Knowledge system for determining soil water status using sensor feedback


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Knowledge system for determining soil water status using sensor feedback
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Thomson, Steven James, 1957-
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Table of Contents
    Title Page
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    Table of Contents
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    Chapter 1. Introduction
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    Chapter 2. Soil-water-plant relationships
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    Chapter 3. Knowledge-based system for irrigation management--development criteria for design
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    Chapter 4. Procedures for measuring evapotranspiration, soil water suction, and weather variables for peanuts
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    Chapter 5. Soil water sensor responses to wetting and drying
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    Chapter 6. Knowledge-based system for irrigation management--development and testing
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    Chapter 7. Summary, conclusions, and suggestions for future study
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    Appendix A. Computer program to read load cell output and excitation voltages for calibration
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    Appendix B. Computer program to reduce load cell data for calibration
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    Appendix C. Computer program to extract and sort load cell data for spreadsheet analysis
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    Appendix D. Programs and files used in knowledge based system
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    Appendix E. "PSTART", knowledge base driver
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    Appendix F. "FIELDRAW", program to input data and modify weather file
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    Appendix G. Spreadsheet macros for data manipulation
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    Appendix H. "DATRUL_1", knowledge base for sensor evaluation
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    Appendix I. "SENPOS", parameter adjustment and irrigation scheduling program
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    Biographical sketch
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Full Text







Copyright 1990


Steven James Thomson


I would like to thank my committee chairman, Dr. Robert

Peart, for his encouragement, enthusiasm and willingness to

exchange ideas any time, and Dr. Wayne Mishoe for his

resolve and encouragement towards getting this broad-scoped

project done. I would like to thank the rest of my

committee, Drs. Dorota Haman, Allen Smajstrla, and Doug

Dankel for their expertise and constant willingness to help.

Drs. Ken Boote and Jim Stansell deserve thanks for

giving me the advice to plant peanuts and Dr. Gerry Isaacs

deserves thanks for his upbeat encouragement throughout my

stay here at Florida. I also thank the executors of the

USDA National Needs Fellowship Program for financial support

during my stay at the University of Florida.

My friends and fellow graduate students have all made

this an "interesting" stay. I give special thanks to my

parents for their encouragement during our infrequent

visits. Finally, I would like to thank my wife, Debra, for

her unfailing support, encouragement and love throughout our

stay at the University of Florida, and my step-son, Eric,

for not letting me take myself too seriously.



ACKNOWLEDGEMENTS ........ ................... iii

ABSTRACT .......... ....................... vii


I. INTRODUCTION ........ ................... 1

Problem Statement ...... .. ............... 1
Research Objective ........ ............... 6
Synopsis of Research ....... .............. 7


Introduction ........................ 12
Soil-Water Relationships ... ............ 12
Soil Water Content ... ............ 13
Field measurement of soil water content 14
Soil Water Potential .. ........... 20
Field measurement of soil water potential 25
Soil Moisture Characteristic Curve . . 41
Soil Water Uptake, Transpiration, and Evaporation 42
Water Uptake by Roots and Plant Transpiration 43
Evapotranspiration Models .. ......... 49
Bowen ratio .... ............. .. 52
Combination formulas for modeling
evapotranspiration ... .......... 55
Plant and Soil Factors Limiting
Evapotranspiration ... ............ 64
Resistance methods ... .......... 65
Crop coefficient curves ....... .. 67
Models that separate evaporation
and transpiration .. .......... 69
Summary ....... .................... 73

FOR DESIGN ........ ................... 79

Introduction ....... .................. 79
Knowledge-Based System--Development Criteria . 82
Literature Review ..... ............... .. 84
Crop Growth Simulation Models ........ .. 84
Knowledge-Based Systems ... .......... 94
Knowledge-Based Syste:n--Design .. ......... 99
Summary ........ .................... 102


Introduction ....... .................. 106
Objectives ....... ................... 107
Lysimeter Installation .... ............. 107
Lysimeter Calibration ... ........... 109
Experimental Procedures .... ............ 110
Peanut Management ...... ............. 110
Soil Water Suction Measurement ... ...... 111
Temperature Measurement ... .......... 112
Load Cell and Temperature Data Acquisition 113
Weather Data Acquisition .. ......... 117
Results and Discussion .... ............. 118
Evapotranspiration Data ... .......... 118
Soil Water Sensor Data ... .......... 120
Summary ........ .................... 122

WETTING AND DRYING ..... ............... ..147

Introduction ....... .................. 147
Literature Review ..... ............... 147
Objectives ...... ................... 149
Experimental Procedures ... ............ 149
Sensor Response to Wetting .. ........ 149
Sensor Response To Drying .. ......... ..151
Soil moisture characteristic curve . 154
Results and Discussion .... ............. 154
Sensor Response to Wetting .. ........ 154
Sensor Response to Drying .. ........ 155
Summary ........ .................... 157


Introduction ....... .................. 169
Knowledge-Based System--Overview .. ........ 169
Development Procedures .... ............. 175
Expert System for Sensor Evaluation . . 175
Data Input, Calculation, and Output Routines 184
Irrigation Scheduling Routines ...... 188
Parameter Adjustment Routines ...... 191
Modification of soil characteristics 194
Root weighting factors .. ........ ..200
Evapotranspiration routine modifications207
Evaluations Using Field Data ... .......... 207
Soil Characteristic and Root Distribution
Modifications ..... ............... ..208
Evapotranspiration Routine Modifications 213
Summary ........ .................... 215

FOR FUTURE STUDY ...... ................ 239
Summary ........ .................... 239
Field Study ...... ................ 240
Expert System for Sensor Evaluation ... 240
Parameter Adjustment Routines .......... 241
System Evaluations Using Field Data ... 241
Future Improvements to Evaluations and System
Components ....... ................... 242
Field Study ...... ................ 242
Expert System for Sensor Evaluation .... 243
Parameter Adjustment Routines ........ ..244
Programmed System .... ............. ..245
Conclusions .................. 247
Suggestions for Future Study ... .......... 248

REFERENCES ......... ...................... 252


DATA FOR CALIBRATION ..... ............... 264


BASED SYSTEM ........ ................... 271


MODIFY WEATHER FILE ...... ............... 275


SENSOR EVALUATION ...... ................ 288


BIOGRAPHICAL SKETCH ....... .................. 326

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



Steven James Thomson

May, 1990

Chairman: Robert M. Peart
Cochairman: J. Wayne Mishoe
Major Department: Agricultural Engineering

A knowledge-based system was developed to

automatically calibrate a crop model for irrigation

scheduling using system interpreted sensor readings. The

system also evaluates a sensor's suitability as a feedback

element for model calibration. Parameters in the root

development and water balance components of a crop growth

model are adjusted to provide a more accurate representation

of soil water status and distribution.

A knowledge system containing a sensor diagnostic was

developed to interpret sensor readings used as feedback to

the model. The system was coded with expert knowledge

regarding expected trends under wetting and drying. Sensor

readings judged to be valid adjusted appropriate parameters

in the crop model. The system informed the user of sensor

status and indicated corrective actions if readings

indicated improper placement, a faulty sensor, or out of

range conditions.

A field experiment was conducted with peanuts grown in

two weighing lysimeters. Soil water sensors were also

installed in the lysimeters. Crop water use measured at the

lysimeters was compared to sensor-based representations to

develop a knowledge base for parameter adjustment routines.

A peanut crop growth model (PNUTGRO) was chosen for

modification because it contains a user-oriented water

balance requiring minimum inputs and delineates water use

from specific soil zones.

The field data was also used to verify proper execution

of the parameter adjustment routines. Results indicated

that model-based representations of soil water status and

distribution converged on sensor-based representations in

four days split between two drying cycles.



Problem Statement

Farming systems require the efficient scheduling of

many operations. Farm managers strive to obtain maximum

output or economic return with a minimum input of labor and

energy. Irrigation is a major consumer of energy on the

farm and efficient water use is essential for energy and

resource conservation and for maximizing crop yield or

economic return. Irrigation scheduling is a particular

challenge in Florida because of the highly variable nature

of rainfall and soils with low water holding capacity.

These conditions provide a stringent test of any new

management strategy and have prompted much research into the

complex soil-water interactions. Simulations of water

movement under a trickle source (Armstrong and Wilson, 1983;

Zazueta et al., 1985) and under center pivot irrigation

systems (Clark and Smajstrla, 1983) have been developed to

gain a better understanding of soil water distribution under

different management practices. Numerical simulations of

water extraction patterns as a function of climate changes

and irrigation management (Stone, 1987) have also been



Many simulations of soil water movement and water use

by the crop have been simplified and incorporated into

simulation models that model growth of the entire plant

(Wilkerson et al., 1983; Jones et al., 1986; Boote et al.,

1989). Physiological processes are modeled along with the

water balance in specific soil zones. These models have

been used in the research environment to evaluate

irrigation, fertilization, pest control, weed control, and

disease control strategies on crop yield.

Boggess et al. (1983) analyzed many different

scheduling criteria used by irrigation managers to present a

detailed economic analysis. The soybean model developed by

Wilkerson et al. (1983) was used to evaluate the economic

impact of various management decisions. The authors

indicated that irrigation managers may have different

objectives and that maximum crop yield does not usually

coincide with maximum profit. Other management objectives

may also influence the final yield and return. For example,

an objective might be to minimize nitrate leaching. This

would influence the level of irrigation and, thus, the yield

and return.

Accurate determination of proper water application

amounts has been attempted using model- and sensor-based

approaches. All irrigation management objectives involve

replenishment of a finite regulation zone at the proper

time. Many model-based approaches use simplified forms of

the original Penman (1948) evapotranspiration (hereafter

called ET) model with accompanying soil water and root

distribution functions.

A crop model for peanuts (Boote et al., 1989) uses a

semi-empirical ET model that requires a minimum of weather

inputs. The model can be run using easily obtained weather

data and without potentially complicated and costly

instrumentation. Root distribution functions from empirical

studies are also included. Thus, soil water contents and

root length densities in specific soil zones can be modeled.

Accuracy of the water balance is limited by the fact that

empiricisms derived may not be universally applicable and

that differences between published and actual soil

characteristics can influence modeled results significantly.

Calibration of the model for the user's particular field

soil could improve estimates, but this requires detailed

soil analysis and still does not account for differences in

root distributions.

Soil water sensors have been used to help the farm

manager schedule irrigations. Soil water sensors read soil

water potential as a function of their resistance (i.e.

gypsum blocks) or directly as a suction value (tensio-

meters). Properly placed sensors can indicate water use in

specific soil zones and can be a great help in determining

precisely when to irrigate and how much water to apply.

Reliability problems and requirements to service

them have prevented many farm managers from using soil water

sensors, however.

In a farm manager's operation, the perception of

unreliability in a method (whether justified or not) may

cause him to abandon the idea in favor of making an educated

guess of when and how much water to apply. This can be a

wasteful practice. Although much work has been done to

promulgate use of soil water sensors, many farm managers

perceive that sensors do not work. However, even with more

reliable sensors being promoted (Larson, 1987), proper

interpretation of the readings is essential for proper

irrigation management. In its simplest form, this usually

involves use of a suction-time chart as described by Stolzy

et al. (1959) and Richards and Marsh (1961).

Interpretation becomes more complicated if water use

and the effects of irrigation are to be delineated in

specific soil zones. This level of interpretation would be

required, for example, if sensors at the bottom of the root

zone did not show a decrease in suction after irrigation.

In that case, the amount of irrigation would be increased on

the next cycle.

A knowledge-based system could provide interpretation

of sensor readings throughout the season. The knowledge

system concept is ideally suited to sensor-based scheduling

because all decisions made regarding use and interpretation

of sensor readings involves experience. For many years,


extension publications have sought to provide the farm

manager with information on the use of sensor readings to

schedule irrigations (Fischbach and Schleusener, 1961;

Smajstrla et al., 1982). To remove the need for a manager to

interpret sensor readings, he could simply enter daily

sensor readings to a knowledge base that contains the

experience of extension personnel, other farm managers, and

researchers. A complete knowledge base would include a

person's experience with many types of sensors and many

types of soils and crops. The knowledge system could

interpret sensor readings and make irrigation

recommendations. The system could also flag certain sensors

that are giving questionable readings and recommend action

be taken to correct the problem. Interactions with the user

should be very clear and informative if the user is to

accept it as a scheduling approach.

