University of Arkansas, Fayetteville University of Arkansas, Fayetteville

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Technical Reports Arkansas Water Resources Center

8-1-1984

Identification of Critical Water Levels in Flooded Rice Fields Identification of Critical Water Levels in Flooded Rice Fields

Carl L. Griffis University of Arkansas, Fayetteville

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Citation Citation Griffis, Carl L.. 1984. Identification of Critical Water Levels in Flooded Rice Fields. Arkansas Water Resources Center, Fayetteville, AR. PUB107. https://scholarworks.uark.edu/awrctr/251

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IDENTIFICATION OF CRITICAL WATER LEVELS IN FLOODED RICE FIELDS

Carl L. GriffisAgricultural Engineering Department

University of Arkansas Fayetteville, Arkansas 72701

Publication No. 107 August, 1984

Technical Completion Report Research Project G-829-02

Arkansas Water Resources Research Center University o f Arkansas

Fayetteville, Arkansas 72701

Arkansas W ater Resources Research Center

Prepared forUnited States Department of the Interior

AWRRC

Id e n t i f ic a t io n o f C r i t ic a l Water Levels In Flooded Rice F ie lds

Carl L . G r i f f isA g r ic u ltu ra l Engineering Department

U n iv e rs ity o f Arkansas F a y e t te v i l le , Arkansas, 72701

Research P ro je c t Technical Completion Report

P ro je c t G-829-02

The research on which th is re p o rt is based was financed in p a rt by the United S tates Department o f the In te r io r as au thorized by the Water Research and Development Act o f 1978, (P .L . 95-467).

Arkansas Water Resources Research Center U n iv e rs ity o f Arkansas

223 Ozark H allF a y e t te v il le , Arkansas 72701

P u b lica tio n No. 107

August, 1984

Contents o f th is p u b lic a tio n do not ne cessa rily r e f le c t the views and p o lic ie s o f the U.S. Department o f the In te r io r , nor does mention o f trade names o r commercial products c o n s titu te th e i r endorsement o r recommendation fo r use by the U.S. Government.

The U n iv e rs ity o f Arkansas, in compliance w ith fede ra l and s ta te laws and re g u la tio n s governing a f f irm a t iv e a c tio n and n o n d isc r im in a tio n , does not d is c r im in a te in the re c ru itm e n t, adm ission, and employment o f s tuden ts , fa c u lty , and s t a f f in the opera tion o f any o f i t s educational programs and a c t iv i t ie s as de fined by law. A cco rd ing ly , no th ing in th is p u b lic a tio n should be viewed as d ir e c t ly o r in d ir e c t ly expressing any l im i ta t io n , s p e c if ic a t io n , o r d is c r im in a tio n as to race, r e l ig io n , c o lo r , o r na tiona l o r ig in ; o r to handicap, age, sex, o r s ta tu s as a d isab led Vietnam-era ve te ran , except as provided by law. In q u ir ie s concerning th is p o lic y may be d ire c te d to the A ff irm a tiv e A ction O ff ic e r .

ABSTRACT

Id e n t i f ic a t io n o f C r i t ic a l Water Levels In Flooded Rice F ie ld s

A mathematical model was developed to s im ula te the tra n s ie n t hydrology o f a flooded r ic e f ie ld . With the model, users can determ ine the c r i t i c a l in te r le v e e areas in which to m onitor the w ater le v e ls so th a t the i r r ig a t io n w e ll can be turned on a t the c r i t i c a l low water le v e l, and turned o f f a t the c r i t i c a l high w ater le v e l, in order to maximize water a p p lic a tio n e f f ic ie n c y . S e n s it iv i ty ana lys is performed w ith the model showed th a t i t w i l l be necessary to c a lib ra te the model fo r each s p e c if ic f ie ld . A c a lib ra t io n procedure has been developed.

Carl L. G r i f f is

Completion Report to the United S tates Department o f the In te r io r , Washington, D .C., August, 1984.

