Evaluation of the possibility for rainfed agriculture using a soil moisture simulation model

••

Agricultural water management

ELSEV 1ER

Agricultural Water Management26 (1994) 187-199

Evaluation of the possibility for rainfed agriculture using a soil moisture simulation model N.D. Binh a'*, V.V.N. Murty a, D.X. Hoan b alrrigation Engineering and Management Program, Asian Institute of Technology, G.P.O. Box 2754, Bangkok 10501, Thailand bDepartment of Land Use Planning, Hanoi Agricultural University, Gialam, Hanoi, Vietnam

Accepted 2 March 1994

Abstract

A soil moisture simulation model was developed to provide the necessary data for evaluating the potential success of rainfed agriculture in a region bordering the Red River in Vietnam. The model considers rain infiltration, evaporation, redistribution, and water uptake by plant roots. A Markovchain model was used to generate daily rainfall for the simulation of soil moisture contents under normal and dry years. The model was validated using field data for three soil types in the region. Application of the model for assessing the possibilities of rainfed agriculture under the specified conditions is outlined. The analysis results, in terms of moisture conditions showed that the model is capable of indicating the stress days for crops grown in the region. The most appropriate planting date to minimize water stress can be determined. Keywords: Unsaturated flow; Numerical model; Rainfed agriculture; Rainfall generation; Irrigation

1. I n t r o d u c t i o n There are considerable fertile areas in the Red River delta of Vietnam wherein agriculture can be extended. As irrigation facilities can not readily be provided for seasonal flooded areas close to the river, agriculture has to be under rainfed conditions. The soils in the area vary from clay loam to sandy loam with good depth and water-holding capacities. The common crops in this area are maize, soybean and sugarcane. Average rainfall of the region is 1670 mm annually, 85% of it occurring mainly from May to October. * Corresponding author. Elsevier Science B.V. SSD10378-3774(94)00015-R

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Information about the soil moisture profiles, under the rainfed conditions, will be useful in deciding the possibility of crop production under given conditions, as well as assisting to make the selection of the crops. The simulation of soil moisture profiles has been attempted by several workers. Nimah and Hanks (1973) considered the problem in terms of the soil, water, plant and atmospheric continuum. Feddes et al. (1976) and Belmans et al. (1983) developed comprehensive solutions to the problem of soil moisture simulation in crop root zone. They considered the governing flow equation describing the unsaturated flow and developed numerical solutions to the same. Jain and Murty (1985) used this approach for the purpose of scheduling irrigations. In this study the objective is to comprehend the impact of fluctuations in the soil moisture profiles on crop production under varying rainfall conditions, across a given set of locations.

2. Model development The movement of soil moisture in the root zone is described by the one dimensional flow equation (Feddes et al., 1988):

Ot

Oz L

oz

where 0= volumetric water c o n t e n t [ L 3 / L 3 ] ; z = vertical coordinate [L], positive downwards; t = time IT] ; K(0) = hydraulic conductivity [L3/L2/T] ; D(0) = diffusivity function [L2/T] ; S(0) = the rate of the water uptake [L3/L3/T] by root at depth z, which can be estimated (Feddes et al., 1976) by S(O) = c~(O)Pt Zr

(2)

where Pt is the potential transpiration, calculated as the difference between potential crop evapotranspiration and potential soil evaporation, zr is the depth of the root zone's bottom side which varies with crop's development stage. The ~(O) parameter is a dimensionless variable given by ~(0)

O- Owe 0Fc - Owe

(3)

in which Owe and 0Fc are soil water contents at wilting point and at field capacity, respectively. The potential soil evaporation, Pe, [L/T] is computed (Belmans et al., 1983) as Pe = exp( - 0.6 LAI) PET~

(4)

where LAI is the dimensionless leaf area index and PET~ is potential evapotranspiration [L/T]. In this study, the potential evapotranspiration was calculated by the modified Penman method (Smith, 1991). The diffusivity function is defined by D ( O ) = K(0)~-~

(5)

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where ~ is the matric potential of the soil water [ L ], which is a negative quantity when the soil is unsaturated. Eq. ( 1 ) holds for homogeneous soils as long as the effects of hysteresis on the function K(0) are ignored. This equation is solved using a numerical finite-difference method. The Crank Nicolson scheme given by Rosenberg (1969), was used for this purpose. In addition to the numerical procedure, the solution requires initial and boundary conditions, and the various parameters in Eq. ( 1 ). These are considered as follows. The initial condition:

