1980).
In the strictest sense Eq. 4-11 is true only instantaneously. How
ever, with the assumption of some degree of system stationarity, various
approaches to remote ET estimates can be made. Two are developed here.
The first makes a minimum of additional assumptions and uses ground-mea
sured air temperature, saturation deficit, and soil heat flux measure
ments. The second assumes that only surface and air temperatures change
in response to changes in radiation, and uses only remote measurements.
Both use the response of temperature gradients to varying net radiation
loads to evaluate surface parameters; these are then used in calculating
ET.


DATA AQUISITION
TTE1
.M
TERMINAL
COMPUTER
SYSTEM
Flow Meters
Mixing Bottles-
SIGNALS
SENSORS
NET RADIATION
SOIL FLUX
REFERENCE TEMPERATURE
4 TEMPERATURE DIFFERENCES
DEW POINT
VALVE CONTROL
VALVE POSITION
-0
NET RADIOMETER
SOIL FLUX
DISK
AIR SAMPLE
PORT
RADIATION \]
SHIELDING'
'ASPIRATING
FAN
THERMOPILE
SENSOR ARM
AIR SAMPLING SYSTEM
Heated Tubing Bundle
PROFILE MEASUREMENT MAST
Figure 3-2. Schematic of ET Measurement System. Details of profile measurement and air
sampling equipment are shown in Figs. 3-3 and 3-4.
45*
CTJ


161
Day
Time
Net
Soi 1
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
FI ux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
148
930
0.62
0.04
0.14
0.43
2.05
27.0
35.4
31.8
.988
1000
0.69
0.05
0.16
0.48
2.35
27.8
36.7
31.3
.990
1030
0.65
0.04
0.15
0.46
2.97
28.1
36.1
30.8
.996
1100
0.82
0.06
0.18
0.57
2.89
28.9
38.6
29.8
.994
1130
0.72
0.07
0.15
0.50
2.97
28.8
37.6
28.2
.996
1200
0.76
0.08
0.16
0.52
2.84
29.4
38.4
27.0
.997
1230
0.66
0.07
0.13
0.46
2.42
29.7
37.7
26.8
.993
1300
0.79
0.08
0.16
0.55
2.95
30.0
38.6
26.1
.991
1330
0.84
0.10
0.19
0.56
2.99
30.4
39.4
26.0
.992
1400
0.86
0.10
0.19
0.57
2.72
31.1
39.9
25.9
.991
1430
0.71
0.09
0.15
0.47
2.89
30.8
38.2
26.1
.994
1500
0.68
0.08
0.15
0.45
2.83
30.8
37.6
26.2
.994
1530
0.44
0.06
0.09
0.29
2.20
30.5
34.9
25.7
.979
1600
0.39
0.05
0.08
0.27
2.24
30.5
34.3
26.5
.984
1630
0.29
0.03
0.05
0.20
1.78
30.2
32.9
26.3
.950
1700
0.22
0.03

--
1.51
30.2
31.6
25.5
.811
1730
0.10
0.02

--
1.01
29.6
28.7
25.3
-.938
1800
0.03
0.01

0.83
29.0
26.3
25.1
-.998
149
630
0.10
0.01
.
...
0.71 .
20.9
22.6

-.418
700
0.17
0.01

--
1.27
21.8
23.3

-.526
730
0.29
0.02

--
1.48
23.5
25.3

.713
800
0.39
0.02
0.06
0.31
1.38
24.8
28.8
30.8
.975
830
0.48
0.03
0.10
0.35
1.21
26.5
33.3
29.6
.984
900
0.57
0.05
0.12
0.41
1.13
27.7
35.6
28.2
.976
930
0.65
0.05
0.15
0.45
1.71
28.5
36.9
26.1
.991
1000
0.73
0.06
0.17
0.50
2.29
29.3
37.9
24.4
.995
1030
0.66
0.07
0.15
0.44
2.46
29.5
37.1
24.2
.994
1100
0.84
0.09
0.17
0.58
1.85
30.3
39.6
22.1
.983
1130
0.79
0.09
0.17
0.54
2.40
30.5
39.0
22.5
.990
1200
0.72
0.10
0.16
0.46
2.82
30.8
38.2
22.8
.992
1230
0.76
0.09
0.15
0.51
2.21
30.9
38.5
22.9
.993
1300
0.85
0.11
0.20
0.54
2.25
31.7
40.1
22.8
.986
1330
0.75
0.10
0.16
0.49
1.96
31.5
39.1
23.2
.990
1400
0.73
0.11
0.15
0.48
1.55
32.2
39.4
23.2
.971
1430
0.66
0.08
0.14
0.44
2.44
31.8
37.9
23.6
.988
1500
0.59
0.07
0.12
0.39
2.41
31.9
37.0
23.9
.985
1530
0.50
0.06
0.10
0.34
2.66
31.8
35.8
23.3
.986
1600
0.40
0.06
0.06
0.28
1.66
32.2
35.3
22.9
.951
1630
0.25
0.03
0.04
0.18
2.00
31.5
33.0
22.9
.925
1700
0.15
0.03