KEYWORDS: Mathematical M odelling / I r r ig a t io n / Rice / Microcomputer

i

TABLE OF CONTENTS

Page

A b s tra c t i

L is t o f F igures i i i

Acknowledgements

In tro d u c tio n 1

A. Purpose and O b jectives

B. Related Research or A c t iv i t ie s

Methods and Procedures 6

General Mathematical P r in c ip le s A p p lic a tio n o f the P r in c ip le s

P rin c ip a l F indings and S ig n ific a n c e 16

Conclusions 18

L ite ra tu re C ited 19

Appendices 20

i i

LIST OF FIGURES

Figure 1 - Id e a lize d In te r le v e e Area

Page

7

i i i

INTRODUCTION

One o f the p r in c ip a l l im it in g fac to rs in the production of

r ic e is the need fo r i r r ig a t io n . The area of land used fo r rice

production is frequen tly lim ite d by the amount o f water ava ilab le

(Ferguson, 1979). In a d d itio n , in many a g r ic u ltu ra l areas of the

United S tates, the amount o f water ava ila b le fo r i r r ig a t io n is

s te a d ily decreasing. Thus, the carefu l use o f the water ava ilab le

is o f v i ta l importance to the producer and to the rest o f

so c ie ty .

The production of r ice requires large q u a n tit ie s o f water. In

Arkansas, on the s ilt- lo a m s o ils o f the Grand P ra ir ie , a producer

may have to add an average of 24 inches of water through i r r ig a ­

t io n in the average year (Engler, 1945). Many producers attempt

to maximize the acreage supported by each well by ir r ig a t in g at

the p ra c tic a l l im i t , 10 ga llons per minute per acre (Ferguson,

1979). One consequence of th is e f fo r t to maximize production is

the fa c t th a t long time in te rv a ls e x is t between the moment when a

w e ll is s ta rte d , and the moment at which water has been applied

successfu lly to the e n tire f ie ld . For example, i f one wished to

apply a flood o f 4 inches o f water to a 40-acre f ie ld , w ith a

w e ll producing 400 ga llons per minute, a period o f more than 7.5

days would be required. The consequences o f such long time

periods include major d i f f ic u l t ie s in c o n tro llin g the a p p lica tio n

o f water in order to minimize losses.

1

Rates of loss through in f i l t r a t io n are re la ted to the depth

o f the flo o d . Thus, the producer has an incen tive to maintain

only as much water on his f ie ld as is required to insure tha t

there are no dry spots in any of the in te rlevee areas. In addi­

t io n , i t w i l l be to h is advantage to w a it as long as possible

before adding add itiona l water. There is a r is k , however, in

w a iting too long. I f any part o f the f ie ld becomes dry, there can

be substan tia l losses in production of r ice (Ferguson, 1979,

Bhuiyan, 1978). Thus, the producer needs a method of determining

the c r i t ic a l moment at which to s ta r t h is well so th a t water w i l l

reach every part o f his f ie ld ju s t before any part is dry.

Another problem o f tim ing ex is ts when the well is in opera­

t io n . Water which is pumped in to the uppermost area of the f ie ld

f i l l s the volume enclosed by the f i r s t levee u n t il i t rises above

the gate in s ta lle d in the levee. Then i t flows in to the next

lower area. The water in the upper area must r ise well above the

gate in order to flow in to the next. Thus, i f the well were sud­

denly cut o f f , there would be some in - t ra n s it water th a t would

continue to flow . Each in te rlevee area overflows in the same way

in to the next lower area. Thus, in a large f ie ld there can be

sizeable q u a n tit ie s o f in - t r a n s it water. For example, i f the flow

ra te produced by the w ell is 1000 gallons per minute, and the

gate is four fee t wide, then according to the rectangular weir

equation, (Roth, et a l , 1975), the water would have to r ise to a

2

leve l o f almost 4 inches above the gate. In a 40-acre f ie ld , the

in - t r a n s it water would amount to almost 4 m il l io n ga llons.

One o f the sim plest methods o f determ ining the time at which

to tu rn o f f the pump is to simply w a it u n t i l water is flow ing

over the la s t o f the gates at the lowest e leva tion in the f ie ld .

This technique, w hile sim ple, is extremely w aste fu l, since much

o f the in - t r a n s it water is lo s t . Careful producers have already

learned to a llow fo r the in - t r a n s it water, and tu rn o f f the pump

w e ll before water begins to flow over the la s t gate. The de te r­

m ination o f the c r i t ic a l water leve l in the f ie ld at which the

pump should be stopped, however, is not a simple problem, and has

fre que n tly been based upon t r i a l and e rro r.

