Robust parametric models of runoff characteristics at the mesoscale

Many hydrologic studies report that runoff characteristics such as means or extremes of a given basin may be modified due to climatic and/or land use/cover changes and that the magnitude of these changes largely depends on the geographic location and the scale at which the study is carried out. Identifying the main causes of variability at the mesoscale, however, is a challenging task because of the lack of data regarding the spatial distribution of relevant explanatory variables and, if they exist, because of their high uncertainty. This study proposes a general method to find a robust non-linear model by solving a constrained multiobjective optimization problem whose solution space is composed of all feasible combinations of given explanatory variables. As a result, a model that simultaneously fulfills several criteria such as parsimony, robustness, significance, and overall performance is expected. Furthermore, it does not require assumptions regarding the sampling distributions neither of the parameters nor of the estimators because their p-values are estimated by a non-parametric technique. Finally, there is no limitation with respect to the functional form adopted for a given model and its estimator because a generalized reduced gradient algorithm is used for the calibration of its parameters. The proposed method was tested in the upper catchment of the Neckar River (Germany) covering an area of approximately 4000 km2. The objective of this study was to detect trends and responses of runoff characteristics in mesoscale catchments due to changes of climatic or land use/cover conditions. In this case, the explained variables are the specific total discharge in summer and winter whereas the explanatory variables comprise several physiographic, land cover and climatic characteristics evaluated for 46 subcatchments during the period 1961–1993. The results of the study indicate a significant gain in performance and robustness of the selected models compared to traditional stepwise methods. The applicability of this method to other disciplines and/or locations is possible.