Agricultural and municipal water demand projection models

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Title:
Agricultural and municipal water demand projection models
Series Title:
Florida Water Resources Research Center Publication Number 61
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Book
Creator:
Heaney, James P.
Lynne, Gary D.
Khanal, Nagendra
Martin, Wayne C.
Sova, Cherie L.
Dickinson, Robert
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
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University of Florida
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Publication No. 61


AGRICULTURAL AND MUNICIPAL WATER


DEMAND PROJECTION MODELS


by


James P. Heaney, Gary D. Lynne,


Nagendra Khanal, Wayne C. Martin,


Cherie L. Sova, and Robert Dickinson


1981


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TABLE OF CONTENTS


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

II. GENERAL BACKGROUND INFORMATION ............................... 5
III. AGRICULTURAL WATER DEMAND MODELS ............................. 7

IV. MUNICIPAL WATER DEMAND MODELS ................................ 78
V. DESCRIPTION OF WRE/SCS DEMAND MODEL ......................... 110
VI. SUMMARY AND CONCLUSIONS ..................................... 149
VII. REFERENCES .................................................... 150
APPENDIX A Description of Subroutines in WRE/SCS Model..... 158
APPENDIX B Program Listing ................................ 170
APPENDIX C Sample Data Forms .............................. 189











LIST OF j .>



Figure Page

1 Hypothetical Demand Curve for Water ........................ 6

2 Schematic of Land Use Breakdown .............. .............. 112

3 Overall Structure of Water Demand Model .................... 113

4 General Structure of Model ..... -..... ............... ..... 116

5 Estimated Residential Consumption in the United States ..... 127

6 Predicted Monthly Demands (MG) from Each Step (1-4) of the
Calibration Exercise ....................................... 145

Al Flow Chart for Program DEMAND .............................. 160

A2 Flow Chart for Subroutine FIND .............................. 163

A3 Flow Chart for Subroutine INPUT ............................. 164

A4 Flow Chart for Subroutine QSORT ............................. 165

A5 Flow Chart for Subroutine RPTSET ............................ 168










LIST OF TABLES



Table Page

1 Total Withdrawals and Consumption, by Functional Use,
for the 21 Water Resources Regions -- "1975", 1985,
2000 .................................................. 2

2 Major Features of Agricultural Water Demand Models.... 16

3 Blaney Criddle Model .............................. .

4 Hargreaves Model ......................... ........... 21

5 Hexem and Heady Models ............................... 23

6 The Hogg, Davidson, and Chang Model .................. 25

7 The Minhas, Parikh, and Srinivasan Dated Input Model 27

8 Penman Model ............................. ............ 30

9 Plant Growth Models ..... ........................... 32

10 Thornthwaite Model .................................... 35

11 Mapp and Eidman Model ................................. 40

12 Moore and Hedges Model ................................ 44

13 Input-Output Models ..................................... 48

14 Kansas Water Model .................................... 51

15 Lowry-Johnson Model ................................... 53

16 New Mexico Model ..... .............................. 55

17 North Carolina Model ...... ......................... 57

18 Pecos Basin Imported Water Model ...................... 61

19 Pennsylvania Model .... ............................. 63

20 Texas High Plains Model ......... .................... 66


21 Utah Model ........................














Table

22

23

24

25

26

27


CARD Model ........................................

Ruttan Model ......................................

Municipal Demand Models ...........................

Camp ........ .......................................

Clouser and Miller ................................

Danielson .........................................


Page

72

74

85

86

88

90


28 Darr, Feldman and Kamen ................................. 91

29 Morgan, D.W. ............................................. 93

30 Cassuto and Ryan ...................................... .. 94

31 Conventional Water Use Model ............................ 96

32 Integrated Supply/Demand Management Model ............... 97

33 Johns Hopkins Model ..................................... 98

34 Main I and II ..... ...................................... 99

35 Mitchell & Leighton ..................................... 100

36 Multistructured Demand Model ............................ 101

37 Municipal Model for the Conterminous U.S. ............... 102

38 Trevor & Gross .......................................... 104

39 Turnovsky ...... ......................................... 105

40 Young .................................................... 106

41 Kanoehe Bay Water Demand Model .......................... 107

42 Yamauchi and Huang ...................................... 109

43 Water Consumption by Selected Industry Type ............. 128

44 Example Output -- Report 2A ............................. 137












Table Page

45A Example Output -- Net Irrigation Requirements for
Soybeans ................................................. 139

45B Example Output -- Gross Irrigation Requirements for
Soybeans ................................................ 140

46 Comparison of "Actual" and Predicted Monthly Demands
(MG) for 1977 (Subarea 1) ......... ... ................... 146












ACKNOWLEDGMENTS


Mr. Aaron Higer of the U.S. Geological Survey was very helpful

throughout this study. He worked closely with us in defining the

problem and describing the intended audience. A large debt is owed to

Doctors Sonnen and Evenson, the original developers of the WRE model.

Their earlier work provided the foundation for this effort. The irri-

gation demand model was obtained from Dr. James Rogers of the University

of Florida. He put the SCS program onto the University of Florida

computer. The original work of the SCS personnel who wrote the program

over ten years ago is appreciated. The financial support of the En-

gineering and Industrial Experiment Station, College of Engineering,

University of Florida, in the early phase of this study is appreciated.










1.L ifc~j .u- ION


The water supply available for human use through agricultural

production processes and/or direct consumption is limited in quantity.

The amount of water available on the earth's surface has not changed

measurably for eons, nor will it change significantly in the future.

Yet, population growth continues, placing pressures on -,- lies, and

thereby giving rise to potential demand-supply imbalances through time.

This is especially true in certain regions of the world where water is

available only in very limited quantities.

In 1975, the United States withdrew 338 billion gallons per day of

fresh water for various uses. According to the Second National Assess-

ment of the U.S. Water Resources Council (1978), this amount is expected

to decrease by 9 percent by the year 2000. This decrease is expected as

the result of more efficient use of water through conservation efforts.

On the other hand, consumptive use of water is expected to increase from

107 billion gallons per day in 1975 to 135 billion gallons per day by

the year 2000. The Second National Assessment also estimates instream

water needs for fish and wildlife, hydroelectric generation, navigation,

and recreation. Most of this need is for fish and wildlife. This

report does not address instream uses. A summary of present and pro-

jected usage patterns is presented in Table 1.

Planners, water managers, investors, and legislators in the U.S.

need information on expected future demands for water. This will be

necessary in order to facilitate correct investments in water supply













Table 1. Total Withdrawals and Consumption, by Functional Use, for the 21
Water Resources Regions -- "1975," 1985, 2000 (U.S. Water Resources
Council, 1978)











[million gallons per day]

Functional Total withdrawals Total consumption
use "1975" 1985 2000 "1975" 1985 2000

Fresh water:

Domestic:
Central (municipal) --- ---21,164 23,983 27,918 4,976 5,665 6,638
Noncentral (rural) ------- 2,092 2,320 2,400 1,292 1,408 1,436

Commercial ------------- 5,530 6,048 6,732 1,109 1,216 1,369

Manufacturing ----------- 51,222 23,687 19,669 6,059 8,903 14,699

Agriculture:
Irrigation -------------- 158,743 166,252 153,846 86,391 92,820 92,506
Livestock -------------- 1,912 2,233 2,551 1,912 2,233 2,551

Steam electric generation-- 88,916 94,858 79,492 1,419 4,062 10,541

Minerals industry --------- 7,055 8,832 11,328 2,196 2,777 3,609

Public lands and others1 1,866 2,162 2,461 1,236 1,461 1,731

Total fresh water -------- 338,500 330,375 306,397 106,590 120,545 135,080

Saline water,2 total -------- 59,737 91,236 118,815

Total withdrawals ----- 398,237 421,611 425,212


I' includes water for fish hatcheries and miscellaneous uses.
2 Saline water is used mainly in manufacturing and steam electric generation.










facilities and in provision of information to users with regard to con-

servation measures. Developers of new water :l... technologies also

need reliable projection information. If severe shortages would be

projected, for example, it is expected this would have an influence on

irrigation technologists or developers of household technology as to the

rate at which new water using appliances are made available. Rising

energy prices could also have an influence on the water supply-demand

balance, possibly due to development of other energy sources. It is

expected, for example, that large scale energy development in the

western U.S. will increase pressure on water supplies currently used by

agricultural and residential categories.

The overall purpose of this report is to highlight the problems and

types of approaches that can be utilized in water demand projection for

the agricultural and residential use sectors. The more specific objec-

tives are a) to identify major types and examples of water demand pro-

jection models which have been developed; b) to highlight the major

features of these currently available demand models including data

requirements and types of output; c) to present detailed discussions of

those models which reflect the current state of the art of water demand

projection techniques; and d) to present, by way of example, the applica-

tion of a "first generation" projection model useful for larger, more

aggregate areas over monthly time periods.

This report is intended to serve as a useful manual for those

agencies and entities concerned with projection of water demand for

these use categories. Additionally, this report should be useful to

these same entities in planning for the development and use of better

models in the future.











State water agencies are required to estimate monthly water use for

the present year as part of a nationally supported program. The analyst

is assumed to be provided, on December 31st of the year, with estimates

of the level of economic activity at the beginning and end of the year,

estimates of the rate of water use per unit of economic activity, monthly

precipitation and air temperature data, and other miscellaneous site

specific data. The desired result is the estimate of the monthly water

demand for each land use in each subarea of each study area during the

forthcoming year.

This report describes available models which may be helpful in

making such estimates. The next section presents general information

regarding modelling and defines key terms. The following two sections

present surveys of available models for estimating agricultural and

municipal water demand, respectively.

The fifth section describes an agricultural/municipal demand model

which is a composite and refinement of two existing models. The muni-

cipal model is based on earlier work by Water Resources Engineers (WRE).

The agricultural model is a computer program of the Blaney Criddle

method for estimating crop consumptive use. The program was developed

by the Soil Conservation Service (SCS). The composite program, dubbed

WRE/SCS, is specifically designed to estimate monthly water use. An

example application is included. The summary and conclusions from the

study are presented in Section VI. A more detailed description of the

model is presented in an appendix.











II. GENERAL BACKGROUND INFORMATION


The title of this study encompasses a relatively broad area of

inquiry. This section provides general background information necessary

to more specifically define the problem to be addressed.

In the context of this r,.~., water use means withdrawal use.

This water is withdrawn from ground and/or t'.. i .- sources and

conveyed to the place of use. This type of use is referred to as "off-

stream" use (U.S. Water Resources Council, 1978). This report estimates

water withdrawals and consumption. Major categories of offstream use

include: domestic, commercial, manufacturing, agriculture, steam electric

generation, and minerals industry. For the purposes of this report

these groups are partitioned into two segments: indoor and outdoor.

The other major category is in-stream use for fish and wildlife,

hydroelectric generation, recreation, and navigation. None of these in-

stream uses are included in this report.

The phrase "water demand" is used to indicate explicitly that the

desire for water is influenced by its price. The alternative phrase-

ology, water requirements, implies that activities require a pre-specified

amount or a "shortage" occurs. In an economic context there is only a

shortage of water at a given price. At one extreme, the requirement for

water could be based on a saturation demand, i.e., the amount requested

if the price were zero. The general shape of a demand curve is shown in

Figure 1. The water demand decreases as price increases. Faced with









20O -
0
0
o0
0
DO

L:


SATURATION DEMAND
0 L I
0 50 100 150 200
PER CAPITAL USAGE gal./day

Figure 1. Hypothetical Demand Curve for Water


rising prices, individuals cut back on their usage. In this report,

water demand will be used instead of water requirements. This jargon is

chosen to remind the reader of the importance of economic factors.

The projections to be made by this model are monthly use rates for

a single year. The objective is quite specific. The analyst is at the

end of the study year and seeks to estimate what the usage patterns were

during that year. Alternatively, the interest could be in next year's

usage pattern for some assumed projection of climatological and economic

conditions. These estimates are being made for relatively large areas

and would typically be aggregated into a forecast for the entire state.

The word model is used to describe a set of procedures for making

the water demand estimates. Within the context of this study, an "opera--

tional" model includes the following features: 1) mathematical relation-

ships for estimating water demand; 2) a documented computer program; and

3) some successful experience in using the program.

The next two sections present the results of the review of agri-

cultural and municipal models.












III. AGRICULTURAL WATER lfi'kii .i(.( EL


The literature in the area of agricultural demand modeling is vast.

There are, for example, at least 11 different methods for estimating

potential evapotranspiration (See Kibler, et al., 1980, p. 89; Israelsen

and Hansen, 1967; Criddle, 1958). There are at least 40 different and

significant journal articles limited to attempts at quantifying the

yield-water relationship published in the last 20 years (See Lynne and

Carriker, 1979, for a listing and brief review). Many other such attempts

are documented in more localized publications. In addition, there is a

vast literature where more aggregate (field, farm, state, regional,

national) models have been developed. Thus, a great deal of judgement

was necessary to select representative articles and models. The goal

was to give the reader enough information to form perspectives regarding

the nature of specific modeling approaches and the overall character of

the water demand projection problem.

Computer search techniques were used to identify the newest litera-

ture. Bibliographic searches were also made from reference lists in the

latest publications as well as searches of major journals, especially

those devoted to the water resources field. In particular, Water Resources

Research Journal, the Water Resources Bulletin, and the Journal of the

Irrigation and Drainage Division of the American Society of Civil

Engineers were reviewed. Also the major agricultural economics journals

were accessed, including the American Journal of Agricultural Economics,

the Southern Journal of Agricultural Economics, and the Western Journal of










Agricultural Economics. The following review of the literature is not all

encompassing; however, the authors propose that it is a good sampling and

fairly representative of the major direction, and reflects the flavor of

this research and development effort.


Conceptual Basis and
Framework for Model Discussion

The factors affecting agricultural water use and demand are many and

complex. The basic soil-water-plant climate relationships have been studied

for a long period of time by a large number of scientists. These relation-

ships are fairly well understood; however, this does not really reduce

the fact that the relationships are still complicated and the quantifica-

tion of many relationships is still on the horizon. In addition, the de-

mand for irrigation water in agriculture is affected by the socio-economic-

institutional-political environment. It is through this environment that

the human actor enters into the agricultural water use process (See Lynne

and Carriker, 1979, for further elaboration on this point).

In fact, the conception guiding the presentation in this report is that

water demand is affected by the physical attributes of nature and the

active involvement of man, The latter element enters through the thinking,

innovative features of the human actor as a manipulator and user of the

"natural" system. The fact that there are irrigation systems at all is

testimony to the fact that man is an active element; thus, attention is

directed to whether models allow inclusion of the various features that

man brings to the water demand process, as well as attention devoted to the

physical factors.

Another consideration in organizing this discussion relates to the

nature of the problem faced by entities charged with projecting water use.








A major consideration in this process is usually related to the availability

of water or the water supply. The notion of water demand becomes useful

only within the context of defining the bounds of the water supply for

which demand considerations then become important. A major feature, in

turn, of the water supply phenomenon is the geographic or spatial nature

of water supply. Thus, if water supply and management agencies are con-

cerned about water demand it is usually in the context of the demands

being placed on a particular supply of water which has spatial (as well

as temporal) properties.

All of the agricultural demand models are classified on the basis

of whether they are at the plant-field, farm-firm, multifarm-county-state,

or the river basin-regional-national level. The emphasis is primarily on

the level at which the model has been developed, as opposed to the level

at which it has been used. That is, the field level model can be aggre-

gated to the farm-firm level and possibly even larger aggregates given

appropriate multiplier and aggregation techniques. In fact, some of the

models defined herein as being field level models have in fact been used

in estimating the demand at higher aggregates.

The spatial dimension is a key property. However, there are also ad-

ditional features which must be understood before the reader can gain

perception of their nature. Basically, there are four major categories

of additional features including the temporal, socio-economic, statistical

properties, and the climatic/soil/crop factors. Each of these are now

discussed in turn.

Temporal Characteristics:

The time features of each model are separated in the following

manner:











Short run--This interval of time represents a period over which

only a few of the various factors affecting water demand

can vary. For example, the fertilizer level for a crop

has usually been specified by the time the producer is in

mid-season. Thus, this would be the "short run."

Long run-- This is an interval of time over which nearly everything

can be varied, except the "bounds of the earth." For

example, the agricultural manager may change the irrigation

system, or possibly adopt new cultural practices or new

varieties and farming approaches.

Static-- This concept implies water demand can be viewed as a

series of water use levels at particular points in time.

Water demand is then compared from one point in time to

another. No "feedback loops" or dynamic processes are modeled.

Dynamic-- This concept suggests the model represents the water demand

processes that operate through time, with events today

affecting features of the water use process tomorrow.

Water demand processes are thus linked through time, and

the models reflect these linkages.


Socio-Economic Factors

These factors reflect involvement of the human element as follows:

Prices and/or
Costs of Water--This element is included on the supposition that man

would consider the cost of installing and operating an

irrigation system and that costs affect his behavior, and

thus affect the amount of water used.









Other Input
Prices or Costs--The price of fertilizer would be expected to affect

the amount of irrigation water applied, for example.

Water has no direct substitutes; however, it is anti-

cipated that the costs of all other inputs including

fertilizer, pesticides, and labor all may affect the

amount of water used in an agricultural operation, as

different mixes of input can generally give the same

yield (except the maximum yield).

Prices of
Products--Agricultural-irrigation managers, in most cases, are

concerned about the sales or additional revenue ob-

tained from irrigation, as well as the costs. Thus,

the price received for the product can be hypothesized

as affecting the amount of water actually used.

Technological
Changes--A new type of crop variety or water control method

could dramatically affect water demand. Also, at

the firm level and beyond, the type of irrigation

system that is used will affect water use dramatical-

ly. Of course, this is a supply phenomena as opposed

to a demand feature (i.e., the irrigation system on a

farm is analogous to the private or municipal utility

in a city, in the sense that this is the water supply

portion of the organization).

Production
Process Changes-- The amount of fertilizer and/or the particular spray

program would both affect the marginal response of

irrigation water and, thus, affect the demand for that











water, as examples. Actual changes in cultural prac-

tices would be included under this particular heading.

Behavioral
Features--The driving force behind the human element is captured

here, at the field and/or firm level. One possible assump-

tion might be that farm managers are profit maximizers,

but plausible goals include cost minimization, risk

aversion or maximization of crop yield. The goals and

objectives of managers will likely affect water use and

demand.

Institutional
Features-- The political-legal-institutional setting can affect

water demand through price support programs of farm pro-

ducts and/or the manner in which water rights are speci-

fied, as examples. Water management districts in Florida,

for example, encourage conservation through such modes as

encouraging irrigation during low evaporative demand

periods. Farm price support programs may make irrigation

more profitable, as another example.


Statistical Properties

This feature relates to the degree to which random events have been

incorporated into the projection processes, as follows:

Stochastic-This concept rests on the hypothesis that random influences

affect the projection level. Given a particular water

demand projection there will be an associated variance of

that estimate. The larger the variance, the less reliable

the estimate is.









Deterministic--The notion here is there is no random error and that

water demand projections exhibit no variance proper-

ties and particular levels are known with certainty.


Climatic-Soil-Crop Features

This category includes all those physical features of the environment

in an agricultural field situation that affect the amount of water used.

These variables are essentially proxies for the complex phenomena involved

in an actual field as follows:

Temperature or
Heat Budget--The mean daily or maybe monthly temperatures are used

in several models. The heat budget notion depends on

an understanding of the relationship among radiation,

actual duration of sunshine, maximum possible duration

of sunshine, vapor pressure in the air, vapor pressure at

mean air temperature, and several other variables (see

Israelsen and Hansen, p. 241).

Length of
Growing Season--This variable will affect the consumptive use of the

plant, for obvious reasons.

Precipitation--This is a stochastic variable which is difficult to

predict but most assuredly affects the water demand

from ground and/or surface sources. This effect is

through influence on the air/environment surrounding

plants, as well as having an effect on soil water

availability.

Soil Character
or Soil Water
Capacity--The water holding capacity of the soil is a key

variable in determining consumptive use. Soil










texture and structure are especially important as these

forces give rise to "capillary phenomena." These affect

the flow or movement of water in soils and the availability

of water or plant growth.

Humidity and/or
Wind Conditions--This is simply another weather factor that affects evapo-

ration and general conditions of the crop.

Sunlight, Solar
Radiation--An energy source, of course, is necessary to drive the

entire plant growth process. The amount of solar radia-

tion will affect the amount of water used.

Specific Crop
Features--The root system and leaf area of the plant in question

will affect the amount of water used. Alsq different

crops are at different stages of growth at different

times of the year. In addition, plants will use varying

amounts of water through their growth process with the

highest consumptive use, relative to the potentialuse, occur-

ring somewhere during the flowering stage (Israelsen and

Hansen, p. 257).

Evaporation or
Potential Evap-
otranspiration-- This factor is a function of many of the soil/climatic/

crop factors mentioned above. It really measures, as a

proxy variable, the overall influence of these elements.

It is included here because many of the yield models rely

on measurements of relative evapotranspiration, where

either evaporation or potential evapotranspiration serves

as the denominator of the ratio.









A listing of the models by the major categories using the above

classification system is presented in Table 2. Tables 3-24 are used to

detail the specifics of each model. The reader should be warned that

it is very difficult in many cases to determine whether the model

developers considered specific factors or not. To this extent, these

tables will be in error. The main criterion was that the variable had

to be mentioned and used explicitly in the model and/or the model

development process.


Overall and Major Features of
Agricultural Water Demand Models

Nearly all models reviewed are short run, static models with deter-

ministic statistical properties (Table 2). Only one model really incor-

porated any stochastic influences in the projection stage. The Pennsylvania

model allowed for yield variability, an estimate of this variance, and the

overall effects on water use.

Another overall feature applicable to the entire set of models is

that some tended to emphasize the socio-economic factors and others,

usually not the same ones, emphasized the climatic-soil-crop factors

(Table 2). If in fact water demand is affected by behavioral, social,

political, institutional elements as well as temperature, precipitation,

soil factors, and crop features, then the "best" models from the set

shown in Table 2 are probably the ones having the most of these features

included. On this ground, it appears that the Mapp-Eidman model is

the most appropriate over the entire set, followed very closely by the

Utah, North Carolina, and CARD models (Table 2).

The plant-growth type of model, if modified to include socio-economic

factors as well, appears to show the most promise for the future with








Table2.--Major features of agricultural water demand models3


Tempo ral


Spatial properties
and model names


Plant-field level
models:


Blaney-Criddle

Hargreaves

Hexem-Heady

Hogg, et al.

Minhas, et al.

Penman

Plant Growth

Thorntwaite


Farm-firm level
models


Mapp-Eidman

Moore-Hedges


County-nulti-
county-river
(or sub) basin
state models



Input-output

Kansas

Lowry-Johnson

New Mexico

North Carolina

Pecos Basin

Pennsylvania

Texas High Plains

Utah


River basin-
regional-national
models


CARD

Ruttan


Chiaracterist ics


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aBlanks sometimes mean the information was not available. See the text for elaboration. An "X" means these elements, factors were
considered explicitly in the model.

bThe plant growth models require detailed information on how the photosynthetic-respiration rate is affected by climate, soil, and p1.
features.

cThe yield simulation portion of this model is really a plan, growth model, although. not as detailed as the models discussed briefly
under the "Plant Growth" category. See footnote a.

dAlso includes interactions among the various inputs of production (e.g., the fertilizer-water interaction effects).









respect to incorporating these different factors into the demand projection

process. The Mapp-Eidman model does incorporate many features of the

plant-growth simulation approach. These types of detailed models are also

the most expensive and difficult to develop.

Several models did include other input prices and/or the costs of

other inputs in the modeling effort. Only in the case of the Hexem-

Heady model did the other input prices affect the water use,nowever. That

is, it can be hypothesized the demand for water may be affected by the

prices of substitutes for water including such things as fertilizer and

other inputs of production to the crop process. The Hexem-Heady study

isolated the effects of fertilizer in order to facilitate the direct con-

sideration of changing fertilizer prices. The other studies tended to

include the costs of all other inputs under one category and not deal ex-

plicitly with the substitutability problem.1 It appears modelers have yet

to successfully deal with this dimension.

Another basic feature of nearly all the models was that technology

was generally assumed constant over the projection interval. The one ex-

ception was the Kansas model which allowed for changes in irrigation ef-

ficiency over the longerrun. An explanation for this invariance in tech-

nology is that most models are short run in nature, in which case it is

logical to hold technology constant. Over longer run periods, however,



This is somewhat misleading with respect to the Texas High Plains
Model. The developers of that model did in fact allow energy prices to
vary, and they map the effect on water demand from rising energy prices.
However, this is essentially the same thing as raising the price of water
and is not necessarily dealing with the substitution phenomena at all. The
CARD model also allows for consideration of some input price changes and
the effect on water demand and use, but the full range of substitutability
among input factors was not allowed in that modeling process either.











technology could have a significant impact on the quantity of water utilized.

This would be exemplified through variety changes and/or changes in the

cultural practices and/or changes in the irrigation system, as examples.


Specific Features of Agricultural
Demand Models by Spatial Property

Each of the models is now discussed in more detail. Emphasis is on

explanation of model similarities and geographic-spatial differences

as the major influence for large model differences.


Plant-field level model

The mathematical description of each model is the first item in each

of the Tables 3-10. All of the approaches are limited to a few equations, all

of which require estimates of various parameters. Some of the more "physi-

cal models" have parameters that have been fairly well established by

researchers, such as for the Blaney-Criddle model. Others require para-

meter estimation for the site of concern such as in the Hexem and Heady

models. This latter feature is also descriptive of the Hogg et al.,

and Minhas et al. models.

The most common feature is that all models project water demands

for some land area, most generally an acre or hectare. Also, all are short

run models usually concerned with estimating demand on an annual crop year

basis. Some are appropriate for growth stage (intraseasonal) projection

such as the Minhas et al., and the plant growth type models. The water

used during growth stages can also be approximated using the Blaney-Criddle

Hargreaves, Penman, and the Thornthwaite models. This is the case as most

of these models use a month during the growing season as the appropriate

time period. Thus, the various monthly periods can be appropriately








Table 3.--Blaney Criddle Model (After Israelsen and Hansen)


SUMMARY DATA


Mathematical description


Type of output


Temporal properties



Spatial properties

Input data required




Technological production
process change



Behavioral assumptions and
institutional settings


kf and U = Ekf = KF, where
consumptive use of crop, inches for a given time period;
empirical coefficient (annual, irrigation season, or growing season);
sum of the consumptive use factors for the period;
monthly consumptive use of the crop in inches;
empirical consumptive-use crop coefficient for a month; and
monthly consumptive use factor (sum of mean monthly temperature and
monthly percent of annual daylight hours or (t x p)/100.
Note: Values of (t), (p), (f), and (k), can also be made to apply to
periods of less than one month.


Total monthly water demand.


Can be used for varying time periods, generally, a season or one year.
It is dynamic only in the sense that climatic factors throughout the
year are used; it is essentially a static model.

Generally, estimates are made on a per acre basis,

Data are needed on temperature, rainfall, the percent of annual daytime
hours, and the empirical crop coefficient. These data are available from
local and/or state agencies, the Soil Conservation Service, and local
experiment stations.


Irrigation and/or crop technology are not considered in this projection
model. Also, the crop is considered to have Lt-il quantities of other
input, commensurate with maximum yields.


Neither of these is made explicit; however, use of this approach assumes
implicitly that farm firm managers wish to maximize yields and that the
institutional environment does not affect use.


CHARACTERISTIC













Table 3.--Blaney-Criddle Model (After Israelsen and Hansen)--Continued


CHARACTERISTIC


SUMMARY DATA


Stochastic/deterministic
features

Climatic/soil/crop factors









Documented computer
program






Data base


References


The model is deterministic.

The Blaney-Criddle model explicitly considers temperature and daytime
hours. Basically, the term F represents a proxy for the potential
evaporation and/or potential evapotranspiration. The sunlight or solar
radiation factor is considered via the length of the growing season and
the percentage of daytime hours for the time period of concern (as a
percent of the total for the year). The specific crop coefficient is
the amount of water that a non-stressed crop will use during a parti-
cular period of time.


A computer program and users manual are available through the Soil Con-
servation Service of the United States Department of Agriculture. This
program also calculates irrigation water needs under the behavioral as-
sumption that producers maximize yields. A detailed documentation of
the actual computer program is not available.

Input data are readily available from national/state data bases for all
input parameters except the empirical crop coefficient. Even for this
need, however, there are estimates in the SCS publication, Technical
Report No. 21. Also, agricultural experiment stations in the respective
states have some information on this coefficient.

Blaney and Criddle (1947); Soil Conservation Service (1969; 1970)













Table 4.--Hargreaves Model


CHARACTERISTIC


Mathematical description










r Type of output


Temporal properties


Spatial properties

Input data required

Technology/production
process changes



Behavioral assumptions and
institutional settings

Stochastic/deterministic
features


SUMMARY DATA


(After Criddle, 1958, pp. 1507-12). e = m(t-32) where e = monthly
evaporation in inches, m = an empirical factor; t = mean monthly temper-
ature in-F. When corrected for the time element, it becomes e = cd(t-32)
where e = climatic factor; d = monthly daytime coefficient. Also, dis-
regarding wind movement, c = 0.38 0.0038 h where h = mean monthly
humidity at noon. Then U = KE = Eke where U = annual or seasonal con-
sumptive use (actual ET) of the crop; K = crop coefficient; E = sum
of monthly evaporation for the period; and k, e = monthly values of
K, E.

The physical requirement or actual ET (total water demand) is estimated
with the model, as shown by U above.

The model is suitable for seasonal predictions and/or shorter periods
like one month intervals.

The equation is suitable over larger areas or at the acre, field level.

Mainly climatic data is required as shown in the above mathematical description.


It is assumed that all other input levels and technology are invariant.
Further it is assumed the plant is not being stressed by any other fac-
tors. Of course, alternative levels of K could be selected.


No explicit statement of the role of the human element.


The model is deterministic.














Table 4.--Hargreaves Model--Continued.


CHARACTERISTIC SUMMARY DATA


Climatic/soil/crop factors






Documented computer program

Data base


Reference


This model basically uses a relationship between evaporation, tempera-
ture and length of day. Wind movement and the influence of water vapor
is also considered via relative humidity included as a variable. A
crop coefficient is also necessary for the model which varies with the
season of the year.

None available.

Climatic data available from the U.S. Weather Service.


Criddle (1958).












Table 5.--Hexem and Heady Models


SUMMARY DATA


Mathematical description


Type of output







Temporal properties


Spatial properties


y = b + blX + b2x2 + b3x1 + b x + b x x
0 1 1 2 2 3 1 4 2 51 2


Profit = T = P Y r lx r 2x2 with x2 = constant ("short run:)

3Hr SY r -P (bl+b5x2
- = Py I r = 0 or P (bI + 2b3x + b5x2)= or0 = yb
Dx1 y1 1 y 1 1 1 2P b3

This is the "short run" demand function. The "long run" (fertilizer
also varying) demand function would be given by the simultaneous solu-
tion of (07/Dx1) = 0 and (0T/x2) = 0. The general form will be x =
f(rl, r2, p ) where xl = total water available, in acre inches,
x2 = fertilizer applie; py = product price: r, = water price and/or
irrigation cost, for that portion applied through the irrigation
system; r2 = fertilizer price; bl, b2, b3, b4, and b5 = parameters.

The production function as exemplified by these models allows the deri-
vation of short run and long run demand functions as illustrated in the
mathematical description. Thus, the quantity of total water demanded
can be shown to be a function of changes in various physical phenomena
as reflected in the production function but also will be affected by
changes in the prices of the water and fertilizer and the product price.

These models are usually annual in their time step. Also, they are
static models and can be used for comparative static analyses.


These models are on a per acre basis.


CHARACTERISTIC














Table 5.--Hexem and Heady Models--Continued


CHARACTERISTIC


SUMMARY DATA


Input data required



Technological/production
process changes



Behavioral assumptions and
institutional settings


Stochastic/deterministic
features


Climatic/soil/crop factors



Documented computer program

Data base


Detailed experimental station kinds of data are needed showing the rela-
tionship between yield response and fertilizer and water applied. Also,
input and product prices are needed.


These water fertilizer models allow the fertilization program to vary.
However, all other cultural practices and technological features are
assumed invariant.


The farm firm manager is assumed to be a profit maximizer. The institu-
tional setting is assumed invariant.


This is a deterministic model where the independent variables are assumed
to be measured without error.

The water variable in these regression models is generally the sum of
water available in the soil plus precipitation plus irrigation water
applied.

None available.

Experimental data on the yield-water relationship are available from agri-
cultural experiment stations on a limited basis, with some states having
much more than others. Product price data are available from the Crop
and Livestock Reporting Service, a cooperative effort between state and
federal entities in each state. Irrigation cost information will also,
be available from the agricultural experiment stations.


Hexem and Heady (1978).


References













Table 6.--The Hogg, Davidson, and Chang Model


CHARACTERISTIC


SUMMARY DATA


Mathematical description


R + (NxS)
Se
E
p


Y


Y
a _
Y
P


E
f() = a + b (E /E ) + c (E /E )
EPa p ap


Profit = 7T = PY r(NxS) TC
a


-= P[f'(Y )] r = 0
I a
e


where E = the actual consumptive use or actual evapotranspiration;
E = the potential evapotranspiration; Re = effective rainfall; N =
the number of irrigation rounds; S = the soil moisture storage; Y =
actual yield; Yp = potential yield, a, b, c, = parameters; P = product
price; r = irrigation costs; and/or price of irrigation water; TC =
other costs of production; Ie = (NxS) = level of effective irriga-
tion water.


Type of output





Temporal properties

Spatial properties

Input data required


The short run, profit maximizing total water demand curve is defined
by the relationship Pf'(Ya) = r. Thus, the demand for Ie is affected
by product price, the cost (and/or price) of irrigation water, and any
other factors affecting the production function.

This is a seasonal and static model.

The yield response is estimated for an acre of land.

Detailed information is required on the relationship between yield and
relative evapotranspiration as well as detailed level measurements on
effective rainfall. Also some estimate of potential evapotranspiration
must be available. Prices are needed for the product and irrigation
cost must be known (and/or prices of irrigation water).














Table 6.--The Hogg, Davidson, and Chang Model--Continued


CHARACTERISTIC


SUMMARY DATA


Technological/production
process changes


Behavioral assumptions and
institutional settings


Stochastic/deterministic
features


Climatic/soil/crop factors





Documented computer program

Data base


All other inputs of production are assumed constant. Technology is
also invariant.


The farm firm manager is assumed to maximize profits. The institutional
setting is assumed invariant.


The model is used in deterministic manner; however, stochastic influ-
ences could be examined.

This model accounts explicitly for the actual to potential evapo-
transpiration, rainfall, and soil moisture storage. An attempt was
made to include "--the relevant aspects of agronomic theory while
retaining reasonable simplicity" (Hogg, Davidson, and Chang, p. 127).

None available

Field experimental data and irrigation cost informationare available in
limited quantities from state agricultural experiment stations. Product
price data are available from the Crop and Livestock Reporting Service
in each state.


Hogg, et al., (1969).


Reference












Table 7.--The Minhas, Parikh, and Srinivasan Dated Input Model


CHARACTERISTIC


SUMMARY DATA


Mathematical description


AET = -rz)/(B + e-rz
x = f(z) = --i = (1-e )/(B + e )


[1(-x 2 b2 [1(x 2 b
[i_( -x2)2] [l_(l-xn) ] n


Y = a[l-(l-x1) 2 bl


w.
wl + w2 = ; (PET)(xl) + (PET2)(x2) = W; Xl = PET.
1

Sy y 1
Sw. Sw. (PET)
1 1

where x = relative ET, or actual ET (AET) divided by potential ET(PET);
z = available soil moisture; r,B = constants, parameters; y = yield per
unit land area; xj = relative ET in growth period j; bl,...,bn = para-
meters associated with yield response in alternative growth stages;
wi, W = wi is water available in crop growth stage i, W is the total
water available for the crop growth season. [Note: The profit maximi-
zing short run (intraseasonal) demand curve for this model would then
be derived from the equation ri = P(---)( 1 ) where p = product prices;
S xi. PET.


ri = price or marginal factor cost
did not calculate this function in
maximum profit demand curves would
all such short run demand curves].


of one more unit of wi. Minhas et al.,
the paper, The optimal seasonal,
result from simultaneous solution of


A total water demand curve can be derived given a production function,
as shown above. Note: the demand for total water (W) is a function
of the product price, the quantity of water available during other por-
tions of the growing season (wi) and the price (or marginal factor cost)
of one more unit of water.


Type of output














Table 7.--The Minhas, Parikh, and Srinivasan Dated Input Model--Continued


CHARACTERISTIC SUMMARY DATA


Temporal properties


Spatial properties






Input data required






Technological/production
process changes


Behavioral assumptions and
institutional settings




Stochastic/deterministic
features


This type of model is suitable for intra-seasonal or seasonal estimates
of water demand. One could also project longer periods.

This model was developed to explain yield response for a hectare. Field
and farm firm level estimates could be made. More aggregate estimates
are also possible but of course, there may be errors in estimation as
we go beyond the type of field and soil conditions for which the function
is developed.

Detailed information is needed on the relationship between relative evapo-
transpiration and available soil moisture. In addition, experimental data
is needed to relate yield to the relative evapotranspiration. Product
prices would have to be estimated and the costs of irrigation and/or the
prices of irrigation water would have to be known.


This particular model assumes all other inputs are at fixed quantities
and technology is invariant.


The farm firm manager is assumed to maximize profits and/or minimize costs
(the latter goal related to some sort of an output constraint). The in-
stitutional setting is assumed invariant, although variations could be
allowed in the model.


The model is deterministic, but the variance on profit could be estimated.
The input variables are assumed to be deterministic and measured without
error.













Table 7.--The Minhas, Parikh, and Srinivasan Dated Input Model--Continued


SUMMARY DATA


Climatic/soil/crop factors








Documented computer program

Data base


These authors were sensitive to the need to establish the relationship
between available stocks of moisture in the soil and the rate of water
used by the plants. Then they define the relationship between the time
profiles of water use and crop yields (p. 383). They choose to sum-
marize many of the climatic soil factors by establishing a functional
relationship between relative evapotranspiration and available soil
moisture. Then they relate yield to relative ET.

None available.

Field experimental data and irrigation cost information is available to
some extent from state agricultural experiment stations. Product price
data can be obtained from the Crop and Livestock Reporting Service in
each state.


Minhas, et al. (1974).


CHARACTERISTIC


Reference














Table 8.--Penman Model


CHARACTERISTIC


SUMMARY DATA


Mathematical description


ET = A + 0.27Ea I = R (l-r) (0.18 + 0.55n/N) 3T4 (0.56 0.092/ed)
A 0.27 A a


(0.10 + 0.90n/N)


Ea = 0.35 (ea ed)(l + 0.0098n2) where 11 =


daily heat budget at surface in mm H20/day; RA = mean monthly extra
terrestrial radiation in mm H20/day; r = reflection coefficient of
surface; n = actual duration of bright sunshine; N = maximum possible
duration of bright sunshine; 3 = Boltzman constant; Ta = mm H20/day;
ed = saturation vapor pressure at mean dew point (i.e., actual vapor
pressure in air) mm Hg; Ea = evaporation in mm H20/day; ea = saturation
W vapor pressure at mean air temperature in mm Hg; n2 = mean wind speed
at 2 meters above the ground (miles/day); ET = evapotranspiration in
mm H120/day; u1 = measured wind speed in miles/day at height h in feet;
A = slope of saturated vapor pressure curve of air at absolute temper-
ature Ta in 0F (mm/Hg/0F).


Type of output




Temporal properties



Spatial properties


Input data required


Consumptive (total water) demand measured in mm of water per day. The
level of aggregation is simply a matter of multiplying the estimates
times the acreage figure. This equation estimates the potential evapo-
transpiration which is not related to crop type.

Generally used for intraseasonal predictions. It is a time dynamic
model to the extent that predictions will vary through the years and are
only limited by the extent of the weather information to the user.

Crop or field level although results can be generalized at the larger
areas.

All of the climatic variables illustrated above in the mathematical
description.












Table 8.--Penman Model--Continued


SUMMARY DATA


Technological/production
process changes



Behavioral assumptions and
institutional settings


Stochastic/deterministic
features


Climatic/soil/crop factors








Documented computer program

Data base


No changes are considered in the agricultural production process or in
technology. This model assumes the crop is not being stressed for any
cultural or technological reasons.


Both of these variables are assumed invariant. The implicit behavioral
assumption is that farm firm managers wish to maximize yield.


The model is deterministic in nature, with no statistical reliability
coefficients having been estimated.

The Penman Model is theoretical in nature and uses basic structural
relationships from physics and other basic sciences to relate several
climatic variables. That is, this model utilizes several climatic
variables most of which are defined above in the mathematical section.
There are no crop factors involved, however. The basic feature is that
consumptive use is assumed to be "--inseparably connected to incoming
solar energy" (Israelsen and Hansen).

Availability unknown.

Climatic variables from the U.S. Weather Service


Israelsen and Hansen (1967); Penman (1948).


CHARACTERISTIC


References













Table 9.--Plant Growth Models


CHARACTERISTIC SUMMARY DATA


Mathematical description As noted by Jones (1979) crop growth is usually related to the differ-
ence between photosynthesis and respiration multiplied by a conversion
coefficient between biomass and CO2 as follows:

1 dW
S- = (Pg RW)/(l + OGR)


where W- = biomass growth rate (kgha-lday )
dt1
0 = biomass: CO2 conversion factor (kg biomass kg CO2)
P = gross photosynthesis (kg CO2 ha-l day1 )
R = maintenance respiration factor (kg CO2 kg-1 biomass day )
W = biomass(kg ha-)
GR = growth respiration factor (kg CO2 kg-1 biomass).
dW. dW. dW.
Production is then represented by: dt- = ai- where ---= biomass growth

rate of leaves (1=l), stems (i=2), roots (i=3), and fruit (i=4). ai =
partitioning coefficient for leaves, stems, roots, and fruit.
Jones notes that "crop growth models vary in detail and complexity---
generalities are used to describe this overall approach because of a
lack of a universally accepted framework for representing crop growth
processes and their interrelationships."
Water stress will reduce photosynthesis; thus, there is a relation-
ship between water availability and yield. Water balance equations are
included in these models, when water demand is of concern.












Table 9.--Plant Growth Models--Continued


SUMMARY DATA


Type of output


Temporal properties






Spatial properties

Input data required








Technological/production
process changes


The yield associated with various levels of total water being made
available are the direct output of these kinds of models.

Usually these are daily models with seasonal yield projections. These
models usually have the capability of telling the state of the plant-
soil-water-condition at any given day in the season. They are also
dynamic in nature with effects causing changes today and on future
days.

These are usually developed on a per plant and/or per acre basis.

Climatic data are needed to estimate evapotranspiration and to calculate
a soil water balance. Detailed information is also needed on maximum
and minimum air temperature-soil data, including soil water retention
curves, root zone depth, and unsaturated hydraulic, conductivity re-
lationships. Crop parameters must be specified as well. Of course,
the detailed structural relationships, some of which are described
above, must also be input.