A. Purpose and Objectives

The ob jec tives of th is study were:

1. To develop a new mathematical model o f the tra n s ie n t flow of

floo d water in a r ic e f ie ld . The model must s a tis fy the

fo llo w in g requirements:

a) The computer program must be executable on the IBM per­

sonal computer and IBM-compatible computers. In a d d itio n ,

the program must be executable on as many other microcom­

puters as poss ib le .

b) The computer program must be w ritte n in a language which

is common to as many microcomputers as possib le .

3

2. To apply the model to discover a general method fo r de te r­

mining the fo llo w in g .

a) The c r i t ic a l high water leve l at which to tu rn o f f the

pump.

b) The c r i t ic a l in te rleve e area in which to measure the high

water le v e l.

3. To apply the model to discover a general method fo r de te r­

mining the fo llo w in g .

a) The c r i t ic a l low water leve l at which to tu rn on the

pump.

b) The c r i t ic a l in te rlevee area in which to measure the low

water le v e l.

4. To te s t the assumptions in the model by gathering f ie ld data

from a production r ice f ie ld and comparing the data to a

s im ula tion of the f ie ld .

B. Related Research or A c t iv it ie s

The techniques of mathematical modeling have been applied to

various aspects o f r ice production. McMennamy (1980) developed a

simple p lant population model which responds to d a ily weather

parameters. Hagan and Wang (1977) developed improved formulas fo r

c a lcu la tin g canal and pump capacities fo r rice i r r ig a t io n . Their

methods re su lt in improved system e ff ic ie n c ie s . Wu (1980) also

developed improved methods of designing water conveyance systems,

leading to higher u t i l iz a t io n e ff ic ie n c y . Clark and Bramley

4

(1982) studied water requirements during the p resatura tion phase

o f flood ir r ig a t io n . None o f these in v e s tig a to rs , however,

modelled mathematically the hydrology o f flooded r ice f ie ld s .

Ferguson and Gilmour (1981) developed a computer sim ulation

o f the hydrology o f flooded r ic e f ie ld s . Their purpose was to

combine th is model w ith a so lu te mass-balance so th a t they could

study the long-term e ffe c ts o f the solutes in the ir r ig a t io n

water. Their model included a dynamic sim ula tion o f tra n s ie n t

hydrology s im ila r to the one developed in th is study. Their

model, however, was w ritte n in P L /I, a language which is not com­

monly used on microcomputers. In a d d itio n , the model used an

em pirica l equation to solve fo r the depth o f water in an in te r ­

levee area when flow was occurring over the gate in to the next

area. F in a lly , th e ir model was based upon a time increment o f 2

hours which appears too long fo r precise water management.

Ferguson (1979) developed a technique fo r qu an tify in g the

moisture stress which may occur in an ir r ig a te d r ic e f ie ld in

which one or more of the in te rle ve e areas may become dry through

im perfect water management. He defined a dryness parameter as

shown below.

1

i t

5

DP ΣΣ(N i , t 2 * PFt ) / 1 06

Where DP is the dryness parameter Ni , t the number o f continuous 2-hr

in te rv a ls during which the water level o f area i is less than 1 inch ,

and PFt is a fa c to r which adjusts fo r these ve rity o f the damage done to the crop by dryness. The seve rity is a function o f tim e, t .

METHODS AND PROCEDURES

The mathematical development o f the model w i l l be described

f i r s t , and then the d e ta ils o f the program w ritte n to implement

the mathematical p r in c ip le s . The model is a combination of

general mathematical p r in c ip le s , s p e c ific f ie ld geometry, and

hydro log ica l p r in c ip le s .

General Mathematical P rinc ip les

Transient responses of the volume of water in an in te rlevee

area can be described mathematically by the General Accounting

Equation:

Rate o f A c c u m u la tio n = In p u t Rate - O u tp u t Rate+ Source R ate — S in k Rate 2

Since we w i l l be in te rested in the height o f the water in the

in te rleve e area, i t w i l l be desirab le to re la te the volume of the

water to the he igh t. There are three possible s itu a tio n s which

occur during the f i l l i n g and depletion of the water in each area.

1. Since there is a d iffe rence in e levation from one levee to

another, the bottom o f the in te rleve e area is not le v e l. The

6

Levee n-1Area = An

Levee n

Fi gure 1. Idealized Interlevee Area

Water CI

7

8

volume occupied by the water w i l l have a shape s im ila r to the

one in Figure 1. The area of the surface of the water w i l l

be a function o f the shape of the in te rlevee area. The

sim plest approach is to assume a rectangular area. Another

com plication arises when the f ie ld is being flooded fo r the

f i r s t time in a season.

