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

Study of the subsurface flow using environmental and artificial tracers: the Haute-Mentue case, Switzerland

HYDRA

Use of environmental tracing to constrain a rainfall-runoff model. Application to the Haute-Mentue catchment

Presented study is aimed at using additional information to improve process representativity of hydrological modelling. The study region is the Haute-Mentue catchment located in the western part of Switzerland, 20 km north of Lausanne. Previous research in this catchment allowed improving of the understanding of the runoff generation by combining point soil moisture measurements (TDR) and integrating measurements both at the hillslope scale (dye tracing) and at the catchment scale (environmental tracing). In this work, environmental tracing information will be integrated into a semi-distributed hydrological model, which is a modified version of TOPMODEL taking into account a rapid stormflow generation above a less permeable soil horizon. Additional information has been incorporated by using a version of simulated annealing adapted for multi-criteria optimisatio

Study of hydrological processes by the combination of environmental tracing and hillslope measurements: application to the Haute-Menthue catchment.

The objective of this research is to improve the comprehension of the hydrological behaviour of natural catchments. The main originality of this work is to associate different types of measurement in order to obtain a better vision of hydrological processes responsible for streamflow generation. First, the hydrological behaviour is studied at the catchment scale by the application of environmental tracing. A three-component mixing model based on the silica and calcium concentrations of water allows one to distinguish the contributions of direct precipitation, soil water and groundwater during flood generation. Despite the different hydrological responses observed between the four subcatchments studied, a common behaviour is apparent. Soil contribution increases with a rise in the basin humidity. The subsurface water dominates the generation of major floods, which occur in wet conditions. In order to discover the processes responsible for the important soil water contributions, a large-scale time-domain reflectometry experiment (64 probes) was conducted. On the whole, this experiment indicates that the water flow in soil is spatially quite heterogeneous and depends on local properties. Macropore flows were clearly identified during a rainfall simulator experiment. Preferential flows may be responsible for the important contribution of soil water and the heterogeneity of the soil moisture. In order to test this hypothesis, a dye-tracing experiment was done. This new investigation confirms that an important part of soil water reaches the stream by preferential flows. So as to synthesize all these observations, a conceptual model is proposed. This model respects both the hydrochemical responses highlighted by the environmental tracing experiment and the observations done at the local scale. This conceptual model suggests that the important contribution of soil water is due to the extent of the hydrographic network and the role of preferential flows