an early warning system for agricultural drought in an arid region using limited data

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( ) Journal of Arid Environments 1998 40: 199 ]209 Article No. ae980437 An early warning system for agricultural drought in an arid region using limited data Vijendra Kumar w Department of Geography, University of Manitoba, Winnipeg, Canada R3T 2N2 ( ) Received 18 December 1997, accepted 26 June 1998 In this paper, an early warning system for agricultural drought in an arid ( ) region Jodhpur district, Rajasthan, India is developed by estimating grain yield of pearl millet, the major food crop in the region. Two multiple linear ( ) regression models, namely the intermediate warning IW model that estimates the yield about a month before the crop is harvested, and the final warning ( ) FW model that estimates the yield at about harvest time, are developed for the purpose. Explanatory variables used in the models are delay in crop sowing, monthly rainfall, and number of rainy days in a month. These variables are derived from the daily rainfall data which are easily available in arid regions. Using the 1963 ] 1987 data for model development, up to 74% and 81% yield variations could be explained by the IW and FW models, respectively. When these models were tested on the 1988 ] 1991 data, mean . absolute per cent error in the estimated yields was found to be 18 5% and . 11 2% for the IW and the FW model, respectively. Models are evaluated and some measures for their improvement discussed. q 1998 Academic Press Keywords: pearl millet; agricultural drought; soil moisture index; rainfall; yield modeling; food security; early warning Introduction ( ) Agricultural drought hereafter referred to as drought is a spatial phenomenon causing significant reduction in agricultural productivity mainly due to an inadequate supply of ( ) soil moisture Kumar, 1988; Agnew & Warren, 1996 . Droughts are experienced on almost all types of agricultural lands in the world, but arid lands are most susceptible . 2 ( ) Le Houerou, 1996 . In India, arid lands occupy 0 32 million km , of which 62% lies ´ ( ) in western Rajasthan Kumar, 1993 . These lands are likely to experience droughts ( ) with a frequency of once in two and a half years Singh, 1978, p. 65 . Average annual ( ) ( ) rainfall in the area is low below 400 mm ; soils are sandy loam 85 ] 90% sand with . . y1 ( ) ( ) low organic content 0 1 to 0 25% , very high infiltration rate 9 ] 10 cm h , poor ( ) moisture storage capacity 120 ] 135 mm in 1 m soil profile , poor microbial activity, ( ) and low fertility Singh & Joshi, 1988 . The agricultural productivity of these arid lands is low yet sufficient in the years when droughts do not occur. In times of drought, ( ) however, agricultural productivity in particular food productivity declines w Previously at the Regional Remote Sensing Service Centre, Department of Space, Central Arid Zone Research Institute Campus, Jodhpur, India-342003. 0140 ]1963r98r020199 q 11 $30.00r0 q 1998 Academic Press

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( )Journal of Arid Environments 1998 40: 199]209Article No. ae980437

An early warning system for agricultural droughtin an arid region using limited data

Vijendra Kumarw

Department of Geography, University of Manitoba, Winnipeg,Canada R3T 2N2

( )Received 18 December 1997, accepted 26 June 1998

In this paper, an early warning system for agricultural drought in an arid( )region Jodhpur district, Rajasthan, India is developed by estimating grain

yield of pearl millet, the major food crop in the region. Two multiple linear( )regression models, namely the intermediate warning IW model that estimates

the yield about a month before the crop is harvested, and the final warning( )FW model that estimates the yield at about harvest time, are developed forthe purpose. Explanatory variables used in the models are delay in cropsowing, monthly rainfall, and number of rainy days in a month. Thesevariables are derived from the daily rainfall data which are easily available inarid regions. Using the 1963]1987 data for model development, up to 74%and 81% yield variations could be explained by the IW and FW models,respectively. When these models were tested on the 1988]1991 data, mean

.absolute per cent error in the estimated yields was found to be 18 5% and.11 2% for the IW and the FW model, respectively. Models are evaluated and

some measures for their improvement discussed.