Model-based approaches to irrigation scheduling also

require a user-friendly approach so that the farm manager

can keep track of all relevant field variables. With this

in mind, Heerman et al. (1985) developed a large scale

irrigation management system to schedule several center

pivots in the Great Plains. This system used an empirically

based water balance to recommend irrigation timing and

amount of water to apply. Although water use in specific

soil zones was not delineated on a per-system basis,


management of several large pivots could be achieved and

effectively scheduled.

In summary, neither model- nor sensor-based approaches

to irrigation scheduling (by themselves) have achieved

widespread acceptance because of the time and labor involved

to properly utilize them. Model-based approaches suffer an

additional problem of requiring extensive field


Research Objective

For this study, an integrated system is proposed which

combines the sensor- and model-based approaches used in

irrigation scheduling. Models of evapotranspiration, soil

water and root distribution, and infiltration combined with

a knowledge-based method of providing water status feedback

is proposed. Properly interpreted sensor readings will

adjust model input parameters and process equations that

influence ET, soil characteristics, and root development.

Thus, sensors will automatically calibrate model components

as the season progresses. The strategy will reduce a labor

intensive aspect of sensor-based scheduling by providing

interpretation of sensor readings at all stages of the

crop's development.

Expert knowledge regarding interpretation of sensor

readings used as feedback to the model will be a key element

of the system. Sensors will be read and the system will

judge the suitability of and interpret the readings. This


will remove the need for interpretation by experienced field

personnel since procedures to make a decision will already

be coded into a knowledge base. The system will also

determine where in the soil zone water use is taking place.

Thus, irrigation can be adjusted to fully or partially

refill only the active root zone.

The overall objective of this study is to develop an

irrigation scheduler that uses sensor information in a

feedback mode to perform parameter or equation adjustments

to a composite model of crop water use, soil water re-

distribution and root distribution.

Synopsis of Research

This study is organized into seven chapters. A

detailed review of previous work and derivation of the basic

equations used in modeling crop water use are presented

first. A detailed presentation of the problem, experimental

procedures, results, conclusions, and suggestions for future

study follow.

Chapter II presents basic soil-water relationships and

presents a detailed background of sensor-based approaches

used to delineate water use in specific soil zones. The

Penman combination formula, which models evaporation and

water use in the soil-plant system, is derived from basic

principles of mass and energy transfer.

In Chapter III, past and present work with crop growth

models is presented. The review of crop growth models


extends the concepts presented in Chapter II by presenting

root growth and soil water distribution functions. A

graphical example of modeled water use in specific soil

zones using the concepts presented by these models is

presented. The role of soil water sensors in delineating

water use in specific soil zones is presented and compared

to the model-based approaches. Previous work detailing

knowledge-based simulations for on-farm crop management are

presented. Justification for a knowledge-based approach to

couple model- and sensor-based methods for irrigation

scheduling is also presented.

Chapter IV details experimental procedures for growing

peanuts in two weighing lysimeters. These lysimeters

present a detailed picture of crop water use for comparison

to sensor-based results. Data obtained are used to develop

a knowledge base for model parameter adjustments and to

verify proper operation of the resulting knowledge system.

The data acquisition system is described and a step-wise

progression of the data acquisition program is presented.

Preliminary analyses of the field data are presented and

possible reasons for differences between actual and modeled

water use are presented.

In Chapter V, results of a laboratory test to determine

the response time of a soil water sensor to wetting and

drying are presented. This test confirmed that the soil


water sensor chosen for the study responded fast enough to

wetting and drying to be used on a daily basis.

Chapter VI details construction of the knowledge-based

system for irrigation management from lysimeter field

experiments detailed in Chapter IV. Flow between the

knowledge bases and calculation programs is detailed using a

block diagram. An expert system for sensor evaluation, data

input and output routines (including user interfaces),

irrigation scheduling routines, and parameter adjustment

routines are detailed. Verifications of program operation

are illustrated using field data and were run in an

interactive mode as a user would. Tests showed that

parameter adjustments dictated by sensor feedback caused

modeled soil water status to converge on sensor-based

representations of soil water status.

Chapter VII presents a summary of procedures and

results of the lysimeter field study, construction of the

expert system for sensor evaluation, parameter adjustment

routines, and system evaluations using the field data.

Suggestions for future improvements to each of these

components are discussed. Recommendations for future

development include the system's use in yield studies and

the economic impact of irrigation decisions.

In addition to the seven chapters, there are nine

appendices. Appendix A is a program listing in BASIC of

load cell calibration routines for the lysimeters. Appendix

B lists BASIC computer programs to further sort load cell

data for easy import to a spreadsheet to derive calibration

curves. Appendix C lists BASIC computer programs to sort

load cell readings for spreadsheet analysis of the

experimental data. These data were taken by the program

listed in Figure 4-7 of Chapter IV. Appendix D lists all of

the files used in the knowledge-based system and indicates

where they are located. Appendix E lists a program written

in the rule development language to provide the user with an

initial screen and call data input routines. Appendix F

lists a Pascal program that allows the user to input soil

water sensor and weather data. The input weather file used

in the crop model is modified with this weather data.

Appendix G lists spreadsheet macros used to move data

between components of the knowledge system. Appendix H

lists a knowledge base for sensor evaluation written in the

rule development language. Calculation and parameter

adjustment routines and irrigation scheduling routines are

listed in Appendix I. Rules based on trends observed in

lysimeter data are incorporated in some of the procedures

listed in Appendix I to perform the crop model parameter

adjustments and determine irrigation adjustments.

In summary, specific procedures to be accomplished in

this study are:

1. to develop a user-oriented knowledge-based system
that determines the validity of and properly
interprets field sensor readings used as feedback


2. to perform a field study in which crop ET is measured
and soil water sensors are read for construction of
model adjustment routines,

3. to utilize a crop growth model that contains a user-
oriented water balance and delineates water use in
specific soil zones that sensors are placed,

4. to identify parameters and processes of the model to
adjust based on data collected in Objective 2 and
develop a knowledge base to adjust the model,

5. to develop irrigation scheduling routines that use
model outputs of soil water content in specific soil
zones and weather forecasting, and

6. to verify model adjustments with field data collected
in Objective 2 to assure that the model is properly
representing soil moisture in the zone of water



In the discussion following, basic soil-water

relationships and sensor-based approaches to measuring soil

water content (8) in layers of the rooting zone are

delineated. Evapotranspiration and root development models

are then discussed as they relate to soil water depletion in

layers of the root zone.

Soil-Water Relationshios

The amount of water contained in the soil and the

energy state of that water are important factors affecting

the growth of plants. Numerous physical properties of the

soil depend on the soil water content. Changes in water

content affect the respiration of roots, activity of micro-

organisms, and the chemical state of the soil. The energy

state of water in the soil is characterized by soil water

potential. Of the many components comprising total soil

water potential, the pressure or matric potential is of main

interest in this study because it characterizes the

persistence with which the soil water is held by the soil

matrix. Matric potential is a measure of the amount of

energy the plant :%ust exert to absorb that water. Soil

water content and matric potential are functionally related



to each other, and the graphical representation of this

relationship is termed the soil-moisture characteristic


Soil Water Content

The wettest possible condition of the soil is that of

saturation, where all of the soil pores are filled with

water. Hillel (1971) indicated, however, that it is very

difficult to obtain complete saturation owing to the

entrapment of air in soil pores. The driest condition of

the soil encountered in nature is air-dryness or, in the

laboratory, an arbitrary state known as "oven-dry" where the

soil is dried in an oven at 1050C for 24 hr (Hillel, 1982).

The 24-hr period has been judged a sufficient amount of time

after which measurable changes in mass water content no

longer occur.

The proportion of water in the soil can be expressed as

either a mass or volume ratio. The mass ratio is given by

w = Mw/MS (2-1)


w = the mass ratio of water mass, Mw,
to dry soil mass, Ms.

Soil water content can also be expressed in terms of a

volume ratio and is given by

0 = Vw/Vt



a = the volume ratio of water volume, Vw, to total
(bulk) soil volume, Vt.

The bulk soil volume Vt is the sum of the volumes of solids

(Vs), water (Vw), and air (Va). Equations (2-1) and (2-2)

can be related to each other by means of the bulk density,

Pb and the density of water, pw.

) = w (Pb/Pw) (2-3)

The above relationship is straightforward for non-swelling

soils where the bulk density is constant regardless of water

content, but it can be troublesome with swelling soils since

the bulk density is a function of mass wetness (water con-

tent). A value for soil water saturation is also difficult

to define with swelling soils because such soils may con-

tinue to adsorb water and swell after all the pores have

been filled with water.

Field measurement of soil water content

There are many methods used to measure soil water

content either directly or indirectly. A standard method of

directly measuring soil water content involves removing a

sample of soil by augering and determining both its moist

and dry masses. This method is called the gravimetric

method of soil sampling. The mass of wet soil is determined

by weighing the soil sample at the time of sampling. The

dry mass is determined by drying the sample to a constant

mass in an oven set at 105 C for 24 hr. The soil water

content on a mass basis is described by

w = (wet mass) (dry mass) (2-4)
dry mass

An alternative method of drying is to impregnate the soil

sample in a heat resistant container with alcohol. The

alcohol is then burned off, vaporizing the water (Hillel,

1980). This method is much faster than oven drying and

allows field personnel to obtain dry weights quickly.

A disadvantage of using the gravimetric method is that it is

destructive and may disturb an experimental plot enough to

distort results.

Neutron scattering. The need for indirect methods of

obtaining water content in soil is apparent when time and

labor involved in gravimetric sampling are considered. The

neutron scattering method allows rapid instantaneous

indications of soil water content and has been reported on

by many investigators over the last 30 years (Stolzy et al.,

1959; Hillel, 1982; Smajstrla and Harrison, 1984; Cassel,

1984). This method of measurement is non-destructive,

practically independent of temperature and pressure, and

allows repeatable measurements of the volumetric water

content in a representative volume of soil (at the same


Neutrons are emitted from a radiation source attached

to a probe which is lowered into the ground through an


access tube. The access tube serves to maintain the hole

into which the probe is inserted and standardize measuring

conditions. Hydrogen nuclei react with fast-moving neutrons

emitted and cause them to lose energy. The number of

resulting slower neutrons are then detected by a detector on

the same probe and counted by a scaler or ratemeter that

monitors the flux of slow neutrons scattered by the soil.

A neutron meter measures soil water content in a

spherical volume of soil around the detector. This "sphere

of influence" varies with a radius of less than 10 cm in a

wet soil to 25 cm or more in a dry soil. (In a dry soil,

the cloud of slow neutrons is less dense and extend farther

from the source.) The relatively large soil volume

monitored can be an advantage in water balance studies since

this volume may be more representative of the field soil

than the small samples taken for gravimetric measurement of

soil moisture.

Neutron probes are attractive for measuring field

moisture conditions for irrigation scheduling on a short

term (hourly) basis since their readings give a rapid

indication of soil moisture. However, the low and variable

degree of spatial resolution makes the neutron moisture

meter unsuitable for the detection of moisture profile

discontinuities (wetting fronts or the boundaries between

distinct layers of soil). Also, accurate measurements near


the surface are hindered because of the escape of fast

neutrons through the surface.

Neutron measuring equipment requires extensive

calibration for the particular soil or group of soils. Even

though most of the hydrogen in mineral soil is associated

with water, there is sometimes a significant enough amount

of hydrogen to warrant calibration of the probe in each

specific soil type it is used. Once a calibration curve has

been developed, however, the meter is easy to use with only

a small expenditure of time at a specific field site.

Gamma-ray attenuation. The gamma-ray attenuation

technique measures the bulk density of the soil matrix or

can be used to determine volumetric water content. If soil

bulk density is known, this technique can measure the water

content of a fixed soil volume. Thus, it has the advantage

over the neutron method where the volume of soil over which

soil water content is measured varies according to the soil

water content. By using the gamma-ray technique, instan-

taneous readings of soil water content can be taken. Ferraz

and Mansell (1979) present a detailed description of theory

and implementation of gamma-ray attenuation methods. Gamma-

ray instruments measure the amount of gamma radiation lost

as a narrow radiation beam is directed through the soil.

Gamma rays lose part of their energy upon striking

water present in the soil. As the volume of water in the

soil changes, the amount of energy lost also changes.


The fraction (dI/I) of gamma rays attenuated is

directly proportional to the thickness of the material, x,

where a proportionality constant, k, is referred to as the

linear attenuation coefficient.

dI/I = -kdx (2-5)

Attenuation coefficients may also be expressed as a mass

attenuation coefficient, g. The mass attenuation

coefficient equals the linear coefficient, k, divided by the

density, p. This coefficient depends upon the chemical

properties of the material. After a collimated beam of

single-energy gamma photons has passed through the material,

measurements of the attenuated radiation permit calculation

of the density of that material. The Lambert-Beer equation

(the integral form of equation 2-5) can be used to calculate

the resulting intensity (number of photons/cm2 sec) after

the beam has passed through the material

I = I. exp [-gpx] (2-6)


I0 = the intensity of the collimated beam and

p = the density (g/cm3) of the homogeneous material.

