A Bayesian Geostatistical Approach for reverse flood routing

Reverse flood routing is a procedure to estimate the discharge hydrographs at ungauged upstream stations by means of information available at downstream sites or the inflows to reservoirs based on the knowledge of the outflow hydrographs and the storage equations. In this work a Bayesian Geostatistical Approach for reverse flood routing in open channels and for reverse level pool routing in reservoirs is presented. The forward model, required for the inversion, was in the first case based on the one dimensional De Saint Venant equations; in the latter the level pool routing continuity equation was solved by means of a Runge-Kutta numerical method. The capabilities of the stochastic approach are shown by means of synthetic test cases and a study case. The reverse routing problem is particularly sensitive to errors present in the available data or in the model or accumulated during the inverse procedure that can cause instabilities and spurious oscillation of the solution. Random errors were added, in almost all the cases, to corrupt the true data before using them for the inversion. The results show that the proposed methodology is able to properly recover the input inflows even in presence of errors, highlighting the robustness and reliability of the approach.