q 1998 Academic Press

Keywords: pearl millet; agricultural drought; soil moisture index; rainfall;yield modeling; food security; early warning

Introduction

( )Agricultural drought hereafter referred to as drought is a spatial phenomenon causingsignificant reduction in agricultural productivity mainly due to an inadequate supply of

( )soil moisture Kumar, 1988; Agnew & Warren, 1996 . Droughts are experienced onalmost all types of agricultural lands in the world, but arid lands are most susceptible

. 2( )Le Houerou, 1996 . In India, arid lands occupy 0 32 million km , of which 62% lies´( )in western Rajasthan Kumar, 1993 . These lands are likely to experience droughts

( )with a frequency of once in two and a half years Singh, 1978, p. 65 . Average annual( ) ( )rainfall in the area is low below 400 mm ; soils are sandy loam 85]90% sand with

. . y1( ) ( )low organic content 0 1 to 0 25% , very high infiltration rate 9]10 cm h , poor( )moisture storage capacity 120]135 mm in 1 m soil profile , poor microbial activity,

( )and low fertility Singh & Joshi, 1988 . The agricultural productivity of these arid landsis low yet sufficient in the years when droughts do not occur. In times of drought,

( )however, agricultural productivity in particular food productivity declines

w Previously at the Regional Remote Sensing Service Centre, Department of Space, Central Arid ZoneResearch Institute Campus, Jodhpur, India-342003.

0140]1963r98r020199 q 11 $30.00r0 q 1998 Academic Press

V. KUMAR200

significantly. This requires immediate attention by the provincial government inRajasthan in order to avoid any food scarcity to the human population which isdependent on these lands. To tackle the situation arising from the food scarcity, theprovincial government has to import an adequate quantity of food grains from otherprovincial governments in the country or from the federal government. If droughts are

( )severe and widespread in the country, as happened in 1987 Kumar, 1988 , the foodgrains may have to be imported from other countries.

The success of planning import of food grains depends significantly on how timelyand accurately the decisions regarding the import quantities are made. It is in this

(context that an early warning of drought i.e. prediction of drop in food grain)production plays an important role.

Current practices followed by the provincial government in making early warningsfor drought are based on the rainfall situation and on field reports about crop

( )conditions in the area Kumar, 1986 . Rainfall is a major source of irrigation in thearea, and is supplied by a south-west monsoon. The south-west monsoon develops eachyear, usually around the end of May, on the south-west coast of India, and movestowards western Rajasthan through central India. Studies of the monsoon conductedby the India Meteorological Department have determined that the monsoon reacheswestern Rajasthan, on average, on the first of July, bringing in the first monsoon rainsof the year. In some years, late onset, early withdrawal, or failure of monsoon causesdroughts.

Early warnings based on rainfall situation or field reports have not proven to be veryeffective, usually because the warnings are qualitative and are available only after the

( )cropping season or drought has passed. To improve the current early warning system,an attempt is made in this paper to provide pre-harvest quantitative estimates of grain

( )yields production per unit area of pearl millet for Jodhpur district, part of westernRajasthan.

Study area

Jodhpur district is bounded between 278 299 N and 258 999 N latitudes, and between718 599 E and 738 469 E longitudes, covering approximately 22,860 km2. About half of

( )the area is occupied by crop lands. Pearl millet Pennisetum Americanum is the major( )food crop average sowing area is about 55% of the total cropped area not only in the

district but in the entire western Rajasthan. The major source of irrigation is rainfall;less than 5% of the total cropped area is irrigated by other means, i.e. canal or

( )ground-water sources Statistical Division, 1990 . Average annual rainfall is about 300( )mm, 90% of which occurs in the rainy season July through September . The

(distribution of monthly rainfall during the rainy season is highly erratic average)coefficient of variation is about 50% .