When dealing with a heterogeneous material such as

soil, components of equation (2-6) in the bracketed term [

include those of the soil, water, and air. The term


involving air is insignificant compared to those of soil and

water and if it is neglected, the equation is

I = ID exp [-gspsxs AwPwXw] (2-7)

where the subscript values s and w correspond to character-

istics for soil and water, respectively. Variables xs and

xw are equivalent thicknesses of the soil and water respect-

ively. Equation (2-7) can be further simplified since the

product of ps (particle density for soil) and x. is the same

as the product of Pb (soil bulk density) and x, the

thickness of the soil sample. Also, Xw, the equivalent

water thickness equals the product of 8, the volumetric

water content, and x. Using these relationships, equation

(2-7) becomes

I = I. exp [-x(Aspb + Awe)] (2-8)

Equation (2-8) describes attenuation of a collimated beam

through the soil as a function of the combined effects of

the bulk density and volumetric water content of the soil.

If the bulk density is known, equation (2-8) can be re-

arranged so 0 can be found if the transmitted intensity, I,,,

is known and the resulting intensity I is measured with a

gamma-ray instrument. If the soil is dry or the value of e

has been determined by gravimetric means, the soil bulk

density, Pb, can be found.

The gamma-ray instrument commonly used to measure soil

moisture in situ consists of two spatially separated probes

which are inserted in parallel access tubes. One probe, the

source, contains a pellet of radioactive cesium (137Cs

emitting gamma radiation with an energy of 0.661 MeV). The

other probe, the detector, consists of a scintillation

counter and amplifier. The instrument readout indicates the

number of counts in a specified period. This technique

permits much better resolution of soil moisture profiles

than the neutron moisture meter. The moisture meter can

focus a narrow beam to study soil profiles as small as 1 cm

thick permitting detection of profile discontinuities such

as wetting fronts or boundaries between soil layers. Thus

water content distributions near the soil surface can also

be accurately measured.

Soil Water Potential

The potential energy of soil water is of particular

interest in relation to the plant environment because it

describes the amount of work the plant must expend to

extract water for its growth processes. Of the two

principal forms of energy, kinetic and potential, potential

energy is the one of significance since the movement of

water in an unsaturated soil is quite slow and considered

negligible. The potential energy of the soil water is due

to its position or internal condition and can vary over a

very wide range. Differences in potential energy of water

between one point and another cause water to flow within the
soil in the direction of decreasing potential energy. Soil

water, as with all parcels of matter, seeks a state of

equilibrium with its surroundings, definable as a condition

of uniform potential energy. Soil-water potential is a

criterion for this energy and expresses the potential energy

of the water in the soil about a standard reference state.

The standard state is usually that of pure free (unbound)

water at atmospheric pressure, at the same temperature as

the soil water, and at a constant elevation. The potential

gradient that describes the force acting on the soil water

is defined by -df/dx. The term -dp/dx describes the change

in energy potential with distance, x. The negative sign

denotes that movement will occur from a higher to lower

potential. The total water potential ft can be thought of

as the sum of many factors that cause its potential to

differ from that of pure water

Ot = 00 + 01 + f2 + 03 + h + 05 + (2-9)

0 = the pressure component due to air pressure and
mass of overlying water at soil surface,

= the matric component determined by water
adsorption and capillarity in the soil matrix,

2 the gravitational component determined by a
difference in elevation of soil water about an
arbitrary datum,

03 the solute component determined by differences in
solute concentrations across an air gap or semi-
permeable membrane such as a plant root,

04 the temperature component, determined by
temperature differences in the soil,

05 the overburden component, determined by the mass
of the overlying soil, and

06 the electrical component, determined by
electrostatic fields in the soil matrix.

Physically, the components of soil water potential are

usually expressed in one of three common ways. Hillel

(1982) listed these as

1. Energy per unit mass -- The dimensions of energy per

unit mass are (ML2T-2)(1/M) which reduce to L2T-2.

In the SI system, units are joules/kg.

2. Energy per unit volume -- The dimensions of energy

per unit volume are (ML2T-2)(l/L3) which reduce to

ML-IT-2. This can be expressed as an equivalent

pressure in SI units as dynes/cm2 or Nt/m2 (Pascals).

Energy per unit volume is also commonly expressed in

bars or atmospheres. This physical representation

can be used since water is nearly incompressible and

hence, its density is almost independent of pressure.

3. Energy per unit weight (hydraulic head) -- The

dimension on hydraulic head is L. Hydraulic head

defines the height of a liquid (water) that exerts a

pressure on the bottom of a column. In SI units,

this is represented by meters of water.

Hillel (1982) pointed out that not all the components

of potential act in the same way and their separate

gradients may not be equally effective in causing flow. The

osmotic potential, 03 becomes important whenever a membrane

or diffusion barrier is present (i.e., a plant root in

contact with the soil) that transmits water more readily

than salts. Osmotic pressure can be thought of as a suction

since water is drawn across the barrier into contact with

the solution. Thus solutes tend to lower the potential

energy of the soil water.

The component P4 reflects the influence of temperature

on soil water potential. Taylor and Ashcroft (1972) noted

that total potential is usually defined for isothermal

conditions and that the introduction of N has a marked

influence on water potential. Taylor et al. (1961) found

that at higher temperatures, water potential was higher at

constant water content. Conversely, at constant water

potential, less water was retained by the soil at high

temperatures. The authors found that temperature effects

were small in moist soils (at high water potentials). They

also found that temperature effects were more pronounced in

fine textured soils than in coarse textured soils.

The overburden component, 05, reflects the influence of

increasing bulk density on water potential. Box and Taylor

(1962) found that increasing soil bulk density resulted in

small increases in matric potential. The maximum change,

however, was about 7% in the range of conditions sampled and

depended on the moisture content and temperature of the soil


sample. Most differences in potential were much lower than

7% over most ranges of bulk density, temperature and water

contents. The electrical component, 06 is important if the

soil-water system is subject to electric fields that may be


The most important components of potential when temper-

ature and air pressure are constant are terms f0, fi, and

02- The sum of 00 and 01 is termed the water pressure or

suction component and is represented by

Op = (00 + 01) = pgh (2-10)


p = density of water,

g = acceleration of gravity, and

h = pressure or suction head.

The term h is pressure head in a saturated soil and suction

head in an unsaturated soil. Therefore, %p is zero or

positive for a saturated soil and negative for an unsat-

urated soil. The term 02 is the gravitational component

defined by

Og = 02 = pgz (2-11)

z = the vertical distance above or
below the reference plane z = 0.

Equation (2-9) can be simplified to include only the

pressure and gravitational head components yielding

= Op + 0g. (2-12)

Eliminating p and g from equations (2-10) and (2-11),

equation (2-12) can also be written as

H = h + z (2-13)

where H is the hydraulic head expressed in energy per unit

weight (cm of water).

Field measurement of soil water potential

Several methods have been used to measure soil water

potential in situ. In irrigation management, the objective

is to keep soil water potential in a range that is non-

stressful to the plant. Taylor and Ashcroft (1972)

presented upper limit suction values (lower limits of water

potential) for several crops based on experimental data

presented by several authors. Supplemental irrigation

should be applied before the soil dries to those suction

values. These upper limit suction values allow maximum

yields for crops grown in deep, well-drained soils that are

otherwise managed for maximum production. For field corn,

typical values range from about 50 kPa suction in the

vegetative stage to 800 kPa during ripening. This variance

indicates that the crop is more sensitive to water stress at

certain periods of growth. During these periods, soil water

suction should be kept at a low value by making sufficient

water available. The suction values illustrated for field

corn are in the range of values encountered for many crops.

Many of the commonly used methods for measuring soil water

potential and field observations associated with them are

described in the discussion following.

Tensiometers. A tensiometer consists of a porous cup

connected through a tube to a Bourdon tube vacuum gauge.

The porous cup is made of ceramic for its permeability to

water and structural strength. The ceramic cup is in

contact with the soil, and a partial vacuum is created as

water moves from the tube. The vacuum is a direct

indication of the energy that a plant would need to exert to

extract this water from the soil.

Many investigators have used tensiometers successfully

for scheduling irrigations and other water use evaluations.

Tensiometers are useful tools for managing irrigation in

sandy soils typical of Florida (Smajstrla et al., 1982;

Smajstrla and Harrison, 1984) because most crops are

irrigated in the range of potentials that can be read with

tensiometers. Some of the earliest field applications of

tensiometers were studied by Richards and Neal (1937).

Their study included evaluation of suction differences that

exist at different plots in a uniform soil, tests on the

effect of various crops or soil treatments on moisture in

adjacent soil plots, and tests on the usefulness of

tensiometers for studying the effect of mulches on soil

moisture. One set of data showed pronounced diurnal

fluctuations in soil water suction at shallow depths. The

authors attributed these fluctuations to re-wetting of the

profile by upward water flow that exceeded evaporation at


Russell et al. (1940) installed tensiometers at several

depths and lateral positions under corn to follow soil

moisture conditions throughout the growing season. The

authors observed that the zone of water absorption extended

laterally after water was initially depleted directly under

the corn plants. Later in the season, the lateral expansion

of the absorption zone occurred at successively lower

depths. Soil water suction readings gave an indication of

the major zones of water uptake and, thus, the distribution

of active roots.

Stolzy et al. (1959) used tensiometers at two soil

depths in several locations of a citrus orchard that was on

a standard irrigation schedule. The shallow depth (30 cm)

served as a guide for scheduling irrigations; the deeper one

(60 cm) was placed at the bottom of the zone of water

regulation and gave an indication of irrigation water

penetration. The authors used a suction-time graph to plot

the responses of the tensiometers over the set irrigation

schedule. At one tensiometer station, a lack of a drying

response was noticed with the deep tensiometer indicating a

nearly impermeable soil horizon beneath the 60 cm depth.

The authors surmised that saturated conditions caused the

roots to disappear, probably due to root rot fungi. Also,

the upper tensiometers indicated very high suction values

between irrigations, placing undue moisture stress on the

trees. Based on these observations, the authors suggested

reducing the amount of water applied per irrigation to

prevent saturation and spacing irrigations closer together

to ensure that the trees were not being stressed.

The idea of using a suction-time graph with tensio-

meters to schedule irrigations was extended by Richards and

Marsh (1961) and Taylor (1965). Richards and Marsh (1961)

recommended that soil suction records be taken at three

stations for any area that is to be irrigated as a unit.

They suggested placing the upper tensiometer in the zone of

maximum root density and the deep tensiometer such that 70

to 80 percent of the feeder roots were above that depth.

Taylor (1965) suggested that, for annual crops, additional

indicating devices be installed within the top 15 cm of soil

to indicate conditions during the seedling stage. The

readings could then be discounted when the crops were well

established. The author also suggested that irrigation be

adjusted so the deep tensiometer reads a final suction value

slightly higher than that corresponding to field capacity.

This would assure that deep percolation is negligible.


More recent studies utilized tensiometers fitted with

commercial pressure transducers to allow automated measure-

ment of soil water potentials. Thomson et al. (1982) used

this type of instrument to test a scheduling algorithm for

center pivot irrigation systems. The tensiometer/pressure

transducer combination provided stable readings up to the

useful tension limit of the tensiometer (about 80 kPa

suction) where the readings would level off. Diurnal

fluctuations in tensiometer readings due to soil water re-

distribution at night were also observed. The minimum and

maximum tension points occurred at almost identical times of

the day as those reported by Richards and Neal (1937). Long

(1982) used a pressure transducer that could be screwed

directly into the tensiometer and later described a data-

logging system for automatically measuring soil water

potential (Long, 1984). Stone et al. (1985) developed a

microcomputer-based data acquisition system that used

pressure transducers with built in signal amplifiers. A

main objective of their work was to field test the entire

system against manually read mercury manometers. The

authors found excellent agreement between potentials read

with the tensiometer/pressure transducer combination and

those read with the mercury manometers.

