Bayesian uncertainty analysis in distributed hydrologic modeling: A case study in the Thur River basin (Switzerland)

Abstract

Calibration and uncertainty analysis in hydrologic modeling are affected by measurement errors in input and response and errors in model structure. Recently, extending similar approaches in discrete time, a continuous time autoregressive error model was proposed for statistical inference and uncertainty analysis in hydrologic modeling. The major advantages over discrete time formulation are the use of a continuous time error model for describing continuous processes, the possibility of accounting for seasonal variations of parameters in the error model, the easier treatment of missing data or omitted outliers, and the opportunity for continuous time predictions. The model was developed for the Chaohe Basin in China and had some features specific for this semiarid climatic region (in particular, the seasonal variation of parameters in the error model in response to seasonal variation in precipitation). This paper tests and extends this approach with an application to the Thur River basin in Switzerland, which is subject to completely different climatic conditions. This application corroborates the general applicability of the approach but also demonstrates the necessity of accounting for the heavy tails in the distributions of residuals and innovations. This is done by replacing the normal distribution of the innovations by a Student t distribution, the degrees of freedom of which are adapted to best represent the shape of the empirical distribution of the innovations. We conclude that with this extension, the continuous time autoregressive error model is applicable and flexible for hydrologic modeling under different climatic conditions. The major remaining conceptual disadvantage is that this class of approaches does not lead to a separate identification of model input and model structural errors. The major practical disadvantage is the high computational demand characteristic for all Markov chain Monte Carlo techniques.