Development of an early warning system

In order to develop an early warning system, the grain yield of pearl millet, the majorfood crop in the area, was selected as a parameter to be modeled. Two broad

( ) ( )approaches to yield modeling exist in the literature: i deterministic, and ii stochastic( )Bair, 1977 . The deterministic approach generally treats the dynamics of plant or cropgrowth over the cropping season through a set of mathematical expressions tyingtogether the inter-relationships of plant, soil, and climatic processes. The stochasticapproach, on the other hand, takes a sample of crop yield data together with the

AN EARLY WARNING SYSTEM FOR AGRICULTURAL DROUGHT 201

corresponding weather data and relates the two through statistical techniques, such as( )regression analysis Parry et al., 1988 . For a large area, the stochastic approach has

been favored over the deterministic approach, mainly due to the difficulty in obtaining( )data over large areas e.g. soil characteristics, plant parameters, and planting dates to

develop even a simple deterministic model.( )In arid regions where lack of data Agnew & Warren, 1996 is often an obstacle to

attempting a complex analysis, use of the stochastic approach is favored even more.Simple regression techniques of the stochastic approach have, therefore, been commonlyused to model crop yields in such regions.

Explanatory variables that are required to conduct a regression analysis are oftenderived from the primary data considered to influence the yield. For example, some ofthe derived variables that have been used in crop yield modeling are: albedo, i.e. ratio

( )of the reflected light to incident light Idso et al., 1978 , canopy temperature indices( ) (Diaz et al., 1983 , evapo-transpiration and potential evapo-transpiration Sakamoto,

)1978; Slabbers & Dunin, 1981; Singh & Ramakrishina, 1992; Raddatz et al., 1994 , and( )the delay in sowing Ramakrishna et al., 1985; Joshi, 1988 . All of these derived

variables depend directly or indirectly on the soil moisture available to the crop,making soil moisture the single most significant parameter affecting crop yield.However, measurement of soil moisture is a tedious task and, therefore, suchmeasurements are confined only to controlled environments created on experimentalplots; soil moisture data are not available for large areas on a regular basis as requiredin a regression analysis. An alternative practical choice on which to build a yield modelare rainfall data that are easily available in arid regions. Hence, the following data werecollected for the period 1963]1991 from the Central Arid Zone Research Institute,

( ) ( )Jodhpur, for the purpose of yield modeling: i grain yields of pearl millet, and ii dailyrainfall from July through September. From the data thus collected, explanatoryvariables were derived and yield models developed.

Derivation and selection of explanatory variables

Considering that limited data are available in arid regions, that simple variables arepreferrable to complex ones, and that fact that amount and distribution of rainfall are

( )the major causative factors of drought Sinha et al., 1992 , the following variables were( )derived from daily rainfall: delay in sowing, monthly rainfall July through September ,

( )and the number of rainy days in each month July through September .To determine the delay in sowing, the ideal date of sowing pearl millet was assumed

( )to be the date of commencement of monsoon in the area i.e. 1 July , and the actualdate of sowing was considered to be the day of the first rainfall of 18 mm or more. If,in July, there was no single day that had a rainfall of 18 mm or more, but the totalrainfall in two successive days equalled or exceeded 18 mm, the second day was

(considered as the date of sowing. Incidence of flash floods heavy rainfall in successive)days , however, is an exception to this assumption. In the case of the flash floods that

occurred in the area in 1979 and 1990, the 10th day following cessation of the rainfallwas considered the date of sowing. Based on the above considerations, seven explanatory

( )variables were derived from the daily rainfall Table 1 : R , R , and R refer to the1 2 3( )total rainfall mm in July, August, and September, respectively; N , N , and N1 2 3

represent the number of rainy days in July, August, and September, respectively; and( )D is the delay in sowing days .