As has been stated previously, tensiometers are well

suited to schedule irrigations in Florida soils since the

suction levels used for scheduling are within the working

range of the tensiometer. Tensiometers would not be the

devices of choice when a plant is irrigated at a higher

suction value. A plant may be irrigated at a higher suction

value in a soil that has smaller particle sizes and whose

characteristic curve shows a more slowly increasing suction

value under periods of high evaporative demand. Sandy soils

reach high suction values much more rapidly because of their

low water holding capacities. Thus, most recommendations

are to irrigate at lower suction values in sandy soils

(Smajstrla et al., 1984) since small changes in soil water

content can cause large changes in water potential.

Depending on the method of irrigation, and under

conditions of high evaporative demand, the upper limit

suction level could be exceeded by the next irrigation cycle

if too high a suction value were chosen as the irrigation

trigger point. Lang and Gardner (1970) and Taylor and

Ashcroft (1972) also pointed out that if the atmosphere is

severely desiccating, plants can suffer from serious water

deficiency even at very low suction values. Under these

conditions, plants cannot extract water from the soil at a

rate sufficient to meet the evaporative demand.

Tensiometers do not record the water potential due to

dissolved salts since the ceramic cup is permeable to both

water and dissolved salts. In low saline soils, this

osmotic potential would not be a problem but would need to

be recorded using appropriate instrumentation if the soil


was saline. In that case, osmotic potential is a large part

of the total potential.

Electrical resistance devices. Direct measurement of

soil water could be greatly facilitated if electrical

resistance of a soil volume depended on the soil water

content alone. Simple resistance measurements would elim-

inate the need for the aforementioned methods of determining

water content. However, the electrical resistance of a soil

volume depends on its composition and soluble salt concen-

tration present as well as its water content.

The electrical resistance of a porous body placed in

the soil and left to equilibrate can be correlated with soil

water potential, however. Electrical resistance devices

that measure soil water potential use this principle. An

electrical resistance device consists of electrodes embedded

in a porous block or solidly packed porous material. Like

soil, the porous matrix has its own characteristic curve

that relates water potential to internal water content. The

electrical conductivity of moist porous material is due

primarily to the permeating fluid rather than the matrix

material. Thus, the electrolyte concentration of the fluid

as well as the water content both influence the electrical


One type of device uses gypsum as the porous material

in which the electrodes are embedded (Bouyoucos, 1961).

Gypsum maintains a nearly constant electrolyte concentration


corresponding to that of a concentrated solution of calcium

sulfate. This tends to buffer the effects of varying

concentrations of the soil solution such as those due to

fertilization or low levels of salinity. Since gypsum is

dissolvable, however, these blocks eventually deteriorate in

the soil. Thus, the relationship between soil water suction

and electrical resistance varies with time. This occurs

because dissolution of the gypsum changes the internal

porosity and pore-size distribution of the block and thus,

the block's characteristic curve. Gypsum has a character-

istic much like a very heavy clay. The pores are very small

and do not begin to lose water until about 30 cb. suction.

For sands typical to Florida, more than half of the water

available to the crop has already been depleted at this

suction level. Thus, gypsum blocks would not be the

instruments of choice for coarse soils typical of Florida.

Blocks made of inert materials such as nylon or

fiberglass have also been developed (Colman and Hendrix,

1949). These blocks have larger pore sizes making them more

responsive in the wet range of soil moisture. However,

these are highly sensitive to small variations in salinity

of the soil solution making them less appropriate for use in

irrigation scheduling.


Another electrical resistance type sensor that has been

developed in recent years is called the Watermark1 sensor.

This device consists of two concentric electrodes buried in

a matrix material that is held in place by a synthetic

membrane. As with the gypsum block, the sensor's resis-

tance varies with the amount and electrical conductivity of

the soil solution between the electrodes. The conductivity

is, in turn, related to the soil water potential by the

characteristic of the reference matrix. Pore sizes in this

matrix are larger than those of the gypsum block allowing

more sensitivity in the wet range of soil moisture

variation. The Watermark sensor uses a matrix material that

releases water at lower suctions (about 10cb.) up to about

200 cb. where readings begin to level off. This sensor,

therefore, works in the same range as tensiometers (and

higher) but does not require servicing. The Watermark

sensor also contains a material in the matrix mixture that

provides a standard reading base and neutralizes the effects

of soil salinity. The matrix material is said not to

dissolve (Larson, 1987), but small calibration shifts may

occur with time as the portion of the matrix mixture that is

reactive dissolves. As this occurs, the sensor's effective-

ness in neutralizing salts may also diminish.

iUse of tradenames in this dissertation does not
constitute endorsement by the author of the products named
nor criticism of ones not mentioned.

Gypsum blocks, fiberglass blocks, and Watermark sensors

require the same type of excitation to read them. Although

resistance ranges may be different in each one's working

range of operation, principles for reading all three are the

same. A low voltage alternating current (A.C.) is impressed

upon the sensor and an output voltage proportional to the

sensor's A.C. resistance can be obtained by one of many

methods. Some methods include placing a resistor in series

with the sensor and reading the voltage drop, using the

sensor in one leg of a bridge circuit, or using the sensor

in the feedback leg of an operational amplifier circuit

(Thomson and Armstrong, 1987). The method used should

guarantee enough output resolution over the working range of


Alternating current excitation is usually used to avoid

polarizing a resistance sensor since it can act as a

capacitor. A capacitor builds up and stores a charge and

thus does not conduct direct current after a very short

period. If a direct current (D.C.) voltage is impressed on

the sensor, it must be read after a very short period. A

way to obtain a value of sensor resistance using this

principle is to apply a D.C. pulse of very short duration

(Strangeways, 1983) and read the resulting voltage drop

across a resistor in series with the sensor.

The relationship for A.C. impedance, Z, of a resistance

type soil moisture sensor is given by

Z R + Xc (2-14)

Z = Impedance (ohms),

R = Resistance (ohms), and

Xc= Capacitive Reactance (ohms).

Capacitive reactance (Xc) is expressed as Xc = i/(2vfC)

where f is excitation frequency (hz) and C is capacitance

(farads). The dielectric properties of the matrix material

change as its moisture content changes. Thus, the

excitation frequency should be chosen so the capacitive

reactance is insignificant compared to its A.C. resistance

over the working range of the sensor.

The A.C. resistance for all resistance type sensors is

a temperature dependent function. For this reason, a

temperature correction must be applied to the resistance-

suction calibration curve for each type sensor. Cary (1981)

developed a temperature correction function for gypsum

blocks. The author presented an equation that corrects the

measured resistance to a 220C standard resistance. An

equation then calculates soil water potential using this

standard resistance. Storm et al. (1984) developed

temperature correction models for gypsum blocks with

parallel electrodes, gypsum blocks with concentric

electrodes, fiberglass resistance cells, and Watermark

sensors. Data was presented relating A.C. resistance to

temperature at a few values of moisture content, but the

relationship of moisture content vs. suction (the soil


moisture characteristic curve) was not presented for the

soil mixture used. Thus, the resistance-suction

relationship could not be inferred from the data presented.

Thomson and Armstrong (1987) presented a mathematical model

that related electrical resistance of the Watermark sensor

to soil water suction and temperature. Soil water

extraction equipment was used to perform the calibration at

several temperatures and suction values in the working range

of the sensor. Larson (1987) indicated that resistance of

the Watermark sensor varies about 1 % of per degree

fahrenheit (OF), or 1.8 % per degree celsius (C). Data

presented by Storm et al. (1984) and Thomson and Armstrong

(1987) suggest, however, that the sensor's resistance can

vary by as much as 2.6 % per C at some temperature ranges

and suctions.

Proper installation of resistance type sensors is

essential if they are to properly represent soil water

conditions in the soil zone. Bruce et al. (1980) suggest

that, in addition to installation procedures described by

sensor manufacturers, the soil be carefully tamped back in

the installation hole to a density slightly higher than

natural density. This should be done to prevent excess

water at the surface from freely running down the hole to

the blocks. The authors also suggest a slight mounding of

the soil surface as a further precaution.

Heat pulse matric potential sensors. Heat pulse

sensors measure the soil-water potential by the rate of heat

dissipation in a porous ceramic. The amount of water in the

ceramic block in equilibrium with soil water affects the

thermal conductivity and thus the temperature response for a

given amount of heat applied. A diode in the block changes

its resistance proportional to the temperature change

resulting from a heat pulse of known duration imposed by a

very small electric heater. Phene et al. (1973) developed a

sensor of this type in which the sensing diode was placed in

one leg of a wheatstone bridge circuit. The resulting

voltage change across the bridge gave an indication of soil

water potential by the amount of water in the ceramic block

in equilibrium with the soil water. The original sensor

used a temperature compensating diode of the same type in

the adjacent leg of the wheatstone bridge to account for

errors caused by temperature fluctuations in the soil.

Phene et al. (1981) described sensor testing and

calibration procedures, signal conditioning circuitry, and a

computerized data acquisition system for sensor

measurements. The authors performed statistical tests to

indicate variability between sensors and give parameters for

matching sensors so a single calibration curve could be

used. Quick tests were also conducted to determine the time

required for the sensor to reach water-pressure equilibrium

with step increases in pressure from 0-60 kPa. The time


required for equilibrium varied from 1 hr at 10 kPa to 9 hr

at 90 kPa. The authors indicated that pressure potentials

in soil change in a continuous rather than the discontinuous

mode represented by the step change. They therefore

surmised that the sensor should respond rapidly to

continuous changes caused by sinks and sources if there is

intimate contact between the sensor and soil. The latest

version of the sensor is claimed to work from nearly

saturated conditions to about 3 bars tension and can be

purchased factory calibrated from 0 to 1 bar (Agwatronics,

1987). The cost of a calibrated sensor was $110.00 in 1987

(C. J. Phene II, personal communication, 1987).

ThermocouDle psvchrometers. Thermocouple psychrometers

are also used for in-situ measurements of soil water

potential. Brown (1970) reviewed the theory of thermocouple

psychrometers and their use for measuring soil water

potential. These "soil psychrometers" consist of a

thermocouple junction contained in an air filled porous

ceramic cup that is inserted into the soil. The other

thermocouple junction is kept in an insulated medium to

provide a temperature reference. The ceramic cup allows

vapor exchange between the soil and internal atmosphere.

Under isothermal conditions, the vapor pressure of the

atmosphere above the soil and around the thermocouple will

come into equilibrium with the water potential of the soil.

The vapor potential is then the matric and osmotic


potentials combined since only water molecules can pass to

the air. In operation, the thermocouple junction in the

ceramic cup is cooled by applying a voltage of the proper

polarity between the two junctions. The junction is cooled

below the dewpoint of the internal atmosphere, causing a

small amount of water to condense on the junction (Peltier

effect). After this cooling, current is stopped to allow

the condensate to evaporate. The rate of evaporation is a

function of the vapor pressure of the air and hence, the

water potential of the sample. The evaporation cools the

junction as a function of the vapor pressure. The

difference in temperature between the sensing junction and

reference junction causes a small voltage output from the


Thermocouple psychrometers are highly sensitive to

temperature fluctuations. Rawlins and Dalton (1967)

explained several ways that temperature changes can

influence the accuracy of thermocouple output. For example,

the relationship between soil water potential to vapor

pressure depression (relative humidity) is temperature

dependent as seen in the basic equation

=R T ln (P/P0) (2-15)


= water potential (bars or atmospheres),

R = universal gas constant,


T = absolute temperature (OK),

p = actual vapor pressure of the system,

P0 = vapor pressure of pure free water, and

V = partial molal volume of water
(18.015 cm3mole-1).

Also, the vapor holding capacity of air within a sample

chamber increases with increasing temperature. The relative

humidity will thus decrease until vapor equilibrium is again

achieved. If the sample chamber is completely sealed (as is

not the case with soil psychrometers), errors can be quite


Rawlins and Dalton (1967) and Weibe et al. (1970)

attempted to provide reasonable estimates of soil water

potential with their designs considering ambient temperature

fluctuations. Throughout the range of variation of soil

moisture, the vapor pressure deficit was less than 2%. This

very small change requires that the soil psychrometer be

very accurate. The soil psychrometer's high sensitivity to

temperature changes requires very accurate temperature

control and monitoring. Since the highest accuracy claimed

is within a few tenths of a bar (Rawlins and Dalton, 1967),

soil psychrometers are not practical for use at low soil

moisture suction values frequently encountered in sandy

Florida soils. Soil psychrometers can be quite useful in

measuring the high suction ranges (2 to 50 bars).

