Modeling of rainfall and its probability distribution

Résumé

Abstract The monthly rainfall data of 80 years were collected from the Nigeria Meteorological Agency Abuja, Nigeria. The data were from seven major synoptic stations in the Northern Nigeria. We measure the trends of intensity in rainfall and obtain the best fit trend on yearly rainfall. The data showed that the average annual rainfalls at different stations are significantly different and degree of peak also varies in each station from the Kernel density test. We observed, there were high intensity of rainfall which exhibits a cyclical trend with frequent periodicities in amount of rainfall owning to high humidity and low temperature in Jos station. The trend increases exhibit exponential distributions at every point of change with high degree of skewness with a similar peak every year; the result of the trend analysis shows clear fluctuations in the pattern of rainfall for the period under study. Three statistical goodness of fit test were carried out in order to select the best fit probability distribution on the basis of highest rank with minimum value of test statistic. It was observed that Generalized Extreme value distribution and Log Pearson are the best fitted from the Anderson Darling test as its produces minimum value than other probability distributions. The chi-square test on associations between the 17 probability distributions, show that five probability distributions; Gamma, Pearson(6), Gamma(2), Weibull(3) and lognormal(3p) are significant at p-value(< 0.001), they are best fitted on yearly rainfall. Kolmogorov Smirnov test was used to rank the 17 probability distributions to obtain the best fit on rainfall, we observed that Normal, Gamma (2p), Gamma(3p), Log Normal and Log Pearson(3p) are the best fitted distributions, they are strong with a robust parameters to measure rainfall.

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