Calibration of conceptual rainfall–runoff models using global optimisation methods with hydrologic process-based parameter constraints

The major difficulty associated with the use of conceptual rainfall–runoff (CRR) models in hydrology is their calibration since most of these models involve a large number of parameters. CRR model calibration is a global optimisation problem since its main objective is to find a set of optimal model parameter values that provides a best fit between observed and estimated flow hydrographs. However, even when using the superior search capabilities of modern global optimisation methods (GOM), the search for a set of optimal parameter values within an inflated multi-dimensional search space can result in an inefficient search and may lead to inaccurate parameter estimates. In addition, in most CRR model calibration studies to-date, no explicit constraint in the search procedure was used that could ensure the physical consistency of the estimated parameters. Improvements in parameter estimates could be achieved if the search space could be reduced through the incorporation of constraints that describe the logical interactions between the rainfall and runoff processes. A methodology is proposed herein for formulating constraints to improve the probability of success of calibration methods. More specifically, inequalities relating CRR model parameters with the available hydrologic data were developed and incorporated into a GOM to reduce the search space. The shuffled complex evolution (SCE) GOM showed that this approach resulted in significant improvements in the estimation of CRR model parameters for the case of synthetic streamflow data without errors as well as for data with heteroscesdastic errors. Furthermore, the suggested constrained SCE-based calibration procedure could provide CRR model parameter estimates that are consistent with the physically plausible interactions between the rainfall and runoff processes under consideration.