Soil Moisture Characteristic Curve

The relationship between soil water content and

pressure is strongly influenced by soil texture and

structure. If a slight negative potential, -h (or positive

suction), is applied to water in a saturated soil and

increased slowly, no outflow will occur until a critical

value is exceeded. This critical value is the point where

the largest pore of entry begins to empty and is called the

air-entry suction (Hillel, 1982). The air entry suction is

usually small in coarse textured soils such as sands. A

gradual increase in suction results in the emptying of

progressively smaller pores until only very small pores

retain water. In a sandy soil, pores are relatively large

and a small amount of water remains when the large pores are

emptied. Clay soils, by contrast, retain a much larger

amount of water at the same suction level since the pore

size distribution is more uniform and more of the water has

been adsorbed. The soil-moisture characteristic curve is an

experimentally derived curve for the soil of interest that

describes soil water retention in the soil as a function of

matric suction (Figure 2-1). In general, the greater the

clay content of any given soil, the greater the water

retention at any given suction value. The amount of water

retained at low suction values on the curve (for all soils)

is chiefly a function of the surface tension of the water,

its contact angle with the solid particles, and the pore

size distribution. Hence, the structure of the soil

strongly affects water retention at the lower suction

levels. Water retention at higher suction levels is more a

function of adsorption (adherence of water to the soil

particles) and is thus more influenced by the texture of the

soil material.

The soil serves as a water reservoir for the plant. In

the field, the soil is heterogenous in nature. Plant roots

can proliferate through two or more zones of soil, each with

a different soil moisture characteristic. Soil types in

contact with each other that differ in texture and structure

will tend towards a state of potential energy equilibrium.

However, the amount of water each soil retains at a given

water potential may be markedly different and is determined

by its individual soil moisture characteristic. Also, soil

layers of the same texture can change their characteristics

through tillage operations that can cause compaction and

decrease the total porosity. A result of this is that the

saturated water content and the initial decrease in water

content with the application of low suctions is reduced.

Soil Water Uptake. Transpiration. and Evaporation

The previous discussion centered on the soil and soil-

water characteristics that define the environment in which

the plant roots propagate. The following discussion focuses

on the processes involved in water uptake by roots, plant

transpiration, and soil evaporation. Equations modeling

each of these processes are presented.

Water Uptake by Roots and Plant Transpiration

Water enters the plant through its roots. Much of the

water enters through epidermal cells on the outside of the

root tip and root hairs that extend out from these cells

among the soil particles around the root. As root tips grow

through the soil, they encounter new regions of moisture.

As the plant grows, the outer protective layers (or root

caps) are continually sloughed off at the forefront and

replenished by divisions of underlying cells.

Two approaches have been used to describe water uptake

by plant roots. The first approach, the "microscopic" one

deals with uptake of a single root. The "macroscopic"

approach, the approach used in this study, deals with the

integrated properties of the entire root system.

In the discussion following, basic equations describing

unsaturated flow in the soil-water system are presented.

These equations are then modified of the soil by intro-

duction of the plant root system.

The generalized form of Darcy's law describes, in three

dimensional space, flow in porous media

q = K grad (H) (2-16)


q = the volumetric flux (the volume of
water flowing through a unit cross-sectional
area per unit time),


grad (H) = the gradient of hydraulic head in three-
dimensional space, and

K = the hydraulic conductivity (the ability of
soil to conduct water) with dimensions of LT-.

The value of K decreases rapidly as soil water content (e)

decreases and suction (h) increases. The function K vs. e

or K vs. h is different for each soil layer. Methods of

estimating unsaturated hydraulic conductivity of soil in

both the laboratory and field can be found in van Genuchten,

(1978); Libardi et al., (1980); Chong et al., (1982), among


Darcy's law indicates that the flow of liquid through a

porous medium occurs at a rate proportional to the hydraulic

conductivity and magnitude of the driving force acting on

the liquid. For the one-dimensional vertical case, the

liquid flow or volumetric flux q (LT-I) is defined by

q = K dH/dz. (2-17)

The continuity equation (conservation of mass) states

that without any sources or sinks, the time rate of change

of water content in a unit volume must equal the change in

flux with distance. The continuity equation is

dO/dt = dq/dz. (2-18)

If a sink term representing water uptake by plant roots is

introduced, the equation is

dG/dt = -dq/dz S (2-19)


where S represents the volume of water taken up by the roots

per unit bulk volume of soil in a unit time (L3L-3T-I). A

schematic representation of equation (2-19) is shown in

Figure 2-2. (The flux, q, is defined by Darcy's equation (2-

17) for one-dimensional flow). Over a rooting depth L, the

actual plant transpiration can then be defined by the

integral of the sink term S

T S dz. (2-20)


Feddes et al. (1978) pointed out that the major

difficulty in solving equation (2-19) was the determination

of S. Resistance analogs have been tried to describe the

flow through the rooted soil zone. With these methods, the

rate of water uptake was assumed to be directly proportional

to the difference in pressure head between the soil and the

root interior, to the hydraulic conductivity of the soil,

and to some empirical root effectiveness function. Various

investigators have described this root effectiveness

function in different ways.

Because of the amount of field work and experimental

difficulties involved in determining the root function,

Feddes et al. (1976) attempted to simplify the process and

defined water uptake by roots as a function of the soil

moisture pressure head. This relationship is illustrated in

Figure 2-3. In the range of pressure heads between OB and


gC (the wilting point), the water uptake decreases linearly

to zero. Feddes et al. (1976) used values of -50 and -400

cm (0.05 and 0.40 bars) for AA and AB respectively. The

value for OB (-400 cm) is based on a previous review by

Feddes of moisture requirements and the effect of pressure

head on yield and quality of various vegetable crops. In

reality, the value of OB is not constant and varies with the

evaporative demand of the atmosphere and plant type. Yang

and deJong (1972) conducted experiments on wheat to

determine the effect of evaporative demand and soil water

potential on transpiration and leaf water status. The

authors found that under conditions of high evaporative

demand, a reduction in root water uptake occurred at higher

values of A than under conditions of low demand.

The value for OA is the limit above which deficient

root aeration exists. This value varies with crop and soil

type (Feddes et al., 1978). OA was taken as -50 cm and

defined for a clay soil and a gas filled porosity

corresponding to the pressure value above which the oxygen

demand of a plant can never be met (Feddes et al., 1976).

Plants draw quantities of water through their roots far

in excess of their metabolic needs. Only about 1% of the

water taken up by plants is actually involved in metabolic

activity (Rosenberg et al., 1983). The atmosphere creates a

high evaporative demand because of its dryness compared with

normally water saturated plant leaves. This vapor pressure


gradient is the driving force behind the evaporation

process, and it varies with the dryness of the air. The

loss of water vapor by plants is called transpiration and is

not in itself an essential physiological function. Plants

can thrive in an atmosphere nearly saturated with vapor and

hence require very little transpiration (Hillel, 1982).

Thus, prevailing climatic conditions determine the amount

that transpiration exceeds the plant's requirements.

Plants are not passive conveyors of water from the soil

to the atmosphere. To understand how water flows from the

soil to the atmosphere via the plant, it is useful to

describe the soil-plant-atmosphere system as a continuum in

which various resistances to water flow exist in the soil,

roots, xylem, stomates, and the aerial boundary layer. Of

these resistances, the resistance to flow in the vapor phase

is greatest of all (Rosenberg et al., 1983). A large

potential gradient between the air and leaf is required to

overcome this large resistance. Rosenberg et al. (1983)

list typical values of water potential for air as -80 MPa

and for the leaf of a corn plant as -0.80 MPa indicating by

far the largest potential gradient in the continuum.

Water vapor is formed within air-filled pores of the

leaf. Vapor then diffuses through the stomates and out into

the open air. Stomates are primary openings on the leaves

that both transpire water and allow entry of CO2 needed for

photosynthesis. Plants can regulate the amount of water

vapor released to the air by closing these stomates.

The plant is continually faced with the problem of

getting as much CO2 as possible from an atmosphere that is

extremely dilute (0.03% by volume), and retaining as much

water as possible (Salisbury and Ross, 1985). Water is

needed to keep all cells turgid and is necessary for the

reduction of CO2 in photosynthesis. Simple sugars are

formed as a result of the photosynthetic reaction. From

these simple sugars, more complex constituents necessary for

plant growth are synthesized.

Many environmental factors influence the stomatal

aperture which regulates transpiration and the intake of

CO2. Stomates of most plants open at sunrise and close at

night, allowing entry of CO2 needed for photosynthesis

during the daytime. Stomatal opening is fast in the morning

hours and closing is gradual throughout the afternoon. The

light intensity influences both the rate of opening and the

final aperture size with bright light causing a wider

aperture. Water potential within the leaf also has a great

effect on stomatal opening and closing. As water stress

increases, the stomates close providing a protective effect

during drought. This effect can override low CO2 levels and

bright light. Thus, the cell water potential (and stomatal

opening) is ultimately governed by the potential of the soil


water in contact with the roots, (Taylor and Ashcroft,


From an agriculturalists point of view, the compromise

between photosynthesis and transpiration corresponds to

achieving maximum crop yield with a minimum of irrigation

water (Cull et al., 1981; Sinclair et al., 1984). The

object is to provide enough water for the plant to prevent

significant water stress and a corresponding reduction in

yield. However, too much water application can waste this

important natural resource, leach applied fertilizers out of

the root zone, or possibly limit root growth due to

deficient aeration. As has been stated, the soil

environment can influence aeration. For example, deficient

aeration for roots can occur if a slowly permeable layer of

soil exists below the root zone (Stolzy et al., 1959).

saturated conditions might occur for long periods causing

roots to rot.

Evapotranspiration Models

In order to determine the proper quantity of water to

apply to a field to prevent plant water stress, both the

amount of transpiration by the plant and evaporation from

the soil need to be known. For this reason, much research

has been done to model both of these processes, known

collectively as evapotranspiration or "ET." When plants

cover only a small portion of the soil surface, most of the

ET is due to evaporation of water from the soil surface. As


the crop grows and leaf area increases, the crop

transpiration component becomes increasingly important.

Many forms of equations describing the evapotrans-

piration process evolved from basic principles of

evaporation. Dalton is credited with the "mass transport"

formula that predicts evaporation as a function of vapor


E0 = f(u) (ea e0) (2-21)


f(u) = a function of windspeed at a stated height,

ea = the vapor pressure of the air at the same
height, and

e0 = vapor pressure at the surface.

This simple method is not easily applied, however, because

of the difficulty in determining the vapor pressure at the

surface, e0. Only in cases where the surface is wet

(saturated) and e0 can be determined at a known surface

temperature has reasonable accuracy on a daily or hourly

basis been achieved (Van Bavel, 1966). Variations on the

basic equation have been developed using site specific

empirical constants for estimating e0 from reservoirs and

lakes (Brutsaert and Yu, 1968). Rosenberg et al. (1983)

pointed out difficulties in the method for estimating ET

from crop surfaces. Estimates of water vapor fluxes from

vegetative surfaces become less accurate as plants


experience water stress. To obtain the saturated E0 from

measurements of surface temperature, it must be assumed that

air spaces within the leaf are at the temperature of the

leaf and are at a relative humidity of 100%. As the crop

experiences water stress, the leaf temperature is elevated.

Because saturated vapor pressure increases with increasing

temperature, e0 evaluated from the elevated temperature will

be over-estimated.

Many of the disadvantages of the Daltonian mass-

balance approach can be surmounted by combining functions

for sensible heat and water vapor with the energy balance


Rn + H + G + LE = 0 (2-22)


Rn = energy flux of net incoming radiation,

H = the flux of sensible heat into the air,

G = flux of heat into the soil, and

LE = latent heat flux, the product of L, the latent
heat of vaporization of water per unit mass
and E, the vapor flux.

The terms latent heat flux (LE) and evapotranspiration (ET)

will be used synonymously to describe the transport of water

vapor from the soil and plant surfaces.

Figure 2-4 illustrates the components of the energy

balance (Equation 2-22) and turbulent transfer of water

vapor away from an evaporating soil surface. The soil


presents a variable resistance to flow of heat and water

vapor which greatly depends upon the degree of surface

wetness. Introduction of a plant into the system

illustrated in Figure 2-4 would add a different component of

resistance to flow of heat and water vapor. Plant factors

that limit evaporation are treated subsequently.

Equations for sensible and latent heat transport are

H = PaCpKh dT and (2-23)

LE = de. (2-24)
T dz


Pa = density of air,

Cp = specific heat of air at constant

= psychometric constant,

Kh,Kw = turbulent exchange coefficients
for sensible heat and water
vapor, respectively,

dT/dz = vertical gradient of temperature, and

dea/dz = vertical gradient of vapor

Bowen ratio

Bowen (1926) used the above relationships and described

the ratio H/LE as

= H = r Kh dT/dz (2-25)
LE Kw de/dz

This relationship can be simplified assuming equality of the

turbulent transfer coefficients for heat and water vapor, as

well as flux constancy with height. Using these

assumptions, equation (2-25) reduces to

H = T, T (2-26)
LE e2 e1


T2 T1 = temperature difference between
two heights, and

e2 el = vapor pressure difference between
two heights.

