User manual | SIMULATION OF MICRO CATCHMENT WATER HARVESTING SYSTEMS. by Noubassem Nanas Namde

SIMULATION OF MICRO CATCHMENT

WATER HARVESTING SYSTEMS.

Noubassem Nanas Namde

A Dissertation Submitted to the Faculty of the

SCHOOL OF RENEWABLE NATURAL RESOURCES

In Partial Fulfillment of the Requirements

For the Degree of

DOCTOR OF PHILOSOPHY

WITH A MAJOR IN WATERSHED MANAGEMENT

In the Graduate College

THE UNIVERSITY OF ARIZONA

1987

THE UNIVERSITY OF ARIZONA

GRADUATE COLLEGE

As members of the Final Examination Committee, we certify that we have read the dissertation prepared by Noubassem Nanas Namde entitled Simulation of Micro Catchment

Water Harvesting Systems and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy

Date e)/

2—e ,ii/t)

Date

(-../

2,r

Dat ya? g

_ /

Date

Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate

College.

I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation retuireznent.

6r/

Date

STATEMENT BY AUTHOR

This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the

University of Arizona and is deposited in The University

Library to be made available to borrowers under rules of the

Library.

Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgement of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgement the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED:

/V OteZ

Moot

/ / Ver.....de

ACKNOWLEDGEMENTS

This paper evolved from a discussion with Dr. W.

Gerald Matlock, Professor of Agricultural Engineering at the

University of Arizona. Funding of the project was provided by my own private means.

I wish to thank Dr. Matlock, my dissertation director, for his day-to-day assistance, his patience and for all the sacrifices he had to make in order to consult with me during many of my unannounced visits. To Dr. Matlock, I am eternally indebted.

Special thanks are given to my academic advisor, Dr.

John L. Thames for his guidance throughout my stay at the

University of Arizona.

I wish to thank the other members of my committee,

Dr. Peter F. Ffolliott, Dr. Martin M. Fogel, Dr. Roger W.

Fox, Dr. Robert R. Firch, Dr. Paul N. Wilson and Dr. Harry

W. Ayer for their contributions.

Special thanks are extended to Dr. Ayer and Dr.

Ffolliott for their helpful comments and criticisms of the thesis. I wish also to thank my uncle, Robert Namangkouma, and my late grandmother, Yandoum, for their life-long support.

iii

Finally, I wish to thank my wife, Joyce Winchel

Namde, and my three children for their moral support and their sacrifices.

To my family, I dedicate this paper.

TABLE OF CONTENTS

LIST OF ILLUSTRATIONS

LIST OF TABLES

ABSTRACT

INTRODUCTION

OBJECTIVES

PREVIOUS STUDIES

Water Harvesting Systems

Rainfall-Runoff Relationships

Catchment treatment

Reservoir Storage

Evaporation Losses

Seepage Losses

Infiltration Opportunity

Plant Water Use

Percolation and Capillary Rise

Production

Functions

MODEL DESCRIPTION

Model Requirements

Summary of Assumptions

The Main Program Structure

The Catchment Area Subroutine

Runoff

The Cultivated Area Subroutine

Evapotranspiration

Distribution of ET in the

Soil Profile

Infiltration

Percolation

Capillary Rise

The Reservoir

Subroutine

Storage

Seepage

Evaporation

Optimization

Page vii

TABLE OF CONTENTS--Continued

CASE STUDY

Variable Estimation and Model Calibration

Results and Discussion

SUMMARY AND CONCLUSIONS

Model Description

Model Validation

Conclusions

APPENDIX A

Guide Manual for Using the Programs

The Rainfall-Runoff Model

The Catchment Subroutine

The Cultivated Area Subroutine

The Reservoir Subroutine

APPENDIX B

Computer Listings

1. Main Program

2. Catchment subroutine

3. Cultivated area subroutine

4. Reservoir subroutine

APPENDIX C

Sample Outputs

Sample No.1: Daily Data

Sample No.2: Weekly Data

Sample No.3: Monthly Data

Sample No.4: Daily Data

Sample No.5: Weekly Data

Sample No.6: Monthly Data

APPENDIX D

Case Study Parameters.

REFERENCES CITED vi

103

106

111

113

117

121

124

129

132

135

136

LIST OF ILLUSTRATIONS

Figure no.

Schematic Drawing of a Compartmented Reservoir

Evapotranspiration as Related to Wind Velocity and Radiation Term

Page

Crop Water Stress Index vs. Time

Hypothetical Total Crop Yield as a Function of Water Quantity

Production Function for Wheat

Production Function for Sorghum

Production Function for Maize at Different

Irrigation Application Efficiencies

Schematic Diagram of a Water Harvesting System

Main Program Flowchart

10. Catchment Area Subroutine Flowchart

11. Cultivated Area and Reservoir Subroutine Flowcharts 50,

12. Rainfall-Runoff Analysis for a Treated Catchment,

Treatment Efficiency = 70 %

13. Rainfall-Runoff Analysis for a Treated Catchment,

Treatment Efficiency = 50 %

14. Rainfall-Runoff Analysis for an Untreated Catchment

With No Vegetation, Runoff Coefficient 0.5

15. Rainfall-Runoff Analysis for an Untreated Catchment

With No Vegetation, Runoff Coefficient 0.45

16. Rainfall-Runoff Analysis for an Untreated Catchment

With Some Vegetation,Runoff Coefficient 0.5

62 vii

viii

LIST OF ILLUSTRATIONS--Continued

17. Rainfall-Runoff Analysis for an Untreated Catchment

With Some Vegetation, Runoff Coefficient 0.45

18. Flow Diagram of Plant-Soil Water System

19. Schematic Diagram of a

Reservoir

LIST OF TABLES

Table no.

Page

Depth and Runoff Ratios for Salt-Treated Catchments .

Cost/Unit of Water Saved by Treatment for Seepage Control 22

Corn Yields from Various Irrigation Methods

Production Functions for Different Crops

Simulation Results

81 ix

ABSTRACT

A mathematical model for personal computers was prepared as a planning tool for development of micro catchment water harvesting systems. It computes runoff from natural or treated catchments, using estimated or actual parameters. The model also computes the water balance of the soil zone in the cultivated area and the water balance of the reservoir system which serves it.

The model was calibrated with hydrolologic data and site characteristics for a location near Tucson, Arizona.

Its prediction of cotton and grain sorghum yields was comparable to that of Morin (1977).

An attempt was made to use weekly or monthly rainfall data for areas where daily data are unavailable. Lack of direct rainfall and runoff durations and infiltration characteristics made this attempt unsuccessful. This option cannot be used with the model in its current form.

INTRODUCTION

Water harvesting has been defined as the collection of local runoff to augment the existing water supply (Morin and Matlock, 1974). Water harvesting systems have catchment areas which vary in size from as small as one square meter to thousands of hectares. To augment runoff, the catchment area surface often is treated physically or chemically.

Many small water harvesting systems channel water directly to the crop area; larger systems often utilize reservoirs for storing excess runoff. Cluff and Frobel (1978) considered the water harvesting process to be incomplete without a provision for storage. Micro catchment water harvesting includes a catchment area, a cultivated area and sometimes a reservoir. In periods of high runoff, the excess water is stored; it is used later during rainless periods for livestock, domestic, or plant use or for recreation activities.

Because the world population has been increasing steadily, there is greater pressure to bring marginal agricultural lands into production. Water harvesting offers an alternative to expensive and technically complex water resources development schemes. Its potential is not limited to arid regions; water harvesting can be utilized in humid regions where rainfall is poorly distributed during the year

But a good water harvesting system also could become expensive. To reduce costs, the system must be carefully planned. A model to improve the planning process would be useful. By manipulating the soil parameters, the sizes of the catchment area, the cultivated area, and the reservoir capacity, planners can determine a combination of components that will operate with high productivity and low cost. This study was undertaken to help planners achieve that goal.

OBJECTIVES

The objectives of this study were:

- to develop a methodology for analyzing various components of a micro catchment water harvesting system and the interrelationships among the catchment area, the cultivated area and the reservoir,

- to estimate the runoff from natural as well as treated catchments, using daily, weekly or monthly rainfall data.

- to compute the water balance on cultivated areas,

- to predict the required and available irrigation amounts throughout the growing season,

- to compute the water balance of the reservoir system, and

- to determine the applicability of this methodology for planning purposes.

PREVIOUS STUDIES

Although water harvesting has been practiced for many years, significant research on the subject has occurred only recently.

The review of previous research on micro catchment treatments, runoff derivations from rainfall, and infiltration theory gave this model a sound basis, provided a pool of information to draw upon and prevented the model from being a "reinvention of the wheel". Extensive use was made of the literature on plant water use, production functions, evaporation, and seepage.

Water Harvesting Systems

Water harvesting techniques were practiced centuries ago by the inhabitants of the Negev Desert in

Israel (Evenari, Shanan and Tadmor, 1971). There, people simply cleared hillsides and smoothed the soil to increase runoff. Contour ditches were used to convey the runoff to lower-lying fields where it was used to irrigate crops.

Morin and Matlock (1975) used a computer simulation technique to study what they called "desert strip farming" in Arizona. Results indicated that for a catchment area to cultivated area ratio (CCAR) of 12, there will be a

5 significant production of short-season grain sorghum in four out of five years. For ratios larger than 12, small improvments in the success rate can be expected. Their model also showed the importance of rainfall distribution in time and space relative to its total amount. They pointed out the advantage of leaving the catchment area in its natural condition so it can be used for grazing in its traditional manner; this will reduce losses in case of a crop failure.

Risley (1984) expanded on an unpublished computer program written at the University of Arizona to model the process of water harvesting. In his model, the user has an option of simulating runoff from untreated or treated catchments. He used the concepts of runoff threshold and catchment efficiency. The derived runoff was used to simulate irrigation of different crops; excess water was stored in a compartmented reservoir.

Rainfall-Runoff Relationships

In the Western United States, runoff has been predicted succesfully from rainfall by the Soil Conservation

Service (SCS) method (Knisel, 1980; Wight, 1982; Risley,

1984). This method was developed by the SCS in the last three decades for use on ungaged, agricultural watersheds.

Its principal application is in estimating quantities of runoff in flood hydrographs or in relation to flood peak rates. Four types of runoff were identified: channel runoff, surface runoff, subsurface runoff and base flow. This

6 method estimates direct runoff, but the proportions of surface runoff and subsurface flow were appraised by means of runoff curve numbers which reflect the probability of flow types: the larger the curve number, the more likely that the estimate is entirely surface runoff. The SCS model estimates runoff as:

(P-Ia)2

(P-Ia) + S

(1) where P = precipitation, in mm,

Ia = the initial abstraction or the amount of precipitation that must accumulate before runoff will start, in mm,

S = maximum retention parameter or the maximum difference between rainfall and runoff, in mm.

Ia consists mainly of interception, infiltration, and surface storage, all of which occur before runoff begins.

Using rainfall runoff data from small experimental watersheds, Ia was found to be equal to 0.2 S.

Substituting this relation into the above equation, runoff can be computed by:

(P - 0.2 S)2

(P + 0.8 S)

(2)

Furthermore, the potential maximum retention S was related to a curve number (CN) by the empirical expression:

CN = 1000 / ( 10 + S ).

(3)

The CN depends on soil type, general hydrologic condition of

7 the watershed, land use and treatment and antecedent moisture conditions

(AMC). AMC was defined as the total amount of rain in the five previous days.

AMC = I if this amount is less than 0.5 inches, AMC = II if it is between 0.5 and

1.5 inches and

AMC = III if it is greater than 1.5 inches.

AMC I is for dry conditions, III is for wet conditions and

II is for average conditions. Knisel (1980) used this CN for

AMC II and an equation of the form :

CN1 = -16.91+1.348(CN2)-0.014(CN2) +0.000118(CN2)

(4) to compute his CN for AMC I.

Knisel also estimated the maximum retention parameter,

S, with the equations: and

Smax = 1000 / CN1 - 10

= Smax [ (

UL-SM)/UL ]

(5)

(6) where UL = the upper limit of soil water storage in the root zone and

SM = the soil water content in the root zone.

