SURFACE ROUGHNESS PARAMETERIZATION TO ACCOUNT FOR SUBGRID SCALE TOPOGRAPHY IN SHALLOW WATER FLOW MODELING

摘要

This paper studies the usage of roughness formulations to account for subgrid-scale effects based on microtopographic features in the context of upscaling overland flow models. The aim is to increase the cell size in order to reduce the computational cost of shallow water models applied to surface runoff in small catchments. The integral discharge is the primary function of concern, however velocity and water depth distributions in the domain are also considered. Two novel roughness formulations are presented and compared. The first formulation has two calibration parameters and the second one has three calibration parameters. Both formulations depend on the inundation ratio, i.e. water depth divided by the characteristic roughness length (determined from microtopography). One formulation takes the slope of the cell as the other free parameter. The formulations are implemented in the Hydroinformatics Modeling System. Upscaling capabilities of the formulations are tested in three numerical cases with simplified geometries. The modelling accuracies are compared by calculating the L_2-errors of the results of the upscaled models with the high-resolution modelling results regarded as the baseline. Additionally, the calibration effort of both models is compared by considering the effort of an automated calibration algorithm. The computational time is given for each model to compare the speed-up gained due to the cell size increase. Overall, a good agreement is achieved between the results of the high-resolution model and the upscaled models with roughness parameterization. As the number of calibration parameters increases, the accuracy of the model results increases. However, the calibration process generally requires more effort. For the presented cases, the simulations on a coarser resolution run about 50 times faster than the simulations on fine resolution meshes. It is concluded that the increased accuracy of the three parameter roughness formulation outweighs its drawbacks associated with the calibration effort.