--
1.05
31.2
31.5
23.0
-.317
1730
0.08
0.02
--
--
1.06
30.7
29.3
24.2
-.965


107
Figure 5-11.
Effect of Heat Transport Coefficient and Soil Heat Flux
Parameter on Temperature Gradients.


TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ii
LIST OF FIGURES vii
LIST OF TABLES ix
ABSTRACT x
CHAPTER 1: INTRODUCTION 1
Potential for Remote Evapotranspiration Estimates 1
Scope of Research '3
Research Approach 5
Experimental Site and Data Collection 7
Organization of Dissertation 11
.CHAPTER 2: EVAPOTRANSPIRATION AND SATELLITE DATA'.". '. ... .12
Overview 12
The Evapotranspiration Process 12
The Energy Balance Approach to ET Estimation 17
The Energy Budget Equation 17
Transport Similarity and Wind Models 20
Latent and Sensible Heat Flux Expressions . 23
Energy Budget ET Estimation Strategies 26
Remote ET Estimation Methods 29
Surface Temperature and Net Radiation 29
Simulation Methods 30
Steady-State Methods 33
Temperature Gradient Response Methods 35
CHAPTER 3: A SYSTEM FOR AUTOMATIC COLLECTION OF ET DATA .... 37
Overview 37
Energy Budget/Profile Bowen Ratio Theory 37
Sensor and Time Constant Considerations 40
Data Collection Equipment 44
Data Collection Programs 51
Operational Considerations 58
v


APPENDIX D
SUPPLEMENTARY FIGURES
178


51
Data Collection Programs
A system of four programs was developed to collect, report, and
analyze the data required for the test surface energy budget. Program
MEASR makes the measurements and calculations, REPRT produces the half-
hourly summary reports, ANALZ does some analysis of data and performs
additional calculations, and SET schedules the other programs. Listings
of these programs appear in Appendix B; brief descriptions of their
functions and interactions follow.
Basically, all sensors are scanned in a computer program loop. De
pending on the status of various indexes in this loop or the system
clock, control is passed to specific calculation and/or reporting rou
tines. This fundamental loop is in program MEASR; it is repeated approx
imately every 30 sec, the measuring rate determined by the dewpoint ana-
. lyzer.
When a program calls for a measurement [i.e., CALL EXEC (1, 9,
DATA, CHANNEL NUMBER, VOLTMETER PROGRAM WORD)] the channel number in the
measurement program statement is passed to the scanner controller, and
the program word indicating type of measurement, voltage range, and de
lay time is passed to the voltmeter. After the scanner has closed on the
proper signal lines, the voltmeter has been set for the type of measure
ment, and a programmed delay is complete, the voltmeter integrates the
signal for 1/60 second and passes the average back to the measuring pro
gram. It resumes execution with the next program step.
During each execution of the measurement loop, one air temperature,
one dewpoint temperature, and all other sensors except soil thermocou
ples are scanned. Immediately after the dewpoint measurement, the scan
ning valve position is changed (Subroutine STEP) so that the dewpoint