Using these modifications, Knisel calculated runoff with good results in different parts of the United States. For example, in Riesel, Texas, he measured 15.95 cm of runoff on

6.44 m2 and predicted runoff of 19.63 cm with the modified

SCS method. In Coshocton, Ohio, the annual measured average runoff was 0.89 cm compared to a predicted value of 1.55 cm on a 3.22 m2 watershed.

Predicted values were equally good in Georgia and other western states.

Wight (1982) adopted

Knisel's method for estimating CN1 but added a weighting factor, W, to the retention parameter equation:

8 s=

S'* W (7) where

The weighting factor, W, decreases exponentially with soil depth to give greater dependence of S on the upper soil layers:

S = Wight's retention parameter,

S' = Knisel's retention parameter and

W = retention parameter weighting factor.

Wi = A exp (-4.16 Di ).

(8) where Di = (depth to the bottom of layer i)/(depth to the bottom of last layer),

A = a constant adjusted so that the sum of

WI over all layers equals 1 and

Wi = weighting factor per layer.

Wight (1982) plotted the runoff obtained by this modified SCS method versus observed data for the Walnut

Gulch Experimental Watershed near Tombstone, Arizona. He found correlation coefficients of 94 percent for one subarea of 3.69 ha and 88 percent for the total area, 43.74 ha.

Schreiber and Kincaid (1967) studied on-site runoff from

1.83m x 3.66m plots on the same Walnut Gulch watershed. A stepwise, multiple linear regression was used to determine the effect of six variables on runoff. The variables included three precipitation indices (depth, maximum five minute intensity and duration), two vegetation cover factors

(basal area and crown spread) and antecedent soil moisture.

The dominant variable was determined to be either precipitation depth or the maximum five-minute intensity. These two variables explained from 72 to 82 percent of the variance in

9 runoff.

When the second most important factor, crown spread, was included in the prediction equation, the coefficient of determination was only improved by 1.6 percent.

They also noted that antecedent soil moisture had little effect on runoff from convective storms. Its inclusion improved the coefficient of determination for runoff prediction by only

0.8 percent. All coefficients are statistically significant at the 95 percent level except the antecedent soil moisture coefficient which is significant at the

99 percent level.

Fogel

(1968) studied the effect of spatial and temporal variation of rainfall on runoff from four small watersheds in Southern Arizona. He used a linear regression of the form:

Q = Bo + El R + B2 T + B3 S + e

(9) where Q = storm runoff,

Bi = (i = 0,1,2,3) coefficients,

R = storm rainfall,

T = time distribution factor,

S = space factor, and e = error of estimation

The time distribution factor, T, was evaluated as a function of the measured time between the mass center of a storm and its maximum 15-minute intensity.

The storm space factor,

S, was estimated as a funtion of the distance from the storm center to the watershed outlet and the area of the watershed that received at least a specified amount of rainfall. The B coefficients of the above equation were

10 determined for convective and frontal storms to be, respectively

-.0964 + .1329 R + .0249 T

+.1227 + .0891 R + .1478 T

;R2 = 86 %

;R2 = 92 %

(10)

(11)

The space factor, S, was found to be insignificant. This was due to the relatively small watershed area compared to the size of storms encountered in the study. Another possibility is that in using the mean value of storm rainfall, the spatial distribution of the storm was already taken into account. The space factor, S, was thus dropped.

Results also indicated that antecedent soil moisture did not affect runoff from convective storms but appears to be an important factor in explaining runoff from frontal storms.

Saplaco (1977) analysed the water budget for a period of one year for the Atterbury watershed in Arizona.

The water budget was expressed as:

P = SRO + SMC + L (12) where precipitation in cm,

SRO = surface runoff in cm,

SMC = soil moisture content in cm and all other water losses, in cm.

Runoff was measured from 1972 to 1976 with an H-flume and regressed against rainfall and maximum 10-minute rainfall intensity.

He found that runoff for the area can be predicted with the relation:

RO = - 0.24 + 0.26 P + 0.19 MAXTR (13)

1 where

= runoff in cm,

= precipitation in cm and

MAXTR = maximum 10-minute intensity in cm/min.

About 77 percent of the variation in surface runoff was explained by rainfall amount and the maximum 10-minute rainfall intensity. Schreiber and Kincaid (1967) found comparable results from their study. Saplaco concluded that surface runoff, soil moisture content and other water losses in the area accounted for 2, 55, and 43 percent of the total rainfall, respectively.

Greengard (1981) experimentally analysed rainfallrunoff hydraulics on a natural micro catchment in the Negev desert using kinematic wave equations.

Kinematic wave models mathematically simulate the hydraulics of open chanel flow and can provide an insight into the mechanics of the rainfall-runoff process.

In its general form, the kinematic wave equation is written as: ah

- + ccp

@t h-1 ah

- =

I(x,t) ax

(14) where h

= depth of flow (L), x = distance downslope (L).

t = time (T) cc, p = empirical parameters (LIT) and

I(x,t) = rate of lateral inflow,variable in time and space and defined as where

I(x,t) = p(x,t)-f(x,t)

P(x,t) = the rainfall rate (L/T) and f(x,t) = the infiltration rate (LIT).

(15)

For laminar flows, p,

was set to 3 and cc was calculated and equal to a mean value of 696. For turbulent flows,

was set to 1.5 and olIC estimated as 0.175. Compared to measured runoffs of 113.8, 66.9, 31.4, 13.9, and 1.8, Greengard predicted, for laminar flows, runoff values of 68.0, 253.0,

116.3, 24.0, and 0.8. For turbulent flows, he predicted runoff values of 42.4, 82.6, 55.4, 25.2, and 4.6. He noted that results were poor. Better results were achieved by excluding the highest rainfall intensity (59.4 mm/hr) from the analysis. The rainfall simulator used in the experiment allowed a wide range of rainfall intensities, which were used to determine the runoff and infiltration capacity curves. Greengard's study required very little input data.

Cluff (1977) utilized a linear relationship between rainfall and runoff for calculating runoff from natural or treated catchments.

His method uses a runoff coefficient, a threshold coefficient and an antecedent soil moisture. The runoff coefficient is an estimated decimal fraction of a quantity of runoff over a quantity of rainfall after a threshold value has been exceeded. The threshold coefficient is the estimated quantity of rainfall required before runoff will begin.

Runoff is calculated with the user inputted coefficients in the equation:

(16) where

Run = KK * (rain-TT)

Run

= runofff in mm,

KK = modified runoff coefficient,

Rain = rainfall amount in mm and

= modified basic threshold in mm

Before calculating runoff, the routine modifies the inputted coefficients by taking the antecedent soil moisture into account as shown in the two following equations:

= TT'- (0.7*TT'* e(-(DAY/3)))

KK = KK'* (1-(0.9* e(TT'/100)*e(-(RAIN/100))))

(17)

(18) where TT'

= basic threshold inputted by the user,

Day

= number of days since previous rainfall event,

KK' = runoff coefficient inputted by the user,

Rain= amount of rainfall from the event in mm and

TT and KK are defined as above

Using a runoff coefficient of 0.45 and a basic threshold of

0.2, Cluff's method estimated a runoff value of 37 mm from a rainfall of 362 mm. From treated catchments, runoff is determined with the equation:

(19)

Run = (RE * Rain) - Tc where Run

= runoff in mm,

= treatment efficiency,

Rain= rainfall amount in mm and

= threshold coefficient

Soil antecedent moisture is not taken into account.

Catchment Treatments

Evett and Dutt (1985) studied the effects of length and slope on sodium dispersed compacted earth micro catchments near Tucson, Arizona. Two replicates, including slopes of 1, 5, 10, and 15 percent and lengths of 3 and 6 meters, were built on a gravelly sandy clay loam. Each plot was 2 meters wide. After rains had wetted the soil, 11.2

tons per hectare of NaC1 were mixed into the top 2 to 5 cm

14 layer and compacted. Total runoff was measured volumetrically after each of the 18 storms studied.

Table 1 illustrates their findings.

Evett and Dutt (1985) found that 7 of storms the 18 studied, which totaled only about 7 mm or 4.4

percent of the total rainfall, produced no runoff. The runoff ratio, defined as the decimal fraction of rainfall that ran off, varied directly with rainfall amount, averaging as high as 0.77 for large rains and as low as 0.008 for smaller ones. Overall runoff ratios were found to increase with plot slope and decrease with plot length. Total runoff depths varied considerably among treatments and differences were directly related to plot length and slope (Table

1). For example, runoff increased by 25 percent going from

8.6 cm for the 6m, 1% treatment to 10.9 cm for the 3m, 15 percent treatment under a total rainfall of 15.8 cm. A best fit linear model of runoff versus rainfall gave the equation:

Q = 0.858 ( P-0.34 )

(20) where

Q = runoff and

P = rainfall

This equation explained 98 percent of the variability in runoff on individual plots for individual storms but not among treatments. A nonlinear model, incorporating slope and length accounted for 99 percent of the variability in average total runoff among treatments. This model was:

Q =

.0453 -.183

+ .183)(P-.339) (21)

Table 1.

Depths and Runoff Ratios for Salt-Treated

Catchments

Treatment

X S

3m, 1%

3m,

3m, 10%

3m, 15%

6m, 1%

6m,

10%

6m, 15%

Total

Runoff depth (cm)

9.6

10.2

10.4

10.9

8.6

8.9

9.5

9.8

Source: Evett and Dutt (1985).

Notes: runoff ratio = runoff depth/rainfall depth

X = plot length; S = plot slope

Runoff ratio

0.61

0.65

0.66

0.69

0.55

0.56

0.60

0.62

16 where

S = plot slope,

X = plot length and

P = rainfall

The exponents 0.0453 and -0.183 were significantly different from zero. Their approximate 95 percent confidence intervals were respectively 0.0026 to 0.0646 and -0.249 to

- 0.118.

The approximate 95 percent confidence intervals for the coefficients 0.183 and -0.339 were 0.96 to 0.27 and

-0.365 to -0.313 respectively.

The model showed that the important differences in runoff among treatments can be explained by slope and length alone.

Reservoir Storage

Frith, Nulsen and Nicol (1974) developed a computer model for design optimization for water harvesting systems with a reservoir. Their model outputs isoquants of various sizes of sheep flocks that can be supported by various sizes of catchment areas and reservoir capacity. Optimum combinations of area/capacity were obtained by the minimum point of tangency between the isoquants and the sizes of sheep flocks. Due to the difficulty in measuring seepage rate,

Frith, et al, excluded it from their analysis.

Risley (1984) used the concept of the compartmented reservoir in his study.

In this instance, the reservoir is subdivided into a number of compartments.

Figure 1 illustrates a three compartment reservoir.

Runoff flows into the receiving compartment A.

During the rainy season, the water in A is pumped or flows by gravity into the deeper

=.--7

18 compartments, B and C, as soon as possible after each runoff producing event. Following the rainy season, water is first withdrawn for plant consumptive use from compartment A until the evaporation and seepage losses from B and C are equal to the remaining water in A. At this point, the remaining water in A is pumped into the unused capacity of B and C.

Water needed for consumptive use is then withdrawn from B until the water in B is equal to the unused capacity of C.

At that point, the remaining water in B is transfered to C.

C is now filled and A and B are empty. The surface area of the reservoir exposed to the atmosphere has been reduced to about one-quarter of what it would have been had the reservoir not been compartmented. This process greatly reduces evaporation.

With low cost, portable electric pumps, this concept was thought to be usable in developing countries. If the site has a slope of more than 3 or 4 percent, the compartments could be positioned to enable the transfer of water from one compartment to another completely by gravity flow.

Evaporation losses

The computation of a water budget includes evaporation losses, which can be substantial in arid regions.

In a water harvesting system, three evaporation processes occur simultaneously: one on the catchment area, a second on the cultivated area and the third on the reservoir. Due to the difficulty in separating soil evaporation and plant transpiration, most soil and plant scientists treat them

19 together as evapotranspiration.

