Chaopeng Shen

Dapeng Feng, Jiangtao Liu, Kathryn Lawson et al.

Predictions of hydrologic variables across the entire water cycle have significant value for water resource management as well as downstream applications such as ecosystem and water quality modeling. Recently, purely data-driven deep learning models like long short-term memory (LSTM) showed seemingly-insurmountable performance in modeling rainfall-runoff and other geoscientific variables, yet they cannot predict untrained physical variables and remain challenging to interpret. Here we show that differentiable, learnable, process-based models (called δ models here) can approach the performance level of LSTM for the intensively-observed variable (streamflow) with regionalized parameterization. We use a simple hydrologic model HBV as the backbone and use embedded neural networks, which can only be trained in a differentiable programming framework, to parameterize, enhance, or replace the process-based model modules. Without using an ensemble or post-processor, δ models can obtain a median Nash Sutcliffe efficiency of 0.732 for 671 basins across the USA for the Daymet forcing dataset, compared to 0.748 from a state-of-the-art LSTM model with the same setup. For another forcing dataset, the difference is even smaller: 0.715 vs. 0.722. Meanwhile, the resulting learnable process-based models can output a full set of untrained variables, e.g., soil and groundwater storage, snowpack, evapotranspiration, and baseflow, and later be constrained by their observations. Both simulated evapotranspiration and fraction of discharge from baseflow agreed decently with alternative estimates. The general framework can work with models with various process complexity and opens up the path for learning physics from big data.

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.

Jiangtao Liu, Yuchen Bian, Chaopeng Shen

For a number of years since its introduction to hydrology, recurrent neural networks like long short-term memory (LSTM) have proven remarkably difficult to surpass in terms of daily hydrograph metrics on known, comparable benchmarks. Outside of hydrology, Transformers have now become the model of choice for sequential prediction tasks, making it a curious architecture to investigate. Here, we first show that a vanilla Transformer architecture is not competitive against LSTM on the widely benchmarked CAMELS dataset, and lagged especially for the high-flow metrics due to short-term processes. However, a recurrence-free variant of Transformer can obtain mixed comparisons with LSTM, producing the same Kling-Gupta efficiency coefficient (KGE), along with other metrics. The lack of advantages for the Transformer is linked to the Markovian nature of the hydrologic prediction problem. Similar to LSTM, the Transformer can also merge multiple forcing dataset to improve model performance. While the Transformer results are not higher than current state-of-the-art, we still learned some valuable lessons: (1) the vanilla Transformer architecture is not suitable for hydrologic modeling; (2) the proposed recurrence-free modification can improve Transformer performance so future work can continue to test more of such modifications; and (3) the prediction limits on the dataset should be close to the current state-of-the-art model. As a non-recurrent model, the Transformer may bear scale advantages for learning from bigger datasets and storing knowledge. This work serves as a reference point for future modifications of the model.

Savinay Nagendra, Chaopeng Shen, Daniel Kifer

The purpose of binary segmentation models is to determine which pixels belong to an object of interest (e.g., which pixels in an image are part of roads). The models assign a logit score (i.e., probability) to each pixel and these are converted into predictions by thresholding (i.e., each pixel with logit score $\geq τ$ is predicted to be part of a road). However, a common phenomenon in current and former state-of-the-art segmentation models is spatial bias -- in some patches, the logit scores are consistently biased upwards and in others they are consistently biased downwards. These biases cause false positives and false negatives in the final predictions. In this paper, we propose PatchRefineNet (PRN), a small network that sits on top of a base segmentation model and learns to correct its patch-specific biases. Across a wide variety of base models, PRN consistently helps them improve mIoU by 2-3\%. One of the key ideas behind PRN is the addition of a novel supervision signal during training. Given the logit scores produced by the base segmentation model, each pixel is given a pseudo-label that is obtained by optimally thresholding the logit scores in each image patch. Incorporating these pseudo-labels into the loss function of PRN helps correct systematic biases and reduce false positives/negatives. Although we mainly focus on binary segmentation, we also show how PRN can be extended to saliency detection and few-shot segmentation. We also discuss how the ideas can be extended to multiclass segmentation.

