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Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. In this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs. 

Accurate prediction of snow water equivalent (SWE) can be valuable for water resource managers. Recently, deep learning methods such as long short-term memory (LSTM) have exhibited high accuracy in simulating hydrologic variables and can integrate lagged observations to improve prediction, but their benefits were not clear for SWE simulations. Here we tested an LSTM network with data integration (DI) for SWE in the western United States to integrate 30-day-lagged or 7-day-lagged observations of either SWE or satellite-observed snow cover fraction (SCF) to improve future predictions. SCF proved beneficial only for shallow-snow sites during snowmelt, while lagged SWE integration significantly improved prediction accuracy for both shallow- and deep-snow sites. The median Nash–Sutcliffe model efficiency coefficient (NSE) in temporal testing improved from 0.92 to 0.97 with 30-day-lagged SWE integration, and root-mean-square error (RMSE) and the difference between estimated and observed peak SWE valuesd_maxwere reduced by 41% and 57%, respectively. DI effectively mitigated accumulated model and forcing errors that would otherwise be persistent. Moreover, by applying DI to different observations (30-day-lagged, 7-day-lagged), we revealed the spatial distribution of errors with different persistent lengths. For example, integrating 30-day-lagged SWE was ineffective for ephemeral snow sites in the southwestern United States, but significantly reduced monthly-scale biases for regions with stable seasonal snowpack such as high-elevation sites in California. These biases are likely attributable to large interannual variability in snowfall or site-specific snow redistribution patterns that can accumulate to impactful levels over time for nonephemeral sites. These results set up benchmark levels and provide guidance for future model improvement strategies.

 

Porous hydraulic structures, such as Large Woody Debris (LWD) and Engineered Log Jams (ELJs), play a very important role in erosion control and habitation conservation in rivers. Previous experimental research has shed some light on the flow and sediment dynamics through and around porous structures. It was found that the scour process is strongly dependent on porosity. Computational models have great value in revealing more details of the processes which are difficult to capture in laboratory experiments. For example, previous computational modeling work has shown that the level of resolution of the complex hydraulic structures in computer models has great effect on the simulated flow dynamics. The less computationally expensive porosity model, instead of resolving all geometric details, can capture the bulk behavior for the flow field, especially in the far field. In the near field where sediment transport is most intensive, the flow result is inaccurate. The way in which this error is translated to the sediment transport results is unknown. This work aims to answer this question. More specifically, the suitability and limitations of using a porosity model in simulating scour around porous hydraulic structures are investigated. To capture the evolution of the sediment bed, an immersed boundary method is implemented. The computational results are compared against flume experiments to evaluate the performance of the porosity model.