169
Day
Time
Net
Soil
Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
290
700
0.01
-0.02

0.00
10.7
9.3
_ _
.937
730
0.07
-0.01

--
0.00
12.5
12.3
--
.150
800
0.15
-0.00

--
0.00
15.3
15.6
--
-.523
830
0.24
0.01


0.35
18.3
19.7

-.826
900
0.34
0.02


1.65
21.9
23.9

-.569
930
0.43
0.02


2.65
23.6
27.5

.595
1000
0.51
0.03
0.24
0.25
2.20
24.6
30.4
13.7
.997
1030
0.58
0.04
0.25
0.29
1.26
25.5
33.0
14.4
.997
1100
0.64
0.04
0.28
0.31
2.25
26.3
35.1
14.5
.998
1130
0.67
0.04
0.32
0.31
2.42
26.5
36.0
15.3
.998
1200
0.69
0.05
0.34
0.30
1.79
27.0
37.4
16.1
.997
1230
0.69
0.05
0.34
0.30
1.56
27.4
37.7
16.3
.997
1300
0.67
0.05
0.34
0.28
1.48
27.7
37.5
16.3
.994
1330
0.63
0.05
0.31
0.27
1.12
28.2
36.9
16.5
.988
1400
0.58
0.04
0.30
0.24
1.66
28.4
36.2
16.5
.990
1430
0.51
0.04
0.23
0.25
1.53
28.6
35.1
16.5
.992
1500
0.43
0.03
0.20
0.20
1.28
28.7
34.0
16.6
.973
1530
0.32
0.03
0.12
0.18
0.70
28.7
32.4
16.6
.956
1600
0.21
0.03
0.04
0.14
1.17
28.6
30.4
16.8
.923
1630
0.11
0.02

-- -
0.59
28.1
28.4
17.0
.457
1700
0.02
0.01
--
0.01
0.79
27.5
26.0
17.2
-.980
291
700
0.02
-0.01
0.00
13.7
13.5
__ _
1.084
730
0.04
-0.00

--
0.00
15.6
15.7

.950
800
0.06
0.00


0.06
17.4
17.5

.699
830
0.20
0.01

--
1.77
19.2
20.5
--
-.759
900
0.31
0.02
--
--
2.95
21.7
24.0

-.877
930
0.43
0.03
--

3.02
24.3
28.3
--
.078
1000
0.52
0.03

--
4.09
25.7
30.7

.602
1030
0.59
0.03
0.28
0.27
3.55
26.8
33.2
19.3
.998
1100
0.62
0.04
0.28
0.30
3.88
27.8
34.9
19.5
.998
1130
0.44
0.03
0.16
0.24
4.11
27.6
32.3
19.3
.997
1200
0.68
0.04
0.27
0.38
4.79
28.7
36.9
18.8
.997
1230
0.50
0.04
0.18
0.28
4.05
28.6
34.5
18.0
.997
1300
0.46
0.04
0.16
0.26
3.81
28.7
34.5
18.8
.999
1330
0.63
0.04
0.24
0.36
4.88
29.1
35.9
18.6
.996
1400
0.49
0.04
0.19
0.26
4.33
29.2
34.8
18.6
.999
1430
0.48
0.03
0.21
0.24
4.72
29.3
34.5
18.7
.992
1500
0.41
0.03
0.18
0.19
4.62
29.4
33.8
18.8
.998
1530
0.29
0.03
0.12
0.15
4.21
28.5
31.1
18.8
.989
1600
0.20
0.02
0.07
0.11
4.62
28.2
29.9
19.1
.995
1630
0.11
0.02
0.02
0.07
3.99
27.6
28.3
19.5
.955
1700
0.02
0.01
""
3.33
26.7
26.2
19.9
-.877


HEIGHT
64
a
Air
A
K
H
K,
Jr
h
a
Turbulent
Layer
Surface.^-
Soil
Figure 4-1. Definition Sketch for Transport Properties. The
surface layer which is dominated by laminar air
flow (molecular thermal diffusivity, k^) is repre
sented by the layer between zs and za. The heat
transport coefficient is used to represent the
combined transport properties of both layers.


(3o)
85
0.0 1.0 2.0
T0-Ta CC)
Figure 5-1. Total vs. Turbulent Temperature Gradients for a Clear
Day'. The total surface-to-air temperature difference
was calculated by subtracting the temperature measured
at 235 cm from the surface temperature. The turbulent
temperature difference was calculated by subtracting the
235-cm temperature from the 35-cm temperature. Data ar.e
from October 17, 1982; numbers indicate true solar time
at end of half-hour averaging period. Individual temper
ature profiles for this day are plotted in Fig. 3 of
Appendix D.


