Surface flow model: inverse problems and predictions

The inverse problem to estimate the scaling coefficients for infiltration, rainfall, intensity, and roughness in a surface flow model is considered. A probability density function (pdf) is constructed from an observed hydrograph associated with a given rainfall event, the deterministic surface flow model, prior information on bounds on the scale coefficients, and prior information on the coefficients. From this pdf a basin pdf is obtained describing the likelihood of basin infiltration and roughness properties within a sample space of basin properties. With the occurrence of a new rainfall event, the basin pdf is utilized to describe the behavior of the basin in the presence of this event with a basin-event pdf. From this information predictions of flooding behavior may be obtained as well as the expected water levels along the stream. Numerical examples are presented that include different observational errors.