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Accurate prediction of snow water equivalent (SWE) can be valuable for water resource managers. Re-cently, 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 values dmax were 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 sta-ble 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.

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.

Hydraulic geometry parameters describing river hydrogeomorphic relationships are critical for determining a channel's capacity to convey water and sediment which is important for flood forecasting. Although well‐established, power‐law hydraulic geometry curves have been widely used to understand riverine systems and mapping flooding inundation worldwide for the past 70 years, we have become increasingly aware of their limitations. In the present study, we have moved beyond these traditional power‐law relationships, testing the ability of machine‐learning models to provide improved predictions of river width and depth. For this work, we have used an unprecedentedly large river measurement data set (HYDRoSWOT) as well as a suite of watershed predictor data to develop novel data‐driven approaches to better estimate river geometries over the contiguous United States (CONUS). Our Random Forest, XGBoost, and neural network models out‐performed the traditional, regionalized power law‐based hydraulic geometry equations for both width and depth, providing R‐squared values of as high as 0.75 for width and as high as 0.67 for depth, compared with R‐squared values of 0.45 for width and 0.18 for depth from the regional hydraulic geometry equations. Our results also show diverse performance outcomes across stream orders and geographical regions for the different machine‐learning models, demonstrating the value of using multi‐model approaches to maximize the predictability of river geometry. The developed models have been used to create the newly publicly available STREAM‐geo data set, which provides river width, depth, width/depth ratio, and river and stream surface area (%RSSA) for nearly 2.7 million NHDPlus stream reaches across the contiguous US. Plain Language Summary: Scientists and river managers use measurements of river geometry such as width and depth to forecast floods and understand river behavior. However, the methods used to estimate river geometry that have been used for decades are imprecise and thus lead to poor predictions of river discharge dynamics. Here, we've used new machine learning‐based modeling approaches to provide better predictions of river width and depth. We tested different machine‐learning models, which were developed based on the HYDRoSWOT set of measurements of rivers across the U.S. These new models all provide better estimates of river width and depth than the old methods. Our research can help us to provide better estimates of flood dynamics and improve our understanding of rivers across the U.S. Key Points: Machine Learning models outperform regional (physiographic) hydraulic geometry equations for predicting stream width and depthModel performance varies by stream orders and geographical regions, demonstrating the utility of multi‐model machine‐learning approachesThe STREAM‐geo data set provides predictions of river width, depth, width‐to‐depth ratio, and river area for the NHDPlus stream reaches [ABSTRACT FROM AUTHOR]

Accurate hydrologic modeling is vital to characterizing how the terrestrial water cycle responds to climate change. Pure deep learning (DL) models have been shown to outperform process-based ones while remaining difficult to interpret. More recently, differentiable physics-informed machine learning models with a physical backbone can systematically integrate physical equations and DL, predicting untrained variables and processes with high performance. However, it is unclear if such models are competitive for global-scale applications with a simple backbone. Therefore, we use – for the first time at this scale – differentiable hydrologic models (full name δ HBV-globe1.0-hydroDL, shortened to δ HBV here) to simulate the rainfall–runoff processes for 3753 basins around the world. Moreover, we compare the δ HBV models to a purely data-driven long short-term memory (LSTM) model to examine their strengths and limitations. Both LSTM and the δ HBV models provide competitive daily hydrologic simulation capabilities in global basins, with median Kling–Gupta efficiency values close to or higher than 0.7 (and 0.78 with LSTM for a subset of 1675 basins with long-term discharge records), significantly outperforming traditional models. Moreover, regionalized differentiable models demonstrated stronger spatial generalization ability (median KGE 0.64) than a traditional parameter regionalization approach (median KGE 0.46) and even LSTM for ungauged region tests across continents. Nevertheless, relative to LSTM, the differentiable model was hampered by structural deficiencies for cold or polar regions, highly arid regions, and basins with significant human impacts. This study also sets the benchmark for hydrologic estimates around the world and builds a foundation for improving global hydrologic simulations. [ABSTRACT FROM AUTHOR]

