Statistical Modeling for Flood Frequency in Upper Chaophraya River Basin

Abstract

The research deals with the probabilistic estimates of annual maximum flood peaks in the upper Chaophraya basin (Thailand) used the extreme value theory, the Block Maxima. The Generalized Extreme Value (GEV) distribution model, the Frèchet distribution (EV2), the extension of the Frèchet distribution such as the Kumaraswamy Frèchet distribution and the new distribution as called the Exponentiated Kumaraswamy Frèchet distribution satisfied the Goodness of fit test (Kolmokorov-smirnov test). The return levels are estimated for 3, 5, 10, 30, 50, 100, 500 and 1000 years which are consistently increasing for designs of flood protection in future. The return period of flood for each stations are estimated.

The investigation of the new distribution and appropriated estimation technique for the flood frequency in upper Chaophraya river basin as we called the Exponentiated Kumaraswamy Frèchet distribution and the differential evolution maximum likelihood estimation were done. We derived the properties of the Frèchet family; such as the Frèchet distribution (EV2), the Kumaraswamy Frèchet distribution (KF) and the Exponentiated Kumaraswamy Frèchet distribution (EKF). We also compared Bias, Variance, Mean Square Error and Mean Absolute Percentage Error for all parameters in each distribution by generating the Frèchet family random number. For the effectiveness of analytical solutions of the parameters we provided the numerical solutions (differential evolution method) to obtain estimates for all parameters by using Scilab program.

Accuracy of flood assessment of extreme event is of fundamental importance for many safety, engineering and financial application. In part of application we provided the probabilistic estimates of annual maximum flood peaks or momentary peak data in the upper Chaophraya river basin (Thailand). The Generalized Extreme Value (GEV) distribution model were used to be gain to compare with as the Frèchet distribution (EV2), the Kumaraswamy Frèchet distribution (KF) and the Exponentiated Kumaraswamy Frèchet distribution (EKF). The Goodness of fit test, the return level and return period were done. The return periods of flood were classified by hazard class using GEV found that in upper Chaophraya river basin flood occurred highly. The result from the Frèchet family also occurred highly, but the return period and return level from the Kumaraswamy Frèchet distribution (KF) quite closed to GEV more than another distribution.