Lionel Berthet

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). Citation Berthet. L., Andréassian, V., Perrin, C., & Loumagne, C. ( 2010 Berthet, L. , Andréassian, V. , Perrin, C. and Loumagne, C. 2010. How significant are quadratic criteria? Part 1. How many years are necessary to ensure the data-independence of a quadratic criterion value?. Hydrol. Sci. J, 55(6): 1051–1062. this issue [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ) How significant are quadratic criteria? Part 2. On the relative contribution of large flood events to the value of a quadratic criterion. Hydrol. Sci. J. 55(6), 1063–1073.

Quadratic criteria are widely used to assess the performance of hydrological models. However, the statistical nature of the errors makes the interpretation of these criteria tricky. In this paper, root mean square error (RMSE) values were computed for a hydrological model over a set of 178 varied catchments on two 5-year data series: the computed RMSE values can actually reflect the content of the data series with which they are calculated as much as the intrinsic skills of the model. The error model proposed by Yang et al. ( 2007 Yang, J. , Reichert, P. , Abbaspour, K. and Yang, H. 2007. Hydrological modelling of the Chaohe basin in China: statistical model formulation and Bayesian inference. J. Hydrol., 340: 167–182. [Crossref], [Web of Science ®] [Google Scholar] ) is used to assess a lower bound of the RMSE confidence interval width, depending on the length of the data series used for the assessment. Our analysis indicates that the data series would have to be longer than several decades to ensure that computed RMSEs are close to their statistical expectation. The practical consequences of this result are raised and discussed. Citation Berthet, L., Andréassian, V., Perrin, C. & Loumagne, C. ( 2010 Berthet, L. , Andréassian, V. , Perrin, C. and Loumagne, C. 2010. How significant are quadratic criteria? Part 2. On the relative contribution of unusual flood events to the value of a quadratic criterion. Hydrol. Sci. J., 55(6): 1063–1073. (this issue) [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ) How significant are quadratic criteria? Part 1. How many years are necessary to ensure the data-independence of a quadratic criterion value? Hydrol. Sci. J. 55(6), 1051–1062.

This paper compares event-based and continuous hydrological modelling approaches for real-time forecasting of river flows. Both approaches are compared using a lumped hydrologic model (whose structure includes a soil moisture accounting (SMA) store and a routing store) on a data set of 178 French catchments. The main focus of this study was to investigate the actual impact of soil moisture initial conditions on the performance of flood forecasting models and the possible compensations with updating techniques. The rainfall-runoff model assimilation technique we used does not impact the SMA component of the model but only its routing part. Tests were made by running the SMA store continuously or on event basis, everything else being equal. The results show that the continuous approach remains the reference to ensure good forecasting performances. We show, however, that the possibility to assimilate the last observed flow considerably reduces the differences in performance. Last, we present a robust alternative to initialize the SMA store where continuous approaches are impossible because of data availability problems.