Long-Term Stochastic Modeling of Monthly Streamflow in River Nile

Shokry Abdelaziz, Ahmed Mohamed Mahmoud Ahmed (), Abdelhamid Mohamed Eltahan and Ahmed Medhat Ismail Abd Elhamid
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Shokry Abdelaziz: Department of Civil Engineering, Faculty of Engineering—Rabigh Branch, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Ahmed Mohamed Mahmoud Ahmed: Construction and Building Engineering Department, Faculty of Engineering and Technology, Arab Academy for Science Technology and Maritime Transport, Cairo 11757, Egypt
Abdelhamid Mohamed Eltahan: Construction and Building Engineering Department, Faculty of Engineering and Technology, Arab Academy for Science Technology and Maritime Transport, Cairo 11757, Egypt
Ahmed Medhat Ismail Abd Elhamid: National Water Research Center (NWRC), Hydraulics Research Institute (HRI), El-Qanater El-Khiriaya 13621, Egypt

Sustainability, 2023, vol. 15, issue 3, 1-15

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.

Keywords: time series; streamflow; Markov chain; Fourier transform; Pearson III distribution; Nile River (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2023
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