142
SVAL = DATA
IF(I .EQ. 1) CALL TNTCH(DATA,1,NMEAS,SVAL, DAT)
IF(I. EQ. 5) CALL TMTCH(DATA,2,NMEAS,SVAL,DAT)
DATA = SVAL
IF( I. NE. 4) GO TO 70
AVG = FILT(13,3042B,.000002)
AVG = CUC0N(AVG,-1)
DATA = DATA+.00000000008131*AVG**4
70 RAD(1,1) = RAD(1,1)+.2*DATA
RAD(1,2) = RAD(I,2)+DATA**2
72 CONTINUE
CALL EXEC(1,9,DATA,2,106,7044B)
W = CONV(DATA)
IF((W .GE. 9.375) .OR. (W .LT. 0.625)) ND(1)=ND(1)+1
IF((W .GE. 0.625) .AND. (W .LT. 1.875)) ND(5)=ND(5)+1
IF((W .GE. 1.875) .AND.
IF((W .GE. 3.125) .AND.
(W .LT. 3.125)) ND(2)=ND(2)+1
(W .LT.
IF((W .GE. 4.375) .AND. (W .LT.
4.375)) ND(6)=ND(6)+1
5.625)) ND(3)=ND(3)+1
IF((W .GE. 5.625)
IF((W .GE. 6.875)
IF((W .GE. 8.125)
(W .LT. 6.875)) ND(7)=ND(7)+l
(W
(W
.LT. 8.125)) ND(4)=ND(4)+1
.LT. 9.375)) ND(8)=ND(8)+l
CONTINUE
.AND.
.AND.
.AND.
CALL EXEC(1,9,DATA,2,105,7043B)
DATA = CONV(DATA)
WSPD = WSPD+.2*(CA(7)*DATA+CB(7))
C*****IF INITIAL (COLD START) MEASUREMENTS COMPLETE.
IF(LEVEL)25,25,74
C*****MAKE DEW POINT MEASUREMENT AND STEP VALVE TO NEXT LEVEL
74 EGG = FILT(107,4042B,.000002)
CALL EXEC(11,1 TIME)
CALL STEP(VMARK)
DPT(LEVEL) = (1508.*EGG-32.768)*DPTC0R
E(LEVEL) = 10.**((7.5*DPT(LEVEL))/(DPT(LEVEL)+237.3)+.7858)
IF (ISSW(0))76,80
76 WRITE(1,78)ITIME(4),ITIME(3),ITIME(2),VMARK,T(LEVEL),
*DPT(LEVEL),E(LEVEL),TBASE,DTEMP,T(LEVT),NVALV,LEVEL,LEVT,NDT,K
78 FORMAT(IX,12,":12,":",I2,F7.3,6F7.1,514)
C*****IF REAL TIME PROFILE COMPLETE, SAVE AVERAGES FOR PROFILE REPORT
80 IF(LEVT .NE. 5) GO TO 95
C*****aT START OF HALF HOUR, MAKE SURE THAT REPRT HAS ZEROED AVERAGES
IF((NPROF .EQ. 0) .AND. (NBR .NE. 0)) STOP 0002
85 DO 90 K=l,6
DATA = FILT(K,3042B,.000002)
AST(K) = AST(K)+CUCON(DATA,-1)
ARAD(K,1) = ARAD(K,1)+RAD(K,1)
ARAD(K,2) = ARAD(K,2)+RAD(K,2)
TRAD(K) = RAD(K,1)
RAD(K,1) = 0.0
RAD(K,2) = 0.0
90 CONTINUE
AWSPD = AWSPD+WSPD
TWSPD = WSPD
WSPD = 0.0


