Learning Deep Insights into Hydrological Processes using Bayesian Neural Hydrology

The study of hydrological processes is of paramount importance in understanding and effectively managing our water resources. These processes are inherently complex and non-linear, posing challenges for hydrological modelling. Traditional approaches, such as physics-based and lumped rainfall-runoff models, are widely used but often face limitations. Their computational demands can be substantial, or inherent simplifications constrain their predictive accuracy. Neural hydrology offers an alternative, leveraging machine learning to learn directly from massive datasets. Deep learning methods, inspired by rainfall-runoff model structures, can estimate fluxes at the watershed outlet and between lumped storage units, providing insights into intermediate processes such as soil moisture and snowpack dynamics.

Despite these advancements in machine learning applications, several challenges remain unaddressed: i) the interpretability of machine-learned dynamic processes is still incomplete,  and ii) the ability of users to insert and re-use the existing domain knowledge is limited.

We believe neural hydrology can be significantly advanced by adopting a Bayesian framework. This approach not only enables meaningful uncertainty quantification and probabilistic predictions but also facilitates the integration of both hard and soft knowledge about hydrological processes through physics-informed machine learning. Moreover, it aligns the learned models with human-level understanding, enhancing their interpretability and applicability. Our research goal is to develop Bayesian Neural Hydrology as a cutting-edge approach with the potential to revolutionize our understanding of hydrological systems.

Within our framework, we integrate an effective hydrological sensitivity function along with prior hydrological knowledge into mass balance equations, which are then modelled using Neural ODEs. This physics-informed integration aims to enhance forecasting accuracy, out-of-sample generalization, and data efficiency. Our method seeks to deliver reliable hydrological predictions without requiring large training datasets, providing a physically consistent and practical tool for watershed modelling.