Based on these variables, it is possible to provide early warnings at three different( ) (times during the growing season: i on 1 August using July data N , R , and D1 1

) ( ) (variables ; ii on 1 September using July and August data R , N , R , N , and D1 1 2 2

V. KUMAR202

Table 1. The data set

( )Monthly rainfall mm Number of rainy days Delay insowingYield July Aug Sept July Aug Sept

y1( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )Year kg ha R R R N N N D, days1 2 3 1 2 3

. . .1963 48 10 1 105 5 40 3 2 8 5 32

. . .1964 141 173 7 264 9 5 4 7 10 2 8

. . .1965 123 146 1 80 7 7 8 12 5 2 5.1966 150 77 154 8 30 9 6 2 5

. . .1967 232 140 9 110 0 105 9 10 9 5 7

. . .1968 12 169 8 8 8 0 0 11 2 0 11

. . .1969 34 6 4 42 6 45 2 4 5 5 17

. . .1970 528 59 4 364 6 91 4 4 18 7 9

. . .1971 233 79 5 103 5 32 7 7 9 3 20

. . .1972 23 27 0 299 4 4 2 5 13 1 48

. . .1973 296 109 9 365 3 70 4 13 17 8 16

. . .1974 15 119 3 16 5 36 1 6 2 2 14

. . .1975 335 147 8 98 8 241 2 14 15 11 12

. .1976 192 74 7 358 216 1 10 12 6 15

. .1977 261 136 6 77 9 18 15 8 6 18

. . .1978 170 162 7 109 9 25 2 17 11 2 15

. . .1979 58 470 6 200 2 5 4 6 9 1 29

. . .1980 64 149 6 4 8 37 4 8 1 4 12

. . .1981 11 53 1 68 5 124 5 6 11 4 22. .1982 68 101 82 1 0 9 5 7 1 21

. . .1983 337 277 1 87 9 10 8 12 11 3 5

. . .1984 179 45 2 85 8 90 1 4 10 4 5

. . .1985 23 62 9 74 2 5 2 7 7 1 16

. . .1986 48 141 4 41 8 0 0 7 4 0 25

. . .1987 20 17 6 14 2 0 0 1 4 0 14

. . .1988 141 96 1 84 7 47 1 14 8 5 18. .1989 211 52 144 3 13 2 6 10 3 16

.1990 387 516 180 77 7 5 16 9 17. . .1991 145 74 7 92 2 11 0 8 9 2 22

) ( )variables ; and iii on 1 October using all seven variables. These warnings were termedthe initial, intermediate, and final warnings, respectively. Such a time-dependentclassification is significant as the earlier the availability of the drought warning, themore effective the decisions regarding import of food grains.

For each of the warnings defined above, more than one model can be developed byemploying one or more of the variables available for that warning. However, only onemodel is finally selected for each warning, based on various considerations as discussedbelow.

Model selection

By choosing a different set of explanatory variables, a definite number of models can bedeveloped. For example, if there are N explanatory variables, models can be developed

( )by including n n s 1, 2, . . . , N variables into the model. Furthermore, for a fixed n,

AN EARLY WARNING SYSTEM FOR AGRICULTURAL DROUGHT 203

Figure 1. Variation of R2 with number of explanatory variables.

different combinations of variables are possible. The number of combinations can bedetermined by the following formulae:

n .Number of combinations s C s N !r n! N y n ! , Eqn 1( ) ( ) ( )N

where n!s n n y 1 n y 2 . . . 1.( ) ( )

Following the above formulae, the number of combinations of choosing 1, 2, 3, 4, 5, 6,and 7 variables out of the total 7 variables are 7, 21, 35, 35, 21, 7, and 1, respectively.Accordingly, a total of 127 regression modes were developed, one for each combination.Which model to select, however, depends on the purpose of the model. If the purpose

( 2 )is only for prediction, as in the present case, the coefficient of determination R plays( ) 2a dominant role Gujarati, 1995, p. 344 . The R is a measure of variation in the

dependent variable that can be explained by the explanatory variables present in the2 2 (model. The greater the value of R , the better the prediction. Variation of R in 127

)models with the number of explanatory variables is shown graphically in Fig. 1. Inorder to understand how the value of R2 changes when an explanatory variable isincluded or excluded from the model, a correlation matrix showing the coefficient of

( )correlation r between any two variables is helpful Table 2 .