Some of the water is required to wet the s o i l , and does

not con tribu te to the height o f water in the area. This is

ca lled the s o il water d e f ic i t . I f the area is assumed

square, the re la tio n sh ip between volume and height during the

period of i n i t i a l w etting can be expressed as fo llo w s .

V = h /2 * h /C I * An + h def 3

Where V is the volume of water in an area in cubicfe e t,

h is the height o f the water above the so il measured at the upstream side of the gate, in fe e t,

hdef is the s o il water d e f ic i t , in fe e t,CI is the contour in te rv a l in fe e t,

and An is the area contained w ith in in te rleveearea n in square fe e t.

For the purpose of a dynamic s im u la tion , one is more

in te res ted in the ra te at which the leve l o f water changes

w ith changes in volume. Such a re la tio n sh ip can be found by

d if fe re n t ia t in g Equation 3 w ith respect to tim e.

d V /d t = h * An /C l * d h /d t 4

For the f i r s t in te rleve e area, the input ra te has only

one of two values, zero i f the well is o f f , or the well ou t­

put ra te i f the well is on. For in te rleve e areas a f te r the

f i r s t , the input rate o f an area is the same as the flow rate

over the gate o f the previous area. The output ra te from an

area consists o f the flow over the gate in to the next area,

plus the losses from in f i l t r a t io n and evapotransp ira tion (ET).

For s im p lic ity , losses from in f i l t r a t io n can be set at a

constant value per hour, depending upon the s o i l .

E vapotransp ira tion , however, is a strong func tion o f t im e -o f-

day, r is in g to a peak during d a y lig h t hours, and dropping to

a minimum at n ig h t. Follow ing Ferguson (1979) the ra te o f

loss due to ET and in f i l t r a t io n can be expressed as a fra c ­

t io n of the to ta l d a ily loss . The f i r s t 2-hour period is from

midnight u n t i l 2 am.

EVAPOTRANSPIRATION FACTORS

2-h r Peri od

Fraction Of Total

12345678 9

0.040.040.040.040.050.100.150.190.150.090.070.04

101112

9

10

Equation 2 can be re w ritte n as fo llow s:

h * An /C I * d h / d t = Qn-1 - Qn - WL 5

Where Qn is the flow ra te o f water out o f an area nin to area n+1

and WL is the water loss rate from in f i l t r a t io nand evapotransp ira tion .

Equation 5 can be solved (approxim ately) fo r the rate of

change of the height o f water w ith in an area as fo llow s:

hn2 = hn1 + Δt * C I * [ Q n-1 - Qn - WL] / ( An * h n1 ) 6

Where Δt is the time increment over which thechanges are to be projected

hn1 is the current value o f hn hn 2 is the projected value o f hn

The appearance of hn1 in the denominator in Equation 6 is

the source of another com plication. I f the area is dry at the

s ta r t o f the s im u la tion , hn1 is zero, and Equation 6 cannot

be used w ithout m o d ifica tio n . Thus, an a lte rn a tiv e procedure

must be used to determine the re la tio n sh ip between the volume

o f water added to an area and the corresponding height w ith in

the area. No change in height is perm itted u n t il s u ff ic ie n t

water has been added to s a tis fy a l l o f the d e f ic i t . Then,

the in i t i a l increase in height from the s ta r t in g value of

zero is ca lcu la ted as fo llow s:

hn = (2 * Qn-1 * Δt * C l /A ) 0 . 5 7

11

Equation 7 is used only once in each in te rlevee area,

then Equation 6 is used u n t i l the water leve l in the area

reaches the contour in te rv a l, as described below.

2. The second p o s s ib i l i ty is th a t the water may have risen u n t il

the e n tire cross section o f the in te rleve e area has been

covered. Thus, the water leve l in the area w i l l be numeri­

c a lly equal to the contour in te rv a l. In th is case there is a

new re la tio n sh ip between the ra te o f change of volume and the

ra te o f change of he igh t.

d V /d t = An * d h /d t 8

Again, th is equation can be substitu ted in to Equation 2

w ith the re s u lt shown below.

d h /d t = [Qn-1 - Qn - W L t]/A n 9

This equation can be solved fo r the height o f water

w ith in an area as fo llo w s , assuming th a t Qn is zero.

h n 2 = h n 1 + Δ t * [ Q n - 1 - W L t ] / A n 10

3. F in a lly , there is the p o s s ib i l i ty th a t the water leve l may

r is e to the po in t at which flow over the gate in to the next

lower in te rle ve e area begins. Then, the ra te o f change of

volume w ith in the area under consideration is a func tion not

only o f the quan tity flow ing in to the area but o f the quan-

12

t i t y flow ing out. The quan tity flow ing out is re la ted to the

height o f the water w ith in the in te rlevee area by the rec­

tangu la r w eir equation.

