Optimized fourier approximation models for estimating monthly streamflow in the vanderkloof dam, South Africa

Abstract

Parametric probability distribution models and nonparametric approximation models were developed for estimating monthly streamflow in the Vanderkloof dam. The probability distribution functions include Normal, Lognormal, PearsonIII, Log-Pearson III, Gumbel and Log-Gumbel probability density functions while the nonparametric approach involves the development of monthly streamflow models using numerical harmonic Fourier series approximation procedure. The parameters of the Fourier series were optimized using differential evolution (DE) algorithm. For a comparison of nonparametric and parametric models, the Mean Relative Deviation (MRD) and Mean Square Relative Deviation (MSRD) statistics were used to measure the goodness-of-fit of the developed models while the Wilcoxon sign rank test was adopted to determine if there is a statistical significant difference in the performance of the models. Results show that the nonparametric Fourier approximation model estimates streamflow into the Vanderkloof reservoir better than the parametric methods. It is concluded that the Fourier series approximation may be adopted as an alternative approach for streamflow frequency analysis.