Table 2. Correlation matrix showing coefficient of correlation r between two variables

Variable R R R N N N D1 2 3 1 2 3

.R 1 001 . .R 0 01 1 002 . . .R y0 18 0 30 1 003 . . . .N 0 37 0 05 0 20 1 001 . . . . .N y0 02 0 78 0 51 0 20 1 002 . . . . . .N y0 16 0 35 0 78 0 31 0 61 1 003 . . . . . . .D y0 08 0 16 y0 18 y0 32 0 09 y0 19 1 00

V. KUMAR204

.( )It can be noted from Table 2 that the correlations between R and N r s 0 78 ,2 2. .( ) ( )R and N r s 0 78 , and N and N r s 0 61 are quite pronounced. If the highly3 3 2 3correlated variables are used to develop a regression model, it becomes difficult toachieve greater precision in estimating regression coefficients.

Besides the R2, the statistical significance of explanatory variables is also consideredin the process of model selection. The t-ratio statistic is commonly used to measure thestatistical significance of an explanatory variable. A greater t-ratio is associated withmore significant variables. A stepwise regression approach uses criteria of R2 andt-ratio in systematically including or excluding variables from the model to ensure thata high value of R2 and least correlated variables are retained in the model.

Before applying a stepwise regression approach in selecting a model, it is prudent toexamine the highest values of R2 obtained for the initial, intermediate, and finalwarnings. From the values of R2 obtained for the 127 models developed earlier, it wasdiscovered that the highest values of R2 for the initial, intermediate, and final warnings

. .( ) ( )were 0 25 using R , N , and D variables , 0 75 using R , N , N , and D variables ,1 1 1 1 2. 2( )and 0 82 using all seven variables , respectively. Since the R is very low in the initialwarning case, it is not worth developing a model for the initial warning. However, in

2 . .( )the case for the other two warnings, R is reasonably high 0 75 and 0 82 . Hence, it is( )appropriate that two yield models, the intermediate warning IW model and the final

( )warning FW model, are developed to provide the early warnings, at the beginning ofSeptember and October, respectively.

Model development is a two-stage process. To execute this process, the complete( ) ( )data set 1963]1991 is split into two groups. The first group of 25 years 1963]1987 is

( )used in model development while the second group of the remaining 4 years 1988]1991is employed in model testing. To begin model development, using the first group of

[ ( )data, a stepwise multiple regression resulted in the following models Eqn 2 for the( ) ]IW model and Eqn 3 for the FW model . In the equations, Y represents the yield of

( y1 ) (pearl millet kg ha , and adj. means adjusted. The DW abbreviation for)Durban]Watson statistic and the autocorrelation are utilized in the process of model

validation as explained later in the paper.

. . .Y s 56 3555 q 22 5322 N y 6 558 D Eqn 2( )2

. .t-ratio 6 94 y4 49( ) ( )2 . 2 .R s 0 7415, adj. R s 0 718, N s 25,

. .DW statistic s 2 3113, autocorrelation s y0 1632.. . . . .Y s 37 1143 y 0 7172 R q 19 3611 N q 22 1120 N y 6 1280 D Eqn 3( )3 2 3

. . . .t-ratio y2 22 5 06 2 64 y4 43( ) ( ) ( ) ( )2 . 2 .R s 0 811, adj. R s 0 773, N s 25,

. .DW statistic s 1 996, autocorrelation s y0 0057.

