Estimating the Structural Uncertainty of Lumped Parameter Models in Karst Hydrology: a Bayesian Model Averaging (BMA) Approach

Uncertainty quantification in hydrological modeling, and noticeably in the lumped modelling of karst systems, generally attributes source of uncertainty only to parameters or to input data.  Uncertainty in model conceptualization, which often leads to one unique model structure, is frequently neglected. This issue is particularly important for karst hydrology, where hydrological systems are highly heterogenous and information about the structure is difficult to obtain. In this work, we present a Bayesian Model Averaging (BMA) approach to assess predictive uncertainty with errors due to either model structure and model parameters. A set of plausible model structures is first selected, and a prior parameter space is sampled. For each model structure, the ability of the model to reproduce the observed behavior (discharge and water level) of the karst system is evaluated and a likelihood measures of acceptable structure is assigned to the model.  Then, the likelihood measures of each acceptable structure are integrated over the parameter space to obtain total likelihood of model structures. The latter is used to weight the predictions obtained with each model structure in the ensemble predictions. This method is illustrated with the KarstMod modeling platform that allows to run large range of lumped parameter model structures dedicated to karst hydrology. Then, the importance of structure error to predict spring discharge and water table levels of a well known karst system, the Lez karst system (Montpellier, France), is discussed.