GraphFlood 1.0: an efficient algorithm to approximate 2D hydrodynamics for Landscape Evolution Models

Abstract. Computing hydrological fluxes at the Earth's surface is crucial for landscape evolution models, topographic analysis, and geographic information systems. However, existing formalisms, like single or multiple flow algorithms, often rely on ad-hoc rules based on local topographic slope and drainage area, neglecting the physics of water flow. While more physics-oriented solutions offer accuracy (e.g. shallow water equations), their computational costs limit their use in term of spatial and temporal scales. In this conrtibution, we introduce GraphFlood, a novel and efficient iterative method for computing river depth and water discharge in 2D on a digital elevation model (DEM). Leveraging the Directed Acyclic Graph (DAG) structure of surface water flow, GraphFlood iteratively solves the 2D shallow water equations. This algorithm aims to find the correct hydraulic surface by balancing discharge input and output over the topography. At each iteration, we employ fast DAG algorithms to calculate flow accumulation on the hydraulic surface, approximating discharge input. Discharge output is then computed using the Manning flow resistance equation, similar to the River.lab model. Iteratively, the divergence of discharges increments flow depth until reaching a stationary state. This algorithm can also solve for flood wave propagation by approximating the input discharge function of the immediate upstream neighbours. We validate water depths obtained with the stationary solution against analytical solutions for rectangular channels and the River.lab and Caesar Lisflood models for natural DEMs. GraphFlood demonstrates significant computational advantages over previous hydrodynamic models, with approximately a 10-fold speed-up compared to the River.lab model. Additionally, its computational time scales slightly more than linearly with the number of cells, making it suitable for large DEMs exceeding 10⁶–10⁸ cells. We demonstrate the versatility of GraphFlood in integrating realistic hydrology into various topographic and morphometric analyses, including channel width measurement, inundation pattern delineation, floodplain delineation, and the classification of hillslope, colluvial, and fluvial domains. Furthermore, we discuss its integration potential in landscape evolution models, highlighting its simplicity of implementation and computational efficiency.