Generally, these models allow that other inputs of production (for example,
fertilizer, pest control programs, other cultural practices) can be
varied, and also affect yield. Thus the interaction between water and
other inputs can be isolated. Technology is generally assumed invariant,
although different varieties can usually be evaluated for any given
crop model.


CHARACTERISTIC














Table 9.--Plant Growth Models--Continued


CHARACTERISTIC


SUMMARY DATA


Behavioral assumptions and
institutional settings




Stochastic/deterministic
features


Climatic/soil/crop factors







Documented computer program

Data base


The human element is not explicitly included in these models. However,
it is recognized implicitly that the manager may wish to vary the
various input and thus this flexibility is built into these models.
The institutional setting is not a consideration for these models.


These models are generally deterministic in nature. It would be possible
to consider stochastic processes.

These models build from knowledge of the structural relationships involved
in soil physics, plant physiology, climatic forces, as well as the
relationships among climatic/soil/plant factors. Of all the modeling
approaches, this particular method utilizes the most theory and concept
as well as empirical measures, with respect to this particular charac-
teristic.

Extent of documentation unknown.

Much of this information is available from agricultural experiment
stations. Basic climatic information will be available from the
U.S. Weather Service.


Jones and Smajstrla (1979); Jones et al., (1972).


References












Table 10.--Thornthwaite Model


SUMMARY DATA


Mathematical description







Type of output


Temporal properties

Spatial properties


Input data required


Technological/production
process changes


Behavioral assumptions and
institutional settings

Stochastic/deterministic
features


A monthly heat index is calculated from the following expression
i = (t/5)1.514 where i = heat index and t = temperature. A seasonal
heat index value is obtained by adding all of these individual monthly
temperature values. A straight line has been drawn from the "index
point" through this heat index which gives a relationship between
temperature and evapotranspiration.

Estimates of the potential evapotranspiration or total water demand
with no allowance made for different land uses or crop.

Usually used to estimate seasonal water use.

Formula has been used to estimate potential ET over extensive portions
of the world.

Basically, only temperature and latitude are needed, beyond the basic
equations (which include some parameters) developed by Thornthwaite.


As noted above, the crops and their particular features are not included
explicitly.


Again, the human element is not explicitly considered in this equation.


The model is deterministic.


CHARACTERISTIC














Table 10.--Thornthwaite Model--Continued


SUIMARY DATA


Climatic/soil/crop factors






Documented computer program

Data base


References


This model basically assumes that all the climatic factors can be
summarized with the proxy variable temperature. Latitude is added to
the measure and projections made over larger areas. No crop coefficients
are included, although some work has shown that accumulated consumptive
use is an excellent index to stages of plant growth.

None available.

Temperature data available from the U.S. Weather Service.

Israelsen and Hansen (1967); Thornthwaite and Mather (1955; 1957).


CHARACTERISTIC








aggregated given some assumptions about the length of each stage of

growth of the plant.

None of the plant-field level models included technological changes

and only two incorporated production process changes. Technological

change phenomena is of course not necessarily included when only very

short run periods are being examined. The production process changes,

however, probably should be included, but again, they are not important

over very short time periods. None of the models at this level included

institutional features and about half of them included behavioral features.

The institutional setting is also probably relatively fixed within a crop

season, and this would be appropriate.

The exclusion of behavioral features tends to reflect a notionthat

man does not affect water use, an hypothesis that could be tested. In

some sense, however, the exclusion of the behavioral element is simply not

possible. Said somewhat differently, even the projection models which do

specifically include man assume (implicitly) the goal of maximizing yield

per unit land area. This is the case for the Blaney-Criddle, Hargreaves,

Penman, and the Thornthwaite methods. The Plant Growth simulation models

could be developed to include the influence of the human element involved

in irrigation processes as well as the features of the plant and the soil

water relationship pertaining to a particular field.

The type of output varies greatly among these plant-field models.

This is the case primarily due to the role ascribed to, and the objective

function assumed for, the human actor. The Hexem-Heady, Hogg et al., and

Minhas et al., models, for example, all assumed that producers will choose

to maximize profit. As a result, it is likely the projections for a par-

ticular area would be different than those from models where maximum yields










are assumed. Of course, this is an empirical question and cannot be

answered in any general way. In all cases the total water demand is pre-

sented for some intraseasonal and/or seasonal period. Irrigation water

requirements then depend on precipitation received. There is substantial

variation in the degree of sophistication used to represent climatic/soil/

crop factors in this group of models. The Hexem-Heady models, for example,

attempt to quantify all the complexity of these factors by simply adding

the sum of available soil water to the precipitation plus the irrigation

water (Table 5). The Plant Growth models at the other extreme (Table 9)

include detailed structural relationships which explain how water moves

through the soil and the plant to affect growth. The Penman model, which

is useful for estimating potential evapotranspiration, has very detailed

theoretical conceptual relationships requiring a large number of parameters

as well as input data. The Hogg-Davidson-Chang model and the Minhas-Parikh-

Srinivasan models do incorporate some agronomic factors and may be a good

compromise between the two extremes for certain types of applications.

Several of the models choose to summarize all of these factors within the

relative evapotranspiration ratio (Tables 6, 7, and sometimes the plant

growth models as in Table 9).

Input data requirements vary extensively across these models. At one

extreme is the plant growth type of model which requires a high degree of

sophistication in the plant-engineering sciences in order for the model to

be developed. Also, if these models included the socio-economic factors, it

would require the same degree of sophistication in the socio-economic

sciences. Models at the other extreme, while not necessarily technically

less sophisticated, require only secondary data sources. The Blaney-

Criddle, Hargreaves, and Thornthwaite models fit in this category. As an









example, only three pieces of information are needed for the Blaney-Criddle

model including temperature, the percent of annual daytime hours, and the

empirical crop coefficient (Table 3).

The models which attempt to relate yield to various proxies for the

water variable, such as the Hexem-Heady, Hogg et al., and Minhas et al.,

models require data from experimental trials. These types of data would

generally have to be obtained from agricultural experiment stations and

a high degree of technical sophistication will be necessary to arrive at

the actual functions. Useful models of this type require successful inte-

gration of knowledge from the crop-soil sciences, economics, and statistics.

The major data sources for this category of models are the agricultural

experiment stations, state/federal weather services, and the federal/state

crop and livestock reporting services. Utilization of such models will

probably require establishing contacts and working relationships with

scientists and personnel of these entities. Generally speaking, there

has been little effort placed into computer program documentation and

user manual development. The only known users manual in this category is

that available from the Soil Conservation Service. This manual explains

how to use the computer program which implements the procedure in Technical

Release 21.


Farm-firm level models

The mathematical description of these kinds of models is characterized

by the simulation approach used in the Mapp and Eidman model (Table 11) and

the linear programming models as developed by Moore and Hedges. The



A third type of mathematical model developed at the firm level but not

represented here is the regression type of model. A large amount of work













Table ll.--Mapp and Eidman Model


CHARACTERISTIC


Mathematical description


SUMMARY DATA


This is a simulation model with a crop yield simulator as an important
and basic component. The basic features of the yield simulator are as
follows:
YR k. = k (StMD ) + bk (P.. P ) YR = IZ YR.
i3 J ij 3 ij A 1j


k k
where YR.. = yield reduction on day i for stage j and crop k; 3. =
yield redaction in units per day as a result of adverse soil-water con-
ditions, stage j and crop k; SMD.. = soil-water depletion in inches on
day i for stage j; bk = yield re~Action coefficient due to severe at-
mospheric demands, stage j and crop k; Pi = pan evaporation in inches,
day i and stage j; PA = critical pan evaporation level; if at or below
o this level, yield reductions odcur due to severe atmospheric conditions.
The SMDi. was calculated by SMD.. = (a SMTij)/b where a,b = parameters
associated with the soil type; STi. = inches of soil water in the entire
profile on day i of stage j. Prices of the products and several of the
inputs (nitrogen, seed, labor, capital, irrigation water) are also input
variables.


Types of output



Temporal properties


Spatial characteristics


Net farm income for a representative farm firm is projected under dif-
ferent water availability and institutional change scenarios. The
demand for irrigation water is predicted.

The model works on an intraseasonal basis but is used to project farm
income over several years of time.

It is a firm level model for a typical 648 acre firm in Oklahoma, using
water from the central Ogallala formation.













Table ll.--Mapp and Eidman Model--Continued


SUMMARY DATA


Input data required








Technological/production
process changes


Behavioral assumptions and
institutional settings


Stochastic/deterministic
features


The yield simulator requires certain types of parameters and input on
precipitation and climatic conditions, as shown in the above description.
In addition, information is needed on resource availability, crop types
to be grown and the cost of growing various crops. Such yield simulators
must be developed by professionals having knowledge of basic plant water
relationships. Generally, this expertise as well as other data re-
quirements are available from agricultural experiment stations.


The simulation model is oriented towards examining the effects of price
changes, or a tax policy, on the water input. Or, it has the capability
of examining the effects of different water availability plans. The
yield simulator is not sensitive to changes in other cultural practices,
such as fertilization programs. Similarly, the current version ap-
parently does not allow for examining alternative technological features
that may occur in the future. Of course, such simulators can be gener-
ally modified to deal with the wide range in types of outside influ-
ences on net farm income.


The farm firm managers are assumed to be profit maximizers. Several
institutional changes relating to the allocation of water to agri-
culture can be examined with the model.


The model is deterministic in nature.


CHARACTERISTIC














Table ll.--Mapp and Eidman Model--Continued


CHARACTERISTIC SUMMARY DATA


Climatic/soil/crop factors











Documented computer program

Data base


The underlying yield simulator for this model requires a fairly de-
tailed consideration of basic relationships. Rainfall pan evapora-
tion distributions were necessary. Soil water is then estimated
given some initial starting value by using the daily rainfall and pan
evaporation values which in turn were generated from probability dis-
tributions. Potential evapotranspiration is calculated from pan
evaporation given some knowledge of the stage of growth. Two layers
in the soil's profile are modeled and the amount of water kept in
each is monitored. The simulation model makes all of these calcula-
tions each day of the growing season.

None available.

Most data available through agricultural experiment stations. Climatic
and product price information will be available from state/federal
sources.


Mapp and Eidman (1976); Mapp, et al., (1975).


References









Mapp-Eidman model uses a plant growth simulator as its basis. This simu-

lator generates the yield for varying levels of water availability. Various

acreage combinations of the crops in the study area are included. Also, a

particular type of farm manager is assumed, namely one who is "rational"

in the sense of seeking profits and/or minimizing costs. The model is

actually used to examine the short and long term effects of a declining

water supply to a farm firm. The price of water is increased over time

and compared with the results when less water is available.

The Moore and Hedges model also has the capability of examining de-

mands over longer time horizons (Table 12). This is a linear programming

model with the normative influence of the assumption that farm managers

maximize profits in dictating the optimal organization of a farm firm.

In this model, not only crop types can vary, but also the crop acreages,

whereas in the Mapp-Eidman model the crop acreage is an estimate of net

farm income as well as demand for irrigation water under different price

assumptions.

Technology is not addressed directly in either of the models, even

though long run projections are provided. This puts both of the models

subject to question. Also, the interaction effects between irrigation

water and other inputs of production process changes are invariant over the

time horizons considered. Both models are deterministic. The Mapp-Eidman

model is much more explicit with respect to including the climatic-soil-



was accomplished by agricultural economists in the 1950's in the attempt
to develop production functions at the firm level using regression tech-
niques. These efforts were generally not successful, because of high
multicollinearity among the independent variables. See Lynne (1977) as
an example of this type of approach.














Table 12.--Moore and Hedges Model


CHARACTERISTIC


SUMMARY DATA


Mathematical description











Type of output


This is a linear programming model with a parametric objective function
where costs are varied. In particular the costs of irrigation are
varied.. The model is a set of linear equations for a farm firm in
California within a highly intensive crop area. Constraints are placed
on the model such as percentage of different grade land, cotton allot-
ments, contract agreements and requirements, production regulations,
certain restrictions on maximum amounts of certain crops, and restrictions
for twelve critical time periods in terms of irrigation water. Nine
alternative crops are considered under three irrigation treatments and
the two soil grades giving rise to 54 possible production activities.

A water demand function showing the demand for irrigation water results
from the model showing costs of irrigation and/or price of water as a
function of the amount of irrigation water used.


Temporal properties


It is shown
irrigation.
of what may


that less irrigation water will be used for higher costs of
The model is static in nature, but gives some perception
occur over longer run periods.


Spatial characteristics


Input data required



Technological/production
process changes


The model is developed for an individual farm, and aggregated using
weights to represent the distribution of farm sizes in the study area.

Detailed data are needed on the costs and returns of production for the
various crops. This includes technical coefficients for irrigation
water during the critical growth periods for various crops.


Although not clear from the model description, it appears that only the
irrigation costs can be changed readily within the model. The other
inputs are evidently entered as cost values and were not considered to
change. Technology is also assumed invariant.













Table 12.--Moore and Hedges Model--Continued


SUMMARY DATA


Behavioral assumptions and
institutional setting










Climatic/soil/crop factors



Documented computer program

Data base


The farm firm managers are assumed to maximize profits and as a result
(as noted by the authors) it is a normative model. The institutional
setting is considered in this model with a discussion of results showing
how total revenue to a water agency may change if the water were sold.
Estimates of the elasticity of demand range from -.702 up to -.188.
The authors advise that policy makers should consider the probable
impact of the type of organization used to develop and deliver irri-
gation water, based on the results they obtained for the water demand
function.

These elements were considered in the model to the extent that irrigation
water requirements for particular crops and yield levels in a particular
region of California were estimated.

None available.

Data necessary to utilize such a model are generally available from
agricultural experiment stations.


Moore and Hedges (1963).


CHARACTERISTIC


References











crop factors. All of these factors are implicit in the Moore and Hedges

model, in that yield for different levels of water are included in the

model. In fact, the Mapp-Eidman model is very similar to the plant growth

models discussed in the previous group with respect to the inclusion of

various structural relationships as regards the climate/soil/crop inter-

action features.

In terms of input requirements, the Mapp-Eidman model requires more

technical expertise in the development of the structure of the model.

Also, this model requires more actual data, at a detailed level with re-

spect to how crops respond to water, but also with respect to how farm

firm managers might deal with particular types of changes in the envir-

onment.

Data base sources are similar to those at the plant-field level. The

only difference lies in the level at which these models are developed to

function.

Linear programming models at the firm level require a high level of

expertise for development but generally they can be considered to be less

complicated than the simulation models of farm-firms. A higher level of

abstraction is usually incorporated in linear programming models. Another

major difference is that the linear programming model allows for an optimi-

zation subroutine to be used. The actual crop mix and water level usage

for various price scenarios then are all developed on the assumption that

the farm firm managers pursue some single dimensional goal, such as to

maximize profits. The Mapp-Eidman model can examine the level of profit-

ability only after the fact. That is, the results of several "real year"

conditions (or postulated conditions) are simulated. The maximum profit

level is then selected from all the model results available to the user.










None of the computer programs developed for this category are documented.

Also, users manuals are not available.

County-multicounty-river
(or sub) basin-state models

The largest share of these are linear programming models with linear

objective functions and linear constraints (Table 13-21). There are also

some single equation (Tables 15 and 16) and simulation models (Tables 17

and 19) and input-output models (Table 13) represented in this category.

Some quadratic programming models have also been developed to predict water

demand at this level (See e.g., Howitt, Watson, and Adams, 1980). This

type of model is identical in nature to the linear programming model except

for the provision of the non-linear objective function. This allowance

is made to facilitate evaluating the effects on water demand of variable

farm commodity prices.

The models in this category are as general as to predict the total

amount of water used for major economic sectors, such as in input-output

modeling (Table 13) and the Kansas model (Table 14), which has the capabil-

ity of predicting water requirements for particular crops on particular

soil types over 16 day time periods. The Lowry-Johnson model, in turn,

considers no economic or socio-political factors, while the Pennsylvania,

Texas High Plains, Pecos Basin, and Utah models all incorporate a sub-

stantial amount of this kind of influence. The output from all these

models is more aggregate in nature than those previously discussed,

generally giving the irrigation water demand over at least the county

level of aggregation. The Kansas, New Mexico, North Carolina, Pennsyl-

vania, and Utah models all have the capability of generating estimates

of the irrigation water demand over at least the county level of aggre-

gation. The Kansas, New Mexico, North Carolina, Pennsylvania, and Utah














Table 13.--Input-Output Models


CHARACTERISTIC


SUMMARY DATA


Mathematical description


Type of output


Temporal properties



Spatial properties


The general formulation specifies that the gross dollar output of an
economy must equal the sum of the intermediate demand and the final
demand, and the gross dollar outlay must equal the dollar value of
the intermediate inputs and the final inputs. The solution of the
model is given by X = (I-A)-lY, where X = a vector, representing all
outputs of the economy; (I-A)-1 is the Leontief inverse [where (I-A) is
the Leontief input-output matrix], and Y = a vector, representing the
dollar flows to final demand. Water use is assumed to be some fixed
proportion of Yi for each sector xj.

Water use per dollar of final demand in each sector of the economy.
This could be as general as a degree of aggregation where all of the
agricultural activity is grouped under one sector. In the Ireri and
Carter model (1970), ten agricultural subsectors were specified, in-
cluding breakdowns by major types of crop and livestock categories. The
output also generally includes "water multipliers," which accounts for
all indirect water use as well as direct uses associated with an increase
in the final demand to a sector.

These are short run models, usually specified on an annual basis. They
can be used for long run projections if the structure of the economy can
be considered invariant.

Generally specified at the state and/or national level, with the possibility
that subregions could be delineated.













Table 13.--Input-Output Models--Continued


SUMMARY DATA


Input data required






Technological/production
process changes


Behavioral assumptions and
institutional setting

Stochastic/deterministic
features



Climatic/soil/crop factors

Documented computer program

Data base


Total gross dollar output must be determined per sector. Detailed
information must be available on the dollar inputs used from other
sectors to generate these dollar outputs. This could entail a massive
primary data collection process. The other alternative is to adjust
available national input-output models.


Technology and production processes are fixed to that existing for the
base year used in the model development.


The situation existing in the base year data is fixed in the model.


These models are generally deterministic in nature, although relation-
ships between dollar outputs and inputs are sometimes obtained using
regression techniques, from empirical information.

These are not considered.

May be available in particular regions.

Publications such as County Business Patterns, the Census of Agriculture,
and the Census of Manufactures will provide overall information on the
types of sectors and industries in the regions of concern. Primary data
may have to be collected if models are not available for the region of
concern, in order to establish technical coefficients. Water use data
i, each sector is not easily obtained, requiring various estimation
techniques and sources of information.


CHARACTERISTIC














Table 13.--Input-Output Models--Continued


CHARACTERISTIC


References


SUMMARY DATA


Ireri and Carter (1970; Palmer et al., (1978); Lofting and Davis, (1968).












Table 14.--Kansas Water Model


SUMMARY DATA


Mathematical description


Type of output


Temporal properties



Spatial properties

Input data required















Technological/production
process changes


Dollar outputs are projected and water demand is related to the dollar
outputs, similar to an input-output model.

Water demand as related to the total value of the product produced over
the state.

Total annual projection in intervals of 20 years. The model is time dy-
namic only in the sense that it steps in 20 year intervals, from one
static situation to another.

Water demand is shown by eleven regions in the state.

Agricultural projections in terms of the total dollar value of output
are necessary by regions. Also, unit water use by type of crop or
activity are needed. This model splits agricultural crops into corn,
sorghum, wheat, and others. The factors were developed for the volume
of water required to produce the unit value of each crop. The
Blaney-Criddle formula was used to estimate consumptive use. Long
term precipitation was then subtracted from that estimate. Data is
needed on total acres sown, total acres harvested, yield per acre,
total production and farm value of crops produced in each county.
Similar information is also developed on irrigated land. The irrigation
requirement per crop was assumed constant across the state. Crop acreage
and production by hydrologic areas were necessary. The proportion of
irrigated land relative to total crop land is needed.


Irrigation efficiency was allowed to change over the projection horizon
from 1965 to 2020. No other cultural practices were allowed to change.


CHARACTERISTIC














Table 14.--Kansas Water Model--Continued


CHARACTERISTIC


SUMMARY DATA


Behavioral assumptions and
institutional setting



Stochastic/deterministic
features

Climatic/soil/crop factors


Documented computer program


Data base


None were made explicit. Implicitly, however, all behavioral and
institutional arrangements existing in 1965 were assumed to be descrip-
tive.


The projection methodology is deterministic in nature.

These elements were included to the extent they are in the Blaney-Criddle
method. That is, the Blaney-Criddle model was utilized to estimate tne
agricultural water use coefficients.

None available.

Input data sources would include U.S. Weather Service climatic data,
county statistics from the agricultural census data, and information from
agricultural experiment stations in each state.


Kansas Water Resources Board (1972).


Reference













Table 15.--Lowry-Johnson Model


SUMMARY DATA


Mathematical description


Type of output

Temporal properties


Spatial properties

Input data required


Technological/production
process changes

Behavioral assumptions and
institutional setting


Stochastic/deterministic
features

Climatic/soil/crop factors


Documented computer program


The consumptive use in acre feet per acre(U) is given by U = 0.8 + 0.156F
where F is effective heat in thousands of degree days.

It gives an estimate of the total consumptive use over larger areas.

Generally used for estimating yearly consumptive use, but has been modi-
fied to estimate monthly use. It is a static model.

The model is intended for area wide application.

Beyond the basic formula, all that is needed is effective heat in thou-
sands of degree days.


Particular crops are not considered.


The human element only implicitly considered, via the assumption that
yields are to be maximized.


The model is deterministic in nature.

Again, as with the Thornthwaite model, several climatic variables are
measured in the proxy called "effective heat." No crop features are
incorporated in this model.

None available.


CHARACTERISTIC














Table 15.--Lowry-Johnson Model--Continued


CHARACTERISTIC


Data base

Reference


SUMMARY DATA


Daily growing season temperature from the U.S. Weather Service.

Lowry and Johnson (1942).












Table 16.--New Mexico Model


SUMMARY DATA


Mathematical description



Type of output



Temporal properties

Spatial properties

Input data required



Technological/production
process changes

Behavioral assumptions and
institutional setting




Stochastic/deterministic
features


The use of single equation crop production functions relating yield to
evapotranspiration. Also, the Blaney-Criddle model is compared with
the production function.

Estimates of the consumptive use of water for seasons where prices are
not allowed to vary and economic considerations are not part of the water
demand projection-process.

Annual, seasonal water demand projection; it is essentially a static model.

Predictions are on a per acre basis.

Knowledge of the yield-evapotranspiration production function is neces-
sary. Crop production functions were developed for cotton, corn,
sorghum, and alfalfa. Estimates of county yield are needed.


All other input levels and technologies are assumed invariant.


All the real world behavioral characteristics are implicit in and affect
the projection as average county yields were used in the model. Insti-
tutional setting was not considered explicitly, but is also to some
extent represented by the use of actual county yields.


The projection models are deterministic.


CHARACTERISTIC














Table 16.--New Mexico Model--Continued


CHARACTERISTIC


SUMMARY DATA


Climatic/soil/crop factors







Documented computer program

Data base


The Blaney-Criddle formula is used and thus all comments pertinent to
that model are also relevant here. Crop features were incorporated from
the use of production functions which related yield to actual evapo-
transpiration. Thus, the ET variable served to proxy all the climatic
factors; the yield-ET relationships serve to quantify all the crop
features.

None available.

Experimental data on the yield water relationship will be available for
some crops at agricultural experiment stations. County yield data will
be available from the Crop and Livestock Reporting Service in each state.


Sammis, et al., (1979).


Reference












Table 17.--North Carolina Model


SUMMARY DATA


Mathematical description









Type of output


Temporal properties






Spatial properties


The North Carolina model is really two different mathematical formula-
tions, namely the IRRI model and the linear programming (optimization)
model. The IRRI model basically determines the water requirement over
61 discreet, 6-day time periods, given different irrigation policies
(time when irrigation takes place). The LP model is used to optimize
across irrigation policies and crop mixes. Basically, IRRI develops
coefficients on yield and water use as well as production and irriga-
tion costs, which are all used in the LP model.

The water demand functions can be developed for varying product prices
and costs of production. The crop mix on what kinds of soil types is
also an output. There is a report writer attached to the LP model. In-
put to the REPORT program comes from the SETUP program and the MPS
solution of the linear program. A water use summary for each time
period, the unit used and the amount unused is output. Also the marginal
value of an additional amount of water available is part of the output.
In addition, the utilization of the soil by soil type is provided and
the acreage of each crop grown. The number of acres of crop grown on
each soil type by irrigation policy is also output.

The model is suitable for estimating water demand over seasonal and
intraseasonal intervals. The IRRI model is dynamic in the sense that
water requirements are estimated for any given policy throughout the
growing season. The LP model is static in the sense that it is a
snapshot-in-time estimate of the total net returns.

The models are suitable for examining demand at a county and/or multi-
county level of aggregation.


CHARACTERISTIC














Table 17.--North Carolina Model--Continued


CHARACTERISTIC


SUMMARY DATA


Input data required


The IRRI model requires information on acreage by soil type, crop
acreage by type, acreage of each crop by soil type, root depth of each
crop, inches of water required by each crop as a function of number of
days after planting, total inches of rainfall during each time period,
moisture deficit level at which irrigation water is applied to a crop
as a function of number of days after planting, total inches of rainfall
during each time period, moisture deficit level at which irrigation water
is applied to a crop, crop yield per acre and each irrigation policy,
per acre production cost for each crop other than for irrigation, irriga-
tion cost divided into fixed cost and variable cost. The output of the
IRRI model become input to the LP model. One of the most important
inputs from IRRI is the net return from growing one acre of crop I on
soil type J under irrigation policy K. There are also limits on the
acreage of various soil types in the areas of concern. Upper limits on
irrigation water must also be provided. These constraints must be
provided by time period within a season. All other production costs are
assumed invariant but must be input. Irrigation costs are allowed to
vary with the level of water used. Thus, functional relationships must
be known regarding the relationship between water pumped and irrigation
cost. Irrigation water may be purchased within the model with a charge
per unit. Very detailed information is needed on soil especially with
respect to the water holding capacity at the soil series level.












Table 17.--North Carolina Model--Continued


SUMMARY DATA


Technological production
process changes


















Behavioral assumptions and
institutional setting


Stochastic/deterministic
features

Climatic/soil/crop factors


A matrix generator is used "up front" to generate the matrix which is
then used in the LP model. In fact, two additional computer programs
are utilized to input the data into the matrix, named SWITCH and SETUP.
SETUP brings in data from cards and from previously prepared files.
Data from cards include the selling price of the crops, production and
irrigation costs, acres of each soil, upper and/or lower limits on crop
acreages, amount of water available in each time period, water require-
ments of each crop-soil-irrigation policy combination, and yield from
each crop-soil-irrigation policy combination. The cultural practices
associated with the various crops are not allowed to change in the model
examples they have presented. However, production costs could be
varied. There is minimal interaction between other cultural practices
and irrigation operation within this model however. Yield, for example,
is a function only of irrigation policy and not fertilization or other
input levels. Of course, input prices as they relate to irrigation
cost and product prices can be changed.


The farm firm is assumed to maximize profits. The institutional setting
is assumed invariant.


The model is deterministic in nature.


Rather detailed soil-water-plant relationships are included in the IRRI
subsection of the larger model. A moisture balance equation was used
in this model which related inches of moisture in the soil to the ET,
the rainfall, and the rooting depth of the crop, as well as the soil's
capacity to hold water. The crop water relationship was established
through estimates of the impact of different water availabilities on yield.


CHARACTERISTIC













Table 17.--North Carolina Model--Continued


CHARACTERISTIC


SUMMARY DATA


Documented computer program


Data base


References


A users manual is provided and the procedure for obtaining the programs
is described therein. Also, a listing of the computer programs is
provided; the programs are not, however, documented.

Much of the data will be available at agricultural experiment stations.
The detailed data regarding crop acreages on various soil types is not
generally available in most states, however. In fact, detailed soil
surveys may also be available only on a limited basis.


Sneed and Sowell (1973); Sowell, et al., (1976).








Table 18.--Pecos Basin Imported Water Modela


SUMMARY DATA


Mathematical description

Type of output





Temporal properties




Spatial properties

Input data required










Technological/production
process changes


Linear programming with linear constraints.

The water demand function for variations in price of water per foot of
imports. Import water prices can be varied through parametric procedures
to give crop mix, irrigation water imported and local water used, the
intensity per acre, the salinity level, and net returns to land and
management.

This program is concerned primarily with the short run indicating the demand
for agricultural water for a year. Arguments are made that the water demand
functions which they derive are also fairly representative of the long run.
It is a static model.

The demand is for a river basin, namely the Pecos basin.

Input is required on the profit per acre, where profit is defined as the
return to land and management, the price of imported water, and the irriga-
tion intensity. Salinity constraints are needed as well as legal con-
straints imposed on the use of local water, acreage constraints in terms
of the total cultivated acreage, the vegetable constraints, and a cotton
constraint. Budget data are needed. They also use four different levels
of water intensity and information on price support programs. Annual
investment costs for irrigation systems were included. Relationships
between imported and local water must also be understood.


Technology is assumed invariant and other cultural practices are con-
stant. Emphasis is on water demand with everything else constant.


Gisser and Mercado (1972) use this same demand model in conjunction with the hydrologic supply
model to show how the economic demand and economic supply functions interact.


CHARACTERISTIC














Table 18.--Pecos Basin Imported Water Model--Continued


CHARACTERISTIC


SUMMARY DATA


Behavioral assumptions and
institutional setting






Stochastic/deterministic
features


Climate/soil/crop factors



Documented computer program

Data base


The farm firm managers are assumed to maximize profits. Legal constraints
are recognized as regards how much water can actually be pumped. Also,
farm programs are explicitly placed in the model by the assumption that
the cotton program would continue indefinitely into the future. Beyond
these considerations the institutional setting was assumed constant.


This is a deterministic model with no random influences allowed to affect
results.

These elements are not explicit variables in this model. However, soil
type and irrigation intensity variables were included. Yield water
relationships were then established through estimates.

None available.

Crop budgets are generally available at agricultural experiment stations.
Incorporation of salinity and other legalistic constraints requires
knowledge of the legal-institutional setting. Most of the other data
needs would be satisfied from the agricultural experiment station and
the Crop and Livestock Reporting Service in the state.


Gisser (1970); Gisser and Mercado (1972).


References












Table 19.--Pennsylvania Model


SUMMARY DATA


Mathematical description


Type of output


Temporal properties


Spatial properties


Input data required


This is a simulation model. Yield (Y) as a function of water stress in-
Y AET 2
dex (WSI), is given in -- = a b [E( ET) Irrigation costs are
max
a function of several features of the irrigation system, such as distance
and depth to water source, gallons pumped per minute per acre, labor cost
per acre per irrigation, energy cost, field size, and elevation drop over
field. Cost equations estimated with regression techniques. Cost equa-
tions for each system type. Probability distributions developed for
yields of crops.

Irrigation water demand for maximum net return production level.

Water demand projections are for 7-day, 14-day, and 28-day periods for
the crop year.

Demand estimated for 23 sub-basins of the state, but based on per acre
models.

Quite extensive requirements. Climatic data to calculate PET and AET,
crop yield production functions at the field level relating yield to
water stress, probability distributions relating yield to various
probabilities of occurrence for each agricultural crop, detailed cost
estimates for each type of irrigation system in the area (with costs
related to such things as distance and elevation to water source, length
and width of field, elevation drop over field, fraction of moisture de-
pleted, depths of soil layer, available moisture content of the soil,
and plant spacing), known interest rate, water source development costs,
crop type and product prices, yield response information acreages of
various crops within each of the regions, soil types within each of
the regions with an aggregate estimate of different soil types. Only


CHARACTERISTIC














Table 19.--Pennsylvania Model--Continued


SUMMARY DATA


Technological/production
process changes



Behavioral assumption and
institutional setting


Stochastic/deterministic
features




Climatic/soil/crop factors


those input prices that affect irrigation costs are needed. A total of
13 different crops and three irrigation systems are considered in the
analysis.


Technology is assumed fixed over the projection interval. Other inputs
of production are also not allowed to vary. The model is designed to
examine the demand for and the supply of irrigation water, assuming a
large number of conditions fixed.

The farm-firm irrigation manager is assumed to maximize profits. The
current institutional setting is taken as a given.


The variance of yield and net returns are considered explicitly. The
equations are used deterministically within the simulation model. (The
discussion is very limited as regarding these properties of the model
and work).

The literature in the area of evapotranspiration estimation processes
was reviewed within the context of the study which developed this model.
A soil moisture simulation model was developed using a water balance
equation. Thus, various climatic variables and soil capability fac-
tors were included. The next phase of the study was to develop crop
water stress yield relationships. The water stress index is related to
the relative evapotranspiration.


Documented computer program


CHARACTERISTIC


None available.












Table 19.--Pennsylvania Model--Continued


CHARACTERISTIC


SUIMARY DATA


Data base


Detailed research efforts at agricultural experiment stations may pro-
vide most of the necessary information. Climatic data is available
from the U.S. Weather Service.


References


Kibler, et al., (1977); Kibler, 1980.














Table 20.--Texas High Plains Model


CHARACTERISTIC


SUMMARY DATA


Mathematical description


Type of output


Temporal properties



Spatial properties

Input data required


Linear programming, which applies a linear objective function with
linear constraints. Some crop flexibility equations were also esti-
mated relating to what shifts to different crop types might be allowed.
The supply of all production inputs is unlimited
except for irrigated land and land in total. No constraints on
groundwater were included.

The model yields estimates of the water demand function under dif-
ferent scenarios as regards prices of products, inputs, period of time
(short vs. long run), and irrigated acreage.

Both short run and long run capabilities but the model is a static form.
Projections are for either one year or for multiple years. The main
emphasis is on an annual basis as opposed to an intraseasonal basis.

A multicounty area in the Texas High Plains.

Detailed cost budgets are needed for each of the crops. Calculation of
crop flexibility restraints requires knowledge of recent cropping pat-
terns in the area. Natural gas, diesel, nitrogen fertilizer, water, and
herbicides are purchased within the model; thus prices are needed. Esti-
mates of dry landrent were necessary as well as management returns.
Prices received by farmers for corn, cotton, grain sorghum, soybeans, and
wheat are input items. Resource restrictions on irrigated land and land
must be known. Acreage restraints were put on the model at levels in
1973. Input-output coefficients are needed as regards yield estimates
and water uses for different crop activities.













Table 20.--Texas High Plains Model--Continued


SUMMARY DATA


Technological/production
process changes



Behavioral assumptions/the
institutional setting






Stochastic/deterministic
features

Climatic/soil/crop factors





Documented computer program

Data base



References


Technology was assumed invariant. Also, other cultural practices were
not allowed to vary within the model. The emphasis was on the water
variable. Also, only one type of irrigation system was used.


The farm firm manager is assumed to maximize profits. The institutional
setting is invariant with respect to the water resource portion of the
model. However, it was recognized that farm programs might change.
Thus, some changes were allowed in federally supported commodities with
respect to acreages over time.


This is a deterministic model with no random influences considered.

Climatic factors are included only to the extent that an irrigation
water requirement is specified. Yield-water relationships are in-
cluded to the extent that actual estimates are obtained from experience
in the study area.

None available.

Budgets and crop production information are generally available from
agricultural experiment stations. Acreage estimates are available
from the Crop and Livestock Reporting Service in each state.

Condra et al., (1975); Condra and Lacewell (1975); Lacewell and Condra
(1976).


CHARACTER









Table 21.--Utah Model


CHARACTERISTIC


SUMMARY DATA


Mathematical description


Type of output


Temporal properties


Spatial properties


Input data required



















Technological/production
process changes


This is a linear programming model.


Output predicted water demand functions for each of ten subregions of
the State of Utah associated with parametrically changed shadow prices
on water.

A single year time dimension is assumed. Intraseasonal variations are
not allowed. It is a static model.

The model is designed to examine the demand in ten major drainage basins
in Utah.

Data requirements include the potentially irrigable and presently irri-
gated land. Climatic information was used to adjust acreage data to
conform to uniform classes. Rotation requirements had to be specified
for crops and restrictions have to be placed on what kinds of crops can
be grown in which regions. Cost data for the production activities were
necessary. Costs and labor hours as well as yields were specified by
county and subregions. Also, irrigation water requirements in irriga-
tion hours were specified by county and regions. Land development and
distribution costs were specified by regions and land class. Yields
were also specified by land class. The Blaney-Criddle model along with
climatic information was used to determine the consumptive irrigation
water requirement. Irrigation efficiency estimates were needed. Two
water and yield levels were necessary for alfalfa. All of the rest of
the crops were inserted with one yield and one water level. Both new
and currently irrigated land were considered and acreage estimates
were necessary. Past research projects were relied upon greatly for
input data.


Technology and cultural practices were considered invariant.












Table 21.--Utah Model--Continued


SUMMARY DATA


Behavioral assumptions and
institutional setting




Stochastic/deterministic
features

Climatic/soil/crop factors



Documented computer program

Data base


The farm-firm manager was assumed to maximize profits,
exemplified at the regional level. Water rights were assumed to
exist, which is part of the institutional setting. This precluded the
development of new lands until current lands had been irrigated.


The model is deterministic in nature. No random variables were considered.

The Blaney-Criddle model was utilized to estimate water requirements.
Yield-water relationships were invariant in the sense that only one relationship
existed, except for one of the crops considered.

None available.

Most agricultural experiment stations will have data sufficient to de-
velop such a model. Climatic data will be available from the U.S. Weather
Service.


Anderson, M. H., et al., (1973).


CHARACTERISTIC


Reference










models all have the capability of generating estimates of the irrigation

water demand for each of the respective states. Input-output models

can also be developed at that level of aggregation.

Input data requirements are quite extensive for most of the models.

Acreage bounds on the various crops are generally needed. Some require

detailed soil information (See North Carolina model, Table 17). The New

Mexico, North Carolina, and Pennsylvania models all require knowledge of

the production function relating yield to water. The other models assume

yield per acre is fixed. Nearly all these models would require consider-

able expertise in their development and an ongoing data collection process

to keep them current.

The Lowry-Johnson model requires the least amount of data, followed

by the Kansas model. All that is needed for the former is effective heat

in thousands of days degree, while the latter model requires dollar value

projections for the various sectors and an estimate of the amount of water

used per dollar of gross output. Of course, both of these models would

be severely limited under changing economic and/or physical conditions, as

would the Input-Output models. That is, sudden or rapid changes in the

economy or in the natural climatic system would create predictions with a

large standard error. Only the Pennsylvania model attempted to deal with

stochastic processes. This is a shortcoming of all the models examined

in this group.

As with the previous categories, major data base sources again include

the agricultural experiment stations, weather service, Soil Conservation

Service and the Crop and Livestock Reporting Service. Dollar output data

could be obtained form U.S. Census sources. Several more aggregate types









of data are generally needed at this level of aggregation.

The Utah model was the most all-encompassing in terms of incorporating

both socio-economic and climatic/soil/crop factors. However, yield-water

relationships were not included in the model. The North Carolina model

on the other hand, had a great deal of detail incorporated into the soil

water balance estimating model as did the Pennsylvania model (Tables 17

and 19).


River basin-regional-national models

The two major models represented here are the national linear pro-

gramming model developed at Iowa State, called the CARD model, and the

Ruttan model (Tables 22 and 23). The latter is an econometric, regression

model using county data and estimating the demand for irrigated land at

regional levels. Both models give estimates of the irrigation demand

for water at larger aggregates. Both models allow some prediction of the

effect of the change in agricultural output on the amount of irrigation

water used. The CARD model is much more extensive than the Ruttan model

and requires considerably more input to its operation. Both water supply

and market regions are considered explicitly in the CARD model (Table 23).

Detailed cost and budget information are developed and necessary for the

CARD model. This is also true for the Ruttan model; however, the data

are usually taken from agricultural census data on counties. Overall, the

CARD model is more appropriate for examining the national demand by re-

gions. As has been argued elsewhere, the Ruttan model has been fraught

with difficulties due to statistical problems, which in turn are due to in-

adequate data (See Lynne, 1978). Input data requirements are much less for the Ruttan

model, however, and are considerably easier to generate. As a result the

Ruttan model is much less costly to develop and to maintain. Climatic/soil/









Table 22.--CARD Model


SUMMARY DATA


Mathematical description


Type of output


Temporal properties


Input data required




Technical/production
process changes



Behavioral assumptions and
institutional setting


A least cost programming model where certain commodity demands are to
be met subject to constraints on available resources.

Demands for water as associated with economic activity in the agricul-
tural sector, by regions of the U.S. The water demand functions that
are provided will vary for the major agricultural crops of the U.S.
Water requirements for other crops are simply fixed in the model.

The model encompasses the whole U.S. with 223 land regions, 51 water
supply regions, and 27 market regions.

Cost and budget information are input on a per crop basis and vary
across producing regions. Detailed information on crop water use
coefficients is needed. Basically, this model utilizes a physical
consumptive use requirements approach for estimating water demand.


Technology is chosen for a base year, in this particular case, 1964.
The model has the capability of being modified to examine different
farming techniques.


The model is developed under the assumption that costs are to be minimized
subject to meeting certain demand constraints in terms of the quantity
of commodity actually provided. The institutional setting is essen-
tially fixed, although some variation is allowed through such devices
as imposing soil loss limitations on alternative land classes or
affecting market prices through market quotas for supply controls.
Export market demands can also be modified. Policies regarding land
use can also be examined.


CHARACTERISTIC








Table 22.--CARD Model--Continued


SUMMARY DATA


Stochastic/deterministic
features

Climatic/soil/crop factors



Documented computer program


Data base


The model is deterministic in nature.

Crop water requirements were determined using various other models such
as the Blaney-Criddle model. Yields do not vary with water levels in the
model.

General documentation of the program is available. The model will be
used through the CARD center at Iowa State.

Massive data requirements from state agricultural experiment stations,
state agricultural agencies, Crop and Livestock Reporting Services,
Soil Conservation Service, U.S. Weather Service, and others.


Nicol and Heady (1975); Heady et al. (1976).


CHARACTERISTIC


References













Table 23.--Ruttan Model


CHARACTERISTIC SUMMARY DATA


Mathematical description Cobb-Douglas function for each region of the U.S.:
R b4 R b
RXt = A(X ) (X4 ) A derived demand function for irrigated

land in each region: RX 4t= (R R R4I) Rb An identity serving as a

perfectly elastic supply function: R 4t = RC4. The national output

P Y -Y e
t t 1le
projection: NXot = X01 (P ) [ + ( ) ]. The regional output pro-
ot1 1

jection: RXt/NX = (RX/01 ot)[(l+r)(l+- r) (1 + )...(l+t -t -r)]
t t

where X0 = value of farm products sold ($); X4 = irrigated land (acres);
X6 = current operating expenses ($); X4 = marginal value product of
irrigated land ($/acre); C4 = average annual cost of irrigated land
($/acre); t = time, 1...27(1954-80); P = population (number); Y =
per capital income ($/person); A = constant term in the production
function; b4 = productivity coefficient for irrigated land; b6 =
productivity coefficient for operating expenses; e = income elasticity
of demand for farm products; r = rate of change in regional share of
national output in past period; N = national total or a variable
measured at the national level; R = regional total or a variable
measured at the regional level.












