A transparent approach for ranking sensitive parameters in hydrological models

Sensitivity analyses of model parameters indicate how changes in the model parameters are reflected on the model outputs. While ranking the importance of model parameters is one of the main applications of sensitivity analyses, there are large uncertainties in the results of such rankings. The main reason for this is that there is no objective approach for defining the ranges of variation of the considered parameters. As parameter sensitivity might vary with changes in the parameter ranges, we might observe variations in the parameter rankings depending on the sampled parameter space. This study presents a more transparent approach for ranking model parameters based on the results of more than 500 catchments across the United States. The procedure consists on the identification of an optimal parameter set using a Monte Carlo calibration approach. It is then estimated how much each parameter needs to vary for reducing the optimal NSE (Nash-Sutcliffe Efficiency) value, for example, by 0.02. Catchments achieving this reduction in the NSE with small parameter changes are then regarded as more sensitive than catchments requiring large deviations from the optimal parameter values for reaching the NSE reduction. This sensitivity measure (i.e., how much do the parameters need to change for achieving a given reduction in the NSE value) does not require the definition of a variation range for the parameters and can be easily interpreted. As the sensitivity measures have different units (e.g., soil depth in mm and snow melt temperature in degrees) it is necessary to rely, for example, on the accuracy of measurements or the expected spatial variability for deciding on the relative sensitivity of the parameters. The approach presented here, requires therefore that the analyst addresses explicitly questions regarding the expected parameter variability and its uncertainties making the underlying information for the rankings more visible. It is further possible to rank the catchments according to the sensitivity of each parameter, allowing, for example, to identify the catchments in which a given parameter is most important.