Comparison of numerical solutions for the flow wave propagation in river networks
Authors: Peronnet Emma , Decharme Bertrand , Munier Simon 
Published: July 2024

River routing models are important tools to document, anticipate and forecast river flows dynamic, and perceive the evolution of water resources in the context of climate change. The performance of these models can evolve through different methods, including resolving more complex physical equations, refining the model spatial resolution, improving the model parametrisation, the hydrological network, the forcings. Our study focuses on the impact of more or less complex physical equations and numerical solutions on the performances of the routing model CTRIP.&#160;The CTRIP model (CNRM version of the Total Runoff Integrated Pathways) is the river routing model developed at the CNRM, at M&#233;t&#233;o France. It converts the runoff simulated by the ISBA (Interaction Sol Biosph&#232;re Atmosph&#232;re) land surface model into river discharge (http://www.umr-cnrm.fr/spip.php?article1092). It is used for many hydrological applications at medium and large scales. ISBA-CTRIP is the hydrological component of the CNRM climate models, and allows to close the water budget at the global scale. CTRIP handles the horizontal transfer of water over continental surfaces, and describes the main processes of the continental water cycle. In particular, it describes the water propagation into the river network.&#160;Currently, CTRIP simulates the propagation of river discharges using the kinematic approximation of the Saint-Venant equations, in a uniform regime. The equation of water mass conservation is used with the water velocity deduced from Manning's equation. The river is described as a single prognostic reservoir whose discharge is linearly related to the river mass [Decharme 2010]. This simple scheme is adapted to low resolutions, but reaches its limits if the resolution needs to be increased. Going to higher resolutions would allow to better represent dynamic phenomenons, and to take into account small scale processes. It would allow a better representation of the hydrological network, and could result in a quality upgrade for the CNRM hydrological productions. Our study aims to go further the simplistic representation of discharge propagation in rivers into CTRIP and to reach a more complex approach.&#160;In our works, many approximations of the Saint Venant equations are studied : the kinematic approximation in a non uniform regime [Yamazaki 2011], the local inertial approximation [Bates 2010], the diffusive approximation [Moussa 1996], and the dynamic approximation. Several numerical methods are used to solve them : Euler, Crank-Nicholson, Gauss-Seidel. It is coded in CTRIP with a 1/12&#176; spatial resolution (~ 8 km at medium latitudes), in offline mode [Munier 2022] over the Adour basin in South-West of France. CTRIP is forced by total runoffs from the hydrometeorological chain SIM2 (https://www.drias-eau.fr/accompagnement/sections/305) [Le Moigne 2020]. The different versions of the model are compared to a full Saint Venant model, for theorical validation. They are also compared to a dense in-situ network of discharge observations.