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The loss of phosphorous (P) from the land to aquatic systems has polluted waters and threatened food production worldwide. Systematic trend analysis of P, a nonrenewable resource, has been challenging, primarily due to sparse and inconsistent historical data. Here, we leveraged intensive hydrometeorological data and the recent renaissance of deep learning approaches to fill data gaps and reconstruct temporal trends. We trained a multitask long short-term memory model for total P (TP) using data from 430 rivers across the contiguous United States (CONUS). Trend analysis of reconstructed daily records (1980–2019) shows widespread decline in concentrations, with declining, increasing, and insignificantly changing trends in 60%, 28%, and 12% of the rivers, respectively. Concentrations in urban rivers have declined the most despite rising urban population in the past decades; concentrations in agricultural rivers however have mostly increased, suggesting not-as-effective controls of nonpoint sources in agriculture lands compared to point sources in cities. TP loss, calculated as fluxes by multiplying concentration and discharge, however exhibited an overall increasing rate of 6.5% per decade at the CONUS scale over the past 40 y, largely due to increasing river discharge. Results highlight the challenge of reducing TP loss that is complicated by changing river discharge in a warming climate. 

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. 

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. 

Characterization of the accuracy of the pressure reconstruction methods is of critical importance in understanding their capabilities and limitations. This paper reports for the first time a comprehensive theoretical analysis, numerical simulation and experimental validation of the error propagation characteristics for the omni-directional integration method, which has been used for pressure reconstruction from the PIV measured pressure gradient. The analysis shows that the omni-directional integration provides an effective mechanism in reducing the sensitivity of the reconstructed pressure to the random noise imbedded in the measured pressure gradient. Both the numerical and experimental validation results show that the omni-directional integration methods, especially the rotating parallel ray method, have better performance in data accuracy than the conventional Poisson equation approach in reconstructing pressure from noise embedded experimental data. 

Abstract Quantification of velocity and pressure fields over streambeds is important for predicting sediment mobility, benthic and hyporheic habitat qualities, and hyporheic exchange. Here, we report the first experimental investigation of reconstructed water surface elevations and three‐dimensional time‐averaged velocity and pressure fields quantified with non‐invasive image techniques for a three‐dimensional free surface flow around a barely submerged vertical cylinder over a plane bed of coarse granular sediment in a full‐scale flume experiment. Stereo particle image velocimetry coupled with a refractive index‐matched fluid measured velocity data at multiple closely‐spaced parallel and aligned planes. The time‐averaged pressure field was reconstructed using the Rotating Parallel Ray Omni‐Directional integration method to integrate the pressure gradient terms obtained by the balance of all the Reynolds‐Averaged Navier‐Stokes equation terms, which were evaluated with stereo particle image velocimetry. The detailed pressure field allows deriving the water surface profile deformed by the cylinder and hyporheic flows induced by the cylinder.