Wight

(1982) and Knisel (1980) predicted soil potential evaporation as:

Eso = Eo exp (-0.4 LAI)

(22) where

Eso = soil potential evaporation,

Eo = potential evapotranspiration and

LAI = plant leaf area index defined as the area of plant leaves relative to soil surface area.

They computed actual soil evaporation in two stages. In the first stage, soil evaporation is limited only by the energy available at the surface and, thus, is equal to the potential soil evaporation, Eso. When the accumulated soil evaporation exceeds the stage one upper limit, the second evaporative stage begins. The stage one upper limit is estimated with the equation:

U = 9 (As-3)

.42

(23) where U = stage one upper limit in mm and

As = soil evaporation parameter dependent on soil water transmission characteristics.

Wight and Kniesel suggested as values of As, 4.5 for loamy soils, 3.5 for clays and 3.3 for sandy soils.

Stage two soil evaporation is predicted with the equation:

Es = As

(VT-VT=1)

(24) where Es

= soil evaporation for day t and t = number of days since stage two soil evaporation began.

20 voirs as

Wight

(1982) estimated the evaporation from reser-

EV = 1/12 A (Eo) SA

(25) where EV

= evaporation from the reservoir in ac-ft,

= evaporation coefficient estimated experimentaly to be

0.6,

= surface area of the reservoir in acre,

Eo = potential evapotranspiration in inches and

1/12 = conversion factor (from inches to feet).

Data from a large number of stock ponds and small reservoirs in Texas and Oklahoma indicated that SA can be computed with

SA = SAmax (VM / VMmax) G

(26) where

G = parameter determined to be equal to 0.9,

VMmax = maximum reservoir volume in ac-ft,

SAmax = maximum pond surface area in acres and

= current reservoir volume.

Seepage losses

In small water harvesting systems, seepage from canals and reservoirs can be a major source of water loss.

Seepage from the structures varies with the soil types, the water quality, the soil erosion processes and the effects of fluctuating water levels and wetting-drying cycles.

Reservoir seepage has been modeled by complex equations that must be simplified for use on digital computers. Water harvesting systems may include treated or natural reservoirs. Matlock (1985), using data from Cluff and

Frobel (1978), analysed costs of using various materials for seepage reduction and calculated the cost per cubic

For a 450 in

3 meter of water saved by their use (Table 2). reservoir, soil covered polyethylene plastic was found to be

3 the cheapest material to use with a cost of $ 0.0016/m saved.

0.03 /m .

Wyoming bentonite was the most expensive at about $

Naney and Thompson (1979) presented a physically based method for estimating the amount of seepage lost from structures in relation to the hydraulic head behind the structure. They analysed a structure with a storage capaci-

3 ty of 555,000 m , an average width of 177 m, an average length of 612 in and a maximum depth of 9.6 m. To compute seepage loss, hydrographs were prepared from continuous lake stage records from December 1965 to November 1966. A stage-volume curve and precipitation data from gages in the site area were used to determine total monthly water losses.

These losses were plotted versus class A

‘ pan evaporation data for the site. A line of best fit developed for the data showed that water loss was equal to 0.6 m/month, when the pan evaporation was 0, and the annual seepage rate was

27000 m . Seepage rates were calculated in this manner for various times and plotted against corresponding stages.

A least squares method was used to fit the line

Y = Ao 10 in X - Al 10 in (27) to the data.

Where Ao = 0.55

Al = 31.9

(experimentally-determined coefficients )

Y = seepage rate and

= stage or total head.

Table 2.

Cost/unit of Water Saved by Treatment for Seepage Control.

Treatment

8/m

Water saved

Rank by order of cost

Chemical

Sodium-chloride

Sodium-carbonate

Polymeric sealant

Wyoming bentonite

Mixed blanket

Pure blanket

(surface)

Earth structures

Compacted earth

Soil cement (10 cm)

Asphalt

0.0045

0.0057

0.012

0.014

0.029

0.0036

0.014

Asphalt fiberglass

Asphalt plastic asphalt chipcoated

Asphalt rubber

Buried asphalt membrane

Asphalt concrete (15 cm)

Concrete

Portland cement concrete (15 cm)

Synthetic membranes

0.0036

0.0034

0.0057

0.0078

0.013

0.017

Soil covered polyethylene plastic

Soil covered polyvinyl chloride

0.0016

0.0035

Reinforced mortar-covered 0.0056

polyethylene plastic

Chlorinated polyethylene 0.019

Artificial rubber 0.024

Source: Matlock (1985)

Note: data for a 450 m3 reservoir (15m x 15m x 2m)

Naney and Thompson used this method of estimating seepage to study the impact of a reservoir on the ground water flow system assuming variable reservoir head conditions.

Infiltration Opportunity

Infiltration rate is the rate at which water moves into the soil. There is a maximum rate at which the soil can absorb water; this upper limit is the infiltration capacity of the soil. If the water application rate, R

(rainfall or irrigation), at a given time is less than the infiltration capacity, all water being supplied is infiltration. If R is greater than the infiltration capacity, infiltration occurs at capacity and the excess water accumulates on the soil surface and/or runs off.

Infiltration of water into the soil thus determines the amount of runoff and water available for crop use. As such, it received considerable attention from research workers. The theory and process of infiltration has been reviewed by workers such as Dunne and Leopold (1978) and

Hillel (1971).

Slack and Larson (1981) presented the use of a physically based, two-stage infiltration model. The first stage of the model uses the Main-Larson equation, which predicts the time when surface ponding begins:

Di*Sav

Fp -

R/Kfs-1

Tp = Fp/R

(28)

(29)

24 where

Fp = cumulative volume of infiltration at the instant of surface ponding,

Di = initial soil moisture deficit,

R = water application rate,

Kfs = soil hydraulic conductivity at field capacity

Tp = time to surface ponding

Say = average suction at the wetting front

The second stage utilizes the Green-Ampt equation to determine infiltration rate after ponding begins:

Fp = Kfs ( 1 + Di*Sav/F )

(30) where

F = volume of infiltration at time t.

For a steady rainfall of 5 cm/hr on a sandy loam which has an initial moisture content of .31, a Kfs of 4.52

cm/hr and a saturated moisture content of .47, Slack and

Larson determined that Fp was equal to .7 cm (5cm/hr) at Tp

.14 hr (about 8 min). The infiltration rate was calculated with the second equation after ponding and equal to

3.82 cm/hr. After .36, .55 and .77 hrs, the infiltration rates decreased to 2.88, 2.42 and 2.13 cm/hr, respectively.

Plant water use

Hanks and Hill (1980) modeled crop response to irrigation. They computed yield, Y, as a function of seasonal transpiration, T, crop factor, M, and average seasonal free water evaporation, Eo:

M T/Eo

(31) where

Y = crop yield,

M = crop factor,

T = seasonal transpiration and

Eo = free water evaporation

A plot of Y versus

TM/Eo indicated a good fit for several crops grown in different years and in different locations in the United States. In Akron, Colorado; Newell, South

Dakota; and Mandan, North Dakota; for example, the correlation between Y and T/Eo was 98 percent for alfalfa, 98 percent for wheat and 99 percent for sorghum.

They assumed that the plant roots growing in a soil composed of 3 layers reached a stable depth at 90 days. Root water extraction from the soil occurred in the second layer after 24 days and in the third layer after 46 days.

They used their model to predict corn yield and dry matter and then plotted it against corn evapotranspiration data from Israel and Logan,

Utah. Their findings indicated a good correlation with actual measured data.

Jensen and

Haise (1963) used solar radiation data to estimate evapotranspiration for field and orchard crops in the Western United States. For each crop studied, the potential evapotranspiration was estimated during the emergence to development period, and then to the maturation period. They plotted PET/radiation against mean air temperature, and derived the following equation:

PET/RS

= 0.014 T - 0.37 (32) where

PET = potential evapotranspiration,

= solar radiation and

= mean air temperature.

Using this equation, one needs only to input the appropriate radiation and temperature data to predict crop PET.

Actual

26 evapotranspiration (AET) was computed by multiplying the potential ET by a crop factor.

AET = PET * Kc

(33) where AET = actual evapotranspiration,

PET = potential evapotranspiration and

Kc = crop factor

The crop coefficient is a factor that modifies PET for different stages of plant development, time of planting, percent of land surface that is shaded by green cover, soil moisture conditions, and climatic conditions. Erie, et al.

(1982), computed PET for different crops in Arizona; they experimentally measured ET values for the same crops and derived the crop coefficients, Kc using equation 33.

Doorenbos and Pruitt (1984) presented crop coefficients for field and vegetable crops for other areas according to the climatic conditions and different stages of crop growth.

The disadvantage of Jensen-Haise method is the difficulty in obtaining the maximum and minimum temperatures.

Some users have circumvented this problem by using only the maximum temperature and later adjusting the PET (Stegman and Coe,

1984).

Doorenbos and Pruitt (1984) modified the Blaney -

Criddle method for computing crop potential evapotranspiration by allowing for the use of measured air temperature, sunshine, and radiation, but not including measured wind velocity and relative humidity. They recommended a relationship of the form:

ET = c ( W Rs )

(34) where ET = crop evaporation in mm/day,

= solar radiation in equivalent evaporation in mm/day,

W = weighting factor which depends on temperature and altitude and

= adjustment factor which depends on mean humidity and day time wind conditions.

Solar radiation data are available in most countries, but

Doorenbos and Pruitt suggest this equation for those locations without data

Rs = (0.25 + 0.50 n/N) Ra

(35) where n/N = ratio between actual measured bright sunshine hours and maximum possible sunshine hours and

Ra = amount of radiation received at the top of the atmosphere.

Monthly values of N and Ra for various latitudes are given in many hydrologic books.

The adjustment factor, c, is given by the relationship between the radiation term (W

Rs) and crop ET.

Figure 2 depicts this relationship for

Tucson, Arizona, assuming that the mean relative humidity is less than 40 %. Other relationships for RH >70 %, and between 40 % and 70%, also were given by Doorenbos and Pruitt.

Adding these climatic conditions, better results were obtained than using the mean temperature and percent of total annual day-light hours alone.

Using this method,

Doorenbos and Pruitt estimated that potential ET for

Cairo, Egypt was 8.4 mm/day.

This compares well with results obtained with the Penman method (8.4 mm/day) and the

I. Daytime

U =8mm/sec

2. Daytime U= 5-8mm/sec

3. Daytime U= 2-5mm/sec

Daytime

U = 0-2mm/sec

4

as.

4 6

W.Rs (mm/day)

Fig.2 Evapotranspiration as

Related to Wind Velocity and Radiation

Term

Source:Doorenbos and

Pruitt (1984)

Notes: U = wind Velocity

W.Rs = radiation term

Blaney-Criddle method (8.0 mm/day).

Ritchie (1972), Wright (1982) and Knisel (1980) used a modified Penman equation to estimate plant consumptive use. They added an albido factor.

Wright and Knisel based their work on the study done by Ritchie.

Actual plant evapotranspiration was calculated in two steps.

Step one calculated soil evaporation as a function of plant cover; step two computed plant transpiration as a funtion of leaf area index and potential evapotranspiration. When soil moisture was limited, this value was arbitrarily reduced by

25 percent. Plant evapotranspiration was then the sum of the plant transpiration and the soil evaporation.

A relatively new method of irrigation scheduling is the use of infrared thermometry. Jackson and others (1981) have successfully determined the crop water stress index

(CWSI) for wheat in Arizona. Canopy temperature, wet and dry bulb air temperature, and an estimate of net radiation were used in equations derived from energy balance considerations to calculate the CWSI. Jackson and his co-workers planted wheat in four experimental plots for their study.

The plots received postemergence irrigation at different times to create different degrees of water stress. They found that CWSI was approximately equal to

1 - E/Ep

(36) where

E = actual evapotranspiration and

Ep = potential evapotranspiration

The CWSI plotted as a function of time closely paralleled a plot of extractable soil water in the zero to 110 cm zone.