Xiaofeng Liu, Yalan Song, Chaopeng Shen

River bathymetry is critical for many aspects of water resources management. We propose and demonstrate a bathymetry inversion method using a deep-learning-based surrogate for shallow water equations solvers. The surrogate uses the convolutional autoencoder with a shared-encoder, separate-decoder architecture. It encodes the input bathymetry and decodes to separate outputs for flow-field variables. A gradient-based optimizer is used to perform bathymetry inversion with the trained surrogate. Two physically-based constraints on both bed elevation value and slope have to be added as inversion loss regularizations to obtain usable inversion results. Using the "L-curve" criterion, a heuristic approach was proposed to determine the regularization parameters. Both the surrogate model and the inversion algorithm show good performance. We found the bathymetry inversion process has two distinctive stages, which resembles the sculptural process of initial broad-brush calving and final detailing. The inversion loss due to flow prediction error reaches its minimum in the first stage and remains almost constant afterward. The bed elevation value and slope regularizations play the dominant role in the second stage in selecting the most probable solution. We also found the surrogate architecture (whether with both velocity and water surface elevation or velocity only as outputs) does not show significant impact on inversion result.

Shuyu Y Chang, Zahra Ghahremani, Laura Manuel et al.

Hydraulic geometry parameters describing river hydrogeomorphic 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 the limitations of these approaches. In the present study, we have moved beyond these traditional power-law relationships for river geometry, 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 dataset (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 0.57 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 dataset, 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 rivers and streams across the contiguous US.

Savinay Nagendra, Chaopeng Shen, Daniel Kifer

Landslides are a recurring, widespread hazard. Preparation and mitigation efforts can be aided by a high-quality, large-scale dataset that covers global at-risk areas. Such a dataset currently does not exist and is impossible to construct manually. Recent automated efforts focus on deep learning models for landslide segmentation (pixel labeling) from satellite imagery. However, it is also important to characterize the uncertainty or confidence levels of such segmentations. Accurate and robust uncertainty estimates can enable low-cost (in terms of manual labor) oversight of auto-generated landslide databases to resolve errors, identify hard negative examples, and increase the size of labeled training data. In this paper, we evaluate several methods for assessing pixel-level uncertainty of the segmentation. Three methods that do not require architectural changes were compared, including Pre-Threshold activations, Monte-Carlo Dropout and Test-Time Augmentation -- a method that measures the robustness of predictions in the face of data augmentation. Experimentally, the quality of the latter method was consistently higher than the others across a variety of models and metrics in our dataset.

Kamlesh Sawadekar, Seth McGinnis, Peijun Li et al.

Systematic biases in Global Circulation Model (GCM) outputs limit their direct applicability in regional planning, necessitating bias correction. Correcting precipitation is particularly challenging due to its non-Gaussian distribution, intermittent nature, and non-linear extremes. However, traditional statistical methods cannot learn from big data and easily address systematic biases in the GCMs, and while machine learning does provide this flexibility, their black-box type functionality hinders us from understanding these biases completely which also further prevents generalization across different GCMs and locations, especially for precipitation. In this study, we propose a differentiable bias adjustment framework called δCLIMBA (or dCLIMBA), that learns a spatiotemporally adaptive parametric bias adjustment procedure between historical CMIP6 model outputs and reference reanalysis datasets (Livneh). Results demonstrate that the proposed method accurately corrects both the magnitude and distribution of extreme storm events, with particularly strong performance in capturing extremes. The quantile distribution of precipitation is well reproduced across diverse U.S. cities, and spatial patterns perform comparably to the widely used LOCA2 statistical downscaling technique. In addition, the framework showed future trend preservation unlike pure quantile based methods and LOCA2; and results from bias correction over unseen regions showed that the marginal biases were attenuated. This work presents a modular, computationally efficient and extensible bias correction approach that is physically informed, scalable, and compatible with both historical and future applications. Its flexibility makes it suitable for integration into Earth system post-processing pipelines and impact workflows.

