Trade-off between cost and accuracy in large-scale surface water dynamic modeling

Recent efforts have led to the development of the local inertia formulation (INER) for an accurate but still cost-efficient representation of surface water dynamics, compared to the widely used kinematic wave equation (KINE). In this study, both formulations are evaluated over the Amazon basin in terms of computational costs and accuracy in simulating streamflows and water levels through synthetic experiments and comparisons against ground-based observations. Varying time steps are considered as part of the evaluation and INER at 60-second time step is adopted as the reference for synthetic experiments. Five hybrid (HYBR) realizations are performed based on maps representing the spatial distribution of the two formulations that physically represent river reach flow dynamics within the domain. Maps have fractions of KINE varying from 35.6% to 82.8%. KINE runs show clear deterioration along the Amazon river and main tributaries, with maximum RMSE values for streamflow and water level reaching 7827m³.s^-1 and 1379cm near the basin’s outlet. However, KINE is at least 25% more efficient than INER with low model sensitivity to longer time steps. A significant improvement is achieved with HYBR, resulting in maximum RMSE values of 3.9-292m³.s^-1 for streamflows and 1.1-28.5cm for water levels, and cost reduction of 6-16%, depending on the map used. Optimal results using HYBR are obtained when the local inertia formulation is used in about one third of the Amazon basin, reducing computational costs in simulations while preserving accuracy. However, that threshold may vary when applied to different regions, according to their hydrodynamics and geomorphological characteristics.