A model has to be validated before it can be recommended for use. Model validationincludes testing the validity of the inherent assumptions: zero mean, constant variance,normal distribution, and independence of residuals produced by the model. Theresidual is the difference of the reported yield and the yield estimated by the model. Toinvestigate whether or not these assumptions have been satisfactorily met, a residualanalysis is conducted. The residuals were found to have a mean of approximately zero

. .( )0 0003 for the IW model and y0 0006 for the FW model . To study variance in theresiduals, the residuals were plotted vs. time. These plots did not indicate the presenceof any trend. Variance was further tested by White’s general heteroscedasticity test

AN EARLY WARNING SYSTEM FOR AGRICULTURAL DROUGHT 205

( ) (Gujarati, 1995, p. 379 . According to this test, the squared residuals dependent)variable are regressed on the original explanatory variables, their squared values, and

the cross products of the regressors. Under the hypothesis that there is no( )heteroscedasticity, i.e. the variance in the residuals is constant, sample size N

multiplied by the R2 follows the Chi-square distribution with degrees of freedom equalto the number of regressors. That is,

N ? R2 ; x 2 . Eqn 4( )

( )In the present case, the sample size was 25 1963]1987 and the original explanatory( ) (variables were N and D in the IW model , and R , N , N , and D in the FW2 3 2 3

)model . Therefore, the explanatory variables, on which the squared residuals were2 2 (regressed as per the White’s test, became N , D, N , D , and N ? D i.e. five2 2 2 2

) 2 2 2 2variables in the case for the IW model , and R , N , N , D, R , N , N , D , R ? N ,3 2 3 3 2 3 3 2(R ? N , R ? D, N ? N , N ? D, and N ? D i.e. 14 variables in the case for the FW3 3 3 2 3 2 3

2 . 2 . . 2 .) ( ) ( )model . The resulting R were 0 1595 or N ? R s 0 40 and 0 7445 or N ? R s 18 61in the cases of the IW and the FW models, respectively. The 5% critical Chi-square

. . ( )values are 11 07 and 23 68 for 5 degrees of freedom in the case of the IW model and( ) 2for 14 degrees of freedom in the case of the FW model , respectively. Since the N ? R

is less than the critical Chi-square values in both cases, it can be concluded that there isno heteroscedasticity in either model. In turn, the residuals have constant variance.

The residuals were further tested for normal distribution using the Anderson]Darling( )test. The straight line fit Fig. 2 for the IW model and Fig. 3 for the FW model

implies that, in both models, the assumption of normal distribution for the residuals iscorrect. Presence of any serial correlation in residuals was examined by the

.[autocorrelation at lag-1, which was found to be very low y0 1632 for the IW model,( ) ( )]Eqn 2 , and y0.0057 for the FW model, Eqn 3 . The DW statistic being about 2,

and low autocorrelation, confirm the independence of the residuals.Hence, the underlying assumptions of the regression analysis were satisfactorily met

[ ( ) ( )]and therefore the models Eqn 2 and Eqn 3 were treated as validated and can beused for making drought early warnings. Subsequently, the models were developed

( )using the 1963]1987 data and tested on the remaining data 1988]1991 to avoid anybias in evaluating the performance of the models. Table 3 and Fig. 4 present the

Figure 2. Testing the normality of the residuals for the IW model.

V. KUMAR206

Figure 3. Testing the normality of the residuals for the FW model.

comparison between the reported yields and the estimated yields. Mean absolute per[ ( )]cent error MAPE, Eqn 5 is used to gauge performance of the models:

n < <Ý Yest , i y Yi rYi = 100is1MAPE s Eqn 5( )

N

where Yest, i is estimated yield in year i, Yi is reported yield in year i, and N is thenumber of observations.

Model evaluation and improvement

Evaluation of the predictive capabilities of the IW and FW models is conducted bycomparing the yields estimated by these models with the reported yields. It can be seen

. .from Table 3 that the mean absolute per cent error was 18 5% and 11 2%, respectively,for the intermediate and the final warning model. On the basis that the MAPE is lowerin the case for the FW model, it can be inferred that the predictive capability of theFW model is better than that of the IW model. Nevertheless, it is worth noting that the