O(z,O) = Oo(z), t = 0 , 0"(Z_~
(6)

where Zmaxis the depth of the lower boundary. This initial condition was obtained from field data. Boundary conditions need to be specified both at the upper and lower surfaces. At the upper boundary, z = 0, a general flux condition specified by

- D ( o)OO+ K( O) =R(0,t) Oz

[L3/L2/T]

(7)

where R(O,t) is the potential surface flux (rainfall, evaporation, or irrigation rates). The three common cases considered for R(O,t) are: R(0,t) > 0 for infiltration or rainfall R (0,t) = 0 for redistribution or drainage R(O,t) < 0 for evaporation The absolute values of R(0,t) in case of rainfall, is set equal to rainfall intensities but not greater than infiltration capacity of the soil or in case of evaporation it is equal to potential evaporation, Ep, from the soil surface. The infiltration capacity of the soil was calculated using measured data from field double-ring infiltration test. The potential evaporation (Ep) from the soil surface is calculated by (Ritchie, 1972)

Ep =6--~yLQ, e x p ( - 0 . 3 9 LAI)

[L3/L2/T]

(8)

where 6 is the slope of saturation vapour pressure curve, Q° is net radiation flux at ground surface, L is latent heat of water evaporation, y is psychometric constant and LAI is leaf area index. The daily rainfall values were simulated using a generation model as outlined subsequently. The "potential" flux rate, R(O,t), for a given soil depends only on atmospheric conditions. The actual flux cross the surface, q(O,t), is determined by the ability of the soil to transmit water through the soil surface. Thus, the exact flux at the soil surface cannot be predicted a priori but is subject to the condition that its magnitude be as large as possible, but not greater than the magnitude of the potential rate, Iq(0,t) I _< IR(0,t) I

[L3/L2/T]

(9)

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190

and that the resulting water content profile does not violate the air dry and saturation limits of equation

0d < O(z,t) < Os

(10)

Here, 0d and 0~ denote air-dry and saturation soil moisture contents. The potential flux rate, R(O,t), is specified as a function of time and the actual flux cross the surface, q(O,t), is calculated iteratively (Ungs et al., 1985) subject to Eqs. (9) and (10). Additional details for determining q(O,t) are given by Ungs et al. (1985), Feddes et al. (1988) and Neuman et al. (1975). At the lower boundary, z = Zmax, considering water table to be deep during dry season (Table 1) and not influencing the root zone (Doorenbos and Pruit, 1977), the following condition is specified. 00 -~z(Z~ax,t)= 0,

t>0

(11)

Z~x was selected as the maximum rooting depth for maize crop. Its values are presented in Table 4.

3. Daily rainfall generation Using historical data at the location, daily rainfall values at different probability levels can be generated. For this purpose, the two stages Markov chain principle (Aldabadh et al., 1982) has been adopted in this study. Phien et al. (1984) used similar procedure for generating daily rainfall patterns in Thailand. The steps in this model are briefly as follows: (1) For each month, the transition probabilities and the parameters of the lognormal distribution are estimated. In this case, the transition matrix can be expressed as:

P = \bj(al(1--b)'l,l

(12)

where a is probability (dry day/dry day), b is probability (dry day/wet day). Using historical data, these parameters are estimated according to the method of maximum likelihood as given by:

a = A ~ / ( f , , +f,2) Table 1 Observedgroundwaterdepth at the study site (averageof nine observationwells) Month

Sept. Oct. Nov.

GW depth (m) Max.

Min.

2.77 3.45 4.30

1.21 2.37 3.55

Month

Dec. Jan. Feb.

GW depth (m) Max.

Min.

4.87 4.57 4.48

4.23 3.95 3.86

Month

March April May

GW depth (m) Max.

Min.

