Uncertainty reduction in watershed water quality (WWQ) modeling remains a major challenge. One important reason is the lack of sufficient available water quality observations because traditional laboratory analysis of water samples has high labor, financial and time costs. Low-cost high-frequency water quality data from in-situ sensors provide an opportunity to solve this problem. However, long-term sensing in complex natural environments usually suffers more significant errors. This study aimed to develop a novel method to utilize in-situ sensor data in WWQ modeling, namely, the Bayesian calibration using multisource observations (BCMSO), which can simultaneously assimilate laboratory-based observations and in-situ sensor data. Both synthetic and real-world cases of nitrate modeling were used to demonstrate the methodology, and the Soil and Water Assessment Tool was employed as the WWQ model. The results indicated that direct assimilation of sensor data using traditional Bayesian calibration generated obvious deviations in parameter inference and model simulation, which could consequently bias future predictions and affect management decision correctness. However, after proper treatment of errors in sensor data, the BCMSO method could extract meaningful information from sensor data and prevent negative impacts of errors. The modeling uncertainty was also greatly reduced. In the real-world case, with 1 yr of subhourly electrical conductivity sensor data incorporated, the modeling uncertainty of nitrate concentration and management cost of controlling nitrate pollution were reduced by 70%. The BCMSO method provides a flexible framework to accommodate nonconventional observations in environmental modeling and can be easily extended to other modeling fields.

This study develops a convolutional recurrent deep learning model to accurately predict fine-resolution spatiotemporal changes in grass coverage in arid regions. Applying the model to the Gobi Desert reveals that ecological flow regulation contributes to 61.8% of the total increase in grass cover (130.6 km(2)) in the study area (40,423 km(2)) over 2005-2015, nearly triple the contribution of local climate change (+23.0%). The transboundary hydrological impact (+32.4%) and interactions between drivers (-17.2%) are also significant. In an intermediate future climate change scenario, we found no statistically significant trend for the total grass-covered area due to the counteracting effects among different drivers. The study findings suggest that timely, adaptive and spatially heterogeneous ecological flow management is crucial for addressing grassland degradation in arid regions. This study provides a promising approach to land surface modeling under climate change and human disturbance and expands the existing understanding of the global greening process.

Differentiable modelling is an approach that flexibly integrates the learning capability of machine learning with the interpretability of process-based models. This Perspective highlights the potential of differentiable modelling to improve the representation of processes, parameter estimation, and predictive accuracy in the geosciences. 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.