Under certain conditions, equality of the transfer

coefficients cannot be assumed. Verma et al. (1978) showed

that under conditions of regional sensible heat advection,

LE was underestimated due to inequality of Kw and Kh. If

advection is great enough, the gradients of heat and water

vapor are of opposite sign and the sensible heat gradient is

downward toward the surface. Under these conditions, warm

dry air passing over a rapidly transpiring, relatively cool

crop supplies energy for transpiration. Sensible heat

energy is consumed instead of generated. The authors

pointed out, however, that in cases where sensible heat

advection is not significant (as in humid regions), equality

of the transfer coefficients can be assumed.

With the transfer coefficients equal to each other and

thus eliminated, equation (2-26) can be combined with the

energy balance equation (2-22) to yield

LE = RD G (2-27)
1+ T T, Ti
e2 el

The above relationship is called the "Bowen Ratio-Energy

Balance" method of estimating LE. McIlroy (1971) developed

an instrument that combined sensing and computing functions

for continuous measurement of evapotranspiration using the

Bowen ratio method. The form of equation (2-26) allowed

measurement of wet bulb temperature differences which are

related to e2 e. Input sensors required for proper

operation of the instrument included a net radiometer for

Rn, ground heat flux plates for G, and pairs of dry bulb and

wet-bulb resistance thermometers. Each wet and dry bulb

thermometer shared a common aspirated radiation shield at

each of two chosen heights. Since temperature gradients

were very small over small height differences, the height of

the temperature sensing elements were alternated and the

instrument re-zeroed to control for errors. The author

found good agreement between LE determined with the

instrument and hourly measurements from weighing lysimeters.

Although Bowen Ratio methods have given good

approximations of LE on a short term basis, they are labor

intensive since they require frequent attention to calib-

ration that can involve periodic relocation of sensors.

Also, there are many precision sensors required to read and

maintain. For these reasons, Bowen Ratio methods have not

been widely used to estimate LE for irrigation scheduling.

Combination formulas for modeling evapotranspiration

Methods of modeling evapotranspiration have been

developed which combine the energy balance and an aero-

dynamic equation. Various forms of combination equations

have been used depending on the available instrumentation

for measuring parameters. One combination formula combines

the energy balance (Equation 2-22) with one form of the

equation for sensible heat transfer (Equation 2-23):

LE = Rn + G + PaCp (Ta Tc) (2-28)


ra = the boundary layer resistance to
sensible heat transfer,

Ta = air temperature, and

Ts = surface temperature.

Montieth (1963) introduced the resistance term ra by analogy

to Ohm's law. The flow of electric current is analogous to

the flux of sensible heat and the "driving force" in this

case is the temperature gradient, (Ta Ts). In fact, the

representation of H as the right-most term of equation (2-

28) is similar to the form of equation (2-23). The term ra

of equation (2-28) can be seen to equal dz/Kh of equation

(2-23). The term dz can be neglected as measurements are


made at a single height and ra represents aerodynamic

resistance in the boundary layer. Thus, as equality of the

transfer coefficients Kh and Kw (Equation 2-23) were assumed

for heat and water vapor, respectively, ra can be used as

the aerodynamic resistance to both flow of heat and water

vapor. To use equation (2-28), one would measure Rn and G

with a net radiometer and soil heat flux plates respect-

ively, derive ra by wind and temperature profile measure-

ments, and measure air and surface temperatures using

thermocouples or other appropriate devices. Heilman and

Kanemasu (1976) used aspirated thermocouples mounted on

masts for determination of Ta and placed them at several

levels above and within the crop canopy to determine ra.

Windspeed measurements were also made at several levels to

determine ra. Spring-mounted thermocouples were mounted on

the undersides of the leaves to measure crop surface

temperature Ts. Much work has been done to produce

estimates of ra from windspeed data (Szeicz et al., 1969;

Brun et al., 1972). Furthermore, Rosenberg et al. (1983)

suggested that equation (2-28) could be more easily applied

by measuring crop surface temperatures (Ts) with infrared


Difficulties encountered in measuring crop surface

temperatures have precluded widespread use of the

combination form (Equation 2-28) for the estimation of LE.

For this reason, forms of the combination equation have been

derived to allow estimates of LE from measurements at a

single height. The ability to calculate LE at a single

height is of considerable advantage, since single-level

measurements do not need to be as accurate as those used to

establish gradients. However, as Taylor and Ashcroft (1972)

pointed out, elimination of the second level of measurement

results in estimates of evapotranspiration which must be

"scaled" by a soil-plant factor in order to obtain actual

crop evapotranspiration measurements.

Penman (1948) developed a combination model which

allowed measurements from a single height. The equation can

be more readily applied than either the energy budget or

aerodynamic equations from which it was derived. The method

was originally designed to estimate evaporation from open

water surfaces and has been modified various ways to predict

crop evapotranspiration. Various forms of the Penman (1963)

equation are among the most widely used in hydrology today

(Thom and Oliver, 1977). There are, however, some

assumptions that are made regarding its use as originally

derived. First, an assumption is made that the evaporating

surface is saturated. This assumption eliminates the need

to measure vapor pressure at the surface but causes the

estimate of evaporation to be potential rather than actual.

Potential evaporation occurs when a surface is wet and

imposes no restriction on the flow of water vapor. The next

assumption is that the surface temperature is the same as

the air temperature at the measurement point. This

eliminates the need to measure the surface temperature.

Derivation of the Penman model makes use of the Bowen

ratio previously mentioned.

H_ = rTj T, (2-26)
LE e2 el

T2 = Ta = temperature of the air at a
certain height,

T1 = Ts = temperature at the soil surface,

e2 = ed = prevailing vapor pressure of the
air at the same height of
temperature, Ta, and

el = e(Ts) = saturated vapor pressure at the
soil surface temperature, Ts.

In order to remove the need to measure surface temperature,

Penman introduced the relationship

ea e(Ts) = 6 (Ta Ts) (2-29)


ea = saturated vapor pressure at Ta, and

6 = first derivative of the function
ea as f(T) known as the saturated
vapor pressure curve (Figure 2-5).

Rosenberg et al. (1983) gave an equation for the curve of

Figure 2-5 as

ea = 0.61078 exp 17.269T, 1. (2-30)
[ Ta+ 237.30 1.

Ta is expressed in 0C and ea is expressed in kPa. The first

derivative, 6 can be calculated at a known air temperature


6 = de, = 2502.9 exp F 17.269T, 1 (2-31)
dTa LTa+ 237.30 J

Ta2 + 474.6OTa + 56311

Combining equation (2-29) with the Bowen ratio, equation (2-

26) yields

H =[ e. e(T 3. (2-32)
LE 6 ed e(Ts)

Ultimately, a relationship is desired that removes the need

to measure e(Ts). Equation (2-32) can be modified by

replacing ea e(Ts) by (ea ed e(Ts) + ed) (Taylor and

Ashcroft, 1972). When this is done, equation (2-32) becomes

H_ = r 1 + ea e (2-33)
E T ed e(Ts) ]

A form of equation for latent heat transport (Equation 2-

24) can be written


LE = p.. (ej e(T.)) (2-34)
r ra

Using the assumption that Ta = Ts implies that ea = e(Ts).

Equation (2-34) can now be written to describe an

"isothermal evaporation" (Feddes et al., 1978) as

LEa = paCp (e4 e.) (2-35)
T ra

Taking the ratio of equation (2-35) to equation (2-34)


= ea ea (2-36)
E ed e(Ts)

Combining equations (2-36) and (2-33) yields

LE 6 1 E

Substituting the remaining terms of the energy balance

(Equation 2-22) for H and re-arranging terms yields

Rn + G + LE ( LEa). (2-38)

Solving for LE yields a form of the Penman combination


L= 6 (Rn + G) + LEa (2-39)
+ 76+ T

Penman's original form of equation (2-39) neglected

soil heat flux (G) because for daily estimates of LE, an

assumption was made that the heat flux downward toward the

soil was cancelled by the upward flux at night. The net

contribution of G was thus assumed to be negligible over a

24 hour period.

The effects of wind on ET depend on crop character-

istics. Equations based on theory have been used to model

the effects of wind on ET. As seen in equation (2-35), LEa

can be written as a function of ra, the boundary layer

resistance to sensible or latent heat transfer, and the

vapor pressure deficit measured in the air at a point above

the surface. Other methods have described LEa as a function

of windspeed using terms analogous to ra. If equation (2-

35) is re-written as LEa = B (ed ea), B was defined by

Van Bavel (1966) as

B = p Z k2 U,
P 2 (2-40)
[ln z


p = density of air,

Z = water-air molecular weight ratio,

P = ambient pressure,

k = Von-Karman constant (0.43),

z0 = roughness parameter,


z = height above soil surface, and

Ua = windspeed.

The roughness parameter z0 is a measure of the aerodynamic

roughness of the surface over which the wind speed profile

is measured.

Equation (2-40) described a transfer coefficient for

water vapor that applied to adiabatic conditions only.

Similarly, Szeicz et al. (1969) defined a coefficient l/ra

for momentum transfer as

1 k2 U 2 (2-41)

in z-d


d = the zero plane displacement.

The zero plane displacement indicates the mean level at

which momentum is absorbed or the level of bulk aerodynamic

drag on the plant community. Szeicz et al. (1969) stated

that under adiabatic conditions of neutral stability, the

transfer coefficient (Equation 2-41) for momentum could be

used to calculate fluxes of heat and water vapor. When z0

is constant, I/ra is a linear function of windspeed. The

authors pointed out, however, that even though z0 may be

constant for surfaces with small or constant roughness

elements, many crops become aerodynamically smoother as


windspeed increases. They also stated that the zero plane

displacement may change as crops are bent down by the wind

though not by an appreciable amount. Brun et al. (1972)

described the diffusion resistance ra (after Fuchs et al.,

1969) as
ra= + ln 1z +z (2-42)

kd Vz


= diabatic profile parameter,

D = d + z0, and

Vz= windspeed at height z.

Szeicz et al. (1969) empirically related z0 to crop height h

using a regression of data for many crops in the windspeed

range of 2 3 m/sec as

logl0 z0 = logl0 h 0.98 (2-43)


h = crop height in centimeters.

Likewise, Stanhill et al. (1969) gave an equation for zero

plane displacement as

lOg10 d = 0.979 logl0 h 0.154. (2-44)

Fuchs et al., (1969) stated that the adiabatic approximation

can be successful only if H (sensible heat flux density) is

small as with irrigated vegetation. Under this assumption,

A of equation (2-42) would be set to zero.

Plant and Soil Factors Limiting Evapotranspiration

Equation (2-39) assumes a well watered crop and

describes a "potential" rather than an "actual" evapo-

transpiration. Doorenbos and Pruitt (1977) defined

potential ET in terms of a reference crop ET as the crop

evapotranspiration... from an extended surface of 8 to 15 cm

tall green grass cover of uniform height, actively growing,

completely shading the ground and not short of water."

Modification of equation (2-39) to account for plant and

soil factors that limit evapotranspiration have been

approached in a number of ways. Some of the more instru-

mentation intensive methods been shown to yield good

estimates on a very short term basis (hourly). These

methods have been limited to research applications, however,

because of the instrumentation required to measure needed

variables whose values are not readily available. Other

methods apply an empirically derived crop coefficient to

equation (2-39) to make it a more practical tool for

irrigation scheduling. This coefficient is used in order to

"scale" the Penman form to reflect actual evapotranspiration

and describes the combined effects of soil and crop

conditions on actual ET. Since it is empirically based,

however, the crop coefficient can be used only for the crop

and conditions under which it was derived. The following

discussion addresses both physically based and more

empirical approaches and detail the aforementioned diff-

iculties associated with attempts to modify the Penman

equation for the plant limiting case.

Resistance methods

Previous discussions focused on the plant's use of

stomatal control to regulate transpiration. Light intensity

and the plant water potential regulate both the rate and

final degree of stomatal opening. The degree of stomatal

opening has been described in terms of the plant's

resistance to transport of water vapor from the stomates,


Monteith (1965) introduced an additional resistance

term, rc into the Penman equation (2-39) which is a function

of rs. A form of the modified equation is

LE = 6 (Rn + G) + p.C. (e(T) ei)/r, (2-45)
(6 + T) [(ra + rc)/ra]

The term rc denotes the surface resistance of the entire

crop canopy or the mean resistance of the various layers of

leaves acting in parallel (Jagtap and Jones, 1986).