(Figure 3) Because the CWSI gives an instantaneous measurement for a whole field, they felt this method could become a valuable tool.

Using the same technique, Geiser and others (1982) developed a linear regression using crop canopy-air temperature difference as the dependent variable and net radiation, relative humidity and available soil water as the independent variables:

-3

-10 5

T = -1.065+4.71*10 +.0274 H+-0.0535AW+4.01*10

AW (37) where R = net radiation in watts/m2

H = relative humidity in %

AW = available water in %

T = delta T, crop canopy-air temperature difference

The parameter, AW, was set at the 50 % depletion level.

With AW set as a constant, the value of delta T can be calculated for various conditions of net radiation and relative humidity.

In the field, T, R, and H were measured and used to determine if the crop required irrigation.

For instance, measured values of R and H on a given day are used to predict T in the above equation. If the measured T on that day is greater than or equal to the predicted T, irrigation is required. Crop yield and water use were compared with that grown under irrigation scheduled by use of electric resistance blocks and a water balance (checkbook) method.

The yields under the three methods were not

0.6

Z5

0.4

1.0

0.8

• Data

—

Trend of data

co Extractable water

(0-110cm depth)

0.2

0.0

50 70 90

TIME (days)

110

130 150

Fig.3 Crop Water

Stress Index vs. Time

Source: Jackson and others (1981)

32 significantly different but the water balance and the resistance block methods called for additional water applications of 39 and 18 percent respectively (Table 3).

Hiler and Clark (1981) and Hiler and others (1974) successfully used the stress day index (SDI) as an irrigation timing device. This method computes the stress day index as a function of the degree and duration of plant water deficit and the stage of growth for the plant species.

Dean (1980) modeled crop water demand for corn in

Georgia. The irrigation decision was based on soil moisture potential.

The soil was divided into a surface layer, an upper layer and a lower layer.

The surface layer, which extended to a few centimeters below the soil surface, was assumed to have little moisture holding capacity. Only the upper layer (from the surface layer to 183 cm below) and the lower layer (from the upper layer to the water table) were considered to be potentially beneficial to plant use. Soil moisture potential in each zone was calculated as:

SMP = a0

(38) where a and b are empirical constants and

0 = percent water by volume.

The calculated SMP's for all layers were integrated to form a soil moisture potential index (SMPI). If its value was greater than a predetermined threshold, irrigation was triggered. A daily water balance was kept throughout the growing season.

When irrigation was triggered on a rainy

Table 3. Corn Yields from Various Irrigation Methods.

Replications delta T

9.4

10.22

9.35

7.69

Average yield

9.17

Water applied

15.88

Scheduling treatments

Resistance block Unirrigated Checkbook

10.56

10.79

9.99

9.56

2.09

4.75

5.03

1.37

9.86

10.11

10.21

10.51

10.23

19.43

3.31

2.54

10.17

26.04

Source: Geiser et al, (1982).

Note: Yields are in tons/hectare; Water applied is in cm.

34 day, it was reduced to zero after precipitation exceeded

0.64 cm. Dean simulated the irrigation scheduling under three management alternatives: no irrigation, irrigation when the SMPI rose above 0.6 bars and irrigation when the

SMPI rose above 15 bars. For the 0.6 bar level, he found that mean seasonal irrigation depth was 19.3 cm, with a standard deviation of 7.37 cm. The 15 bar practice required

8.38 cm per season on the average with a standard deviation of 5.59 cm. Corn yields were not reported for the different management alternatives.

Percolation and Capillary Rise

Percolation is the movement of water through the soil. Kniesel (1980), in his study, used a storage routing model to predict flow through the soil layers of the root zone.

Inflow was allowed to fill each soil layer to field capacity before percolating down into the next layer.

When the last layer was above field capacity, the excess water becames deep percolation and was no longer useful to plants.

Percolation can be computed with the equations:

= 0

(SWi - FCi)[ 1 - exp(-Dt/Ti)] if SWi>FCi if SWi<FCi

(39) where

T i

= amount of percolation in mm, initial soil water content in mm, field capacity water content in mm, time interval in hours, travel time through the layer i in hours and, soil layer number, increasing with depth.

In equation (39), the amount of percolation through the bottom of layer i is assumed zero if the soil moisture in that layer is less than its field capacity. The travel time is calculated as:

Ti = ( SWi - FCi ) / Hi

(40) where Hi = hydraulic conductivity for layer i.

The hydraulic conductivity is varied from the specified saturation conductivity value by:

Hi = SCi (SWi/ULi)

(41) where SCi = saturation conductivity for layer i in mm/hr and

Bi = parameter that causes Hi to approach a very small constant (e.g. 0.002 SC) as SWi approaches FCi.

Kniesel (1980) estimated that

Bi = -2.655 / [ log(FCi/ULi) ]

(42)

The constant -2.655 assures that Hi = 0.002 SC at field capacity. In Georgia, on a clay loam soil grown with corn, his model calculated deep percolation of 125 mm from an annual rainfall of 1023 mm. An annual rainfall of 1226 mm yielded deep percolation of 351 mm.

In addition to the downward movement, water moves upward through small soil pores by capillarity as the result of water surface tension. Linsley (1982) showed that ideal soils, in which the capillary soil tubes are triangular in cross-section, the water will rise to a height of:

Ht = 1.5/d where Ht = height of water in cm and d = soil particle diameter in mm

(43)

Production Functions

All production is a function of some physical relationships between inputs and outputs. To produce a given crop, for example, one needs seeds, fertilizers, water, labor, technical management, land and capital. These factors (inputs) are applied to a particular area and the resulting product (yield) is the output. Without adequate water, plants do not develop; likewise, too much water can drown or kill the plant. Between these limits, yield varies.

The physical relationship for making the particular production decision is called a production function (Fig.

4). In deriving Figure 4, all other inputs were held constant; only water was changed. An increasing amount of water application (wl, w2, w3) yielded more product (yl, y2, y3).

Beyond w3, crop yield started to decrease due to excess water. The production function then showed the output resulting from different input (water) quantities.

Ayer and Hoyt (1981) statistically estimated the production functions for Arizona's most important crops-cotton, wheat, sorghum, and alfalfa--on soils of three different textures. The independent variables included nitrogen applied, pan evaporation, and water. Seasonal pan evaporation used in the wheat production functions was held

WI W2

WATER QUANTITY

Fig.

4 Hypothetical

Total

Crop Yield as a

Function of Water

Quantity

38 contant at 86.36 cm, 101.4 cm, and 118.87 cm for the coarse

(Wc), medium (Wm), and fine textured (Wf) soils, respectively. Nitrogen levels were held at 22.7 kg for Wc, 68.1

kg for Wm and 90.8 kg for Wf.

The grain sorghum production utilized a pan evaporation of 96.52 cm on all three soil

textures.

Ayer and Hoyt's production functions for wheat and sorghum took the forms given below:

Coarse textured soil

1.5

Wheat: Yw = 12083.008+372.87W-44.014W

+15.237N (44)

-1.368N1.5+.571WN-424.168EVAP

R sqr = .58; F = 32.87

Medium textured soil

Wheat: Yw = 288.111+5.834 WEVAP-3.119 W +16.784 N (45)

R sqr = .62; F = 15.18

Sorghum: Ys = 7.57W

.312

EVAP

1.38

R sqr = .64; F = 18.08

(46)

Fine textured soil

Wheat: Yw = -4385.796+495.812W-3.752W

- 2.778WEVAP+5.819N- .016N

R sqr = .71; F = 42.8

Sorghum: Ys = 7.57W

.312

EVAP

1.38

R sqr = .64 F = 18.08

where Yw

= wheat yield in lb/ac,

= sorghum yield in lb/ac,

= gross water applied and effective rainfall from preplant irrigation to harvest in acre-inches,

(47)

(48)

EVAP = total pan evaporation for the season in inches,

WEVAP = W*EVAP,

= nitrogen applied in lb/ac,

WN = W*N,

R Sqr = coefficients of determination adjusted for degrees of freedom

The production function for wheat grown on coarse soil explained 73 % of the variance in yields. All variables, except the nitrogen polynomial term, were significant at the 10% level. Pan evaporation was very significant

(t=8.3). On medium textured soils, the production function for wheat explained only 62 % of the variance in yields.

All coefficients were statistically significant at the 10 % level except the coefficient for the water squared term which was significant at the 12 % level. On fine textured soils, all variables in the wheat production function were significant at or near the 10 % level.

The functionexplained 71 % of the variance in yields.

The production functions for sorghum grown on medium and fine soils explained 64 % of the variance in yields.

Both the water and the pan evaporation variables were significant at the 10

% level.

For ease of interpretation, the production functions were plotted in Figures 5 and 6.

Figure 5, for instance, shows that wheat gave better yields on medium soils for any amount of water used.

Barret and Skogerboe (1980) developed a production function for maize in Grand Junction, Colorado. A constant fertility level was assumed. They only changed the irriga-

cr 1362

-J

908

454

2724

2270

1816

1028

2056

(N))

3084

(30)

4112

WATER IN CUBIC METERS

(oc -in)

540

(50)

6168

(60)

Fig. 5 Production Function for Wheat.

Source: Ayer and Hoyt

(1981)

Note: unit conversion by author

2724

2770-

1816-

454

0 o i

1028

(10)

2056

(20)

30 84

(30)

6168

(40)

(50) (60)

WATER IN CUBIC METERS

(0c-in)

Fig.

Production

Function for

Sorghum.

Source: Ayer and

Hoyt

(1981)

Note: unit conversion by author

42 tion application efficiency.

Figure 7 summarises their findings.

At an irrigation depth of 600 mm, for example, grain yields were 8000, 7000, 6000 and 5000 kg/ha for efficiencies of 100, 82, 71 and 48 percent. These curves show that water can be conserved for highly efficient systems.

Kumar and Khepar (1980) used quadratic and square root type production functions for wheat, grain, mustard, berseem, cotton, sugarcane and paddy in a linear programming model. The empirical functional relationships were expressed as: square root function Y = a - bW + cW

2 quadratic function

Y = a + bW - cW

(49)

(50) where

Y = crop yield in quart/ha,

W = amount of water/unit area to produce Y and a,b,c = empirical coefficients.

Table 4 gives the values for the a, b, c coefficients, the coefficients of determinations and the different levels of water that result in maximum crop yield.

Morin (1977) reported a production function developed experimentally by Morin and Matlock (1975) at the

Atterbury Watershed located near Tucson. On plots of various sizes, they planted grain sorghum from 1970 to 1973 and measured the sorghum water use and the yields. The following production function resulted: when sorghum consumptive use was less than 150 mm, grain yield was 0 kg/ha;

10000

8000

7 a

6000

Cri

2 C

4000

NIP nIN

ir 2000

/ /

/ / /

•

! / /

/ /

/ /

/1/ I

200

400

600

I I

800

1000 it

DEPTH OF IRRIGATION WATER APPLIED

(x)

(mm)

4=1

1200

Fig.7 Production Functions for Maize at Different

Irrigation Application Efficiencies.

Source: Barret and Skogerboe (1980)

Table 4. Production Functions for Different Crops.

Crop Coefficients R2 Values of W at which

Y min. Y max.

Sq rt. Function a b c

Wheat

26.52 .033 1.15 .65

Mustard 14.74 .012 0.41 .90

Berseem 25.54 1.07 57.2 .98

Cotton 6.60 .013 0.624 .95

Paddy

5.94 .035 2.41 .30

307.2

320.7

716.2

526.1

1173.5

Max value of Y.

36.58

18.44

791.20

13.76

47.25

Quadr.Function

Grain

15.48 .046 .0002 .86

Sugarcane

-11.54 2.93 .0027 .99

65.89

119.76

542.30

18.21

782.50

Source: Koumar and Khepar (1980)

Notes: yields are in quart/ha (qt/ha), conversion factor from quart to kg was not reported.

Y = yield

W = applied water.

45 when consumptive use was between 150 mm and 220 mm, yield was between 500 kg/ha and 800 kg/ha; when consumptive use was greater than 220 mm, yield was greater than 1700 kg/ha.