Qn = 3 .3 3 * [L - 0 .2 * hn ] hn 1 . 5 11

Where Qn is the flow rate o f water across thenth w e ir, in CFS

L is the width o f the gate in fe e t, and hn is the height o f the water surface

above the s o il at the base of the nth gate on the upstream side in fe e t.

I t is , thus, possible to solve fo r the height o f water in

an area from which there is an overflow by su b s titu tin g

Equation 11 in to Equation 9.

hn 2 = h n 1 + Δt * [Qn-1 - WLt

-3 .3 3 * (L - 0 .2 * hn2 ) * hn21 . 5 12

Equation 12 must, o f necessity, be solved by an ite ra t iv e

process, since, hn 2 appears on both sides of the equation.

A pp lica tion o f the P rinc ip le s

The fo llow ing procedure was used to simulate the changes

which occur in the water leve ls h in each area of the f ie ld .

1. The projected value of h in each area was calcu la ted from the

previous value, the mathematical p r in c ip le s described above,

and the assumed time increment.

2. I f the previous value o f h in an area was less than the con­

to u r in te rv a l, CI , then Equation 4 was used to p ro je c t in to

the fu tu re .

3. I f the previous value o f h in an area was greater than or

equal to C l, but less than the gate he igh t, then Equation 8

was used to p ro jec t in to the fu tu re .

4. I f the previous value o f h in an area was greater than the

gate he igh t, Z, then Equation 12 was used to p ro jec t in to the

fu tu re . An i te ra t iv e procedure must be used, since h appears

on both sides.

5. The time increment to be used fo r the s im ula tion was chosen

by s e n s it iv ity te s t in g . The equations used in the sim ula tion

are approximations to the d if fe re n t ia l equations derived

above. The approximations are more re lia b le when very short

time in te rv a ls are used fo r At . Short time in te rv a ls ,

however, re s u lt in long c a lc u la tio n tim es, leading one to

attempt to use time increments which are as long as poss ib le .

Since the s im ula tion method is a p ro jec tio n in to the fu tu re ,

i t is important to minimize the cumulative e rro rs which might

re s u lt from such long increments. The s tra tegy was to simu­

la te p a r t ic u la r f ie ld cond itions w ith successively sho rte r

tim e increments u n t i l no fu r th e r changes resu lted from

reducing the increment. An increment o f 2 hours was tested

f i r s t . Then increments o f 1 hour, 0.1 hours, and 0.01 hours.

13

The model was used to p red ic t the time at which water would

flow over the la s t gate in a 50-acre f ie ld w ith 10 levees

enclosing 5 acres each. The assumed well capacity was 600

galIons per minute.

Calculated Time to Flow Over Last Gate

Time Increment (hours) Elapsed Time (hr)

2 4761 4790.1 4800.01 480

6. The e ffe c ts o f assumptions about water d e f ic its and loss

rates were investiga ted through s e n s it iv ity te s t in g , a lso.

These two assumptions have a great impact on the ca lcu la tion

o f the time which passes between the moment at which the well

is turned on and the moment at which water begins to flow

over each gate. Thus, a series o f runs were made w ith the

mathematical model to p red ic t the time at which water began

to flow over the la s t gate in a simulated f ie ld w ith d i f ­

fe re n t values fo r i n i t i a l water d e f ic its and in f i l t r a t io n

ra tes . The resu lts are shown below fo r a 50 acre f ie ld w ith

10 levees and a pump which produces 600 gallons per minute.