Manning's roughness coefficient, n, is used to describe channel roughness, and is a widely sought‐after key parameter for estimating and predicting flood propagation. Due to its control of flow velocity and shear stress, n is critical for modeling timing of floods and pollutants, aquatic ecosystem health, infrastructural safety, and so on. While alternative formulations exist, open‐channel n is typically regarded as temporally constant, determined from lookup tables or calibration, and its spatiotemporal variability was never examined holistically at large scales. Here, we developed and analyzed a continental‐scale n dataset (along with alternative formulations) calculated from observed velocity, slope, and hydraulic radius in 200,000 surveys conducted over 5,000 U.S. sites. These large, diverse observations allowed training of a Random Forest (RF) model capable of predicting n (or alternative parameters) at high accuracy (Nash Sutcliffe model efficiency >0.7) in space and time. We show that predictable time variability explains a large fraction (∼35%) of n variance compared to spatial variability (50%). While exceptions abound, n is generally lower and more stable under higher streamflow conditions. Other factorial influences on n including land cover, sinuosity, and particle sizes largely agree with conventional intuition. Accounting for temporal variability in n could lead to substantially larger (45% at the median site) estimated flow velocities under high‐flow conditions or lower (44%) velocities under low‐flow conditions. Habitual exclusion of n temporal dynamics means flood peaks could arrive days before model‐predicted flood waves, and peak magnitude estimation might also be erroneous. We therefore offer a model of great practical utility. Plain Language Summary: Stream channel roughness is a critical variable for many river‐related applications including modeling of flood inundation extent, pollutant transport, stormwater management, aquatic ecosystem health, infrastructural safety, and so on, and is traditionally assumed as being constant over time. Here we estimate channel roughness using in‐stream measurements from thousands of sites across the United States and show that its temporal dependence can be substantial. Our machine learning model can serve as a valuable and state‐of‐the‐art prediction of roughness, providing great practical value and a holistic view of the spatiotemporal variability of roughness. Moreover, the longstanding exclusion of temporal dynamics means that flood peaks could arrive days before model‐predicted flood waves, and peak magnitude estimation might also be inaccurate. Raising awareness of this issue can advance our understanding of channel flows, improve the accuracy of modeling, and save lives. Key Points: We developed a continental‐scale dataset of Manning's channel roughness values and trained accurate random forest models to predict themPredictable time variability explains a large fraction (∼35%) of variance in Manning's roughness compared to spatial variability (50%)Ignoring temporal dynamics means flood peaks could arrive days before predicted, and peak magnitude estimation might also be erroneous [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Predicting the response of hydrologic systems to modified driving forces beyond patterns that have occurred in the past is of high importance for estimating climate change impacts or the effect of management measures. This kind of prediction requires a model, but the impossibility of testing such predictions against observed data makes it difficult to estimate their reliability. Metamorphic testing offers a methodology for assessing models beyond validation with real data. It consists of defining input changes for which the expected responses are assumed to be known, at least qualitatively, and testing model behavior for consistency with these expectations. To increase the gain of information and reduce the subjectivity of this approach, we extend this methodology to a multi-model approach and include a sensitivity analysis of the predictions to training or calibration options. This allows us to quantitatively analyze differences in predictions between different model structures and calibration options in addition to the qualitative test of the expectations. In our case study, we apply this approach to selected conceptual and machine learning hydrological models calibrated for basins from the CAMELS data set. Our results confirm the superiority of the machine learning models over the conceptual hydrologic models regarding the quality of fit during calibration and validation periods. However, we also find that the response of machine learning models to modified inputs can deviate from the expectations and the magnitude, and even the sign of the response can depend on the training data. In addition, even in cases in which all models passed the metamorphic test, there are cases in which the quantitative response is different for different model structures. This demonstrates the importance of this kind of testing beyond and in addition to the usual calibration–validation analysis to identify potential problems and stimulate the development of improved models. [ABSTRACT FROM AUTHOR]

Transportation corridors constructed using through- and side-cuts are susceptible to hazardous slope failures, potentially causing infrastructure damage, operational suspensions and loss of life. To monitor the stability of known geohazards at the local scale, geotechnical investigation of each slope is typically performed to calculate a factor of safety. In many corridors, however, this method is labour-intensive due to the quantity of geohazards and statistical methods are instead used to identify hazardous sections. This paper introduces a new slope failure hazard assessment technique, utilising susceptibility mapping of geospatial information and computer vision-based analysis of right-of-way videos recorded by railroad track inspection vehicles, applied to a section of railroad track near Harrisburg, Pennsylvania. Combining these results, an enhanced relative hazard assessment algorithm was formulated. Using the developed framework, geohazards of primary concern were determined which should be prioritised for future geotechnical investigation and remediation efforts. [ABSTRACT FROM AUTHOR]