5.18 4.08 1.51

4.80 2.61 0.00

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191

a=flll(fll +fl2) wherefj (i,j = 1,2) denotes the historical frequency of transitions from state i to statej in the daily values. It should be noted that the dry state corresponds to all daily rainfall amounts less than 1 m m while the wet state corresponds to all daily rainfall amounts greater than 1 mm. Likewise, the parameters of the lognormal distribution can be estimated using the following equations: /x = ~ " In (x - Xo)

0 -2

=~

[In ( x - Xo) - / z ] 2

( 14a) ( 14b)

where n is the number of days with rainfall amount x > Xo = 1 mm in that month, and the sum extends all over the n values. (2) A uniform random number U between 0 and 1 is then generated. (3) Knowing the state i of one day ( i = 1 for a dry day, i = 2 for a wet day), the statej of the following day is determined by comparing U with a for i = 1, or with b for j = 2, respectively. If U < a (or b), the following day is dry and hencej = 1; otherwise j = 2. (4) I f j = 1 (the following day is dry) the rainfall amount on that day is set equal to zero. I f j = 2 it is a wet day; a lognormal variable X with parameters/z and o- is generated, and the rainfall amount is computed by:

R=X-Xo

(15)

Steps (2) through (4) are repeated after setting i=j; until the desired length of generated sequence is reached. The state and the rainfall amount on the first day must be determined first, and this is done as follows: Let q denote the probability that the first day is dry, then q may be estimated according to the following equation.

q=Fl/(Fl +Fz)

(16)

where Fi (i = 1,2) is the historical frequency of rainfall amounts on the first day being in state i. Having obtained q, the state of the first day is determined as follows: (a) Generate a uniform random number V on (0,1 ) (b) Compare V with q. If V < q then the first day is dry (i = 1 ) and the rainfall is set equal to zero. Otherwise (i.e. if V > q) the first day is wet (i = 2), and the rainfall amount is obtained as expressed by Eq. (13). In this study available rainfall data for 30 years has been used to generate the parameters as outlined as well as generating daily rainfall values at different probability levels.

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192

Table 2 Soil physical characteristics of experimental sites Soil types

Clay Clayloam Loam

Texture Sand

Bulk density (g/cm 3)

Saturated hydraulic conductivity (m/day)

Clay

Silt

42.0+1 36.0_+2 26.5_+4

36.0_+1 22.0_+1 1.5+_0.06 11.0_+2.1 35.0_+2 29.0_+3 1.4+0.1 21.3_+1.4 37.5_+5 36.0_+4 1.2_+0.2 28.2_+2.2

Saturated Field water capacity content (%vol.) (%vol.)

Permanent wilting point (%vol.)

Air dry value (%voi.)

44_+1 47-+2 52_+4

14+3 12_+2 12±2

7_+1.4 6_+1.1 2_+0.5

36_+2 34_+3 31-+3

Note: The "_+" shows the spatial variation of measured data over the soil profile (up to 1.20 m depth).

4. Model validation and application Field experiments were conducted at three locations in Gialam district (Red River Delta, Vietnam) in order to study the variability in soil moisture conditions in three soil types with corn crop as well as bare soil. The soils on the experimental sites, deposited by floods from the Red River, are classified as seasonal flooded, alluvial type (Cao Liem et al., 1990). Their main physical characteristics are presented in Table 2. The soil water retention curves (drying) were determined in the laboratory without considering hysterisis. For the hydraulic conductivity functions, the steady-state headcontrol method ( Klute and Dirksen, 1986) with undisturbed soil cores was used. The values of hydraulic conductivity K(0), and diffusivity D(0), functions are shown in Table 3. In the computer program, intermediate values are determined using a linear interpolation method. In the field, the moisture content of the soil was monitored weekly at 30 and 60 cm depths, and monthly 10, 20, 60, 90 cm depths using gravimetric method. Growth and development of the crop were analyzed at regular time intervals by measuring height, leaf area and average rooting depth (Table 4). Climatic data (e.g. air temperature, air relative humidity, rainfall, pan evaporation, observed solar radiation, and wind speed) were measured at a nearby weather station. The same climatic data was used for simulation soil Table 3 Soil water diffusivity and hydraulic conductivity as functions of soil water content of the experimental sites Water content ( % vol. )

0.07 0.10 0.15 0.25 0.42 0.44

Diffusivity (cm2/day)

Hydraulic conductivity (cm/day)

Loam

Clay loam

Clay

Loam

Clay loam

0.015 1.20 9.67 9231 79056

0.013 0.97 8.38 8725 77080 -

0.011 0.85 8.16 8166 76852 -

7.52×10 -6 8.76x 10 -5 1.04× 10 -3 2.2× 10 -~ 26.2 28.2

6.85×10 -7 8.6×10 -5 9.6× 10 -4 9.4× 10 -2 12.5 21.3

Clay

7.02 X 10 -8 8.3 × 10 -5 6 . 9 × 10 - 4

2.7×10 3 5.28 11.03

193

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Table 4 Measured leaf area and root density of corn crop grown on clay loam soil Date