Brown and Rosenberg (1973) used a slightly modified

form of equation (2-45) and calculated rc by summing

stomatal resistances for both sides of each leaf layer as

parallel resistors. They also calculated rc by measuring

other variables in the combination equation including crop

surface temperatures. The authors found good correlation


between rc calculated by both methods indicating that rc is,

indeed, a physiological factor. Values of rc were derived

for sugar beets under well watered conditions but were only

about 1/2 to 1/3 as large as those reported by Monteith

(1965). The authors attributed the discrepancy to the

possibility that Monteith's crops may have been water

stressed or composed of older leaves having greater stomatal


Attempts to simplify and increase the usefulness of the

Brown and Rosenberg (1973) resistance model were made by

Verma and Rosenberg (1977). They developed empirical

functions that describe canopy resistance as a function of

irradiance. This method still disregarded the fact that rc

is also heavily dependent on plant water stress since,

again, the results represented conditions of an adequate

water supply. The authors did indicate that the dependence

of rc on irradiance must be modulated for decreasing soil

moisture content before the model can be used widely.

Others have used the Montieth (1965) approach in models

that separate soil evaporation and transpiration components

for crops with incomplete cover (Black et al., 1970; Brun et

al., 1972; Jagtap and Jones, 1986). Later discussion will

focus on the merits of modeling evaporation and transpir-

ation separately.

Crop coefficient curves

Difficulty in determining the canopy resistance, rc,

has precluded widespread use of the Montieth form of the

combination equation for determining irrigation water

requirements. As has been indicated, instrumentation

intensive research investigations can yield good estimations

of LE on a short term basis. Rc is usually calculated from

individual leaf resistances using instruments called

porometers that measure stomatal diffusion (Black et al.,

1970; Brun et al., 1972; Jagtap and Jones, 1986). Use of

this instrumentation is not practical in the field, however,

and resistance modifications have not yet been incorporated

into practical procedures for determining irrigation

requirements (Wright, 1985). As a result, practical tools

have been developed to modify the basic Penman ET equation

using crop coefficients.

As has been stated, crop coefficient curves have been

developed which describe the combined effects of soil and

crop conditions on actual ET. Actual crop ET is estimated

by multiplying potential ET (Equation 2-39) by a crop

coefficient, kc, or

ET = kc ETp (2-46)

Jensen et al. (1971) conceived a computer based

irrigation management program using a form of the Penman

(1963) ET equation for potential evapotranspiration.


Jensen's computer program kept a water balance on individual

fields, taking into account climate, crop, and soil factors

that influence soil water depletion. The program used an

empirically derived coefficient to adjust the equation to

reflect actual evapotranspiration by the crop. The

program's crop coefficient reflected the combined effects of

crop stage, available soil water, and the effects of a newly

wetted soil surface. The authors described a multi-termed

crop coefficient as

kc = kco ka + ks (2-47)


kco = the mean crop coefficient based on experimental
data where soil water is not limiting,

ka = the relative coefficient as available soil
water becomes limiting, and

ks = the increase in the coefficient at a given
stage of growth when the soil surface is wetted
by irrigation or rainfall.

Stegman et al. (1977) derived crop curves for several

crops in North Dakota and observed that periodic field

visits were needed to verify that the crop's phenological

development was compatible with crop curve position relative

to days post-emergence. Jones et al. (1984) presented

coefficients for many crops derived at specific sites.

Coefficients presented were derived under well watered

conditions and depended on rainfall and irrigation patterns

and on the method used for estimating potential

evapotranspiration. Values of crop coefficients varied with

days post-emergence.

Models that separate evaporation and transpiration

Where many crops have incomplete cover during most or

all of the season, the soil evaporation component of ET is

often quite large. The aforementioned methods of applying a

crop coefficient to the potential ET equation were designed

to take soil evaporation into account since they applied

over the entire season. However, many coefficients were

derived only under well watered conditions.

Jensen et al. (1971) used a coefficient that took into

account changes in soil evaporation as a function of

available soil moisture and the ET increase due to a newly

wetted soil surface. This method did not account for

changes in the proportion of sunlit or shaded soil as the

season progressed, however. This could yield inaccuracies

in different parts of the season. Ritchie (1985) observed

that for developing crops, the soil evaporation component

becomes limited when the water content of the soil near the

surface drops below a threshold value. Transpiration,

however, continues at an energy limited rate until the water

deficit in the root zone reaches some critical level.

Ritchie (1972) developed a model that treated

evaporation and transpiration from a row crop with

incomplete cover as separate processes. Evaporation from a

drying soil was calculated in two stages: (1) The "constant


rate" stage in which evaporation is only limited by the

supply of energy to the surface and (2) the "falling rate"

stage in which water movement to evaporating sites near the

surface is controlled by the hydraulic properties of the

soil. Ritchie used a relationship that describes soil

evaporation as the product of an empirically derived factor

(a function of the hydraulic properties of the soil) and the

square root of time. A form of the Penman combination

equation with an empirical wind function (Penman, 1963) was

used to define the approximate potential evapotranspiration

above the canopy. The author's modification of the equation

included a locally calibrated function for net radiation

above the canopy (Rno). As with the original Penman

equation, soil heat flux was also neglected. Potential

evaporation below the canopy at a freely evaporating soil

surface was predicted using a modified form of the same

Penman equation neglecting the vapor pressure deficit and

wind function terms. Net radiation at the soil surface

(Rns) was determined as an empirically determined fraction

of Rno depending on leaf area index (LAI). The author

stated that neglecting the vapor pressure deficit and wind

function terms could yield inaccuracies when the canopy is

small. When cover is sparse, however, conditions favoring

free evaporation from the soil do not exist for long periods

of time. Evaporation from the plant surface was also

predicted by an empirical function relating evaporation from

the plant surface to potential evapotranspiration by the

LAI. The model applied only where available soil water in

the root zone was not limiting. The model was tested on a

weighing lysimeter with a grain sorghum crop of incomplete

cover. Differences between measured and calculated values

of daily ET were less than 1 mm per day for most days.

Tanner and Jury (1976) proposed a similar approach to

that of Ritchie (1972) where an alternate method of

calculating soil evaporation was compared to the Ritchie

method. This was done to evaluate possible improvements in

soil evaporation equations. The authors found the two soil

evaporation models tested to be close in agreement. Like

the Ritchie (1972) model, the Tanner and Jury (1976)

evapotranspiration model was developed for a well watered

crop and no attempt was made to determine the decrease in

transpiration as water deficits developed.

Al-Khahaf et al. (1978) defined empirical relationships

which proportioned evaporation and transpiration by the LAI.

The authors also defined a dynamic crop coefficient from

empirical relationships of ET/ETp for irrigated cotton as a

function of days post emergence. The authors presented two

years of data for a water limiting case where a function was

derived relating the ratio of transpiration over potential

transpiration (T/Tp) as a function of the fraction of

available water left in the soil. Available water was

defined as the difference in volumetric water content


between -10 and -1500 kPa soil water tension. The authors

found that the ratio of actual to potential transpiration

was close to unity until about 60% of the available water

had been depleted from the soil. After this, the ratio T/Tp

began to decrease rapidly and could be described by a

negative exponential.

Tanner and Jury (1976) stated that the soil evaporation

component used in their and Ritchie's models can serve only

as an approximation to the behavior of a field soil. Thus,

the soil evaporation component is not desirable from a

theoretical point of view. This limitation can be extremely

critical if simulating water use in the early stages of a

crop's development. Evaporation from soil is most dominant

in these early stages and modeling it correctly is critical,

especially if short term estimates are desired.

Realizing limitations in previous soil evaporation

models, Butts (1988) developed a mechanistic model that

coupled energy and mass transfer processes to simulate the

evaporation of water from the soil. Since temperature

gradients play a significant role in the movement of water

vapor in the soil, the model also included functions to

simulate their effect on water profiles. The model

simulated diurnal variation of evaporation, soil water and

temperature profiles in response to conditions at the soil

surface and could provide resolution on a short term basis


If plant transpiration could be simulated reliably on a

short term basis and coupled to a model like one described

by Butts (1988), significant gains could be realized in the

effort to accurately estimate short term evapotranspiration

over the entire life span of the crop. As has been noted

previously, however, the only models to date that have the

potential of allowing accurate estimates of transpiration

require measurement of stomatal resistance (Montieth, 1965

and, more recently, Jagtap and Jones, 1986). Thus, semi-

empirical models such as those of Ritchie (1972) have found

wider use in irrigation scheduling programs and crop growth

simulations that require ET estimates. The Ritchie (1972)

model requires only daily solar radiation, and maximum and

minimum air temperatures as weather inputs.

Basic soil water relationships and methods of soil

water measurement were detailed. Special problems involving

water management in a heterogeneous soil environment and

limitations of sensor-based approaches to irrigation

scheduling were also discussed. Methods and limitations of

evapotranspiration models were detailed. The Penman

combination formula, from which most presently used

evapotranspiration models originated, was derived from basic

principles of mass and energy transfer.

Soil water content

Figure 2-1. Soil water retention curves.

de -q S
dt dz

Figure 2-2. Schematic representation of continuity
equation with added sink term (Feddes et
al., 1978).

S1.0 ,";

i "

," wilting point

'Za 0 b

Soil Water Potential q

Figure 2-3. Relative extraction vs. soil water potential.

LE H ed, Ta

wind, U air

e(Ts), Ts

// / ////// ////// / /7

Figure 2-4. Energy and mass balance at soil surface
(typical mid-day representation).

Temperature (deg. C)

Figure 2-5. Saturation vapor pressure of water as a
function of temperature.



As has been indicated, there are difficulties

associated with scaling potential ET models to reflect

actual evapotranspiration. Models that require measurement

of stomatal resistance, although having the potential for

great accuracy, require that frequent manual measurements be

made throughout the day. For this reason, use of this

method is not practical for on-farm use in irrigation


Crop coefficient equations were meant to allow

practical use of ET models but are site and crop specific.

These models must also be calibrated for the particular

field. Jagtap and Jones (1989) observed that seasonal

errors could be as high as 190 mm water when crop coeff-

icients developed under one set of conditions were used

under different climate and management conditions.

Models that separate the soil evaporation and crop

transpiration components allow a better representation of

water use in the early stages of a crop's development.

These models have acknowledged limitations based on


assumptions made in their development, and may be inaccurate

under certain stages of crop growth and weather conditions.

In summary, evapotranspiration models can provide good

water use estimates on a short term basis, but their accu-

racy depends on the number of variables that can be measured

and the method used to scale the model to predict actual

water use by the crop. Potential ET can be predicted quite

accurately if a weather station is installed on the farm

manager's field. However, all practical methods of scaling

potential ET models to reflect actual evapotranspiration

involve simplifying assumptions. Since these assumptions

have been shown to cause errors under certain weather or

growing conditions, methods have been adopted that use soil

water sensors as a substitute for or with model-based


Jensen et al. (1971) used sensor-based feedback to an

on-farm empirically based water balance simulation. Field

personnel would make periodic visits to check soil water

status with sensors to confirm adequacies of previous

irrigations. This verified that predicted soil moisture

status was consistent with observed measurements.

Approaches like the above are difficult to implement on

a large scale, however, because of the time, labor, and

interpretive skill involved in properly interpreting sensor

readings. If model estimates were needed on an hourly basis

(as might be needed in drip irrigation of vegetable crops),


automatic sensor readings would be required. These sensor

readings could then be interpreted at a central computer.

Soil water sensors themselves have limitations, also.

Sensors that require little maintenance and provide good

resolution in the desired range of water potentials are most

desirable for practical use. However, tensiometers, heat

pulse, and resistance type sensors have response time lags

associated with them. The time lag is a function of the

potential gradient, the porosity of the matrix material in

contact with the soil, and the mass flow caused by the

potential gradient. Even if time lags are quantified and

accounted for, most sensors in use today cannot provide

enough resolution in time steps much less than one day.

To properly delineate water status in specific soil

zones, infiltration, water re-distribution, and root

functions are needed to augment an ET model. If this

composite model is used as the primary predictor of when to

irrigate and how much water to apply, visits by field

personnel could be minimized as more knowledge is gained

from sensor responses in a given field. An experienced

field person could also make inferences about adequacies of

previous irrigations by the observed sensor responses to

wetting. Also, if sensors are placed at many depths, their

readings relative to each other could provide information

about where in the soil water is being used. Thus, a

logical extension of an approach like that used by Jensen et

al. (1971) would be to observe sensor responses to drying,

infer the location of water use in the root zone, and apply

this feedback to correct the water balance and root model.

