Diagnosing model-structural errors with a sliding time window Bayesian analysis

When a deterministic hydrological model is calibrated, parameters applied in the model are commonly assigned time-constant values. This assignment ignores that errors in the model structure lead to time-dependent model errors. Such time-dependent error occurs, among other reasons, if a hydrological process is active in certain periods or situations in nature, yet is not captured by a model. Examples include soil freezing, complex vegetation dynamics, or the effect of extreme floods on river morphology. For a given model approximation, such missing process could become visible as apparent time-dependent best-fit values of model parameters. This research aims to develop a framework based on time-windowed Bayesian inference, to assist modelers in diagnosing this type of model error.

We suggest using time-windowed Bayesian model evidence (tBME) as a model evaluation metric, indicating how much the data in time windows support the claim that the model is correct. We will explain how to make tBME values a meaningful and comparable indicator within likelihood-ratio hypothesis tests. By using a sliding time window, the hypothesis test will indicate where such errors happen. The sliding time window can also be used to obtain a time sequence of posterior parameter distribution (or of best-fit calibration parameters). The dynamic parameter posterior will be further used to investigate the potential error source. Based on Bayes rule we can also observe how influential a parameter may be for model improvement.

We will show a corresponding visualization tool to indicate time periods where the model is potentially missing a process. We provide guidance to use showing how to use the dynamic parameter posterior to obtain insights on the error source and potentially to improve the model performance. The soil moisture model (HYDRUS 1D) was applied for a pilot test to prove the feasibility of this framework.