How significant are quadratic criteria? Part 1. How many years are necessary to ensure the data-independence of a quadratic criterion value?

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) 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.