Table 3. Measuring performance of the yield models

Difference betweenEstimated yield reported andReported y1( ) ( )kg ha estimated yields %yield

y1( )Year kg ha IW model FW model IW model FW model

. . . .1988 141 118 8 158 5 y15 9 12 4

. . . .1989 211 176 8 189 6 y16 2 y10 2

. . . .1990 387 305 4 386 0 y21 1 0 0

. . . .1991 145 114 9 112 9 y20 8 22 1. .MAPE 18 5% 11 2%

AN EARLY WARNING SYSTEM FOR AGRICULTURAL DROUGHT 207

( )4-year period 1988]1991 available for model testing does not show much variation in(yield; in particular, severe droughts i.e. when yields are extremely low, say, lower than

y1 )100 kg ha did not occur during these 4 years. Therefore, the models could not betested for the case of severe drought. In contrast it would be worth studying, thoughwith a bias, how the models performed over the 1987]1963 period which included nine

( )cases of severe drought Table 1 . Barring 1981 and 1986, the estimated yields are in( )fair agreement with the reported yields Fig. 4 . A general inference can, therefore, be

drawn that the models have performed well in predicting the yields.With a view to suggesting improvement in the models, it is essential to highlight

factors that may have contributed to lowering the performance of the models in certainyears. Spatial variability in rainfall is an important factor responsible for deviations inthe estimated yields. It should be emphasized that, in both models, the spatial

( )variability in the dependent variable i.e. yield is well accounted for because the yielddata are averages for the entire district. However, the spatial variability in theexplanatory variables is not well accounted for because these variables are derived fromthe rainfall data pertaining to only a single site located at Jodhpur.

Spatial variability in rainfall in July causes spatial variability in sowing dates that arerequired to determine a variable ‘delay in sowing’ in the yield model. This variable is

( )established as statistically significant absolute t-ratio well above 2 . The variable hasbeen determined based on an assumption about minimum rainfall required for sowingpearl millet. However, in addition to rainfall, other factors such as availability of seedand accessibility to farming equipment to complete the pre-sowing farming operationsinfluence sowing date. These factors are difficult to determine or model. Furthermore,in presence of flash floods, determination of sowing date becomes even more difficult.

Although the inclusion of reliable rainfall data collected from additional sites is likelyto improve the model performance, reliable data for a sufficient period was notavailable for additional sites, as is usually the case in arid regions.

In addition to spatial variability in rainfall and its associated factors described above,flash floods that occurred in 1979 and 1990 have caused distortions in the models

( )because of their opposing relationships with yield Table 1 . While the yield in 1979

( ) ( )Figure 4. Comparing reported yields l with those estimated using the IW model B and the( )FW model ^ .

V. KUMAR208

( y1 ) ( y1 )was very low 58 kg ha , the yield in 1990 was well above average 387 kg ha .This significant difference in yield may be attributed to the difference in the areaaffected by the flood, possibly because of spatial variability in rainfall. The size of theflood-affected area in 1979 could have been much greater compared to 1990.

Considering that flash floods are a rare phenomena, exclusion of observationspertaining to the floods from the data set used in the regression could result in an

(improvement of the models. Also, it can be seen from Fig. 4 that, in 1986 a severe)drought year , the estimated yields are negative. To make the model more realistic, a

(suitable modification restricting the estimated yield to a minimum threshold zero or)positive is required.

Besides reasons drawn from the rainfall availability and spatial variability, drop inyield may also be gauged by widespread crop disease. In 1974, persistent cloudyweather and high humidity, particularly during the grain formation stage of the crop,caused widespread disease, and thus contributed significantly to yield reduction. Forfurther improvement in the model, it may also be appropriate to exclude from theregression data years when yield was known to have been significantly influenced bycrop disease.

Summary

Two multiple linear regression models are developed in this paper to estimate pearl( )millet yield capable of providing early warnings intermediate and final of agricultural

drought in Jodhpur district, at two different times during the growing season. Macro-level decisions regarding import of food grains can be initiated based on intermediatewarning. Decisions can then be refined based on the final warning. Such a warningsystem will aid drought planners in Jodhpur district in making more accurate andtimely decisions as to whether or not and how much food grains to import from withinthe country or outside to tackle the drought situation effectively.

The author thanks anonymous reviewers for their constructive comments.

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