Gumbel Weibull distribution function for Sahel precipitation modeling and predicting: Case of Mali

Climate change, trend of precipitation variation is greatly affected by Sahel countries economy in general and Mali in particular, which increased the social instability in recent years. In this paper, we proposed Gumbel Weibull distribution function for modeling and predicting the precipitation of Mali. The methodology is composed of two steps: parameters computations and estimations. We computed the parameters using four computations methods such as: method of moments (MOM), maximum likelihood method (MLM), method of least squares (MLS) and probability weighted moments (PWM). To estimate the best method, firstly we used several good fit tests like: Kolmogorov-Smirnov (Ks), Chi-square, Anderson-Darling and D-index to analyze each method parameters, then the ratio of the standard error to return period for final estimation. For simulation, daily data of the period, 1949 to 2006 provided by Mali Meteorology Department of four localities (Kayes, Koutiala, Mopti and Hombori) was used. Results of simulations were suitable for Anderson-Darling good fit technique and PWM for Koutial, Mopti and Hombori precipitation; and MLS for Kayes precipitation. The plotting of the return period of the precipitations for PWM and MLS in the 1000 years has also confirmed this result.     Key words: Rainfall modeling and predicting, Gumbel and Weibull distribution function, method of moments (MOM), maximum likelihood method (MLM), method of least squares (MLS) and probability weighted moments (PWM) parameters optimization, statistical analysis, good fit test estimation.