Table 23.--Ruttan Model--Continued


SUMMARY DATA


Type of output


Temporal properties



Spatial properties


Input data required





Technological/production
process changes



Behavioral assumptions and
institutional setting


The demand function for irrigated land allows estimation of irrigated
acreages. It must then be assumed that the quantity of water use per
irrigated acre is fixed. The total economic value of the agricultural
production is allowed to affect the total irrigated acreage. Also the
R 4 is a function of the variable X6 where X6 is the current operating
expenses in agricultural operations.

The model allows for projection of demand over time, where time is a
year. Basically it allows projection at different points in time to
be compared; thus it is really a static model.

A regional model has been developed for each of the major water re-
source regions in the U.S.

Data on cost of production, irrigated acreage, and other input data are
needed to estimate the regression equations. These data can be derived
from agricultural census data. Data is at the county level of aggrega-
tion.


The particular cultural and technological data in existence at the time
of the model estimation has to be assumed to prevail throughout the
projection interval.


Farm firm managers are assumed to act as they did in the historical
period in which the data were developed. The institutional setting is
assumed invariant.


CHARACTERISTIC














Table 23.--Ruttan Model--Continued


Stochastic/deterministic
features


Climatic/soil/crop factors

Documented computer program

Data base


Reference


The model is essentially deterministic. It is a regression model,
however, and stochastic influences 'could be considered.

This model does not account for this characteristic explicitly.

None available.

The U.S. Agricultural Census provides the data base for this model,
which becomes available every five years.

Ruttan (1965).









crop factors are not included in the Ruttan model. Some of these ele-

ments are incorporated in the CARD model through the fact that several of

the potential evapotranspiration-consumptive use formulas (such as the

Blaney-Criddle equation) were used to determine water requirements in

different regions of the nation.

The general features ofthe CARD model are documented (Nicol and

Heady, 1975). Any use of this model would have to be coordinated through

the Center for Agricultural and Rural Development (CARD) at Iowa State

University in Ames, Iowa. The Ruttan model is documented in the early

book (Ruttan, 1965).











IV. MUNICIPAL WATER DEMAND MODELS


The simplest, quickest and least expensive of all municipal water

use forecasting methods is the "conventional method." This approach

ignores all influences on water use except one population. Expected

population is multiplied by daily per capital use to obtain water use.

Water use may or may not be broken down into the major sectors of resi-

dential, commercial, agricultural or industrial use. A number of more

refined forecasting methods have been proposed (Albertson, 1979).

The ideal forecasting procedure should draw upon past and present

trends, as well as consider the demand for each water using sector in

the area (Mitchell and Leighton, 1977). It should incorporate variables

reflecting various factors (demographic, social, economic, and environ-

mental) affecting water demand, utilizing state-of-the-art in modeling

and be in terms readily understandable to the model builder (Reid,

1971).

Problems are likely to involve serially dependent errors, (correla-

tion among successive observations in a time series), multicollinear

explanatory variables and difficulties inherent in the presence of

explanatory variables that must themselves be predicted (Domokos, Weber,

and Duckstein, 1976).

Before implementing a particular model, preliminary research is

necessary to determine which variables should be included and how they

should be measured and introduced (Clouser and Miller, 1979). While it

may be relatively easy to identify the variables to include in forecasts,









operating constraints frequently exclude their systematic consideration.

Also, measurement problems may preclude the incorporation of other

variables into forecasts (Mitchell and Leighton, 1977). Consideration

must then be given to data availability and manpower needs.

Many variables are used to explain variation in household water

consumption. Household demand is a function of price, consumer wealth,

prices of other goods, and consumer tastes and preferences. The following

variables were used in various studies to measure their effects (Cassuto

and Ryan, 1979).

Socioeconomic Variables

Income

Income was used as a variable in several of the models. It is

normally expected to have a positive effect on the amount of water

consumed.

Price of Water

In a number of studies, the quantity of water demanded has been

found to be significantly affected by the price of water. According to

economic theory, the higher the price of the commodity, the lower the

demand. This is especially true where price changes are significant and

well publicized. The sensitivity of water use to changes in the real

price of water is known as the price elasticity of demand (Hanke, 1978).

Lawn sprinkling in the western U.S. has been reported with an elasticity

as high as -.70 (Howe and Linaweaver, 1967). Much more research is

needed, however, to assess the effects of price on water demand for

various geographical locations, incomes of households, and other variables

(Flack, 1980).

Two different prices are used in existing models, average prices and

marginal prices. The marginal price, while theoretically the correct one











to use, is very difficult to estimate. Thus, most of the models use

average price as the measure of the scarcity value of water.

Property Value

Assessed valuation is one of the more readily available parameters.

It is used in several of the models as a measure of income. As with income,

property value is assumed to be directly proportional to the amount of

water used in the household. Consumers in higher valued areas are more

likely to have more water using appliances and larger lawn areas.

Cultural Factors

Race or country of origin are cultural factors that may affect

water use. Education could also be considered a cultural factor. High

level water use was found for college postgraduates and low level for

high school graduates (Csallany and Neill, 1972). Few of the models

reviewed, however, included cultural factors as a water use parameter.

This may be attributed to difficulty in obtaining data. Two models

(Darr, Feldman, and Kamen, 1975, and Camp, 1978) which did include

cultural factors were based on household by household surveys. Cultural

considerations were found to be especially significant in determining

the importance of maintaining lawns and shrubbery.

Water Consumption Behavior

Water consumption behavior includes consumer habits such as water con-

servation practices and reactions to uncertainty of supply. Few models

were found to incorporate this parameter.

Climatic Variables

Precipitation

Water use was found in various studies to be inversely proportional

to the amount of precipitation. During months of low precipitation, lawns











and gardens require more watering. Excellent information is available

on the expected use of water by vegetation based on numerous studies in

agricultural areas.

Evaporation

Where evaporation is found as a water use variable, it is used to

measure outdoor consumptive use from free water surfaces or as a proxy

for transpiration by plants (see the previous chapter for more informa-

tion regarding evapotranspiration).

Temperature

The use of water throughout the year is subject to fluctuations in

temperature. The amount of water for personal hygiene (baths, showers)

could decrease during the winter months because people are constrained

to less physical activity and more indoor recreation. This is especially

true for regions with colder winters.

Other Independent Variables

Population

Studies indicate that a strong relationship exists between popula-

tion and water consumption. Population was used as an explanatory

variable in nearly every forecasting method examined. When the study

focuses on the microunit of a household, population is replaced by

family size. Family size is expected to have a positive effect on

household water consumption (Clouser and Miller, 1979).










Technology

Although new technology continues to be developed, few demand studies

incorporate it in household estimation techniques.

Appliances or household activities that require water include washing

machines, dishwashers, lawn sprinklers or garden watering, and swimming or

wading pools. All are anticipated to have a positive effect on the amount

of waLer used in the household. It is also possible for technology to

decrease the household demand for water. Several technological innovations

of this sort have been developed. One example is flow restrictors which

may be used on faucets or in showers to retard water flow,

Technology may be geographic specific and therefore not a useful

explanatory variable in all locations.

Irrigated Area

Irrigated area for the household includes lawn and garden areas (all

outside use). Well developed procedures with a national data base exist

for estimating water use by vegetation. However the efficiency of applica-

tion of the water varies widely.

Land Use

Land use data are available for most communities. Unfortunately, no

standardized system of defining land use exists. Thus, "low density resi-

dential" may have different meanings. This lack of standardization makes

it much more difficult to do cross sectional studies of water use.

Number of Dwelling Units

An alternative but related measure of urban activities is to estimate

dwelling units rather than houses. The advantage of using dwelling units is

that it incorporates directly the effect of multi-family housing.










Lot Size

Water use is expected to be directly proportional to lot size. A large

lot size generally means a larger lawn area (more water needed for irriga-

tion) and higher property values which were found to have a positive effect

on demand.

Summary

Above are just a few of the many factors that may affect water use. Those

variables listed (with the exception of land use) were found to be signifi-

cant in more than one of the models reviewed. It is important to note,

however, that particular explanatory variables proven highly significant

within the confines of one study might be proven otherwise under different

conditions.

Other factors of the water use models include outputs, spatial properties,

temporal properties, statistical properties, and validation. Most of the

residential water use models reviewed projected monthly or annual water

use in gallons per day. The scale varied from household to regional.

Models developed at the household level include those based on studies of

individual households. City and regional level models were based on areal

averages. All of them were found to reflect long run behavior and were

static in nature. None of the variables change for a given time period.

It is assumed that consumers have had time to completely adjust to the

parameters they face. Because none of the models reviewed were found to

contain a random element, they were judged to be deterministic as opposed

to stochastic. Deterministic models predict what will happen as the result

of a given action (or actions). The water use models project increases

or decreases in water use as the result of increases (or decreases) in











population, price, income, etc. The final feature of the water use models

is validation. Few of the models reviewed were found to have a documented

case of validation.

Table 24 summarizes the models which have been found in the litera-

ture for estimating municipal water use. The models are grouped accord-

ing to the level of aggregation being used in the study: household (5

models), city (11 models), and regional (2 models). Without exception

the models are very simple from an analytical point of view. The only

theoretical question that has arisen is how to properly incorporate

price effects (Morgan, 1980). No systematic national data bank of water

use patterns has been available over the years. The early Johns Hopkins

studies during the 1960s appear to be the most ambitious effort to date

along these lines.

Detailed summaries of the models are presented in Tables 25 to 42.

The Sonnen-Evenson model is by far the best documented of the available

models. Thus, it was an obvious choice for our test application to be

presented in the next chapter.












Table 24. Municipal Demand Models


Spatial Properties
and Model Name
and/or Originator


Temporal


Socioeconomic Variableb


I
0


Id M 0 .)
0 N0 o5 xn 0
0 o a- (d s4
f-< 0) -i M h f>


Statistical Climatic Variables


a
o
T< I 04



A40
cm 5c*0 sm
0. 4-1.. N-
-,4 o 0 a
o as 0t .

0, 40o. H*


Other Independent Varlablda



4-4

0 60 wt *-
ot- 00 04 V 0 0 <
,-4 0- 4 000 01
4-4 r- .0 m 0 N
a" .0 BO4 01 -o < .t
3. NS T Ce 3 1
0^ 04 44 Sy 04 0
Q lU 4 -4< K1 3


HOUSEHOLD
LEVEL

Clouser & Miller
(1979)

Danielson (1979)

Darr, Feldman &
Peretz (1975)

Morgan (1973)

Camp (1978)

CITY LEVEL

Municipal Demand
Model for the
Conterminous U.S.
(Burke, 1970)

Conventional
Water Use Model
(Holtz & Scott,
1976)

Mitchell &
Leighton (1977)

Irevor & Cross
(1979)

MAIN I & II
(Albertson, 1971)

Cassuto & Ryan
(1979)

Integrated Supply-
Demand Management
Model (Hanke, 1978)

Multistructured
Demand Model
(Reid, 1971)

Turnovsky (1969)

Young (1973)

Johns Hopkins
Model (Howe &
Linaweaver (1067)

REGIONAL,

Yn nu'chf & Huang
(1977)

Kanoehe Bay W.'Ler
Demand Model (Sonnen
& Evenson (1979)


x x


x x


x x x


x x X


x x x








x x xK


X X


X X X


x X


X X


X X X


x x




x x




X x


x x x


x x








Table 25. --Camp


SUMMARY DATA


Mathematical Description


Type of Output


Temporal Properties


Spatial Properties


Input Data Required


Q = a + blx1 + b2x2 + + bl3x3 where
w 11 22 2 1 13 '
Q = quantity of water demanded (gal/household),
a = constant,
xI = number of occupants of household,
x2 = age of head of household,
x3 = market value of residence,
x4 = irrigable lawn area of residence,
x5 = number of bathrooms/residence,
x6 = number of clothes washers/residence,
x7 = number of dishwashers/residence,
x8 = existence of a swimming pool at residence,
x9 = race,
x10= average maximum temperature for the area,
x11= annual precipitation in the area,
x12= price of water in each city at the mean level of consumption for all domestic
users included in the study, and
x 1= education index.
b to b13 = regression coefficients.

Residential water consumption is estimated using linear regression considering
socioeconomic and climatic factors.

The model predicts water use for any time period although yearly projections
are usually made.

Water use is projected at the household level. All data are collected for the house-
hold with the exception of price, precipitation and maximum temperature.


Data required for the household are: number of occupants, age and race
of household, property value, irrigable lawn area, number of bathrooms,
of clothes washers, number of dishwashers, existence of a swimming pool
education index; for the city: temperature, precipitation-and price of


of the head
number
and t
water.


CHARACTERISTIC








Table 25. --Camp, Continued


CHARACTERISTIC


SUMMARY DATA


Documented Computer Program


Data Base


None


The model is based on a household, from information obtained by a household
(single family) survey of water use by 288 consumers in ten cities in northern
Mississippi. Climatological data were obtained from meteorological records
of the Department of Commerce. Rate structures and monthly water use were
obtained from water utility officials and records. City studies were selected
on the basis of similarity in water pricing and allocation policies and
because there was a diverse cross section of water prices in the group.
Population ranged from 5000 to 20,000.


Camp (1978)


Reference









Table 26. --Clouser and Miller


CHARACTERISTIC


SUMMARY DATA


Mathematical Description


Period 1 (Winter-Jan., Feb., Mar., and Dec.):
In QWD = a + W + DW K + BIln FS + B21n NB + B3 In Y

Period 2 (April, May, June and July):
ln QWD = a + W + DW + SP + WL K + B 11n FS + B21n NB + B31n Y

Period 3 (Aug., Sept. Oct., and Nov.):
Identical to model for the second period excluding SP, where


QWD
W
DW
SP
WL
K
Y
FS
NB
BI,
a


Type of Output


Temporal Properties

Spatial Properties


Input Data Required


= total water used by household during period (gal/day),
= washing machine, 0 = no, 1 = yes,
= dishwasher, 0 = no, 1 = yes,
= swimming pool if is filled, 0 = no, 1 = yes,
= if lawn is watered, 0 = no, 1 = yes,
= household knowledge of water saving devices,
= total net income of household during period,
= family size, and
= no. of bathrooms.
B2, B3 = regression coefficients
= constant


The model estimates household: water use based primarily upon household data.

Seasonality of household water use is incorporated into the estimation.

The study focuses on the micro-unit of a household. Population is replaced
by family size.

Data must be collected on family size, household facilities (showers, toilets,
tubs) and appliances (washing machines, dishwashers, pools and lawn sprinklers),
household knowledge of water saving devices and income.


Documented Computer Program


None








--Clouser and Miller, Continued


CHARACTERISTIC


SUMMARY DATA


Data Base


Data were obtained from a questionnaire mailed to two communities located
in central Indiana, both in rural areas within a 30 minute drive of a larger urban
area. The majority of households were classified as middle income ($12,000-
$15,000). One third of all households were widowed individuals or elderly
couples.


References


Clouser and Miller (1979, 1980)


Table 26.










Table 27. --Danielson


CHARACTERISTIC


SUMMARY DATA


Mathematical Description


Type of Output


Temporal Properties

Spatial Properties



Input Data Required


Documented Computer Program

Data Base


Qt = f(X X, X2 x X5), where

Qt = water consumption (1000 gal/household) during period t,
X1 = average daily rainfall during period t,
X2 = average air temp/period,
X3 = appraised house and lot value of residential customer,
X4 = real water price (cents/1000 gal), and
X5 = household size.

The model predicts water consumption during period t at the microlevel.

Projections are made for any time period.

The model predicts water use at the household level. It estimates how specific
households respond rather than how individuals in different areas respond to
spatial differences in the parameters.

Data needed are price of water, rainfall, temperature, property value and
household size.

None

This model was developed using monthly cross section and time series data from
261 residential households in Raleigh, North Carolina.


Danielson (1979)


Reference









Table 28. --Darr, Feldman and Kamen


SUMMARY DATA


Mathematical Description


Qd =
Qa
Qs

(log


Type of Output


Temporal Properties

Spatial Properties


Input Data Required


f(I N N r, A, C,
f(Ic, N Nr, A, C,
f(Ic, N Nr, A, C,

linear forms used),


E, S)
E, S)
E, S)

where


Qd = quantity of water not including water for gardening (m3/yr per capital per d.u.)
Qa = quantity of water including water for gardening (m 3/yr per capital per d .u.),
33
Q = quantity of water for gardening only (m /yr per capital per d.u.),
a

I = monthly income per capital per d.u. (gross, in Israeli pounds),
N = number of persons per dwelling unit,
N = number of rooms per dwelling unit,
A = age of head of household (or spouse),
C = cultural factor determining water use preferences, country of origin,
S = urban area or municipality in which dwelling unit is located, and
E = education of head of household (or spouse).

The model forecasts water consumption per dwelling unit using socioeconomic and
demographic factors.

Yearly predictions are made.

The study describes variables from disaggregated data. Projections are made at
the household level.

Required data are household size, income per capital, urban area, country of
origin, education of the head of household, and the type of metering.


Documented Computer Program


CHARACTERISTIC


None










--Darr, Feldman and Kamen, Continued


CHARACTERISTIC


Data Base


Reference


SUMMARY DATA


The model is based on a questionnaire survey of 1892 households (both metered
and non-metered) in four urban areas of Israel conducted from Oct. to Dec. 1971.
Water use data (for gardening as well as within house consumption) were obtained
for the 1970-71 fiscal year.

The sample is representative of urban metropolitan areas of Israel. An additional
set of data (for time series analysis) was combined with the above cross sectional
data; it consisted of 14 points from 1954-1968 for the municipality of Jerusalem.


Darr et al. (1975)


Table 28.









Table 29. --Morgan, D.W.


CHARACTERISTIC


SUMMARY DATA


Mathematical Description


qd = f(v, d );
d~p


aqd
av


qd
> 0, and > 0, where
pd
p


qd = yearly water usage, hundreds of cubic feet,
v = assessed value of the property, in $1000, and
d = number of people/dwelling unit.

The model forecasts water use for individual households.


Type of Output


Temporal Properties

Spatial Properties


Input Data Required


Documented Computer Program

Data Base


The model predicts yearly water usage. Results are reported on a seasonal basis.

This model was tested using detailed micro data on the use of water in individual
dwelling units.

Input information includes assessed property value and number of people per
dwelling unit.

None

This model is based on 92 observations from single family residences of Santa
Barbara County, California (metered and public sewer). Water usage data
(qd) was provided by the local water district for 1971 and assessed value (v)
was obtained from county records. Coefficients were derived for Nov. Dec.
and Jan Feb periods separately and combined. In semiarid areas such as S.
California, inclusion of winter month water usage does not initially capture
pure domestic demand because intermittent rainfall (and therefore sprinkling)
continues even during winter months; as a result, qd contains some amount
of sprinkling usage.


Morgan (1974, 1979, 1980)


References




Full Text

PAGE 1

I r WATER IiRESOURCES researc center Publication No. 61 AGRICULTURAL AND MUNICIPAL WATER DEMAND PROJECTION MODELS by James P. Heaney, Gary D. Lynne, Nagendra Khana1, Wayne C. Martin, Cherie L. Sova, and Robert Dickinson 1981 UNIVERSITY OF FLORIDA

PAGE 3

LIST OF FIGURES Figure 1 Hypothetical Demand Curve for Water ....................... 6 2 Schematic of Land Use Breakdown ...................... 112 3 Overall Structure of Water Demand Model,." .... ; ... ..... 113 4 General Structure of Hodel 116 5 Estimated Residential Consumption in the United States 127 6 Predicted Monthly Demands (MG) from Each Step (1-4) of the Calibration Exercise .......................... ..... 145 Al Flow Chart for Program DEMAND .......... .. !J .. fI ., ... O.G .......... 160 A2 Flow Chart for Subroutine FIND .......................................................... 163 A3 Flow Chart for Subroutine INPUT ....................................................... 164 A4 Flow Chart for Subroutine QSORT ........................................................ 165 AS Flow Chart for Subroutine RPTSET ............ 01 ........................................ 168

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TABLE OF CONTENTS Page I. INTRODUCTION. . 1 II. GENERAL BACKGROUND INFORMATION .............................. 5 III. AGRICULTURAL WATER DEMAND MODELS ................... 7 IV. MUNICIPAL WATER DEMAND MODELS ................... 78 V. DESCRIPTION OF WRE/SCS DEMAND MODEL ............... 110 VI. SUMMARY AND CONCLUS IONS .......... 149 VII. REFERENCES ........................... 150 APPENDIX A -Description of Subroutines in WRE/SCS Model ... 158 APPENDIXB Program Listing .............. 170 APPENDIX C Sample Data Forms .. .. 189

PAGE 5

LIST OF TABLES Table Page 1 Total Withdrawals and Consumption, by Functional Use, for the 2l.Water Resources Regions --"1975", 1985, 2000 fit III III III e III III II III III <;I ... III 2 2 Major Features of Agricultural Water Demand Models .... 16 3 Blaney Criddle Model ... 0 0 0 19 4 Har greaves Model ................................. 21 5 Hexem and Heady Models ............................ 23 6 The Hogg, Davidson, and Chang Model '0' 25 7 The Minhas, Parikh, and Srinivasan Dated Input Model 27 8 Penman Model 30 9 Plant Growth Models iii iii II III 32 10 Thornthwaite Model III III c 35 11 Mapp and Eidman Model ............................... 40 12 Moore and Hedges Model .............................. 44 13 Input-Output Models ................................. 48 14 Kansas Water Model ................................ 51 15 Lowry-Johnson Model ............................. 53 16 New Mexico Model ............................... 55 17 North Carolina Model 57 18 Pecos Basin Imported Water Model .................. e 61 19 Pennsylvania Model .................................. 63 20 Texas High Plains Model ............................. 66 21 Utah Model ......... &60.11> ......................... 68

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Table 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 CARD Model ................................................ Ruttan Model ............................................ Municipal Demand Models Camp '" e II! Clouser and Miller Danielson ....................................... ...... Feldman and Kamen Darr, Morgan, D.W. ........................................... Cassuto and Ryan Conventional Water Use Model Integrated Supply/Demand Management Model Johns Hopkins Model It '" ,'II Main I and II 'II" Mitchell & Leighton Multistructured Demand Model Municipal Model for the Conterminous U.S. 'II Trevor & Gross ........................................... Page 72 74 85 86 88 90 91 93 94 96 97 98 99 100 101 102 104 39 Turnovsky ....................... 'II, .......... 'II. 105 40 Young "'II II!' 106 41 Kanoehe Bay Water Demand Model .. 107 42 43 44 Yamauchi and Huang Water Consumption by Selected Industry Type Example Output --Report 2A 109 128 137

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Table Page 4SA Example Output --Net Irrigation Requirements for Soybeans . . .. . . . . . . . . . 139 4SB Example Output --Gross Irrigation Requirements for Soybeans ................................................ 140 46 Comparison of "Actual" and Predicted Monthly Demands (MG) for 1977 (Subarea 1) ....... 146

PAGE 8

ACKNOWLEDGMENTS Mr. Aaron Higer of the U.S. Geological Survey was very helpful throughout this study. He worked closely with us in defining the problem and describing the intended audience. A large debt is owed to Doctors Sonnen and Evenson, the original developers of the WRE model. Their earlier work provided the foundation for this effort. The irrigation demand model was obtained from Dr. James Rogers of the University He put the SCS program onto the University of Florida computer. The original work of the SCS personnel who wrote the program over ten years ago is appreciated. The financial support of the Engineering and Industrial Experiment Station, College of Engineering, University of Florida, in the early phase of this study is appreciated.

PAGE 9

I. INTRODUCTION The water supply available for human use through agricultural production processes and/or direct consumption is limited in quantity. The amount of water available on the earth's surface has not changed measurably for eons, nor will it change significantly in the future. Yet, population growth continues, placing pressures on supplies, and thereby giving rise to potential demand-supply imbalances through time. This is especially true in certain regions of the world where water is available only in very limited quantities. In 1975, the United States withdrew 338 billion gallons per day of fresh water for various uses. According to the Second National Assessment of the U.S. Water Resources Council (1978), this amount is expected to decrease by 9 percent by the year 2000. This decrease is expected as the result of more efficient use of water through conservation efforts. On the other hand, consumptive use of water is expected to increase from 107 billion gallons per day in 1975 to 135 billion gallons per day by the year 2000. The Second National Assessment also estimates l.nstream water needs for fish and wildlife, hydroelectric generation, navigation, and recreation. Most of this need is for fish and wildlife. This report does not address instream uses. A summary of present and projected usage patterns is presented in Table 1. Planners, water managers, investors, and legislators in the U.S. need information on expected future demands for water. This will be necessary in order to facilitate correct investments in water supply 1

PAGE 10

Table 1. Total Withdrawals and Consumption. by Functional Use. for the 21 Water Resources Regions --"1975." 1985. 2000 (U.S. Water Resources Council. 1978) [million gallons per day] Functional Total withdrawals Total consumption use "1975" 1985 2000 "1975" 1985 Fresh Water: Domestic: Central (municipal) ______ 21,164 23,983 27,918 4,976 5,665 Noncentral (rural) _______ 2,092 2,320 2,400 1,292 1,408 Commercial _____________ 5,530 6,048 6,732 1,109 1,216 Manufac:turing ----------51,222 23,687 19,669 6,059 8,903 Agriculture: Irrigation ______________ 158,743 166,252 ,846. 86,391 92,820 Livestock ______________ 1,912 2,233 2,551 1,912 2,233 Steam electric generation ___ 88,916 94,858 79,492 1,419 4,062 Minerals industry _________ 7,055 8,832 11,328 2,196 2,777 Public lands and others' ____ 1,866 2,162 2,461 1,236 1,461 2000 6,638 1,436 1,369 14,699 92;506 2,551 10,541 3,609 1,731 Total fresh water ________ 338,500 330,375 306,397 106,590 120,545 135,080 Saline water,2 total ___________ 59,737 91,23.. 118,815 Total withdrawals _______ 398,237 421,611 425,212 1 Includes water for fish hatcheries and miscellaneous uses. 2 Saline water is used mainly in manufacturing and steam electric generation. 2

PAGE 11

facilities and in provision of information to users with regard to conservation measures. Developers of new water using technologies also need reliable projection information. If severe shortages would be projected, for example, it is expected this would have an influence on irrigation technologists or developers of household technology as to the rate at which new water using appliances are made available. Rising energy prices could also have an influence on the water supply-demand balance, possibly due to development of other energy sources. It is expected, for example, that large scale energy development in the western U.S. will increase pressure on water supplies currently used by agricultural and residential categories. The overall purpose of this report is to highlight the problems and types of approaches that can be utilized in water demand projection for the agricultural and residential use sectors. The more specific objectives are a) to identify major types and examples of water demand projection models which have been developed; b) to highlight the major features of these currently available demand models including data requirements and types of output; c) to present detailed discussions of those models which reflect the current state of the art of demand' projection techniques; and d) to present, by way of example, the application of a "first generation" projection model useful for larger, more aggregate areas over monthly time periods. This report is intended to serve as a useful manual for those agencies and entities concerned wi.th projection. of water demand for these use categories. AdditionaJJ.y, this report should be useful to these same entities in planning for the development and use of better models in the future. 3

PAGE 12

State water agencies are required to estimate monthly water use for the present year as part of a nationally supported program. The analyst is assumed to be provided, on December 31st of the year, with estimates of the level of economic activity at the beginning and end of the year, estimates of the rate of water use per unit of economic activity, monthly precipitation and air temperature data, and other miscellaneous site specific data. The desired result is the estimate of the monthly water demand for each land use in each subarea of study area during the forthcoming year. This report describes available models which may be helpful in making such estimates. The next section presents general information regarding modelling and defines key terms. The following two sections present surveys of available models for estimating agricultural and municipal water demand, respectively. The fifth section describes an agricultural/municipal demand model which is a composite and refinement of two existing models. The muni cipal model is based on earlier work by Water Resources Engineers (WRE). The agricultural model is a computer program of the BlaneyCriddle method for estimating crop consumptive use. The program was developed by the Soil Conservation Service (SCS). The composite prograin, dubbed WRE/SCS, is specifically designed to estimate monthly water use. An example application is included. The summary and conclusions from the study are presented in Section VI. A more detailed description of the model is presented in an appendix. 4

PAGE 13

II. GENERAL BACKGROUND INFORMATION The title of this study encompasses a relatively broad area of inquiry. This section provides general background information necessary to more specifically define the to be addressed. In the context of this report, water use means withdrawal use. This water is withdrawn from ground and/or surface-water sources and conveyed to the place of use. This type of use is referred to as "offstream" use (U.S. Water Resources Council, 1978). This report estimates water withdrawals and consumption. Major categories of offstream use include: domestic, commercial, manufacturing, agriculture, steam electric generation, and minerals industry. For the purposes of this report these groups are partitioned into two segments: indoor and outdoor. The other major category is in-stream use for fish and wildlife, hydroelectric generation, recreation, and navigation. None of these instream uses are included in this report. The phrase "water demand" is used to indicate explicitly that the desire for water is influenced by. its price. The alternative phraseology, water requirements, implies that activities require a pre-specified amount or a "shortage" occurs. In an economic context there is only a shortage of water at a given price. At one extreme, the requirement for water could be based on a saturation demand, i.e., the amount requested if the price were zero. The general shape of a demand curve is shown in Figure 1. The water demand decreases as price increases. Faced with 5

PAGE 14

2.00 "0 a> c 0 0 0 "-.... LOO l.LI U a: a... SATURATION DEMAND o o 50 200 PER CAPITA USAGE I gol./ day Figure 1: Hypothetical Demand Curve for Water rising prices, individuals cut back on their usage. In this report, water demand will be used instead of water requirements. This jargon is chosen to remind the reader of the importance of economic factors. The projections to be made by this model are monthly use rates for a single year. The objective is quite spec:Lfic. The analyst is at the,' end of the study year and seeks to estimate what the usage patterns were during that year. Alternatively, the interest could be in next year's usage pattern for some assumed projection of climatqlog:Lcal and economic conditions. These estimates are being made for relatively large areas and would typically be aggregated into a forecast for the entire state. The word model is used to describe a set of procedures for making the water demand estimates. Within the context of this study, an "opera--tional" model includes the following features: 1) mathematical relation--ships for estimating water demand; 2) a documented computer program; and 3) some successful experience in using tpe program. The next two sections present the results of the review of agri-cultural and municipal models. 6

PAGE 15

III. AGRICULTURAL WATER DEMAND MODELS The literature in the area of agricultural demand modeling is vast. There are, for example, at least 11 different methods for estimating potential evapotranspiration (See Kibler, et al., 1980, p. 89; Israelsen and Hansen, 1967; Criddle, 1958). There are at least 40 different and significant journal articles limited to attempts at quantifying the yield-water relationship published in the last 20 years (See Lynne and Carriker, 1979, for a listing and brief review). Many other such attempts are documented in more localized publications. In addition, there is a vast literature where more aggregate (field, farm, state, regional, national) models have been developed. Thus, a great deal of judgement was necessary to select representative articles and models. The goal was to give the reader enough information to form perspectives regarding the nature of specific modeling approaches and the overall character of the water demand projection problem. Computer search techniques were used to identify the newest literature. Bibliographic searches were also made from reference lists in the latest publications as well as searches of major journals, especially those devoted to the water resources field. In particular, Water Resources Research Journal, the Water Resources Bulletin, and the Journal of the Irrigation and Drainage Division of the American Society of Civil Engineers were reviewed. Also the major agricultural economics journals were accessed, including the American Journal of Agricultural Economics, the Southern Journal of Agricultural Economics, and the Western Journal of 7

PAGE 16

Agricultural Economics. The following review of the literature is not encompassing; however, the authors propose that it is a good sampling and fairly representative of the major direction, and reflects the flavor of this research and development effort. Conceptual Basis and Framework for Hodel Discussion The factors affecting agricultural water use and demand are many and complex. The basic soil-water-plant climate relationships have been studied for a long period of time by a large number of scientists. These relation-ships are fairly well understood; however, this does not really reduce the fact that the relationships are still complicated and the quantifica-tion of many relationships is still on the horizon. In addition, the de-mand for irrigation water in agriculture is by the socio-economic-institutional-political environment. It is through this environment that the human actor enters into the agricultural water use process (See Lynne and Carriker, 1979, for further elaboration on this point). In fact, the conception guiding the presentation in this report is that water demand is affected by the physical attribq.tes of nature and the active involvement of man. The latter element enters through the thinking, innovative features of the human actor as a manipulator and user of the "natural" system. The fact that there are irrigation systems at all is testimony to the fact that man is an active element; thus, attention is directed to whether models allow inclusion of the various features that man brings to the water demand process, as well as attention devoted to the physical factors. Another consideration in organizing this discussion relates to the nature of the problem faced by entities charged with projecting water use. 8

PAGE 17

A major consideration in this process is usually related to the availability of water or the 1;\later supply. The notion of water demand becomes useful only within the context of defining the bounds of the water supply for which demand considerations then become important. A major feature, in turn, of the water supply phenomenon is the geographic or spatial nature of water supply. Thus, if water supply and management agencies are concerned about water demand :it is usually in the context of the demands being placed on a particular supply of water which has spatial (as well as temporal) properties. All of the agricultural demand models are classified on the basis of whether they are at the plant-field, farm-firm, multifarm-county-state, or the river basin-regional-national level. The is primarily on the level at which the model been developed, as opposed to the level at which it has been used. That is, the field level model can be aggregated to the farm-firm level and possibly even larger aggregates given appropriate multiplier and aggregation techniques. In fact, some of the models defined herein as being field level models have in fact been used in estimating the demand at higher aggregates. The spatial dimension ia a key property. However, there are also additional features which must be understood before the reader can gain perception of their nature. Basically, there are four major categories of additional features including the temporal, socio-economic, statistical properties, and the climatic/soil/crop factors. Each of these are now discussed in turn. Temporal Characteristics: The time features of each model are separated in the following manner: 9

PAGE 18

Short run--This interval of time represents a period over which only a few of the various factors affecting water demand can vary. For example, the fertilizer level for a crop has usually been specified by the time the producer is in mid-season. Thus, this would be the "short run." Long run--This is an interval of time over which nearly everything can be varied, except the "bounds of the earth." For example, the agricultural manager may change the irrigation system, or possibly adopt new cultural practices or new varieties and farming approaches. Static--This concept implies water demand can be viewed as a series of water use levels at particular points in time. Water demand is then compared from one point in time to another No "feedback loops" or dynamic processes are modeled. Dynamic--This concept suggests the model represents the water demand processes that operate through time, with events today affecting features of the water use process tomorrow. Water demand processes are thus linked through time, and the models reflect these linkages. Socio-Economic Factors These factors reflect involvement of the human element as follows: Prices and/or Costs of Water--This element is included on the supposition that man would consider the cost of installing and operating an irrigation system and that costs affect his behavior, and thus affect the amount of water used. 10

PAGE 19

Other Input Prices or Costs--The price of fertilizer would be expected to affect the amount of irrigation water applied, for example. Water has no direct substitutes; however, it is anti-cipated that the costs of all other inputs including fertilizer, pesticides, and labor all may affect the amount of water used in an agricultural operation, as different mixes of input can generally give the same yield (except the maximum yield). Prices of Products--Agricultural-irrigation managers, in most cases, are concerned about the sales or additional revenue ob-tained from irrigation, as well as the costs. Thus, the price received forfue product can be hypothesized as affecting the amount of water actually used. Technological Changes--A new type of crop variety or water control method could dramatically affect water demand. Also, at the firm level and beyond, the type of irrigation system that is used will affect water use dramatical-ly. Of course, this is a supply phenomena as opposed to a demand feature (i.e., the irrigation system on a farm is analogous to the private or municipal utility in a city, in the sense that this is the water supply portion of the organization). Production Process Changes--The amount of fertilizer and/or the particular spray program would both affect the marginal response of irrigation water and, thus, affect the demand for that 11

PAGE 20

water, as examples. Actual changes in cultural prac-tices would be included under this particular heading. Behavioral Features--The driving force behind the human element is captured here, at the field and/or firm level. One possible assump-tion might be that farm managers are profit maximizers, but plausible goals include cost minimization, risk aversion or maximization of crop yield. The goals and objectives of managers will likely affect water use and demand. Institutional Features--The political-legal-institutional setting can affect water demand through price support programs of farm pro-ducts and/or the manner in which water rights are speci-fied, as examples. Water management districts in Florida, for example, encourage conservation through such modes as encouraging irrigation during low evaporative demand periods. Farm price support programs may make irrigation more profitable, as another example. Statistical Properties This feature relates to the degree to which random events have been incorporated into the projection processes, as follows: Stochastic-This concept rests on the hypothesis that random influences affect the projection level. Given a particular water demand projection there will be an associated variance of that estimate. The larger the variance, the less reliable the estimate is. 12

PAGE 21

Deterministic--The notion here is there is no random error and that \'vater demand projections exhibit no variance proper-ties and particular levels are known with certainty. Climatic-Soil-Crop Features This category includes all those physical features of the environment in an agricultural field situation that affect the amount of water used. These variables are essentially proxies for the complex phenomena involved in an actual field as follows: Temperature or Heat Budget--The mean daily or maybe monthly temperatures are used in several models. The heat budget notion depends on an understanding of the relationship among radiation, actual duration of sunshine, maximum possible duration of sunshine, vapor pressure in the air, vapor pressure at mean air temperature, and several other variables (see Israelsen and Hansen, p. 241). Length of Growing Season--This variable will affect the consumptive use of the plant, for obvious reasons. Precipitation--This is a stochastic variable which is difficult to Soil Character or Soil predict but most assuredly affects the water demand from ground and/or surface sources. This effect is through influence on the air/environment surrounding plants, as well as having an effect on soil water availability. Capacity--The water holding capacity of the soil is a key variable in determining consumptive use. Soil 13

PAGE 22

texture and structure are especially important as the.se forces give rise to "capillary phenomena." These affect the flow or movement of water in soils and the availability of \.,rater or plant growth. Humidity and/or Wind Conditions--This is simply another weather factor that affects evapo-ration and general conditions of the crop. Sunlight, Solar Radiation--An energy source, of course, is necessary to drive the entire plant growth process. The amount of .solar radia-tion will affect the amount of water Specific Crop Features--The root system and leaf area of the plant in question Evaporation or Potential Evap-will affect the amount of water used. Alsq different crops are at different stages of growth at different times of the year. In addition, plants will use varying amounts of water through their growth process with the highest consumptive relative to the potential use, occur-ring some\vhere during the flmvering stage (Israelsen and Hansen, p. 257). otranspiration--This factor is a function of many of the soil/climatic/ crop factors mentioned above. It really measures; as a proxy variable, the overall influence of these elements. It is included here because many of the yield models rely 1 on measurements of relative wl;rere either evaporation or potential evapotranspiration serves as the denominator of the ratio. 14

PAGE 23

A listing of the models by the major categories using the above classification system is presented in Table 2. Tables 3-24 are used to detail the specifics of each model. The reader should be warned that it is very difficult in many cases to determine whether the model developers considered specific factors or not. To this extent, these tables will be in error. The main criterion was that the variable had to be mentioned and used explicitly in the model and/or the model development process. Overall and Major Features of Agricultural Water Demand Models Nearly all models reviewed are short run, static models with deter-minis tic statistical properties (Table 2). Only one model really incor-porated any stochastic influences in the projection stage. The Pennsylvania model allowed for yield variability, an estimate of this variance, and the overall effects on water use. Another overall feature applicable to the entire set of models is that some tended to emphasize the socio-economic factors and others, usually not the same ones, emphasized the climatic-soil-crop factors (Table 2). If in fact water demand is affected by behavioral, social, political, institutional elements as well as temperature, precipitation, soil factors, and crop features, then the "best" models from the set shown in Table 2 are probably the ones having the most of these features included. On this ground, it appears that the Mapp-Eidman model is the most appropriate over the entire set, followed very closely by the Utah, North Carolina, and CARD models (Table 2), The plant-growth type of model, if modified to include socio-economic factors as well, appears to show the most promise for the future with 15

PAGE 24

Table 2 .--Major features of aRricultural water demand mooels.'l --------------------Tempor;ll Characll'r istil's .--. --, .-----,-t--'-1 t:-j:-s-' t-l:-c-' a-1:r-----------------------....:------------------Spatidl properties and model Plant-field level models: Blaney-Criddle Hargreaves Hexem-Heady Hogg, et al. Minhas, et a1. Penman Plant Growth Thorntwaite Farm-firm level models Mapp-Eidman Moore-Hedges Coun ty-r.lUl t icounty-river (or sub) b.:lGin state models Input-output Kansas Lowry-Johnson New Mexico North Carolina Pecos Basin Pennsylvania Texas High Plains Utah River basinregional-national models CARD Ruttan ... '-' '" o .c 'tl .., :> "'.0 ... OJ .., "-'" g '" ",.c E-< x x X x x x x x factors o III <11 OJ '" 'H o '" '5 'S 000 ... "''-'l ...< x X X X X X x X x x x x X X X "' Qj '" .., '" OJ .... ..... .... o '" x x X X X X X x X X x c: 0 ........ -= ... eo", .., ..... ..... '" <11 ... '" X X x X x x x '" '" ...... ... ... ... OJ '" "' .... til X X x X X x x x x X x X X x X X x X aBlanks sometimes mean the information was not available. See the text for elaboration. An "X" means these elements, fac.tors were considered explicitly in the model. b The plant growth models require detailed information on how the photosynthetic-respiration rate is affected by climate, soil, and pi, features. c The yield simulation portion of this model is really a plane growth model, altiloug;, not as detailed as the models discussed briefly under the "Plant Growth" category. See footnote a. dAlso includes interactions among the various inputs of production (e.g., the fertilizer-water interaction effects). 16

PAGE 25

respect to incorporating these different factors into the demand projection process. The Mapp-Eidman model does incorporate many features of the plant-growth simulation approach. These types of detailed models are also the most expensive and difficult to develop. Several models did include other input prices and/or the costs of other inputs in the modeling effort. Only in the case of the HexemHeady model did the other input prices affect the water use, however. That is, it can be hypothesized the demand for water may be affected by the prices of substitutes for water including such things as fertilizer and other inputs of production to the crop process. The Hexem-Heady study isolated the effects of fertilizer in order to facilitate the direct con-sideration of changing fertilizer prices. The other studies tended to include the costs of all other inputs under one category and not deal ex-1 plicitly with the substitutability problem. It appears modelers have yet to successfully deal with this dimension. Another basic feature of nearly all the models \vas that technology was generally assumed constant over the projection interval. The one ex-ception was the Kansas model which allowed for changes in irrigation ef-ficiency over the longer run. An explanation for this invariance in tech-nology is that most models are short run in nature, in which case it is logical to hold technology constant. Over longer run periods, however, lThis is somewhat misleading with respect to the Texas High Plains Hodel. The developers of that model did in fact allmv energy prices to vary, and they map the effect on water demand from rising energy prices. However, this is essentially the same thing as raising the price of water and is not necessarily dealing with the substitution phenomena at all. The CARD model also allows for consideration of some input price changes and the effect on water demand and use, but the full range of substitutability among input factors was not allowed in that modeling process either. 17

PAGE 26

technology could have a significant impact on the quantity of water utilized. This would be exemplified through variety changes and/or changes in the cultural practices and/or changes in the irrigation system, as examples. Specific Features of Agricultural Demand Models by Spatial Property Each of the models is now discussed in more detail. Emphasis is on explanation of model similarities and geographic-spatial differences as the major influence for large model differences. Plant-field level model The mathematical description of each model is .the first item in each of the Tables 3-10. All of the approaches are limited to a few equations, all of which require estimates of various parameters. Some of the more "physical models" have parameters that have been fairly well established by researchers, such as for the Blaney-Criddle model. Others require para-meter estimation for the site of concern such as in the Hexem and Heady models. This latter feature is also descriptive of the Hogg et aI., and Minhas et ale models. The most connnon feature is that all mode.ls project water demands for some land area, most generally an acre or hectare. Also, all are short run models usually concerned with estimating demand on an annual crop year basis. Some are appropriate for growth stage (intraseasonal) projection such as the Minhas et al., and the plant growth type models. The water used during growth stages can also be approximated using the Blaney-Criddle Hargreaves, Perunan, and the Thornthwaite models. This is the case as most of these models use a month during the growing season as the appropriate time period. Thus, the various monthly periods can be appropriately 18

PAGE 27

f-' \D Table 3.--Blaney Criddle Model (After Israelsen and Hansen) CHARACTERISTIC Hathematical description Type of output Temporal properties Spatial properties Input data required Technological production process change Behavioral assumptions and institutional settings SUMMARY DATA u = kf and U = = KF, where U consumptive use of crop, inches for a given time period; K empirical coefficient (annual, irrigation season, or growing season); F sum of the consumptive use factors for the period; u monthly consumptive use of the crop in inches; k = empirical consumptive-use crop coefficient for a month; and f = monthly consumptive use factor (sum of mean monthly temperature and monthly percent of annual daylight hours or (t x p)/lOO. Note: Values of (t), (p), (f), and (k), can also be made to apply to periods of less than one month. Total monthly water demand. Can be used for varying time periods, generally, a season or one year. It is dynamic only in the sense that climatic factors throughout the year are used; it is essentially a static model. Generally, estimates are made on a per acre basis. Data are needed on temperature, rainfall, the percent of annual daytime hours, and the empirical crop coefficient. These data are available from local and/or state agencies, the Soil Conservation Service, and local experiment stations. Irrigation and/or crop technology not considered in this projection model. Also, the crop is considered to have optimal quantities of other input, commensurate with maximum yields. Neither of these is made explicit; however, use of this approach assumes implicitly that farm firm managers wish to maximize yields and that the institutional environment does not affect use.

