Catchment-scale multi-process modeling with local time stepping

Numerical modeling is an important tool for prediction, analysis and understanding of the dynamics of land surface processes. To increase the usage and impact of such tools, it is crucial to decrease runtime by increasing computational efficiency. Dynamic processes such as water flow are typically described by higher-order differential equations. Solving these accurately requires numerical integration over time, where numerical errors depend on the time steps taken. Typically, flow simulation use the smallest required time steps in a model's domain to simulate flow. In this paper, we analyze the usage of local time stepping, for catchment-scale simulation of land surface processes such as water flow, infiltration, slope stability and landslide runout. In such a scheme, temporal integration is cell specific, allowing for higher numerical efficiency. The implemented scheme works with fully free local time steps that are synchronized only for visualization. We implement this method in a monotonic upwind scheme for conservation laws (MUSCL). We investigate the influence on stability and the resulting changes in computation time and accuracy in a hydrology-coupled, catchment-scale flood simulation. Results show that local time stepping can be implemented in a total variation diminishing (TVD) numerical scheme that is second-order spatially accurate. Simulation results in both 1D dam-break scenarios and catchment-scale flash flood scenarios show insignificant changes in modeling result, while computation time reduces with over 50%. Finally, the method is successfully implemented in a multi-process lands surface model with hydrology, flooding, slope failure, and runout. The implementation of a local time stepping for computation of dynamic land surface processes could be implemented widely for increased computational efficiency without significant loss of accuracy.