A STOCHASTIC INTEGRAL-EQUATION ANALOG OF RAINFALL-RUNOFF PROCESSES FOR EVALUATING MODELING UNCERTAINTY

In this paper a very general rainfall-runoff model structure (describe d below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. T he spatial and temporal rainfall distribution over the catchment is pr obabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall w ith respect to the rain gauge measured data. The resulting link node m odel structure is a series of stochastic integral equations, one equat ion for each subarea. A cumulative stochastic integral equation is dev eloped as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The re sulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realiz ations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, ea ch outcome being the results of calibration to a known storm event.