Efficient subspace probabilistic parameter optimization for catchment models

The estimation of catchment model parameters has proven to be a difficult task for several reasons, which include ill-posedness and the existence of multiple local optima. Recent work on global probabilistic search methods has developed robust techniques for locating the global optimum. However, these methods can be computationally intensive when the 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 effort by confining the search to a subspace within which the global optimum is likely to be found. The approach involves locating a local optimum using a local gradient-based search. It is assumed that the local optimum belongs to a set of optima which cluster about the global optimum. A probabilistic search is then conducted within a hyperellipsoid defined by the second-order approximation to the response surface around the local optimum. A case study involving a five-parameter conceptual rainfall-runoff model is presented. The response surface is shown to be riddled with local optima, yet the second-order approximation provides a not unreasonable description of parameter uncertainty. The subspace search strategy provides a rational means for defining the search space and is shown to be more efficient (typically twice, but up to 5 times more efficient) than a search over a hypercube. Four probabilistic search algorithms are compared: shuffled complex evolution (SCE), genetic algorithm using traditional crossover, and multiple random start 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.