Southeast Asian Studies, Vol. 23, No.1, June 1985

A Model for the Assessment of Rainfed Agriculture in Thailand
Huynh Ngoc PRIEN, * Apichart ANUKULARMPRAI**
and Yu-Min W ANG**

Abstract

A general model consisting of three submodels for daily rainfall generation, daily
evapotranspiration estimation, and daily water balance computation, respectively,
was developed in this study for the assessment of rainfed agriculture in Thailand.
It can be used to obtain the information on important factors related to rainfed
agriculture such as the number of stress days with their frequency and period of
occurrence, the amount of supplementary water requirement and drainage requirement.
Through simulation runs made by shifting assumed planting dates, one may arriveat the most suitable planting period for each crop.

out with the use of a mathematical model
Introduction
In many countries

inwhich takes into account the important factors
SoutheastAsia

rainfed agriculture is still widely practiced.

of rainfed agriculture.

The main purpose ofthis study is to develop that needed model.

The national economies of these countries

In Thailand, the work related to rainfed

depend heavily on the agricultural production,

agriculture may be considered to have started

which in turn depends largely on the distri-in 1974 with a study made by the Mekong

bution of rainfall in space and time.

Secretariat [1974], where a simple model wasTo

improve the agricultural production, it isdeveloped for Northeastern Thailand.

desirable to make full use of the amount of

was followed by two consecutive studies

available water, possibly by shifting themade by the Asian Institute of Technology

planting dates of the economic crops to avoid[AIT 1978; 1981] for the same region (seethe frequent occurrence of stress conditions

also Phien and Sunchindah [1981] and Phienor waterlogging.

[1983]).

In order to help in the

The

model

developed

in

This

1981

selection of these planting dates, it is importantconsists of a Markov chain model for daily

that the effect of them be evaluated in a

rainfallquantitative manner.

formula for estimating daily evapotranspi-

Such an evaluation

would be enhanced and conveniently carried* Division of Computer Applications, Asian
Institute of Technology, P.O. Box 2754,
Bangkok, Thailand** Division of Agricultural and Food Engineering, Asian Institute of Technology, P.O.
Box 2754, Bangkok, Thailand

ration.

generation

andthe Jensen-Haise

The model was later applied [AIT1983], with some minor modifications, toseveral areas carefully selected throughout
Thailand in order to evaluate the potential
success of important economic crops underrainfed conditions.

It is modified again in61this study to make it more comprehensive.

because it is better than the model with sevenstates [Phien 1982]. The generation procedure is as follows:

Model Development

For each month, the transition proba-(1)

Three important processes which involve

bilities and the parameters of the lognormal

in the development of a crop, viewed macro-

distribution are estimated.

In this case, thescopically, are the rainfall, evapotranspiration
and water movement in the field. The

transition matrix
expressed as:

be

p=[

mathematical model being attempted should
properly combine these components. Itabshould be noted that for the effect of shiftingcanconveniently

I-a]
I-b

(1)

planting dates of a crop to be clearly seen,

where

a=Prob (dry day/dry day)a daily basis is used, because a longer time

andb=Prob (dry day/wet day)(2)

period would not be able to reveal all the

Using the historical data, these parameterschanges in the occurrence and severity of

can be easily estimated according to thedrought conditions.

method of maximum likelihood:

Therefore, all the threecomponents are modelled on a daily basis
in this study.

a=f l1 /(f ll +f 12 )(3)

b=f 2 t1(f 21 +f 22 )where fjj 0, j = I, 2) denotes the historical

Rainfall Component

A mathematical model is needed for thegeneration of daily rainfall data.

To thisfrequency of transitions from state i to state
j in the daily values.

It should be noted that

aim, three different models have been de-

the dry state corresponds to all daily rainfall

veloped at AlT.

amounts

These are, respectively, the< 1 mm while the wet state cor-

Markov chain model with seven states [Phien

responds to daily amounts > 1 mm as definedandpreviously [AITWarakittimalee1981],

theMarkovchain model with two states [Phien andLukkananukul 1981], and the model based
upon the method of fragments [Balmadres
1983].

Even though Balmadres found that1981].

Likewise, the pa-

rameters of the lognormal distribution can be
estimated as:1

p. = - L In (x-x o)nthe model based on the method of fragments

(4)
(5)

is relatively superior to the others, it is notsuitable for use in the present work, because

in which n is the number of days with rainfall

the generation scheme involved in that model
produces more data than needed. Conse-amount x> Xo = 1 mm in that month, and thesum extends all over the n values.

quently, the Markov chain model with two(2)

A uniform number U between 0 and 1

states where rainfall amounts on wet days
are represented by a shifted lognormal

is then generated.
(3) Knowing the state i of one day (i=ldistribution was employed in this study

for a dry day, i=2 for a wet day), the state62

H. N. PHIEN et al.:A Model for the Assessment of Rainfed Agriculture in Thailand

j of the following day is determined by com-

So a method of estimating the potential

paring U with a for i=l, or with b for i=2,

evapotranspiration must be selected.

respectively.

If U::;;a (or b), the following

There exist several methods for the esti-

day is dry and hence j = 1; otherwise j =2.
(4) If j = 1 (the following day is dry) themation of potential evapotranspiration (PET),

rainfall amount on that day is set equal to[1977] have become increasingly popular.

zero.

If j =2, it is a wet day; a lognormal

Since the Blaney-Criddle method should bevariable X with parameters p. and (J is gener-used for periods no shorter than one monthated, and the rainfall amount is computed by:[ibid.: 4], it is not suitable for the present(6)

R=X+xoSteps (2) through (4) are repeated after
setting i = j,until

the desired length ofgenerated sequence is reached.
It is clear that the state and the rainfall

amount on the first day must be determined
first.

This may be done as follows:

Let q denote the probability that the firstday is dry, then q may be estimated according
to the following equation:

but those described by Doorenbos and Pruitt

work where a daily basis was adopted.

Theradiation method requires the use of solar
radiation or sunshine duration data which
are not available for most meteorologicalstations in Thailand.

Moreover, when solar

radiation or sunshine radiation data are
available at a station, the other data requiredby the Penman method are also available.
In such case, the Penman method is usedinstead because it is commonly believed toto provide most reliable estimates.

Thus only(7)

two methods, namely the Penman and Pan

where F j (i = 1, 2) is the historical frequencyof rainfall amounts on the first day being in

Evaporation methods, were employed in thisstudy with the second one being morestate i. Having obtained q, the state andrainfall amount of the first day are determined

applicable because the data needed are available at many areas. These are briefly describedas follows:in the following.

(a)
(b)

Generate a uniform random number

Penman FormulaVon (0, 1).

There have been many modifications ofCompare V with q.

