Alison Appling

Chaopeng Shen, Alison P. Appling, Pierre Gentine et al.

Process-Based Modeling (PBM) and Machine Learning (ML) are often perceived as distinct paradigms in the geosciences. Here we present differentiable geoscientific modeling as a powerful pathway toward dissolving the perceived barrier between them and ushering in a paradigm shift. For decades, PBM offered benefits in interpretability and physical consistency but struggled to efficiently leverage large datasets. ML methods, especially deep networks, presented strong predictive skills yet lacked the ability to answer specific scientific questions. While various methods have been proposed for ML-physics integration, an important underlying theme -- differentiable modeling -- is not sufficiently recognized. Here we outline the concepts, applicability, and significance of differentiable geoscientific modeling (DG). "Differentiable" refers to accurately and efficiently calculating gradients with respect to model variables, critically enabling the learning of high-dimensional unknown relationships. DG refers to a range of methods connecting varying amounts of prior knowledge to neural networks and training them together, capturing a different scope than physics-guided machine learning and emphasizing first principles. Preliminary evidence suggests DG offers better interpretability and causality than ML, improved generalizability and extrapolation capability, and strong potential for knowledge discovery, while approaching the performance of purely data-driven ML. DG models require less training data while scaling favorably in performance and efficiency with increasing amounts of data. With DG, geoscientists may be better able to frame and investigate questions, test hypotheses, and discover unrecognized linkages.

Yingda Fan, Runlong Yu, Janet R. Barclay et al.

Water temperature can vary substantially even across short distances within the same sub-watershed. Accurate prediction of stream water temperature at fine spatial resolutions (i.e., fine scales, $\leq$ 1 km) enables precise interventions to maintain water quality and protect aquatic habitats. Although spatiotemporal models have made substantial progress in spatially coarse time series modeling, challenges persist in predicting at fine spatial scales due to the lack of data at that scale.To address the problem of insufficient fine-scale data, we propose a Multi-Scale Graph Learning (MSGL) method. This method employs a multi-task learning framework where coarse-scale graph learning, bolstered by larger datasets, simultaneously enhances fine-scale graph learning. Although existing multi-scale or multi-resolution methods integrate data from different spatial scales, they often overlook the spatial correspondences across graph structures at various scales. To address this, our MSGL introduces an additional learning task, cross-scale interpolation learning, which leverages the hydrological connectedness of stream locations across coarse- and fine-scale graphs to establish cross-scale connections, thereby enhancing overall model performance. Furthermore, we have broken free from the mindset that multi-scale learning is limited to synchronous training by proposing an Asynchronous Multi-Scale Graph Learning method (ASYNC-MSGL). Extensive experiments demonstrate the state-of-the-art performance of our method for anti-sparse downscaling of daily stream temperatures in the Delaware River Basin, USA, highlighting its potential utility for water resources monitoring and management.

Xiaowei Jia, Shengyu Chen, Yiqun Xie et al.

This paper proposes a new data-driven method for predicting water temperature in stream networks with reservoirs. The water flows released from reservoirs greatly affect the water temperature of downstream river segments. However, the information of released water flow is often not available for many reservoirs, which makes it difficult for data-driven models to capture the impact to downstream river segments. In this paper, we first build a state-aware graph model to represent the interactions amongst streams and reservoirs, and then propose a parallel learning structure to extract the reservoir release information and use it to improve the prediction. In particular, for reservoirs with no available release information, we mimic the water managers' release decision process through a pseudo-prospective learning method, which infers the release information from anticipated water temperature dynamics. For reservoirs with the release information, we leverage a physics-based model to simulate the water release temperature and transfer such information to guide the learning process for other reservoirs. The evaluation for the Delaware River Basin shows that the proposed method brings over 10\% accuracy improvement over existing data-driven models for stream temperature prediction when the release data is not available for any reservoirs. The performance is further improved after we incorporate the release data and physical simulations for a subset of reservoirs.

Shengyu Chen, Alison Appling, Samantha Oliver et al.

Accurate prediction of water temperature in streams is critical for monitoring and understanding biogeochemical and ecological processes in streams. Stream temperature is affected by weather patterns (such as solar radiation) and water flowing through the stream network. Additionally, stream temperature can be substantially affected by water releases from man-made reservoirs to downstream segments. In this paper, we propose a heterogeneous recurrent graph model to represent these interacting processes that underlie stream-reservoir networks and improve the prediction of water temperature in all river segments within a network. Because reservoir release data may be unavailable for certain reservoirs, we further develop a data assimilation mechanism to adjust the deep learning model states to correct for the prediction bias caused by reservoir releases. A well-trained temporal modeling component is needed in order to use adjusted states to improve future predictions. Hence, we also introduce a simulation-based pre-training strategy to enhance the model training. Our evaluation for the Delaware River Basin has demonstrated the superiority of our proposed method over multiple existing methods. We have extensively studied the effect of the data assimilation mechanism under different scenarios. Moreover, we show that the proposed method using the pre-training strategy can still produce good predictions even with limited training data.

