An adaptive time step solution for raster-based storage cell modelling of floodplain inundation

Since 1962 storage cell codes have been developed to simulate flow on fluvial and coastal floodplains. These models treat the floodplain as a series of discrete storage cells, with the flow between cells calculated explicitly using some analytical flow formulae such as the Manning equation. Recently these codes have been reconfigured to use regular Cartesian grids to make full use of widely available high resolution data captured from remote sensing platforms and stored in a raster GIS format. Such raster-based storage cell codes have many of the advantages over full two-dimensional depth averaged schemes but without the computational cost, however their typical implementation results in a number of fundamental limitations. These include an inability to develop solutions that are independent of time step or grid size, and an unrealistic lack of sensitivity to floodplain friction. In this paper, we propose a new solution to these problems based on an optimal adaptive time step determined using the Courant–Freidrichs–Levy condition for model stability. Comparison of this new adaptive time step scheme to analytical solutions of wave propagation on flat and sloping planar surfaces shows considerable improvement over a standard raster storage cell model. Moreover, the new scheme is shown to yield results that are independent of grid size or choice of initial time step and which show an intuitively correct sensitivity to floodplain friction over spatially complex topography.