MODEL DESCRIPTION

A simulation model of micro catchment water harvesting systems was developed. The purpose of the model is to assist planners/designers in determining component sizes for micro catchment systems and in evaluating their performance.

Conceptually, the model is represented by the schematic diagram given in Figure

The components and processes shown in the figure are treated sequentially in the model, beginning with rainfall and ending with evapotranspiration and related crop yield.

The computer model consists of a main program and three subroutines. Figures

9, 10, and

11 show how the main program and the three subroutines are integrated in the overall systems model.

Model Requirements

Potential users of the model will need the following hardware, software, and input data.

Hardware

- an IBM-compatible, personal computer with 64 K or more random access memory (RAM) and a single floppy disk drive and

- a line printer

Rainfall

Evaporation

Rainfall

Evaporation

RESERVOIR Runoff losses

Infiltration

I nf i f

'ration

Consumptive use

Seepage

SOIL LAYERS

(

- n )

Deep percolation

Fig. 8 Schematic Diagram of a

Water Harvesting System.

START

LIST

RAINFALL DATA

FILES

YES NO

Y__

READ DATA

INPUT AND

ERONLOLD_EILE

STORE NEW

DATA INTO NEW

FILE

COMPUTE

RUNOFF

ILI

D. cc I

0 cO

5 g

r -

5 —

INPUT

RESERVOIR cc

PARAMETERS

MIMP

PRINT

RAINFALL RUN-

OFF DATA

SELECT

CROP

-J

00'

READ TEMP.,

S. RADIATION a

SOIL

PARAMETERS

1. .111•11.

•••••

ORMa

•nn•

COMPUTE

PRINT RAINFALL

INFLOW, OUTFLO4

SW, AET

•Ms. MEN. =10

COMPUTE &

PRINT INFLOW,

OUTFLOW,

IRRIGATION,

EVAPORATION

Fl SFFIVAF

Fig. 9 Main Program Flowchart.

CREATE

NEW

r"FtAINFALL DATA

FILE

Fig.

Catchment Area Subroutine Flowchart.

INPUT

PARA-

E TERS ti CATCHMENT

AREA

SELECT OF

READ

EMERGENCE

DATE

YES

TCHMENT

C OM

PUTE

RUNOFF

COMPUT

RUNOFF

INPUT

S01

1.1

PAR

AMETE

COMPUTE SOL

MOISTURE

BALANCE

RINT

DAiLY,

EEKLY

MONTHLY

RESULTS

ADJUST

RUNOFF

Cultivated Area

Reservoir

Fig.

Cultivated Area and Reservoir Subroutine Flowcharts

2. Software

- the program diskette (single sided or double sided) and an enhanced beginners all-purpose symbolic instructional code (BASICA) language.

(The BASICA program can be copied onto the program diskette if desired.)

3. Input data

The input data requirements are extensive.

Missing data must be estimated or calculated from secondary sources.

Data required for the catchment include:

daily, weekly, or monthly rainfall,

- initial choices of sizes for the catchment area and cultivated area,

catchment area infiltration rate,

catchment treatment and treatment efficiency, runoff threshold, and runoff coefficient.

For the cultivated area the user will need in addition:

daily, weekly, or monthly maximum temperature and solar radiation.

number of soil layers and thickness of each

soil characteristics of each layer, soil porosity, soil water content at 1/3 and at 15 bars tension, saturated conductivity, initial soil moisture content,

infiltration rate,

crop rooting depth,

crop evapotranspiration (ET),

number of days from planting to maximum evapotranspiration,

production function (of water).

For the reservoir, the following parameters will be needed:

maximum seepage rate when the reservoir is full,

minimum seepage rate when the reservoir is nearly empty

reservoir side slope,

reservoir maximum capacity,

reservoir maximum depth,

pond evaporation coefficient and

initial reservoir water content.

Summary of Assumptions

Several simplifying assumptions were made in developing the model. They are summarized here to emphasize the limitations they place on use of the model in different locations and the continuing need to collect and integrate local data for calibrating the model.

For the catchment area the assumptions are:

daily rainfall can be derived from weekly or monthly data,

on treated micro catchments, vegetation and antecedent moisture have little effect on runoff,

evaporation loss is negligible.

For the cultivated area the assumptions are:

- a daily infiltration rate can be used (short-term infiltration characteristics are not considered),

- there is no drainage problem, and no drainage problem will occur,

- the depth to ground water is low enough that it has no effect on the system,

- crack flow is negligible in percolation,

- ET is distributed equally among the active soil layers,

- root depth increases linearly from the planting date to the date of maximum consumptive use,

- after the date of maximum consumptive use, root growth stops.

The Main Program Structure

The main program acts as a regulator for the three subprograms. It stores rainfall data files and allows the creation of new ones. The main program also stores all the solar radiation and temperature data. As soon as a rainfall file is selected, the main program passes the control to the catchment area subroutine, which calculates the rainfallrunoff relationship; results are printed in this subroutine.

The control comes back to the main program, which contains a list of five possible crops, their coefficients and the soil parameters.

Additional crops and coefficients can be included in the program. Upon choosing a crop, control passes to the cultivated area subroutine, which computes the soil water balance and prints it. From the cultivated area

54 subroutine, the control comes back to the main program which directs it to the reservoir system subroutine. The reservoir water balance is computed in this subroutine and printed.

If the daily rainfall option is selected, all other routines are "daily"; if the weekly rainfall option is selected, all other routines are "weekly" and likewise if the monthly rainfall option is selected, all other routines are "monthly".

The Catchment Area Subroutine

This subroutine, called Collect, is adapted from

Cluff (1977) and modified to calculate runoff from the catchment area. Evaporation and infiltration, although included in the model, are embedded in the runoff coefficients and not treated as such. The subroutine arranges the data in an appropriate form to be inputted in the cultivated area and reservoir system subroutines. Collect offers three

Options for rainfall data entry: the first option allows the user to empty a daily rainfall data file into an array. If this data file does not exist, Collect creates one where rainfall is inputted into the computer and stored in the new file before emptying it into an array. The rainfall data file is then stored on disk for other users or for the next session; it can be called up any time. Each rainfall event is represented by three values: the month, the day, and the amount in millimeters or in inches.

Runoff

Runoff is calculated for two different catchment conditions: the first catchment option is for non-treated or natural conditions. Here, runoff is computed using a runoff coefficient and a runoff threshold. The runoff coefficient is a decimal fraction which yields the quantity of runoff from a given quantity of rainfall after a threshold value has been exceeded. The runoff threshold is the quantity of rainfall required before runoff will commence.

The following equation calculates runoff on a daily basis:

RC (RAIN

- BT ) (51)

Where RO

= daily runoff in mm,

RAIN

= runoff coefficient,

= rainfall amount in mm, and

BT = basic threshold.

Collect offers a choice for computing runoff for vegetated or bare areas; runoff decreases when the catchment is vegetated. A subroutine also keeps track of the amount of rainfall during the five previous days because runoff increases as the antecedent moisture increases.

The second catchment option is for treated surfaces.

Collect requires a catchment treatment efficiency and a runoff threshold to calculate runoff according to the equation:

(52)

Where

(TE

RAIN)

-RT

= runoff in mm,

= treatment efficiency,

RT = runoff theshold and

RAIN = rainfall amount.

Rainfall option 2 allows the user to input weekly rainfall data starting with the first year, the first week and the rainfall amount. Thereafter, Collect increases the week by one until all 52 weeks of the year are considered.

In this option, the antecedent moisture and runoff coefficients are no longer applicable because weekly rainfall data are not representative of individual storms. Collect therefore uses a linear regression technique to compute runoff as a function of rain.

Given weekly rainfall amounts, the model computes the average daily values by dividing the weekly values by 7.

This method assumes that there is a rainfall event each day of the week and that the total amount will add up to equal the weekly amount. Using the daily averages, Collect goes back to rainfall option one and computes runoff with daily runoff coefficients. The process of determining daily runoff coefficients was repeated several times using data from several storms and runoff events in Tucson. These values, in turn were used to fit a regression model of the form:

Runoff

= a

+ b

(rainfall)

(53) where a = constant (y intercept of the regression line) and b = constant

( slope of the regression line

)

The values of a and b implicitly include the antecedent moisture conditions and runoff coefficients.

Figures 12 through 17 show some of the points fitted with the regression equation.

Figures 12 and 13 represent rainfall runoff analysis for treated catchments with treatment efficiencies of 70 % and 50 % respectively. Figures

14 and 15 represent rainfall-runoff analysis from untreated catchments with no vegetation.

Runoff coefficients and basic thresholds are 0.5 and 3.1 in Figure 14, and 0.45 and

0.2 in Figure 15. Figures 16 and 17 represent rainfallrunoff analysis for untreated catchments with some vegetation. Runoff coefficients and basic thresholds are 0.5 and

3.1 in Figure 16, and 0.45 and 0.2 in Figure 17. These

Figures reveal a nearly perfect correlation between the dependent variables (runoff) and the independent variables

(rainfall). From 90 % to 99 % of the variances in runoff are explained by the rainfall, therefore by the antecedent soil moisture conditions and the runoff coefficients. The slopes of the regression lines (h) are all significant at the 95% level.

Finally, the third rainfall option allows the user to calculate runoff data even if only monthly storm data are available. The procedure is similar to the one described above for weekly rainfall data. All three rainfall options require the user to input new rainfall data for each year because of the changes that occur in the physical characteristics of the catchment area from one year to the next.

18 -

14 -

1•111

Elf o

Rainfall

(mm)

Fig. 12 Rainfall -Runoff Analysis for a Treated Catchment.

Notes: treatment efficiency

= 70%; runoff threshold

= 3.5;

Y-intercept

= -1.06; slope

= 0.572

58-

10 20

.Rainfall (rm)

Fig. 13 Rainfall-Runoff Analysis for a Treated Catchment.

Notes: treatment efficiency= 50%; runoff threshold=3.5

Y-intercept

= -0.79; slope = 0.355

26 -

24 1

60 a

10.

Rainfall

(=)

Fig.

14 Rainfall-Runoff Analysis for an

Untreated

Catchent wit'a No

Vegetation.

Notes: runoff coefficient

Y-intercept

= 0.5; basis threshold

= 3.1

= -1.024; Slope

= 0.596

24 -

20 -

18 -

16 -

-I

12 -

g 10

6 -

4 -

2 -

o o

Rainfal (mm)

Fig. 15 Rainfall-Runoff Analysis for an bntreated

Catchment with No Vegetation.

Notes: runoff coefficient = 0.45; basic threshold = 0.2

Y-intercept = -0.144; Slope = 0.72

20 -

18 -

16 -

14 -

12 -

's go 10 -

8 -

6 -

2 -

EP ri

20 3

Rainfall (rin)

Fig.

16 Rainfall-Runoff Analysis for an

Untreated Catchment with Some Vegetation

Notes: runoff coefficient = 0.5; basic threshold = 3.1

Y-intercept=

-C.943; Slope = 0.676

24 -

22-

- 14 -

12 -1

10 -

16 -

O a rP

. 20

Rainfall (mm)

Fig. 17 Rainfall-Runoff Analysis for an Untreated Catchment with Some Vegetation.

Notes: runoff coefficient = 0.45; basic threshold = 0.2

Y-intercept = -3.136; Slope = 0.675

The Cultivated Area Subroutine

The model uses a "bookeeping" method for calculating soil water content on a daily basis. The soil in the cultivated area is divided into layers. The user can specify up to 7 layers and their characteristics. This method is based on techniques used by Morin

(1977), Risley (1984), Knisel

(1980) and Wight (1982). soil water system.

Figure 18 illustrates the plant-

The following equation calculates daily soil water balance in the surface layer as:

SW = SWo + Pt + Qin + IR + Cr - ET - Pr - Qo (54) where SW

= current soil water content in mm,

SWo = previous soil water content in mm,

Pt = rainfall in mm,

Qin = water inflow from the catchment area in mm,

IR = irrigation amount in mm,

Cr = capillary rise from layer below in mm,

ET = evapotranspiration in mm,

Pr = percolation to layer below in mm,

Qo = water outflow in mm and

(Pt+Qin+IR)-Qo = amount infiltrated in the soil.

