Evaluating loss functions for extreme streamflow predictions

Accurately predicting hydrological extremes is critical for effective flood risk and water resources management, yet it remains a major scientific and operational challenge. A wide range of loss functions is available for evaluating predictive performance, ranging from well-established hydrological metrics to less known alternatives drawn from the broader statistical literature. These loss functions differ in their mathematical properties and implicit assumptions, which might lead to substantially different model behaviour and predictive skills when they are used for model calibration.We compile and systematically evaluate a comprehensive suite of loss functions for calibrating hydrological models, with a particular emphasis on the prediction of streamflow extremes. By comparing their performance across a range of conditions, we highlight how the choice of calibration objective influences model sensitivity to high and extreme flows. Our findings provide practical guidance for selecting appropriate loss functions in hydrological modelling applications, with the aim of improving the reliability and robustness of predictions for high-impact hydrological events.Acknowledgements: This work was funded by the Research Center on Climate Change Impacts - University of Padova, Rovigo Campus - supported by Fondazione Cassa di Risparmio di Padova e Rovigo.