We now routinely model flood inundation using reduced complexity
models. Traditionally, these have involved both depth-averaging and
width-averaging of the mass and momentum equations. Strictly, this
assumption is only valid when the flow is shallow and the topographic
forcing term is dominant and it still leaves the problem of
discretisation and solution, given the strong sensitivity to
topographic resolution. In this paper, we present and validate an
alternative sub-grid formulation that introduces an explicit
representation of finer resolution topographic. This approach 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 than traditional calibration of
sub-grid-scale effects using Manning's n.