The effect of grid scale on calibration of two-dimensional river models through the drag coefficient

New survey technologies are able to provide detailed data on the form and topography of riverbeds. With this increased data resolution, the required computational time rather than data availability has become the limiting factor for river models. Detailed bathymetric data can be used to provide better empirical representation of drag and roughness at fine scales, allowing a priori selection of roughness using known physics rather than a posteriori calibration. However, we do not have sufficient guidance or understanding from the literature to represent known heterogeneities smaller than our practical grid scale. The problem is what to do with known subgrid-scale bathymetric features and roughness when our models must use a coarser computational grid. In this project, we simplify this complex problem to analyzing flow in a simple open channel with a single patch of relatively high roughness against an otherwise uniform background of low roughness. We model this open channel with a two-dimensional, depth-averaged river model. By running multiple simulations using different grid sizes we gain insight into how the relationship between the grid cell size and the patch size affects the appropriate physical selection of roughness parameter. As the primary focus, the present work proposes and investigates several methods for upscaling known fine-scale drag coefficient data to a coarser grid resolution for a model. For the tested conditions, it appears that a simple area-weighted linear average is simple to apply and creates a flow field very similar to the best results achieved by calibration.
As a secondary issue, the present work examines grid-dependent behaviors when using model calibration. Although recalibration of models for different grid scales is a common practice among modelers, we could find relatively little documentation or analysis. In our work, we examine both single-cell calibration (i.e. changing roughness in only the cell containing the rough patch) and multiple-grid cell calibration involving neighbor cells. With either method, improving calibration required multiple model simulations and comparative analysis for each tested grid size and was inefficient compared to the upscaling approach. As expected, the calibration at a given grid size was always inappropriate for a different grid size.