If V <q then thefirst day is dry (i = 1) and the rainfall
is set equal to zero.

the Penman formula.

In this study, thefollowing equation is used:

Otherwise (Le.,

if V> q), the first day is wet (i = 2),
and the rainfall amount is obtained aspresented in step (4) with j =2.

PET=C[w*Rn +(l-w)*f(u)*(ea-ed)]where:w= a weighting factor

Rn=net radiation in equivalentevapotranspiration (mm/day)

Potential Evapotranspiration Component
The evapotranspiration can be computed
as the product of the potential evapotranspiration with a coefficient to be defined later.

(8)

feu)

=wind functione. - ed = difference between the saturation

vapor

pressureat63

mean air temperature andactualvapor

pressure,= adjustment

Pan Evaporation Method
The relationship recommended by Dooren-

respectively, andC

Table 16, 28].

factortobos and Pruitt [ibid.] can be written as:compensate for the effect of
day and night weather

where Kp is the pan coefficient and EP

conditions.
The weighting factor w depends on

represents the pan evaporation in mm/day.
The values of the pan coefficient may betemperature and altitudes, with typical values

obtained from Doorenbos and Pruitt [ibid.:

given in Doorenbos and Pruitt [ibid.: 13].

Tables 18 and 19, 34].

(a)

(b)

(12)

The net radiation (Rn) can be measured

but such data are seldom available.

It iscommonly calculated from solar radiation(or sunshine duration),

temperature andhumidity data by the following equation:

where:

The water balance model employed in thisstudy was modified from that developed by

AIT [1981] in an attempt to make it more
(9)

Rn=Rns-Rnl

Water Balance Component

Rns=net short-wave radiation, and
Rnl =net long-wave radiation.

realistic.

The most important modification

was the introduction of the two water depths
corresponding respectively to the saturationand field capacity.

The net short-wave radiation canbeobtained from the measured solar radiation(Rs) by:of the model are redefined in the following:
Water Depth at Saturation (WDS).

This

water depth varies with the crop and soil

Rns=(l-a)Rs
with a=0.25.

The important factors

characteristics and may be estimated by the

The net long-wave can beequation:(13)

WDS=f*B*D/100

computed as follows:

where f is the porosity (or total pore space,1

Rnl=(0.34-0.044eI) (0.1 +0.9n/N)W(T)(10)

in percentage), B is the apparent gravity andD is the depth of root zone (mm).

in which WeT) is a function of temperature,

Water Depth at Field Capacity (WDFC).

with values given in Doorenbos and Pruitt

Like the WDS, this water depth varies with[ibid.: Table 14, 27].

the soil characteristics.

(c)

The wind function expresses the effectof wind on PET and can be written as:

It may be estimatedas follows:
WDFC=FC*B*D/IOO

(14)

(11)

where Fe is the field capacity in percentage.

where U 2 is the 24-hr wind run in km/day

For definition and typical values see Hansen

at 2 m high.
(d) The adjustment factor C may be

et at. [1979].

obtained also from the same report [ibid.:

limit is introduced in order to determine thef(u) =0.2(1 +U 2 /1(0)64Upper Limit of Water Depth (UP).

This

H. N. PHIEN et al.:A Model for the Assessment of Rainfed Agriculture in Thailand

maximum water depth allowed to be storedday (to be given).

on the ground surface.

which the crop starts to respond to the

All the excess water

shortage of soil moisture.

will overflow.
For paddy fields, the maximum standing
water,

denotedIt indicates the level atby DMAX,to be 150 mm as in AIT [1983].

isassumedThe upper

limit for water depth in this case is given by:(15)

UP=WDS+150 (mm)where WDS is given byeq. 13.

mation, it is defined as follows (Figs. 1 and 2):
for paddy:

DMIN=WDFC

assumed (DMAX=O mm), and the upper
limit is set equal to the equivalent water

for upland crops:(16)

Lower Limit of Water Depth (DMIN). This
concept is needed in the definition of stress

I

Mathematically, it is

written as:
DMIN =[FC - p*(FC - WTP)]*B*D/l00(18)

where p is a fraction of available soil
water and WTP is the permanent wilting
point with values (in percentage) obtained
from Hansen et al. [1979].
p

UP

a dynamic approachis used in this study in the definition of

depth at saturation:
UP=WDS(17)(simplified from Wickham [1975: 158])

the lower limit.

For upland crops, no standing water is

As an approxi-isThe value of

estimated as recommended by

Doorenbos and Pruitt [1977].

It should

75 mm

be noted that since p varies with theWORatmospheric evaporative demand, and0~

7~i mm

.c
Q.

wos

L(f)

.,
.,

0

<;

WOFC = OMIN

~

(FC)

the depth of the root zone (D) in eq. 18
varies with the growth stage, DMIN is
not fixed. If the water depth corresponding to the permanent wilting point is

woo

(WTP)

WDO=WTP*B*D/l00

oFig. 1 Definition Sketch for Water Depth
Computation (Paddy)+-.:.;...WO;;,.:s'--(f)=~+_---------

then eq. 18 can be rewritten as:
DMIN =pWDO+(1-p)*WDFCDeep Percolation (DPER).

(19)

For paddy,

deep percolation occurs when there is watero.:.;...WO:..:..F-=-C

denoted by WDO, i.e.:(FC)stored on the ground surface.

.c

It may beQ.

~assumed to be constant for each soil.

OMIN_._._._._.--::-._._.-.L._.~.
•
__._

~

W"'-'OO,--,--

~
-+

t
(WTP)

this study, it is set equal to 3 mm/day forsandy loam [Adhikaryfor clay.

oFig. 2 Definition Sketch for Water Depth
Computation (Upland Crops)In

1979] and 1 mm/day

For upland crops, deep percolationis neglected, i.e., DPER=O.

Stress Days.

Again as an approximation,65

a stress day is defined as a day when thewater depth is less than D MIN.

DRk.=OFLk.+PER k

The water balance computation is carriedout by first computing tentatively the water
depth (WD) on day k:
WDk. = WDk._l + Rk. - ETk. - PERk.

as the sum of the overflow and percolation:

(20)

(25)

The water balance computation as describedis carried out day-arter-day so that the carryover effect can be accounted for.
Computation of Evapotranspiration.

The

where WD t , R1<' ET1< and PERt are respectively the water depth, rainfall, evapo-

actual daily evapotranspiration (ET) depends
upon the availability of soil water, andtranspiration, and percolation on that day.

decreases as the depletion increases.

