Quantifying the Uncertainty of a Conceptual Herbicide Transport Model With Time-Dependent, Stochastic Parameters

Abstract

Small 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.