Analysis of the response surface of the objective function by the optimum parameter curve: how good can the optimum parameter values be?

This paper presents an optimum parameter curve as a visualisation of all th e possible local and global peaks on the multidimensional response surface of the objective function associated with the calibration of hydrological m odels, coupled with an auxiliary curve called the search step index curve t o facilitate analysis of the shape of the response surface. The constructio n of such an optimum parameter curve to analyse the response surface of a p arametric model (conceptual or black-box) is directly prompted by the conce pt of equifinality embodied in the GLUE methodology of Beven and Binley, i. e. that there may be many parameter sets equally acceptable, in terms of ne ar-equal model efficiency values, as simulators of the response of a waters hed to rainfall. With the suggested methods, several numerical experiments have been conducted, firstly for a 2-parameter blackbox model (the Gamma fu nction model), using synthetic error-free data for selected sets of paramet er values, and secondly for a typical primitive conceptual rainfall-runoff model (the 9-parameter Wuhan-01 model), using the real data of three catchm ents. It is deduced that the goodness of the optimum parameter set estimate d by optimisation is determined more by the shape of the response surface i tself rather than by the optimisation methods used. It is also demonstrated that both multivariate normal distribution sampling and Markov chain sampl ing (the Metropolis algorithm) are more efficient in constructing the propo sed optimum parameter curve than the method of uniform random sampling init ially investigated for this purpose. (C) 2000 Elsevier Science B.V. All rig hts reserved.