If the irrigator knows how deep the crop is rooted, he can

replenish the entire root zone or a fraction of that zone

depending on his management objectives.

In summary, model- or sensor-based approaches used by

themselves have limitations when applied to practical

irrigation scheduling on the farm. A system is needed that

couples the most useful characteristics of sensor- and

model-based approaches and removes the labor intensive

aspect of interpreting sensor readings.

Knowledge-Based System--Development Criteria

With the aforementioned model and sensor limitations in

mind, it is instructive to summarize the problem with a

pictorial diagram (Figure 3-1). For this discussion, an

assumption is made that the sensors illustrated in Figure 3-

1 are properly placed to represent conditions in their

respective zones. The terms of the energy balance

previously defined with the driving potentials ed and Ta for

latent and sensible heat transfer are represented. These

are terms required to model evapotranspiration. The water

content, el, in each layer is influenced by evapo-

transpiration, flow to or from an adjacent soil layer, and

the sink term, root uptake. An appropriate relationship

can be made relating root uptake to root length density

(RLD, which also changes with time).

The object of irrigation is to apply enough water into

a specified zone of water regulation (which changes with

time) to bring that zone to a desired water content, usually

field capacity or the drained upper limit of water content.

A soil water sensor (Si) in each layer can indicate, after a

specified period, if applied water reached the zone that it

represents. If the initial condition ei, corresponding

water potential f, and hydraulic conductivity K in each zone

are known (or assumed), the change in 8 caused by irrigation

(I), rainfall (R), and soil water re-distribution as a

function of space and time (f(z,t)) can be modeled for each

layer. An amount of root water uptake, weighted by the RLD

and driven by ET over the period, will reduce 8 more rapidly

and cause field capacity to be reached at a shallower depth

than if no sink term were present. If an assumption is made

that no water table is present nearby and ET, drainage rate

from a soil layer, and 68 = f(RLDi) are modeled properly,

sensors responding should indicate the same depth of water

penetration as the model. Likewise, modeled soil water

contents ei for each layer should equal measured values as

the soil dries. Soil water content 8 can be measured

directly by many methods described previously or estimated

using soil water sensors that measure water potentials.

Before commencing irrigation, a trigger level of soil

water potential weighted by simulated RLD could be specified

according to the crop and its stage of development. A

function that determines this trigger level as a function of

time is determined for the crop as in Taylor and Ashcroft

(1972). Uptake predicted by the model reduces e to a

corresponding value of trigger potential, 0 (by the

characteristic curve). Meanwhile, there are also readings

from soil moisture sensors, Si. If these readings are

extrapolated forward to compensate for their inherent

response time lags, inferences can be made about the

correctness of the model's predictions and appropriate

corrections can be made. Strong inferences can also be made

about the root distribution component of the model based on

sensor responses to root extraction.

Literature Review

Crop Growth Simulation Models

In addition to predicting crop growth and yield under

simulated and actual conditions, crop growth simulation

models maintain a water balance in specific rooting zones.

These simulation models use one of the evapotranspiration

models discussed in Chapter II. All models to be discussed

have rooting, drainage, and soil water re-distribution

functions which can be used to model water uptake in

specific soil zones. A model chosen for this study must

have all these components because predicted water use in

specific zones to be compared to sensor-based represen-

tations of water use. Characteristics of several crop

growth models as they are relevant to the aforementioned

system development criteria are outlined.

Meyer et al. (1979) developed a simulator of soybean

growth and yield called SOYMOD/OARDC. This model used a

mechanistic approach to model the growth processes. A

complete water balance and rooting function were

incorporated into the model. The basic Penman equation

modified by Montieth (1965) to include aerodynamic and

canopy resistance terms was used to model the ET process.

The aerodynamic resistance (ra) was an empirical function of

wind velocity and canopy resistance (rc) was computed as a

function of the available light and leaf water potential.

Although actual stomatal resistances could be measured in

the field and entered into the model, the authors chose an

empirical function described by Brady et al. (1977) that

related leaf water potential to soil water potential. Soil

water potential could be obtained from the soil charac-

teristic curve and predicted soil water content in the root

zone. Thus, if soil water potential and photosynthetically

active radiation (PAR) were known, canopy resistance could

be calculated. Using this method to calculate canopy

resistance removed the need for frequent measurements of

stomatal resistance. The rooting zone was assumed to be a

single region shaped like an inverted wedge that migrated

downward. Thus, the soil zone was not compartmentalized and

detailed studies of water use in soil layers were not


Baker et al. (1983) developed GOSSYM, a simulator of

cotton crop growth and yield which included a detailed two-

dimensional model of root growth and distribution. The soil

was divided into cells into which roots could grow.

Potential root growth in a cell was a function of day

length, soil layer temperature, and soil water potential.

The model assumed exponential growth based on the mass of

roots present in the age category capable of growth. Actual

root growth occurring for a given cell was determined by the

amount of carbohydrate partitioned to the roots by the main

growth routine and the potential growth previously

calculated. Growth of roots could proceed in four

directions (left, right, below, or within the cell). Growth

within the present cell or to the three adjacent cells was

based on relative water potentials of the four cells.

Heavier weighting was given to downward growth.

GOSSYM adapted the ET method developed by Ritchie

(1972) to provide an empirical estimate of water removed

from the profile each day. Potential evapotranspiration was

calculated using the Penman (1963) equation with an

empirical wind function. Soil evaporation took place in an

energy limited or soil limited stage that depended on soil

dryness (Ritchie, 1972). Plant transpiration was the sum of


water uptake from all soil cells that contained roots.

Uptake of water from each cell was proportional to the

product of root weight capable of uptake and the hydraulic

conductivity of the cell.

Hoogenboom and Huck (1986) described a crop growth

model called ROOTSIMU 4.0 that could simulate root and shoot

growth of any type of plant. The model contained both

carbon and water balance algorithms but did not partition

dry matter to the reproductive structures of the plant. The

model's primary function was to simulate the effects of

water stress on plant growth. The model assumed that the

supply of nutrients would be optimal and that growth would

not be inhibited by insects, diseases, or weeds. Root

growth was a function of the soil water potential in the

soil layer. The roots grew more rapidly in wetter parts of

the soil profile than in dryer parts of the soil profile, so

younger roots with higher tissue conductivity formed in wet

soil, while older, non-functioning roots would die in dry

soil. A partitioning function allowed more dry matter to be

partitioned to the roots as the crop underwent water stress.

The model did not account for soil environmental constraints

such as poor aeration, chemical toxicity, salinity, or

temperature extremes.

A method of determining ET for ROOTSIMU was discussed

by Hoogenboom and Huck (1986). When weather data were

needed, ROOTSIMU 4.0 included sections to interpolate

between discrete points (recorded at daily intervals)

obtained from standard weather observations. These program

sections were used if the only long-term weather data

available were those collected by conventional meteor-

ological observation stations.

Huck and Hillel (1983) discussed the ET calculations

included in ROOTSIMU. Instantaneous potential ET rate was

interpolated from daily total pan evaporation measurements

and proportioned according to instantaneous radiation.

Actual evapotranspiration was partitioned between

transpiration and evaporation from the exposed soil surface

by the leaf area index (LAI). Soil evaporation equalled

potential ET for a wet soil (proportioned by the LAI) until

the top soil layer attained a constant state of dryness.

After that point was reached, flow across the lower boundary

of the top soil layer controlled evaporation. Actual

transpiration was also a fraction of potential ET

proportioned by the LAI. A factor was also included to

modulate the equation for stomatal opening. The authors

pointed out that stomatal response to water stress can vary

among crops. The authors present typical curves for

"sensitive" plants (such as corn or soybeans) and "tolerant"

plants (such as cotton or sorghum). ROOTSIMU 4.0 used

Darcian flow equations to compute unsaturated water flow

between soil layers, and infiltration was based on the

assumptions for plug flow made by Green and Ampt (1911).

All water was allowed to drain from the bottom layer to

prevent accumulation in the water profile.

In a rhizotron study of soybeans (Hoogenboom et al.,

1988), root growth and water uptake were compared to

simulated values using ROOTSIMU 4.0. No differences were

indicated between simulated root systems of non-irrigated

and irrigated treatments early in the season. The model

showed, however, that during a drought period later in the

season, total root length was greater for non-irrigated

plants than irrigated plants. The experimental data showed

more of a difference in total root length between irrigated

and non-irrigated treatments than the simulation did. The

authors surmised that the reason for the discrepancy may

have been that the model used a constant factor to convert

root dry matter to root length. The model did not consider

changes in size of the taproot and may have over-estimated

total root length for the irrigated treatment. Soil water

contents in all soil zones were also over-predicted by the

model for both irrigated and non-irrigated treatments.

Jones et al. (1986) described a simulation model for

growth and development of corn called CERES-MAIZE. Another

simulation model for growth and development of wheat (CERES-

WHEAT) was described by Ritchie (1985). The CERES models

implemented root growth and water balance components that

allowed simulation of soil water content in each of several

soil layers. Daily growth of the root system (g/plant) was


a function of the amount of carbohydrate partitioned to the

roots. Like ROOTSIMU 4.0 (Hoogenboom et al., 1986), the

models used a constant factor to convert root dry matter to

root length. Rooting depth (incremented daily) was a

function of air temperature and soil profile water content.

Root growth in a soil layer was a function of a soil water

deficit factor in that layer and a root growth weighting

function. This weighting function was given by

WR(I) = EXP (-4.0 Z(I)/200) (3-1)


Z(I) = depth to the center of soil layer I (cm).

Equation (3-1) is the simplest form of the root weighting

function. Jones et al. (1986) pointed out that WR(I) should

be reduced to reflect physical or chemical constraints on

root growth in certain soil layers. In the CERES computer

models, a WR(I) value was specified for each layer in the

soil characteristic input files.

The evapotranspiration model used in the CERES

simulations was adapted from Ritchie (1972). Potential ET

was calculated from temperature and radiation using the

Priestley and Taylor (1972) equilibrium evapotranspiration

(EEQ). The Priestley-Taylor method is a simplified form of

the Penman equation which replaces Penman's wind/vapor

pressure deficit term with an empirically derived constant.

For CERES-Wheat, Ritchie (1985) used a multiplier of 1.1 to


account for the effects of unsaturated air and increased the

multiplier to allow for advection when the maximum

temperature was greater than 240C. In Jones et al. (1986),

the multiplier was increased after the maximum temperature

was greater than 350C for CERES-MAIZE. In both CERES

models, actual soil evaporation was modeled as a two stage

process (as it was in the GOSSYM Cotton model of Baker et

al. (1983)). An amount of water representing the upper

limit of stage one (energy limited) evaporation (U) was

specified in the soil characteristic input files. After

this upper limit was reached, soil evaporation continued in

stage two (the soil limited stage) as a declining function

of time. Plant transpiration was determined by a root water

absorption sub-model. Radial flow of water into a single

root was calculated as

qr = 4rK(2 (3-2)
ln c


qr = water absorption rate (cm3/cm),

K(O) = hydraulic conductivity (cm/day),

O = soil water content (cm3/cm3),

Or = water potential at root surface (cm),
Ps = water potential in soil (cm),

c = radius of cylinder of soil through
which water is moving (cm), and

r = root radius (cm).


Ritchie (1985) developed an empiricism used to

calculate K(e) for all soils:

K(e) = 10-5 exp (62 (9 e1)) (3-3)


e1 = lower limit soil water content (cm3/cm3).

By combining equations (3-2) and (3-3), using the

relationship that c = (r Lv)-1/2 (where Lv is the root

length density (cm/cm3)), and assuming that r = 0.02 cm and

(Or Js) = 21 cm water, an equation was derived to find
root water uptake as a function of soil water content and

root length density:

qr = 2.64 x 10-3 exp (62 (8 8)) (3-4)
6.68 ln Lv

The potential difference (Or Os) = 21 cm was derived from

experiments using equation (3-2) and measuring or

approximating the other variables. Water absorption rates

were chosen when the soil dry enough that absorption rates

were clearly limited by soil water conductivity.

Equation (3-4) was used as the maximum soil-limited

water absorption rate for calculating plant transpiration.

Root water uptake (RWU) was added for all soil layers which

contained roots to obtain a value of plant transpiration

(TRWU). This value was compared with potential

transpiration (EPl) which was calculated by weighting

potential ET (EO) by the leaf area index (LAI). If the