Rainfall Frequency Analysis
PROBABILITY DISTRIBUTION FUNCTIONS IN RAINFALL ANALYSIS Sugandh Pratap Singh (2016CEW2427)
INTRODUCTION
Water is the source of all life on Earth. The total amount of water present on the earth is fixed and does not change. Rainfall intensities of various frequencies and durations are the basic input in hydrologic design. Precipitation frequency analysis is used to estimate rainfall depth at a point for a specified exceedence probability and duration. Rainfall frequency analysis is usually based on annual maximum series at a site (at-site analysis) or from several sites (regional analysis).
The maximum value may not always yield the true maximum amount for a specified duration. For
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chi-square test, Nash and Sutcliffe (1970) efficiency (NSE) and relative error (RE). It was seen in the review of literature that most of the researchers have used chi-square test. Therefore, results (shown in Table 4.5) of the other two tests viz. NSE and RE were not considered and chi square test results were considered for further discussion in the following sections.
Chi-square test was performed on the weekly, monthly and annual rainfall data. It was identified that Gumbel’s distribution was best fit for the weekly and monthly rainfall but the same for the annual rainfall was log-Pearson type III. The results of the chi square test are shown in Table 4.5.
In the present study the NSE and RE methods also used for GOF test for the periods of weekly, monthly and annual rainfall. Here, according to RE method, it was found that Gumbel PDF was most suitable for weekly rainfall but NSE showed that gamma (2P) was best fit for the monthly rainfall. In monthly rainfall, RE showed that Gumbel was the best fit but NSE proposed that log-Pearson type III was most suitable for monthly rainfall. The RE and NSE showed that log-Pearson type III was most suitable for annual rainfall
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• For annual rainfall predictions, the log Pearson type III was found to be the best fit PDF as suggested by the results of the three of the goodness of fit tests viz. chi square test, NSE and RE.
• The average weekly rainfall data showed that 26th week has experienced the highest rainfall of about 229 mm and the minimum rainfall of 3.3 mm was received during the 33rd week.
• The weekly values indicated that out of 52 weeks, 42 weeks have received rainfall of more than 21 mm (considering the crop water demand of 3 mm per day) whereas the remaining 10 weeks have received less than 21 mm of rainfall.
• Weekly rainfall pattern over the 5-year interval showed that the onset of the monsoon was usually in the 2nd standard week (June 8) and withdrawal was in the 30th week (December 27).
• The monthly rainfall data analyses indicated that the month of July has received the maximum rainfall of 547.4 mm followed by the month of June which has received the second highest rainfall of 543.4 mm.
• The month of December has received the lowest rainfall of 18
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