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N o Table 3.--B1aney-Cridd1e Model (After Israe1sen and Hansen)--Continued CHARACTERISTIC Stochastic/deterministic features Climatic/soil/crop factors Documented computer program Data base References Sill1HARY DATA The model is deterministic. The Blaney-Criddle model explicitly considers temperature and daytime hours. Basically, the term F represents a proxy for the potential evaporation and/or potential evapotranspiration. The sunlight or solar radiation factor is considered via the length of the growing season and the percentage oE daytime hours for the time period of concern (as a percent of the total for the year). The specific crop coefficient is the amount of water that a non-stressed crop will use during a particular period of time. A computer program and users manual are available through the Soil Conservation Service of the United States Department of Agriculture. This program also calculates irrigation water needs under the behavioral assumption that producers maximize yields .. A detailed documentation of the actual computer program is not available. Input data are readily available from national/state data bases for all input parameters except the empirical crop coefficient. Even for this need, however, there are estimates in the SCS publication, Technical Report No. 21. Also, agricultural experiment stations in the respective states have some information on this coefficient. Blaney and Criddle (1947); Soil Conservation Service (1969; 1970)

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N f-' Table 4.--Hargreaves Model CHARACTERISTIC Hathematical description Type of output Temporal properties Spatial properties Input data required Technology/production process changes Behavioral assumptions and institutional settings Stochastic/deterministic features SmmARY DATA (After Criddle, 1958, pp. 1507-12). e = m(t-32) where e = monthly evaporation in inches, ill = an empirical factor; t = mean monthly temperature in"F. Hhen corrected for the time element, it becomes e = where e = climatic factor; d = monthly daytime coefficient. Also, disregarding wind movement, c = 0.38 0.0038 h where h = mean monthly humidity at noon. Then U = KE = L: ke where U = annual or seasonal consumptive use (actual ET) of the crop; K = crop coefficient; E = sum of monthly evaporation for the period; and k, e = monthly values of K, E. The physical requirement or actual ET (total demand) is estimated with the model, as shown by U above. The model is suitable for seasonal predictions and/or shorter periods like one month intervals. The equation is suitable over larger areas or at the acre, field level 0 Mainly climatic data is required as shown in the above mathematical description. It is assumed that all other input levels and technology are invariant, Further it is assumed the plant is not being stressed by any other tors. Of course, alternative levels of K could be selected. No explicit statement of the role of the human element. The model is deterministic.

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'" '" Table 4.--Hargreaves Model--Gontinued. CHARACTERISTIC Climatic/soil/crop factors Documented computer program Data base Reference SUMHARY DATA This model basically uses a relationship between evaporation, temperature and length of day. Wind movement and the influence of water vapor is also considered via relative humidity included as a variable. A crop coefficient is also necessary for the model which varies with the season of the year. None available. Climatic data available from the U.S. Weather Service. Criddle (1958).

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N W Table 5.--Hexem and Heady Models CHARACTERISTIC Hathematical description Type of output Temporal properties Spatial properties SUMMARY DATA 2 2 y b O + blxl + b 2 x 2 + b 3 x l + b 4 x 2 + bSxlx2 Profit 'IT = PyY -rlxl -r 2 x 2 with x 2 constant ("short run:) rl-P (bl +b_x2 ) y ) 2PybJ d'IT dY aXI = P y dXl -r l 0 or P y (bl + 2b3x l + b S x 2)= rlor xl This is the "short run" demand function. The "long run" (fertilizer also varying) demand function would be given by the simultaneous solution of (d'IT/dx l ) = 0 and (d'IT/dX2 ) = O. The general form will be Xl = f(rl' r2' p) where Xl = total water available, in acre inches, x 2 = fertilizer applied; Py = product price; rl = water price and/or irrigation cost, for that portion applied through the irrigation system; r 2 = fertilizer price;-bl b 2 b 3 b 4 and b S = parameters. The production function as exemplified by these models allows the derivation of short run and long run demand functions as illustrated in the mathematical description. Thus, the quantity of total water demanded can be shown to be a function of changes in various physical phenomena as reflected in the production function but also will be affected by changes in the prices of the water and fertilizer and the product price. These models are usually annual in their time step. Also, they are static models and can be used for comparative static analyses. These models are on a par acre basis.

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N .p. Table 5.--Hexem and Heady Hodels--Continued CHARACTERISTIC Input data required Technological/production process changes Behavioral assumptions and institutional settings Stochastic/deterministic featureS Climatic/soil/crop factors Documented computer program Data base References SUHHARY DATA Detailed experimental station kinds of data are needed showing the relationship between yield response and fertilizer and water applied. Also, input and product prices are needed. These water fertilizer models allow the fertilization program to vary. l-lmvever, all other cultural practices and technological features are assumed invariant. The farm firm manager is assumed to be a profit maximizer. The institutional setting is assumed invariant This is a deterministic model where the independent variables are assumed to be measured without error. The water variable in these regression models is generally the sum of water available in the soil plus precipitation plus irrigation water applied. None available. Experimental data on the yield-water relationship are available from agricultural experiment stations on a limited basis, with some states having much more than others. Product price data are available from the Crop and Livestock Reporting Service, a cooperative effort between state and federal entities. in each state. Irrigation cost information will: also",: be available from the agricultural experiment stations. Hexem and Heady (1978).

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N \..n Table 6.--The Hogg, Davidson, and Chang Model CHARACTERISTIC !1a thema tical desc rip tion Type of output Temporal properties Spatial properties Input data required SID-IHARY DATA E R + (NxS) Y E a + b (E /E ) + c (E /E )2 a e a a -= -= f(-) E E Y E a pap p p p p r (NxS) chr Profit = 7f = PY TC = P[f' (Y )] -r O. a dI a e where E = the actual consumptive use or actual evapotranspiration; Ep = potential evapotranspiration; Re = effective rainfall; N = the number of irrigation rounds; S = the soil moisture storage; Y = actual yield; Yp = potential yield, a, b, c, = parameters; P = price; r = irrigation costs; and/or price of irrigation water; TC = other costs of production; Ie = (NxS) = level of effective irrigation The short run, profit maXLm1ZLng total water demand curve is defined by the relationship Pf'(Ya ) = r. Thus, the demand for Ie is affected by product price, the cost (and/or price) of irrigation water, and any other factors affecting the production function. This is a seasonal and static model. The yield response is estimated for an acre of land. Detailed information is required on the relationship between yield and relative evapotranspiration as well as detailed level measurements on effective rainfall. Also some estimate of potential evapotranspiration must be available. Prices are needed for the product and irrigation cost must be (and/or prices of irrigation water).

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N 0'1 Table 6.--The Hogg, Davidson. and Chang Model:--Continued CHARACTERISTIC Technological/production process changes Behavioral assumptions and institutional settings Stochastic/deterministic features Climatic/soil/crop factors Documented computer program Data base Reference ._----_ .. _--,--------SUHMARY DATA All other inputs of production are assumed constant. Technology is also invariant. The farm firm manager is assumed to maximize profits. The institutional setting is assumed invariant. The model is used in deterministic manner; however, stochastic influences could be examined. This model accounts explicitly for the actual to potential evapotranspiration, rainfall, and soil moisture storage. An attempt was made to include "--the relevant aspects of agronomic theory while retaining reasonable simplicity" (Rogg, Davidson, and Chang, p. 127). None available Field experimental data and irrigation cost information are available in limited quantities from state agricultural experiment stations. Product price data are available from the Crop and Livestock Reporting Service in each state. Hogg, et al.,(1969).

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"j 1, '1 I "' N ....... Table 7.--The Minhas, Parikh, and Srinivasan Dated Input Model CHARACTERISTIC Mathematical description Type of output x Y SUMMARY DATA fez) = AET = (l_e-rz)/(B + e-rz) PET 2 bl 2 b2 a [ 1-(l-x )] [ 1-(l-x ) ] I 2 WI + w 2 = W; (PET)(xl ) + (PET 2 ) (xZ ) oy 1 ow. oW. (PET) 1 1 b [l-(1-x ) 2] n n v1; Xl w. 1 PET i where x = relative ET, or actual ET (AET) divided by potential ET(PET); z = available soil moisture; r,B = constants, parameters; y = yield per unit land area; Xj = relative ET in growth period j; b l ... ,bn = parameters associated with yield response in alternative growth stages; Wi' W = Wi is water available in crop growth stage i, W is the total water available for the crop growth season. [Note: The profit maximizing short run (intraseasonal) demand curve for this model would then be derived from the equation ri = where p = product prices; ri"= price or marginal factor cost of one more unit of Wi' Minhas et al., did not calculate this function in the paper. The optimal seasonal, maximum profit demand curves would result from simultaneous solution of all such short run demand curves]. A total water demand curve can be derived given a production function, as shown above. Note: the demand for total water (W) is a function of the product price, the quantity of water available during other portions of the growihg season (Wi) and the price (or marginal factor cost) of one more unit of water.

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i i N co Table 7.--The Minhas, Parikh, and Srinivasan Dated Input Model--Continued CHARACTERISTIC Temporal properties Spatial properties Input data required Technological/production process changes Behavioral assumptions and institutional settings Stochastic/deterministic features SUMt1ARY DATA This type of model is suitable for intra-seasonal or seasonal estimates of water demand. One could also project longer periods. This model was developed to explain yield response for a hectare. Field and farm firm level estimates could be made. Hore aggregate estimates are also possible but of course, there may be errors in estimation as we go beyond the type of field and soil conditions for which the function is developed. Detailed information is needed on the relationship between relative evapotranspiration and available soil moisture. In addition, experimental data is needed to relate yield to the relative evapotranspiration. Product prices would have to be estimated and the costs of irrigation and/or the prices of irrigation water would have to be known. This particular model assumes all other inputs are at fixed quantities and technology is invariant. The farm firm manager is assumed to maximize profits and/or mlnlmize costs (the latter goal related to some sort of an output constraint). The institutional setting is assumed invariant, although variations could be allowed in the model. The model is deterministic. but the variance on profit could be estimated. The input variables are assumed to be deterministic and measured withQut error.

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N \.D Table 7.--The Minhas, Parikh. and Srinivasan Dated Input Model--Continued CHARACTERISTIC Climatic/soil/crop factors Documented computer program Data base Reference SUMNARY DATA These authors were sensitive to the need to establish the relationship between available stocks of moisture in the soil and the rate of water used by the plants. Then they define the relationship between the time profiles of water use and crop yields (p. 383), They choose to summarize many of the climatic soil factors by establishing a functional relationship bet,veen relative evapotranspiration and available soil moisture. Then they relate yield to relative ET. None available. Field experimental data and irrigation cost information is available to some extent from state agricultural experiment stations. Product price data can be obtained from the Crop and Livestock Reporting Service in each state. Minhas, et al. (1974).

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w o Table 8.--Penman Model CHARACTERISTIC Mathematical description Type of output Temporal properties Spatial properties Input data required t\H + 0.27Ea ET t\ 0.27 (0.10 + 0.90n/N) SUMlvfARY DATA II RA(l-r) (0.18 + 0.5Sn/N) 8T4 (0.56 O.092/ed) a Ea 0.35 (ea -ed)(l + O.Ou9Sn 2 ) where II daily heat budget at surface in mm H20/day; RA = mean monthly extra terrestrial radiation in mm H 20/day; r = reflection coefficient of surface; n = actual duration of bright sunshine; N = possible duration of bright sunshine; a = Boltzman constant; Ta = mm H 20/day; ed = saturation vapor pressure at mean dew point (i.e., actual vapor pressure in air) mm Ug; Ea = evaporation in mm H20/day; e a = saturation vapor pressure at mean air temperature in mm Hg; n2 = mean wind speed at 2 meters above the ground (miles/day); ET = evapotranspiration in mm H 20/day; u l = measured wind speed in miles/day at height h in feet; t\ = slope of saturated vapor pressure curve of air at absolute temperature Ta in OF (mm/Hg/OF). Consumptive (total water) demand measured in mm of water per day. The level of aggregation is simpli a matter of mUltiplying the estimates times the acreage figure. This equation estimates the potential evapotranspiration which is not related to crop type. Generally used for intraseasonal predictions. It is a time dynamic model to the extent that predictions will vary through the years and are only limited by the extent of the weather information to the user. Crop or field level although results can be generalized at the larger areas. All of the climatic variables illustrated above in the matheniatica:l description.

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t; \H l I i W I--' Table 8.--Penman Model--Continued CHARACTERISTIC Technological/production process changes Behavioral assumptions and institutional settings Stochastic/deterministic features Climatic/soil/crop factors Documented computer program Data base References SUMMARY DATA No changes are considered in the agricultural production process or in technology. This model assumes the crop is not being stressed for any cultural or technological reasons. Both of these variables are assumed invariant. The implicit behavioral assumption is that fann firm managers wish to maximize yield. The model is deterministic in nature, with no statistical reliability coefficients having been estimated. The Penman Model is theoretical in nature and uses basic structural relationships from physics and other basic sciences to relate several climatic variables. That is, this model utilizes several climatic variables most of which are defined above in the mathematical section. There are no crop factors involved, however. The basic feature is tllat consumptive use is assumed to be "--inseparably connected to jncoming solar energy" (Israelsen and Hansen). Availability unknown. Climatic variables from the U.S. Weather Service Israelsen and Hansen (1967); Penman (1948).

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W N Table 9.--Plant Growth Hodels CHARACTERISTIC SilllNARY DATA Hathematical description As noted by Jones (1979) crop growth is usually related to the difference between photosynthesis and respiration multiplied by a conversion coefficient between biomass and CO2 as follows: dl-l = (P R W) / (1 + 0G R ) o dt g 0 dW -1 -1 where dt = biomass growth rate (kgha day ) o biomass: CO2 conversion factor (kg biomass kg-l CO2 ) Pg = gross photosynthesis (kg CO2 ha-l day-I) Ro maintenance respiration factor (kg CO2 kg-l ,biomass day -1) W ==. biomass (kg ha -1). GR growth respiration factor (kg CO2 kg-l biomass). dW. dW. dH. 111 Production is .thenrepresented by:. = where dt -biomass growth rate of leaves (1=1), stems (i=2) roots (i=3), and fruit (i=4). (.(.i = partitioning coefficient for leaves, stemS, roots, and fruit. Jones notes that "crop growth models vary in detail and complexity--generalities are uSed to describe this overall approach because of a lack of a universally accepted framework for representing crop growth processes and their interrelationships." Water stress will reduce photosynthesis; thus, there is a relationship between water availability and y:i,eld. Water balance equations a!'e'. L included in these models, when water demand is of Concern. /

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L,..) L,..) Table 9.--Plant Growth Hodels--Continued CHARACTERISTIC Type of output Temporal properties Spatial properties Input data required Technological/production process changes SUMMARY DATA The yield associated with various levels of total water being made available are the direct output of these kinds of models. Usually these are daily models with seasonal yield projections. These models usually have the capability of telling the state of the plantsoil-water-condition at any given day in the season. They are also dynamic in nature with effects causing changes today and on future days. These are usually developed on a per plant and/or per acre basis. Climatic data are needed to estimate evapotranspiration and to calculate a soil water balance. Detailed information is also needed on maximum and minimum air temperature. soil data, including soil water retention curves, root zone depth, and unsaturated hydraulic, conductivity relationships. Crop parameters must be specified as well. Of course, the detailed structural relationships, some of which are described above, must also be input. Generally, these models allow that other inputs of production (for example, fertilizer, pest control programs, other cultural practices) can be varied, and also affect yield. Thus the interaction between water and other inputs can be isolated. Technology is generally assumed invariant, although different varieties can usually be evaluated for any given crop model.

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VJ Table 9.--Plant Growth Models--Continued CHARACTERISTIC Behavioral assumptions and institutional settings Stochastic/deterministic features Climatic/soil/crop factors Documented computer program -Data base References SUMMARY DATA The human element is not explicitly included in these models. However, it is recognized implicitly that the manager may wish to vary the various input and thus this flexibility is built into these models. The institutional setting is not a consideration for these models. These models are generally deterministic in nature. It would be possible to consider stochastic processes. These models build from knowledge of the -structural relationships involved in soil physics, plant physiology, climatic forces, as well as the relationships among climatic/soil/plant factors. Of all the modeling approaches, this particular method utilizes the most theory and concept as well as empirical measures, with respect to this particular characteristic. Extent of documentation unknown. Huch of this information is available from agricultural experiment stations. Basic climatic information 'l1ill be available from the U.S. Weather Service. Jones and Smajstrla (1979); Jones et al., (1972).

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ij ,) j J \ W \J1 Table IO.--Thornthwaite Model CHARACTERISTIC Mathematical description Type of output Temporal properties Spatial properties Input data required Technological/production process changes Behavioral assumptions and institutional settings Stochastic/deterministic features SUMMARY DATA A monthly heat index is calculated from the following expression i = (t/5)1.514 where i = heat index and t = A seasonal heat index value is obtained by adding all of these individual monthly temperature values. A straight line has been drawn from the "index point" through this heat index which gives a relationship between temperature and evapotranspiration. Estimates of the potential evapotranspiration or total water demand with no allowance made for different land uses or crop. Usually used to estimate seasonal water use. Formula has been used to estimate potential ET over extensive portions of the world. Basically, only temperature and latitude are needed, beyond the basic equations (which include some parameters) developed by Thornthwaite. As npted above,fue crops and their particular features are not included explicitly. Again, the human element is not explicitly considered in this equation. The model is deterministic.

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1 j l.iJ 0"1 Table IO.--Thornthwaite Hodel--Continued CHARACTERISTIC Climatic/soil/crop factors Documented computer program Data base References Sill1MARY DATA This model basically assumes that all the climatic factors can be summarized with the proxy variable temperature. Latitude is added to the measure and projections made over larger areas. No crop coefficients are included, although some work has shown that accumulated consumptive use is an excellent index to stages of plant growth. None available. Temperature data available from the U.S. l.-leather Service. Israelsen and Hansen (1967); and Hather (1955; 1957).

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aggregated given some assumptions about the length of each stage of growth of the plant. None of the plant-field level models included technological changes and only t\vO incorporated production process changes. Technological change phenomena is of course not necessarily included when only very short run periods are being examined. The production process changes, however, probably should be included, but again, they are not important over very short time periods. None of the models at this level included institutional features and about half of them included behavioral features. The institutional setting is also probably relatively fixed within a crop season, and this would be appropriate. The exclusion of behavioral features tends to reflect a notion that man does not affect water use, an hypothesis that could be tested. In some sense, however, the exclusion of the behavioral element is simply not possible. Said somewhat differently, even the projectioh models which do specifically include man assume (implicitly) the goal of maximizing yield per unit land area. This is the case for the Blaney-Criddle, Hargreaves, Penman, and the Thornthwaite methods. The Plant Growth simulation models could be developed to include the influence of the human element involved in irrigation processes as well as the features of the plant and the soil water relationship pertaining to a particular field. The type of output varies greatly among these plant-field models. This is the case primarily due to the role ascribed to, and the objective function assumed for, the human actor. The Hexem-Heady, Hogg al., and Minhas al., models, for example, all assumed that producers will choose to maximize profit. As a result, it is likely the projections for a particular area would be different than those from models where maximum yields 37

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are assumed. Of course, this is an empirical question and cannot be answered in any general way. In all cases the total water demand is presented for some intraseasonal and/or seasonal period. Irrigation water requirements then depend on precipitation received. There is substantial variation in the degree of sophistication used to represent climatic/soill crop factors in this group of models. The Hexem-Heady models, for example, attempt to quantify all the complexity of these factors by simply adding the sum of available soil water to the precipitation plus the irrigation water (Table 5). The Plant Growth models at the other extreme (Table 9) include detailed structural relationships which explain how water moves through the soil and the plant to affect growth. The Penman model, which is useful for estimating potential evapotranspiration, has very detailed theoretical conceptual relationships requiring a large number of parameters as well as input data. The Hogg-Davidson-Chang model and the Minhas-ParikhSrinivasan models do incorporate some agronomic factors and may be a good compromise between the two extremes for certain types of Several of the models choose to summarize all of these factors within the relative evapotranspiration ratio (Tables 6, 7, and sometimes the plant growth models as in Table 9). Input data requirements vary extensively across these models. At one extreme is the plant growth type of model which requires a high degree of sophistication in the plant-engineering sciences in order for the model to be developed. Also, if these models included the socio-economic factors, it would require the same degree of sophistication in the socio-economic sciences. Models at the other extreme, while not necessarily technically less sophisticated, require only secondary data sources. The BlaneyCriddle, Hargreaves, and Thornthwaite models fit in this category. As an 38

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example, only three pieces of information are needed for the Blaney-Criddle model including temperature, the percent of annual daytime hours, and the empirical crop coefficient (Table 3). The models which attempt to relate yield to various proxies for the water variable, such as the Hexem-Heady, Hogg al., and Hinhas al. models require data from experimental trials. These types of data would generally have to be obtained from agricultural experiment stations and a high degree of technical sophistication \vill be necessary to arrive at the actual functions. Useful models of this type require successful tntegration of knowledge from the crop-soil sciences, economics, and statistics. The major data sources for this category of models are the agricultural experiment stations, state/federal weather services, and the federal/state crop and livestock reporting services. Utilization of such models ,viII probably require establishing contacts and 'vorking relationships with scientists and personnel of these entities. Generally speaking, there has been little effort placed into computer program documentation and user manual development. The only known users manual in this category is that available from the Soil Conservation Service. This manual explains how to use the computer program which implements the procedure in Technical Release 21. Farm-firm level models The mathematical description of these kinds of models is characterized by the simulation approach used in the Happ and Eidman model (Table 11) and the linear programming models as developed by Hoore and Hedges.l The lA third type of mathematical model developed at the firm level but not represented here is the regression type of model. A large amount of work 39

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o Table ll.--Mapp and Eidman Hodel CHARACTERISTIC Mathematical description Types of output Temporal properties Spatial characteristics SUHMARY DATA This is a simulation model with a crop yield simulator as an important and basic component. The basic features of the yield simulator are as follows: = + (P" -P A ) YR L L YR" 1J J 1J J 1J 1J J 1 where = yield reduction on day i for stage j and crop k; = yield readction in units per day as a result of adverse conditions, stage j and crop k; SMD., = soil-water depletion in inches on day i for stage j; = yield readction coefficient due to severe atmospheric demands, stage j and crop k; Pi' = pan evaporation in inches, day i and stage j; P A = critical pan evaparation level; if at or below this level, yield reductions occur due to severe atmospheric conditions. The SMD., was calculated by SMD .. = (a SHTi,)/b where a,b = parameters with the soil type; SMTi = inchesJof soil water in the entire profile on day i of stage j. of the products and several of the inputs (nitrogen, seed. labor, capital, irrigation water) are also input variables. Net farm income for a representative farm firm is projected ferent water availability and institutional change scenarios. demand for irrigation water is predicted. under difThe The model works on an intra seasonal basis but is used to project farm income over several years of time. It is a firm level model for a typical 648 acre firm in Oklahoma, using water from the central Ogallala formation.

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I-' Table ll.--Mapp and Eidman Model--Continued CHARACTERISTIC Input data required Technological/production process changes Behavioral assumptions and institutional settings Stochastic/deterministic features SUMMARY DATA The yield simulator requires certain types of parameters and input on precipitation and climatic conditions, as shown in the above description. In addition, information is needed on resource availability, crop types to be grown and the cost of growing various crops. Such yield simulators must be developed by professionals having knowledge of basic plant water relationships. Generally, this expertise as well as other data requirements are available from agricultural.experiment stations. The simulation model is oriented towards examining the effects of price changes, or a tax policy, on the water input. Or, it has the capability of examining the effects of different water availability plans. The yield simulator is not sensitive to changes in other cultural practices, such as fertilization programs. Similarly, the current version apparently does not allow for examining alternative technological features that may occur in the future. Of course, such simulators can be generally modified to deal with the wide range in types of outside influences on net farm income. The farm firm managers are assumed to be profit maX1ID1Zers. Several institutional changes relating to the allocation of water to agriculture can be examined with the model. The model is deterministic in nature.

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N Table 11. --Happ and Eidman Hode1--Continued CHARACTERISTIC Climatic/soil/crop factors Vocunented computer program Data base References Sill1MARY DATA The underlying yield simulator for this model requires a fairly detailed consideration of basic relationships. Rainfall pan evaporation distributions were necessary. Soil "mter is then estimated given some initial starting value by using the daily rainfall and pan evaporation values which in turn were generated from probability distributions. Potential evapotranspiration is calculated from pan evaporation givenffime knowledge of the stage of growth. Two layers in the soil's profile are modeled and the amount of water kept in each is monitored. The simulation model makes all of thet;e calculations each day of the growine season. None available. Host data available through agricultural experiment stations. Climatic and product price information will be available from state/federal sources. Happ and Eidman (1976); Happ, et a1.. (1975).

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Happ-Eidman model uses a plant grO\vth simulator as its basis. This simu-lator generates the yield for varying levels of water availability. Various acreage combinations of the crops in the study area are included. Also, a particular type of farm manager is assumed, namely one who is "rational" in the sense of seeking profits and/or minimizing costs. The model is actually used to examine the short and long term effects of a declining water supply to a farm firm. The price of water is increased over time and compared with the results when less water is available. The Moore and Hedges model also has the capability of examining mands over longer time horizons (Table 12). This is a linear programming model with the normative influence of the assumption that farm managers maximize profits in dictating the optimal organization of a farm firm. In this model, not only crop types can vary, but also the crop acreages, whereas in the Mapp-Eidman model the crop acreage is an estimate of net farm income as well as demand for irrigation water under different price assumptions. Technology is not addressed directly in either of the models, even though long run projections are provided. This puts both of the models subject to question. Also, the interaction effects between irrigation water and other inputs of production process changes are invariant over the time horizons considered. Both ITIodels are deterministic. The Napp-Eidman model is much more explicit with respect to including the climatic-soil-was accomplished by agricultural economists in the 1950's in the attempt to develop production functions at the firm level using regression tech-. niques. These efforts were generally not successful, because of high multicollinearity among the independent variables. See Lynne (1977) as an example of this type of approach. 43

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Table l2.--Moore and Hedges Model CHARACTERISTIC Hathematical description Type of output Temporal properties Spatial characteristics Input data required Technological/production process changes SUMMARY DATA This is a linear progranuning model with a parametric objective function \lThere costs are varied. In particular the costs of irrigation are varied.. The model is a set of linear equations for a farm firm in California within a highly intensive crop area. Constraints are placed on the model s'uch as percentage of different grade land, cotton allotments, contract agreements and requirements, production regulations, certain restrictions on maximum amounts of certain crops, and restrictions for twelve critical time periods in terms of irrigation water. Nine alternative crops are considered under three irrigation treatments and the two soil grades giving rise to 54 possible production activities. A water demand function showing the demand for irrigation 1:lTater results from the model showing costs of irrigation and/or price of water as a function of the amount of irrigation water used. It is shown that less irrigation water will be used for higher costs of irrigation. The model is static in nature, but gives some perception of what may occur over longer run periods. The model is developed for an individual farm, and aggregated using weights to represent the distribution of farm sizes in the study area. Detailed data are needed on the costs and returns of production for the various crops. This includes technical coefficients for irrigation water during the critical growth periods for various crops. Although not clear from the model it ap.p.ears. that. only .. the irrigation costs can be changed readLLy within the modeL c. Theother inputs are evidently entered as cost values and were not considered>t,o change. Technology is also assumed invariant.

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VI Table and Hedges Model--Continued CHARACTERISTIC Behavioral assunptions and institutional setting Climatic/soil/crop factors Documented computer program Data base References SUMMARY DATA The farm firm managers are assumed to maX1m1ze profits and as a result (as noted by the authors) it is a normative model. The institutional setting is considered in this model WIDth a discussion of results showing how total revenue to a water agency may change if the water were sold. Estimates of the elasticity of demand range from -.702 up to -.188. The authors advise that policy makers should consider the probable impact of the type of organization used to develop and deliver irrigation water, based on the results they obtained for the water demand function. These elements were considered in the model to the extent that irrigation water requirements for particular crops and yield levels in a particular region of California were None available. Data necessary to utilize such a model are generally available from agricultural experiment stations. Moore and Hedges (1963).

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crop factors. All of these factors are implicit in the Moore and Hedges model, in that yield for different levels of water are included in the model. In fact, the Mapp-Eidman model is very similar to the plant growth models discussed in the previous group with respect to the inclusion of various structural relationships as regards the climate/soil/crop interaction features. In terms of input requirements, the 11app-Eidman model requires more technical expertise in the development of the structure of the model. Also, this model requires more actual data, at a detailed level with respect to how crops respond to water, but also with respect to how farm firm managers might deal with particular types of changes in the environment. Data base sources are similar to those at theplartt-field level. The only difference lies in the level at which these models are developed to function. Linear programming models at the firm level require a high level of expertise for development but generally they can be considered to be less complicated than the simulation models of farm-firms. A higher level of abstraction is usually incorporated in linear programming models. Another major difference is that the linear programming model allows for an optimization subroutine to be used. The actual crop mix and water level usage for various price scenarios then are all developed on the assumption that the farm firm managers pursue some single dimensional goal, such as to maximize profits. The Mapp-Eidman model can examine the level of profitability only after the fact. That is, the results of several "real yearll conditions (or postulated conditions) are simulated. The maximum profit level is then selected from all the model results available to the user. 46

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None of the computer programs developed for this category are documented. Also, users manuals are not available. County-multicounty-river (or sub) basin-state models The largest share of these are linear programming models with linear objective functions and linear constraints (Table 13-21). There are also soDie single equation (Tables 15 and 16) and simulation models (Tables 17 and 19) and input-output models (Table 13) represented in this category. Some quadratic programming models have also been developed to predict water demand at this level (See e.g., Howitt, Watson, and Adams, 1980). This type of model is identical in nature to the linear progralll1liing model except for the provision of the non-linear objective function. This allowance is made to facilitate evaluating the effects on water demand of variable farm commodity prices. The models in this category are as general as to predict the total amount of water used for major economic sectors, such as in input-output modeling (Table 13) and the Kansas model (Table 14), which has the capabil-ity of predicting water requirements for particular crops on particular soil types over 16 day time periods. The Lowry-Johnson model, in turn, considers no economic or socio-political factors, while the Pennsylvania, Texas High Plains, Pecos Basin, and Utah models all incorporate a sub-stantial amount of this kind of influence. The output from all these models is more aggregate in nature than those previously discussed, generally giving the irrigation water demand over at least the county level of aggregation. The Kansas, New Mexico, North Carolina, Pennsyl-vania, and Utah models all have the capability of generating estimates of the irrigation water demand over at least the county level of aggre-gation. The Kansas, New Mexico, North Carolina, Pennsylvania, and Utah 47

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.j. .... 00 Table 13.--Input-Output Models CHARACTERISTIC description Type of output Temporal properties Spatial properties SUMMARY DATA The general formulation specifies that the gross dollar output of an economy must equal the sum of the intermediate demand and the final demand, and the gross dollar outlay must equal the dollar value of the intermediate inputs and the final inputs. The solution of the model is given by X = (I-A)-ly, where X = a vector, representing all outputs of the economy; (I-A)-l is the Leontief inverse [\vhere (I-A) is the Leontief input-output matrix], and Y = a vector, representing the dollar flows to final demand. Hater use is assumed to be some fixed proportion of Yi for each sector Xj. Water use per dollar of final demand in each sector of the economy. This could be as general as a Jegree of aggregation where all of the agricultural activity is grouped under one sector. In the Ireri and Carter model (1970), ten agricultural subsectors were specified, including breakdowns by major types of crop and livestock categories. The output also generally includes "water multipliers, II. which accounts for all indirect water use as \Olell as direct uses associated with an increase in the final demand to a sector. These are short run models, usually specified on an annual basis. They can be used for long run projections if the structure of the economy can be considered invariant. Generally specified at the state and/or national level, with the possibility that subregions could be delineated

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"',I t ,1 :J ." ., !; 'i ./::-1.0 Table l3.--Input-Output Models--Continued CHARACTERISTIC Input data required Technological/production process changes Behavioral assumptions and institutional setting Stochastic/deterministic features Climatic/soil/crop factors Documented computer program Data base SUMMARY DATA Total gros1s dollar output must be determined per sector. Detailed information must be available on the dollar inputs used from other sectors to generate these dollar outputs. This could entail a massive primary data collection process,. The other alternative is to adjust available, national input-output models. Technology and production processes are fixed to that existing for the base year used in the model development The situation existing in the base year data is fixed in the model. These models are gene'rally deterministic in nature, although relationships dollar outputs and inputs are sometimes obtained using regression techniques, from empirical information. These are not considered. Hay be available in particular regions. Publications such as County Business Patterns, the Census of Agriculture, and the Census of Hanufactures will provide overall information on the types of sectors and industries in the regions of concern. Primary data may have to be collected if models are not available for the region of concern, in order to establish technical coefficients. Hater use data Iv": each sector is not easily obtained, requiring various estimation techniques and sources of information.

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VI o Table l3.--Input-Output Mode1s--Continued CHARACTERISTIC SUMMARY DATA References Ireri and Carter (1970; Palmer et al., (1978); Lofting and Davis, (1968).

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V1 I-' Table 14.--Kansas Water Hodel CHARACTERISTIC Hathernatical description Type of output Temporal properties Spatial properties Input data required Technological/production process changes SUMMARY DATA Dollar outputs are projected and water demand is related to the dollar outputs, similar to an input-output model. vlater demand as related to the total value of the product produced over the state. Total annual projection in intervals of 20 years. The model is time dynamic only in the sense that it steps in 20 year intervals, from one static situation to another. Water demand is shmvn by eleven regions in the state. Agricultural projections in terms of the total dollar value of output are necessary by regions. Also, unit water use by type of crop or activity are needed. This model splits agricultural crops into corn, sorghum, vJheat, and others. The factors were developed for the volume of water required to produce the unit value of each crop. The Blaney-Criddle formula was used to estimate consumptive use. Long term precipitation was then subtracted from that estimate. Data is needed on total acres sown, total acres harvested, yield per acre, total production and farm value of crops produced in each county. Similar information is also developed on irrigated land. The irrigation requirement per crop was assumed constant across the state. Crop acreage and production by hydrologic areas were necessary. The proportion of irrigated land relative to total crop land is needed. Irrigation efficiency was allowed to change over the projection horizon from 1965 to 2020. No other cultural practices were allowed to change.

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\J1 N Table 14 .--Kansas Water Mode1--Continued CHARACTERISTIC Behavioral assumptions and institutional setting Stochastic/deterministic features Climatic/soil/crop factors Documented computer program Data base Reference SIDiMARY DATA None were made explicit. Implicitly, however, all behavioral and institutional arrangem?nts existing in 1965 were assumed to be descriptive. The projection methodology is deterministic in nature. These elements were included to the extent they are in the Blaney-Criddle method. That is, the Blaney-Criddle model was utilized to estimate the agricultural \17ater use coefficients. None available. Input data sources would include U.S. Weather Service climatic data, county stat.istics from the agricultural census data, and information from agricultural experiment stations in each state. Kansas Water Resources Boa1:"d(1972).

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V1 W Table 15.--Lowry-Johnson Model CHARACTERISTIC Hathematical description Type of output Temporal properties Spatial properties Input data required Technological/production process changes Behavioral assumptions and institutional setting Stochastic/deterministic features Climatic/soil/crop factors Documented computer program Sill1MARY DATA The consumptive use in acre feet per acre(U) is given by U where Fis effective heat in thousands of degree days. 0.8 + O.lS6F It gives an estimate of the total consumptive use over larger areas. Generally used for estimating yearly consumptive use, but has been modified to estimate monthly use. It is a static model. The model is intended for area wide application. Beyond the basic formula, all that is needed is effective heat in thousands of degree days. Particular crops are not considered. The human element only implicitly considered, via the assumption that yields are to be maximized. The model is deterministic in nature. Again, as with the Thornthwaite model. several climatic variables are measured in the proxy called "effective heat." i.'ilo crop features are incorporated in this model. None available.

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\.il Table l5.--Lowry-Johnson Model--Continued CHARACTERISTIC SUMl1ARY DATA Data base Daily grovling season temperature from the U.S. Heather Service. Reference Lowry and Johnson (1942).

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In In Table 16.--New Mexico Model CHARACTERISTIC Mathematical description Type of output Temporal properties Spatial properties Input data required Technological/production process changes Behavioral assumptions and institutional setting Stochastic/deterministic features Sill1HARY DATA The use of single equation crop production functions relating yield to evapotranspiration. Also, the Blaney-Criddle model is compared with the production function. Estimates of the consumptive use of water for seasons where prices are not allowed to vary and economic considerations are not part of the water demand projection-process. Annual, seasonal water demand projection; it is essentially a static model. Predictions are on a per acre basis. Knowledge of the yield-evapotranspiration production function is necessary. Crop production functions were developed for cotton, corn, sorghum, and alfalfa. Estimates of county yield are needed. All other input levels and technologies are assumed invariant. All the real world behavioral characteristics are implicit in and affect the projection as average county yields were used in the model. Institutional setting was not considered explicitly, but is also to some extent represented by the use of actual county yields. The projection models are deterministic.

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VI 0'1 Table l6.--New Mexico Model--Continued CHARACTERISTIC Climatic/soil/crop factors Documented computer program Data base Reference SUHMARY DATA The Blaney-Criddle formula is used and thus all comments pertinent to that model are also relevant here. Crop features were incorporated from the use of production functions which related yield to actual evapotranspiration. Thus, the ET variable served to proxy all the climatic factors; the yield-ET relationships serve to quantify all the crop features. None available. Experimental data on the yield water relationship will be available for some crops at agricultural experiment stations. County yield data will be available from the Crop and Livestock Reporting Service in each state. Sammis, et al., (1979).

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l.r1 Table l7.--North Carolina Model CHARACTERISTIC Mathematical description Type of output Temporal properties Spatial properties SID1l'1ARY DATA The North Carolina model is really two different mathematical formulations, namely the IRRI model and the linear programming (optimization) model. The IRRlmodel basically determines the water requirement over 61 discreet, 6-day time periods, given different irrigation policies (time when irrigation takes place). The LP model is used to optimize across irrigation policies and crop mixes. Basically, IRRI develops coefficients on yield and water use as well as production and irrigation costs, which are all used in the LP model. The water demand functions can be developed for varying product prices and costs of production. The crop mix on what kinds of soil types i6 also an output. There is a report writer attached to the LP model. Input to the REPORT program comes from the SETUP program and the solution of the linear program. A water use summary for each time period, the unit used and the amount unused is output. Also the marginal value of an additional amount of water available is part of the output. In addition, the utilization of the soil by soil type is provided and the acreage of each crop grown. The number of acres of crop gro\vu on each soil type by irrigation policy is also output. The model is suitable for estimating ,..:rater demand over seasonal and intraseasonal intervals. The IRRI model is dynamic in the sense that water requirements are estimated for any given policy throughout the growing season. The LP model is static in the sense that it is a snapshot-in-time estimate of the total net returns. The models are suitable for examining demand at a county and/or multicounty level of aggregation.

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VI co <, Table l7.--North Carolina Model--Continued CHARACTERISTIC Input data required SUMMARY DATA The IRRI model requires information on acreage by soil type, crop acreage by type, acreage of each crop by soil type, root depth of each crop, inches of water required by each crop as a function of number of days after planting, total inches of rainfall during each time period, moisture deficit level at which irrigation water is applied to a crop as a function of nu,mber of days after planting, total inches of
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lJI \.0 Table l7.--North Carolina Model--Continued CHARACTERISTIC Technological production process changes Behavioral assumptions and institutional setting Stochastic/deterministic features Climatic/soil/crop factors SUMHARY DATA A matrix generator is used "up front" to generate the matrix which is then used in the LP model. In fact, two additional computer programs are utilized to input the data into the matrix, named SWITCH and SETUP. SETUP brings in data from cards and from previously prepared files. Data from cards include the selling price of the crops, production and irrigation costs, acres of each soil, upper and/or lower limits on crop acreages, amount of water available in each time period, water requirements of each crop-so iI-irrigation policy combination, and yield from each crop-soil-irrigation policy combination. The cultural practices associated with the various crops are not allowed to change in the model examples they have presented. However, production costs could be varied. There is minimal interaction between other cultural practices and irrigation operation within this model however. Yield, for example, is a function only of irrigation policy and not fertilization or other input levels. Of course, input prices as they relate to irrigation cost and product prices can be changed. The farm firm is assumed to maximize profits. The institutional setting is assumed invariant. The model is deterministic in nature. Rather detailed soil-water-plant relationships are included in the IRRI subsection of the larger model. A moisture balance equation was used in this model which related inches of moisture in the soil to the ET, the rainfall, and the rooting depth of the crop, as well as the soil's capacity to hold water. The crop water relationship was established through estimates of the impact of different water availabilities on yield.

