Abstract
AbstractSmall streams in catchments with agricultural land use are at high risk of diffuse pollution by herbicides. Fast transport processes can cause concentration peaks that exceed regulatory requirements. These processes have a high spatio‐temporal variability and data characterizing their occurrence is often sparse. For this reason, such systems show a stochastic behavior at the resolution we observe them (same input and initial conditions lead to different output). Realistic model representations should acknowledge this pronounced apparent intrinsic stochasticity. However, a deterministic description of the physical and chemical processes at the catchment scale is state of the art in research and practice. We explore the potential of stochastic process formulations in combination with the Bayesian learning paradigm to (a) improve the quantification of the uncertainty of conceptual catchment‐scale pesticide transport models and (b) gain new mechanistic insights about the system by interpreting the temporal evolution of the stochastic processes. This is done with the help of a framework for time‐varying stochastic parameters. Thereby, we find that (a) the stochastic process formulation can lead to a more realistic characterization of the uncertainty of internal states and model output compared to the deterministic one, and that (b) the temporal dynamics of parameters resulting from the inference can highlight model deficits (and inspire improvements) such as a better sustained baseflow in dry periods. We also identify two key challenges: numerical difficulties in sampling the posterior and the question of where to introduce and how to constrain the additional degrees of freedom such that they are not misused.
Highlights
Hydrological catchments are complex systems in which various interacting processes transport water and pollutants at different spatio-temporal scales
Thereby, we find that (a) the stochastic process formulation can lead to a more realistic characterization of the uncertainty of internal states and model output compared to the deterministic one, and that (b) the temporal dynamics of parameters resulting from the inference can highlight model deficits such as a better sustained baseflow in dry periods
After a short introduction to the study site and the data (Section 3.1), we describe in detail how that approach is applied in this study by (a) introducing stochasticity in a previously deterministic model by making some of its parameters stochastic, time-dependent quantities (Section 3.2), (b) screening for patterns in the inferred temporal dynamics of time-dependent parameters (Section 3.3), (c) based on the identified patterns, formulating model improvements to eliminate systematic model deficits (Section 3.4), and (d) subsequent prediction for uncertainty quantification (Section 3.5)
Summary
Hydrological catchments are complex systems in which various interacting processes transport water and pollutants at different spatio-temporal scales. For two cases of the same measured volume of precipitation, input pollutant mass and catchment state; the true output (e.g., streamflow and pollutant concentration in the stream) will not respond identically in the two cases. This is because the observations of the driving forces and of the states are highly aggregated, which means that they are compatible with many different true realizations of those quantities
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