Flood frequency analysis using Mathematica

Authors: MOHAMMAD ALI GHORBANI, HEIKKI RUSKEEPAA, VIJAY.P. SINGH, BELLIE SIVAKUMAR

Abstract: This study analyzes flood frequencies using discharge data from 6 gaging stations in the Aji River basin in Iran. Eighteen different distributions are fitted to the maximum annual discharges from each of these stations, and parameters of these distributions are estimated using the method of maximum likelihood and the method of moments. Calculations are performed with Mathematica}, a computer algebra system developed by Wolfram Research. The advantage of using this software is that the symbolic, numerical, and graphical computations can be combined and all quantities can be accurately calculated; in particular, there is no need to resort to any approximate methods for the calculation of quantiles. There is a ready-to-use command for calculating quantiles from distributions that are built in Mathematica}, while for other distributions they can be easily and accurately calculated by inverting the cumulative distribution functions or by solving nonlinear equations where the inversion is not possible. The best distribution is selected based on the root mean square error (RMSE), the coefficient of determination (R^2), and the probability plot correlation coefficient (PPCC). Relations between the distributions' parameters and the area, average discharge, and time of concentration are explored. The complete Mathematica} code and sample data files are included in http://users.utu.fi/ruskeepa/.

Keywords: Flood frequency analysis, Probability distribution, Annual discharge, Aji River basin, Mathematica

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