14

S e n s it iv ity Testing o f S o il Water D e f ic it

CalculatedAssumed D e f ic it

FeetTime at which Water Tops

The Last Gate (Hours)

0.0450.0500.055

477480482

S e n s it iv ity Testing o f Water Loss Rate

Overal l Water Loss Inches per Day

CalculatedTime u n t i l Water Tops The Last Gate (Hours)

0.3240.3600.396

457480507

7. I t has, thus, been shown th a t i t w i l l not be possib le to use

the model to sim ulate a general r ic e f ie ld , unless one has

very precise in fo rm ation about ce rta in s o il physical proper­

t ie s . I f the estimate o f the s o il water d e f ic i t is in e rro r

by as l i t t l e as 10%, the estimated time at which flow would

begin across the la s t gate can be in e rro r by as much as

th ree hours. I f the estimated d a ily loss ra te is in e rro r by

as l i t t l e as 10%, the estimated time at which flow over the

la s t gate would begin can be in e rro r by as much as 27 hours.

I t is u n lik e ly th a t a producer w i l l have in fo rm ation about

h is s o il th a t is accurate enough to use in the model w ith any

degree of confidence. I t w i l l , thus, be necessary to

c a lib ra te the model to each f ie ld .

15

A c a lib ra tio n procedure which can be used is as fo llow s:

1. F ir s t , make a record of the exact time at which the well is

s ta rte d .

2. Next, make sure th a t the flow ra te produced by the well is

known, measuring i t i f necessary.

3. Make sure th a t the area of the f ie ld above the f i r s t gate is

known to a high degree o f accuracy.

4. Determine the exact time at which flow begins over the f i r s t

gate.

5. At th is p o in t, there are three parameters to be adjusted, the

moisture d e f ic i t , the in f i l t r a t io n ra te , and the evapotrans-

p ira t io n ra te .

6. A fte r the f ie ld has been flooded fo r the f i r s t tim e, and the

w ell has been stopped, the combined in f i l t r a t io n rate and

evapotranspira tion rate can be estimated by monitoring the

de c lin ing water leve l in one of the areas.

7. When i t is time to s ta r t the well again, the s ta r t in g water

d e f ic i t can be estimated by a comparison of the time required

to f i l l the f i r s t area w ith the in i t i a l f i l l i n g tim e.

PRINCIPAL FINDINGS AND SIGNIFICANCE

A computer model has been developed to simulate the hydrology

o f flood water in an ir r ig a te d r ice f ie ld . The model has been

w ritte n in M-BASIC, the version o f BASIC developed by M icroso ft.

16

This version o f BASIC has become the defacto standard fo r m icro­

computers. The program has been executed on three types o f com­

puters to te s t i t s machine independence. I t has been successfu lly

executed on an Osborne 1, on an IBM PC, and on a Columbia VP.

Results have been equivalent on a l l three machines.

The maximum time increment th a t can be used fo r Δt in the

s im ula tion was found to be 0.1 hours, or 0.004167 days. Assuming

the model can be properly ca lib ra te d fo r a p a r t ic u la r f ie ld , i t s

advice to the user about the appropria te time fo r tak ing action

w ith respect to the w ell should be w ith in an hour o f the optimum

tim e .

In the development o f the model, two assumptions were made

which necessitate c a lib ra tio n o f the model fo r each f ie ld where

i t is to be used. The f i r s t assumption is the ra te at which

in f i l t r a t io n and evapotranspira tion w i l l take place in the f ie ld .

The second assumption is the volume of water required to saturate

the s o il when water is f i r s t added to the f ie ld . Each of these

parameters has a s ig n if ic a n t e ffe c t upon the tim ing required in

c o n tro llin g the w e ll, as shown by s e n s it iv ity te s t in g .

The model ca lcu la tes and disp lays some parameters which help

the user to optim ize water management in the f ie ld sim ulated. The

f i r s t o f these, o f course, are the ca lcu la ted water leve ls in

each in te rleve e area, at the end o f each hour. Another parameter

is the amount o f water which the model estimates would be lo s t by

17

fo llo w in g the management s tra tegy sim ulated. T y p ic a lly , the model

can be used to simulate the e n tire growing season, in d ica tin g the

appropria te times fo r s ta r t in g and stopping the w e ll, based upon

the c r i te r ia supplied by the user.

CONCLUSIONS

Most o f the ob jectives ou tlined at the beginning of th is

study have been achieved.

1. The computer program developed pred ic ts water leve ls which

change in a way th a t is consistent w ith r e a l i ty .

2. S e n s it iv ity analysis has demonstrated th a t the time in c re ­

ments used in some previous models may have been too long fo r

precise water management.

