How significant are quadratic criteria? Part 2. On the relative contribution of large flood events to the value of a quadratic criterion

Quadratic criteria (i.e. based on squared residuals) are widely used to assess the performance of hydrological models. However, the largest errors have a relatively strong influence on the final criterion values, which may be considered a drawback for a complete assessment. This paper studies the case of updated models used for real-time forecasting. It is shown that the fraction of the data series actually impacting the final criterion value is small on many catchments and corresponds to the time steps characterised by the greatest runoff variations. In fact, model updating makes the error distribution more peak-shaped, giving even more relative importance to the time steps with the largest errors. Therefore, assessing the performance of an updated model with a quadratic criterion emphasises that these criteria focus more on the most difficult time steps to model (and the most interesting ones in the case of short-term flood forecasting).