Jared D. Willard, Jordan S. Read, Alison P. Appling et al.

Most environmental data come from a minority of well-monitored sites. An ongoing challenge in the environmental sciences is transferring knowledge from monitored sites to unmonitored sites. Here, we demonstrate a novel transfer learning framework that accurately predicts depth-specific temperature in unmonitored lakes (targets) by borrowing models from well-monitored lakes (sources). This method, Meta Transfer Learning (MTL), builds a meta-learning model to predict transfer performance from candidate source models to targets using lake attributes and candidates' past performance. We constructed source models at 145 well-monitored lakes using calibrated process-based modeling (PB) and a recently developed approach called process-guided deep learning (PGDL). We applied MTL to either PB or PGDL source models (PB-MTL or PGDL-MTL, respectively) to predict temperatures in 305 target lakes treated as unmonitored in the Upper Midwestern United States. We show significantly improved performance relative to the uncalibrated process-based General Lake Model, where the median RMSE for the target lakes is $2.52^{\circ}C$. PB-MTL yielded a median RMSE of $2.43^{\circ}C$; PGDL-MTL yielded $2.16^{\circ}C$; and a PGDL-MTL ensemble of nine sources per target yielded $1.88^{\circ}C$. For sparsely monitored target lakes, PGDL-MTL often outperformed PGDL models trained on the target lakes themselves. Differences in maximum depth between the source and target were consistently the most important predictors. Our approach readily scales to thousands of lakes in the Midwestern United States, demonstrating that MTL with meaningful predictor variables and high-quality source models is a promising approach for many kinds of unmonitored systems and environmental variables.

Xiaowei Jia, Beiyu Lin, Jacob Zwart et al.

Effective training of advanced ML models requires large amounts of labeled data, which is often scarce in scientific problems given the substantial human labor and material cost to collect labeled data. This poses a challenge on determining when and where we should deploy measuring instruments (e.g., in-situ sensors) to collect labeled data efficiently. This problem differs from traditional pool-based active learning settings in that the labeling decisions have to be made immediately after we observe the input data that come in a time series. In this paper, we develop a real-time active learning method that uses the spatial and temporal contextual information to select representative query samples in a reinforcement learning framework. To reduce the need for large training data, we further propose to transfer the policy learned from simulation data which is generated by existing physics-based models. We demonstrate the effectiveness of the proposed method by predicting streamflow and water temperature in the Delaware River Basin given a limited budget for collecting labeled data. We further study the spatial and temporal distribution of selected samples to verify the ability of this method in selecting informative samples over space and time.

Xiaowei Jia, Jacob Zwart, Jeffrey Sadler et al.

This paper proposes a physics-guided machine learning approach that combines advanced machine learning models and physics-based models to improve the prediction of water flow and temperature in river networks. We first build a recurrent graph network model to capture the interactions among multiple segments in the river network. Then we present a pre-training technique which transfers knowledge from physics-based models to initialize the machine learning model and learn the physics of streamflow and thermodynamics. We also propose a new loss function that balances the performance over different river segments. We demonstrate the effectiveness of the proposed method in predicting temperature and streamflow in a subset of the Delaware River Basin. In particular, we show that the proposed method brings a 33\%/14\% improvement over the state-of-the-art physics-based model and 24\%/14\% over traditional machine learning models (e.g., Long-Short Term Memory Neural Network) in temperature/streamflow prediction using very sparse (0.1\%) observation data for training. The proposed method has also been shown to produce better performance when generalized to different seasons or river segments with different streamflow ranges.

Arka Daw, R. Quinn Thomas, Cayelan C. Carey et al.

To simultaneously address the rising need of expressing uncertainties in deep learning models along with producing model outputs which are consistent with the known scientific knowledge, we propose a novel physics-guided architecture (PGA) of neural networks in the context of lake temperature modeling where the physical constraints are hard coded in the neural network architecture. This allows us to integrate such models with state of the art uncertainty estimation approaches such as Monte Carlo (MC) Dropout without sacrificing the physical consistency of our results. We demonstrate the effectiveness of our approach in ensuring better generalizability as well as physical consistency in MC estimates over data collected from Lake Mendota in Wisconsin and Falling Creek Reservoir in Virginia, even with limited training data. We further show that our MC estimates correctly match the distribution of ground-truth observations, thus making the PGA paradigm amenable to physically grounded uncertainty quantification.