  Deterministic hydrological models with uncertain, but
inferred-to-be-time-invariant parameters typically show time-dependent model
structural errors. Such errors can occur if a hydrological process is active in
certain time periods in nature, but is not resolved by the model. Such missing
processes could become visible during calibration as time-dependent best-fit
values of model parameters. We propose a formal time-windowed Bayesian analysis
to diagnose this type of model error, formalizing the question \In which period
of the calibration time-series does the model statistically disqualify itself
as quasi-true?" Using Bayesian model evidence (BME) as model performance
metric, we determine how much the data in time windows of the calibration
time-series support or refute the model. Then, we track BME over sliding time
windows to obtain a dynamic, time-windowed BME (tBME) and search for sudden
decreases that indicate an onset of model error. tBME also allows us to perform
a formal, sliding likelihood-ratio test of the model against the data. Our
proposed approach is designed to detect error occurrence on various temporal
scales, which is especially useful in hydrological modelling. We illustrate
this by applying our proposed method to soil moisture modeling. We test tBME as
model error indicator on several synthetic and real-world test cases that we
designed to vary in error sources and error time scales. Results prove the
usefulness of the framework for detecting structural errors in dynamic models.
Moreover, the time sequence of posterior parameter distributions helps to
investigate the reasons for model error and provide guidance for model
improvement.