3. Further s e n s it iv ity analyses have shown tha t ce rta in s o il

physical property data must be known w ith an e rro r o f less

than 10% before the model can be used to aid the user in

achieving optimum water management. These properties are:

a) The in i t i a l water d e f ic i t .

b) The ra te o f in f i l t r a t io n .

4. Further work must be done w ith the model to te s t the c a lib ra ­

t io n procedure described. Work w i l l continue during the next

yea r, inc lud ing the development o f a sensing device which

w i l l signal to the operator when the c r i t ic a l high and low

water leve ls have been reached.

18

LITERATURE CITED

1. Bhuiyan, S. I . , and A. Sumayao. Q ua n tifica tio n o f Rice Yield. B enefits A ttr ib u ta b le to I r r ig a t io n Water. Paper No. 78-2022 ASAE Summer Meeting, Logan Utah, June, 1978.

2. C la rk, W. M., M. E. Bramley, and R. F. Thorp. Water Requirements fo r Flooded Rice C u lt iv a t io n . P roc .Ins t.C iv .E ng - (London) v73 p t 2, Dec.1982, p769-788.

3. Engler, Kyle, David G. Thompson, Raphael G Kazmann. GroundWater Supplies fo r Rice I r r ig a t io n in the Grand P ra ir ieRegion, Arkansas. U n ive rs ity o f Arkansas. College of A g r ic u ltu re , B u lle t in 457, June, 1945.

4. Ferguson, James A ., The E ffe c t o f Selected E le c tr ic Power In te rru p tio n s on Rice I r r ig a t io n . Special Report 74,A g r ic u ltu ra l Experiment S ta tio n , U n ive rs ity o f Arkansas, F a y e tte v ille , Arkansas, J u ly , 1979.

5. Ferguson, James A ., and John T. Gilmour. A HydrologicCarbonate Chemistry Model o f Flooded Rice F ie ld s . ArkansasWater Resources Research Center, P ub lica tion No. 78, Dec 1981.

6. Gilmour, J. T . , James A. Ferguson, B. R. W ells. S a lt andWater Balance Model fo r a S i l t Loam S o il Cropped to Rice and Soybeans. Arkansas Water Resources Research CenterP ub lica tion No. 82, December 1981.

7. McMennamy, John A. Dynamic S im ulation o f Ir r ig a te d Rice Crop Growth and Y ie ld . Paper 80-4008, ASAE Summer Meeting, San Antonio, Tex, Jun 1980.

8. Roth, L. 0 ., F. R. Crow, G. W. A. Mahoney. An In trod uc tion to A g r ic u ltu ra l Engineering, AVI Publish ing Company, Westport, Connecticut, 1975.

9. Wu, Chian Min. Canal Capacity Design Formulae fo r Ir r ig a te d R ice. Proc o f the In t i Conf on Water Resour Dev, v l , Ta ipe i, Taiwan, May 1980, p303-312.

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APPENDIX A

COMPUTER PROGRAM

10 DEFDBL A-Z20 DIM A(30), H(30), XDEF(30), Q(31), WL(12)30 REM ZN IS THE GATE HEIGHT40 REM XDEF(I) IS THE MOISTURE DEFICIT REMAINING IN AREA I50 REM ZWETN IS THE VARIABLE USED FOR DEFICITS IN THE ITERATIONS60 HOUR = 070 DAY% = 080 CI=.290 ZN = .6100 PRINT "HOW MANY DAYS TO SIMULATE " ;110 INPUT NDAYS 120 WL0SS=0130 REM WL IS THE WATER LOSS RATE DUE TO INFILTRATION AND

