Long-Term Stochastic Modeling of Monthly Streamflow in River Nile

Abstract

Synthetic time series created from historical streamflow data are thought of as substitute events with a similar likelihood of recurrence to the real event. This technique has the potential to greatly reduce the uncertainty surrounding measured streamflow. The goal of this study is to create a synthetic streamflow model using a combination of Markov chain and Fourier transform techniques based on long-term historical data for the Nile River. First, the Markov chain’s auto-regression is applied, in which the data’s trend and seasonality are discovered and eliminated before applying the Pearson III distribution function. The Pearson III distribution function is substituted by a discrete Fourier transform (DFT) technique in the second approach. The applicability of the two techniques to simulate the streamflow between 1900 and 1999 is evaluated. The ability of the generated series to maintain the four most important statistical properties of the samples of monthly flows, i.e., the mean, standard deviation, autocorrelation lag coefficient, and cumulative distribution, was used to assess the quality of the series. The results reveal that the two techniques, with small differences in accuracy, reflect the monthly variation in streamflow well in terms of the three mentioned parameters. According to the coefficient of determination (R2) and normalized root mean square error (NRMSE) statistics, the discrete Fourier transform (DFT) approach is somewhat superior for simulating the monthly predicted discharge.