Stochastic time-dependent parameters to improve the modeling and characterization of catchments

Catchments are complex dynamical systems exposed to highly-variable inputs (rainfall). Despite this complexity, it is uncommon to model these systems as stochastic ones. Previous works offer a large number of examples where deterministic (conceptual or physics-based) models are used to describe hydrological basins in spite of the fact that, in some cases, the output of the model shows substantial deviations from the observed data even after meticulous calibration.
There are different ways to include stochasticity in the hydrological modeling of catchments. With this contribution we explore a systematic way to improve our knowledge of the system at hand by using time-dependent parameters, which are driven by suited stochastic processes. The fundamental idea, which dates back to seminal works carried out about ten years ago, is to correlate the evolution of the selected time-dependent parameters to catchment features, input variables, or possible changes over time within the catchment area, to improve the structure of the model in a data-driven fashion, rather than to merely resort to including a bias term on the output of the model.
In doing so for different catchments, we make use of a newly-developed inference framework called SPUX, which is particularly suited to deal with non-linear stochastic models as it enables the usage of high-performance computing clusters for (Bayesian) inference coupled with the particle filter method. This allows us to explore and show our approach at work on different settings, such as models of different complexity and data-sets of different resolutions, lengths, and relevant to catchments with different characteristics, which have (or not) changed over time.