For subsequent layers, the equation is:

SW = SWo + Pr(in) + Cr - ET - Pr(out)

(55) where terms are as defined for equation 54 and

Pr(in) = precolation from layer above,

Pr(out)= percolation to layer below or to the ground water system for the last layer.

Before the simulation begins, total storage, field capacity and initial water storage in the various soil layers are computed from inputted parameters as follow:

ULi = ( PORi - SM15i ) THKi (56)

Plant

Components

ET t

Qin

---

---0

Soil Surface

Infiltratio n a

Soil

Components

Soil Layer I

Soil

Loyer n

Fig. 18 Flow

Diagram of Plant-Soil Water System

- -- -

FCi = ( SM3i - SM151 ) THKi

SW! = FCi - STF

(57)

(58) where

ULi = upper limit of soil water in layer i,

PORi = soil porosity for layer i,

SM15i = 15 bar water content for layer i

THKi = thickness of layer i and

FCi = field capacity soil moisture in layer i,

SM3i = 1/3 bar water content for layer i,

SWi

STF

= initial soil water in layer i,

= initial water content as a fraction of FC.

Evapotranspiration

The evapotranspiration (ET) component which is the driving force is computed using a modified Jensen-Haise

(1963) method and the equations:

PET = Ct ( T- Tx ) Rs

Ct = 1 / ( Cl + C2*Ch )

Cl = 38 - 2*E1/305

Tx = -2.5 - 0.14 ( e2-el ) - E1/550

Ch = 50mb / ( e2-e 1 ) es = 33.8639[(.00738*T+.8072)

- .00001911.8*T+481 + .001316]

(59)

(60)

(61)

(62)

(63)

(64) where PET = estimated potential evapotranspiration in mm/day

= maximum daily temperature in OC,

Rs = daily solar radiation in cal/cm2/day,

El = site elevation in m, e2 = saturated vapor pressure at the mean maximum daily temperature for the warmest month of the year in mb, el = saturated vapor pressure at the mean minimum daily temperature for the warmest month of the year in mb, es = saturated vapor pressure at temperature T in mb.

The solar radiation is divided by the latent heat of vaporization, L (585 cal/gram), to get the equivalent evaporation

67 units of cm/day. The original Jensen-Haise equation uses mean daily temperature values; the method described herein uses daily maximum temperatures because they are easier to obtain. The subroutine allows the user to enter temperature data in degrees Celsius or Farenheit. evaporation is estimated as:

Daily crop

ET = Kc * PET (65) where ET = estimate of daily actual plant evaporation and,

Kc = crop coefficient.

(1982) computed PET for different crops in Arizona; they experimentally measured ET values for the same crops and derived the crop coefficients, Kc using Equation 65.

Doorenbos and Pruitt (1984) presented crop coefficients for field and vegetable crops for other areas according to the climatic conditions and different stages of crop growth.

Distribution of ET in the Soil Profile

Given the computed ET for a particular day, it must be distributed in the soil layers based on the rooting depth. For plants having established root systems, an average root depth and distribution can be used for the entire simulation period. For systems starting from the plant seedling or early growth stages, however, a root growth

68 function is necessary. The root depth increases at a particular rate throughout the growing season, or the first few years in the case of perennial crops. By the time an annual crop has reached its maximum water consumptive use, root growth is assumed to have reached the maximum root depth and be stabilized.

At this point, the root growth function is stopped and the root remains at maximum depth until the end of the growing season.

Root depth is assumed to increase linearly from the planting date to the date of its maximum water use. The root depth is found by dividing the estimated maximum root depth by the total number of days elapsed from the planting date to the date of the maximum consumptive use, and by multiplying the result by the time increment:

RG =

(RD/DST)

* D

(66) where

RG = actual root depth,

= maximum root depth (inputted by the user),

DST

= days from planting to maximum water use day and

= days from planting

As an example, if DST is equal to

95 days, on the

95th day from planting,

RG would be equal to RD. The computed daily root depth is checked against the thickness of the first layer. If the root depth is less than the layer thickness, all ET is assumed to come from this layer; nothing is taken from layer

2 and the deeper layers. ET is calculated in this fashion until the root has grown enough to reach layer

At this point, ET is assumed to come equally from

69 both layers 1 and 2. Distribution of ET among active layers is obtained by dividing ET by the number of layers.

This process is repeated until the end of the growing season. At the end of the season, the root depth may or may not reach the lowest soil layer.

DST can be as high as 1500 for perennial crops.

For weekly or monthly analysis, DST and D will refer to the number of weeks or months; RG then will become the weekly or monthly growth.

Infiltration

To determine intake opportunity time, the duration of runoff from the catchment must be known, as well as the duration of direct rainfall. These data were not available, therefore the model uses an inputted average daily infiltration rate, I, for the cultivated area.

The model then calculates the total volume of water infiltrated at the end of the day, using a time increment of one day.

The water supply rate is computed as the rainfall amount that falls directly on the cultivated area plus the runoff from the catchment area. If this water supply rate is greater than the infiltration rate, the excess water becomes runoff to the reservoir. If the supply rate is less than the infiltration rate, all the water supplied infiltrates.

Percolation

The percolation component of the water budget is based on work by Kniesel (1980) and uses a storage routing

70 model to predict flow through the soil layers of the root zone.

Inflow is allowed to fill each soil layer to field capacity before percolating down into the next layer.

When the last layer is above field capacity, the excess water becomes deep percolation and is no longer useful to the plant. It may, however, contribute to ground water recharge.

Percolation is computed with the equations:

Pi = (SWi - FCi)[ 1 - exp(-Dt/Ti)]

Pi = 0 if SWi>FCi if SWi<FCi

(67) where

P = amount of percolation in mm,

= initial soil water content in mm,

FC = field capacity water content in mm,

Dt = time interval in hours,

T = travel time through the layer i in hours and, i = soil layer number, increasing with depth.

In Equation

67, the amount of percolation through the bottom of layer i is assumed to be zero if the soil moisture in that layer is less than its field capacity.

This soil water will increase the water content of that layer until the next day. The travel time is calculated as:

Ti = ( SWi - FCi ) / Hi

(68) where Hi = hydraulic conductivity for layer i.

The hydraulic conductivity is varied from the specified saturated conductivity value by:

Hi = SCi (SWi/ULi)

(69) where SCi = saturated conductivity for layer i in mm/hr and

Bi = parameter that causes Hi to approach a very small constant (e.g., 0.002 SC) as SWi approaches FCi.

Kniesel (1980) estimated that

Bi = -2.655 / [ log(FCi/ULi) l

(70)

The constant -2.655 assures that Hi = 0.002 SC at field capacity.

Capillary Rise

At the end of the day, a check is made to determine if a particular layer has more moisture than the one immediately above it. If it does, capillary rise is determined by averaging the the moisture in the two layers. The moisture from below will rise by capillarity until the moisture content in the two layers reaches an equilibrium or,

(8Woi + SWoi+1)/2 = Swo+1

(71) where SWoi = soil moisture of layer i,

SWoi+1 = soil moisture of layer i+1 and

SWo+1 = equilibrium moisture between layers i and i+1.

Reservoir Subroutine

The model provides a reservoir for water storage.

For systems without reservoirs, an inputted reservoir volume of zero will eliminate the reservoir subroutine. Excess water flows by gravity from the cultivated area to the reservoir. Then water is pumped back to the cultivated area for irrigation when needed. The reservoir is assumed to be of the shape of an inverted truncated pyramid with four equal sides and a constant slope. A cross-section taken

72 perpendicular to any pair of opposite sides has the shape of a trapezoid

(Fig.19).

The top surface area of the reservoir is calculated using the following equation:

TA = [(VM/DM) +(S*DM)]*[(VM/DM) +(S*DM)]

(72) where

= surface area of the top of the reservoir,

VM = maximum reservoir volume

= maximum depth of reservoir and

S = slope of the reservoir sides.

The surface area, TA, is used subsequently to calculate the area of the bottom of the reservoir taking into consideration the side slope :

= [

TA - (2*DM*S)]

(73) where BA

= bottom surface area of the reservoir

Storage

This routine calculates the daily, weekly or monthly water balance for the reservoir. Before the simulation begins, the user inputs values for the beginning volume of water, maximum volume, maximum depth, and the slope of the reservoir sides.

The water surface area and depth are calculated using the formulas:

= [ (6*CV*S) +

(BA)

WD = 2*CV / ( BA+SA )

3/2 2/3

(75) where SA

= surface area of the water in the reservoir,

= current water volume in the reservoir,

S = slope of the reservoir sides,

= bottom area of the reservoir,

WD = current water depth in the reservoir

Fig.

Schematic Diagram of a Reservoir.

Notes: BA

= bottom area

WD = water depth DM = maximum depth

Only the volume of the water and its depth will change with time. If the total calculated volume of water in the reservoir exceeds the maximum reservoir volume, the excess water overflows and is considered lost from the system.

Seepage

The model addresses reservoir seepage with the use of a simple linear relationship as done by Risley

(1984).

For seepage calculation, the model asks the user to provide as input a maximum seepage rate when the reservoir is filled near capacity and a minimum seepage rate when the reservoir is nearly empty. The actual seepage rate is then calculated using the following equations: where

= (((MA-MI)/DM) * WD) +

= maximum seepage rate,

= minimum seepage rate,

= maximum reservoir depth,

= seepage rate and

WD = current water depth in the reservoir

(76)

Evaporation

The reservoir subroutine computes the evaporation by the pond coefficient method. This method modified after

Wight

(1982) utilizes a pond coefficient that was allowed to vary from

0.6 to

0.8.

Total evaporation from the reservoir surface is computed by multiplying the monthly, weekly or daily potential evaporation rates by the total reservoir surface area and by the pond coefficient.

75 where

PET

Pc (77)

= reservoir evaporation rate,

= current water surface area in the reservoir,

PET

= potential evaporation rate and

= pond coefficient

Optimization

Optimization is required if the model is to accomplish its purpose of providing design information. Optimization is the process by which the different components of the model--cultivated area and its parameters and catchment area and its parameters can be tested and results checked in order to eliminate unrealistic values. Various reservoir sizes and shapes can be tried as desired until an optimum reservoir size for the given catchment and cultivated areas is found: a size big enough to accommodate the incoming runoff but small enough to stay full throughout the growing season. If the optimum size is not feasible, the catchment and the cultivated areas may be changed to determine a more suitable reservoir size. Often reservoir construction is the most expensive part of a water harvesting system. Seepage and evaporation control are additional costs. An option that utilizes a smaller reservoir will be helpful in reducing costs.

CASE STUDY

A case study was used to validate and to demonstrate the capabilities of the model. It shows how the model can be used to:

- design a water harvesting system,

- study the relationships between system components

(catchment area, cultivated area and reservoir) and their sizes, and

- determine potential crop yield from a specific design.

Variable Estimation and Model Calibration

The data for the case study came from the literature or from previous work at the University of Arizona.

An effort was made to use data that reflect as closely as possible the conditions near Tucson, Arizona. See Appendix

D for a complete list of site parameters used.

Rainfall and elevation data for Tucson for 1984 were taken from Arizona Climatological Data (1984). Mean maximum monthly temperatures for Tucson were taken from Arizona

Climate (1982) for the period from 1949 to 1982.

The maximum weekly and daily temperatures data were averaged over a shorter period (1975-1979). Temperature values reported in degrees Farenheit were converted to

Celsius.

Mean maximum solar radiation data also were taken from Arizona Climate (1975-1979). Daily data were averaged over five years and then used to compute weekly and monthly averages. All solar radiation data were reported in watt hours per square meter and were converted to calories/cm.

Catchment treatment efficiency for various materials used was obtained from Matlock (1985). Runoff coefficients and basic thresholds were estimated from the general soil types and conditions (texture, water holding capacity, degree of compaction, type of crop supported and land use).

