Enhancing 2D Hydrodynamic‐Based Flash Flood Simulations in Mountain Catchments: Analytical Insights From a Novel Steep‐Slope Shallow Water Framework

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Abstract
Flash floods frequently occur in steep mountainous catchments, where topographic gradients play a crucial role in concentrating and accelerating runoff processes. Two‐dimensional (2D) shallow water equations (SWE) are widely used to simulate such events; however, these equations are classically derived assuming small bottom slopes, typically less than 10%. This assumption, seldom questioned, may introduce inaccuracies when SWE models are applied to mountain watersheds, where slopes commonly exceed the theoretical range of validity. This study addresses this inconsistency by revisiting the theoretical foundations of SWE‐based modeling and extending the recently proposed 2D Steep‐Slope Shallow Water Equations (SSSWE) to overland flow. The formulation explicitly accounts for steep‐slope geometric effects, offering a more physically consistent description of flow dynamics in mountainous terrain. A kinematic‐wave‐based reference framework in one‐ and two‐dimensional domains is presented to quantify errors arising from the use of conventional SWE under the small‐angle approximation on steep slopes. Results from idealized test cases (including a V‐shaped catchment) show that the standard SWE predicts lower equilibrium water depths and response times and higher flow velocities than the improved steep‐slope model. These discrepancies become substantial for slopes steeper than 20°. To incorporate steep‐slope effects without modifying existing SWE‐based numerical solvers, an analytically derived, slope‐dependent adjustment to the Manning roughness coefficient is proposed; in 2D, the correction is anisotropic. Overall, this study provides the first systematic analytical assessment of inaccuracies in SWE‐based flash‐flood modeling for steep watersheds, addressing a long‐standing theoretical gap and improving the physical realism of hydrodynamic models in mountainous environments.

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