The value of percolation water is computed

computed from the daily potential evapo-

as follows:transpiration (PET) by the equation:
=0

(26)

if WDk_1:::;;WDS

PERt

(21)

=DPER

It is

if WDk._l>WDS

The computation of the evapotranspiration(ET) will be considered later on at the end

where Ck is a coefficient which is expressedin terms of the crop coefficient (Kc) and thestress coefficient (Ks) as follows:
Ck=Kc*Ks(27)of this section.
After the tentative computation according

There exist several formulas for computing

to eq. 20, there are three possibilities to

Ks (see Boonyatharokul and Walker [1979]).

account for:In this study, the popular linear form is used(1)

If WD,,> UP,
place.

overflow willtake

The overflow water (OFL) isthen computed as:(22)
Afterwards the water depth is set
equal to the upper limit:with the following simple modification:
if

WD~DMIN:

if

WDO~WD<DMIN:

Ks=l

(28)

WD-WDO
KS=DMIN-WDO
DMIN-WD= 1 - DMIN _ WDO(29)

WDk.=UP
Correspondingly, the effective rainfall(ER) on that day is computed from:

Clearly, with this definition, Ks indicatesthe severity of stress conditions. It is

ERk.=WDk.-WDk._l+ETk.+PER t(23)equal to 1 when the day is not a stress day,If DMIN:::;; WD" < UP, the tentativeand equal to 0 when the water depth reaches(2)water depth in eq. 20 becomes theactual depth for day k. In this case:
(24)

(3)

If WD,,<DMIN, day k is a stress day:that at the permanent wilting point.
The atmospheric evaporative demand ofa crop at a growth stage is represented by
ETcrop, which is defined as:
ETcrop=Kc*PET(30)

The value of ETcrop is used in the deterThe drainage requirement (DR) is computed
66

mination of p, the fraction of available soil

H. N. PHIEN et ai.:

A Model for the Assessment of Rainfed Agriculture in Thailand

water as suggested by Doorenbos and Pruitt[1977].
With

thisdefinition,theactualdaily

evapotranspiration, eq.26, can be rewrittenas:
ET=Ks*ETcrop(31)

Computation of Supplementary Irrigation
Water.

When a stress day occurs (WD<to vary with time for upland crops. During
the first 10 days, it is set equal to 5 em,then is increased linearly to the full length
at the end of the third stage, and remains
constant afterwards.
(v) Immediately following a rainfall or an
irrigation, there will be additional evaporation from the soil surface [Kincaid andHeerman 1974]. However, this part isneglected in the present study.

DMIN) and under the assumption thatwater is available, the amount of supplementary requirement (SWR) is computed by
the equation:

The Simulation WorkIn the overall simulation,

the rainfall

generation model is used to provide the valueof daily rainfall on any day of the growing

SWR=WDR-WD(32)

season.

Similarly, the daily evapotranspi-

The water depth requirement (WDR) is

rationisdefined as follows:balance model is applied in order to determine

For paddy:

the important factors related to rainfed
agriculture,

WDR=WDS+75 (mm)(33)

(In Thailand, the standing water required isobservedtonamelyFinally

stress

the

day,

water

drainagerequirement, effective rainfall and supple-

For upland crops:
WDR=WDFC

estimated.

be approximately equal to

75 mm).

mentary

water.

In

reality,rainfalldata

and other meteorological data are available
for different periods.

For example, reliable

rainfall data are available in many stations
since 1952, while most pan evaporation data

Remarks

are available for much shorter periods (see( i ) The water balance computation presented
above does not take into account the watercoming from other fields. It is consequently applicable to rather flat and large
areas only.
(ii) The amount of water due to capillary force
from the soil layers underneath the rootzone is neglected in this study in conformity
with the simplified scheme adopted in thewater balance computation.
(iii) The drainage requirement (DR) for paddy
fields is modified for the last two weeks ofthe growing season. During this period,
all the standing water on the ground surface
must be drained because it is no longer
useful. This is also intended to keep the
paddy fields dry for harvesting.
(iv) The depth of the root zone (H) is assumed

Anukularmphai et al. [1980]).

If the actual

data of all meteorological factors involved
were used, then their records would be cut
short to the same overlapping period; thisobviously reduces the length of the existingdata of other factors.
notThis shortening isdesirable in any statistical analysis.

In order to overcome this situation, simulation
models can be used.

For rainfall, the model

presented previously is intended for thispurpose.

Another scheme forgenerating

daily potential evapotranspiration is needed.
In the following, all details related to thesimulation work are described whereby the67relevance and suitability of the presented
scheme can be seen.

As mentioned before, the Penman and
Pan Evaporation methods were used for theestimation of PET, depending upon availability of the data required.

Daily Rainfall Simulation

The overall simulation is applied to different
crops with the differing growth seasons.

This

The simulation

procedures are now described accordingly.
Penman Methodmeans that the starting day and starting

Since a number of meteorological factors

If theinvolve in this approach, all the corresponding

historical data are read in when the rainfall

data should be read in once and the values

model is used, the computer time and com-of PET are computed.

puter storage needed will be unnecessarily
large. In fact the historical record is needed

the historical data required in the estimation

month may vary from crop to crop.

only for the estimation of the model para-

This means that all

are used and the result comprises the estimatedvalues of PET.

Conse-In the overall simulation, however, due toquently, it is read in only once and these

the reason mentioned at the beginning ofparameters are estimated.

Only the estimatedthis section, the estimated values (treated asvalues for all the 12 months are stored forhistorical data) cannot be used directly.

later use.

Instead, they are used to estimate the para-

meters, namely a, b, /1, a and q.

In the rainfall generation model, uniform

meters of the model which is built to generaterandom numbers on (0, 1) and lognormal

PET.

variables are used.

by following the scheme of Thomas andFiering [1962]. The resulting generation

There have been many

random number generators of which thebest may be that proposed by Wichmannand Hill [1982].

This generator is used in

Such a model may be readily obtainedmodel can reproduce the mean, standard
deviation and serial correlation coefficientof daily values.

the present work.
The lognormal variables can be generated
by first producing normal variables andthen by applying the exponential function.
Standard normal variables can be conveniently generated by the method of Box

It can be written as:

PETJr. = PETJr. + bJr.(PETJr.-I
I-PET k_I)+ SIt(l-r~)2ZIt(34)

where PETk is the potential evapotranspiration on day k;
PET k and SIl are the mean and standard

and Muller [1958]:
z=( -21n U)2 cos (2IlV) [or sin (2IlV)]

deviation of the historical values of PET
on day k,where U and V are two uniform random

rlt is the correlation coefficient between theInumbers on (0, 1).

