Modelling uncertainty for flash floods in coastal plains using adjoint methods

This paper shows the application of adjoint sensitivity analysis to flash flood wave propagation in a river channel. The adjoint sensitivity analysis is used to assess flood hazard in a coastal area caused by river discharge. The numerical model determines the sensitivities of predicted water levels to uncertainties in key controls such as inflow hydrograph, channel topography, frictional resistance and infiltration rate. Sensitivities are calculated using the adjoint equations and are specified in terms of water levels being greater than certain safe threshold levels along the channel. The flood propagation model is based on the St. Venant equations while the propagation of sensitivity information is based on the corresponding adjoint equations. This analysis is achieved using a numerical model that integrates The St. Venant equations forward in time using a staggered finite difference scheme. An enhanced method of characteristics at the downstream boundary provides open boundary conditions and overcomes the problem of reflections from the boundaries. Then, the adjoint model is integrated backwards in time to trace the sensitivity information back through the model domain towards the inflow control boundary. The adjoint model has been verified by means of an identical twin experiment.