Approximating rainfall-runoff modelling response using a stochastic integral equation

Rainfall-runoff modelling uncertainty can be analysed by the use of a stochastic integral formulation. The stochastic integral equation can be based on the rainfall-runoff model input of model rainfall or model rainfall excess. Similarly, the stochastic integral equation can be based on the rainfall-runoff model output of the modelled runoff hydrograph. The residual between actual measured runoff data and modelled runoff (from the rainfall-runoff model) is analysed here by the use of a stochastic integral equation. This approach is used to develop a set of convolution integral transfer function realizations that represent the chosen rainfall-runoff modelling error. The resulting stochastic integral component is a distribution of possible residual outcomes that may be directly added to the rainfall-runoff model's deterministic outcome, to develop a distribution of probable runoff hydrograph realizations from the chosen rainfall-runoff model.