Leaf area ( m2. in - 2)

Max. depth of root zone (cm)

Average root density (cm.cm-3) a

25 Oct. 2 Nov. 9 Nov. 16 Nov. 23 Nov. 30 Nov. 7 Dec. 10 Jan.

1.260 1.742 2.730 3.448 3.836 2.062 2.642 2.510

25 40 52 80 95 100 100 100

0.077 0.102 0.171

0.265 0.267

"Calculated from measured weight of roots and average root diameter. Note: Growth duration of corn crop is from 2nd October to 10th January.

moisture contents in the three soils since the three experimental sites are within 7 km distant to each other. A comparison of measured and computed soil water content for a period of 4 months (October 1991 to January 1992), is given in Fig. 1. It can be seen that there is a general agreement between observed and predicted values. Discrepancies between measured and computed data may be partly due to the fact that hysterisis was neglected and that the entire soil profile was treated as homogeneous. Fig. 2 shows the simulated soil moisture profiles in three-dimensional form for three types of soil in the study area. Using the generated rainfall with occurrence probabilities of 50, 60, 70, 80 and 90%, soil moisture contents profiles were predicted and its values at 30 and 60 cm depths are shown in Fig. 3. Several simulation runs were made in order to evaluate soil moisture condition for corn crop growth. The decision factors used are stress day and minimum amount of supplementary water requirement (Phien et al., 1984). The stress day is defined as a day when the soil water content is less than a minimum value, 0m~, 0,~. = 0FC -- (0FC -- 0Wp) "MAD

[L3/L 3]

(17)

where M A D is the dimensionless maximum allowable deficiency (James, 1988). In this study M A D is taken as 0.65 of the available soil moisture-holding capacity of the soil. For stress day, all important descriptions (namely, the total number, time of occurrence and severity) were considered. The severity is represented by a dimensionless stress day factor, Sd, defined as (Hiler and Clark, 1971 ).

0 - 0wp Sd=l

0min--0wp

(18)

where 0n~n is critical value of soil water content for crop growth calculated with Eq. (17). The amount of deficit water ( A D W ) corresponding to each duration of stress day is also evaluated.

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N.D. Binh et al. /Agricultural Water Management 26 (1994) 187-199

Water

C o n t e n t

(vC)l)

Rainfall,

Evaporation

(crntdayI

Q 3

0

"

28

-Clay-Loam

Soil

/ ~

026

0:;24

0

22

02

018

016

i o/1

1 o/=

1

11 / 1 o

1 i/30

12/2o

1/9 Time

Water

C o n t e n t

(v(~l)

Rainfall,

Evaporation

1/29 (month/day) (cm/cJay)

03

.

.

.

.

.

.

.

Loam

-soi~

.

.

.

.

0.2e

o24

0

22

02

018

0.1e 10/1

10/21

i 1 / 10

11/30

I 2/20

1/g Time

Water

C o n t e n t

(vol)

a~lnfall,

1/29 (month/may)

Evaporation

(cm/day)

o3

0

28

0

=e

~".

.

.

~i .

024

.

.

.

.

.

.

.

.

.

.

" .

Sahdy-Loam

.

.

.

.

Soil .

%- ~

.

.

.

.

.

.

_

#-

.

_

"

. "

"

o22

o2 .

.

.

.

4 "

q_

.

.

.

.

.

.

.

018

O16 10/1

1 o121

11 / 1 o

11130

12/20

119

1 / ~9

2/18

311 o

313o

Time

(month/day)

Fig. I. Measured and computed soil moisture.

ADW = maximum

[ DWk]

k = 1 ..... N s

(19)

[L]

(20)

where D W k = ( Omi~ -- 0k)" D R Z

N.D. Binh et al. /Agricultural Water Management 26 (1994) 187-199

195

:

tlj

+

~lJ

~

,,-,---v----~ +

~ ~

~ _. . _

~

'

~

~o'

196

~

2

N.D. Binh et al. /Agricultural Water Management 26 (1994) 187-199

oo~

oQ

E o oo

o

0 to

& iii

© 03 >. r~

c'~0

~

.=.