185
Figures 8, 9, 10, 11, and 12. Data and ET Estimates for October 17, 18,
21, 22, and 23, 1981. Each figure presents one day's data in 9
graphs on 5 pages. The numbers on the graphs indicate the true so
lar time at the end of the half hour averaging period that the
corresponding point represents. The graphs are labelled (a)
through (i), and are described below:
(a) Sensible Heat Flux vs. Surface-to-Air Temperature Difference. The
slope of the line passing through the origin and the data points
is the average heat transport coefficient.
(b) Latent Heat Flux vs. Surface-to-Air Vapor Pressure Difference. The
surface vapor pressure is the saturation vapor pressure at the
surface temperature. The slope of the line passing through the
origin and data points is the average vapor pressure transport co
efficient, from which average moisture availability can be com
puted.
(c) Vapor Pressure Gradient vs. Temperature Gradient. The slope of the
line fitted to the points is the slope of the saturation vapor
pressure curve at the average temperature, and the intercept is
the average vapor pressure deficit.
(d) Soil Heat Flux vs. Net Radiation. The slope of the line passing
through the origin and the data points is equal to the average
fraction of net radiation conducted into the soil (G/R). The soil
heat flux parameter (f) is calculated from f =1 G/R.
(e) Daily Course of Net Radiation. This graph shows the general cloud
iness of the day in question.
(f) Surface-to-Air Temperature Gradient/Net Radiation Relationship.
The equation in the lower right corner has been "eye fit" to the data.
(g) Comparison of Bowen Ratios in Time. The solid line ratios were
calculated from half-hour average temperature and vapor pressure
profiles; the data plotted are from periods in which the profile
correlation was at least .95. The dotted ratios were computed by
the simple residual method, and the dashed using the correlation
developed from the temperature gradient/net radiation correlation.
The heat transport coefficient used in the latter two methods was
constant (the same for each time period) but separately determined
for the day in question.
(h) Comparison of Instantaneous ET Estimates. Estimates by the simple
residual method and the ATGR method are compared to actual ET
rates under more realistic estimation conditions. The residual and
ATGR estimates are calculated using an "average conditions" heat
transfer coefficient (h = .035 ly/minC) and soil heat flux param
eter (f = .94); see Figs. 5 and 6 for "average conditions" plots.
(i) Comparison of Instantaneous Measurements and Estimates over Time.


IF(ABS(RCOEF) .LT. .85)42,44
42 HLTNT = 0.0
HSENS = 0.0
GO TO 75
44 BNR = (391.7*BNR)/HV
HLTNT = (RNET-SFLX)/(1.+BNR)
HSENS = BNR*(RNET-SFLX)/(1.+BNR)
IF(BNR .GE. 0.0)45,60
45 IF(AT(1) .GT. AT(5))75,50
50 HLTNT = -ABS(HLTNT)
HSENS = -ABS(HSENS)
GO TO 75
60 IF(AT(1) .GT. AT(5))65,70
65 HSENS = ABS(HSENS)
HLTNT = -ABSCHLTNT)
GO TO 75
70 HSENS = -ABS(HSENS)
HLTNT = ABS(HLTNT)
75 WRITE(6,95)
ET = 600.*HLTNT/HV
CALL EXEC(9,DTIME,1)
WRITE(6,80)DIR
WRITE(6,85)RNET,SFLX,HSENS,HLTNT,CWSP,NBR,NPROF,BNR,RCOEF
80 FORMAT!/,IX,"NET RAD. SOIL H.F. SENS. H.F. LAT. H.F.",
*2A2," WINDS RSQ. >. 95 B'.R. AVG.R.",/,78("-"))
85 FORMAT(F4.2," LY/M",F6.2," LY/M",F6.2," LY/M",F6.2," LY/M",
*F7.2," M/S ",12," OF ",I2,F6.3,F7.3)
TSURF = CRAD(5)
CRAD(5) = 273.2+CRAD(5)
CRAD(5) = .98*I00000000008131*(CRAD(5)**4)
WRITE(6,100)
DO 90 K=l,5
WRITE(6,105)NAM(K),NAM(K+6),CRAD(K),VCR(K),NA(K),
*CAT(6-K),VCT(6-K),NA(K),CAE(6-K),VCE(6-K),NA(K),RH(6-K),
*NS(K),CST(K)
90 CONTINUE
WRITE(6,110)ET,NA(6),TSURF,VCR(5),ABR,R,NS(6),CST(6)
95 FORMAT(2/,22X,"BEEF RESEARCH UNIT ET PROJECT DATA",2/,2X,
*"AVERAGES AND ( PERCENT VARIATION ) FOR HALF HOUR ENDING")
100 F0RMAT(1/,4X,"RADIATION",6X,"AIR TEMP",9X,"VAP PRESS",9X,
*"REL HMDTY",3X,"SOIL TEMP",/,5X,"(LY/M)",8X,"(CM) (*C)",
*9X,"(CM) (MB)",9X,"(CM) (%)",4X,"(CM) (*C)",/,78("-"))
105 FORMAT(A2,A2,F6.3," (",F3.1,")",2(I6,F6.1," (",F3.1,")"),
*2(16,F6.D)
110 FORMAT(" ET ",F6.3," MM/HR",16,F6.1," (",F3.1,")",2X,
*" **.95+ BR =",F5.3,",+0R-",F4.3,"**",16,F6.1,1/)
DO 115 K=1,6
AST(K) = 0.0
ARAD(K,1) = 0.0
ARAD(K,2) = 0.0
115 CONTINUE
DO 120 1=1,2


