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). Further, the choice of objective function (i.e. the criterion or combination of criteria for optimization) can significantly impact the parameter set values identified as optimal by the algorithm. 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 a hydrograph. We show in a catchment set that the impact of these transformations on the obtained time series can sometimes be different from their expected behaviour. Extreme transformations, such as squared or inverse 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 and the Box–Cox and logarithmic transformations, can be categorized as more generalist and show good performance for the medium range of streamflows, along with acceptable performance for extreme streamflows.