Quantifying hydrological modeling errors through a mixture of normal distributions

Bayesian inference of posterior parameter distributions has become widely used in hydrological modeling to estimate the associated modeling uncertainty. The classical underlying statistical model assumes a Gaussian modeling error with zero mean and a given variance. As hydrological modeling residuals rarely respect this basic assumption, data transformations are carried out. The present technical note points out the problems that can arise using such data transformation techniques and proposes instead the use of a finite mixture model. The hydrological and the statistical model parameters are inferred using a Markov chain Monte Carlo method known as the Metropolis-Hastings algorithm. The proposed methodology is illustrated for a rainfall-runoff model applied to a highly glacierized alpine catchment. The associated total modeling error is modeled using a mixture of two normal distributions, the mixture components referring respectively to the low and the high flow discharge regime. The obtained results show that the use of a finite mixture model constitutes a promising solution to model hydrological modeling errors and could give new insights into the model behavior.