Savinay Nagendra, Kashif Rashid, Chaopeng Shen et al.

Few-shot segmentation is the problem of learning to identify specific types of objects (e.g., airplanes) in images from a small set of labeled reference images. The current state of the art is driven by resource-intensive construction of models for every new domain-specific application. Such models must be trained on enormous labeled datasets of unrelated objects (e.g., cars, trains, animals) so that their ``knowledge'' can be transferred to new types of objects. In this paper, we show how to leverage existing vision foundation models (VFMs) to reduce the incremental cost of creating few-shot segmentation models for new domains. Specifically, we introduce SAMIC, a small network that learns how to prompt VFMs in order to segment new types of objects in domain-specific applications. SAMIC enables any task to be approached as a few-shot learning problem. At 2.6 million parameters, it is 94% smaller than the leading models (e.g., having ResNet 101 backbone with 45+ million parameters). Even using 1/5th of the training data provided by one-shot benchmarks, SAMIC is competitive with, or sets the state of the art, on a variety of few-shot and semantic segmentation datasets including COCO-$20^i$, Pascal-$5^i$, PerSeg, FSS-1000, and NWPU VHR-10.

Nicholas Kraabel, Jiangtao Liu, Yuchen Bian et al.

Stewarding natural resources, mitigating floods, droughts, wildfires, and landslides, and meeting growing demands require models that can predict climate-driven land-surface responses and human feedback with high accuracy. Traditional impact models, whether process-based, statistical, or machine learning, struggle with spatial generalization due to limited observations and concept drift. Recently proposed vision foundation models trained on satellite imagery demand massive compute and are ill-suited for dynamic land-surface prediction. We introduce StefaLand, a generative spatiotemporal earth foundation model centered on landscape interactions. StefaLand improves predictions on four tasks and five datasets: streamflow, soil moisture, and soil composition, compared to prior state-of-the-art. Results highlight its ability to generalize across diverse, data-scarce regions and support broad land-surface applications. The model builds on a masked autoencoder backbone that learns deep joint representations of landscape attributes, with a location-aware architecture fusing static and time-series inputs, attribute-based representations that drastically reduce compute, and residual fine-tuning adapters that enhance transfer. While inspired by prior methods, their alignment with geoscience and integration in one model enables robust performance on dynamic land-surface tasks. StefaLand can be pretrained and finetuned on academic compute yet outperforms state-of-the-art baselines and even fine-tuned vision foundation models. To our knowledge, this is the first geoscience land-surface foundation model that demonstrably improves dynamic land-surface interaction predictions and supports diverse downstream applications.

Da Fan, David John Gagne, Steven J. Greybush et al.

This study evaluated the probability and uncertainty forecasts of five recently proposed Bayesian deep learning methods relative to a deterministic residual neural network (ResNet) baseline for 0-1 h convective initiation (CI) nowcasting using GOES-16 satellite infrared observations. Uncertainty was assessed by how well probabilistic forecasts were calibrated and how well uncertainty separated forecasts with large and small errors. Most of the Bayesian deep learning methods produced probabilistic forecasts that outperformed the deterministic ResNet, with one, the initial-weights ensemble + Monte Carlo (MC) dropout, an ensemble of deterministic ResNets with different initial weights to start training and dropout activated during inference, producing the most skillful and well-calibrated forecasts. The initial-weights ensemble + MC dropout benefited from generating multiple solutions that more thoroughly sampled the hypothesis space. The Bayesian ResNet ensemble was the only one that performed worse than the deterministic ResNet at longer lead times, likely due to the challenge of optimizing a larger number of parameters. To address this issue, the Bayesian-MOPED (MOdel Priors with Empirical Bayes using Deep neural network) ResNet ensemble was adopted, and it enhanced forecast skill by constraining the hypothesis search near the deterministic ResNet hypothesis. All Bayesian methods demonstrated well-calibrated uncertainty and effectively separated cases with large and small errors. In case studies, the initial-weights ensemble + MC dropout demonstrated better forecast skill than the Bayesian-MOPED ensemble and the deterministic ResNet on selected CI events in clear-sky regions. However, the initial-weights ensemble + MC dropout exhibited poorer generalization in clear-sky and anvil cloud regions without CI occurrence compared to the deterministic ResNet and Bayesian-MOPED ensemble.