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0\ o Table 17.--North Carolina Mode1--Continued CHARACTERISTIC Documented computer program Data base References SUMHARY DATA A users manual is provided and the procedure for obtaining the programs is described therein. Also, a listing of the computer programs is provided; the programs are not, however, documented. Much of the data will be available at agricultural experiment stations. The detailed data regarding crop acreages on various soil types is not generally available in most states, however, In fact, detailed soil surveys may also be available only on a limited basis. Sneed and Sowell (1973); Sowell, et al., (1976).

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0\ f-' Table 18.--Pecos Basin Imported Water Model a CHARACTERISTIC Mathematical description Type of output Temporal properties Spatial properties Input data required Technological/production process changes SUMMARY DATA Linear programming with linear constraints. The water demand function for variations in price of water per foot of imports. Import water prices can be varied through parametric procedures to give crop mix, irrigation water imported and local water used, the intensity per acre, the salinity level, and net returns to land and management. This program is concerned primarily with the short run indicating the demand for agricultural water for a year. Arguments are made that the water demand functions which they derive are also fairly representative of the long run. It is a static model. The demand is for a river basin, namely the Pecos basin. Input is required on the profit per acre, where profit is defined as the return to land and management, the price of imported water, and the irrigation intensity. Salinity constraints are needed as well as legal constraints imposed on the use of local water, acreage constraints in terms of the total cultivated acreage, the vegetable constraints, and a cotton constraint. Budget data are needed. They also use four different levels of water intensity and information on price support programs. Annual investment costs for irrigation systems were included. Relationships between imported and local water must also be understood. Technology is assumed invariant and other cultural practices are constant. Emphasis is on water demand with everything else constant. aGisser dnd Hercado (1972) use this same demand model in conjunction with the hydrologic supply model to ShOK how the economic demand and economic supply functions interact.

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0\ N ........ Table l8.--Pecos Basin Imported Water Model--Continued CHARACTERISTIC Behavioral assumptions and institutional setting Stbrchasticldeterministic features Climate/soil/crop factors Documented computer program Data base References SUMMARY DATA The farm firm managers are assumed to profits. Legal constraints are recognized as regards how much water can actually be pumped. Also, farm programs are explicitly placed in the model by ,the assumption that the cotton program would continue indefinitely into the future. Beyond these considerations the institutional setting was assumed constant. This isa deterministic model with no random influences allowed to affect results. These elements are not explicit variables in this model. Hmvever, soil type and irrigation intensity variables were included. Yield water relationships were then established through None available. Crop budgets are ge,neral1yavailable at agricultural experiment stations. Incorporation of salinity and other legalistic constraints requires knowledge 'of the setting. Mos.t of the other data needs would be satisfied from the agricultural experiment station and ,the Crop and Lives tock Reporting Service in the state. Gisser (1970); Gisser and Mercado (1972).

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0\ (..oJ Table 19.--PennsylvaniaModel CHARACTERISTIC description Type of output Temporal properties Spatial properties Input data required SUMMARY DATA This is a simulation model. Yield (Y) as a function of water stress in-dex (WSI), is given in = a b [L(l Irrigation costs are max a function of several features of the irrigation system, such as distance and depth to water source, gallons pumped per minute per acre, labor cost per acre per irrigation, energy cost, field size, and elevation drop over field. Cost equations estimated with regression techniques. Cost equations for each system type. Probability distributions developed for yields of crops. Irrigation water demand for maximum net return production level. Water demand projections are for 7-day, l4-day, "and 28-day periods for the crop year. Demand estimated for 23 sub-basins of the state, but based on per acre models. Quite extensive requirements. Climatic data to calculate PET and AET, crop yield production functions at the field level relatiing yield to water stress, probability distributions relating yield to various probabilities of occurance for each agricultural crop, detailed cost estimates for each type of irrigation system in the area (with costs related to such things as distance and elevation to water source, length and width of field, elevation drop over field, fraction of moisture depleted, depths of soil layer, available moisture content of the soil, and plant spacing), known interest rate, water source development costs, crop type and product prices, yield response information acreages of various crops within each of the regions, soil types within each of the regions an aggregate estimate of different soil types. Only

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0'1. Table 19.--Pennsylvania Model--Continued CHARACTERISTIC Technological/production process changes Behavioral assumption and institutional setting Stochastic/deterministic features Climatic/soil/crop factors Documented computer program SUMMARY DATA those input prices that affect irrigation costs are needed. A total of 13 different crops and three irrigation systems are considered in the analysis. Technology is assumed fixed over the projection interval. Other inputs of production are also not allowed to vary. The model is designed to examine the demand for and the supply of irrigation water, assuming a large number of conditions fixed. The farrnrfirm irrigation manager is assumed to maximize profits. The current institutional setting is taken as a given. The variance of yie.ld and net returns are considered explicitly. The equations are used deterministically within the simulation model. (The discussion is very. limited as regarding these properties of the model and work). The literature in the area of evapotranspiration estimation processes was reviewed within the context of the study which developed this model. A soil moisture simulation model was .developed using a water balance equation. Thus, various climatic variables and soil capability factors were included. The next phase of the study was to develop crop water stress yield relationships. The water stress index is related to the relative evapotranspiration. None available.

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0\ VI Table 19.--Pennsylvania MOdel--Continued CHARACTERISTIC Data base References Sill-fivfARY DATA Detailed research efforts at agricultural experiment stations may provide most of the necessary information. Climatic data is available from the U.S. Weather Service. Kibler. et al., (1977); Kibler, 1980.

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0\ 0\ Table 20.--Texas High Plains Model CHARACTERISTIC !futhematical description Typ.e of output Temporal properties Spatial properties Input data required SUMMARY DATA Linear programming, which applies a linear objective function with linear constraints. Some crop flexibility equations were also estimated relating to what shifts to different crop types might be allowed. The supply of all production inputs is unlimited except for irrigated land and land in total. No constraints on groundwater were included. The model yields estimates of the water demand function under different scenarios as regards prices of products, inputs, period of time (short vs. long run), and irrigated acreage. Both short run and long run capabilities but the model is a static form. Projections are for either one year or for multiple years. The .main emphasis is on art annual basis as opposed to an intraseasonal basis. A multicounty area in the Texas High Plains. Detailed cost budgets are needed for each of the crops. Calculation of crop flexibility restraints requires knowledge of recent cropping patterns in the area. Natural gas, diesel; nitrogen fertilizer, water, and herbicides are purchased within the model; thus prices are needed. Estimates of dry land rent were necessary as well as management returns. Prices received by farmers for corn, cotton, grain sorghum, soybeans, and wheat are input items. Resource restrictions on irrigated land and land must be known. Acreage restraints were put on the model at levels in 1973. Input-output coefficients are needed as regards yield estimates and water uses for different crop activities.

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0\ -...J Table 20.--Texas High Plains Model--Continued CHARACTER Technological/production process changes Behavioral assumptions/the institutional setting Stochastic/deterministic features Climatic/soil/crop factors Documented conputer program Data base References SUMMARY DATA Technology was assumed invariant. Also, other cultural practices were not allowed to vary within the model. The emphasis was on the water variable. Also, only one type of irrigation system was used. The farm firm manager is assumed to maximize profits. The institutional setting is invariant with respect to the water resource portion of the model. However, it ,vas recognized that farm programs might change. Thus, some changes were allowed in federally supported commodities respect to acreages over time. This is a deterministic model with no random influences considered. Climatic factors are included only to the extent that an irrigation water requirement is specified. Yield-water relationships are included to the extent that actual estimates are obtained from experience in the study area. None available. Budgets and crop production information are generally available from agricultural experiment stations. Acreage estimates are available from the Crop and Livestock Reporting Service in each state. Condra et al., (1975); Condra and Lacewell (1975); Lacewell and Condra (1976)

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0\ 00 Table 21.--Utah Model CHARACTERISTIC Mathematical description Type of output Temporal properties Spatial properties Input data required Technological/production process changes Sill1MARY DATA This is a linear programming model. Output predicted water demand functions for each of ten subregions of the State of Utah associated with parametrically changed shadow prices on water. A single year time dimension is assumed. Intraseasonal variations are not allowed. It is a static model. The model is designed to examine the demand in ten major drainage basins in Utah. Data requirements include the potentially irrigable and presently irrigated land. Climatic information was used to adjust acreage data to conform to uniform classes. Rotation requirements had to be specified for crops and restrictions have to be placed on what kinds of crops can be grown in which regions. Cost data for the production activities were necessary. Costs and labor hours as well as yields were specified by county and subregions. Also, irrigation water requirements in irrigation hours were specified by county and regions. Land development and distribution costs were specified by regions and land class. Yields were also specified by land class. The Blaney-Criddle model along with climatic information was used to determine the consumptive irrigation water requirement. Irrigation efficiency estimates were needed. Two water and yield levels were necessary for alfalfa. All of the rest of the crops were inserted with one yield and one water level. Both new and currently irrigated land were considered and acreage estimates were necessary. Past research projects were relied upon greatly for input data. Technology and cultural practices were considered invariant.

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0\ \.0 Table 2l.--Utah Hodel--Continued CHARACTERISTIC Behavioral assumptions and institutional setting Stochastic/deterministic features Climatic/soil/crop factors Documented computer program Data base Reference SUl1HARY DATA The farm-firm manager was assumed to maX1m1ze profits, exemplified at the regional level. Water rights were assumed to exist, which is part of the institutional setting. This precluded the development of new lands until current lands had been irrigated. The model is deterministic in nature. No random variables were considered. The Blaney-Criddle model was utilized to estimate water requirements. Yield-water relationships were invariant in the sense that only one relationship existed, except for one of the crops considered. None available. Most agricultural experiment stations will have data sufficient to develop such a model. Climatic data ,.,ill be available from the U.S. Heather Service. Anderson, H. H., et al., (1973).

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models all have the capability of generating estimates of the irrigation water demand for each of the respective states. Input-output models can also be developed at that level of aggregation. Input data requirements are quite extensive for most of the models. Acreage bounds on the various crops are generally needed. Some require detailed soil information (See North Carolina model, Table 17). The New Mexico, North Carolina, and Pennsylvania models all require knowledge of the production function relating yield to water. The other models assume yield per acre is fixed. Nearly all these models would require considerable expertise in their development and an ongoing data collection process to keep them current. The model requires the least amount of data, followed by the Kansas model. All that is needed for the former is effective heat in thousands of days degree, while the latter model requires dollar value projections for the various sectors and an estimate of the amount of water used per dollar of gross output. Of course, both of these models would be severely limited under changing economic and/or physical conditions, as would the Input-Output models. That is, sudden or rapid changes in the economy or in the natural climatic system would create predictions with a large standard error. Only the Pennsylvania model attempted to deal with stochastic processes. This is a shortcoming of all the models examined in this group. As with the previous categories, major data base sources again include the agricultural experiment stations, weather service, Soil Conservation Service and the Crop and Livestock Reporting Service. Dollar output data could be obtained form U.S. Census sources. Several more aggregate types 70

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of data are generally needed at this level of The Utah model was the most all-encompassing in terms of incorporating both socio-economic and climatic/soil/crop factors. However, yield-water relationships were not included in the model. The North Carolina model on the other hand, had a great deal of detail incorporated into the soil water bal.ance estimating model as did the Pennsylvania model (Tables 17 and 19) River basin-regional-national models The two major models represented here are the national linear programming model developed at Iowa State, called the CARD model, and the Ruttan model (Tables 22 and 23). The latter is an econometric, regression model using county data and estimating the demand for irrigated land at regional levels. Both models give estimates of the irrigation demand for water at larger aggregates. Both models allow some prediction of the effect of the change in agricultural output on the amount of irrigation water used. The CARD model is much more extensive than the Ruttan model and requires considerably more input to its operation. Both water supply and market regions are considered explicitly in the CARD (Table 23). Detailed cost and budget information are developed and necessary for the CARD model. This is also true for the Ruttan model; however, the data are usually taken from agricultural census data on counties. Overall, the CARD model is more appropriate for examining the national demand by regions. As has been argued elsewhere, the Ruttan model has been fraught with difficulties due to statistical problem!:;, which in turn are due to in-adequate data (See Lynne, 1978). Input data requirements are much le.ss for the Ruttan model, however, and are considerably ea:;;ier to generate. As a result the Ruttan model is much less costly to develop and to maintain. Climatic/soil/ 71

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-...J N Table 22.--CARD Model CHARACTERISTIC Mathematical description Type of output Temporal properties Input data required Technical/production process changes Behavioral assumptions and institutional setting SUMMARY bATA A least cost programming model where certain commodity demands are to be met subject to constraints on available resources. Demands for water as associated with economic activity in the agricultural sector, by regions of the U.S. The water demand functions that are provided will vary for the major agricultural crops of the U.S. Water requirements for other crops are simply fixed in the model. The model encompasses the whole U.S. with 223 land regions, 51 water supply regions, and 27 market regions. Cost and budget information are input on a per crop basis and vary across producing regions. Detailed information on crop water use coefficients is needed. Basically, this model utilizes a physical consumptive use requirements approach for estimating water demand. Technology is chosen for a base year, in this particular case, 1964. The model has the capability of being modified to examine different farming The model is developed under the assumption that costs are to be minimized subject to meeting certain demand constraints in terms of the quantity of commodity actually provided. The institutional setting is essentially fixed, although some variation is allowed through such devices as imposing soil loss limitations cim alternative land classes or affecting market prices through market quotas for supply controls. Export market demands can also be modified. Policies regarding land use can also be examined.

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-...J W Table 22.--CARD Model--Continued CHARACTERISTIC Stochastic/deterministic features Climatic/soil/crop factors Documented computer program Data base References SUMMARY DATA The model is deterministic in nature. Crop water requirements were determined using various other models such as the Blaney-Criddle model. Yields do not vary with water levels in the model. General documentation of the program is available. The model will be used through the CARD center at Iowa State. Massive data requirements from state agricultural experiment stations, state agricultural agencies, Crop and Livestock Reporting Services, Soil Conservation Service, U.S. Weather Service, and others. Nicol and Heady (1975); Heady et ale (1976).

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"-J .J:'Table 23.--Ruttan Hodel CHARACTERISTIC Mathematical description SillfMARY DATA Cobb-Douglas function for each region of the U.S.: RXot = RA(X!t)b4 A derived demand function for irrigated land in each region: R X4t (RXo/RA4)Rb4' An identity serving as a perfectly. elastic supply function: RA4t RC4' The national output projection: p y -y X = X [1 + (t l)e] 01 P Y 1 1 The regional output pro-jection: RXot/NXot (R X OlI0ot) [(l+r) (11 (1 + ... (1 +t t;!.r)] where Xo = value of farm products sold ($); X 4 = irrigated land (acres); X6 = current operating expenses ($); A4 = marginal value product of irrigated land ($/acte); C 4 = average annual cost of irrigated land ($/ acre); t = time, 1,..27 (1954-80); P = population (number); Y = per capita income ($/person); A = constant term in the production fuilction;b4 = productivity coefficient for irrigated land; b 6 = productivity coefficient for operating expenses; e = income elasticity of demand for farm products; r = rate of change in regional share of national output in past period; N = national total or a variable measured at the national level; R = regional total or a variable measured at the regional level.

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-...J V1 Table 23.--Ruttan Model--Continued CHARACTERISTIC Type of output Temporal properties Spatial properties Input data required Technological/production process changes Behavioral assumptions and institutional setting SUMMARY DATA The demand function for irrigated land allows estimation of irrigated acreages. It must then be assumed that the quantity of water use per irrigated acre is fixed. The total economic value of the agricultural production is allowed to affect the total irrigated acreage. Also the RA4 is a function of the variable X6 where X6 is the current operating expenses in agricultural operations. The model allows for projection of demand over time, where time is a year. Basically it allows projection at different points in time to be compared; thus it is really a static model. A regional model has been developed for each of the major water resource regions in the U.S. Data on cost of production, irrigated acreage, and other input data are needed to estimate the regression equations. These data can be derived from agricultural census data. Data is at the county level of aggregation. The particular cultural and technological data in existence at the time of the model estimation has to be assumed to prevail throughout the projection interval. Farm firm managers are assumed to act as they did in the historical period in which the data were developed. The institutional setting l5 assumed invariant.

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-....J 0\ Table 23.--Ruttan Hodel--Continued Stochastic/deterministic features Climatic/soil/crop factors Documented computer program Data base Reference The model is essentially deterministic. It is a regression model, however, and stochastic influences be considered. This model does not account for this characteristic explicitly. None available. The U.S. Agricultural Census provides the data base for this model, which becomes available every five years. Ruttan (1965).

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crop factors are not included in the Ruttan model. Some of these elements are incorporated in the CARD model through the fact that several of the potential evapotranspiration-consumptive use formulas (such as the Blaney-Criddle equation) were used to determine water requirements in different regions of the nation. The general features of the CARD model are documented (Nicol and Heady, 1975). Any use of this model would have to be coordinated through the Center for Agricultural and Rural Development (CARD) at Iowa State University in Ames, Iowa. The Ruttan model is documented in the early book (Ruttan, 1965). / 77

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IV. MUNICIPAL WATER DEMAND MODELS The simplest, quickest and least expensive of all municipal water use forecasting methods is the "conventional method." This approach ignores all influences on water use except one -population. Expected population is multiplied by daily per capita use to obtain water use. Water use mayor may not be broken down into the major sectors of residential, commercial, agricultural or industrial use. A number of more refined forecasting methods have been proposed (Albertson, 1979). The ideal forecasting procedure should draw upon past and present trends, as well as consider the demand for each water using sector in the area (Mitchell and Leighton, 1977). It should incorporate variables reflecting various factors (demographic, social, economic, and environmental) affecting water demand, utilizing state-of-the-art in modeling and be in terms readily understandable to the model builder (Reid, 1971) Problems are likely to involve serially dependent errors, (correlation among successive observations in a time series), multicollinear explanatory variables and difficulties inherent in the presence of explanatory variables that must themselves be predicted (Domokos, Weber, and Duckstein, 1976). Before implementing a particular model, preliminary research is necessary to determine which variables should be included and how they should be measured and introduced (Clouser and Miller, 1979). While it may be relatively easy to identify the variables to include in forecasts, 78

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operating constraints frequently exclude their systematic consideration. Also, measurement problems may preclude the incorporation of other variables into forecasts (Mitchell and Leighton, 1977). Consideration must then be given to data availability and manpower needs. Many variables are used to explain variation in household water consumption. Household demand is a function of price, consumer wealth, prices of other goods, and consumer tastes and preferences. The following variables were used in various studies to measure their effects (Cassuto and Ryan, 1979). Socioeconomic Variables Income Income was used as a variable in several of the models. It is normally expected to have a positive effect on the amount of water consumed. Price of Water In a number of studies, the quantity of water demanded has been found to be significantly affected by the price of water. According to economic theory, the higher the price of the commodity, the lower the demand. This is especially true where price changes are significant and well publicized. The sensitivity of water use to changes in the real price of water is known as the price elasticity of demand (Hanke, 1978). Lawn sprinkling in the western u.S. has been reported with an elasticity as high as -.70 (Howe and Linaweaver, 1967). Much more research is needed, however, to assess the effects of price on water demand for various geographical locations, incomes of households, and other variables (Flack, 1980). Two different prices are used in existing models, average prices and marginal prices. The marginal price, while theoretically the correct one 79

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to use, is very difficult to estimate. Thus, most of the models use average price as the measure of the scarcity value of water. Property Value Assessed valuation is one of the more readily available parameters. It is used in several of the models as a measure of income. As with income, property value is assumed to be directly proportional to the amount of water used in the household. Consumers in higher valued areas are more likely to have more water using appliances and larger lawn areas. Cultural Fa,ctors Race or country of origin are cultural factors that may affect water use. Education could also be considered a cultural factor. High level water lise was found for college postgraduates and low level for high school graduates (Csallany and Neill, 1972). Few of the models reviewed, however, included cultural factors as a water use parameter. This may be attributed to difficulty in obt-aining data. Two models (Darr, Feldman, and Kamen, 1975) and Camp, 1978) which did include cultural factors were based on household by household surveys. Cultural were found to be especially significant in determining the importance of maintaining lawns and shrubbery. Water Consumption Behavior Water consumption behavior includes consumer hab.its such as water conservation practices and reactions to uncertainty of supply. Fe\V models were found to incorporate this parameter. Climatic Variables Precipitation Water use was found in studies to be inversely proportional to the amount of precipitation. During months of low precipitation, lawns 80

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and gardens require more watering. Excellent information is available on the expected use of water by vegetation based on numerous studies in agricultural areas. Evaporation Where evaporation is found as a water use variable, it is used to measure outdoor consumptive use from free water surfaces or as a proxy for transpiration by plants (see the previous chapter for more information regarding evapotranspiration). Temperature The use of water throughout the year is subject to fluctuations in temperature. The amount of water for personal hygiene (baths, showers) could decrease during the winter months because people are constrained to less physical activity and more indoor recreation. This is especially true for regions with colder winters. Other Independent Variables Population Studies indicate that a strong relationship exists between population and water consumption. Population was used as an explanatory variable in nearly every forecasting method examined. When the study focuses on the microunit of a household, population is replaced by family size. Family size is expected to have a positive effect on household water consumption (Clouser and Miller, 1979). 81

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Technology Although new technology continues to be developed, few demand studigs incorporate it in household estimation techniques. Appliances or household activities that require water include machines, dishwashers, lawn sprinklers or garden watering, and swimming or vliHUng pools. All are anticipated to have a positive effect on the amount of water used in the household. It is also possible for technology to decrease the household demand for water. Several technological innovations of this sort have been developed. One example is flow restrictors which may be used on faucets or in showers to retard wate.r flow. Technology may be geographic specific and therefore not .a useful explanatory variable in all locations. Irrigated Area Irrigated area for the household includes lawn and garden areas (all outside use). Well developed procedures with a national data base for estimating water use by vegetation. However the efficiency of applica ... tion of the water varies widely. Land Use Land use data are available for most communities. Unfortunately, no standardized system of def;ining land use exists. Thu.s, "low density residential" may have different meanings. This lack of standardization makes it much more difficult to do cross sectional studies of water use. Number of Dwelling Units An alternative but related of urban activities is to estimate dwelling units rather than houses. The advantage of using dwelling units is that it incorporates directly the effect of multi-family housing. 82

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Lot Size Water use is expected to be directly proportional to lot size. A large lot size generally means a larger lawn area (more water needed for irrigation) and higher property values which were found to have g positive effect on demand. Summary Above are just a few of the many factors that may affect water use. Those variables listed (with the exception of land use) were found to be significant in more than one of the models reviewed. It is important to note, however, that particular explanatory variables proven highly significant within the confines of one study might be proven otherwise under different conditions. Other factors of the water use models include outputs, spatial properties, temporal properties, statistical properties, and validation. Most of the residential water use models reviewed projected monthly or annual water use in gallons per day. The scale varied from household to regional. Models developed at the household level include those based on studies of individual households. City and regional level models were based on areal averages. All of them were found to reflect long run behavior and were static in nature. None of the variables change for a given time period. It is assumed that consumers have had time to completely adjust to the parameters they face. Because none of the models reviewed were found to contain a random element, they were judged to be deterministic as opposed to stochastic. Deterministic models predict what will happen as the result of a given action (or actions). The water use models project increases or decreases in water use as the result of increases (or decreases) in 83

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population, price, income, etc. The final feature of the water use models is validation. Few of the models reviewed were found to have a documented case of validation. Table 24 summarizes the models which have been found in the literature for estimating municipal water use. The models are grouped according to the level of aggregation being used in the study: household (5 models), city (11 models), and regional (2 models). Without exception the models are very simple from an analytical point of view. The only theoretical question that has arisen is how to properly incorporate price effects (Morgan, 1980). No systematic national data bank of water use patterns has been available over the years. The early Johns Hopkins studies during the 1960s appear to be the most ambitious effort to date along these lines. Detailed summaries of the models are presented in Tables 25 to 42. The Sonnen-Evenson model is by far the best documented of the available models. Thus, it was an obvious choice for our test application to be presented in the next chapter. 84

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Tab h' 24. Municipal Demand Mod"l" Spatial Properties Temporal Socioeconomic Val' 1"[,1,,,; CH"Ii' t ic Variables Other 111d" pend,' n t Variable" and HoLiDl Name and/or Originator ., "" ... "" 0 "" ., > .. u ., ... >, IH <1l .. ;> 0 co .... >, .-. 0'<: ., u .. 0 .-l M U 0 ... .. ., u II> ] "" ... 0 .. .... 'fil en N U ... ... .. '" "" ........ .. III 0 :.,.:-( .... ""' fl ., .. '" '" :I t ... .<: d o ... .. .... "" "' .... '" ... 0 .. co.;) ., u U P.. Co .c "" '" '0 .0 .. i .. c: u ..... ., 0 .... U '" 0 0 OJ m '" .. c: ... ,., ... .. ... .. ;j .. tU .. i '"' OJ .. .... 0 '" .. '"' '" :l ., 0 tI'> "" "';': ::;. ... III Cl '" '" "'" ... '" H H< ,.J :;:; .., HOUSr:IIOLD LEVEL Clouser 6. Miller ( 1979) x x x x x x Danielson (1979) x x x x x x x DarrJl Feldman Peretz (1975) x x. x x Morgan (1973) x x x X Camp (1978) x x x x x x x x x x CITY LEVEL Municipal UI' .. :nnand Model for the Conterminous U.S. (Burke, 1970) x x x x x x x Conventional Water Use Model (Holtz & Scott, 1976) x x x Mitchell 6. Leighton ( 1977) v ::.{ x x x x x Trevor 6. Cross (1979) x x x x MAIN I & II (Albertson, 1971) x x Cassuto 6. Ryan (1979) x x x x x x x x Supply-Demand }funagemen t Model (Hanke, 1978) x x x Multistructured Demand (Reicl, 1971) x x x x X Turn,,," sky (1969) x x x x Young (1573) x x x x Johns HopUns Model (HmifC', & Lin .. lweavcr (l 7) x x x x X x RECIONAf. Ytlmauchl & Huang (1971) x Knnoelie ,1)' W .. ler Dem;t:1(\ 1 (;:\('IIltlen & Evenson (1979) x x :< x X X X X 85

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(Xl 0'\ Table 25. --Camp CHARACTERISTIC Mathematical Description Type of Output Temporal Properties Spatial Properties Input Data Required SUMMARY DATA = a + blxl + b2x2 + .... + b13x13 where quantity of water demanded (gal/household), a = constant, Xl X = x2 = 3 X -4 X -5 x6 x7 x -8 x 9 x10-XII: x12-number of occupants of household, age of head of household, market value of residence, irrigable lawn area of residence, number of bathrooms/residence, number of clothes washers/residence, number of dishwashers/residence, existence of a swimming pool at residence, race, average maximum temperature for the area, annual precipitation in the area, price of water in each city at the mean level of consumption for all domestic users included in the study, and Xl = education index. b l 3to bl3 = regression coefficients. Residential water consumption is estimated using linear regression considering socioeconomic and climatic factors. The model predicts water use for any time period although yearly projections are usually made. Water use is projected at the household level. All data are collected for the household with the exception of price, precipitation and maximum temperature. Data required for the household are: number of occupants, age and race of the head of household, property value, irrigable lawn area, numberc. oi. bathrooms, .numbeli: ... of clothes washers, number of dishwashers, existence of liI.:swimming pooilimand education index; for the city: temperature, precipitationcand. pj-ice-:'ofwater:;.

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00 Table 25. --Camp, Continued CHARACTERISTIC SUMMARY DATA Documented Computer Program Data Base Reference None The model is based on a household, from information obtained by a household (single family) survey of water use by 288 consumers in ten cities in northern Mississippi. Climatological data were obtained from meteorological records of the Department of Commerce. Rate structures and monthly water use were obtained from water utility officials and records. City studies were selected on the basis of similarity in water pricing and allocation policies and because there was a diverse cross section of water prices in the group. Population ranged from 5000 to 20,000. Camp (1978)

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Table 26. --Clouser and Miller CHARACTERISTIC Mathematical Description 00 00 Type of Output Temporal Properties Spatial Properties Input Data Required Documented Computer Program SUMMARY DATA Period I (Winter-Jan., Feb., Mar., and Dec.): In QWD = a + W + DW -K -+Blln FS + B 2ln NB +-B3 In Y Period 2 (April, May, June and July): In QWD = a + W + DW + SP + WL -K + Blln FS +B2 1n NB +B3ln Y Period 3 (Aug., Sept. Oct., and Nov.)! QWD W DW SP WL K Y FS NB B I a Identical to model for the second period excluding SP, where :: total water used by household during period (gal/day), = washing machine, Q = no, 1 = yes, = dishwasher, 0 = no, I = yes, = swimming pool if is filled, 0 = no, I = yes, = if lawn is watered, 0 = no, 1 = yes', = household knowledge of water saving devices, = total net income of household during period, = family size, and, no. of bathrooms. B 2 B3 = regression coefficients = constant The model estimates household water use based primarily upon household data. Seasonality of householdwater use is incorporated into the estimation. The study focuses on the micro-unit of a household. Population is replaced by family size. Data must be collected on family size, household facilities (showers, toilets, tubs) and appliances (washing machines, dishwashers, pools and lawn sprinklers), household knowlege of water saving devices. ami. income. None

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00 \.0 Table 26. --Clouser and Miller, Continued CHARACTERISTIC Data Base References SUMMARY DATA Data were obtained from a questionnaire mailed to two communities located in central Indiana, both in rural areas within a 30 minute drive of a larger urban area. The majority of households were classified as middle income ($12,000-$15,000). One third of all households were widowed individuals or elderly couples. Clouser and Miller (1979, 1980)

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o Table 27. --Danielson CHARACTERISTIC Mathematical Description Type of Output Temporal Properties Spatial Properties Input Data Required Documented Computer Program Data Base Reference SUMMARY DATA Qt f(X1 X2 X 3 X4 X s)' where Qt = water consumption (1000 gal/household) during period t, Xl = average daily. rainfall during period t, X 2 = average air temp/period, X3 appraised house and lot value of residental customer, X 4 = real water price (cents/lOOO gal), and Xs = household size. The model predicts water consumption during period t at the microlevel. Projections are made for any time period. The model predicts water use at the household level. It estimates how specific households respond rather than how individuals in different areas respond to spatial differences in the parameters. Data needed are price of water, rainfall, temperature, property value and household size. None This model was developed using monthly cross section and time series data from 261 residential households in Raleigh, North Carolina. Danielson (1979)

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\,C) ..... Table 28. --Darr, Feldman and Kamen CHARACTERISTIC Mathematical Description Type of Output Temporal Properties Spatial Properties Input Required Documented Computer Program SUMMARY DATA Qd f(I N, N A, C, E, S) cpr Q = f(I N N A, C, E, S) a cpr Q = f(I N N A, C, E, S) s cpr (log linear forms used), where. Qd = quantity of water not including water for gardening (m3/yr per capita per d.u.): Qa = quantity of water including water for gardening (m3/yr per capita per d.u.), Q = quantity of water for gardening only (m3/yr per capita per d.u.), s I = monthly income per capita per d.u. (gross, in Israeli pounds), c N = number of persons per dwelling unit, p N = number of rooms per dwelling unit, r A = age of head of household (or spouse), C = cultural factor determining water use preferences, country of origin, S = urban area or municipality in which dwelling unit is located, and E = education of head of household (or spouse). The model forecasts water consumption per dwelling unit using socioeconomic and demographic factors. Yearly predictions are made. The study describes variables from disaggregated data. Projections are made at the household level. Required data are household size, income per capita, urban area, country of origin, education of the head of household, and the type of metering. None

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\0 N Table 28. --Darr, Feldman and Kamen, Continued CHARACTERISTIC Data Base Reference SUMMARY DATA The model is based on a questionnaire survey of 1892 households (both metered and non-metered) in four urban areas of Israel conducted from Oct. to Dec. 1971. Water use data (for gardening as well as within house consumption) were obtained for the fiscal year. The sample is representative of urban metropolitan areas of Israel. An additional set of data (for time series analysis) was combined with the above cross sectional data; it consisted of 14 points from 1954-1968 for the municipality of Jerusalem. Darr et al.(1975)

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\0 W Table 29. --Morgan, D.W CHARACTERISTIC Mathematical Description Type of Output Temporal Properties Spatial Properties Input Data Required Documented Computer Program Data Base References qd = f(v, d p); SUMMARY DATA dqd dV dqd > 0, and > 0, p where qd = yearly water usage, hundreds of cubic feet, v = assessed value of the property, in $1000, and d p = number of people/dwelling unit. The model forecasts water use for individual households. The model predicts yearly water usage. Results are reported on a seasonal basis. This model was tested using detailed micro data on the use of water in individual dwelling units. Input information includes assessed property value and number of people per dwelling unit. None This model is based on 92 observations from single family residences of Santa Barbara County, California (metered and public sewer). Water usage data (qd) was provided by the local water district for 1971 and assessed value (v) was obtained from county records. Coefficients were derived for Nov. Dec. and Jan Feb periods separately and combined. In semiarid areas such as S. California, inclusion of winter month water usage does not initially capture pure domestic demand because intermittent rainfall (and therefore sprinkling) continues even during winter months; as a result, qd contains some amount of sprinkling usage. Morgan (1974, 1979, 1980)

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Table 30. --Cassuto and Ryan CHARACTERISTIC Mathematical Description .\C SUMMARY DATA. Q /N .. ::; f[(C .. ), W., E., H., L., T.k (P. or G.), I., D., M., R.k 0.1' (Z .. )] 1.J 1.J 1.J J 1. 1. 1. J J J J J J J J 1.J where the subscript: i= j == k = 1 = each of 246 census tracts entirely within the District's service area. each of 72 months between January 1970 and December 1975, a binary variable indicating whether a particular census tract is east or west of the hills, a seasonal subscript representing the month of consumptian. December is used as the basemanth, so it varies fram 1 to. 11. and where the variables in the model are: Q = N ::; H = C = W= E = L = T ::; G = P = I = D = M = R = o = z == monthly water usage by active separately metered single family residential account within each census tract, number of single family accounts per census tract, average number of persons per household, real mean family incame (in $100), weekend days per month, weighted average elevation of the census tract, land per housing unit, temperature (if less than 65 I value is zero; if greater than 65, value is T -65), lagged price of Water in first block, actual price of water in first block, time trend variable, time trend variable, days per month, precipitation, binary month,and the residual. Both linear and logarithmic functional foI'1!1S were fit to.Lt/he data using least squares regression.

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\0 U1 Table 30. --Cassuto and Ryan, Continued CHARACTERISTIC Type of Output Temporal Properties Spatial Properties Input Data Required Documentep Computer Program Data Base Reference SUMMARY DATA Average residential water consumption is estimated. This model can also be used to forecast the residential elasticity of demand for water within a district. The model predicts water use on a monthly basis. Water use is predicted for a census tract and then disaggregated to the microlevel. Data required includes number of single family accounts, average number of persons per household, real mean family income, weekend days per month, land per housing unit, temperature, price of water, days per month and precipitation. None This model combines cross sectional and time series data for a single agency (East Bay Municipal Utility District) servicing a population of 1,029,000 in the 304 square mile area of urban Oakland, CA. Geographic, sociologic, and personal economic measures comprising most of the cross sectional data were taken from the 1970 census and other stationary measures across census tracts. Time series data were gathered for each census tract within the District's boundaries for each month from Jan. 1970 through Dec. 1975. Cassuto and Ryan (1979)

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10 0\ Table 31. --Conventional Water Use Model CHARACTERISTIC Mathematical Description Type of Output Temporal P:toperties Spatial Properties Input Data Required Documented Compute:t Program Data Base Reference SUMMARY DATA Qf = GPCD x P where p Qf = future water requirements, gal/day, GPCD = average per capita consumption, gal/day, and P = projected population. p Future water requirements in gallons per day irrespective of all socioeconomic and climatic factors. Predicts water use for a future year. Estimates are made for a city. Population projections must be determined and per capita use (GPCD) known for the city. None This model was used extensively prior to the 1960's in various cities including New York, Chicago, Philadelphia, Detroit, Baltimore, Houston, Washington, D.C., St. LoUiS, St. Paul and Minneapolis. The model is still used by smaller municipalities. Holtz and Scott (1976)

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\0 ...... Table 32. --Integrated Supply/Demand Management Model CHARACTERISTIC Mathematical Description Type of Input Temporal Properties Spatial Properties Input Data Required Documented Computer Program Data Base References Q1 Q1 P a b SUMMARY DATA b = a P where quantity of water demanded, price of water per kiloliter, constant, and = price elasticity coefficient, which equals dP/P' Variables such as population, standard of living and land use patterns can be accommodated in one equation: Q r Q1' where Q water demand in year 2, r = growth rate in the base demand from year 1 to 2, and Q1 quantity of water demanded. (This equation represents the growth in demand when the real price is held constant from year 1 to 2) The model predicts residential in-house and outdoor use. The model is essentially a long run model. Projections are for a year. Water use estimates are made for a city. Initial water demand (demand projected for the start of the model), initial price, projected base growth rate (the rate, r, that indicates the growth or decline in water use when real prices are held constant), the marginal cost curve, and price elasticities must be known. None Residential in-house and outdoor use were estimated using time series data (1955 -1968) for Boulder, Colorado. Hanke (1978, 1979)

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\0 00 Table 33. --Johns Hopkins Model CHARACTERISTIC Mathematical Description Type of Ouput Properties Spatial Properties Input Data Documented Computer Program Data Base Reference Q g Q c a L -s E pot P eff V SUMMARY DATA Qd + .6 caL (E spot P ) eff Qd = 157 + 3.46V a = expected average demand for any period, gal/day, where = expected average domestic (household) use, gal/day, = coefficient to adjust for difference between actual and potential evapo-transpiration from lawns, 4 = constant to adjust for units, 2.72 x 10 gal/acre-in of water, = number of dwelling units (d.u.), average irrigable area, acres/d.u., = estimated average potential evapotranspiration for the period of demand in question, inches/day, = amount of natural precipitation effective in satisfying evapotranspiration for the period, inches/day, and = average market value per dwelling unit, in $1000. The model. predicts average demand for any period in gallons per day irrespective of prices. The model provides no information on the relative frequency or duration of extreme demands. The model predicts water use for any period, generally a year. It is a static model in that parameters are averaged over the period in question. All of the data (excluding ET and precipitation) are collected at the household level and then aggregated to derive predictions for residential areas. Data are needed on evapotranspiration, precipitation, irrigable area, number of dwelling units, market valuation and whether consumers have metered or flatrate service. None originally. Programs called MAIN I and II were written later. Relationships were based on a study of 41 homogeneous metered and flat-rate areas) ranging in size from 44 to liO dwelldng, undits>,lin:l:,,,'C{i1:" various climatic regions in the U.S. Howe and Linaweaver (1967)

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Table 34. --Main I and II CHARACTERISTIC Mathematical Description Type of Output Temporal Properties Spatial Properties Input Data Required Documented Computer Program Data Base Reference SUMMARY DATA These mathematical models were drawn from the work of Howe and Linaweaver (1967) and computerized. Average daily water use is estimated for various user categories. Mean annual water use in gallons per day is predicted. Water requirements are forecast by disaggregating water users into some 150 user categories. These estimates are then reaggregated and total municipal water requirements produced. The data needed to perform predictions include the values of the water use parameters contained in the models. (See Howe & Linaweaver, 1967). The program is available as Main II. Also, the EPA SWMM Model contains the program (Metcalf and Eddy, et al., 1971). The Main II system has been used to prepare forecasts for Baltimore, Maryland, and seven metropolitan areas in Louisana. It is presently being employed to estimate future municipal water needs in Arkansas. Tennessee, and several other lower Mississippi states as part of a Corps of Engineers framework study. Albertson (1979)

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I-' o o Table 35. --Mitchell & Leighton CHARACTERISTIC SUMMARY DATA Mathematical Description Type of Output Temporal Properties Spatial Properties Input Data Required Documentated Computer Program Data Base Reference Q = f(xl x 2 x 3 x 4 xs x 6 x 7), where Q Xl x2 water requirement, = housing density, household size, x3 x4 Xs X = 6 X -7 lot size, climate, number and type of water using appliances, water consumption behavior, and fire flow requirements. The model forecasts urban water use. The procedure does not explicitly incorporate the impact of changing technology or social taste upon water use patterns. The estimate is usually made on a year-to-year basis. Water requirements are forecast for smaller municipalities. Data needed includes number of dwelling units, number of different housing types, (single family, multiple family, etc.), lot size, population size, water requirements for lawns, precipitation, number of water using appliances and fixtures, and fire flow requirements. None This model is based on 1974 cross sectional data for a proposed subdivision & two existing subdivisions (for which metered records are available) in Barrie, Ontario. Lot sizes were determined from zoning by-laws. Actual water requirements for lawns were assumed to be 1.5" per week based upon information published by the Ministry of Agriculture and Food (1963). A reduction of .6" was made to account for natural rainfall (32"/yr in Barrie). The number of water using appliances an.d fixtures was estimated on the basis of-data obtained from Information Canada. Other data sources were interviews with realtors and contracrtors, as well as field observations. Water demand for fire flow was calculated based upon insurance guidelines. Mitchell and Leighton (1977)

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f-' o f-' Table 36. --Multistructured Demand Model CHARACTERISTIC Mathematical Description Type of Output Temporal Properties Spatial Properties Input Data Required Documented Computer Program Data Base Reference SUMMARY DATA WDt = (POPt) (uuo ) (ppctt ) x (lnc.t ) y ppct Inc s s WDt = water demand at time t, gallons, uu = units of use, gpcd, o ... ppct= prec1p1tat10n, Inc = income, Pop = population, and t = future, s = present. (POPt) z Pop s where The model projects municipal sector requirements under various "life styles" goals for either possible or probable worlds. Long range objectives are considered. National values are disaggregated to a region; then regional values are distributed to the urban cluster. Data must be collected on population, urbanization, settlement criteria, income, precipitation and unit use. None The.model was applied to Tulsa, Oklahoma in 1970. Population and income projectior were developed for the city by regression techniques using a national data base. Reid (1971)

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I-' o N Table 37. --Municipal Model for the Conterminous U.S. CHARACTERISTIC Mathematical Description Type of Output Temporal Properties Spatial Properties Input Data Required SUMMARY DATA log Y = log A + a log xl + b log x 2 + .+ p log x 16 xl population served (millions), x 2 = value added by manufacturer, x3 = land area (square miles), x 4 population/square mile, Xs = aggregated income, x6 = number of families, x 7 precipitation (inches/year), Xs = median family income ($), x9 family income under $3000 (%), x lO = family income over $10,000 (%), xII = housing units, xl2 owner occupied housing units (%), xl3 = median value of housing units ($), x 14 manufacturers -all employees (annual average), xIS = manufacturers -production workers (annual average), x 16 number of retail establishments, and Y = water pumpage (gallons/year). A constant a p = regression coefficients where, The model provides estimate of water requirements. No consideration is given in the analysis to the effects of price on the quantity of water that is demanded. Projected water requirements are on a year-by-year basis. Model predicts water use only for communities in the conterminous United States with a population of 25,000 and over. Data needed depend upon the pseudo state in which the community is located; possible factors are population, value added by manufacture, landarea,income, precipitation, number of housing units, and per cent owner occup.ied, property value, number of retail establishments, and manufacturers.

