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.

中文翻译：

---

使用与时间相关的随机参数量化概念性除草剂传输模型的不确定性

使用农业用地的集水区的小溪流受到除草剂扩散污染的风险很高。快速的运输过程可能会导致超过法规要求的浓度峰值。这些过程具有很高的时空变异性，表征其发生的数据通常很少。出于这个原因，这样的系统在我们观察到的分辨率下表现出随机行为（相同的输入和初始条件导致不同的输出）。现实模型表示应该承认这种明显的内在随机性。然而，流域尺度物理和化学过程的确定性描述是研究和实践中的最新技术。我们探索了随机过程公式与贝叶斯学习范式相结合的潜力，以 (a) 改进概念流域尺度农药运输模型的不确定性的量化，以及 (b) 通过解释随机过程。这是在时变随机参数框架的帮助下完成的。因此，我们发现（a）与确定性的相比，随机过程公式可以更真实地表征内部状态和模型输出的不确定性，并且（b）推理产生的参数的时间动态可以突出显示模型赤字（并激发改进），例如在干旱时期更好地持续基流。我们还确定了两个关键挑战：