Parallel Processing for a Better Understanding of Equifinality in Hydrological Models

The aim of conceptual modeling of watersheds is to realize a numeric scheme for determining rainfallrunoff at the outlet of a basin. This modeling consists of a number of parameters that are identified by calibration methods using a series of measured rainfall-runoff data. One of the difficulties of this method is due to equifinality problems. The definition of the parameters, and their relation with the data, extends the space of acceptable parameters (zone of equivalence), which in turn makes the combination of acceptable parameters very large. In addition, the calibration methods currently used simplify the parameter hyper-space and yield equally acceptable results which may be situated in the zone of equivalence, but which are not necessarily the optimal combination parameters of the model. Therefore, a possible approach for determining the optimal combination of parameters is to simulate an important set of possible parameters. This needs a considerable number of simulations that exceeds the capabilities of traditional computation. For example, the systematic exploration of the objective function structure of the four-parameter model MEDOR, specific to the Mediterranean climate, requires 1,476,800 simulations which needs days of computation using a personnel computer. To accelerate this computation, parallel processing based on a master-slave model was used. This model allows a dynamic task scheduling among the different processors, thus maximizing the efficiency. The surface criteria exhibits a ridgeline which indicates that the origin of equifinality resides in the existence of a relationship between parameters. The use of parallel processing , and consequent reduction of the computational time, allows for an exhaustive exploration of the parameters space and its characteristics.