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..... o w Table 37. --Municipal Model for the Conterminous U.S., Continued CHARACTERISTIC Documented Computer Program Data Base Reference SUMMARY DATA None Data were derived from two published sources; Public Health Service/Federal Water Pollution Control Administration's Inventory of Municipal Water Facilities (1963) and the U.S. Department of Commerce's County and City Data Book (1963). The model was formulated using cross sectional data from 488 cities in the conterminous U.S. Selected cities from this total were disaggregated and grouped into 19 distinct geographic regions or "pseudo states". Burke (1970)

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I I-' o Table 38. --Trevor & Gross CHARACTERISTIC Mathematical Description Type of Output Temporal Properties Spatial Properties Input Data Required Documented Computer Program Data Base Reference D /c = avg D /p = avg D /c = Davg/p = avg SUMMARY DATA 4.60 5.40 In (P) + 2.39 (1) 3.91 -29.32 In (P) +24.64 (I), where average demand (1000 gal/connection/mth), average monthly demand (gallons/capita/day), P = retail costs of water ($/1000 gal.), and I outdoor use index which characterizes the system in terms of the portion of irrigation demand provided by the domestic system. The model predicts average water demand for domestic water systems in gallons per person (or connection) per day. Monthly water demand can be forecast reflecting long run behavior. Demand functions were developed for several municipal water systems. Input data needed are average price per thousand gallons for the water syste!U and degree to which separate irrigation systems are used to supplement the domestic water system. None Data used were either obtained from .water utility managers or actually measured by the study team. The 14 system sample (all Utah systems except for two Celorado systems included to. provide data peints in the high price range) varied in size from very small low density rural systems to. Salt Lake City's water system and were included from all types of Utah climates and cultural settings. Sampleselected covered a large variatien in water price; all systems were completely metered. Trever and Gress (1979)

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I-' o Ln Table 39. --Turnovsky CHARACTERISTIC Mathematical Description Type of Output Temporal Properties Spatial Properties Input Data Required Documented Computer Program Data Base Reference SUMMARY DATA 2 where X. = A + Ala. + A 2P. + A 3h. + A 4P., 1 0 1 1 1 1 X. planned per capita consumption in town i, gal/day, 1 0 2 fl 2 = var1ance 0 supp y 1n town 1, (gal/day) 1 P. 1 average price of water in town i given by metered revenue divided by metered gallons used, e/lOOO gal, h. = index of per capita housing space given by average number of rooms per dwelling 1 unit in town i/median number of occupants per dwelling unit in town i. and p. = percentage of population under 18 in town i. A1 constant Al -A4 = regression coefficients. The model predicts per capita water consumption in gallons per day for town i. Cross sectional estimates indicate long-run behavior. Few data describing individual behavior are available so that aggregation to the municipal level is inevitable. Price, variance, percentage of population under 18 and the per capita volume of housing are needed as input data. None available Estimation of the demand equations involved a combination of cross section and time series analysis. The basic regressions were run on cross-sectional data from nineteen Massachusettes towns for the years 1962 and 1965. These three years were selected to determine whether consumers' responses to the parameters altered as a result of the drought that occurred2during the intervening years. Time series were used in deriving estimates of O. (variance) for each town over the periods 1950-1962 and 1950-1965. 1 Turnovsky (1969)

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...... o 0'1 Table 40. --Young CHARACTERISTIC Mathematical Description Type of Output Temporal Properties Spatial Properties Required Documented Computer Program Data Base Reference SUMMARY DATA Q = f(Xl X 2), both arithmetic and logarithmic equations, Q = water pumped per active service per year (1000 gaL), Xl = rainfall, inches, and X2 = average price, $/1000 gal. The model predicts demand for municipal water supplies during a specific time period. The model provides long run consumption forecasts. One year time periods are usually considered. Estimates are made per active service. Data are collected at the municipal level and then disaggregated Data subjected to statistical analysis 'are rainfall and average charge per 1000 gallons (derived by dividing total billings for each period by the quantity of water, in thousands of gallons, produced in the None Time series data included annual observations of consumption, price and other factors in Tucson, Arizona. Summary information on water production, charges and the number of active services (individual customer accounts) for each month from 1946 to 1971 were from records made available by the City of Tucson Water Utility. Water fees were based on metered records of consumption by each customer. -Average charge/lOOO gal was derived by dividing total billings for each period,by the quantity of water (1000 gal) produced in that period. Average charge was then deflated using the consumer price index (100 for 1968). Measurements of rainfall, temperature and evaporation were obtained from U.S Weather Bureau," publications. Young (1973)

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t-' o --.J Table 41. --Kanoehe Bay Water Demand Model CHARACTERISTIC Mathematical Description Type of Output Temporal Properties Spatial Properties Q SUMMARY DATA [UI WR UF (l-CI) + 27,152.4 (UO-G) A EA (I-CO)] PR + OP + E(PR-OP) PR + OP E(PR-OP) (l-SL) where, Q gal/month, UI units of usage in each land use (homes, people, 1000's of square feet, hotel rooms or acres), WR = seasonality factor for indoor usage (gal. this month/gal. average month), UF = the average usage rate for each land use category (gallons per day per dwelling unit, per hotel room, or per 1000 square feet of floor space), CI = anticipated average indoor conservation fraction that can be foreseen for each future projection period (year) as compared with the historical period, UO water requirement for crops, grasses, or other outdoor uses of water (in/month), G = effective precipitation (in/month), A = gross area occupied by each land use (acres), EA ratio of irrigable acres to gross acres in each land use, CO = outdoor conservation percentage in future years, PR current price for water, OP an older price, in a previous year in the simulated prediction period, E = elasticity of demand with respect to price for each land use, and SL fraction of total water demanded that is supplied locally. This model predicts the demand for water for any land use in any subarea of any study area in any month of the year. The model projects annual water demands for a future year(s). The model is applicable to specific regions. The entire area is then subdivided into two levels of geographic detail.

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...... o 00 Table 41. --Kanoehe Bay Water Demand Model, Continued CHARACTERISTIC Input Data Required Documented Computer Program Data Base References SUMMARY DATA Required data includes historical unit usage rates for water among various users, precipitation, acreages of each land uSe (gross and irrigated), price of water, elasticity of demand with respect to price, percentage of water demanded that is locally supplied, and the degree to which water conservation can be expected increase or decrease. Yes This model was developed and tested for use on the island of Oahu, Hawaii. Values of UO for each land use must be given as data. It is suggested that the Lowry Johnson expression be consulted to determine the annual consumption use requirement and the Blaney-Criddle method be used to determine monthly distribution of consumption use. Land use data were obtained from historical records in the Honolulu County Planning Dept. Input years were 1964, 1966, 1968, 1970, 1972, and 1974. Sonnen, (1977) and Sonnen and Evenson (1979)

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I-' o \0 Table 42. --Yamauchi and Huang CHARACTERISTIC Mathematical Description Type of Output Temporal Properties Spatial Properties Input Data Required Documented Computer Program Data Base Reference SUMMARY DATA m Q = T + C + S + I ,or t t t t t m Q = T C S I t t t t t where = average daily consumption in month m and time interval t (10,000 gal/day), T t = .trend component, C t cyclical component, St = seasonal component, and It = irregularities. Average daily water consumption is forecast for a particular month within some time interval. Both models are potentially useful for long-run forecasting and capital investment purposes. Models are based on studies of water consumption patterns and trends in the Honolulu Board of Water Supply Service Area. In order to statistically analyze the data, these models require further specification in operational terms. None Stepwise regression method was applied to 187 data points (Jan. 1960-Jan 1975) each representing average daily water consumption within the service area of the Honolulu Board of Water Supply. Yamauchi and Huang (1977)

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v. DESCRIPTION OF WRE/SCS DEMAND MODEL This chapter describes an adaptation of a computer program to predict monthly water dettand. The original program to estimate domestic water use was developed by Water Resource Engineers, Inc. (WRE) for the Pacific Ocean Division of the U.S. Army Corps of Engineers (Sonnen & Evenson, 1979). ever, for our purposes, a more general model was needed. Fortunately, the WRE domestic water Use model can be adapted to estimating industrial and/or agricultural water use by making some relatively minor changes as summarized below. 1) The w.R.E model used two levels of geographic detail: "water districts" and "census tracts." These were changed to "study areas" and "subareas," respectively_ 2) The predictive equation was modified in two ways. First, the use of the phrase "conservation factor" was replaced by "calibration factor" to better indicate the purpose of this coefficient, since whether water conser" vat ion is being practiced or not depends on local circumstances. Second, the procedure for estimating price elasticity was mOdified based on discussion in the literature regarding this model (Sonnen and Evenson, 1979; Morgan, 1980). The primary value. of the computer program lies in its convenient input and output formats. Future refinements can be made by adding subroutines as needed. The subsequent sections describe the revised model and show how it was used to estimate monthly water use for a test case. the format of the write-up follows that of the primary reference by Sonnen (1977). 110

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General Description The program is set up to estimate monthly water use for land uses within subareas within study areas. Water use for a given land use in a subarea is the sum of two components: indoor use and outdoor use. For domestic users, indoor use is related to household activities whereas outdoor use is primarily for lawn watering. Industrial use is comprised of in-plant process water plus outdoor use by, say, cooling ponds. Agricultural water use would be predominantly outdoor use for managing crop growth. The areal breakdown and the maximum sizes of the planning units are shown in Figure 2. Program Structure and Function The Water Demand Model consists of the seven subroutines shown in Figure 3. The program listing is included as part of the Appendix. Each subroutine is described below: 1) Main Program -DEMAND -Statements 1-88. This program does the actual water use calculations. 2) Linking Routine -FIND -Statements 89-111. This program checks land uses with the master list. 3) Input Data Routine INPUT -Statements 112-735. This program reads the time invariant and temporally varying data for each study area. 4) Sorting Routine QSORT -Statements 736-758. This program ranks land uses and assigns classification numbers. 5) Reporting Routine RPTSET -Statements 759-1071. This program takes the output from DEMAND and prints summary reports. 6) Outdoor Water Use Routine -BLANEY -Statements 1072-1348. This subroutine computes irrigation requirements as described in SCS Technical Report 21. 111

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Study Area 1 Sub Area 1 1=fJ Use 1 ,,' .. 0 ... /," I Sub Area j Land Use k Figure 2. Schematic of Land Use Breakdow.n 112 "'. r I .' ( Study Area 10 Sub Area 35 Land Use 40

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..... ..... w Input fl fl ,-(uVl:\,.1, I I Rank Land l.1se r INPUT Inputl Read Run Data Read Invariant Data Input2 Read Tic:,e-V:=.rying Data by Study Area l Linking Routine FIND Check Land rses with Master List Main Program r-----I DEMAND I I ,I I I I I I Start Simulation Call INPUTI Call RPTSET Call INPUT2 Call REPTl Compute Total Monthly Demands Compute Annual Demands Call REPT5 -7 Call REPSUM End Simulation i DOINT IRRIGATION Calculates Monthly and Annual Outdoor Use II I BLANEY Primary pro gram for I Estimating Outdoor Use 'II OUTPUT Transmits I I I-I 1/ Does Linear Interpolation Results to I I I I DEMAND L -------' Figure 3. Overall Structure of Water Demand Model Output f --_. -. --l i I RPTSET /' I I Establish Headings and Spac ings REPTI Input Data REPT2 General Land Use REPT3 ",Tater Use REPT5 Monthly Demands REPSUM Area Su.TIlIllary I L. t _-.J

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7) Interpolation DOrNT Statements 1349-1387. Tpis subroutine doe.s and linear interpolation. 8) Monthl.y Outdqor Water Use. IRIUG Statements 1388-1438. Given effective. rainfall, consumptive and carryover storage, IRRIG qomput;es monthly and seasonal irrigation menta. Subroutine OUTPUT stores the calculated irrigatioI),requirement for Use Model A single. is ul?ed forpred;i.t;t;ipg use as the sum of indoor and outdoo r water. TW(M) = x (I-WI) UF e-Kl(Pr) + (l-WO) ACRE e-KO(PO) ... where TW(M) = wate:r;use in a give.n la.nd d,uring month M, gal. / lIlonth; UF = h:i.storical u.n:i.t wa.ter 4emand Imonth WI = indoQr calibration faetQr l;>.ase.d on between es.timated and actu1:il water dimensionless; WR = relative water use. in this mQnt.h cOlilPared to ave.r1:ige montp, dimensionles.s.; UI =number of activity units in land use, KI = indoor price coefficient, 1000 gal./$; PI = price of indoor water, $/1000 gal.; 1.;1..4 (1)

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AGNEED WQ ACRE KO PO net monthly irrigation water demand, gal,/month/acre; = outdoor calibration factor based on difference between estimated and actual water use, dimensionless; irrigable area of land use, acres; outdoor price responsiveness coefficient, 1000 gal./$; and price of outdoor water. $/1000 gal. Each of these components is discussed below in more detail for the following simple example. Example Application Two categories of data forms must be completed: general information regarding the run and the study areas (forms 1-3) and detailed information for each study area (forms 4-10) repeated for all of the study areas. The general organizational structure is shown in Figure 4. The demand forecasting procedure was developed and tested using hypothetical data. The input data and the "actual" values against which predicted values were to be compared are hypothetical. The area for which monthly water demands were to be predicted was assumed to be contained within one study area. This study area (Utopia County) was then divided into two subareas, Nos. I and II, representing a variety of land uses. Although the categories of land use within one subarea may be entirely different from those within another, the two subareas differ only in the number of acres in each category. The two major land use categories represented are residential and agricultural. Minor land use categoriescincluded under residential land use are 115

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FORM 10 9 8 7 6 5 FORM 10 IRRIGATION WATER REQUIREMENTS FORM 9 MONTHLY OUTSIDE DEMAND FACTORS MONTHLY INSIDE WATER USE UNIT RATIOS ANNUAL INSIDE WATER USE UNITS 6 LAND USE AND WATER SUPPLY DATA LAND USE UNIT FACTORS CENSUS TRACT DATA FORM 3 LAND USE DATA FORM 2 STUDY AREA DATA I CONTROL DATA Figure 4. General Structure of Model 116

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single family residential, multi-family residential, duplexes and other. Minor land use categories included under agricultural land use are soybeans, corn and pasture. Agriculture, especially corn, is the predominant land use in terms of acreage in the two subareas. The calibration exercise was performed for the year 1977. Data were prepared and read as inputs for the beginning and end of the output year. Preparing the Data Ten data forms were used to encode the input data in the proper formats. Indicated on each form are the type of data that is'to be provided and the Fortran format to be used. Completed forms for the first simulation of the example problem can be seen on the following pages following a brief description. Run Control Data Run control data include all of the input data from the first three data forms. These data are placed at the beginning of the data deck. Data Form 1 Input Data Form 1 contains the first three cards of the data deck. The first two cards state the title for the current simulation and must be centered in columns 11-50. They will be printed as headings on the Monthly Water Demand (WDM) reports. Columns 73-80 are used to state the data type but they may be left blank. They are not read by the computer (only columns 11-50 are read as indicated by the corresponding format statement) but were found to be useful in handling the data deck. 117

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Coded by ______ Dote __ 1_._. 1 __ WATER DEMAND MODEL INPUT DATA FORM NO. I GENERAL RUN CONTROL DATA I TIT L E OF W AT E R DEMAN 0 PROJ E CT ION TO BE USED IN REPORT TITLES (Center in col. II-50) Poge __ of __ I-' I-' FORMAT (lOX, IOA'l) (Xl I.ZI (4 (3X, J Z), 7 IZ X, A3), Z (ZX,13 DATA TYPE .. IDEF = I = PRICE ELASTICITY eASED ON OLD PRICE E. DEMAND 10EF = Z" PRICE ELASTICITY BASED ON AVG. PRICE E. DEMAND

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The third card is called the Control Card. In the example problem, "1" study area (Utopia County), "2" subareas (Subarea No. I and Subarea No. II), "7" land use categories (4 residential and 3 agricultural), "2" input periods and "1977", the output year, are all indicated in the appropriate columns. Two reports are also specified: Report 1, the input data by study area (from forms 4-8) and Report 2, monthly water demands by subarea (the WOM report).' A YES is indicated in the appropriate spaces for each of the two reports. Report 1, however, prints regardless of whether or not a YES is indicated and these columns could have been left blank. Again, columns 73-80 are only used to indicate to the user the data type and may be omitted. This follows for the remainder of the cards also. The objective of this report was to take the Water Resource Engineers' Model and use it to predict monthly water demands for a particular year. For this reason, the number of output periods is always 1 and the number of input periods is always 2 (data must be submitted for the beginning and the end of the output year). Data Form 2 Data Form 2 contains ten lines since up to ten study areas may be included in the simulation. In the example problem, however, only one study area is considered and just one line of data from this form is needed. The study area number (or counter 1-10) is specified in columns 2-4 and the name of each study area is centered in columns 9-44. In the example problem, the single study area is numbered "1" and named "Utopia County". Columns 46-48 are used to indicate the number of subareas in the study area (2), columns 51-55, the unit cost of water (dollars per 119

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I-' N o Codee by ______________ __ Dcte __ I __ I __ __ STUDY t.REA NO_ STUDY AREA NAME ViATER DEfl.t:ND MODEL INPUT DATA FORM-NO.2 STUDY AREA DATA TO 8E USED IN REPORT TITLES "eme in-col. S-44) 1/\ NO OF! UNIT COST SUB tJF WATER d ARE;..S ($ / 1000 gols) roge ____ ol __ PROPOSED PRICE TY?E T!ME il2\! 1 "i I .. : 7; f I 1 I! !." i "q;, i ]f,-: r: \!1 \: ,(c:" .. t-:::..op .. : .. :: 17( !-i'.( pi :1;' !a.:'" 4_f-lliil-l I I I I I I I II 1o:U1H .l..I\.oILHj-! I IJ!l l1l!AiR;EIAI I I I lillJJ i! I I I I I 1 1 -II II I'jill j)-H Ii A'R!EiAI I I I I ji!l II I! I 1 I I I Ii II II-IIi)! I Ii II jAi R i E iA! I i I II IJJid I I Ii II 1111 III 1llllli! 11111:iAR]EiA!II: 'Iiifijll I I1I11 /11 II IT\ 11-li-!lHI 11111 t:!AiRiE:Allll 111!!!!!1 I I Illtl 1111. Ti ITIIli]! 111;1 j!iAiRiEiAIIiI :1 it::]!11 Iii 1111111 T Illlil!:j Il'iilll ill,l,l:jA!R:EIAIIII I I jl i ; I I I I I I I I i I I I I I I I I I I i 11 I I Iii. I I I Ii! 11 I 1 I! I i iAiR:E;Ai I II 111 ;1;;jlll III!IIII II II I \lllii;IIIIII;.;! 1 11,1!!';;111 1IIIIiili lUll 1.llliJji1lJI 1 .. i.111J [::ll.:A:R;SAil!ii {iX, F5,2, 5X, FS.2. 3X, 2) .... Lti,j = CF r' ;_0\ "'Tn.',E. r-':=:;:":

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1000 gallons), columns 61-65, the amount of a proposed price change (dollars per 1000 gallons) and columns 69 and 70, the number of the output period during which that change is to take place. By limiting the number of output periods to one particular year this number will always be "1" unless, of course, no change in price is anticipated during the output year. When no change in price is indicated, as in the example case, columns 61-65 and 69-70 are left blank and the price of water will remain constant throughout the simulation. The unit cost of water in the example is .66 dollars per 1000 gallons. The number, ".66" is entered with decimal in columns 63-65. Because of the format, the number of cents, 66 could have been entered right adjusted without the decimal and the correct number read. Data Form 3 From Data Form 3, the master list is read for all land use categories, major and minor, in all the study areas and subareas in the simulation. As many as 40 land uses may be included. However, only 35 lines are provided on the data form so two data forms may be necessary. The land use category number is specified in columns 7-9, the major land use category classification in column 7 and the minor land use classification in column 9. The decimal in column 8 need not be entered. It is advisable to enter it however because, although it is not read as part of the number, it is read as part of the name. The major land use categories (residential and agricultural) are given in the example problem. Major land use categories are distinguished from minor land use categories by entering a zero in column 9, in place of the minor land use classification. Four minor land use categories are under residential land use and three are included under agricultural land use. Indentation of the 121

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i-' N N Coded by ______ DOle_'_I._ LAND WATER DEMAND MODEL INPUT DATA FORM NO.3 LAND USE CATEGORIES Poge __ of __ USE LAND USE CATEGORY NAME DATA TYPE CAT. I 1213!.1' i> 1718 9 i 10 II 4Z j7' IT, itll>\1 PllllElSll ElNnllAlLJ I I I II II ll l! Llu! c!AITI.1 1 j.!jl; Ii III i:! iii 111 II! I I I 1>ITf\ Ii i I. III II'! iii! II i II I. II Ill>} Ii> ........ It<:Tlli 1;! I j I L!ul c:Air:.i j I: .> Ifill! Ii I r 11 Liu: iciAiT;.' I ; I I I I I I I ; I I I I Iii I I II Ii! !i ii'I'< 1 \ Liul IIIrl1 I.) id : i I I i I J I I I I! !! I I I I i 11< l'I+H ll Ll L(;l;id I! I ; i LU leAL' 11 ill il': !! i!! ii' i : III i I [JI1+L'1:ll ri :! ;1 LU 'CAT. _.' 1 : 1 ':,1 ) I ; 1 !! ;!;! ill j I i ::, ,:: f J i I } ill i L : U C A: T .. 1111 I) : j il I l i i I I In r i r : I' I I I I I I i-Lj I i!i i i 1 11 ILiu!c ATi. i Ii 1 j)TITT:-I-I-j I i I Ii: I Ii! t : I: !: II Ii: Illt>!)l. IILllLH
  • ilILj!H 1 i tIl I ill L IU :CAiT!. II 11.i rttI; I!! i i! i;! I'I!: 1111 f Ii 11I1111 i,iTfilfllLll!1 ilLI 1111 L:ui lelA:T!.; Illl11.: i i III! i i!!' iii! iii I! II i 11I11 lttl} '!J+!+lf;>l! !! Iii I i I L:ui iC:A'TI.: ill! ii 1 : I I Ii! I I I I I I i I I I I I I I I I I I I IILJlrllllllJ 1 i!! i I I I I L lui ICIAT:.! Til j i ( i I I I i I I i iii I I I i I I I I I I I IllI1Jrllllll!!flJ)Lll.1JLL!; tl i 1 Iii 1 l LU! tCIAT!. i I i I I I I I ; : I : II I I : I I II I i I !!llltlJT{.lll!illLf!! jIll i j I! L!Ui ICA;T!.! iii 11 : ,r :1!!!!!!!!! : i : I I I : I i I I I I I !41<1!lltLIL ilL! i 11 1 i II Hi L !u! !CAT; .1 1 11'_ ,....;Jj ,U 11i I It! : I I I I I I II I I I I J 11[llllJullllll i j ii ii Ii 1 11! Liu' leAT!.! j II ) t-1._i_i_i_I_1 U_l I I I II I I I I I I I I !lL.Illtl'fll!IH r! j f 1! i j j I L!U :c ATI.i I I I ']={. +-+1 I I I I I I 1 I I I I I I I i I I I I I I' .,... .. 'l .. ... .. '.' I I .. f' ; I I .i_LJ. I _' _! .. I ,i.:" i.. i!. I I ... iHllJJ llll..I.!;i Ii l i ; i :1 I LIU IC AIT,., iii; I i I'D i I!:;! t! i I!! It! I i 1111.111 lillllII': .;. :t.:' t..:: "'"7 '&.E; .70' -;" :-21-! ; ; ;':'6 ., ;:0: FORMAT (5X,11,lX,ll,T6.9A4l

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    minor land use categories, as in the example form, is not necessary, but will aid in clarity on the form. Data For Each Study Area The remaining data are input by study area. When there is more than one study area, data for each are all grouped together. Thus, the user prepares forms 4 through 9 for each study area. A single study area was considered in the example problem, therefore the following sample forms were the only forms completed for the first simulation. Had there been more than one study area involved, forms 4 through 9 would then have been completed for the next study area and this data added to the data deck behind the data for the first study area and so on. Data Form 4 The name and number of each of each subarea within the study area are listed on Form 4. When the study area includes more than 26 subareas (there may be up to 35) two data forms will be necessary. The number of the study area "1" is entered in columns 2-4. Although indicated on the example form, this number is not read by the computer and is optional; it is there only to aid in the handling of the data deck. The subarea number (or counter 1-35) is entered in columns 11 and 12. The decimal in column 10 is not read. Following the subarea numbers (1 and 2) and centered in columns 16-45 are the subarea names (Subarea No. 1 and Subarea No.2). Data Form 5 Unit Indoor Usage Factor (UF) A rapidly growing data base on indoor water use factors is available. 123

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    I-' N +:-. (uded _______ uole __ I __ I __ DEt/,AND ht.ODEL DATA FORI", NO,4 sua AREA DATA Poge __ of __ I sus I SUB AREA NAMES I I AREt.. AREA TO 3E USED TITI,-ES ,,' DATA TYPE NO NO, (Cenler nG",E In col 16-<:5) '" : ;: i if; lei! 111'2 '::,1101; I :!tJ ..... j 17 i ;-(1,2 lol::'it',,;;:; ; Co. L'!,:-":); ... ;""!f .... j'" (. 1< .... :{.':!O ...... .. 1"-1. \.:'r r':--. :'; !' :.'L;_ i ;71 >!:::.: /.:. j4.i.:4 i"'-l ;:'1 .. !!'!..-.I. '''-l!.t ;,_:-"i. 1 1i ... ::-: ,7f :;-:-fC''':''',L.1 (X,;3, lX,12 ,16,iO:"4 1 2X, F3,2)

    PAGE 133

    Interest in this area has been stimulated directly by water shortages in several parts of the country and emphasis by the Federal government on water conservation and indirectly through response to higher energy costs. Figure 5 shows the approximate breakdown in residen-tial water use. Of the estimated total of 140 gallons per capita per day, 70 gallons is used for indoor purposes with toilet flushing being the largest single user category. Similar data are available for industrial water users, e.g., Table 43. In all cases, site specific measurements are the preferred data source. Data Form 5 pertains to all of the minor land use categories included in the study area. The study area number is entered in columns 2-4. Although indicated on the example form, it is optional and need not be included. Land use categories are entered in columns 7-9 and must correspond with those included in the master list. Inside water use unit factors in gallons per month per unit (gallons per month per dwelling unit in the calibration exercise) are specified in columns 11-15. When these numbers are entered without decimals, as in the example problem, a decimal is automatically placed, according to the format statement, to the right of the digit in column 15 (e.g., 10600 becomes 10600.) On the other hand, when a decimal is included as part of this number, the specified decimal overrides the format statement. On the example form, inside water use unit factors are given only for the four minor land use categories under residential land use. When indoor water use does not apply to the minor land use category these columns are either left blank or a zero is entered in column 15. If, as in the example case, no price elasticity coefficients are used in the calibration, those minor land 125

    PAGE 134

    I-' N 0\ ) Coded by ____________ WATER DEMAND MODEL INPUT DATA FORM NO.5 LAND USE UNIT FACTORS DOle __ I __ I_-Poge ___ STUDY AREA NO. LAND USE CAT. INSIDE WATER USE UNIT FACTOR PRICE ELASTICITY COEFFICIENT INSIDE WATERCAU8RATION FACTOR IN OUTPUT PERIOD; -OUTSIDE WATER CALIBRATION FACTOR IN OUTPUT PERIOD: if* i:;j f I '.::::;l!:I;i:::Mi:;T TIl .:j I ... \i \ I. :.'J [iii D it:: IWh:j'i\in::: .:. F ACT 0 R is i 1 i'i;j 11. 1.4:1 ',liJ':@hiHf 1 i:l4t'::m: I f:) F ACT 0 R-IS #iT I II I:: __ '1: I In 1.1 Itl II I t itlfW:::;lt:J I Ll U::l:j::j.1illJJJ I II I I I I: I I I I I II I I I I I III I I I I. I I I r !I n l IllFIAlciTloiRiS lJ}lfJ:::J I l.l I tJ:j'il;:]'ill 111111/11 r 1I1I1I III 11111] [IJ I t I f i Ii I! II !!:IF!AlcITloiR:s TO-, I I I I : If' -I I -, -1 .. -. ;.::1 : ::: ... J.:::: .. :: .. :.:. ..,. .... :.;.::F:.:::: 'I 1.: FIAlc]T'O:R'S' ; .. _........... ...... .... .. I I ."+-, ( .... :, :: I ,I I Lt:t:;t:!I} I I. fIr:j:r: I. I, I I. i I I II I I I: i I ; I I I'FIAlcITio,R:s; r:: [:lSl I. E/' I I k,,!:tl::j? I I !iLl:Fl: ; I I iii I I! I -:1 ;F;Alcrr:OR:S rl i iL, [C : I :; 111ft;! i ; : : ; I; I I 'I E R++H" I., d I I 'i'LHi ILHH I 'i I 'I : I' : :;ft i j !:jilt\! i !J:ltlJ; i j ,;:1-i ; .' i '. i I j !L !.:! 'I I I I l 1 I TH1) l i I I : Ii I !' 1 i; l!! ;:-it. Ie iT iORS )1"T1T11.1! 11 t! l' i .. 1 I .1 '-1, f -! i 'i, I .!,I .1 :F!A!cIT.Q,RS J i :.1 I 'I I. I 1.l:14+.....!' I iii,' I I I! I I !_:J:! I! F!A!clTlo'R.S LJ iii I.'! i : iTIT] 1, '!' I g. I iii'! i", I' I ,!.! A;CiT'O R'S' I J I'TTTl : I .,! 1 I J I i I I ; I l ; l' 1 1 1 I I Iii' i F,A'C T'O R 5' .' :.! .. I: : ,I '. I I : I : :., I I :, I I 1 'T J;:'" i I :17TI i I Iii:! 1 I. 1, l l; I I I !: 1 Ii! I ; ; k ,A.CIT 0 R SI =ffi--,------+-IT: ij i '-. I I :, I 1 I I i a I!! J j ill I I 1 I : I I I I I I I::!! i I F ,A C. TOR S 1 -. I I j j 1 I I I .' I I I J J ,---1...., 1;'!I:l.:! U_ I!: _..Ll; iill I' I I i J j"'; __ I FIACIT!OR'S, iii! I t 1 I: iii' III i!! I I : I i I :T':-tl.+-I--= c-'"t FjAlCiT.o R'S II i ; I -=:oJ : I ,.j ill Ii.; I I '! i I I I I I: I!" 1 : :. ;. i FIA,C'T'O R.S I' :< !... J (. ,-:' Eo 1:.1 I; ,; ..... i ,It,'! i If ;!.1 -=<.0"', C"".: ... f, ..... r"'fo :-..& '::.Eo :'" '1> U t..:. f: "70 7, '71 !/C!?!o'""1{ '. H ,";:.'e-:::: (EX',II, :X,II.1''', 2(F5 O,5X:l, IOF2.2,IOF2.2) ... GAL./MO.-UNIT FORM"n "". ENTER OECIMAL

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    Daily per capita water consumption 140 gal. Variable assumed @8 to 10% Indoor consumption 70 gal. Outdoor consumption 70 gal. Toilets 3.5 gal.lflush 32 gal. Bathing & personal 21 gal. Laundry & dishes 14 gal. Cooking 3 gal. Irrigation Swimming pools Washing cars & Paved areas Figure 5.' Estimated Residential Consumption in the United (I-Hlne, 1976) 127 45% 30% 20% 5% Variable Variable Variable

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    Table 43. Water Consumption by Selected Industry Type (Metcalf and Eddy, 1972) Process Cannery Green beans, gal/ton Peaches and pears, gal/ton Other fruits and vegetables, gal/ton Chemical industries Ammonia, gal/ton Carbon dioxide, gal/ton Gasoline, gal/i,OOO gal Lactose, gal/ton Sul fur, gal/ton Food and beverage industries Beer, gal/1,000 gal Bread, gal/ton Meat packing, gal/ton live weight Milk products, gal/ton Whiskey, gal/l,OOO gal Pulp and paper Pulp, gal/ton Paper, gal/ton Textil es Bleaching, gal/ton cotton Dyeing, gal/ton cotton 128 Consumption 20,000 5,300 2,000-10,000 37,500 24,500 7,000-34,000 235,000 3,000 15,000 600-1,200 5,000 4,000-5,000 80,000 82,000-230,000 47,000 72,000-96,000 9,500-19,000

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    use categories for which indoor use does not apply are simply omitted from the form. For this reason the three agricultural minor land use categories were excluded from the sample form. Finally, an endform card ("ENDFORM" is entered in the first seven columns) is placed at the end of this data to signify the end of the inside water use unit factors for this study area. Data Form 6 Data Form 6 includes land use acreages for the two input periods. In the example problem, acreages are reported for the beginning and end of 1977. Entries are made for all of the minor land use categories within each subarea of the study area. The study area number is entered in columns 2-4. As in forms 4 and 5 this number is optional. Subarea numb'ers are given in columns 11 and 12, and land use category numbers in columns 15-17. Acreages are then indicated for each of the land use categories in each of the two subareas; the number of acres at the beginning of 1977 in columns 21-25 and the number of acres at the end of 1977 in columns 31-35. Acreages are entered in the appropriate columns with or without a decimal. When a decimal is not included as part of the number, one is automatically placed by the program to the right of the last digit. For example, 2000 is read 2000.0, 2100 is read 2100.0, etc. Columns 28-29 and 38-39 are used to indicate the decimal fraction of the total water supply that is supplied by local sources For the example case, none of the water was considered locally supplied, therefore these columns were left blank. An endform card is placed at the end of the above data to signify the end of the land use data for this study area. 129

    PAGE 138

    ....... W o ) Coeed by __ ____ Dole __ 1_,__1 __ ,_ STUDY .ARE:A NO, t :fTTIT1'i sus AREA NO. ). I ,)1 J 1;t.,H j JJ J. :ilf, .. [I! i -I i-1 .' ',' t i I'; J II : .:, ,i LAND USE CAT. ViAl ER DElM'H-JD MODEL INPUT DATA FORM NO.6 LAND USE AND WATER SUPPLY DATA YEAR tq",\'"\ BEGTNtHNG r EN,O: loCRES SWL" ACRES SWL ,1 ;: I i'-;;,::-!' L':; i .: :.:. ::: +-+-i :rT 11 i i. ,. I:; II i ; i. I:; I i I 'ii i i'j::jttt Poge __ '_ of _' __ FO::\MAT [EX. J3,IX,lZ, 2X,] I, IX,JI, 3X,:2 \F6.0, X, F 2.2,IX DEctMAL FRACT ION OF TOTAL WATER SUPPLY TO THIS LAND USE; IN THI S SUB AREA, SUPPUED BY OTHER WAHR !>OURCES __ PRIVATE WELLS AND THE LIKE. i

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    Data Form 7 The seventh data form contains the number of indoor water use units for each minor land use category. The units of measure employed may be ( ,I people, dwelling units, etc. as long as they coincide with the units of Form 5. In this example, the units of measure are dwelling units. These data are indicated for subareas 1 and 2 and for the beginning and end of the output year (1977). The number of dwelling units at the beginning of the output year is given in columns 21-25 and the number at the end of the output year is given in columns 31-35. Decimals are automatically placed to the right of these numbers unless specified on the form. Columns 2-4 are for the study area number and, although specified on the sample form (1 in column 4), are optional. Subarea numbers (1 and 2) are entered in columns 7-12 and minor land use category numbers in columns 15-17. In the example, indoor use applies only to residential land use categories and therefore, agricultural land use categories are omitted. Again, an endform card follows the above data. Data Form 8 Data Form 8 contains the monthly inside water use unit ratios (current month/average month) for each of the minor land use categories (those for which indoor water use applies) in the study area. Values are the same for each subarea within the study ,area and, for this reason, are not entered separately for subareas 1 and 2 on the sample form. In the example case,a value of 1.0 for each month was used under 131

    PAGE 140

    ..J W 0 0 2 0 :;:: :r u 0 wJ t-q S -(J) fz r--::> Ow ZIJ) z.::> n: OC o LJJ LL.I_ 1-;.
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    I-' W W Coded by ________ Date __ 1 __ 1 __ STUD) LAND WATER DEMAND MODEL INPUT DATA FORM NO.8 MONTHLY INSIDE WATER USE UNIT RATIOS Poge ___ of __ ARE4 USE DATA TYPE NO. CAT. I I 11' I:!! i Iii I I kl"1 l Ilf II}I I N I lr 1:1 lIlt / \1 l 1>1 I I I, r .( I I N I S II olE I F I> II F !ill i i Ij I II! II Illi I PI lwl I ri I ,li I I Ii it I Iii 11 I I k I IN! S II 10 I EI IF .1 Ij I il : 11 I 1/ Ii H1A Iii :. I I) I d I v>. IjrJlslllojEI IF L !kill.lli iilillil!! 11 Ii llill b'I!N!S!I!oIE:jF L II 1.1 IJ ; I I I 11 Iii Ifl 1:1 I : I I 1M PI: Ii I iNIS! IIO'E: IF 1< 11I.!I1 I!j I [11.ld! 111111; i 11 !/J! III I:N'S:IiO'Ei iF A I I j !. U tl I I I \!; I i :i! II I I iA I Ii /'l I ITI !Al: T 11 id I I I >1 I I I i I iN: S i I D' E I ; F .j I.Ull I-I Ii I i Ii I Ii III I I Ij !::j II I In : I 11 11 I Ii i II IIN;siliDiE' IFj Iii.! I 11 I I II I i 11 I I 11 I. 11 I) I \1 i i II : i I }I I I I I i I .i I!N:S:I:O EliFI U I i I II I I :1 : 1:1 I Ii i 1 IJ I I I II I II I 13 II I II iii I I ,N' S, I o.E' iF tir!J.JL1J.1 LJ I i I )1 I I 1 i:J I I lil I Il I : Ii I i{1 I 1)1 I I }j I 11 I I II : :! il iN;s; IDlE! iF 'jJi I U ...l.Jll .. 1 i Ij I 11 11<11111 III i! II/I I III : Ill! II 111 :lljN.slIIO:E! iFI r-tLLLLUJJ.:::,lIlll 11 III 111 I {j Ii... III I I[lill ,INSI,!o:E: if J! : j I ; 1.1 n I I I 1, I I I /1 I I I\j 11 I I II I I TIT I iT I II I IJ 1 I II I i Ii IINS! I :o:EI IF 11 it IT1Tl Ij I i II i I I }.j I I Ix I 11 I I fl 11 11 I i 11 I II I I 11 I I Iii I I 1 I I 1 I INs! I i E! IF : Ie' 1::;11; 112 1"'; "";:2":i .( I iZ2 x: 1:1:':1):!-4 i i !S;.:O C1142i( 3]<4j.o;! "'6 50 t:.: &0 E,r i ,;7 : t..o: io:? ''7:l :-,.72 7) 1,<4 \':"";. :eO lEX, J I, IX, II, IX, 12 (IX, F4.0)) .. OeCII.'.AL FRACTION OF AVERAGE MONTHLY USE --SUM OF VALUES FOR EACH LAND USE CATEGORY SHOULO EOUAL 12.0

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    the assumption that indoor use does not vary from month to month. This may be assumed when water supply records appear to be by equal billing periods rather than billing by 28, 30 and 31 day months, or when no apparent changes in indoor use can be found in historical records over the year. The study area number "I" is indicated in columns 2-4 (once again it is not read and therefore is optional) and the land use category numbers in columns 7-9. Twelve sets of columns (4 columns each) are provided on the form for the decimal fractions of average monthly indoor use. The format here for each set of columns is F4.0; that is, a decimal will be placed automatically to the right of the digit in the 4th column unless a decimal is entered as part of the number. This means that the l's on the sample form are all read as 1.0. Note that the sum of the twelve decimal fractions for each minor land use category should equal 12.0. The last card from this form is an endform card. Data Form 9 All of the input data for the Blaney-Criddle method, to be used for estimating monthly irrigation requirements for the study area, are contained on Form 9. Filling out the form is fairly straightforward. One thing to note, however, is that in most cases, decimals are to be omitted. In temperature and precipitation data, a decimal is automatically read to the left of the second to last digit (values are significant to two decimal places). For example, 6333 would be 63.33; 5145 would. be read 51.45, 630 would be read 6.30, etc. The same is true for planting data, harvest data, soil moisture carryover (in inches) and all crop information 134

    PAGE 143

    WATER D=:W.AND MODEL INPUT DA TA FORM NO.9 IRRIGATION }VATER REQUIRMENTS (TR 21) PAGE __ OF __ TllLE .!..?D 1'1n .. ".::J lrrig.=.cien Rec;uireO'le.nt by-Corn in Study Area during .197_ I .. I I r, 12 I I : JO 1 : : 2; :...: It : : \ :! I 17 : :; I:';:: I I I ,!.Rfl )..N:--rCAL J 1,nv l I I. ... ". '. I I I c.:.9"45 J ::t .Tut'l: : Y Nnv. i-' I I ..&..\qO I """* I lloeL'II,) I I-,-\C I l J I<.:":.:: .. :.::'.:'-:::"'1:':'::::-.:: =i:::'.j :'.::'.:: ".:: :::::: .. .:, .. I eRn? I:; r r. 1 I ON .. :i::: r:':".: ::::::':::'+:'. '.:::":,::: I I I C..,,,p '. J I .. '. SOlL C-:;-!C(\:\:\L ",u, ": :::.::;::.::-:.:::. "-'-..... r'rl!oJ.... :j ;. Pi -;":.!.?VC' 1-,,'n1cT u-.O\.lT" C'P'C"" ::: <.J:.. !...J J __ 'l',"-"-'" .... Cr.[FF "I 't r ... ll W-;::": :.:.::\-.:.:::: I C!.1\.RY ,._ ..,C:t. F.'I:'>! 0" (-;,,')p >."vt; ::::.:-::::'::':':' I I .. ;;. fIGURE -".' U ::' ,," .''-_. };';::fX< :-..' T\' Hr'--"V (hER T' ru f.e.lL l-'PJr:: .. : ...... .. >.J .... y .1.),\. u ..... LO\.: til"" ,,"","'1.';'>""0 --". G.. : I .. :::::::.,.:.'::>. UJ I.) ...... \. "...... ....... Sc::P I 'SOC> qOO I 'sec \00 \oS '0 h; .. fCC,OI \00 I I ...... I I 1:'::>< /{.I 1 I I t":':-:':" I i.t .:.::-:.:: I:" _._--, --. ---,-T-"' t, 1 I r:::: ;:.: ( .: I I '1 I 1 c-I: i I I i J ';;',1 I I

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    with the exception of % chance rainfall (a decimal is used here). The printout code 1 refers simply to the type of output desired. The above information must be supplied for each crop type within the study area. In the example case, pasture estimates were used as lawn irrigation requirements in residential areas. OUTPUT REPORTS Results of the analYsis are printed in two reports, Report 1 and Report 2. Repot't 1 prints out all of the input data frOlI1 Forms 4 through 8 for each study area, along with the monthly irrigationre .... quirements for each land use category within the study area {results of input data from 9). water demands for the output year, in which we are interested, are given in Report 2. Report 2 is divided into two reports, Report 2A and R.eport 2B. Report 2A gives the water demands on the water agency's system by each minor land use category and for each month of the Qutput year (1977 in the example problem). This report and its companion, 2B, are printed for each subarea in the study area. Report 2B contains the total demand ,values as distinguished from the water supply demands,which means they contain the locally supplied watet' as well.' Since in the example case all demands were expected to be met from the water agency, the values in Report 2B were identical with those shown in Report2A. An exatnple of Report 2A is shown in Table 44. For the first simulation of the test case, two pages of data were printed, one for Subarea No. 1 and one for Subarea No.2. The units of use are million gallons per month. 136

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    I-' Vol "'-J LAND USE CATEGORY JAN FEB 1.1 SINGLE RES. 259. -4 247.8 1.2 26. 7 25. 5 1.3 MULTI-FAMILY RES. i06. 9 1 1 1. 4 OTHER ;:;=:SI.,ENTIAL 17.8 17.0 6. 1 SOYBEANS C. 0 O. () 6. 2 CORN O. 0 O. 0 6.3 PASTURE 0, 0 O. 0 TOTALS 411. 392. CALIBRATiON TEST UTOPIA COUNTY TEST AREA REPORT 2A MONTHLY DEMANDS ON BWS SYSTEM --MGM STUDY AREA 1 SUBAREA NO. 1 YEAR= 1977 MAR APR MAY ",IUNE JULY ,'lUG SEPT 332. 3 411. :2 i'77.4 461.3 48'::;,,5 401.0 386. 4 29. 8 2 37.3 38. 6 6 37. 1 35. 6 113. 1 125. 7 1 .-,....., ., .. \,.j .... :I. A.t 142. 2 1,,9.8 142. 8 136. 8 20. 3 23. 5 26. ;:'s 26. 5 27.9 25. 1 1 O. 0 O. 0 O. 0 4. 1 64.6 70. 6 19. 5 O. 0 150.7 362. 5 293. 2 209,3 O. 0 0, 0 50. 0 91. 8 132. 8 100. 5 104. :5 47. 0 47,0 545. 837. : 169. 1066. 1031. 724. 650. Table 44. Example Output --Report 2A OCT NOV DEC 40::';. 8 290. 0 2 E. c;. 3:, 3 29. 4 7. 6 127. 1. 117. () () '-" ...; 23, 5 19.7 ::3. 4-O. 0 O. 0 c. 0 0.0 O. 0 o. 0 82.3 5. 2 O. 0 671. 461.