The lognormal variable

X with parameters p. and a is obtained as:
X=exp (aZ+ p)
Simulation of Daily Potential Evapotranspiration
68

historical PET data on days k and k -1,
bk=rkSIt/Sk-l, andZk is a variable with zero mean and unit
standard deviation.
As commonly practiced, Zk is considered as

H. N. PHrEN et aZ.:A Model for the Assessment of Rainfed Agriculture in Thailand

Pir. being the correlation coefficient between

a standard normal variable in this study.
In order to conform with the fact thatthe historical values of EP on days k and k -1.

only one transition matrix is used for each

From eq. 12, if PET with values computedmonth in the rainfall generation model, allfrom pan evaporation data is generated byrk are replaced by their average value:eq. 35, and EP is generated by eq. 36, thenthe following relationships hold:

1 m
r = - L.: f km k=1

PETk=KpEPIr.

where m is the total number of r k in the monthunder

consideration.

With

this

simplifi-

cation, eq. 34 becomes:
PETk= PETk+rSk(PETk-l

Sk=Kp Skr=p
As in the previous method, the parameters
EP k, Sir. and p are stored instead of the

1

2-PET k_I )/Sk_l +Sk(1-r )2Z k(35)

historical record of EP itself.

The parameters PETk, Sk and r are stored
for each month of the year instead of all thevalues of PET estimated from the related
historical meteorological data.

RemarkSince PETIr. or EP k cannot be negative, when anegative value is generated, it is set equal to themean, viz.

Pan Evaporation Method

if PETk~O, set PETk= PETk

As seen from eq. 12 the values of PET in

EPk~O, set EPk=EP kthis case can be obtained directly from thehistorical record of pan evaporation (EP).
Once the values of PET have been estimated,
the parameters PETk, Sk and r can be estimated and stored for use in the simulation
using the Thomas-Fiering model.

Another

way to generate PET values is first to use theThomas-Fiering model in producing values

Water Balance Computation(l)Crop Coefficient

The determination of actual evapotranspiration

frompotential

evapotranspiration

requires knowledge of a proportionality factor
called crop coefficient (Kc).

It varies fromcrop to crop and also from growth stage tofor EP, and then multiply them by Kp togrowth stage.

get the values for PET.

of paddy and upland crops can be divided into

In this case, theequation involved is as follows:

Generally, the growing season

three stages and four stages, respectively.

EPk=EP k+siEPk- 1- EPk_1)/sk_1

The crop coefficient for each growth stage isI+Sk(1- p2)2 Zk(36)

where EP k is the pan evaporation on day k,
EP k and Sk are respectively the mean andstandard deviation of the historical pan
evaporation on day k,
Zir. is a standard normal variable, andp=~'tPIr.
m
1.=1then obtained by the method presented by
Doorenbos and Pruitt [1977].
(2)

Depth of Root Zone

Attempts have been made to collect thefield data on root zone for the crops underconsideration.

However, no clear pattern

could be identified.

Consequently the generalvalues- suggested by Doorenbos and Pruitt
69

[ibid.] for different crops are used in thiswork.

For each crop, the values for different

according to the following equation =D(clay loam) =D(clay)

soils are determined from the maximum andminimum values where the maximum value is+[D(sandy loam) - D(clay)]j3

assigned to sandy loam, minimum value toWhen actual data available, the estimatedclay.

maximum and minimum values are adjusted

The depths for clay loam are computed( input variables for planting
date. crop, soil type)( input parameters of rainfall model)(input parameters of potential
evapotranspiration)( NG : No. of sequences to be generated)(JSTA: Planting month)(JEND: Harvesting month)(to generate doily rainfall values
in month J)(to generate daily values of PET
in month J)( IK : Assumed planting dote)( MDAY: No. of days in month J)( to estimate crop coefficient aadjust water depth limit)( to estimate fraction of available
soil moisture)~_ _--'L...-_ _..., (tocompute stress day I stress factor,
deficit water, effective rainfall I
drainoge requirement and supplementarywater requirement)( to compute dry spells I maximum stressfoetor and deficit woter corressonding
to each spell )Fig. 3 Flow Chart of the Overall Simulation Scheme70

H. N. PHIEN et at.:A Model for the Assessment of Rainfed Agriculture in Thailand

accordingly.

With detailed information presented in
the foregoing sections, the related computer

Remarkprograms have been developed.

For several provinces, there are many soil
series of which the most popular ones are the Pak
Chong and Chok Chai series, especially in the
Northeast. The general values of soil characteristics provided by Hansen et al. [1979] areadjusted using the actual data provided by
Kubota et al. [1979].

The flowchart of the overall simulation scheme ispresented in Fig. 3, and details of the waterbalance computation are shown in Fig. 4.
Several simulation runs are made in order
to arrive at suitable planting dates for the
economic crops under consideration.

(3)

Al-

Decision Factors in the Simulation

though these dates depend on many factors

Worksuch as labour availability, farmers' habit,---------------~Com pute Water Depth for Day kw ATE R

LAN c

E

1

I
1

Yes

I
I
I
I

I
Compute Overflow
Effective Rainfall and
Set Water Depth atUpper Limit

No

Compute Stress Day]
Deficit Water
Set Effective
Rainfall = 0.0

I
I

I

a

I
I

I

I
I

No

I

I
I

I

I
I

I

I
I

I

I

1

I
I

I
I

Effective Rainfall =Actual Rainfall
Deficit Woter = 0

I
I

I
I
I
I

I

Compute Supplementa ry Water
Requirement and Set Water
Depth at Water Depth Requirement

I
I

I
I
I

-

_

I

-----------------~

Fig. 4 Water Balance Computational Scheme
71

etc., only two of them were used as thedecision factors in this work.

Typical Simulated Results

These arestress days and drainage requirement.

Almost all monthly rainfall sequences in

For stress days, all the important de-different regions of Thailand may be fitted

scriptions (namely the total number, time ofby the leakage law [Phien et af.

occurrence, frequency of occurrence for eachMoreover, during the wet season, monthly

duration

considered.

rainfall sequences may also be fitted by the

The severity is considered most important inthis study. It is represented by the stresslognormal and gamma distributions. Verification of this fitting has also been made forcoefficient Ks or by the stress day factor

many more stations selected throughout the[Hiler and Clark

country.

andseverity)

were1971] defined as:(37)

Sd=1-Ks

The amount of deficit water corresponding
to each duration of stress days can also be

Tables 1 through 5 for five stations: Nan,
Chaiyaphum, Nakhon Sawan, Surat Thaniand Trang.
potential(38)

k=l, ..., Ns

Typical results are collected inThis fitting was used as a basis

for the first evaluation of rainfed agriculture

evaluated by the following equation:
ADW=Maximum [DWIL]

1980].

inThailand.