EVAPOTRANSPIRATION140 WL(1)=.0144: WL(2)=.0144: WL(3)=.0144: WL(4)=.0144: WL(5)=.018 150 WL(6)=.036: WL(7)=.054: WL(8)=.0684: WL(9)=.054 160 WL(10)=.0324: WL(11) = .0252: WL(12) = .0144 170 INPUT "HOW MANY LEVEES?";N%180 LPRINT "THERE ARE",N%;" LEVEES"190 REM DELT ESTABLISHED BY SENSITIVITY200 DELT = .004167210 TENTH=0220 DELT = .004167230 ZWETN=.05240 FOR I % = 1 TO N%250 XDEF( I %) = ZWETN260 PRINT "Area of levee"; I %;" in acres?";270 INPUT A(I%)280 LPRINT "LEVEE " ;I% ;" ENCLOSES ";A (I% );" ACRES 290 A( I %)=A( I %)*435601 300 NEXT 1%310 INPUT "Well discharge in gpm?";Q(1)320 LPRINT "THE WELL DISCHARGES ";Q (1 );" GPM"330 LPRINT "THE GATE HEIGHT IS " , ZN;" FEET"340 Q(1) = Q(1)*192.51 350 WELL = Q(1)360 INPUT "CRITICAL TURN OFF LEVEE ";L%370 INPUT "CRITICAL HEIGHT " ;HT380 LPRINT "TURN-OFF LEVEE IS ";L%;" AT HEIGHT OF " ;HT 390 INPUT "CRITICAL TURN ON LEVEE ";L2%400 INPUT "CRITICAL HEIGHT ";HT2

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410 LPRINT "TURN-ON LEVEE IS ";L2%;" AT HEIGHT OF ";HT2 420 LPRINT430 LPRINT "HR H1 H2 H3 H4 H5 H6

H7 H8 H9 H10"440 FOR I % = 1 TO NX 450 QN = Q (I%)460 AN = A ( I %)470 HN = H(I%)480 ZWETN=XDEF( I %)490 GOSUB 920500 IF HOUR<2 THEN J%=1: GOTO 620510 IF HOUR<4 THEN J%=2: GOTO 620520 IF HOUR<6 THEN J%=3: GOTO 620530 IF HOUR<8 THEN J%=4: GOTO 620540 IF HOUR<10 THEN J%=5: GOTO 620 550 IF HOUR<12 THEN J%=6: GOTO 620 560 IF HOUR<14 THEN J%=7: GOTO 620 570 IF HOUR<16 THEN J%=8: GOTO 620 580 IF HOUR<18 THEN J%=9: GOTO 620 590 IF HOUR<20 THEN J%=10: GOTO 620 600 IF HOUR<22 THEN J%=11: GOTO 620 610 J%=12620 H(I%) = HN - DELT*WL(J%)630 IF H(I %)<0 THEN H (I%)=0 640 Q(I%+1)=QNEXT 650 XDEF( I%)=ZWETN 660 NEXT I%670 WLOSS = WLOSS + QNEXT*DELT680 IF H(LX) > HT THEN Q(1) = 0690 IF H(L2%) < HT2 THEN Q(1) = WELL700 TENTH=TENTH+1710 IF TENTH < 10 THEN GOTO 440720 TENTH=0730 HOUR=HOUR+1740 LPRINT HOUR;750 FOR I%=1 TO N%760 LPRINT USING "#.### " ;H (IX );770 NEXT I%780 LPRINT790 IF HOUR < 24 THEN GOTO 440 800 HOUR = 0 810 DAY% = DAY% + 1 820 LPRINT "DAY";DAY%;830 PRINT "DAY";DAY%;840 FOR I % = 1 TO N%850 LPRINT USING "#.### ";H (I% );860 PRINT H (I%) ;

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870 NEXT 1%880 LPRINT890 IF DAY%=NDAYS THEN LPRINT "LOSS IS ";WLOSS;: END 900 PRINT 910 GOTO 440920 REM subroutine to determine height in in te rlevee area 930 QNEXT=0940 IF HN>0 THEN GOTO 1020 950 IF ZWETN <= 0 THEN GOTO 980 960 ZWETN = ZWETN - QN*DELT/AN 970 IF ZWETN>0 THEN RETURN 980 ZZN# = 2*QN*DELT*CI/AN 990 REM LPRINT TIME 1000 HN = SQR(ZZN#)1010 RETURN1020 IF HN>CI THEN GOTO 1080 1030 H3=HN:H2=HN1040 H2 = HN + DELT*CI*QN/((HN+H2)/2*AN)1050 IF ABS(H3-H2)>.001*H2 THEN H3=H2: GOTO 1040 1060 HN=H2 1070 RETURN1080 IF HN > ZN THEN GOTO 11101090 HN=HN +DELT*QN/AN1100 RETURN1110 H3=HN:H2=HN1120 H2=HN + DELT*(QN-QNEXT)/AN1130 QNEXT = 86400!*13.33*((HN+H2)/2-ZN)^1.51140 IF ABS(H3-H2)>.0001*H2 THEN H3=H2:GOTO 11201150 HN=H21160 RETURN1170 END

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