Monte Carlo approach for modelling uncertainty in hydraulic flood routing in ephemeral streams in arid regions

Abstract

Flood routing in ephemeral streams of arid regions is characterized by high uncertainty due to limited data, variable transmission losses, and the transient nature of flow events. To address these challenges, this study introduces a newly developed convection–decay-based flood routing model that captures both the translation of the flood wave and the attenuation of peak discharge and volume caused by channel transmission losses. The model simulates hydrograph evolution in response to uncertain hydraulic conditions typical of arid environments. The model is applied to the Yiba Basin in western Saudi Arabia, a highly arid and data-scarce watershed where steep upstream slopes, permeable alluvial channels, and substantial infiltration losses strongly influence flood-wave propagation. The analysis uses observed inflow and outflow hydrographs from four hydrometric stations and 22 historical storm events. Uncertainty in flood-wave travel time and peak decay is incorporated using a Monte Carlo simulation framework. One thousand realizations are generated by randomly sampling the lag time between stations (K) and the decay factor (λ) from their fitted probability distributions to produce an ensemble of plausible outflow hydrographs while reflecting the natural variability in ephemeral channels. The resulting ensemble of simulated outflow hydrographs falls within a 90% confidence interval in most of the events. Flood peaks and volumes lie extremely close to the 1-to-1 line, indicating a highly successful and robust model for future predictions (r = 0.72 and RMSE = 30.9 m³/s for peak flows, and r = 0.73 and RMSE = 11.9 MCM for runoff volume). The probabilistic framework enables a more realistic and risk-informed understanding of flood behavior, supporting sustainable flood management in data-scarce arid regions. This approach offers a practical and adaptable tool for resilient infrastructure design and disaster preparedness under uncertain hydrologic conditions.