Other

statisticalproperties of monthly rainfaIJ sequences inThailand have been provided elsewhere [ibid.;
Anukularmphai et af. 1980]. In this study,

where
DWI<=DMIN-WD k(when WDI«DMIN)

only typical simulated results are presented(39)

for evaluating the performance of the Rainfall

and Ns is the duration (in days) of the spell

Model and showing the capability of theof stress

days

being

considered.

This

may be treated as the minimum amount ofTable 1

supplementary water in order to avoid thecorresponding stress spell.

The Kolmogorov-Smimov Statistic Computed in Fitting
Monthly Rainfall at NAN (Long. :100 86 ' E, Lat.: 18°46 /N, Record:
0

The minimum

1952-1978)

amount of supplementary water required ina month or during the entire growing season
may be computed accordingly by summingup the individual amounts needed in the
different spells, if any, covered by thatmonth or the growing season.
From several simulation runs, a 30-year
period was found to provide stable results(in the sense that a longer simulation period
provides almost the same results).

Month
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jui.
Aug.
Sept.
Oct.
Nov.
Dec.
-

72

j

Distributions
Leakage I Log-normal I Gamma
0.127
0.077
0.088
0.120
0.100
0.113
0.135
0.089
0.121
0.086
0.174
0.092

-

-

-

0.163
0.111
0.150
0.179
0.118
0.161
0.136

0.138
0.092
0.127
0.145
0.097
0.136
0.094

-

-

not applicable because of existing zero
valuesH. N. PHIEN et ai.:Table 2

Month
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jui.
Aug.
Sept.
Oct.
Nov.
Dec.
-

A Model for the Assessment of Rainfed Agriculture in Thailand

The Kolmogorov-Smimov Statistic
Computed in Fitting Monthly
Rainfallat
CHAIYAPHUM(Long.: 102°02'E, Lat.: 15°48'N,
flecord: 1952-1978)
Distributions
I Leakage
0.075
0.050
0.139
0.084
0.112
0.125
0.101
0.162
0.128
0.093
0.113
0.067

I Log-normal I

Gamma

-

-

-

-

-

-

0.062
0.141
0.153
0.070
0.090
0.086
0.202

0.070
0.130
0.134
0.095
0.065
0.113
0.178

-

-

-

-

Table 4Month

The Kolmogorov-Smimov Statistic
Computed in Fitting Monthly
Rainfall at NAKHON SAWAN(Long.: 100 1O'E, Lat.: 15°48 'N,
Record: 1952-1978)

-

Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
-

Distributions
I Leakage I Log-normal I Gamma
0.160
0.176
0.083
0.105
0.119
0.090
0.059
0.058
0.061
0.116
0.088
0.071
0.121
0.145
0.110
0.086
0.096
0.099
0.131
0.109
0.098
0.145
0.094
0.073
0.222
0.040

not applicable because of existing zero
valuesTable 5

Water Balance Model.

Month
Jan.
Feb.
Mar.
Apr.
May
Jun.
JuI.
Aug.
Sept.
Oct.
Nov.
Dec.
-

Distributions
Leakage I Log-normal I Gamma
0.131
0.117
0.884*
0.082
0.094
0.143
0.174
0.940*
0.096
0.099
0.102
0.075
0.082
0.107
0.074
0.091
0.071
0.106
0.132
0.117
0.099
0.110
0.130
0.143
0.129
0.135
0.100
0.134
0.116
0.115
0.136
0.170

not applicable because of existing zero
values* not fitted at the 5 % significance level

0

Month

I

Jan.
Feb.
Mar.
Apr.
May
Jun.
Jui.
Aug.
Sept.
Oct.
Nov.
Dec.

not applicable because of existing zero
valuesTable 3

The Kolmogorov-Smimov Statistic
Computed in Fitting Monthly
Rainfallat
SURAT THANI(Long.: 99°21 'E, Lat.: 09°07'N,
flecord: 1952-1978)

The Kolmogorov-Smimov Statistic
Computed in Fitting Monthly
flainfall at TflANG(Long. :99°38 'E, Lat.: 07°31 'N, Record:
1952-1978)
I

Distributions
Leakage I Log-normal I Gamma
0.157
0.096
0.107
0.066
0.137
0.082
0.091
0.125
0.102
0.103
0.129
0.106
0.077
0.097
0.075
0.062
0.094
0.075
0.072
0.080
0.064
0.127
0.158
0.137
0.070
0.108
0.082
0.094
0.181
0.115

not applicable because of existing zero
valuesgeneration was made in AIT [1981; 1983],
using

the reproductionof the following

Performance of the Rainfall Modelstatistics as criteria: distribution of monthly

Evaluation of the model for daily rainfall

rainfall, maximum amounts of daily rainfall,

( 1)

73

*m7~71Uf1G

23~ 1 {}

Table 6 Reproduction of Monthly Rainfall Distribution Accessed by the Mann-Whitney Test·
StationI Jan. Feb. Mar. Apr. May Jun. Jut Aug. Sept. Oct. Nov. Dec. I Overall
10
10
10
10
10
10
Nan
10 10
10 10 10 10
100%
10
10
9
10
Chaiyaphum
10
10
9
9
10 10 10 97.5%
10
10
10
10
10
10
10
10
10
10
10
10
9
Nakhon Sawan
99.2%
10
10
10
10
10
10
10 10 10 10 10 10
Surat Thani
100%
Trang
10
10 10 10 10 10 10
10
10
10
10
10
100%

* for 10 generated sequences, each having the same length as the historical recordand frequencies of wet and dry spells.

Be-(12 months), 12 relative errors for the meancause of its importance in this simulation

are obtained.

study, typical results are also provided forsmallest values of these 12 errors are thenthe aforementioned five additional stations.

computed and tabulated.

Reproduction of Monthly
tribution

Rainfall Dis-

Instead of using the Kolmogorov-

The largest, average, andThe same defi-

nition and computation apply to the standard
deviation.

They are both shown in Table 7.

Smirnov test for each of the distribution:
leakage law, gamma and lognormal, theMann-Whitney test [Gibbons 1971] was usedin order to simply check if the generated andTable 7 Relative Errors (in Percentage)in Reproducing the Mean and. Standard Deviation of Maximum
Amounts of Daily Rainfall

historical sequences have the same distribution (without particular reference to anyof the above distributions).