140
IF(ITIME(3) .GT. 3) MIN = 32
CALL EXEC(12,MEASR,2,0,ITIME(4),MIN,3,0)
40 CALL EXEC(10,REPRT,1)
CALL EXEC(10,ANALZ,1)
45 KFLAG = 0
END
SUBROUTINE ZERO(AST,ARAD,AE,AT,AWSPD,ND,BR,NBR)
C*****ZERO INITIALIZES SUMMATIONS USED IN CALCULATING AVERAGES
DIMENSION AST(6),ARAD(6,2),AE(5,2),AT(5,2),ND(8),BR(2)
DO 50 1=1,2
BR(I) = 0.0
DO 50 K=l,5
AE(K.I) = 0.0
AT(K,I) = 0.0
50 CONTINUE
AWSPD = 0.0
DO 55 K=l,8
ND(K) = 0
55 CONTINUE
DO 60 K=l,6
AST(K) = 0.0
ARAD(K,1) =0.0
ARAD(K,2) = 0.0
60 CONTINUE
NBR = 0
RETURN
END
SUBROUTINE FIND(VMARK)
C*****FIND turns SELECTOR VALVE ONE PORT AND RETURNS MARK VOLTAGE
DO 65 K=l,10
CALL EXEC(1,9,DATA,2,19,4043B)
CALL EXEC(1,9,DATA,2,0,4043B)
CALL EXEC(12,0,2,0,-2)
CALL EXEC(1,9,DATA,2,110,4045B)
VMARK = CONV(DATA)
IF(VMARK .GT. 6.0)RETURN
65 CONTINUE
WRITE(6,70)
70 FORMAT(IX,"NO MARK VOLTAGE. CHECK PANEL PLUGS AND POWER TO BOX.")
STOP 0001
END
ENDS


E (LY/min) H (LY/min)
206
Oct. 23, 198!
Figure 12. Data and ET Estimates for Oct. 23, 1981. See p. 185
for brief explanation of individual graphs.


24
The expressions for latent and sensible heat flux that are commonly
used are simplified versions of Eqs. 2-14 and 2-15. For sensible heat
flux from the surface to a reference level above the surface, the inte
gral expression is abbreviated either as a bulk thermal conductivity or
as a bulk air resistance:
pCo(Ts V
H = pc K(T T ) = L s 2-16
p s a ra
where T is the surface temperature,
Ta is the air temperature at a reference level above the surface,
Ka is the bulk thermal conductivity for the slab of air between
the surface and the reference level, and
r is the bulk resistance to heat transport of the slab of air
a between the surface and the reference level.
In this study, the sensible heat flux expression is condensed even fur
ther to
H = h(T T ) 2-17
b a
where h is referred to as the bulk heat transport coefficient. Since the
fundamental definition of h is
PCn
h = 2-18
la dz
use of a wind model (to evaluate K^) is implied any time the bulk heat
transport coefficient or bulk air resistance is used (Monteith, 1973,
1975; Thom and Oliver, 1977).
Applying the similarity concept to a description of latent heat
flux is complicated because it is impossible to measure the vapor pres
sure at the vegetation surface. The air inside the leaves is usually
assumed to be at the saturation vapor pressure corresponding to the sur-
face temperature [e$ = e (Tg)]. A unitless parameter M, which varies


156
PROF
R
RATM
RCOEF
RH(5)
RHO
RNET
RSTM
RTOT
SFLX
SUM(5)
SVAL
.SWIO
TBASE
TOT
TST
TSURF
UH
UE
VCE(5)
VCR(6)
VCT (5)
VMARK
W
ZO
ZNGL
Number of profiles collected in last half-hour period
(floating point NPROF)
Average correlation coefficient of profiles collected in
last half hour
Atmospheric diffusion resistance (s/m)
Correlation coefficient of half-hour average profiles
Relative humidity for 5 levels (%)
3
Air density (g/cm )
Half-hour average net radiation (ly/min)
Bulk stomatal diffusion resistance (s/m)
Total resistance to vapor pressure transport (s/m)
Half-hour average soil heat flux (ly/min)
Regression summations in RATIO and PROFT
Weighted average returned by subroutine TMTCH
Intensity of solar shortwave radiationwithout atmosphere
Air temperature at lowest level (1) on profile measurement mast
Used to sum good readings in subroutine FILT
True solar time
Half-hour average surface temperature (C)
Friction velocity calculated from the temperature profile
(m/min)
Friction velocity calculated from the vapor pressure pro
file (m/min)
Variation coefficient for vapor pressure at 5 levels (%)
Variation coefficient for readings in RAD (%)
Variation coefficient for temperature at 5 levels (%)
Mark voltage from scanning valve (0 or 12 volts)
Voltage from wind direction sensor (between 0-10 volts)
Roughness height (cm)
Zenith angle of the sun (degrees)