For the reservoir system, a high seepage rate of

.005 mm/hr and a low seepage rate of .002 mm/hr were assumed.

Evapotranspiration was computed using the Jensen-

Haise method (refer to equations 59 through 65). For a location near Tucson, Arizona, the following constants were estimated

maximum average temperature = 101.4 oF, therefore e2=27.9 nib

minimum average temperature = 73.2 oF, el=68.3 nib therefore e2-el = 40.4 mb

(67)

(68) - Ch =

50mb/(e2-el)

= 50/40.4 = 1.238

- Cl =

38 - 2* E1/305

= 38-2*744/305 = 32.833

(69)

- Ct =

1/(C1+7.3*Ch) = 1/(32.833+7.3*1.238) = 0.0239

(70)

Tx = -2.5 -.14 (e2-el) - E1/550 =

-2.4 -.14 (40.4) - 744/550 = -9.509

PET = Ct(T-Tx)Rs = .0239(T+9.509)Rs/58.5 mm/day.

(71)

(72) where PET = estimated potential evapotranspiration (mm/day)

Ch = humidity index

Cl = elevation adjustment factor for temperature/radiation relationships

Ct = air temperature coefficient

El = Tucson elevation (meter) el = saturated vapor pressure at the mean minimum daily temperature for the warmest month of the year (mb) e2 = saturated vapor pressure at the mean maximum daily temperature for the warmest month of the year (mb)

= maximum daily temperature (oC)

Rs = daily solar radiation (cal/cm2/day) es = saturated vapor pressure at temperature T (mb).

Equation (72) was used to compute potential water use by the plant. To get the actual consumptive use, the potential use was multiplied by the crop coefficient. The crop coefficients for cotton, grain sorghum, navel oranges, potatoes, beans, sugarbeets, barley, broccoli, wheat and other crops were given by Erie, et al. (1982).

Soil porosity (44%), water content at 1/3 bar (12%) and at 15 bars (5%) and saturated conductivity (9mm/hr) represent average values for a loamy soil.

For the rainfall-runoff calculations, the following basic parameters were first chosen:

catchment area 1000 m2,

cultivated area 1000 m2,

runoff coefficient 0.45,

basic threshold 0.5 mm catchment treatment efficiency 70 %

runoff threshold 3.5. mm

reservoir capacity 100 m3,

reservoir initial content 50 m3

maximum reservoir depth 3 m,

maximum reservoir seepage .005 mm/hr and

For yields estimated production functions developed by Ayer and Hoyt (1981), and Morin and Matlock (1975) were used.

minimum reservoir seepage rate .002 mm/hr

cultivated area infiltration 10 mm/hr

Results and Discussions

The model was first tested with the parameters as given above. Grain sorghum and cotton were chosen to be planted on the cultivated area.

Using daily rainfall data, the computed runoff amounted to 64.4 mm or 36 perc h ent of the annual rain (Table

5). Results indicated that larger storm events produced more runoff on a percentage basis; this may be explained by the fact that smaller events went primarily to satisfy the initial soil abstractions.

The model results showed no yield for cotton and grain sorghum with the initial basic parameters; therefore the parameters were modified until positive yields were obtained. To do this, the cultivated area was kept at 1000 m2 but the catchment area and the reservoir parameters were changed as follows:

- the reservoir parameters were maintained at the initial levels, but the catchment area was increased until there was no further increase in crop yields and in the amount of water infiltrated in the cultivated area. At this point the catchment area was fixed with a catchment-cultivated area ratio (CCAR) of 40;

- the reservoir parameters were then increased until the amount of overflow from the reservoir became positive; this meant varying the reservoir side slope, maximum volume and maximum depth relationships. The new reservoir parameters were:

maximum volume = 1000 m

maximum depth = 5 meters.

The rest of the parameters remained unchanged.

In addition to the catchment-cultivated area ratio

(CCAR) of 40, and a reservoir volume of 1000 m , the model was run with two more values of CCAR to determine what reservoir sizes would be required to maintain the same

3 yield. A CCAR of 30 required a 1200 m reservoir and a CCAR

3 of 50 required an 800 m reservoir to maintain the yield of

3700 kg/ha of grain sorghum obtained with the CAR of 40 and

3 the 1000 m reservoir combination.

The model then was run with daily rainfall data using cotton in case 1 and grain sorghum in case 2. Input values and results are summarized in Table 5.

In case 1, the initial soil moisture was 112 mm on January 1 and the final soil moisture was 102 mm on

Table 5. Simulation Results.

DAILY data case

WEEKLY data

MONTHLY data numbers

4 5 6

INPUT DATA

Crop

Rain

(mm)

Catchment area

(m2)x100

Cultivated area

(m2)x100

Reserv. volume

(m3)x100

Reser . depth

(m)

Maximum.seepage

(mm/hr)

Minimum seepage

(mm/hr)

RESULTS

Infiltration

(mm)

Percolation

AET

(mm)

Irrigation

(mm)

Reser.evaporat.

(m3) reser.seepge

(m3)

Crop yield

(kg/ha)

Initial S.water

(mm)

Final S. water

(mm)

Difference

(mm) cot sor

181 181

400

10 10

.005

.002

603 603

270 277

1056 621

713 332

791

804

405

403

1345

3700

112 112

102

148

-10 +36 cot

181

400

859 859

481 496

1024

602

721 349

413

315

420

321

1300 3580

112 112

187

222

+75

+110 sor

181

400

5 5

.005

.002

cot sor

180 180

400 400

10 10

.005

.002

644 644

284

278

897 556

493 136

417 421

314 317

1145 3300

112 112

93 120

-19

MORIN data

Notes: cot=cotton; sor=sorghum; AET=actual evapotranspiration sor

191

650

.005

.002

277

2000

111

-21

549

260

512

567

December 31. Total water infiltrated was equal to 603 mm and the irrigation amounted to 713 mm. Actual cotton water use was estimated to be 1056 mm with a yield of 1345 kg/ha.

The soil water balance on the cultivated area as predicted by the model was therefore: initial soil water + infiltration + irrigation - actual ET - percolation=final soil moisture; or 112+603+713-1056-270 = 102 mm.

In case 2, the initial soil moisture was 112 mm on January 1 and the final soil moisture was 148 mm on

December 31. Total water infiltrated was equal to 603 mm and the irrigation amounted to 332 mm. Actual sorghum water use was estimated to be 621 mm with a yield of 3700 kg/ha.

The soil water balance on the cultivated area was therefore:

112+603+332-277-621=149 mm as predicted by the model.

The model was next run using weekly data with cotton in case 3 and grain sorghum in case 4.

In case 3, the initial soil moisture was 112 mm on January 1 and the final soil moisture was 187 mm on

December 31. Total water infiltrated was equal to 859 mm and the irrigation amounted to 721 mm. Actual cotton water use was estimated to be 1024 mm with a yield of 1300 kg/ha.

The soil water balance on the cultivated area was therefore:

112+859+721-1024-481=187 mm as predicted by the model.

In case 4, the initial soil moisture was 112 mm on January 1 and the final soil moisture was 222 mm on

December 31. Total water infiltrated was equal to 859 mm and the irrigation amounted to 349 mm. Actual sorghum water

83 use was estimated to be 602 mm with a yield of 3580 kg/ha.

The soil water balance on the cultivated area was therefore: 112+349+859-602-496=222 mm as predicted by the model.

Using weekly data as in cases 3 and 4, total irrigation and plant actual water uses, compared to the daily data

(cases 1 and 2), were overestimated; since the rainfall and the crop data were the same as in cases 1 and 2, these values should be nearly the same as the daily data. The infiltration opportunity time on the cultivated area was therefore adjusted. In the weekly case, the infiltration opportunity time was double the daily time. These modifications allowed the actual evapotranspiration (AET) and irrigation water, the two most important results to approach and be more compatible with the daily results.

The model was again run using monthly data with cotton in case 5 and grain sorghum in case 6. As with the weekly data, water infiltration opportunity time also was modified by a factor of 4.

In case 5, the initial soil moisture was 112 mm on

January 1 and the final soil moisture was 93 mm on December

31. Total water infiltrated was equal to 644 mm and the irrigation amounted to 493 mm. Actual cotton water use was estimated to be 897 mm and a yield of 1145 kg/ha. The soil water balance on the cultivated area was therefore:

112+644+493-897-93=259 mm or 166 mm above the 93 mm final soil water predicted by the model.

In case 6, the initial soil moisture was 112 mm on

January 1 and the final soil moisture was 120 mm on December

31. Total water infiltrated was equal to 644 mm and the irrigation amounted to 136 mm. Actual sorghum water use was estimated to be 556 mm with a yield of 3300 kg/ha. The soil water balance on the cultivated area was therefore: 112+136

+644-278-556=58 mm or 62 mm below the 120 mm predicted .

The last case involved data from experiments of

Morin and Matlock (1975). They measured sorghum yields near Tucson in 1970, 1971 and 1972.

The 1970 results were chosen for testing the model because the total rainfall of that year, 190 mm, was close to the total rainfall of 181 mm used in the model. Actual daily rainfall data for 1970, obtained from Morin (1977), were used. Other data were:

- crop: sorghum

- cultivated area soil: clay loam

- catchment area: 6.5 ha ( 65,000 m2 )

- cultivated area: 0.2 ha ( 2,000 m2 )

- total annual rain: 191 mm

- measured sorghum yield: 800 kg/ha- 2300 kg/ha

The catchment area was not treated, and some vegetation was growing on it.

Using these data and Morin's production function, the model predicted a yield of 2000 kg/ha which was within the range of measured sorghum yield.

SUMMARY AND CONCLUSIONS

A computer-based model of a micro catchment water harvesting system was developed for planners and designers.

The model requires at least 64 K of random access memory. It was written for an IBM-compatible personal computer.

Model Description

This model is a sequential step water budget analysis device. It facilitates study of the different components of a micro catchment water harvesting system and the interactions among them. It contains a main program, a catchment subroutine, a cultivated area subroutine and a reservoir subroutine.

Daily, weekly or monthly data can be used. The catchment subroutine calculates the runoff from rainfall on the catchment. Catchment surfaces can be natural or treated to increase runoff. Existing runoff equations were adapted for use in the model.

The cultivated area subroutine calculates the amount of water available to a chosen crop by a soil water balance method. Up to 7 soil layers can be included. Perennial or annual crops can be selected. The various components of the water budget are initial soil moisture content, precipita-

86 tion, water inflow from the catchment area, irrigation, evapotranspiration, infiltration, percolation, capillary

Production functions are rise and excess water outflow. used to estimate crop yield.

Existing equations were adapted for analysis of evapotranspiration, infiltration, percolation and capillary rise.

The reservoir subroutine uses a water balance method to calculate reservoir water content at the end of each period. The reservoir contents depend on water inflow, irrigation outflow, evaporation, seepage, and excess water outflow. Existing equations were used to determine evaporation and seepage losses.

Model

Validation

The model was first tested with artificial data on a daily, weekly and monthly basis with cotton and sorghum crops. Initially, actual evapotranspiration and yields were higher in the daily cases for both crops. Catchment area, cultivated area and reservoir parameters then were adjusted to insure that results using weekly and monthly data would approach results obtained using daily data.

Subsequently the model was tested using data reported by Risley (1984) and Morin (1977). Risley's experiment was based on weekly data; for comparison the model was run with the weekly option. AET for sorghum was 49 mm lower than Risley's measured AET and irrigation fell 116 mm

87 short of his actual irrigation. For cotton, AET and irrigation were also underestimated.

Morin's experiment were based on daily data; for comparison with his work the model was run using the daily option. Morin predicted 251 mm for sorghum water use and measured an irrigation amount of 520 mm. This model predicted 512 mm crop water consumptive use and no irrigation water. Morin's grain yield was 1550 kg/ha; here, the estimated sorghum yield was about

2000 kg/ha. On a daily basis, the prediction of crop water use and irrigation was close to the measured data.

