Investigation of the optimal complexity to simulate flow dynamics in a global river routing model.

Global hydrological models represent the terrestrial water cycle across the globe and help to study the impacts of climate change on water stress and flood risks. They are generally based on the coupling of a land surface model and a river routing model (RRM). RRMs were first created to close the water budget at the global scale in climate studies. They convey the runoff generated by land surface models to the sea by propagating the water through the river network. In the climate model community, for example in the CMIP6 exercise, most models use a very simplified routing scheme such as the kinematic wave, or no routing scheme at all. With the increase of computing capacities and observational global datasets, there is a recent and general tendency to increase the spatial resolution of models. As a consequence, some processes that can usually be neglected at coarser resolutions (such as backwater effects or overbank flows) have to be accounted for. More complex RRMs have been developed based on simplifications of the Saint-Venant equations (e.g., the local inertia approximation). They allow to more realistically represent the flow dynamics in rivers, and are then better suited to higher resolutions. In parallel, numerical methods like the Preissmann scheme are used in the hydraulic community to solve the full Saint-Venant equations for river reach to catchment scale applications. Yet, such methods are not adapted to global scale simulations due to their high computing demand. With the increase of computing capacities, the hydraulic community is also evolving towards larger scale modelling. Both communities tend to get closer, and there is a scientific debate on the best approach to improve process based hydraulic models.

The CTRIP model (CNRM version of the Total Runoff Integrated Pathways) is the RRM developed at CNRM (Météo France). Currently, CTRIP simulates the propagation of river discharges using the kinematic approximation of the Saint-Venant equations. Our study aims to complexify the routing scheme of CTRIP and try to investigate at which optimal complexity river dynamics should be simulated over various basins. As a first step, the complete Saint-Venant equations are integrated by a Crank Nicolson scheme with a Gauss Seidel iterative method in CTRIP. This scheme runs over the globe with a reasonable computing time. It is then comparatively analysed with the Saint-Venant equations integrated with a Preissmann scheme with a double sweep method, over an idealized test channel. Then, simplified models can be derived from the complete model of Saint-Venant, by neglecting terms of the momentum equation. Different wave types can be obtained: dynamic (with or without advection), gravity, diffusive or kinematic waves. We analyse over France at 1/12° resolution the governing conditions of those wave types (slope and friction bed, wave period) and the order of magnitude of the Saint-Venant terms over the domain. The complete model is compared to the simplified models in term of stability, physical realism, and computing time, and then evaluated against discharge observations.