On the use of streamflow transformations for hydrological model calibration

Abstract. The calibration of hydrological models through the use of automatic algorithms aims at identifying parameter sets that minimize the deviation of simulations from observations (often streamflows). It is a widespread technique that has been the subject of much research in the past. Indeed, the choice of objective function (i.e. the criterion or combination of criteria to optimize) can significantly impact the parameter set values identified as optimal by the algorithm. Besides, the actual goal of the model application (flood or low-flow estimation, for instance) influences the way calibration is undertaken. This article discusses how mathematical transformations, which are sometimes applied to the target variable before calculating the objective function, impact model simulations. Such transformations, for example square root or logarithmic, aim at increasing the weight of errors made in specific ranges of the hydrograph. Typically, a logarithmic transformation tends to increase the fit of streamflows to lower values, compared to no transformation. We show in a catchment set that the impact of these transformations on the obtained time series can sometimes be different from what could be expected. Extreme transformations, such as squared or inverse of squared transformations, lead to models that are specialized for extreme streamflows, but show poor performance outside the range of the targeted streamflows and are less robust. Other transformations, such as the power 0.2, the Box–Cox and the logarithmic transformations, can be qualified as more generalist, and show a good performance for the intermediate range of streamflows, along with an acceptable performance for extreme streamflows.