FastFlood: a fast and simple 2D hydrodynamic or hydrostatic numerical solution to river flow in landscape evolution models

Modelling river hydrodynamics in an efficient approach remains a technical challenge which limits our ability to assess river flood hazard or to use process-based erosion laws at a high-resolution in landscape evolution models. Here we present a fast iterative method, entitled FastFlood, to compute river depth and velocity in 2D on a digital elevation model (DEM). This new method solves for the 2D shallow water equation, without the inertia terms, by iteratively building the river water depth using classical flow routing algorithms based on directed acyclic graphs, including the classical single or multi-flow, applied to the water surface. At each iteration, the water depth of each cell of the DEM increases by an increment that is a function of water discharge, computed using a flow accumulation operation, and decreases based on a flow resistance equation, in a manner similar to the Floodos model (Davy et al., 2017). In the hydrostatic mode, this operation is repeated until reaching a near constant water depth over the entire DEM, which occurs after a few tens or hundreds of iterations. FastFlood can also solve for the dynamic propagation of a flood in the hydrodynamic mode. In this case, the water depth increment is only a function of the water discharge exiting the direct upstream neighbors and the iterations are replaced by a time evolution of the water depth. Water depths obtained with the hydrostatic solution were validated against an analytical solution in the case of a rectangular channel and with the Floodos model for natural DEMs. Compared to previous hydrodynamic models, the main benefits of FastFlood are its simplicity of implementation, which mainly requires a classical flow routing algorithm, and its efficiency. Indeed, for a DEM of 10⁶ cells, the algorithm takes about 2 minutes on a laptop to find the hydrostatic solution, about 10 times faster than using the Floodos model (Davy et al., 2017) that was already significantly faster than other hydrodynamic models. Moreover, the computational time scales a little more than linearly with the number of cells, which makes FastFlood a suitable solution even for DEMs larger than 10⁶ – 10⁷ cells. In the future, we expect to make progress on the numerical method by adapting graph-based solutions to the issue of flow water routing. Following Davy et al. (2017), we will also include FastFlood in a landscape evolution model to couple it to process-based laws for erosion, transport and deposition of sediments.