A precipiton method to calculate river hydrodynamics, with applications to flood prediction, landscape evolution models, and braiding instabilities. Issue 8 (2nd August 2017) - Davy, Philippe; Croissant, Thomas; Lague, Dimitri
Abstract: The "precipiton" method is a particle‐based approach that consists of routing elementary water volumes on top of topography with erosive and depositional actions. Here we present an original way to calculate both river depth and velocity from a method that remains embedded in the precipiton framework. The method solves the governing equations for water depth, where the water depth is increased by a constant quantity at each precipiton passage and decreased by a value based on a flow resistance equation. The precipitons are then routed downstream on top of the resulting water surface. The method is applicable even if the precipitons are routed one by one (i.e., independent of each other), which makes it simple to implement and computationally fast. Compared to grid‐based methods, this particle method is not subject to the classic drying‐wetting issue, and allows for a straightforward implementation of sediment transfer functions between the river bed and running water. We have applied the method to different cases (channel flow, flow over topographic barriers, and flood prediction on high‐resolution lidar topography). In all cases, the method is capable of solving the shallow water equations, neglecting inertia. When coupled with erosion and sediment transport equations, the model is able to reproduce both straight and braided patterns with geometries independent of grid size. Application of the model in the context of multithread rivers gives new insight into the development of braiding instability. Key Points: A particle‐based, numerical approach is presented for rapidly solving the shallow water equations The method can solve both hydrodynamics and erosion and sediment transport equations The method is successful in creating a large variety of channel forms from straight to braided channels Plain Language Summary: The "precipiton" method is a numerical method that consists in routing elementary water volumes on top of topography with erosive and deposition actions. Here we present an original way to calculate both river depth and velocity. The method consists in solving water depth from a differential equation, where the water depth is increased by a constant quantity at each precipiton passage and decreased by a value based on a flow resistance equation. The precipitons are then routed downstream on top of the resulting water surface. The method is applicable even if the precipitons are routed one by one, i.e., independently of each other, which makes it simple to implement and quite fast. Compared to grid‐based methods, this particle method is versatile, fast, and allows for a straightforward implementation of sediment transfer functions between river bed and running water. We have applied the method to different cases (channel flow, flow over topographic bumps, or real cases with high‐resolution lidar topography). In all cases, the method does very well in predicting the distribution of flood on landscapes. When coupled with erosion and sediment transport equations, the model is able to reproduce both straight and braided river patterns.