"6

§ z.

o

o~

~

E.o_ E

~z

o "6 8

8

5 E J

N.D. Binh et al. /Agricultural Water Management 26 (1994) 187-199

197

and Ns is the duration (in days) of the spell of stress days being considered and DRZ is the depth of the root zone. This may be treated as the minimum amount of supplementary water required in order to avoid the corresponding stress spell. The minimum amount of supplementary water required in a month or during the entire growing season may be computed accordingly by summing up the individual amount needed in the different spells, if any, covered by that month or the growing season. The analysis results in term of moisture condition for corn crop growing season are presented in Tables 5 and 6 corresponding to rainfall probability levels of 60 and 80%, respectively. Considering a rainfall probability level of 60%, the most severe stress spell would be expected to occur in January with maximum value of stress day factor Sd = 0.11, duration of spell = 3 days in loam soil case. For the entire growing season, the total number of stress days is 16 days. The values of Sd for clay loam and clay soils are 0.06 and 0.02, respectively. These values of Sd is considered quite small. Consequently, there should be no damage to the crop. For the probability of rainfall occurrence of 80%, Sd values are 0.41, 0.14 and 0.09 and duration of the most severe stress spell are 5, 5 and 3 days in case of loam, clay loam and clay soils, respectively. These clearly shows irrigation is necessary when corn is grown on loam soils. The minimum amount of supplementary water requirement is also provided in Tables 5 and 6. From the tables, one can concludes that stress day may occur frequently but as long as the corresponding stress day factor, Sd, and the amount of deficit water is small, one should expect no damage to the crop. Table 5 Predicted number of critical moisture condition for crop growth: rainfall probability of 60% Month

Stress condition (1)

Oct.

Nov.

Dec.

Jan.

Total

(2)

Minimum supplentary water (mm)

Drainage requirement (mm)

Effective rainfall (mm)

(S) (L) (C) (S) (L) (C) (S) (L) (C) (S) (L) (C)

0.0 0.0 0.0 0.0 0.0 0.0 7.0 0.0 0.0 9.4 8.3 5.2

(0.00; 0) (0.00; 0) (0.00; 0) (0.00; 0) (0.00; 0) (0.00; 0) (0.07; 2) (0.00; 0) (0.00; 0) (0.11; 3) (0.06; 3) (0.02; 2)

0. 0. 0. 0. 0. 0. 52. 0. 0. 110. 90. 53.

43. 46. 50. 0. 0. 0. 0. 0. 0. 0. 0. 0.

35. 32. 28. 26. 26. 26. 8. 8. 8. 8. 8. 8.

(S) (L) (C)

16.0 8.0 5.0

(0.11; 3) (0.06; 3) (0.02; 2)

162. 90. 53.

43. 46. 50.

77. 74. 70.

( 1) Total number of stress days. (2) Most severe stress condition (maximum value of SD; duration in days. (S) Loam soil; (L) clay loam soil and (C) clay soil. Note: Growth duration of corn crop is from 2ud October to 10th January.

198

N.D. Binh et al. /Agricultural Water Management 26 (1994) 187-199

Table 6 Predicted numberof critical moistureconditionsfor crop growth: rainfallprobabilityof 80% Stress condition (1)

(2)

Minimum supplentaryw a t e r (mm)

(S) (L) (C) fS) (L) (C) (S) (L) (C) (S) (L) (C)

0.0 0.0 0.0 9.0 6.0 4.0 24.0 14.0 6.0 9.0 9.0 9.0

(0.00; 0) (0.00; 0) (0.00; 0) (0.09; 9) (0.06; 6) (0.04; 4) (0.10; 8) (0.08; 5) (0.06; 2) (0.41; 5) (0.14; 5) (0.09; 3)

0. 0. 0. 63. 54. 32. 130. 68. 61. 198. 141. 122.

0. 2. 6. 0. 0. 0. 0. 0. 0. 0. 0. 0.

34. 32. 28. 12. 12. 12. 3. 3. 3. 3. 3. 3.

(S) (L) (C)

32. 29. 19.

(0.41; 5) (0.14; 5) (0.09; 3)

391. 263. 215.

0. 2. 6.

52. 50. 46.

Month

Oct.

Nov.

Dec.

Jan.

Total

Drainage requirement (mm)

Effective rainfall (nun)

( 1) Total numberof stress days. (2) Most severe stress condition (maximumvalue of SD; durationin days. (S) Loam soil; (L) clay loam soil and (C) clay soil. Note: Growthdurationof corn crop is from 2nd Octoberto 10thJanuary.