Haoyu Ji, Yalan Song, Tadd Bindas et al.

To track rapid changes within our water sector, Global Water Models (GWMs) need to realistically represent hydrologic systems' response patterns - such as baseflow fraction - but are hindered by their limited ability to learn from data. Here we introduce a high-resolution physics-embedded big-data-trained model as a breakthrough in reliably capturing characteristic hydrologic response patterns ('signatures') and their shifts. By realistically representing the long-term water balance, the model revealed widespread shifts - up to ~20% over 20 years - in fundamental green-blue-water partitioning and baseflow ratios worldwide. Shifts in these response patterns, previously considered static, contributed to increasing flood risks in northern mid-latitudes, heightening water supply stresses in southern subtropical regions, and declining freshwater inputs to many European estuaries, all with ecological implications. With more accurate simulations at monthly and daily scales than current operational systems, this next-generation model resolves large, nonlinear seasonal runoff responses to rainfall ('elasticity') and streamflow flashiness in semi-arid and arid regions. These metrics highlight regions with management challenges due to large water supply variability and high climate sensitivity, but also provide tools to forecast seasonal water availability. This capability newly enables global-scale models to deliver reliable and locally relevant insights for water management.

Amirmoez Jamaat, Yalan Song, Farshid Rahmani et al.

Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations as inputs (called "data integration") or variational DA has shown success in improving forecasts. However, it is unclear which methods are performant or optimal for physics-informed machine learning ("differentiable") models, which represent only a small amount of physically-meaningful states while using deep networks to supply parameters or missing processes. Here we developed variational DA methods for differentiable models, including optimizing adjusters for just precipitation data, just model internal hydrological states, or both. Our results demonstrated that differentiable streamflow models using the CAMELS dataset can benefit strongly and equivalently from variational DA as LSTM, with one-day lead time median Nash-Sutcliffe efficiency (NSE) elevated from 0.75 to 0.82. The resulting forecast matched or outperformed LSTM with DA in the eastern, northwestern, and central Great Plains regions of the conterminous United States. Both precipitation and state adjusters were needed to achieve these results, with the latter being substantially more effective on its own, and the former adding moderate benefits for high flows. Our DA framework does not need systematic training data and could serve as a practical DA scheme for whole river networks.

Yalan Song, Chaopeng Shen, Xiaofeng Liu

Shallow water equations are the foundation of most models for flooding and river hydraulics analysis. These physics-based models are usually expensive and slow to run, thus not suitable for real-time prediction or parameter inversion. An attractive alternative is surrogate model. This work introduces an efficient, accurate, and flexible surrogate model, NN-p2p, based on deep learning and it can make point-to-point predictions on unstructured or irregular meshes. The new method was evaluated and compared against existing methods based on convolutional neural networks (CNNs), which can only make image-to-image predictions on structured or regular meshes. In NN-p2p, the input includes both spatial coordinates and boundary features that can describe the geometry of hydraulic structures, such as bridge piers. All surrogate models perform well in predicting flow around different types of piers in the training domain. However, only NN-p2p works well when spatial extrapolation is performed. The limitations of CNN-based methods are rooted in their raster-image nature which cannot capture boundary geometry and flow features exactly, which are of paramount importance to fluid dynamics. NN-p2p also has good performance in predicting flow around piers unseen by the neural network. The NN-p2p model also respects conservation laws more strictly. The application of the proposed surrogate model was demonstrated by calculating the drag coefficient $C_D$ for piers and a new linear relationship between $C_D$ and the logarithmic transformation of pier's length/width ratio was discovered.

