Reverse flow routing in open channels: a Bayesian Geostatistical Approach

Reverse flow routing in open channels is a procedure of practical interest: it allows to obtain hydrographs in upstream ungauged stations by means of information available at downstream monitored sites. In this paper a Bayesian Geostatistical Approach for reverse flow routing in open channels is presented. The capabilities of the methodology are shown by means of synthetic test cases. Input hydrographs of different shape were routed downstream using a numerical flow model that solves the one dimensional De Saint Venant equations; the resulting outflow hydrographs were, in almost all the cases, corrupted with random errors and then used for the inversion. Both prismatic and non-prismatic irregular channels, under subcritical flow conditions, were analyzed as well. The considered non-prismatic channel with irregular cross sections and variable friction coefficients represents a very practical situation that can be encountered in the field. The results show that the proposed methodology is able to properly reproduce the input inflows even in presence of errors affecting the downstream discharges up to 10%.