From Table 6,

the percentage of times that the generated
monthly sequence has the same distribution
as the historical record is very high (97.5 %),indicating that monthly rainfall distribution
Amounts of

Daily Rainfall In order to save space, thelargest, average and smallest values of therelative errors for the mean and standard
deviation of the maximum amount of rainfall
for all the months of the year are collected.
The relative error (in percentage) for themean is defined as:

e=I00(R-R')/R

(3)
0
0

37
39

(2) (3)
-10 4
7 0.9

26
10
22

0
-1
-4

0
0.2
1

44
35
43

9 4
1 4
-10 0

(1) Largest (in absolute value) error

is reproduced by the presented model.
Reproduction of Maximum

(2)
-4
9

(1)

23
24

(1)

Nan
Chaiyaphum
Nakhon
Sawan
Surat Thani
Trang

Standard
Deviation

Mean

Station(2) Average error(3) Smallest (in absolute value) error

The largest relative error may appear to behigh but with only 10 generated sequences,even larger discrepancy is commonly experienced in simulation studies.

Moreover, theaverage relative error is quite small indicatinga good reproduction of the mean and standard(40)

deviation of maximum amounts of daily

where R and Ii I are the means of maximum
amount of daily rainfall (in a month) com-

rainfall.
Reproduction of Frequencies of Dry andputed from the historical record and 10

Wet Spells

generated sequences, respectively.

74

In a year

Although the dry and wet spells

at different duration were defined accordingH. N. PHrEN et ai. :A Model for the Assessment of Rainfed Agriculture in Thailand

Table 8 Average Relative Errors(in Percentage) in Reproducing Frequencies
of Dry and Wet Spells
StationNan
Chaiyaphum
Nakhon
Sawan
Surat Thani
Trang

Dry
SpellsWet
Spells

9
2

0.7
7

10

I
-2
-0.4

-3
-2

results at Nakhon Sawan are presented forillustrations and discussions.
(a)Paddy.

For paddy, two soil types

namely clay and clay loam were considered
because they are most suitable for paddy.
As indicated by AIT [1983], August 1 is asuitable planting date for paddy on bothsoil types.

The simulated results are shownin Table 9.

Since there is no stress day in all

the months of the growing season, the most
severe condition is expressed by (0; 0; 0)1981], and their

where generally, (a; b; c) indicates that thefrequencies of occurrence were computed

most severe case occurs with a stress day factor

accordingly for all the 12 months of the(Sd)=a, a duration=b days, and a frequency

year, only the average relative error for all=c% (meaning c times in 100 years).

the durations (from one day to m = the number

though the drainage requirement is relativelyof days in the month under consideration) islarge, the amount of effective rainfall is largepresented.

also indicating that rain water is effectively

to the theory of runs [AITComputed values are shown inAl-

Table 8 for both dry and wet spells.
From the table it is clear that thefrequencies of dry and wet spellsof the historical record are well

Table 9 Simulated Results for Paddy Planted August
1 in Nakhon Sawan
StressCondition

(mm)

(H)

0.0

(2)
(0; 0; 0)

Effective
Rainfall
(mm)

37.4

179.9

(M)
(H)

0.0
0.0

(0; 0; 0)(0; 0; 0)

59.2
46.8

183.8
205.5

(M)
(H)

0.0
0.0

(0; 0; 0)(0; 0; 0)

58.1
196.4

218.6
106.8

(M)
(H)

0.0
0.0

(0; 0; 0)(0; 0; 0)

272.3
0.4

112.6

(M)
(H)

0.0
0.0

(0; 0; 0)(0; 0; 0)

0.4
281.1

6.6
498.8

(M)

0.0

(0; 0; 0)

383.7

521.7

Month

reproduced.
(2)

(1)

Capability

of

the

Water

AugustBalance Model
The revised Water Balance Model
was used in many simulation trials
in

order

to

determinesuitable

September

Octoberplanting dates and related information for eight economic crops being

soybean,mungbean, cotton andkenaf; and the information contains
stress conditions, drainage requirement, effective rainfall, and supplementary water requirement.
section,some

typicalIn thissimulated

6.6

November*cultivated in Thailand. These crops
are paddy, corn, peanuts, sorghum,

Drainage
Requirement

Overall* Growing season extends only eight days into
November(1) Total number of stress days (days)(2) Most severe stress conditions: (0; 0; 0) means thatthe maximum stress day factor is 0, the duration ofstress is 0, and the corresponding frequency is O.
(H): clay; (M): clay loam
75

used.

So, August 1 is clearly a suitable

For clay, September 1 wasin Nakhon Sawan [ibid.].

Simulated Results for Com Planted September 1
in Nakhon Sawan on Clay

From

Minimum
Drainage
SuppleEffective
Requirementary
Rainfall
ment
Water
(mm)
(mm)
(mm)

Stress Condition

Month

Corn.

found to be a suitable planting date for corn

planting date for paddy in Nakhon Sawan.
Table 10(b)

thesimulated

results collected in Table
10, the most severe stressspell would be expected
to occur in

September

(1)

(2)

September

4.6(0.14;3;17)

I

9.9

49.6

I

183.1

October

3.0(0.03; 10; 7) I

8.3

0.3

I

106.1

0.14, duration of spell=

November* I

3.4(0.05; 10; 10) I

10.0

0.01

17.1

three days and frequency

Overall

11.0(0.14; 3; 17)

28.1

49.9

I 306.3of occurrence = 17 %. Forwith the maximum valueof stress day factor Sd =I

I

* Growing season extends only 19 days into November

the entire growing season~
the total number of stress(1) Total number of stress days

(2) Most severe stress conditions (Maximum value of Sd; duration in days; frequency in %)days is 11 days.

How-

ever, even in the most
severe case, the value ofTable 11

Simulated Results for Com Planted August 25 on Clay
Loam (M) and Sandy Loam (L) in Nakhon Sawan

Stress Condition

Month

Minimum
Drainage
SuppleEffective
Requirementary
Rainfall
ment
Water
(mm)
(mm)
(mm)
5.7
15.2
22.3

quently,

there

shouldbe no damage to
crop.

the

In Table 10, theminimum supplementary

(M)

0.4

(2)
(0.08; 1; 13)

(L)
(M)

0.9
0.0

(0.16; 1; 27)(0; 0; 0)

6.3
0.0

14.0
30.4

21.4
167.3

(L)
(M)

0.0
0.0

(0; 0; 0)(0; 0; 0)

0.0
0.0

4.2
0.4

212.9
133.1

(L)
(M)

0.0
0.0

(0; 0; 0)(0; 0; 0)

0.0
0.0

0.0
0.0

135.8

(L)
(M)

0.0
0.4

(0; 0; 0)(0.08; 1; 13)

0.0
5.7

0.0
46.1

9.6
323.3

(computed as the quan-

(L)

0.9

(0.16; 1; 27)

6.3

14.9

383.4

water depth back to the* Growing season extends only seven days and 12 days into Augustand November, respectively(1) Total number of stress days
(2) Most severe stress conditions (for example, maximum value of
Sd=0.08; duration=one day; frequency of occurrence=13
times in 100 years)

water depth requirement(1)

August*Septemberwater requirement is also
provided.
amountThisofis theirrigationwater to be supplied in
order

to

avoid

the

occurrence of stress days.

