Search for: All records

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology. 

Hydrologic signatures are quantitative metrics that describe streamflow statistics and dynamics. Signatures have many applications, including assessing habitat suitability and hydrologic alteration, calibrating and evaluating hydrologic models, defining similarity between watersheds and investigating watershed processes. Increasingly, signatures are being used in large sample studies to guide flow management and modelling at continental scales. Using signatures in studies involving 1000s of watersheds brings new challenges as it becomes impractical to examine signature parameters and behaviour in each watershed. For example, we might wish to check that signatures describing flood event characteristics have correctly identified event periods, that signature values have not been biassed by data errors, or that human and natural influences on signature values have been correctly interpreted. In this commentary, we draw from our collective experience to present case studies where naïve application of signatures fails to correctly identify streamflow dynamics. These include unusual precipitation or flow regimes, data quality issues, and signature use in human-influenced watersheds. We conclude by providing guidance and recommendations on applying signatures in large sample studies.