Conclusions

The model serves as a planning tool. It can be used for feasibility studies and for design of micro catchment water harvesting systems. The model is more useful in developing countries where adequate hydrologic data are difficult to find. The program and subroutines can be run with available data and estimates of other parameters based on values from hydrology handbooks. The program is not copy-protected, nor copy-righted, and copies can be made and used as desired. The model is flexible. The catchment area parameters can be changed one at a time and the resulting runoff checked before proceeding to the next step.

The cultivated area and the reservoir subroutines offer the same type of flexibility. With a minimum knowledge of BASIC language, the user can add crops to the five available in the program.

In its current form the model cannot simulate production of plants with root depth greater than 3 meters.

The infiltration function is greatly distorted by the assumption necessary to include infiltration as a component.

Additional work will be needed to increase model accuracy in this respect.

The model is user friendly. However, if the user is not a hydrologist, soil scientist, or engineer, assistance will be required from qualified professionals in estimating variables. The accuracy of the results depends on the accuracy with which the parameters are estimated.

The use of weekly and monthly rainfall data requires knowledge of daily rainfall characteristics. The coefficients derived for the model are based on Tucson, Arizona data and will not be suitable anywhere else. Weekly and monthly results did not adequatly relate to daily results.

Estimates may provide a starting point for design, but ultimately field checking and/or a pilot project will be necesary.

APPENDIX A

GUIDE MANUAL FOR USING THE PROGRAM

After booting the computer in BASICA and loading the program into memory, the user can run it by typing RUN.

The user has to answer questions or type in numbers as prompted by the computer, step by step. These steps are reproduced here, like they appear on the screen when running the program.

The Rainfall - Runoff Model

Steps 1 through 8.2 pertain to the rainfall-runoff model.

THE FOLLOWING IS A SELECTION OF RAINFALL DATA FILES.

The user is presented with a list of data file names, numbered from 1 to 10. Some numbers do not have any file names assigned to them; -these numbers are available for creating new data files for users who want to try a different area.

TYPE IN THE CORRESPONDING NUMBER OF THE FILE YOU WISH TO

USE. FOR A NEW FILE, TYPE A NUMBER THAT IS AVAILABLE.

The user simply chooses the number of the data file to be used. If the file does not exist yet,it can be created by typing any number that does not have a corres-

90 ponding file name assigned to it.

ENTER THE YEAR OF THE RAINFALL DATA FILE.

This step allows the computer to make adjustments for leap and regular years.

4. ENTER 1 FOR DAILY RAINFALL DATA 2 FOR WEEKLY DATA, OR

CARRIAGE RETURN FOR MONTHLY DATA.

This step tells the computer whether the data file is daily, weekly or monthly data. If the file chosen in step 2 does not exist yet, entering 1 here will let the user input daily data from 1 to 365/366; entering 2 or

<CR> will allow the entry of weekly ( 1 to 52 ) or monthly ( 1 to 12 ) data.

ENTER 1 IF CREATING A NEW RAINFALL DATA FILE, ENTER 2 IF

USING AN EXISTING ONE.

If the user choses 2, the data file identified by the number entered in step 1 is read into memory.

The user is now ready for step 1 in the catchment area.

If 1 is chosen, the user will go through the following steps to create the new file and assign it to the number entered in step 2.

ENTER THE NAME OR LOCATION OF THE NEW RAINFALL DATA

FILE.

This name will be assigned to the number chosen in step 2 and will be included in the data file listing from now on.

For this reason, the name chosen here should describe the type of data that will be stored in the file.

For example, the year, the location and the type of data can be coded.

ENTER 1 IF THE STORM AMOUNTS ARE IN INCHES, ELSE PRESS

RETURN.

This step merely lets the user enter data either in inches or millimeters. Inches will be converted to millimeters later in the program.

ENTER MONTH (1-12), DAY (1-31) AND STORM AMOUNTS.

This step is the result of choosing 1 in step 4.

Suppose a particular year has rainfall of 2.8 mm on March 12 and 15.3 mm on June 27. The user will enter 3, 12, 2.8 then

RETURN. The program will proceed to steps 8.1 and 8.2.

8.1 ENTER 1 IF THIS INPUT WAS INCORRECT, PRESS RETURN TO

CONTINUE.

Entering 1 will take the user back to step 8 for corrections; entering RETURN will lead to step 8.2.

8.2 ENTER 1 IF THIS IS THE END OF THE YEAR, ELSE PRESS

RETURN.

A carriage RETURN will allow the user to enter the next set of data in step 8; in this case, 6, 27, 15.3. If no rain occurred on a particular date, a carriage RETURN will enter a zero value for that date.

The user will press

RETURN as often as it takes to enter all the data. After this, the user will be directed to the program for the catchment area.

8.3 WEEK No, STORM AMOUNT ?

If the weekly option is chosen in step 4, the user can enter the storm amounts in front of the week numbers.

After each item is entered, the week is automatically increased by 1.

8.4 MONTH, STORM ?

This step operates in the same manner as step 8.3

except that the monthly option was chosen in step 4. At the end of this data entry routine, a file is created and the new data stored. This data file is given the number chosen in step 2. It is written on the diskette and becomes a permanent part of the program.

Every time the program is run it will appear on the list in step 1.

The Catchment Subroutine

ENTER THE CATCHMENT AREA IN SQUARE METERS.

This step and the next are self explanatory

ENTER THE CULTIVATED AREA IN SQUARE METERS.

ENTER THE CULTIVATED AREA INFILTRATION RATE IN MM/HR.

ENTER 1 IF THE CATCHMENT AREA HAS BEEN TREATED, ELSE

ENTER 2.

If the catchment area has been treated to enhance runoff, the user will enter 1; this choice will prompt step

4.1. If the catchment has not been treated, the user will enter 2 which will direct the user to step 4.2.

4.1 ENTER PERCENT RUNOFF EFFICIENCY AND RUNOFF THRESHOLD.

The runoff efficiency is the estimated treatment efficiency that depends on the material used. From here the user is ready for step 5.

4.2 ENTER RUNOFF COEFFICIENT AND BASIC THRESHOLD.

The runoff coefficient is an estimated decimal fraction of a quantity of runoff over a quantity of rainfall after the basic threshold has been exceeded. The basic

93 threshold is the estimated quantity of rainfall required before runoff will begin. A trial and error method may be used to find appropriate coefficient values.

4.3 ENTER 1 IF VEGETATION IS GROWING ON THE CATCHMENT AREA,

ELSE ENTER RETURN.

For natural or untreated catchments, this option will adjust the runoff because vegetation has been found to reduce the amount of runoff. This option is not available for treated areas because the effect of vegetation here is assumed negligible.

5. ENTER 1 IF YOU WISH TO CHANGE WATERSHED PARAMETERS, ELSE

ENTER RETURN.

Before this step is executed, rainfall-runoff results are computed and printed.

Thus the user has an opportunity to review the output before making any changes.

Step 5 gives the user the option of holding some variables constant and changing others or changing all the parameters.

A carriage RETURN will terminate this subroutine and the cultivated area subroutine will commence.

The Cultivated Area subroutine.

1. ENTER 1 IF THE WATER BALANCE FOR THE ENTIRE SOIL PROFILE

IS DESIRED; ENTER 0 FOR LAYER BY LAYER OUTPUT. (THIS

WILL BE A MUCH LONGER OUTPUT)

The program calculates the soil moisture balance from layer 1 through layer 7 but gives the user the option of printing only the summarized results for the whole soil profile.

This makes the results more legible and saves paper.

Entering 0 here will result in a long printout

94 because the computer has to go through 7 layers for each day. Seven times 366 will give 2562 rows of printed material. The user can choose to reduce the number of lines by printing only at the end of rainy days.

ENTER YEAR, MONTH AND DAY TO START THE SIMULATION

ROUTINE.

(IT IS BETTER TO START WITH THE CROP

EMERGENCE DATE). FOR WEEKLY AND MONTHLY SIMULATIONS,

ENTER THE YEAR AND 1, 1.

Because this subroutine computes the crop consumptive use by a modified version of the Jensen-Haise method, the number of days after emergence is needed. For weekly or monthly output, the user starts with the first week or month of the season.

At this point the user is shown a list of names of crops before moving to the next step.

ENTER CROP NUMBER.

The user is asked to choose one of the crops listed on the screen. The program then computes the water use for that crop and the moisture balance up to the end of the year. It then proceedes to the reservoir subroutine.

The Reservoir Subroutine

ENTER THE RESERVOIR SIDE SLOPE.

The program assumes the reservoir to be of the shape of an inverted truncated pyramid with four equal sides and a constant slope. The slope is computed as rise/run. For a slope of 1:1 for example, the user will enter 1; for a slope of 1:2, the user will enter 0.5 and so on.

ENTER THE RESERVOIR MAXIMUM VOLUME IN CUBIC METERS.

This is the maximum storage capacity for the reservoir. Any volume of water greater than this capacity will produce losses by overflow.

ENTER MAXIMUM RESERVOIR DEPTH IN METERS.

This step tells the computer how deep the user wants the reservoir to be.

ENTER THE MAXIMUM SEEPAGE RATE WHEN THE RESERVOIR IS

FULL.

ENTER THE MINIMUM SEEPAGE RATE WHEN THE RESERVOIR IS

NEARLY EMPTY

Estimates of these two values are required for a realistic simulation.

ENTER THE INITIAL VOLUME OF WATER IN THE RESERVOIR.

This is the amount of water in the reservoir before the beginning of the simulation.

7. ENTER 1 IF YOU WISH TO CHANGE THE RESERVOIR PARAMETERS,

ELSE PRESS RETURN.

The last option allows the user to change some of the reservoir parameters and or adjust others. Entering 1 will lead the user to step 1 and repeat the loop until a carriage RETURN; this will terminate this subroutine and the program.

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134

APPENDIX D

CASE STUDY PARAMETERS

Soil Layer Parameters

LAYERS

1 2

3 4 5

6 7

Soil

Porosity(mm/mm) 0.44

0.44

0.40

Water at 1/3 bar(mm/mm)

0.12

Water at 15 bars(mm/m)

0.045

0.045 0.056

0.056

Saturated Cond.(mm/hr)

12.7

11.43

7.62

Layer Depth (mm)

305 305 305

305 305

% of Water Extracted

40 30

20 7 1 1

1 by Roots in each Layer

Maximum Monthly Temperature and Mean Monthly Solar Radiation

(Tucson Data)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec oF 66.4 70.0 74.5 82.9 90.7 100.2 100.6 98.7 96.2 87.1 75.2 67.4

Rad. 289 384 477 614 672

706

579 581 510 423 330

Mean Maximum Weekly Temperature (oF)

67.2

66.9

66.7

66.5

65.8 66.6

67.5

68.4

70.4

71.3

72.3

73.3

74.4

76.2

78.1

80.1 82.1

83.9

85.7

87.4

89.2

91.0

93.2

95.5

97.7

99.9

100.3 100.4

100.5 100.6

100.4

100.0

99.6

99.1

98.7

98.2

97.6

97.0

96.4

94 7 92 7 90.6

88.0

86.3

83.5

80.8

78.0

66.0

67.2

66.9

Mean Weekly

Solar Radiation(langley/cm2)

287 311 274 317 329

313 361 448 425

430 462 525

504

576

578 586 692 619

668 694 667 718 689 723

715

692

658 608 536 531

611

608 561 533 593 505 507 551

501

476 457 443

367 386

381 319 325 288 318 304

268

255

135

REFERENCES CITED

Anderson, C. E., H. P. Johnson and W. L. Powers. 1978. A

Water Balance Model for Deep Loess Soils. Transactions of the ASAE. Paper No. 76-2004. pp. 314-319.

Ayer, H. W. and Paul G. Hoyt. 1981. Crop Water Production

Functions: Economic Implications for Arizona.

Agric. Experim. Station Technical Bulletin # 242.

The University of Arizona. Tucson.

Barrett, J. W. H. and G. V. Skogerboe. 1980. Crop Production Functions and the Allocation and Use of Irrigation Water. Agric. Water Management. 3 (1): 53-64.

Beasley, D. B.,

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