15
the concepts and simplifications conventionally applied in evapotranspi-
ration theory.
The heat energy stored in the plant canopy is represented by its
temperature (T ). The bulk of this energy comes into the vegetation in
the form of direct or scattered solar short wavelength (0.3 to 3 pm)
radiation (Qs); it also intercepts thermal or long wavelength (3 to
50 pm) radiation emitted by the atmosphere (Q ). A substantial fraction
G
of the shortwave radiation received by the surface is reflected (Qr), a
very small part is used to drive photosynthetic reactions in the plants,
and the remainder becomes heat energy absorbed and stored temporarily in
the biomass. Part of this energy is reradiated to the atmosphere (Qg).
The difference between the downwelling radiation (direct and atmo
spheric) and.the upwelling radiation (reflected and emitted) is referred
to as net radiation (R).
Besides these radiant energy fluxes, the vegetation exchanges en
ergy with its environment in several other ways. Thermal energy ex
changed with the air by the process of molecular conduction and turbu
lent diffusion is referred to as sensible heat flux (H); energy ex
changed with the soil is soil heat flux (G). Energy used in the change
of state from water to water vapor is transported with water vapor and
is referred to as latent heat flux (E).
In this generalized view of the surface system, the plant canopy is
considered to have a uniform temperature representative of its heat con
tent. There are complex energy exchange processes that occur within the
canopy because of differences in temperature. For example, radiation is
exchanged between plant surfaces, and sensible heat released from one
leaf may be reabsorbed and released from another as latent heat.


177
Day
Time
Net
Soi 1
- Sens
Lat
Wind
Air
Surf
Vap
Prof
Rad
Heat
Heat
Heat
Temp
Temp
Pres
Corr
Flux
Flux
Flux
EDT
LY/M
LY/M
LY/M
LY/M
M/S
C
C
MB
312
1030
0.51
0.02

_
2.23
20.1
26.5
-.491
1100
0.58
0.03


1.86
20.7
27.7

.520
1130
0.62
0.03
0.35
0.24
2.22
21.5
30.2
12.1
.999
1200
0.64
0.03
0.36
0.25
2.86
21.9
31.4
11.9
.998
1230
0.64
0.03
0.36
0.25
2.87
22.5
32.2
11.9
.999
1300
0.62
0.03
0.35
0.25
2.80
23.0
32.4
12.2
.996
1330
0.59
0.02
0.32
0.25
2.94
23.5
31.7
11.7
.994
1400
0.53
0.02
0.21
0.29
2.46
23.8
31.2
11.1
.904
1430
0.46
0.01
0.24
0.20
2.33
24.1
23.9
11.9
.991
1500
0.36
0.01
0.19
0.17
2.47
24.3
28.6
12.4
.989
1530
0.27
0.01
0.13
0.13
2.17
24.4
27.0
12.0
.981
1600
0.15
0.01
0.06
0.09
1.66
24.2
24.9
11.8
.969
1630
0.03
0.00


0.83
23.8
22.1
12.3
.300


72
The quantity used in calculations is (R G), which for convenience can
be written
R G = (1 g)R = fR 4-24
Typical daytime values of "g" in the literature range from approximately
0.0 to 0.2, so for a vegetated surface "f" will have values between 1.0
and 0.8.
Substituting Eq. 4-24 into Eq. 4-11,
Ts Ta hOCTT)'^ hM5ea>
Formalizing the approximation of system stationarity,
4-25
h, M, f, s, Se, f f(t) 4-26
a
Eq. 4-25 reduces to the form
T, T = AR B
s a
where A and B are constants:
a = ri_ '
h(Ms + y) and
4-27
4-28
M6e
B =
4-29
(Ms + y) ,
and the parameter values are averages for the time period over which the
surface system is considered stationary. The constants A and B can be
evaluated by correlating the temperature differences (T T ) and net
radiation (R) data. Simple linear regression equations can be used:
E R.AT. nRAT
A = and 4-30
? 2
E (Rt) nR
B = AT AR 4-31
where the summations are done with clear sky data only,
AT = (T T ), and
b a
t is a subscript denoting the time of the measurement.


