Bayesian multiresponse calibration of TOPMODEL: Application to the Haute‐Mentue catchment, Switzerland

Abstract

[1] This paper introduces a general framework that evaluates a numerical Bayesian multiresponse calibration approach based on a Gibbs within Metropolis searching algorithm and a statistical likelihood function. The methodology has been applied with two versions of TOPMODEL on the Haute-Mentue experimental basin in Switzerland. The approach computes the following: the parameter's uncertainty, the parametric uncertainty of the output responses stemming from parameter uncertainty, and the predictive uncertainty of the output responses stemming from an error term including, indiscriminately in a lumped way, model structure and input and output errors. Two case studies are presented: The first one applies this methodology with the classical TOPMODEL to assess the role of two-response calibration (observed discharge and soil saturation deficits) on model parameters and output uncertainty. The second one uses a three-response calibration (observed discharge, silica, and calcium stream water concentrations) with a modified version of TOPMODEL to study the uncertainty of the parameters and of the simulated responses. Despite its limitations, the present multiresponse Bayesian approach proved a valuable tool in uncertainty analyses, and it contributed to a better understanding of the role of the internal variables and the value of additional information for enhancing model structure robustness and for checking the performance of conceptual models.

Optimization of rain gauge sampling density for river discharge prediction using Bayesian calibration

“…For example, Engeland, Xu & Gottschalk (2005) showed that model structural uncertainty is larger than model parameter uncertainty for simple conceptual models with few well-defined parameters. Our results also confirm the study of Talamba, Parent & Musy (2010) for a lumped hydrological model. Talamba, Parent & Musy (2010) showed, for a fully distributed hydrological model, that accounting for input rainfall uncertainty did not lead to a substantial change in terms of estimated parameters and model performance, because other sources of uncertainty dominated the total predictive uncertainty.…”

“…Our results also confirm the study of Talamba, Parent & Musy (2010) for a lumped hydrological model. Talamba, Parent & Musy (2010) showed, for a fully distributed hydrological model, that accounting for input rainfall uncertainty did not lead to a substantial change in terms of estimated parameters and model performance, because other sources of uncertainty dominated the total predictive uncertainty. This is similar to our case study, where in all three approaches the prediction intervals have a similar width and range.…”

Sampling design optimization for geostatistical modelling and prediction

“…For example, Engeland et al (2005) showed that model structural uncertainty is larger than model parameter uncertainty for simple conceptual models with few well-de ned parameters. We also con rm the study of Talamba et al (2010) for a lumped hydrological model. Talamba et al (2010) showed, for a fully distributed hydrological model, that accounting for input rainfall uncertainty did not lead to a substantial change in terms of estimated parameters and model performance, because other sources of uncertainty dominated the total predictive uncertainty.…”

“…We also con rm the study of Talamba et al (2010) for a lumped hydrological model. Talamba et al (2010) showed, for a fully distributed hydrological model, that accounting for input rainfall uncertainty did not lead to a substantial change in terms of estimated parameters and model performance, because other sources of uncertainty dominated the total predictive uncertainty. This is similar to our case study, where in all three approaches the prediction intervals have a similar width and range.…”

Addressing subjective decision-making inherent in GLUE-based multi-criteria rainfall–runoff model calibration

“…These efforts generally indicate relatively close agreement between informal and formal methods (Beven et al, 2008;Jeremiah et al, 2011;Jin et al, 2010;Li et al, 2010;Qian et al, 2003;Vrugt et al, 2008;Yang et al, 2008). Most of the above comparative papers only considered single-criterion calibration cases, and only a few, e.g., Balin-Talamba (2004) and Balin-Talamba et al (2010), considered multi-criteria calibration of hydrologic models.…”