EFFICIENT SUBSPACE PROBABILISTIC PARAMETER OPTIMIZATION FOR CATCHMENTMODELS

The estimation of catchment model parameters has proven to be a diffic ult task for several reasons, which include ill-posedness and the exis tence of multiple local optima. Recent work on global probabilistic se arch methods has developed robust techniques for locating the global o ptimum. However, these methods can be computationally intensive when t he search is conducted over a large hypercube. Moreover, specification of the hypercube may be problematic, particularly if there is strong parameter interaction. This study seeks to reduce the computational ef fort by confining the search to a subspace within which the global opt imum is likely to be found. The approach involves locating a local opt imum using a local gradient-based search. It is assumed that the local optimum belongs to a set of optima which cluster about the global opt imum. A probabilistic search is then conducted within a hyperellipsoid defined by the second-order approximation to the response surface aro und the local optimum. A case study involving a five-parameter concept ual rainfall-runoff model is presented. The response surface is shown to be riddled with local optima, yet the second-order approximation pr ovides a not unreasonable description of parameter uncertainty. The su bspace search strategy provides a rational means for defining the sear ch space and is shown to be more efficient (typically twice, but up to 5 times more efficient) than a search over a hypercube. Four probabil istic search algorithms are compared: shuffled complex evolution (SCE) , genetic algorithm using traditional crossover, and multiple random s tart using either simplex or quasi-Newton local searches. In the case study the SCE algorithm was found to be robust and the most efficient. The genetic algorithm, although displaying initial convergence rates superior to the SCE algorithm, tended to flounder near the optimum and could not be relied upon to locate the global optimum.