Potential and Challenges of Investigating Intrinsic Uncertainty of Hydrological Models with Stochastic, Time-Dependent Parameters

The same observed precipitation falling onto seemingly the same initial state of a catchment will not lead to the same streamflow. The following causes are contributing to this non-deterministic behavior: (i) Unobserved spatial heterogeneity and limited time resolution of rainfall and other climatic observations limit the accuracy of observing the true input and other influencing factors. (ii) The knowledge about the initial state of the hydrological system is even more incomplete than about the input. (iii) Temporal changes in catchment properties that are not or not accurately described by the model also affect its response. As the same observed input can lead to different, unobserved internal states that affect streamflow for quite some time after a precipitation event, a description of such a system exclusively by considering input and output errors is not considering all relevant mechanisms. The description of such non-deterministic behavior (at the resolution of input and output observations) requires a stochastic model. To account for this apparent stochasticity of the system while still exactly maintaining mass balances, mass transfer processes should be made stochastic, rather than the mass balance equations. This can easily be done by turning the parameters of a deterministic, hydrological model into stochastic processes in time. As an additional advantage of this approach, the inferred time series of the parameters can be used to find relationships to input and model states that can (and have to) be used to improve the underlying hydrological model. On the other hand, the additional degrees of freedom for parameter estimation can lead to overparameterization, non-identifiability, and even “misuse” of “stochasticity” by “shifting” mechanistic relationships to the time-dependent parameter. These potential drawbacks require a very careful analysis.

In this talk, we will briefly review the methodology of stochastic, time-dependent parameters and investigate the potential and challenges of the suggested approach with a case study. In particular, we will demonstrate how we can learn about model deficits and how to reduce them, how the incautious application of the methodology can lead to (very) poor predictions, and how predictive cross-validation can help identifying whether the time-dependence of the parameters were “misused” to represent relationships that were not considered in the model or whether they can be assumed to represent true randomness.