October

9.6

November*Overall76

Sd is quite small. Conse-

Of course,theactualsupplementarywatertity needed to bring theimmediately following a
stress day) can also be
estimated.
For clay

loam

and

H. N. PHI EN et ai.:sandy loam, August 25
is a

suitable

A Model for the Assessment of Rainfed Agriculture in Thailand

Table 12

Simulated Results for Peanuts Planted June 25 in Nakhon
Sawan

planting

date for corn in Nakhon
Sawan [ibid.].

The sim-ulated results

collected

in

Table

M onthclearly

11

indicate that this is a

(H)

(M)

June*

(L)

good planting date: thenumber of stress

days

(H)

(M)

July

is small, and the stresscondition is not severe
at all.

Moreover, while

(L)
(H)
(M)

Augus t(L)(H)

the drainage requirement
issmall, theeffective

Septen1ber (M)

(L)
(H)

rainfall is high indicatingthat available rain water(M)

Octobe

~r

(L)
(H)

is used effectively.
June 25

Novem ber* (M)was found to be a suitable

(L)
(H)

(c)

Peanuts.

planting date for peanuts(M)

Overal I(L)

on all soil types underconsideration [ibid.]. The
corresponding simulated
results

on

clay

(H),

clay loam (M), and sandy

Minimum
Drainage
SuppleEffective
Stress Condition
Requirementary
Rainfall
ment
Water
(I)
(2)
(mm)
(mm)
(mm)
(0.05; 1; 20)
2.5
0.5
5.2
17.5
0.7
(0.09; 2; 20)
3.6
19.1
3.5
1.1
(0.17; 2; 20)
9.2
1.3
19.3
(1.11;7;13)
11.9
17.3
12.4
92.7
12.3
(0.13; 6; 17)
17.7
7.2
95.5
(0.20; 2; 40)
17.1
11.3
3.3
107.4
1.2
(0.05; 3; 7)
4.4
59.4
106.6
1.2
(0.05; 3; 7)
5.1
21.7
144.1
(0.04; 2; 13)
3.8
0.9
166.7
0.0
(0; 0; 0)
0.0
0.0
128.2
128.1
(0; 0; 0)
0.0
0.0
93.7
162.6
(0; 0; 0)
0.0
0.0
18.3
227.4
(0; 0; 0)
0.0
37.6
106.0
I
0.0
I
(0; 0; 0)
23.1
120.5
0.0
0.0
(0; 0; 0)
0.0
0.0
0.0
139.9
I
(0; 0; 0)
0.0
0.0
8.0
7.7
(0; 0; 0)
0.0
0.0
5.8
9.9
(0; 0; 0)
0.0
0.0
0.0
15.7
13.6
(0.11; 7; 13)
24.2
250.8
458.7
(0.13; 6; 17)
26.3
155.1
551.7
14.2
(0.20; 2; 40)
30.1
22.9
678.2
13.3

* Growing season extends only six days and 11 days into June andNovember, respectively(1) Total numter of stress days
(2) Most severe stress conditions(H): clay; (M): clay loam; (L): sandy loam

loam (L) are shown in
Table 12. The number of stress days foryears.

However, for all these soil types, thegiven in AIT [ibid.] for all the soil types while

corresponding value of the stress day factor
is quite small, therefore, no damage to thethe drainage requirement is smaller.

In thecrop would be caused by the stress conditions.

present study, the most severe stress spell

In other words, June 25 is a suitable planting

is found to have different duration for different

date for peanuts in Nakhon Sawan.

the entire growing season is higher than thatsoil type.

On clay, the most severe spell(d)Sorghum.

As indicated in AIT [ibid.],lasts for seven days in July with a frequency

August 1 is a suitable planting date forof occurrence of 13 times in 100 years.

Onsorghum on all the soil types under con-clay loam, it lasts six days and the frequencyof occurrence is 17 times in 100 years.

sideration. With this planting date, thesimulated results are collected in Table 13.

Finally, on sandy loam it lasts two days with

These results clearly support the previously

a frequency of occurrence of 40 times in 100

recommended date: the total number of stress77

Table 13 Simulated Results for Sorghum Planted August 1 in
Nakhon Sawan
Minimum
Drainage
SuppleEffective
RequireStress Condition
mentary
Rainfall
Month
ment
Water
(2)
(mm)
(mm)
(mm)
(I)

(H)
August

(M)
(L)

(H)
September (M)(L)(H)

October

(M)
(L)

(H)
November (M)(L)(H)
December· (M)
(L)

(H)

6.5
6.9
7.2
0.3
0.3
0.5
0.3
0.3
0.4
1.0
1.0
1.0
0.4
0.4
0.4
8.5
8.9
9.5

(0.13; 7; 13)(0.17; 3; 20)(0.19; 2; 40)(0.06; 3; 7)(0.06; 3; 7)(0.02; 3; 7)(0.01; 6; 3)(0.01; 4; 3)(0.02; 3; 3)(0.02; 3; 3)(0.02; 30; 3)(0.01; 13; 3)(0.02; 13; 3)(0.02; 13; 3)(0.02; 13; 3)(0.13; 7; 13)(0.17; 3; 20)(0.19; 2; 40)

186.1
186.5
201.4
32.2
32.1
36.4
23.4
20.8
21.2
51.8
51.3
50.5
42.1
41.9
42.0
335.7
332.6
351.5

42.7
35.4
27.5
85.3
30.1
0.0
17.0
7.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
145.0
72.6
27.5

(M)
Overall(L)• Growing season extends only 13 days into December(1), (2), (H), (M), (L) as in Table 12

127.5
132.7
146.7
174.7
229.9
260.6
118.2
128.1
135.2
24.8
24.8
24.8
1.9
1.9
1.9
447.1
517.2
569.3

days is small; the stresscondition is not severe;
the drainage requirement
is small; and the available rain water is usedeffectively.
(e)Soybean.

In thisstudy, it was found that
August 20 is a suitable
planting date for all thesoil types (not only for
clay, as in AIT [ibid.]).
The simulated results arecollected inTable 14.

Clearly August 20 is asuitableplanting

date

for soybean in Nakhon
Sawan.
(f)

Cotton.

