Diffusion-based modelling of flood inundation over complex floodplains

High-resolution data obtained from airborne remote sensing are increasing opportunities for representation of small-scale structural elements (e. g. walls, buildings) in complex floodplain systems using two-dimensional (2D) models of flood inundation. At the same time, 2D inundation models have been developed and shown to provide good predictions of flood inundation extent, with respect to both full solution of the depth-averaged Navier-Stokes equations and simplified diffusion wave models. However, these models have yet to be applied extensively to urban areas. This study applies a 2D raster-based diffusion wave model, either loosely-coupled or tightly-coupled to a ID river flow model, to determine patterns of fluvial flood inundation in urban areas using high-resolution topographic data. The aim of this study is to explore the interaction between spatial resolution and small-scale flow routing process, through model validation and verification. The model assumes that the prime source of the flood is fluvial: pluvial floods and floods associated with urban drainage systems are not addressed. The topographic data are based upon airborne laser altimetry (LiDAR) obtained for the City of York, U. K. Validation data were available in the form of inundation patterns obtained using aerial photography at a point on the failing limb of the flood event. Inflow data is provided either by a loosely-coupled or a tightly-coupled ID river flow model. The model was used to simulate a major flood event which occurred in the year 2000 in the City of York on the River Ouse at 4 different sites. Applications of the basic model showed that even relatively small changes in model resolution have considerable effects on the predicted inundation extent and timing of flood inundation. Timing sensitivity would be expected given the relatively poor representation of inertial processes in a diffusion wave model. Compared with previous work, sensitivity to inundation extent is more surprising and is associated with three connected effects: (i) the smoothing effect of mesh coarsening upon input topographical data; (ii) poorer representation of both cell blockage and surface routing processes as the mesh is coarsened, where the flow routing is especially complex; and (iii) the effects of (i) and (ii) upon water levels and velocities which in turn determine which parts of the floodplain the flow can actually travel to. The combined effects of wetting and roughness parameters can compensate in part for a coarser mesh resolution. However, the coarser the resolution, the poorer the ability to control the inundation process as these parameters not only affect the speed but also the direction of wetting. Thus, high resolution data will need to be coupled to more sophisticated representation of the inundation process in order to obtain effective predictions of flood inundation extent. A sub grid scale wetting and drying correction approach was developed and tested for use with 2D diffusion wave models of urban flood inundation. The method recognises explicitly that representations of sub grid scale topography using roughness parameters ill provide an inadequate representation of the effects of structural elements on the floodplain (e. g. buildings, walls) as such elements not only act as momentum sinks, but also have mass blockage effects. The latter may dominate, especially in structurally complex urban areas. The approach developed uses high resolution topographic data to develop explicit parameterization of sub grid scale topographic variability to represent both the volume of a grid cell that can be occupied by the flow and the effect of that variability upon the timing and direction of the lateral fluxes. This approach is found to give significantly better prediction of fluvial flood inundation in urban areas as compared with traditional calibration of sub grid-scale effects using Manning's n. In particular, it simultaneously reduces the need to use exceptionally high values of n to represent the effects of using coarser meshes, whilst simultaneously increasing the sensitivity of model predictions to variation in n. Finally, the model was coupled (tightly) to a one-dimensional solution of the Navier-Stokes equations. This showed that significantly better representation of urban inundation could be achieved in a tightly-coupled formulation as a result of better representation of boundary condition effects.