5. Conclusions The soil moisture simulation model based on a numerical solution to the differential equation describing flow under unsaturated conditions, gave satisfactory results when compared with field observations. Daily rainfall values simulated using a Markov-chain model provided an input to the soil moisture model for the purpose of studying the variation of soil moisture conditions under rainfed agriculture. Such a simulation indicated that at 70% or less rainfall probability levels, soil moisture conditions are satisfactory for agriculture production with crops likes corn and soybean. Using the model, the analysis predicts relatively moderate variation of water contents in the region along the Red River. This prediction, based on numerical results, is in agreement with results of the experiments conducted in Gialam (Red River Delta) in Winter 19911992. In order to avoid the expected moisture-deficit periods, the crops to be grown in the area should be planted as early as possible. The simulation results also can be used to plan irrigation schedules where irrigation is indeed possible, as well as to predict crop yields when combining with crop growth models.

References Aldabadh, A.S., Rasheed, N. and Ramamothy,M.V., 1982. Dry day analysisfor planningsupplementalirrigation schemes, Trans. ASAE, 25: 150-153, 159.

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Belmans, C.J., Wesseling, G. and Feddes, R.A., 1983. Simulation model of the water balance of cropped soil: SWATRE, J. Hydrol., 63:271-286. Cao Liem, Thu, T.C. and Nga, T.T., 1990, Agroecological zoning of the Red River plain region, Vietnam. International Rice Research Institute Bulletin, Manila, Philippines, 15: 4-5. Clarke, R.T., 1973, Mathematical models in Hydrology. FAO Irrigation and Drainage paper no. 19. Food and Agriculture Organization of the United Nations, Rome. Doorenbos, J. and Pruitt, W.O., 1977, Guidelines for predicting crop water requirements. FAO irrigation and Drainage paper no. 24. Food and Agriculture Organization of the United Nations, Rome. Feddes, R.A., Kabat, P., Van Bakel, P.J.T., Bronswijk, J.J.B. and Halbertsma, J., 1988. Modelling soil water dynamics in the unsaturated zone - state of the art. J. Hydrol., 100:69-1 l 1. Feddes, R.A., Kowalik, P., Kolinska, K. and Zaradny, H., 1976. Simulation of field water uptake by plant using a soil water dependent root extraction function. J. Hydrol., 31 : 13-26. Jain, A.K. and Murty, V.V.N. 1985, Simulation of soil moisture profiles for scheduling irrigations. Agric. Water Manage., 10: 175-181. James, L.G., 1988, Principles of Farm Irrigation System Design. John Wiley & Sons, Washington, U.S.A.. Klute, A. and Dirksen, C., 1986, Hydraulic conductivity and diffusivity: Laboratory methods. Methods of soil analysis, Part I. Physical and Mineralogical Properties, SSSA, U.S.A., 703-716. Hieu, N.T., 1993. Meteorological and Hydrological Records of Vietnam (in Vietnamese). Hydrometeorological Department, Hanoi, Vietnam. Hiler, E.A. and Clark, R.N., 1971, Stress day index to characterize effects of water stress on crop yield. Trans. ASAE, 14: 757-761. Neuman, S.P., Feddes, R.A. and Bresler, E., 1975. Finite element analysis of two-dimensional flow in soils considering water uptake by roots: 1. Theory. SSSA Proceedings, 39: 224-230. Nimah, M.N. and Hanks, R.J., 1973. Model for estimating soil water, plant and atmospheric interrelations: 1. Description and sensitivity. Soil Science Society of America Proceedings, 37: 522-527. Phien, H.N. and Apichart, A., 1984. Agricultural practices under rainfed conditions in Thailand Research report no. 165, Asian Institute of Technology, Bangkok, Thailand. Rosenberg Von, D.U., 1969. Methods for the Numerical Solution of Partial Differential Equations. EIservier, New York. Ritchie, J.T., 1972, A model for predicting evaporation from a row crop with incomplete cover, Water Resour. Res., 8: 1204-1213. Smith, M., 1991, Report on the expert consultation on procedures for revision of FAO guidelines for predicting of crop water requirements. Land and Water Development Division, Food and Agriculture Organization, Rome. Ungs, M.J., Boersma, L. and Akratanakul, S., 1985, A numerical analysis of transport of water and solutes through soil and plants, Volume 1. Theoretical basis, Special report no.753. Agricultural Experimental Station, Oregon State University, U.S.A.