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. For hydrological modeling residuals, this assumption however rarely holds; the present paper proposes the use of a mixture of normal distributions as a simple solution to overcome this problem in parameter inference studies. 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 in parameter inference studies and could give additional insights into the model behavior.