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    Before the above reports have been printed, the monthly irrigation requirements (XIRM) for each crop type within each study area are printed. In the example problem, six pages of data were printed, data for net irrigation requirements and for gross irrigation requirements (seasonal totals) for each of the three crop types (soybeans, corn and pasture) in Utopia County. An example (net and gross irrigation requir,e ments for soybeans) can be seen in Tables 45A and 45B. 138

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    I-' (..oJ \0 WATER REQUIREMENTS FOR CO. AG. CROPS 1977 LATITUDE= 29 DEQ 40 MIN PLANTING DATE= 5/15 HARVEST DATE= 9/15 NORMAL NET IRRIGATION= 1.00 INCHES CARRYOVER1 00 INCHES cu
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    I-' o **********u************ ********************************* GROSS IRRIGATION REQLiIREMENTS/SEASONAL TOTALS EFFICIENCY TOTAL 100 ::;.86 95 6. 16 90 6. 51 85 6.89 80 7.32 75 7.8" 70 8.26 65 9.01 60 9.76 Table 45B. Example Output --Gross Irrigation Requirements for Soybeans

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    Calibration The literature review on water demand modeling in the early part of this report suggests that water use is a function of many variables. The diversity in the types and numbers of variables provides insights into possible reasons why projections from the WRE/SCS model (or any other model) maynot be identical with actual observations. The WRE/SCS model is a relatively simple model and as a result, includes many of the variable effects within single terms. With respect to "indoor uses," such as residential, the WI factor must account for the income, property value, cultural and water behavior, and all the climatic variables identified earlier in this report as possibly significant in residential use determination (Table 24). Similarly, the wo term in the "outdoor uses" part of the equation must account for product price effects, technological change, crop cultural practices, behavioral characteristics of the water user, institutional features, and the entire set of climatic-soil-crop factors (Table 2). These are large burdens to expect WI and WO to carry; however, for this "first generation" model, it appears a "calibration approach" can alleviate the difficulty. The other option, of course, is to use one of the more explicit models, as discussed earlier in this report, as a substitute for this equation in the WRE/SCS model. This is possible and highly suggested for those users having the more detailed water demand models. The balance of the computer program developed in the WRE/SCS model still be used to aggregate the projection to subareas and study areas, and to provide format for output reports. The strategy in calibrating the WRE/SCS model will have to be modified somewhat depending on the knowledge available in the study area for 141

    PAGE 150

    each of the parameters. Obviously, if all the parameters of Equation (1) are known with a high degree of accuracy, calibration may not be necessary. If, as another example, there is good information on all the parameters except WR, historical water use records may be sufficient to facilitate calibration. That is, once the model is adjusted to "track" previous years, it is reasonable to expect some similarity in "next months" water use. Of course, any model not explicit in the socio-economic and climatic-physical-biological factors of Tables 2 and 24 is subject to question in projections of future events. Said somewhat differently, the WRE/SCS model, once calibrated, should predict fairly well, as long as no major structural changes occur in the socia-economic and/or biological-physical systems. If such changes are known to have occurred, the WRE/SCS model will have to be re-calibrated. It is assumed in the following calibration process that information is available on DI, DF, KI (assumed zero), and KO (assumed zero). The projection is made of use in a year of known record, 1977 in this case, and calibration is facilitated by adjustments in WI, WR, and WOo For a "real" projection situation, the user should attempt to get as much information as possible on each economic sector in order to facilitate "educated judgments" as to choice of parameters and adjustments to be made. In the following, we assume the existence of the following knowledge: 1. that household incomes in the study area are relatively high, which suggests a negative influence on the size of WI; 2. that households in the area have not historically had any real reason to conserve water, as there had always been relatively large quantities; this would tend to make WI small; 142

    PAGE 151

    3. that the modified Blaney-Criddle formula tends to overpredict needs in hot-humid regions during rainy periods; some adjustment will be necessary to AGNEED during these periods; 4. that farmers-irrigators in the area are generally progressive, using the latest technology, high fertilization rates. advanced cultural practices, and that no bounds have been placed by the institutional structure on water pumping. This implied tvO is very near zero. (In addition, we have already assumed KO = 0 which implies the knowledge that irrigators find irrigation costs an insignificant part of their expenses, and as a result, the optimal irrigation level is not influenced by the additional gain recei.ved for additional expenditures). Now, given this knowledge, the problem is essentially reduced to modifying the value of WR, as WI and WO can safely be assumed as "in-the-ballpark" at some low number like WI WO = 0.1, or possibly assumed 0.0. After the first run has been completed, the results are compared to historical data in order to check the accuracy of the model. "Actual" and predicted values of water demand from the first run in the t\vO calibration areas for 1977 are shown in Table 46. In the example case, the model estimated 7929 million gallons while the actual demand was 7220 million gallons, a difference of 10%. Many factors could cause this variation. For example, it is known that the Blaney-Criddle technique used to estimate the agricultural portion of the outdoor water usage is usually high. Comparisons were made between the Blaney-Criddle estimates and the actual irrigation usage for the three different crops 143

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    involved and they were indeed found to differ. In order to correct the Blaney-Criddle estimates, a very simple technique was used. First, the estimated water usage for each month was assumed to be off by the same factor as the estimated water usage for the year. Then the "correction factor" is that number which, when multiplied by the estimated water usage, yields the actual water usage. To find this correction factor, the actual water usage for 1977 was divided by the estimated water usage for 1977. In the case of soybeans, the estimated Blaney-Criddle water usage was 5.86 inches per month whereas actual water usage was found to be 5.40 inches per month. Dividing actual usage by predicted resulted in a correction factor (l-WO) of ".92". Therefore, WO is 11.08". Using the same procedure described above, WO was also found for corn and pasture. The three WO's were then entered (without the decimal) in columns 51 and 52 on Data Form 5. Replacing the old Data Form 5 with this one, the program was again run. Results of this simulation are represe:p.ted by curve 2 in Figure 6. The concern at this point is the explanation for this variation. A number of things could be responsible. One of the main sources would be the efficiency of the irrigation systems in operation. Other factors would be the economic conditions during the time period considered, specifically the cost of water. Of course, other sources of unexplained variation should be taken into account. Once the Blaney-Criddle estimates were adjusted the model was run again. This time the estimated total water usage was 6649 million gallons, still differing from actual demand by 8%. Since the outdoor water usage estimates are now considered correct, the remaining variation is assumed to be in the indoor water usage estimates. These estimates were corrected in the following manner. 144

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    1100 Curve 1 Description 2 -----------3 -----4 -----1000 900 800 700 600 500 400 J F M A M J J A s o N o Figure 6. Predicted Monthly Demands (MG) from Each Step (1-4) of the Calibration Exercise 145

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    Month January February March April May June July August October November December Annual Table 46 Comparison of "Actual" and Predicted Monthly Demands (MG) for 1977 (Subarea 1) Actual* Predicted** 400 420 400 420 410 550 700 809 930 1127 870 978 875 965 600 612 540 561 500 634 540 433 415 420 7220 7929 ,'t "Actual" values are hypothetical; they are included for the sake of comparison and calibration of predicted values. ** First simulation; curve 1 on Figure 6. 146

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    Land use acreages were assumed to be correct; therefore, remaining variation can be accounted for by either or both of two factors affecting indoor water demand, unit demand factors and indoor water demand ratios. The 8% difference between predicted and actual demands for the year 1977 suggests that the unit demand factors may havebeentoo low. This may be attributed to high incomes and low conservation. High incomes are known to have a positive effect on the gross daily per capita consumption (Larson and Hudson, 1951). Because of the relatively high incomes within the study area, and therefore a greater demand for water, unit demand factors needed to be calibrated. This was done effectively through the use of a second calibration factor (WI). An increase in the unit demand factors of .1 seemed reasonable, therefore each of the inside unit demand factors entered on Data Form 5 was multiplied by 1.1 (l+WI). For example, 10600 gallons per dwelling unit (in single family residential areas) becomes 11660 gallons per dwelling unit, 9100 becomes 10010, etc. The former unit demand factors were then replaced with the calibrated factors and a third simulation run (curve 3 on Figure 6). Predicted and actual values for the year 1977 were now found to be much closer in value. evident. Monthly variation, however, was still Predicted estimates of water usage for summer months were found to be lower than actual values whereas predicted estimates of water usage for winter months were found to be higher than actual values. The reason for this variation is most likely due to the monthly indoor water demand ratios. When a value of 1 is used for all 12 months, as in the example case, it is assumed that indoor water usage does not vary from month to month. The estimates indicate this is not so. The water usage 147

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    ratios were therefore adjusted (following a review of "historical" w.ater USe records, and keeping the sum of all ratios equal to 12) so that summer months showed a higher indoor water usage than winter months. The reason for greater water usage during summer months could be attributed to an increased'number of showers, more laundry, wading pools, etc. After the indoor water demand ratios were corrected,the model was again run and a closer fit was found between actual and predicted values. Results from this step of the calibration exercise can also be seen in Figure 6 (curve 4). This calibration exercise can be used to estimate relevant determinants of water demand (outdoor demand factors, indoor unit demand factors, and indoor water demand ratios). Through calibration, better results are possible. Note, however, that changes in the data to improve the closeness of fit between measured and predicted results must be plausible. 148

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    VI. SUMMARY AND CONCLUSIONS This report summarizes available models for estimating agricultural and municipal water demands. A total of twenty-one agricultural models and nineteen municipal models were reviewed. The primary objective of this study was to assess those models which might be suitable for term, e.g. one-year forecasting. The models range in complexity from very simple ones which relate water use to population to relatively complex linear programming models for projecting agricultural water use. Unfor tunately, very few of the models have documented computer programs. Most of them were used only once. A composite model based on an urban model developed by Water Resources Engineers was combined with a Soil Conservation Service model (TR2l) for estimating consmnptive use. The composite model estimates water use for any area as the sum of an indoor and outdoor component. It is specifically set up to estimate monthly water use for a one-year period within subareas within study areas. A complete example, including sample coding sheets, is included. The program flow charts and listing are presented in the appendix. Overall, the models are very simple. The main source of complexity is manipulating the data base to run the model and print out the results. 149

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    VII. REFERENCES Albertson, M.L. et al., editors. Treatise on Urban Water Systems. Colorado State University, Fort Collins, 1979. Anderson, M. H., J. C. Anderson, J. E. Keith and C. G. Clyde. The Demand for Agricultural Water in Utah, Logan, Utah: Utah Water Research Lab, College of Engineering. Anderson, R. L., D. Yaron and R. Young. Models Designed to Efficiently Alloc.ate Irrigation Water Based on Crop Response to Soil Moisture Stress. Technical Report No.8, Fort Collins, Colorado: Environmental Resources Center, Colorado State University, May 1977. Andrews, D. R. An Estimation of Residential Demand for Water in Dade County, Florida. University of Florida, 1974. Biere, A. W., "Economic Irrigation Scheduling and the Demand for Irrigation Water," Western Agricultural Economics Association Proceedings, July 1971. Blaney, H. F. and W. D. Criddle, A Method of Estimating Water Requirements in Irrigated Areas from Climatological Data, U.S.D.A.-S.C.S., December 1947. Burke, T. R. "A Municipal Water Demand Model for the Conterminous United States," Water Resources Bulletin, Vol. 6, No.4, JulyAugust 1970, pp. 661-681. Camp, R. C. liThe Inelastic Demand for Residential Water. New Findings," Journal American Water Works Association, Vol. 70, No.8, August 1978, pp. 453-458. Cassuto, A. E. and S. Ryan. "Effect of Price on the Residential Demand for Water Within an Agency," Water Resources Bulletin, Vol. 15, No.2, April 1979, pp. 345-353. Christensen, D. A., A. S. Morton and E. O. Heady. National and Regional Surface and Groundwater Demand Function Estimates: A National Linear Programming Approach to Simulated Increases in Water Prices and Their Effect on U.S. Agriculture CARD Report. Ames, Iowa: Center for Agricultural and Rural Development, 1980. Clouser, R. L. and W. L. Miller. Household Demand for Water and Policies to Encourage Conservation. Technical Report 124. Water Resources Research Center, Purdue University, August 1979. Clouser, R. L. and W. L. Miller. "Household Water Use: Technological Shifts and Conservation Implications," Water Resources Bulletin, Vol. 16, No.3, June 1980, pp. 453-458. 150

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    Condra, G. D. and R. D. Lacewell. Effect of Alternative Product and Input Prices on Demand for Irrigation Water: Texas Plains, Staff Report, College Station, Texas: Department of Agricultural Economics, Texas A&M University System, July 1975. Condra, G. D., R. D. Lacewell, J. M. Sprott and B. M. Adams. A Model for Estimating Demand for Irrigation Water on the Texas High Plains. Technical Report No. 68, College Station, Texas: Texas Water Resources Institute, May 1975. Criddle, W. D. "Methods of Computing Consumptive Use of Water." Journal of the Irrigation and Drainage Division, Proceedings of the American Society of Civil Engineers, Vol. 84, No. IRl, January 1958. Csallany, S. C. and J. C. Neill. "Statistical Analysis of Water Consumption," Water Resources Bulletin, Vol. 8, No. i, February ]972, lp. 77-86. Danielson, L.E. "An Analysis of Residential Demand for Water Using Micro Time-Series Data," Water Resources Research, Vol. 15, No.4, 1979. Darr, P., S. L. Feldman and C. S. Kamen. "Socioeconomic Factors Affecting Domestic Water Demand in Israel," Water Resources Research, Vol. 11, No.6, December 1975, pp. 805-808. Domokos, M., J. Weber and L. Ducks tein. "Prob lems in Forecas ting Water Requirements," Water Resources Bulletin, Vol. 12, No.2, April 1976, pp. 263-273. Dunn, D. F. and T. E. Larson. "Relationship of Domestic Water Use to Assessed Valuation, with Selected Demographic and Socio economic Variables," Journal American Water Works Association, Vol. 55, No.4, April 1963, pp. 441-450. Economic Research Service. Our Land and Water Resources, Supplies and Uses, Misc. Publication No. 1290, Washington, D.C.: U.S.D.A., May 1974. Ekholm, A. L., D. F. Schreiner, V. R. Eidman and G. A. Doeksen. Adjustments Due to a Declining Groundwater Supply: High Plains of Oklahoma and Texas Technical Bulletin T-142, Stillwater, Oklahoma: Agricultural Experiment Station, Oklahoma State University, January 1976. English, B. C. and D. Dvoskin. National and Regional Water Production Functions Reflecting Weather Conditions, CARD Miscellaneous Report. Ames, Iowa: Center for Agricultural and Rural Development, Iowa State University, September 1977. English, M. J. and G. T. Orlob. Decision Theory Applications and Irrigation Optimization. Contribution No. 174. Davis, California: California Water Resources Center, University of California, September 1978. 151

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    Flack, J. E. "Achieving Urban Water Conservation," Water Resources Bulletin, Vol. 16, No.1, February 1980, pp. 139-145. Florida Input Output Model. (Personal Communication with David Mulkey, Food and Resource Economics Dept., IFAS, University of Florida, Gainesville, Florida. Fluegel, R. L. Connecticut Prototype Water Use Data System: System Documentation. CAeI, Inc., Federal Database and Information Services Division, October 27, 1978. Gibbs, K. C. Price Variables in Residential Water Demand Models. Water Resources Research, Vol. 14, No.1, February 1978, pp. 15-18. Gisser, M. Demand Water "Linear Programming Models for Estimating Agricultural Functions for Imported Water in the Pecos River Basin," Resources Research, Vol. 6, No.4, August 1970. Gisser, M. and A.Mercado, "Integration of the Agricultural Demand Function for Water and the Hydrologic Model of the Pecos Basin," Water Resources Research, Vol. 8, No.6, December 1972. Got1ieb, C. C. "Sorting on Computers," Applications of Digital Computers, W. R. Freiberger and W. Prager (editors), Ginn and Company, Boston, 1963, pp. 68-84. Hanke, S. H. "A Method for Integrating Engineering and Economic Planning," Journal American Water Works Association, Vol. 70, No.9, September 1978, pp. 487-491. Hanke, S. H. "An Optimal Sampling Procedure for the Collection of Residential Water Use Data," Water Resources Research, Vol. 15, No.6, December 1979, pp. 1343-1348. Heady, E. 0., A. D. Mesiter, K. J. Nicol and R. W. Strohbehn. U. S. Agricultural Production in Relation to Alternative Water, Environmental, and Export Policies. CARD Report. Ames, Iowa: Center for Agricultural and Rural Development, Iowa State University, June 1976. Hernandez, P. A. Estimating Agricultural Consumptive Use Values. Regulatory Division, Southwest Florida Water Management District, June 1977. Hexem, R. W. and E. L. Heady. Agriculture. Ames, Iowa: Water Production Functions for Irrigated The Iowa State University Press, 1978. Hogg, H. C., J. R.Davidson and J. Chang. "Economics of a Water Yield Function for Sugar Cane," Journal of the Irrigation and Drainage Division, ASCE, Vol. 97, No. IR1. Proc. Paper 6448, March 1969, pp. 127-138. Holtz, D. and S. Sebastian, editors. Municipal Water Systems: The Chal lenge for Urban Resource Management, 1976. 152

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    Howe, C. W. and F. P. Linaweaver. "The Impact of Price on Residential Water Demand and its Relation to System Design and Structure," Water Resources Research, Vol. 3, No.1, 1967. Hughes, T. C. and R. Gross. Domestic Water Demand in Utah. Water Resources Planning Series. Utah Water Research Laboratory, Utah State University, May 1979. Ireri, D. and H. O. Carter. California Arizona Economic Interdependence and Water Transfer Patterns. Giannini Found. Research Rpt. 313. California Agricultural Experiment Station, Giannini Foundation of Agricultural Economics, October 1970. Israelsen, O. W.and V. E. Hansen. Irrigation Principles and Practices. New York: John Wiley and Sons, Inc., February 1967. Jones, J. W. and A. G. Smajstrla. "Application of Modeling to Irrigation Management of Soybeans." Published in Proceedings of the World Soybean Conference-II, Raleigh, North Carolina, March 1979. Jones, J. W., R. F. Colwick and E. D. Threadgill. "A Simulated Environmental Model of Temperature, Evaporation, Rainfall and Soil MOisture," Transactions of the ASAE, Vol. 15, No.2, pp. 366-372, 1972. Kansas Water Resources Board. Kansas Long-Range Water Requirements. Topeka, Kansas: State Water Plan Studies Part B. 1972. Khanal, N. Predictive Water Demand Model for Central and Southern Florida. Technical Publication No. 76-2, South Florida Water Management District, West Palm Beach, 1976. Kibler, D. F. Economic Evaluation of Irrigation in Pennsylvania. DER File No. WP69:l-l06.2, University Park" Pennsylvania, The Institute for Research on Land and Water Resources, The Pennsylvania State University, July 21, 1980. Kibler, D. F., D. O. Fritton, E. L. White, R. J. Trotter and D. F. Tandy. Analysis of Water Requirements for Agricultural Irrigation in Pennsylvania. Research 99. University Park, Pennsylvania: rnstitute for Research on Land and Water, The Pennsylvania State University, September 1977. Lacewell, R. D. and G. D. Condra. The Effect of Changing Input and Product Prices on the Demand for Irrigation Water in Texas. Technical Report No. 75, College Station, Texas: Texas Water Resources Institute, Texas A&M University, June 1976. Larson, T. E. and H. E. Hudson, Jr. "Residential Water Use and Family Income," Journal American Water Works Association, Vol. 43, No.8, August 1951. 153

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    Linaweaver, Jr., F. P., J. C. Geyer and J. B. Wolff. "Summary Report on the Residential Water Use Research Project," Journal American Water Works Association, Vol. 59, No.3, March 1967, pp. 267-282. Lofting, E. M. and H. C. Davis. "The Interindustry Water Content Matrix: Application on Mu1tiregiona1 Basin." Water Resources Research, Vol. 4, No.4, August 1968. Lowry, Jr., R. J. and A. F. Johnson. "Consumptive Use of Water for Agriculture," Transactions of ASCE, Vol. 107, pp. 1243-1302, 1942. Lynne, G. D. "Issues and Problems in Agricultural Water Demand Estimation from Secondary Data Sources," Southern JOl.lrna1 of Agricultural Economics, Vol. 10, No.2, December 1978, pp 137-143. Lynne, G. D. "Water Price Responsiveness and Administrative Regu1ation--The Florida Example." Southern Journal of Agricultural Economics, Vol. 9, No.1, July 1977, pp. 137.,..143. Lynne, G. D. and R. R. Carriker. "Crop Response Information for Water Institutions." Journal of the Irr.iga,tion and Drainage Division, ASCE, Vol. 105, No. IR3, Proc. Paper 14814, September 1979, pp. 221-232. Mapp, Jr., H. P. and V. R. Eidman. An Economic Analysis of Regulating Water-Use in the General Ogallala Formation. Technical Bulletin T-141, Stillwater, Oklahoma: Agricultural Experiment Station, Oklahoma State University, January 1976. Mapp, Jr., H. P., V. R. Eidman, R. F. Stone and J. M. Davidson. Simulating Soil Water and Atmosphere Stress-Crop Yield Relationships for Economic Analysis. Technical Bulletin Stillwater, Oklahoma: Agricultural Experiment Station, Oklahoma State University, February 1975. Mather, J. R. The Climatic Water Budget in Environmental Analysis, Lexington Books, Lexington, Mass., 1978. Mather, J. R. The Influence of Land-Use Change on Water Resources. Water Resources University of Delaware, 1979. Metcalf and Eddy, University of Florida, and Water Resources Engineers, Storm Water Management Model, Volume I -First Report, U.S. Environmental Protection Agency, 11024DOC07/71, Washington, D.C., 1971. Metcalf and Eddy, Wastewater Engineering: Collection, Treatment, and Disposal. McGraw-Hill, Inc., New York, 1972. 154

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    Milne, M. A. Residential Water Conservation. California Water Resources Center Report No. 35. University of California, Davis, CA, 1976. Minhas, B. H., K. S. Parikh and T. N. Srinivasan. "Toward the Structure of a Production Function for Wheat Yields with Dated Inputs of Irrigation Water," Water Resources Research, Vol. 10, No.3, June 1974, pp. 383-393. Ministry of Agriculture and Food, 1963. Mitchell, B. and P. H. Leighton. "A Comparison of Multivariate and Trend Forecasting Estimates with Actual Water Use," Water Resources Bulletin, Vol. 13, No.4, August 1977, pp. 817-824. Moore, C. V. and T. R. Hedges. "A Method for Estimating the Demand for Irrigation Water." Agricultural Economics Research, Vol. XV, No.4, October 1963. Morgan, D. W. "A Time Series Demand for Water Using Micro Data and Binary Variables," Water Resources Bulletin, Vol., No.7, August 1974, pp. 697-702. Morgan, D. W. "Residential Water Demand: The Case from Micro Data," Water Resources Research, Vol. 9, No.4, August 1973, pp. 1065-1067. Morgan, D. W. "An Economist's View of Demand Projections Considering Conservation," Water Resources Bulletin, Vol. 16, No.5, October 1980, pp. 941-943. Palmer, C., N. Bills, and R. Niehaus. and Cooperative Service, Regional The Use of Input-Output Analysis, Washington, D.C., May 1978. 1-0 Concepts in Economics, Statistics, Development and Plan Evaluation: Agricultural Handbook No. 530, Penman, H. C. "Natural Evaporation from Open Water, Bare Soil and Grass," Proceedings of the Royal Society, Series A, 1948. Priestly, C. H. B. and R. J. Taylor. "On the Assessment of Surface Heat Flux and Evaporation Using Large Scale Parameters," Monthly Weather Review, Vol. 100, pp. 81-92, 1972. Reid, G. W. "Multistructured Municipal Water Demand Model," Water Resources Bulletin. Vol. 7, No.6, December 1971, pp. 1238-1248. Ruttan, V. W. The ECQnomic Demand for Irrigated Acreage: New Methodology and Some Preliminary Projections, 1954-1980. Baltimore: Johns Hopkins Press, 1965. Sammis, T. W., E. G. Hanson, E. C. Barnes, H. D. Fuehring, E. J. Gregory, R. E. Hooks, T. A. Howell and M. D. Frinkner. Consumptive Use and Yields of Crops in New Mexico. WRRI Report No. 115. Las Cruces, New Mexico: Water Resources Research Institute, New Mexico State University, December 1979. 155

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    Shell, D. L. "A High-Speed Sorting Procedure," Communications o,f the Association for Computing Machinery, Vol. 2, No.7, 1959, pp. 30-32. Shumway, C. R. "Derived Demand for Irrigation Water:: The California Aqueduct," Southern Jou:J:"nal of Agricultural Economics, Vol. 5, No.2, December 1973. Sneed, R. and R. S. Sowell. Agricultural Water Demands in' North Carolina: Phases I and II. Report No. 83. Raleigh,North Carolina: Water Resources Research Institute, The University of North Carolina, September 1973. Soil Conservation Service. Automatic Data Users Guide, Management Technical Note 1. Washington, D. C.: U. S. Depa:J:"tment of' Agriculture, Soil Conservation Service. Irrigation Tech. Release No. 21. Washington, D.C.: V.S. Department of AGriculture, Revised September 1970. Soil Conservation Service. Irrigation Water Requirements (TR21) (Documentation). ADP 6-9-69 Notice #3. Washington, D.C.: U,S. Dept. of Fort Worth, June 1969. Sonnen, M. B. A Model for Estimating Water Demands. Users Manual. Water Resources Engineers, Walnut Creek, California, May 1977. Spnnen, M. B. a1;ld D. E. Evenson. "Demand Proje'ctions Considering Con servation," Water Resources Bulletin, Vol. 15, No.2, April 1979, pp. 447-460. Southwest Florida Water Management District. "Agricultural Consumptive Use Explained," October 1975. Sowell. R. S., R. E. Sneed and L. R. Chen. "Agricultural Water Demands in North Carolina. Report No. 114. Raleigh, 'North Carolina: Department of Biological and Agricultural Engineering, North Carolina State University, May 1976. Thompson, R. G. "Forecasting Water Demands." Arlington, Virginia: National Water Commission, November 1971. Thompson, R. G. "Forecasting Water Use for Policy Making; A Review," Water Resources Research, Vol. 9, No.4, Augus,t 1973, pp. 792-799. Thornthwaite, C. S. An Approach Toward a Rational Classification of Climate, Geographical Review, Vol. 38, No.1, 1948. Thornthwaite, C. W. and J. R. Mather. "The Water Balance, Publications in Climatology, Laboratory of Climatology, Vol. 8, No.1, 1955. 156

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    Thornthwaite, C. W. and J. R. Mather. "The Water Budget and Its Use in Irrigation." Water. Washington, D.C.: U.S. Department of Agriculture, Yearbook of Agriculture, 1955. Thornthwaite, C. W. and J. R. Mather. Instructions and Tables for Computing Potential Evapotranspiration and the Water Balance, Publications in Climatology, Laboratory of Climatology, Vol. 1, No.3, 1957. Trevor, C. H. and R. Gross. Domestic Water Demand in Utah. Water Resources Planning Series, URWL/D-79/04. Utah State University, Logan, Utah, May 1979. Turnovsky, S. J. "The Demand for Water: Some Empirical Evidence on Consumers' Responses to a Commodity Uncertain in Supply," Water Resources Research, Vol. 5, No.2, 1969, pp. 350-361. U. S. Water Resources Council, The Nation's Water Resources, 19752000, Volume I: Summary, USGPO, Washington, D.C., 1978, 84 pp. Wehle, J. R. and H. F. Oleson. Determination of the Consumptive Use of Water by Agricultural Practices. Southwest Florida Water management District. Whitford,P. W. "Residential Water Demand Forecasting," Water Resources Research, Vol. 8, No.4, August 1972, pp. 829-931. Yamauchi, H. and W. Huang. "Alternative Models for Estimating the Time Series Components of Water Consumptive Data," Water Resources Bulletin, Vol. 13, No.3, June 1977, pp. 599-610. Yaron, D. "Empirical Analysis of the Demand for Water by Israeli Agriculture," Journal of Farm Economics, Vol. 49, No.3, 1967, pp. 461-473. 'Young, R. A. "Price Elasticity of Demand for Municipal Water: A Case Study of Tucson, Arizona," Water Resources Research, Vol. 9, No.4, August 1973, pp. 1068-1072. 157

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    APPENDIX A Description of Subroutines in WRE/SCS Model The subroutines used in the WRE/SCS model are described in the original references (Sonnen, 1979; and Soil Conservation Service, 1969). The material in this appendix is a reproduction of the original material with minor modifications. 158

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    SUBROUTINE DESCRIPTIONS Program DEMAND (Sonnen, 1979) The main program for the entire Water Demand Model is called DEMAND. It has two major functions. First, it drives the remainder of the program by calling the subroutine INPUT to read all the data cards and by calling RPTSET to print all the answers. Second,it performs the basic computations of water demand over time. A flow chart for the program DEMAND is given in Figure AI. / In addition to what has been explained already about the compu-tations in this program, here are some highlights. 1) Knowing the definitions of various DO-loop counters will help a great deal in following the workings of the program: N = counter for study areas; NOWD = total number. I = counter for output time periods;NOP = total. J = counter for subareas; NUM2 = number per study area. L = counter for land uses; NUMI = total number. M = counter for months; 12 per year (1 = January). 2) Connnon terms are: BSW(M) = monthly demands on system. BWSN(N,I) = annual demands on system in study area N. BWSI(I) = annual demands on system for all study areas. TW(M) = monthly total demands. TWN(N,I) = annual total demands in study area N. TWI(I) = annual total demands for all study areas. 159

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    Figure Al. No READ Run Control Data-'" All Constant READ Time Varying Data Land Use Water use Sub-areas' Land Use .. Flow Chart for Program DEMAND (Sonnen, 1979) 160 ..... .'

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    3) Since the arrays, TW and BWS, are written for each land use on ITAPE4 (line 79), these are really the monthly values of total demand and agency demand for each land use category in each subarea of each study area. These are printed separately or aggregated in various ways and then printed at the user's option. The subscripted variable ORO stands for "output report option" and is given a value of YES or NO as input. The report numbers for which YES is specified are the ones that are printed later in RPTSET. '4) The variable IFG2(J,L), which appears at line 48, is an index to signify whether land use L in the master list for all land uses in the simulation occurs in subarea J. When its value is -1, the land use does not occur, and the computations for that land use are skipped. The discerning programmer may that data are read for that land use anyway at lines 45 and 46 above. That is done because it is simpler to write ITAPE2 and ITAPE3 (in INPUT) for all the land uses and subareas, even if the data are zeroes, and then to read through the zeroes for irrelevant land uses in DEMAND. Subroutine FIND (Sonnen, 1979) While the subroutine FIND is also only 22 statements long, and while'its function ;is important in the model, its problem is much less difficult than the basic sorting problem. The purpose is to compare a number just read from the last data card with an already sorted array of numbers to see whether the new number occurs there 161

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    and to determine its location in the array. While this problem does noi. sound as compelling as the original sorting, nonetheless the subroutine to solve it is clever and efficient in its own right, and we acknowledge D. P. Russell of WRE's staff for its development. The flow chart is given in Figure A2. Subroutine INPUT (Sonnen, 1979) The subroutine used to read all the data cards, INPUT, may seem a bit involved. All the apparent complications are there really to make life easier, not more difficult, for the user. The flow chart, shown in Figure A3, gives the important steps that are followed in the subroutine. Actually, the purpose of the subroutine can be stated very simply. It reads a set of data cards that are constants throughout the simulation, and then it reads a set of data for each study area. Subroutine QSORT (Sonnen, 1979) This subroutine was developed and reported in 1959 by Shell. It was described by Gotlieb in 1963 as approaching the ideal in both minimizing the storage locations needed and the number of comparisons of pairs -of numbers in the array to assure they are all in the proper sequence. The flow diagram showing each step of the 19 required is given in Figure A4. While the flow chart given is accurate in terms of what happens, the user should not (necessarily) be dismayed to find that the logic of this simple-looking program is so difficult to follow. A numerical example, which is left to the reader, since we have been through one, is the best proof that it works. Suffice it to say that it does work, and 162

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    Enter with H. J3. lEND. IFlND. IS Figure A2. Flow Chart for Subroutine FIND (Sonnen, 1979) 163

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    Figure A3. !nt .. r Enter Initialize Variables Interpolate Acre. and SWL as Necessary Interpolate Water Use a. Necessary .rroDi DDWID READ FORK i Titles Run Controls Output Yesr In ut Years From DEIWID READ FORK 4 READ FORK 5 Unit Factors by Land Use READ FORM 7 Indoor Water Use Units To DE!WID \ Flow Chart for Subroutine INPUT (Sonnen, 1979) 164

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    Figure A4. Flow Chart for Subroutine QSORT (Sonnen, 1979) 165

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    extremely efficiently, for the problems at hand, which are to sort the land use category numbers of INPUT 1 and to sort for each study area the subarea numbers of INPUT2. Very simply stated, QSORT is entered with an array A of N numbers in length and, with another array, KEY, also N items long that correspond to theA array and that must be kept paired with the A array. The subroutine then puts the N numbers in the A array in order from small to large and puts the KEY names or attendant information in the same order. In this program, as an example, the land use categories are numbered and have a natne associated with them. For example: 1.1 Residential Single Family 2.4 Utilities and Transportation 6.4 Diversified Agriculture 1.3 Multiple-family Residential 3.2 Wholesale Business The numbers as read from cards are first changed to 11, 24, 64, 13, and 32. Then QSORT uses these same numbers as the A array and the corresponding names as the KEY array, sorts them through its miraculous process, and returns with the arrays in this order: 11 Residential Single Family 13 Multiple-family Residential 24 Utilities and Transportation 32 Wholesale Business 64 Diversified Agriculture This is precisely what is needed. The decimal point is now gone, but for internal machine purposes it is not needed. The subroutine FIND, described below, is used to search for a particular number in such a 166

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    sorted array. FIND is highly efficient only because the arrays it searches are already in ascending order--hence the underlying need to sort the arrays at all. If the user were always careful to place the data cards for land uses and subareas in the deck in ascending order, i.e., already sorted, the QSORT calls and the subroutine could be removed, and FIND would work equally well. QSORT is there because cards do get out of order despite the best intentions, and it represents an aid to the user who experiences the momentary lapse that is bound to occur. The user is implored to take advantage of it. Subroutine RPTSET (Sonnen, 1979) This is the second longest subroutine in the program; and like INPUT, it looks more imposing than it is. Again much of the elaborate programming has been included, not to baffle the user but to have the program solve some of the problems which may be encountered. A flow chart of the subroutine is given in Figure AS. The purpose of this subroutine is also very simple, it prints the answers. Most of the statements in the subroutine are there to get the answers into a form that will be useful and to specify table headings and spa"cing formats. The subroutine can be entered at separate points, all of which are called from subroutine DEMAND. The first portion of code is primarily directed to making it possible to have variable printing formats. Subroutine BLANEY (Soil Conservation Service, 1969) This program computes monthly and seasonal consumptive irrigation as described in SCS Technical Release No. 21 (1969). This program was modified by J. S. Rogers of the Department of Agricultural Engineering, University of Florida. 167

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    ITAPE4 Figure AS. Enter Compute Spacing and Output Formats Ent:er Enter Write Study Area Values From DEMAND From DEMANU ToDEKAND 2B Monthly Total. By A Study "Area By B Study Annual Total Area Flow Chart for Subroutine RPTSET (Sonnen, 1979) 168

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    The WRE model calculated effective precipitation using a formula for Hawaii. The report also shows the early formula of Linaweaver et ale as an alternative. The TR21 program has a better procedure for estimating effective precipitation. Thus, this part of the WREmodel was deleted in favor of the SCS procedure. The user should carefully review the TR21 manual prior to using this model. 169

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    APPENDIX B Program Listing 170

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    1 .., 1 _IJ..