ESTIMATED ET (LY/min) BOWEN RATIO
Figure 12. (cont.)


E(LY/min) H(LY/min)
201
e*-ea (MB)
Oct. 22,1981
Figure 11. Data and ET Estimates for Oct. 22, 1981. See p. 185 for
brief explanation of individual graphs.


ACKNOWLEDGMENTS
The work reported in this dissertation grew out of National Aero
nautics and Space Administration (NASA) sponsored water resources re
search. It was primarily supported by a grant from the Office of Water
Resources Technology in the U.S. Department of the Interior and Agri
culture and Resources Inventory Surveys Through Aerospace Remote Sens
ing (AgRISTARS) program funds administered through the U.S. Department
of Agriculture (USDA). Some support was also received in the form of an
assistantship from the Agronomy Department at the University of
Florida. All these sources of support.are gratefully acknowledged.
I would especially like to thank Dr. Wayne C. Huber and Dr. L.
Hartwell Allen, Jr. for signing the original research proposal as prin
ciple investigators and seeing this project through to its completion.
Without their initial confidence in me and the day-to-day administra
tive efforts of Dr. Allen none of the work would have been possible. I
would also like to thank them and the rest of my supervisory committee,
Dr. Howard T. Odum, Dr. Ralph W. Swain, and Dr. James P. Heaney for
improvements they made possible with their comments on the manuscript.
The research reported in this dissertation stretched over four
years and required the help and cooperation of many people. Sensors and
other equipment were borrowed from USDA, NASA, Center for Wetlands,
Fruit Crops Department, and Environmental Engineering Sciences Depart
ment of the University of Florida. The Animal Science Department per
mitted ET measurements in part of one of its pastures and the Agronomy


Mixing
Chambers
Analyzer Sample
Flowmeter
Styrofoam Insulation
1/4" Plywood
Figure 3-4. Detail of Air Sampling Equipment.
-Valve Control Electronics
Sampling Valve
Air to Analyzer
Air to Pump
5 Sample
Tubes from
Mast
Polypropylene
Foam Rubber
Insulation
Heater Cable
Tubing
Bundle
CT
o


Department provided space for an instrument room. The people I owe spe
cial thanks to are Bill Ocumpaugh and Fred McGraw for patiently working
around the measurement equipment and giving up some space; Johnny
Weldon for allowing me the use of the Agricultural Engineering Depart
ment machine shop; Jim Hales for use of his tools and advice in fabri
cating apparatus in the machine shop; Mark Lester for his fine machin
ing; my brother Stephan Heimburg for conscientiously checking and ad
justing the thermopile time constants; Mike Baker for designing and
helping build the scanning valve control electronics, and repairing the
dewpoint analyzer after a lightning strike; Wayne Wynn for help in
maintaining the measurement system; Dan Ekdahl at the Digital Design
Facility for electronics repairsespecially a lightning-damaged compu
ter-controlled voltmeter and similarly damaged computer interface
boards; and finally, Beth Chandler for expeditiously inking most of the
figures in this dissertation.
I also wish to thank Dr. Tom R. Sinclair for finally revealing why
Real Scientists don't do micrometeorology in a neat five-minute sermon-
ette.
I owe a debt of gratitude beyond words to three people who went
miles out of their way to help me. Gene Hannah was invaluable in the
original field installation and helped with problems throughout the
course of the project. I'm thankful to Ferris Johnson for his tireless
assistance in use of the computer system and trouble-shooting computer
hardware problems. Finally, I enthusiastically acknowledge the work of
Pattie Everett, who spared no effort and sacrificed evenings, weekends
and holidays in moving this manuscript through countless drafts toward
perfection.


106
Figure 5-10. Effect of Moisture Availability and Vapor Pressure Param
eters on Temperature Gradients. The solid straight lines
represent the temperature gradient response that would be
observed if all parameters remained constant at their av
erage value. They represent the same temperature gradients;
they have been offset to show the pattern of variations.