Frequency analysis of water deficit for crop planning in Gujarat

The frequency analysis of extreme weekly water deficit in different Agro-climatic Zones of Gujarat using the three most common distributions have been computed. ÷ 2 test for goodness of fit of the observed data to the theoretical distribution was also performed. The distribution that gave the lowest chi-square value has been selected as the best for that location and the predicted maximum weekly water deficit values have been reported.

Extreme values of any hydrological variables are important from designing and planning point of view, as it is the extreme, which plays a deciding role in success or failure of any design. During the past years many investigators (Gupta, 1992;Kaledhonkar et al., 1996;Sharma, 1997;Kumar et al., 2000;Suresh, 2003) have analysed the rainfall, flood, drought and other climatic parameters for probabilistic estimates. However, no study was made on water deficit for this region. With this in view, using three well-known extreme probability distribution functions, the extreme weekly water deficit data for Gujarat were analyzed.

MATERIALS AND METHODS
Frequency distribution analysis of largest water deficit, obtained through water balance, during monsoon season was carried out for the selected fifteen stations from eight agro-climatic zones of Gujarat. The study was based on largest weekly water deficit data to understand the distribution pattern of extreme value at the selected stations representing the region and thereby making possible selection of the required water deficit rate for various return periods that may be used in the planning and design of water resource development projects for drought prone areas.
The analysis was preceded by test criterion for adequacy of length of record. The adequacy of length of record was determined following Mockus (1960): Y= (4.30 t log 10 R) 2 + 6.0 …(1) where, Y = minimum acceptable years of record t = student's statistical value at the 95% level of significance with (Y-6) degrees of freedom R = ratio of magnitude of the 100 years event to the 2 years event

Methods of frequency analysis
Frequencies of extreme weekly water deficit have been evaluated by fitting the data to the extreme value frequency distribution functions. Three most commonly used extreme probability functions viz. (i) Gumbel for maxima, (ii) Weibull for maxima, and (iii) log Pearson Type-III were selected and the distribution that best fitted the data have been used for determining the extreme values at different return periods (probabilities).

Test for goodness of fit of probability distributions
Chi-square test was selected among the most commonly useful procedures for testing goodness of fit test. The test statistic (χ 2 ) has been estimated from the expression: where, * Present address : Deptt. of Rural Engg. SD Agril. University, S.K.Nagar-385 506 [Vol. 10,No. 2  The water deficit data occurrences at 1, 2, 5, 10, 20, 50 per cent levels were worked out. The data were analysed by a computer-based routine VTFIT package for fitting probability distribution function that also provides goodness of fit tests.

Test of adequacy of record
The results of adequacy of length of record (Table  1) indicate that water deficit data considered for extreme value analysis is adequate, as required length of record for each station is within the range of data considered for the respective station.

Frequency distribution of water deficit
All the selected probability distributions fit the extreme weekly water deficit data well, since their Chisquare values are within the critical limits at 0.05 level of significance. To arrive at best probability model for determining seasonal maximum weekly water deficit in different agro-climatic zones, the distributions with lowest Chi-square value were sorted out (highlighted in Table 2). Results of best-fit frequency distribution revealed that at Radhanpur, Amreli, Khedbrahma, Arnej, Anand, Bharuch and Navsari only Log Pearson Type-III distribution; at Dhandhuka, Junagadh, Mahuva, Nawagam and Surat only Weibull (maxima) distribution and at Kothara only Gumbel distribution fitted closest to the observed data. Log Pearson type-III and Gumbel distribution gave closest fit to the observed data at SK Nagar. All the three distributions fitted closest to the observed data at Rajkot. The comparison of Chi-square test of best fit distributions clearly indicates that Log Pearson Type-III distribution is the best probability model for predicting weekly maximum water deficit at Radhanpur, Rajkot, Amreli, SK Nagar, Khedbrahma, Arnej, Anand, Bharuch and Navsari. Weibull (maxima) fitted best at Dhandhuka, Junagadh, Mahuva, Nawagam and Surat while Gumbel at Kothara.
Frequency distributions of weekly maximum water deficit at different return periods obtained by using the best probability model selected above are shown in Fig. 1. Weekly maximum water deficit obtained from the long term historical data can be used for designing of protective/life saving irrigation systems and water resource structures in drought prone areas of Gujarat