For cot-

ton, July 10 was foundto be a suitable planting

Table 14 Simulated Results for Soybean Planted August 20 in
Nakhon Sawan
Minimum
Drainage
SuppleEffective
Stress Condition
RequirementaryMonthRainfall
ment
Water
(1)
(2)
(mm)
(mm)
(mm)

(H)

(0.08; 3; 10)
32.3
25.9
44.5
(0. to; 4; 10)
49.3
17.6
August·47.1(0.10; 5; 13)
21.4
9.2
51.0
(0.06; 7; 7)
(H)
19.5
93.7
132.7
(0.03; 7; 3)
September (M)
49.1
20.0
170.3
(0.03; 7; 3)
(L)
0.2
36.4
221.0
(0.02; 25; 3)
72.9
10.2
(H)
123.2
(0.01; 12; 3)
43.5
(M)
1.8
131.6
October(0; 0; 0)
13.7
(L)
0.0
135.6
(0.08; 3; 10)
0.0
11.0
(H)
9.6
(0; 0; 0)November· (M)
0.0
0.0
9.6
(0; 0; 0)
0.0
0.0
9.6
(L)
(0.08; 3; to)
135.7
129.8
(H)
310.1
(M)
(0.10; 4; 10)
141.9
48.3
358.7
Overall(0.10; 5; 13)
71.5
(L)
9.4
417.2
• Growing season extends only 12 days into August and November(1), (2), (H), (M), (L) as in Table 12

(M)
(L)

78

1.2
1.5
1.8
0.7
0.7
0.6
1.6
0.7
0.2
0.5
0.0
0.0
4.0
2.9
2.5

date for all the three soil
types.

The simulated

results are collected inTable 15.

The numberof stress days is small ;the stresscondition is

not severe; and available
rain water is used effecIn other words,

tively.

July 10 is a good planting
date

for

cottonin

Nakhon Sawan.
It should be noted thatfor clay, the maximum
value of Sd was 0.10 in
the months of July andAugust.

However, from

inspection of the amountH. N. PHIEN et at.:A Model for the Assessment of Rainfed Agriculture in Thailandof deficit water in these

Table 15spells it was found that

Simulated Results for Cotton Planted July lOin Nakhon
Sawan

the first stress spell ismore severe.

Month

Discussions

( 3)

(a)

As

,-

mentioned

(H)
July*

considered most impor-(H)
Augusttant in the selection ofsuitable planting dates.
With the definitions of

(M)

(L)

(H)
September (M)

(L)

(H)

the stress day factor (Sd)and the amount of deficit

(M)

(L)

previously, severity was

October(M)(L)

water (ADW), the most(H)

severe spell can be picked

November (M)up easily.

(L)

It is the spell
to

(H)

the

December* (M)largest values of both Sd(L)corresponding
and ADW.

The

most

(H)
Overall(M)(L)

Minimum
Drainage
SuppleEffective
Stress Condition
Requirementary
Rainfall
ment
Water
(I)
(2)
(mm)
(mm)
(mm)
5.0
(0.10; 8; 10)
124.9
22.5
74.1
(0.17; 3; 17)
5.3
154.4
15.3
75.5
(0.11; 2; 20) II
5.3
86.5
8.7
80.2
(0.10; 3; 13)
1.3
23.8
38.6
141.8
1.4
(0.10; 2; 17)
28.3
5.8
164.5
(0.10; 3; 10)
0.8
15.0
0.0
181.3
(0; 0; 0)
0.0
0.0
83.3
150.2
(0; 0; 0)
0.0
0.0
20.3
191.3
(0; 0; 0)
0.0
0.0
1.5
230.9
(0; 0; 0)
0.0
0.0
29.0
124.8
(0; 0; 0)
0.0
0.0
15.8
119.7
(0; 0; 0)
0.0
0.0
0.0
153.8
0.0
(0; 0; 0)
0.0
0.2
40.0
(0; 0; 0)
0.0
0.0
0.0
40.2
(0; 0; 0)
0.0
0.0
0.0
40.2
(0; 0; 0)
0.0
0.0
0.2
0.6
(0; 0; 0)
0.0
0.0
0.0
0.6
(0; 0; 0)
0.0
0.0
0.0
0.6
(0.10;8;10)
6.3
158.7
173.6
531.4
6.7
(0.17; 3; 17)
192.7
57.1
601.8
(0.18;2;20)
6.1
101.5
10.2
687.1

severe stress conditions
collected in Tables 10-15* Growing season extends 22 days into July and six days into December.

were selected according(1), (2), (H), (M), (L) as in Table 12

to this scheme.
(b)

From the results collected in Tables 12

provided in the detailed output of the com-through 15, a clear pattern seems to exist

puter program for the simulation work foramong the drainage requirement and effective

careful evaluations of alternative planting

rainfall for upland crops grown on different

dates.)

soil types: the drainage decreases and the(d)The minimum amount of supple-

effective rainfall increases from clay (H) tomentary water may be computed as theclay loam (M) and sandy loam (L).
(c) More information on stress condition

minimum amount needed to avoid theoccurrence of stress days. During any stress

was made available by the scheme presented

spell, when an amount of water equivalent toin

ADW is available, the crop may consume it

thisstudy.

Stress

days

may

occur

frequently but as long as the corresponding
stress day factor (Sd) and the amount ofand thus avoid the spell.
(e)

The supplementary irrigation water

deficit water are small, one should expect noshould correspond to the actual amount ofdamage to the crop.

water to be supplied.

(Since the time of stressdays occurrence is important, it is also

However, in practicalsituations, one does not know when a stress19

day occurs so that irrigation can be madeimmediately following it.

It would be desira-ble to forecast daily rainfall amounts with leadtime equal to several days so that the assumption could be practically applied.

At present,no successful methods are available for suchforecasting purposes.

Acknowledgements
The authors wish to express their gratitude
to the Committee for Coordination and Acceleration of Water Resources Development, theSecretariat of the Prime Minister, Kingdom ofThailand for' sponsoring the research project
which is reported partly in this paper. They
also wish to thank the Asian Institute ofTechnology for use of its research facilities
throughout the period of study.

Summary and Conclusions
In this study, a general model was developed
for the assessment of rainfed agriculture in
Thailand.

It consists of three submodels forthe three main components, namely, rainfall,evapotranspiration and water balance computation.

The rainfall submodel was shown tobe able to reproduce all important statisticsof the historical record, and hence it wasused to generate daily rainfall needed in thewater balance computation.

The selection of

formulas for estimating the potential evapotranspiration depends largely on the timeframe employed andthe data

available.

For Thailand, Penman's formula and evaporation method were found suitable, with thelatter being moreless requirement
water balanceofapplicable due to its
recordeddata.

computation was

Theroughlyschematized, however, all the simulated results
shown in this study and elsewhere [AIT1984] seemed to be reasonable.

As such, thedeveloped comprehensive model is clearly
useful in providing all important information
related to rainfed agriculture practices.

The

model is quite general in its structure.
Consequently, it is expected to be applicableto many other areas in Southeast Asia withsome minor modifications.

80

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