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    7It Ir(DRD(2).EI. YES) CALL IEPT2 SIt 75 1006 CDMTIJIUE IS 74 ClLL REPSUII 71 STUP 1'1 11 DID 88 ; DmB' i5",J],mp,IEIII, IS) DIn Is ) C ., D'IMM 111 l .11=1 '12 8] J2=IDI 10 lilt !f(D.LT.") IlII TD 25 'lit as J)rJ212 2. A.XS, UFD(ItO, 12), PREClP(2,12) 11t11 115 CDnnDNILATERlCFl
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    130 131 1]2 m 1Jt 135 134 Jt 138 1]11 lItO 114 IIt2 Ilt7 lite 1 .... 150 151 152 153 15It 155 157 158 1511 140 161 162 1 165 164 167 ta t1101lO, 't01O, 10110, 10110. 0, 1 .... 01 144 NTA LllUC,LUCHMIIO,16011' 'I 167 OATil ISPftCE/IIH 1 148 NTft IUlltHaa! 141t OATA DUN 1'c1lUll1 170 NTft IKS IltHICS 1 171 NTA KIIIEll[) 1n NTA YES/'y[S 'I 17] NTA EJeF/'EJlDF'1 1711 C CJBIIf ..... I888IIII8IIHI888IJI_ ............... II_ ................. I8I. 176 C ........ IfIOIIBfI8l ........ ................... ____ ....... 177 C In C UMIMlS nP DESCRIPTION 111t C C ITITLE(2,10) A IlITPUT REPORT TITl 181 C NDU DR I IUlBEi II' STUDY MEM 182 C NIULUC I _I Of' UR LAND USE CATEIDIES 183 C NftILUC I _III' IIDIIJR LftD USE CATEmaES 1811 C NIP I _I or TIII PWIJ)S 185 C ORD(2) A IIJTPUT IEPllfT DPTIDIIS 186 C ICftLYR(10) I ClLIMI YEARS IF CIllPUTIITIIIt 187 C llUO(10) I I.IJIK LIST TO STVOY .[ftS _as 188 C MI'H10.8) A IIF STIY REA$ 1 act C HeTM (10) I IUlBEi Of' $til ftIIEftS PEl SlWV IllEftS 1110 C I UCOU (10) I llUT COST IF UIlTER ay STIV AIDS 1111 C IPPC(lO) I PlllJPDSEO PRICE BY S_Y MlEftS IIf2 C CIll8l .... I888111I8IIOOIIOS8III ......... I8lJ8II(I08IIfIIIAMIIf ........... IBIIIIOIIOIJ8O(.. 1 .. CI8III .. IIUI88OOIIIIUIlOI ..... _JIIIIJ8OIIUI ... IOII88I ..... JBI ... IIIIJllIIUIJBIIOlIR8lllllI8l. 1.., C C F1IftTS FDR INPUT FOllIS 5 10 1117 C 1. 500 FlIRIttIT(20AA) I1P1 507. FlJItMT<6X, 2,lOF2. 2) 200 508 FIlRMT<6X. D.1l(,I2.2X,I1.1X. I1,3J(,5(F5 .0.2X,F2.2.1X 201 202 510 FORnAT(6X,Il,lX,Il.iX,12(lX,FIf.O 203 C C FIIIIMTS FDR IIDII REPDRr 11 205 C 400 FDIlr.aT(lHlIIISql(,l2111D1'1 I(fIORT 1 1/ 207 PRImM; If DfUT II> 208 601 I ......... 1 ......... 2 ......... 3 ......... It .. 20q S ....... 5 ......... 6 ......... 7 .......... 8 I) 210 602 FDRMTVI> 2U 606 212 C 213 C SET UNIT NlIIIERS FOR f'DRT1WI lID UHITS 211t C UHlT 5 = CMII) REIIDEI 215 C UHIT 6 = LD PRIMTER 216 C lIIIT 11 = DISI( FIlE USEO TO DlUERT IIilTPUT 217 C UJIIT 16 = CMD REREftDER 218 C 21q c C IM=5 220 W IDISK=11 222 DIHII SPt\CR/' 'I 223 ITIlPE2=2 221t ITAP=3 225 ITAPIt=It 226 FIJIII 1.1 (mLE CARDS) IEAD(IH,501) (ImLE(l,K). K=1.10) IlEAO(lJ(,501> (Iml<2,IO, K=l, 10) 50 1 FIIIM TC lOX, 101114) C FlJRrt 1.2 (1M! CDJITRDl 11Ir8TIOII) 227 228 22'1 230 231 232 233 2311 235 236 237 238 2311 21.tO 21d 21t2 21U 21t1t 216 21t6 21t7 2 .. 2 .... READ(IH,502)MOU,MHJLUC,MnIlUC,HCP,(DAO(K),K=1,2),NDIP1,IDEr 502 II1II0 = NOlI C FUll 1.3 (CDnPUTftTIDM YEftRS) REIID(IN,50J) (ICftlU(IU),IU=1,HDP) 503 FIJRMT(1015) C FIIIII 1.It (IJIIUT US) REftO(IH,503) (ICftlR1(I1),IR=l,NDlP1) C FIIIII 2 (UftTEI DISTRICT DIITft) DO 12 H = l.NDU REAO(IN,50It)LLUO(N),(MUD(H,K),r=l.Q),MCTPUD(H), 1 IUCDUCH),IPPC(H) ,ITneN) 12 ClJHTIIftJE 501t C FDRII J (tNl US[ CATE;(JRY IWIES RHO l1li0) a = IIULUC + lIIII1.OC lUll = 0 173

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    1" 170 171 In 173 1711 115 "'4 178 I11t 180 181 182 18] 181t 185 186 187 188 1811 1110 l'U. 1112 lIB 1'" 1115 law IIf1 1. IIP1 200 201 202 20] 2011 205 206 207 .0 .d1 212 213 211t 215 216 217 218 21 .. 220 221 222 22l 22It 225 226 C DO lie K I: 1,1(( 1E8D(IK,505)ID1,ID2,(LUCN(K,L),L-l,lI) SET ErrECTIVE IRR1_E M:RES PER GIIIU ACE ErFA(l) II 1.0 U(Dl.tT.1> ;0 lO 1000 U(ID2.EQ.1> Ern(K) 0.10 Jf(ID2.EI.2) EFfft(K) 0.55 !r(ID2.[I.l) EFTAU) = 0.,. If(D2.EO.Ie) EFf8(K) 0.1t5 m lO ,.00 1000 IF = 1011110 + ID2 II1II1 = Hllll + 1 IX1) = K lit CIJII TIHUE 505 fDRnftT(6X,I1,lX,Il,T', .. ftIc) ctLL mJRT = LUCHCn,l) DO 222 K II 1.KI 222 lUtH(!C,l) = IYS(K) 220 CUMTtHllE DO 22l It = 1,KK n = IX1 .EI.ltALR1(J QJ TO 120 GIl TO 1]0 ITERPi(I,1)=J lTERP1(I.2)=J .... 130 If(ICllLIl.;T.ICftLR1(J-1>.8ND.ICflU(I>.LT.ICflR1 = ISPfICE .31 201t COIf TIIIUE 218 201 COHTIIIUE 2JII DO 205 J=1.2 2'10 DO m1 l-l,ItO DO 2052 II:l,10 2It2 ftCRES(J,L,II) 0.0 2'<3 2.,2 CDMTIIIUE 174 318 31 .. 320 121 122 ]23 32'1 ]25 326 327 128 32ft 330 3]1 J12 133

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    2051 CONTINUE 2'15 m CDlfTIHUE C lJt 335 336 337 338 ]]11 2lt6 2It8 2I4It 250 M. 25J 25It 255 25& 2'57 258 260 261 242 263 265 2eU 207 268 2e1 270 271 2n 273 21't 275 276 277 278 2711 280 1 !62 283 28ft 285 286 287 288 28It ZCIO 2'H. 2'12 2113 ZCh 2115 2116 2qJ 2111 2IPI 300 301 302 ]OJ JOI4 305 306 ]07 1O8 JOlt 110 t 313 DO 206 l = 1.1tO 1f1(l) = 0.0 PEC(l) .. 0.0 UCfI .. 0.0 ucrU(U 0.0 SU(U = 0.0 206 CllHTIU DO 2061 L=I,ItO DO 2U I = 1,MOP Cf'ICL,I> = 0.0 crU(l,I> '" 0.0 211 CDMTlMUE 2061 CDHTIIIlE 3110 31d. 3112 lIt3 lltlt 3115 llt6 llt7 l1t8 31t11 350 351 352 353 355 356 357 358 3514 360 3&1 362 363 3eU 341 368 3e1 370 3n 3n 373 371f 375 376 377 378 3711 380 381 382 383 381t 385 386 387 388 38'4 31fO 3111 31:12 3113 3'1't 31!5 3116 3Cf7 31!8 lIP! 1t00 1t01 Itt2 it03 1t0lt 1t65 it06 DO 208 L=I.1fO )"-1 208 Ir;2(2.l)=-1 DO 2081 L=I.ItO DO 207 '" 1. 12 IIDIHL,JI) = 1.0 IJ'O(L,ft) = 0.0 20 7 CDHTIHUE 2081 DO 250 L=l.1tO DO 255 J"'l,2 UHITS(J.L.1) 255 250 260 C REftO(KDME.260) UKITS(J.l,2) CIIHTDU: CDlfTIHUE R1RMT (1) C C C C C C C C C C C C DO 2O't J=I,2 IFGHJ) = -1 DO 2tO n = 1,12 PRECIP(J,ft) '" 0.0 210 CDHTIIIUE 201f CDJITIHUE flJRftS THIN 10 ftR REM ftI [ftCH STUDY ftID FDRJI it (SOO ftREft IIftIS) JJ = HCTPUD(HO) NUft2 :: 0 1'111 lq J = I.JJ REftl>(IM,506) IDl,ID2,(HCT(J,K),K::l,10) LLCT W, D2, (US11lfl0 t 102 stU it13 fIle Tt INDEX IF THE SNlE LAlfD USE CftTEQIRY DI THE ft 1t1'c LlLUC -fLftG 1IHD SID i\U lJillhHCIlED LOC las !t15 J THE DlDEX OF ItfITaD I Itid '" 1 InpUtS ft !OCCtSSflJl.. 1t17 175

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    C 1t18 311t calL flMD(ft,L,MUI1,IFLA',LLLUC) Ittll C 1t20 315 1f USlCU) 1t24 1 .1=1+12 1t27 122 crD(l,I) = USl(") 1t28 m 27 ClDfTIHUE "211 32It MT ft(ll1)UPftCE "30 325 D6TA(2O) lSJltllCE 1t31 lU QlTD2It "32 321 28 "11 321 2.. CDltTIIIUE "lit ]2q ISU=ISQ+1 "35 1lO IF(lC.LT .55) GO TD 11 "34 111 LC = 10 1t37 m URITECIP,'"> 1t38 m illITE (IP 601) "]It Dt 31 URtTE(IP,606) ml, DftTIl ItItO 115 lC=LC+1 "Itt 334 GO TO 211 ,,1t2 111 25 CDHTIHlJE Itltl 118 URITECIP ,602) ,,1tIe ]311 LC=LC+2 ItIt5 C It'" C f1II!II DATA TYPE = LI\HD USE Itlt7 C "'" }to 33 cmfTIIIIE "IA 3Id. IEAO(DI,500) MTA Ja If 1M FllRM IS THRU 10 1t711 C TO M.UII THE USER TD IHPUT DHl 'f TIlE 8-2ERII MTA. 1t75 C 1t74 1S1 311 cmtTnu: 1t77 l58 If"t
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    m DO .... K 1,10 502 l7It I1-D+l 50] :m $&l(Jl,J2,IR) = US2(IR) SOl! ]74 AClES(J1,J2.IR) = US1(I) 505 'HI It[lIalSEl+l 506 318 U(lC.LT .55) gJ TO '" 507 ]lit lC -10 501 lIQ IIITE(IP ,600) 501t 11 UlITE(lP ,601> 510 A2 1t4 IIITE(IP,404) lSEQ, MTA 511 18l lCalC+1 5U JIll GIl TO D 513 315 lit CllHTIIIE 511t lIW IIITE(IP,402) 515 187 lCalC+2 516 C 517 318 lID 1,. J=1,2 518 ]lit U 550 IdS 153 CONTIIIUE 551 It1"1 152 CDltTIHUE 552 It 151 CDHTIIIUE 553 .. 21 DID fILE ITftPE2 5511 't22 DO 6 12=1, It80 555 It2l 6 ft
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    .... If CD TO :150 5V I6S IREftD = 5 ,. It57 IlIITD" ,,, .. 550 IRE. .. IIIIPl 400 It5II I1"S 401 It60 DO 57 K = 1,IREftD 602 It61 I1=IR+1 60] IIQ 57 UUU(J1,J2,IR) = USl(K) 4011 It6] 56 ISEQ=ISEQ+l 605 IF(LC.LT .55) ;0 TD 58 404 It45 LC = 10 607 It66 URITE(IP,600) 608 It67 UlITE(IP ,601) 60'1 It48 58 URITE(IP,604) lSEi,MTA 610 It4II lC=lC+l 611 1t1O QlTDSO 612 "71 51 CDHTDIUE 613 Itn VRIT[(IP,602) 611t 1t73 LC=lC+2 615 C 616 '4711 DO 350 J=1,2 417 1t75-If(IfGl(J,l5O,]55 618 1t76 355 CDHTLIU 61q '477 PI! 360 L=l,1tO 620 1t78 621 1t1'f 365 CDHTIHUE 422 1486 DO 370 I = 1,NDIP1 623 It81 ]70 US2(I) = UUU(J,l,I) 621t It82 DO 380 I "' 1, lflii 625 It8l HX1 = ITERP1(I,l) 626 I.QIt NX2 = ITERP1(I,2) 627 5 MY=ICftLR1(HX2)-ICAlR1(HKl) 628 -46 If (MY .HE. 0) "' TD 375 It87 UUU (J,L/I). US2(NXl) 630 ... CD TD 380 631 It8II ]75 R = flOAT (ICALU(I 632 W R1 = flDAT(ICftLR1(MX1 633 ItII1 R2 "' FlDftT(ICftLR1(HX2 6Jt C 635 IfII2 UUU(J,L,I) = US2(NKl)+(US2(NX2)-US2(MX1I(R-I1)/(I2-R1) 636 C 637 ItI(J 380 ClPfTIIII: 638 .... 340 CDlfTIIIUE 6]1t ....., 350 CDIITIJU: 61tO C 61d ItII6 IEUI. ITftPEJ 61t2 ItIf7 DO 351 I = 1, HIJI 61t] .... DO 352 J = 1, MUII2 61f11 ItIIII 00 ?i3 L "' 1, HUII1 616 500 URIT[(ITftPEl,]5It) UUU(J,L,I),UMITS(J,l,1),UHITS(J,l,2) 61td 501 351t 6lt7 502 353 CDlfT IIIUE 61t8 50] 352 CDMTIIIJ[ 61t11 50It 351 CDHTDIUE 650 505 EItO mE ITAPEl 651 C 652 C FIlII 8 DATA TYPE INSIDE F 653 C 6511 504 cS 1 CUM T.DIIE '" REftD(IM, MTft 656 508 Ir CI TD 6l 657 !JOlt 658 NTft(20)=ISHC 4511 5U URITE(MTft80,5OO) MTII 660 512 IlEftO (DATMO,510) IDl, 1. (US2(I),I=1,12) 661 -u II=1Dl110 + ID2 662 C 643 nit CftlL FlJID(n,L,MUII1,IfU',LLLIJ:) 6c111 c cScS5 515 If( IFL'" EI.1) QI TD 40 466 5U NU(20)=ISl ,61 517 eDTD6It 441 m 60 cnHTIHUE 66'1l 178

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    DO 45 (.1,12 470 520 65 YOR(L,() :I 1S2(r) 671 C III) I(GAL/ftU. no. ) 6n 521 6" CliMTDU: 47] m lSEQalS[Q+l &7It m IHLC.LT .55) liD TO 67 SlIt LC -10 676 525 UlITt(IP .'00) 677 'H UlITt(IP ,601) 678 67 URIT[(IP,'06) lSEII, MTA 47'1 '28 LC-LC+1 680 5211 liD TO &1 681 530 63 ClJllTIIIUE 682 5J1 URIT[(IP ,602) 683 m LC=lC+2 6811 C 485 C 686 C F[III q MTA TVPE IIITSIOE 687 C 488 m Lq 1 6 ... 9t 70 CllHTIIU: &110 535 !lADel0,500,EMD=11) MTA 6111 5lcS IF(DI'ITft(1) IiO TO 71 6112 537 DATA(1q) ISPAC 6 If] 538 MTft(20) ISM 5]11 URITE(DATA80,SOO) OftTA 6'f5 5ItO !lAD(OATftSO,510) ID1,ID2,(U$2(K),K=I,12) 61f6 5Id. It 101-10 + 102 &117 C 6. 5It2 CALL flHD(n.l,HUK1.IFlAG.lLLUC) 6" C 700 5Itl If 71te 5'tO A(I>=ft(U 7"" 5'U 750 5112 KT:o([Y(l) 751 5113 KY(I>WEl'(U 752 1'Q

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    ISO

    PAGE 189

    C t C C C C C C C c c 181

    PAGE 190

    C 1120 cS86 URITE(IP,IrnT2)eICftlYlCI),I=I,MDP) 1121 687 DO JO L = 1,1100 "22 688 LUL,2) = 1123 ... U(L,1) = 0 112't 6'10 IL = LLLOC(l) 1125 At 1ft = III)(ILI0) "24 6112 IFClft.EI.O) n = L "27 If(Ift.EI.O) LL(L,l) II "28 ;It DO 28 I = 1,HIII ,,2ft A5 ftCRES(J,II,I) = ftCRSeJ,II,I) + ftCREseJ,L,I) 1130 6IW ACYT(J,I) = ACYT(J,I) + ftCRES(J,L,I) IIll 6ff1 ACYn(II,I) = ftCTft(II,I) + ftCRES(J,L,I) "32 At ACTYI(I) = ACTYR(I) + AClESeJ,L,I) "]] 6'Pf 28 ClJlfTIIIUE "lit 700 30 CDHTIIIUE '135 701 DO 51 L 1,111111 "34 702 11 1137 70] = LUl,!) "38 70It IF(II.EtI.O) gJ TO 51 ,]II 705 UlITE(IP,IFnTl)(LUCMCn,r),K=I,II),eftClES(J,n,I),I=I,HDP) IlItO 704 51 COHTIHUE IIId. 707 .. 708 1t5 CDHTIHUE qlt] C II ..... C WITE REPORT 18 q", C (ft SUIIIMY or RE,...T 1ft fOR THE ENTIRE SW ftREft) 1I&e6 C 1I1t7 7 ... UlITECIP,400) (CITITLE(I,K),K=1,10),1=1,2) "'" 710 URITE(IP,602)IDST,CMUDCIDST,K),K=I,II) lilA 7U URITE(IP,IrnT2) (ICftLYRCK),K=I,HQP) "50 712 DO 71 L = I,HIII1 1151 713 II = 0 1152 IL = LllOCCL) 1153 715 1ft = OUL,10) q", 716 IFCIA.EO.O) II = L 1155 717 !F(II.EG.O) GO TO 71 "54 718 URIT{IP,IFnTl)(lUCHCn,K),K=I,q),CAC'lCII,I),I=I,HDP) 1157 7111 71 COHTIHUE 1158 720 11511 721 RETURH 1140 C 1f61 2 ENTRY REPT2 1142 C q&3 723 REUIlfO ITftflElt 11411 72't DO 1000 I = I,HOP 1145 m IFIm = 0 q66 7U IFCI.QE.ITn(IDST IFITII = 1 1167 7'1T U(ITn. LT .1) IFITII = 0 q68 728 III = nDl)(ICAl. '(RCI), 1) 11611 7211 DO "" J = 1, HUft2 "70 730 DO 1001 n = 1,12 1171 731 BUSHn) = 0.0 qn 132 TULHII' = 0.0 q73 73l DO 1001 l = 1,HIIIl q7't 7Jt TUlnCL,n) = 0.0 q", 735 1001 CDHTIHUE q76 73& IF (IIIITHS(II),11=1,12) 1181 7ItO 615 fCSlMH/I5I!X,lItHUDIt RUIm 1ft I 1182 Y DDtNIDS III BUS MTEII -IIlIII q83 255X, ftR[fI I 1fItlI, 81, 5tfYEftR=, I6) qllt 7'd. FDRMT<1I6X,17iUMD US[ q85 ru "5 DO ft l = 1, HtIII1 1184 7Itl IF'(IFI:2(J,l).EQ.-l) GIl TO 'IS .. 87 Nt .. 88 7'15 U(III.HE.O) '0 TO IN ... N DO l1li7 II = 1,12 "110 7147 BUST(II) = BUST(II) + &US(II) "'11 714 TUlT(II) = TUlT(II) + TUCII) .. 112 Nt TUln(l,lI) = TUlII(L.n) + TU(II) "'D 750 Iff7 CIIITIHUE .... 751 URIT(IP,620)(lUCM(L,K),K=1,8),(8US(II),lI-l,12) q", C M(n) II BUS DE,. BY lftll> USE IJI EM:II /IINTK .,'" j2 QQS CDifT.DIU[ qq] m If'(III.JC[. 0) TD IPPI "'II 420 FIrilMTC8ft&t,12F7 .1) II'" 755 421 1000 756 URIT(IP,621) (TDTAlS(I),K=l,S),(BUST(II),ft=1,12) 1001 C MT< II) = TOTAl BUS DElWtO BY !lllTH FIll THE STUDY AEft 1002 C 1003 182

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    7I:fIf MlIlOOTIIi: Bli\llty 1012 Boo REAL tHy 1m 1m I!Al n,I(ILn,WJ,nClS),mU6(12) 107'4 802 1075 C 1676 00] 1077 c 1078 Ij _..5 IJiIl'iCWlIllll 1nl'l$(25) ,f(l5) .IJIGH(2;5) I.Ir.lllhH25), GIiI](25) 1080 1081 007 1082 808 smil\E(25} ml'IlJ(25), SDftM
    PAGE 193

    185

    PAGE 194

    1155 '& 1!57 It58 l15li IWO 1161 IW2 -, .it It65 '166 1167 'WI l16'li tt70 m IJ72 m If7It If7'5 1176 1177 1!78 'i8O qaj, rt82 qsJ ... It85 't86 1117 .. ... qqo Ipt1 l1li2 ] ...,. IfII5 IPI6 Iff? qqe .,.. 1000 1001 1002 1003 100II 1005 1006 1007 1008 100q 1010 lOU 1012 1013 101 .. 1015 1016 1017 1018 10111 1020 1021 1022 ''123 102lt 1025 1026 1027 1028 102it nn .. o 1253 1t2 IItOH(I>=O 12,. It] 1-1-1 1255 125& UftDH(I).unDH(I)If(DftYS(I+l)-tEG)/(DftYS(I+l)-DftYS(I-l 1251 IF (0-365) 1ttI. 50. 50 1258 Itlt DO It6 L-l,25,2 12,.. I=21t-l 1260 IF(DflYS 1278 KI=sunu/SUIF 12711 IF' (KI-U 52, 52, 53 1280 52 KftI)J=I. 1281 I:lJ TO 56 1282 53 If (KI-H) 55, 55, SIt 1283 5 .. KflDJ=KH 12811 QI TO 56 1285 55 KllDJ=U 1286 56 ftDJ=KAI)JIKI 1287 C----ftDJUSTED nlllTll Y CIIISUIIPTIlJ[ USE -------------------1288 DO 57 1=2,2",2 128'1 57 unDMft(I)=UnDH(I)IftDJ 12'10 C----ftDJUSTED CDMSUnPTIUE SUllUI\=SUIIJ .OJ 12112 C---[ffECTIU[ eY lDfCDLH ]-83-611 -----12'13 58 rtMX=l 1291 ftPfIF'-om:HHft, ftX, NIP I tYPX, tYPFX, IIIAX) 12't5 DO qqq I = 2, 214,2 12116 Cffl RE(l) 0.0 12117 DO 68 I=2,214,2 12. ftTID=GRD(1+l)-QRO(1-lIf(LEHKCll00. I(DftYS(I+1)-DftYS(I-l 1300 65 UllJHX = IIIDHIl 1304 (,8 CDHTIH 1307 C-----------EJID Of PRlllMn Clll\1IG[ 8Y LIHCIlH----------------1308 13M DO 611 I=2,21t,2 1310 3H CftlL IRRIG(1l[ ,UIOIA,CII, XIRII, XIU) 1313 c----IfET CIJIIl.TE PRINTOUT 131 .. 75 URlTE(6, (30)(ISTAR(I),I=1,56) 1315 !lUTEC', 6'tO) 1316 URIT[(6, 6JO)(ISTftR(I),I=1,56) 1317 URITE (6, 600) 1318 DO n .1-1,25,2 13111 I=J 1320 DftfS=OftYSCl) 1321 UlUT(', 5'tO) SIIIM8(l),SIJM[(l) 1322 1=1+1 1323 IF (1-26) 74, 77, 77 1321t 76 URITE (6, 570) IIJH(l), TEJII(I),RT,F(l),n(l),KC(l), 1325 lUIIDH(l), 111'*"(1),1[(1), SIIIJ8(l),SIiIlJ(C1),XIRII(1) 1326 77 CDHTIJIU[ 1327 IIlITH6, 6SOH1DflSH(l),Ist,111) 1328 IIRIT (6, 580) 5mr,UU,5mIM,SU\'lR,SUIlIB,SU.,XIRS 132't c---GRIISS 85 URIT(6, 550) 1331 UIlTE (6, 7(0) (ISTAI(X),I=1,2'I) 1332 URITE(6, 730) 1333 YRlTE (6, 760) (IS1"(1),1=1,2'I) 13Jit UlITE(6, 7'tO) 1335 DCI U K=5,I6,' Uld OJ:

    PAGE 195

    10]0 I=5H 1031 IEFF-55+1 1032 pI 10]] Efr-o.55+t1100.0 10:JI MIllaXIRSIEf'F 1035 84 WlTE (4, 750) IEFF ,MllIII 1034 CM.L IIITPUT( IJS*'E,XIIII ) 1037 CO TO 15 18 87 UlITE(10,640) 440 FDlKAT(IEMDrORftI) 1M RTURJI 101d. DfD 1337 1338 13311 131tO llltl lllc2 llitl llltlc llltS ll'" 13lt7 lllt8 C --11 FlMCiliM .tid". DiiIlI PERF. SIHiJU liD DIi08L -D5O C---lDiEM INTElPlUnDH------------------------1351 101tl DltlEMSmM AX(:JI) 8X(12) ,CX(lt08) 1152 C 1353 101t1t 11=0 115&l 101c5 1 11-"+1 1355 101t6 IF (AXOO-A) 1, 2, 2 1356 1 ... 7 2 11=0 1357 1N 1 H=lf+1 1158 101t11 IF (9X(HHc) ], It, It 1351t 1050 If J=fI+ftllftXl(H-l> 1051 .ll=J-l 13tU 1052 JM=ft+ftftAXI(H-2) 1362 1053 .IIM=JlI-1 1343 1051t IF (n-1) 5, 5, 8 13614 1055 5 If (H-1) 6, 6, 7 1365 C---fI=l, 11=1---------------------------------13" 1056 6 C=CX(J) 1347 1057 m TO 11 1168 C--ft=1,M 1-----------------------------------13611 7 l)::CX(J) 1370 10511 E=CX(JH) 1371 1060 8lATa(8X(H)-9)/(8X(M)-8X(H-l 1372 1041 C=D-(D-E)'9RAT 137J 1043 8 AlAT=(AlH)-t\)/(AX(H)-AX(ft-1 1375 1061t O=CX(J)-(CX(J)-tX(JnIARftT 1376 1065 IFOf-1) II, II. 10 1377 C---ft 1. Hal---------------------------------1378 II C=D 137ft mrou C---tI 1,H 1---------------------------------1381 1048 10 lIRl'T=(8XOI)-9)/(8X(H)-8X(H-l 1382 10611 E=CX(JH)-(CX(JH)-CX<'JIHJl8RAT 1383 1070 C=O-(D-)I8RAT 13111t 1071 11 DOIHT=C 1385 lOn RETURH 1386 1073 EHI) 1387 C----SU8ROUTIH CIJIIUTES l'UITIlY SWDHIIL 10.---13110 1075 01nEHSIDH "AIH25), uratft(25) R[(25),SIlttft9(25) I sonU8(25) 131ft 1076 DII1EHSmN SlMAE(25),SIIIUE(25),XIt"(25) 13112 1077 CDllIIIH SDftIl[, SDIlI[,SllMB,SIIII.-,IIftR.SUftIJ[(,SUIlUE lJ'G C-----UATER 1078 00 1 1-2, 2it. 2 13qs 1 YAI(I)=UnDHft(I)-R[(I) stIlSON CMRYDUER---------------------------131f7 C----SDtL /lJISTURE IWtiLII8lE ---------------------..--------13. 1080 SDftM(1)=CDl2 13 .. 1081 00 3 1=3,25,2 lit .. 1082 SDftftr.(1)=SDftft8(I-2)-uftR(I-l) 1083 1f=O litO] 1085 3 CDMTIHUE C----SUIl IIlISTURE US[D------------------------llt05 1086 DO '" 1=2,2'1,2 11t04 1087 '" SliftUB(l)=SDM9 11t07 C-----EltD $EASOM CARRYlJUER----------------------------------11t08 C---SDIL IIIUTiJR MllULMlE -------------------------1Itoq SllltM: (25 )=0 1"'10 1 00 6 L= 2,214.2 lieU .... I=25-l 1lt12 lOIn li113 101t2 If (SIIII'I(I)-CD/2) 6,',:1 litllt 10-0 5 lit 15 101Jt cS CDHTIHUE llt16 C---SDIl IIIlSTtME USfJ----------------------------llt17 loq:j 00 7 1-2, 2't. 2 1"'18 187

    PAGE 196

    . "2 J 110i1 1105 1106 1107 1108 c lID 1112 10 1ill lUIt mRV URIT[(10,10) g RETtmM 00 STATEHEHTS EXECUTED: 0 CIlREIWtG ClllPIlE TlI'IE= C$STlIP sec, 188 I), un OF [l
    PAGE 197

    APPENDIX C Sample Data Forms 189

    PAGE 198

    I-' \D o Coded. b)' _______ Dote __ 1 __ 1 __ WATER DEMAND MODEL INPUT DATA FORM NO. I GENERAL RUN CONTROL DATA Poge __ of __ .1 r PH] 11 TITLE OF WATER OEM;'.ND PROJECTION TO BE USED IN REPORT TITLES (Center in col. II-50) FORflA1 (10 x. IOA4l 1.2 NO NO REPORT NO. OF .' (YES OR STUDY SUB LAND YEAR DATA TYPE AREAS AREAS USE NO. I : \ 2! 3! 41 (f.l; i 6] 11:: ii [:.t: IE! Ii! lei !si:.::' 7!17.: ill Ill! ILL: I 11'1! ::jOiNI,iR;OiLI FO'it.'.AT (4 (3X, J2l, 7(2X, A31. 2 (2X,I3ll ... IDEF = 1 = PRICE ELt.STICITY 8!.SED ON OLD PRICE E.. IDEF = 2= PRICE EL.c.STICITY 8!.SED ON AVG. PRICE [. DEMAND

    PAGE 199

    I-' 1.0 I-' Coded by ______________ Dote __ I __ I __ STUDY t-.REA NO. STUDY AREA NAME WATER DEMAND MODEL INPUT DATA FORM' NO.2 STUDY AREA DATA TO eo: USED IN REPORT TITLES (Ce .. !er nome in col. 9 44 ) NO. OF SUB ,.1 AREAS UNIT COST tJF WATER ($/1000 gols) PROPOSED ... I PRICE CHANGE AMOUNT Tl""E ?oge __ of __ DATA TYPE t-1!S7 jq 17 r!: j?411'!. in" i"'t Ie.:; II.! .1L I I I 1 I.I! j I r .. I IA .. + I-t .... +--+-i-I ..l--:I l .j i-lj I I T I I I I I I-;, .. ..... I j-l I I I 1 IpTTI I 1:;<;11 1 I I liii 1 i.i 1 i I I!J 1 I 114--111111 i ":1 -I 1 t!' ; '. 1 1 I I L I I I I [ ; i 1 ill 11 I I l' 1!,1rrnl' I I ,I I 1\111J I-!' II I II I : i j i I I I I I i I I I III II i I I II II II liTI rl IUli TT1TTlrn lllTf! i ill I 11TI; i lTll iAIRIEIA '.1 : : ; rn 1TTT1 11 I Ii II rrIlITTll-ITT T1TTTfTTT1TllTnT1TTTi; l :1 I I ITI j r I I iAIRIEIA llTTTTTlI I I II I I II I I I II I II II I I II I II I I I I I-I Ii II III nTI i I lj IIII I jl II :IAIRIEIA ; .... 1 III I j n Ii IAIRIEIA 11 [TITTJJ-mTITTI-1 I l !l 1 I IIjAIRIEIAI I I I FOR:.',AT t ,x, 13, 4X, 9':'4, .X, 13, 2X, F5.2, SX, F5 2, 3X, 12) ""!.dI.T:: OF 221(E.,$/1000 go\ lUJ,E = O'J/?UT (1-10) Ch,UJ':;[ IS ,0 OCCUR

    PAGE 200

    F-' '" N Coded by ______________ __ DOle _1 ___ 1 __ LAND WATER DEMAND MODEL INPUT DATA FORM NO.3 LAND USE CATEGORIES Poge ___ of ___ USE LAND USE CATEGORY NAME DATA TYPE CAT. 1 I z 131 -1 [ I I i I I I I I I I I I Ii ItT> I.> i [I, r> rl [lhll: Llu C AiTI.) l3111. k. I I! I I IIII I II I I 1< I> ll!!LluIICAITj.1 Ell; /1 1.1 !! I i I I I I I I I I I I I IttCFl.l!i fii ILII Llll L!U CIAITI; I Ii I I! I I i I i I I I I I I I fT1JJfll Llui ICAITi.! /II.j I.; It! II I!! I I I II III I Ii! kL!r>ilrrLl l! Llu! Ic,AITI.1 il Ij I i/ I I l'l! I I I I i I I 1.;CkfJll+! jill j/ll L!U: iC,AiTil ri.I .. I Illl I! I I I I I I Iii trL ,< [c. hi hi Til ;1) II ':uj IC;AiT;.i >/ 1.1 h i!! I I I I I I I I I i Ii /C>tHJlf'ltlIAn! L!ui ICjAiTi. i >11,11 I i I 1'1 I I I I I I I I I I I I I I il< if} i ,rllill j I; Liul IC[AiT:.1 1.: I .!! II!, Ii:! I II!! I! I! II 111+ '.' .. / t) i.AI!l!llldj l!LU: !C:AT:.! tllii i.1 L iii I II i: I! i ill i!;!! III II \1'1'/11.\ IrllL! '11; is L:U: :C:A!T:.I bLllt;!:;:II!1 II Iii III Illllilll 11!I) liTT J11<1i!f Llu:iCA!Ti IIJlti t.! It i I I Ii: I i I I I I I! I i!C".b2{' t< li HI.I>JJ[.j L;U !cATi.1 I') I !< ;"1 i I I I I I I I I I! I I I .h;.iT>; I [ l!lrl Llu 'ctATI.: I ....! iii I: i ; [ I Iii! I I I I I I i[itt> }J>I. i itll LjU; :C:AITII ,",,,,,1 I i\ !! I I I I Iii i I! I I I i I I I I(i.d.\/i! fli>lt I LIUI IcIAiTI.1 r ..... IA!.I I I I I I : i I I I i I I I I I I 1 ... i>+1 } liT:>! ItLlllljillLiu, IcIAiTI! IllljLl! I i II I I I 1 I I:! tllrr!ItL>lllfjFlt L'uIIC[A:TI.' 1 j j" .J. "., I I 1.--: J,.-i .1.'--" '" ,_,f. :'.'.,-.". 1 ..... ."' __ .0..-. T ,'1: .. -f-{ __ .;. .-.. j I I I>.'! k!TTT I I I 1'1 I I I' -----1 I .... I,'-t'I'.Il.,-, ... I' i'l'! '1.1 "----: --I '-1 I : II;:: rritt' ': I,,> ... '*:l;.L'Ill,I;L!U: ;C:A!T,. 1111< 1.....l-f8 +J I : I I I I I I I 111'lliFlill+!HJl .. L U !C,A;TI.I I I::. I I, I I I : I : I I 1 I lili/. I;! L u ;CiA;T! .1 I : I-Hr-; I I I I I.! II I 1 I I I I i 'Iii> k>JlhlLlflllfllllll L u [cIAill.1 j IT1 I I Ii! I! i I I I I I I I I I I CUi..} 1:1+:Fllflllllil! 1111 Llu! !cIAiTI.1 I! '2 3: .. ; i l' e 19! 10 it 17i1S: 1'311'0:21 :!!l;3. ... .. FORMAT (6X, 11, lX,Il,T6,9A41

    PAGE 201

    I-' \0 W Coded by ______ DOle __ I __ I __ WATER DEMAND MODEL INPUT DATA FORM NO.4 sua ARE'A DATA Poge __ of __ STUDY I SUS SUB AREA NAMES AREA AREA TO BE USED DATA TYPE NO. NO. (Cenler nomE In col. 16-45) 121114 t fi 171 t!:-l2QZI Z2 :'!i:2'(' 1.1 '1btnfnl1'!-1&'i ;1:1 I :,1 '!:j i I g : n *-I,: :1' 1-i-I.::.::: i .. -f;t : : .< :: .' .:-1 1:1 L!di.f':11_'l'!!H!:.ll-JldI1! .! __ !l-; SUA E A I,; i m 1 ,,-,., I '1','-' -J.! .. ,-'1 dj,IW I! 1 ,lS U A E A t +tufffllt1fITITi HImHii.:g 1 1-:1' 11:1 i-' i ltd i j j '.1 .j II fj i '} 11.j i'1 II l i 1 j .js U A E A kll'_:) t'! I ": :i :.1':1 J ; 1.1 J J. I -l-1 l 1 1 1 j i SUA E A ;.. ..., "-'j I I 'j l ., .. :., .. j' IJ I I I 1 ... Is U A E A ::j i oj i 'J::;:! .j I' .! 3 -i .... :! j ; ; 1 .. .1 'T:;;'! i [-H-1" r It !.-! I 'i IT! 1 U l j I 11 i i j l is U B A E A I :1 ):'1.' 1 .::! ,,+
    PAGE 202

    I-' \.0 Codec by ____________ __ Dote __ 1 __ 1 __ STUDY AREA NO. LAND USE CAT. I. 12 I : I. 171 E 1 -I "'1 I:m I I !'H1 1.1 F ;:::;. f2ITl.. ":'l I ,.;.];j 1.1 N INSIDE WATER USE. UNIT FACTOR !'"'''I:t.!'"! .. I t:[ I ;'i It! : If4 I i:ii :ij I hi,@l I H I it] m I I ,':r ftN i'OJ!"' l'Ji'!' 'm. M' PRICE ELASTICITY COEFFICIENT (ENTER _. SIGN 1 W;lflj'" WATER DEMAND MODEL INPUT DATA FORM NO.5 LAND USE UNIT FACTORS INSIDE WATER CALlBRA.TION FACTOR IN OUTPUT PERIOD: '. -OUTSIDE WATER CALIBRATION FACTOR IN OUTPUT PERIOD: "** Poge __ of ___ DATA TYPE I 4 I 5 I 6 I 7 lAlclTlolRls IFIAlS:1TloIRls lAic liIolR Is I I:fiJFlA Ic IT IOTR Is 111111111111111111 II m:;::lFIAicjTloIRiS IA IcTilOIR is lAic ITiojR is ttt:JF !Aicli!OiR:S .,)2 --.-'1 ,-.-, "+' I I II I 1 I I ; I II II I I ; I I I 1.....1-:1 I Ii' I" :'"I'i'; F!A!C T:O'R!S I II I I I I I I' I I I I I I I ::n" F!A!cITlo'Ris FMM/lWI I! I I! I I I I r I! I I I,; ""FiArCjT!O'RS iFl:l':t% I I I I I I i I 1 I : I I ;J F:AiCITiOR-:S I! : .:i !.1 : ;t f+: I 'til +:1 '1 : : ":lj:.11,::: I III I I I ;;ji I: I::,j i i:i 1:':'11 t-r I ',,:1', .1: f I I ",:l:,J::]Hh'i I ,I -! .. !I If FIA!c TiolRis! iii!! !i-lrllti: I i:i l1-I i
    PAGE 203

    I-' \0 Ln Ceded by _______ Dole __ 1 __ 1 __ STUDY .AREA J ':<;1 1 ':1 .. J ., ":, ; .. t -; i ., .. :j SUB AREA NO. I! Ii : Ii 1++' A 1 i i I 1:, Lt...ND USE CAT. WATER DEMAND MODEL INPUT DATA FORM NO.6 LAND USE AND WATER SUPPLY DATA Poge __ of __ Y EAR I 1 BEGINNING.' END I DATA TY?E ACRES SWL ACRES SW:L 1 FO;::,',AT ( EX, J3, IX ,12, 2X, J I, IX, J I, 3X; 2 \F6.0, 1 X. F 2.2, I Xl) 'SWL=DECIMAL FRACTION OF TOTAL WATER SUPPLY TO THIS lAND USE, IN THIS SUB AREA, SUPPLIED BY OTHER WAHR SOURCES PRIVATE WELLS AND THE LJ KE.

    PAGE 204

    \0 0'\ Coded by __ ________ __ 1 __ 1 __ STUDY NO. SUS AREA NO. LAND USE CAT. WATER MODEL INPUT DATA FORM NO.7 ANNUAL INSIDE WATER USE UNITS INSIDE WATER USE UNITS!!' YEA R Pcge __ of __ UNITS DATA TYPE BEGINNING 1 END !, '-'-1 '-'-"-"1-' 1-."'--; 7": '-'-1 "'I-'::;,ol'-"r-c:112T: 1"+I,"T41,::-T'i-:-;""-=-,7r-c:1 ;11 '-',"I":" 1"'137 !"I,*"I. i4'!;) "'!'""i70"r'I" T":")Tr i" i7'!'" 1 1 1 I I. I b.'i.' J.J I. B.1.'. I !!11!J I 1\ I .. : liLJ1Gl:tljiFrlrfij.f+ 1 I LLL II I. wIJI 11 1; Iii I I 1 Ii. (TiL l. Ld],cI"h,; HJr ( 1.);[ 1 I: I Iu FIT 1l:,l!J1l:j I I II J.LII 1'111 1<11'T[j11 I I I I ,'I4'H:}r 'rdx"':{XLgi'lt!L'. I I !N:si I iDIEI lu :i i:q I>J>! i.1 1"'Jld I I I I t I [.::; Fd:f':::Li).k, .>:. Tl ITTfPT11II'J .. '-.. :.lTITL!111111tl i i 11 I II r r :. 1-: ... 1 i "1 11J f i I I t ,... IJ I i :-1 11 f:
    PAGE 205

    i-' \0 "'-J WATER DEMAND MODEL Coded by ________ INPUT DATA FORM NO.8 MONTHLY INSIDE WATER USE UNIT RATIOS Dote __ 1 __ 1 __ Page ___ of __ STUDY LAND AREA USE DATA TYPE NO. CAT. I z 131 -4 5 CiT Ie, Fe) -liz 14115 ;& 171:a !:!ti2 21 zz 23fZ" 26 272829 _x 31 32 U 34 .36137 38 39J.ao 41 42434.445 4i -47 48 .9 50 31 56 571!08 39160 61 621631&4 U T 68 69 70 71 n .5 1BlnJeo ".' :;:::::::::1 :];:: ::;:::! I I :: I :;!:i; I :::::1 :!ili ;:;:1:1 :::\:,!! i :1:;: I I I : : i r i I! f:!l i II:: I II I I J +!!i FI r i I",{ bl-II [;';,I:r i : I t: .. t l it r 1 i i i : ; i i =! i : i i ; iii! i i i : t ;!!! i i = i i :!li: :: 1<;:;, ::i K 1 IT = iii i I! i : I i H i = Ii! i i:1 i i = i! ;: i i = : Ii : !:I:!: : : "'11.1 il\j I rrhlill (::.:::i IIII;J,III I l:t:1 IIII::M I i I (;;::':ll IllMl : i I hj II Ed III \:::::11/ rtllljNIS!iTDiEi IF .::::: FFl 1.ITtll TTPrIII t';lll! MM III EM 1111Wlll! I'U III hi:1111 btl III hOI 1IIIt:llllltl!! 1Jt[jIINjsil;DiEIIF ':.:{ 1>1'11.1 r.LI I I I II 1111(j iii I,ii::j II i 1:,:;1 I II It I I I I:d I I I iri I I I i:{j iii h;j I I i j,ii iii j;,:;j I I i 1,:fIIIN!slliD!EI IF .;.;. .q:j l.rtldIJ I b'llll tM 1111:!::':lllll:,,:llll fdJ I i Ill!11 Pi! I II 1m III Iq III kill I FH LWtJtlNSiIIDiE! IF ,., ':J.'j I. d 1/1:'::\ III lilill :':"j 111::lllld I! 1'\111 i 'i lll?llil (d II' /1 i II 'r I NrSiliDiEllF, a II IF:l 1.1 11 111:/111 ':,j IlL tllll ,(1! liN III '(11 i Itlill': IlllIIII,"! 1/\111 If: I N;s:t!DIE! IF I III 31 "I J ;, 11 S I 9 r 10 of: /13; '.11' "'117j1S! llll.ll H:loll lall'!l....: "'I j"li"3j"","'! )1 6Ifr..zi&li64 6' % :oi7joaIS'J:7:I r; :"'1 In.eo FORMAT (6X, I I, IX, II, IX, 12 (IX, F4.0) I *DECIMAL FRACTiON OF AVERAGE MONTHLY USE --SUM OF VALUES FOR EACH LAND USE CATEGORY SHOULD EOUAL 12.0

    PAGE 206

    I-' \0 00 \I,,'ATER DEMAND MODEL INPUT DATA FORM NO 9 IRRIGATION WATER REQUIRMENTS (TR 21) CODED BY t:. PAGE __ OF DATE __ 1 ___ S,UDY AREA .!..RD NO : ........... :. : ........ .... _.; ..... _.... ........ 'of Average "Monthly Clnd Season.::!l :.: ::' j ::f .. :.g -Irrigaticn RequireOTlent by-Corn in Sludy Area during .197_ 'I l2 T A L DEG. HIN. PR I P ::::.: .. ::::::.:::.: ;;\';':':::5,:::.::: :.' :::.;.:.::.:: AV r:P.A GE Mnr;TilL Y Eft.; 1 iJl\ ES .1 FEB. }i.!. R APR. :-'.A Y J1r.'lE JU L Y 1 A ur.. I !' PT. OCT. NOV. DEC. I::.: "::"'-}':" .>.::-:':'.: .::..:.-::A? ... ::.:::::::;. 1 I I 1 I NOV.- J'!..6J\ r ::.5. :.::'.=.:' ::. : .:::: '.:: ,i; ::.;.: :,,:; ': 7.;:;:::1: r .. ARVt.ST I SOIL t:or ST --j CA3.RY oVER CR0P .4 i ?IGURE 'INilRHAL HI LL I H P. I r. LO\.: .:. :?:.:.:: :.::::.::,:1 :.:: ;:::1-:':, '.: ::: ::: .:::. ';.;':/':::::::' I PI:: :l : 0.: t.! OO? CROP CROP f .. TAr.r. HIGH DAY DAY ::.!: G.., ::-I I -+ -ft-4 l:::'::"<:: {-t'l Ii ." -J----+---t---4--=---t----t J ToA FP,7oF. I ---f .... :::._. :.;.. _':-. '.:-: :'.::" .j ... : .. .:.:-:;:: .... _,:.::.:::: ....... f-::.:.::.:31::.:t.:c:.Z:E::: .. ::: .. :. :'::::-:.':';'.;' .. : .. 1'::;: .. : 1 .; n .. c.J.:... : .. ... .,.: : ::'::::".:'.::.: