Stochastic Rational Method for Estimation of Flood Peak Uncertainty in Arid Basins: Comparison between Monte Carlo and First Order Second Moment Methods with a Case Study in Southwest Saudi Arabia

Nassir S. Al-Amri, Hatem A. Ewea and Amro M. Elfeki ()
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Nassir S. Al-Amri: Department of Hydrology and Water Resources Management, Faculty of Meteorology, Environment & Arid Land Agriculture, King Abdulaziz University, P.O. Box 80208, Jeddah 21589, Saudi Arabia
Hatem A. Ewea: Department of Hydrology and Water Resources Management, Faculty of Meteorology, Environment & Arid Land Agriculture, King Abdulaziz University, P.O. Box 80208, Jeddah 21589, Saudi Arabia
Amro M. Elfeki: Department of Hydrology and Water Resources Management, Faculty of Meteorology, Environment & Arid Land Agriculture, King Abdulaziz University, P.O. Box 80208, Jeddah 21589, Saudi Arabia

Sustainability, 2023, vol. 15, issue 6, 1-18

Abstract: The flood peak is commonly estimated using the rational method for the design of hydraulic structures. The method is mainly used in a deterministic context. However, there is often uncertainty in flood predictions, which should be incorporated in the design of mitigation schemes. This research proposes a methodology to cope with uncertainty in the rational method via the application of a stochastic framework. Data from 158 storms, recorded in the period 1984–1987 in 19 subbasins in the southwestern part of Saudi Arabia, were used to implement the proposed methodology. A tri-variate log-normal probability density function was used to model the joint relationship between the rational method parameters. The model considered the parameters as random variables. The uncertainty in the rainstorms was represented by intensity or depth; the uncertainty in basin delineation (due to the use of different digital elevation model resolution) was represented by the basin area; and the uncertainty in the land use/land cover was represented by the runoff coefficient. The Monte Carlo method was used to generate realizations of the peak flow and runoff volume with 95% and 99% confidence levels from the input parameters. Although the correlation between the parameters was weak, the model was capable of simulating the rational model parameters and estimating the peak flow and runoff volume relatively well, and the generated realizations fell within the confidence levels, except for a few marginal cases. The model can be used to generate peak flows and the associated confidence limits in ungauged basins from the statistics of the input parameters using the equations developed in this study.

Keywords: rational method; Monte Carlo method; uncertainty quantification; tri-variate distribution; first-order-second-moment method (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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