Effect of Input and Parameter Uncertainties in Rainfall-Runoff Simulations

Abstract

The uncertainty or reliability of model simulation results produced by rainfall-runoff models is a function of uncertainties in model parameters, input data, and model structure. The present study considers a stochastic instantaneous unit hydrograph (SIUH) model describing the catchment as a single linear reservoir with input and transfer functions treated as random processes. Errors in runoff predictions caused by errors in input data and model parameters are analyzed by solving the governing stochastic differential equation (SDE) analytically, thus quantifying—in a general way—the error propagation structure and the relative importance of input errors and parameter errors. The result shows that the SIUH parameter variance has a direct bearing on the runoff variance, whereas the error contribution from the effective rainfall variance depends on the parameter mean value and the ratio between effective rainfall and simulated runoff. Data from 34 rainstorms are selected to verify the analytical SDE approach. The selected events represent varying: (1) rainfall intensity and duration; (2) single/multiple peak events; and (3) catchment initial losses. The results from the simulations are compared with observed runoff peaks and flood volumes. It is concluded that: (1) the SIUH model is a simple yet robust method, for which the parameter uncertainty can be realistically assessed; (2) the application of a theoretical SDE to estimate the prediction variance is supported by the statistical analysis of simulated and observed runoff; and (3) the estimation of flood peak variance can improve the design of flood control measures.