Wenyu Ouyang, Kathryn Lawson, Dapeng Feng et al.

A large fraction of major waterways have dams influencing streamflow, which must be accounted for in large-scale hydrologic modeling. However, daily streamflow prediction for basins with dams is challenging for various modeling approaches, especially at large scales. Here we examined which types of dammed basins could be well represented by long short-term memory (LSTM) models using readily-available information, and delineated the remaining challenges. We analyzed data from 3557 basins (83% dammed) over the contiguous United States and noted strong impacts of reservoir purposes, degree of regulation (dor), and diversion on streamflow modeling. While a model trained on a widely-used reference-basin dataset performed poorly for non-reference basins, the model trained on the whole dataset presented a median Nash-Sutcliffe efficiency coefficient (NSE) of 0.74. The zero-dor, small-dor (with storage of approximately a month of average streamflow or less), and large-dor basins were found to have distinct behaviors, so migrating models between categories yielded catastrophic results, which means we must not treat small-dor basins as reference ones. However, training with pooled data from different sets yielded optimal median NSEs of 0.72, 0.79, and 0.64 for these respective groups, noticeably stronger than existing models. These results support a coherent modeling strategy where smaller dams (storing about a month of average streamflow or less) are modeled implicitly as part of basin rainfall-runoff processes; then, large-dor reservoirs of certain types can be represented explicitly. However, dammed basins must be present in the training dataset. Future work should examine separate modeling of large reservoirs for fire protection and irrigation, hydroelectric power generation, and flood control.

Kuai Fang, Daniel Kifer, Kathryn Lawson et al.

When fitting statistical models to variables in geoscientific disciplines such as hydrology, it is a customary practice to regionalize - to divide a large spatial domain into multiple regions and study each region separately - instead of fitting a single model on the entire data (also known as unification). Traditional wisdom in these fields suggests that models built for each region separately will have higher performance because of homogeneity within each region. However, by partitioning the training data, each model has access to fewer data points and cannot learn from commonalities between regions. Here, through two hydrologic examples (soil moisture and streamflow), we argue that unification can often significantly outperform regionalization in the era of big data and deep learning (DL). Common DL architectures, even without bespoke customization, can automatically build models that benefit from regional commonality while accurately learning region-specific differences. We highlight an effect we call data synergy, where the results of the DL models improved when data were pooled together from characteristically different regions. In fact, the performance of the DL models benefited from more diverse rather than more homogeneous training data. We hypothesize that DL models automatically adjust their internal representations to identify commonalities while also providing sufficient discriminatory information to the model. The results here advocate for pooling together larger datasets, and suggest the academic community should place greater emphasis on data sharing and compilation.

Dapeng Feng, Kathryn Lawson, Chaopeng Shen

While long short-term memory (LSTM) models have demonstrated stellar performance with streamflow predictions, there are major risks in applying these models in contiguous regions with no gauges, or predictions in ungauged regions (PUR) problems. However, softer data such as the flow duration curve (FDC) may be already available from nearby stations, or may become available. Here we demonstrate that sparse FDC data can be migrated and assimilated by an LSTM-based network, via an encoder. A stringent region-based holdout test showed a median Kling-Gupta efficiency (KGE) of 0.62 for a US dataset, substantially higher than previous state-of-the-art global-scale ungauged basin tests. The baseline model without FDC was already competitive (median KGE 0.56), but integrating FDCs had substantial value. Because of the inaccurate representation of inputs, the baseline models might sometimes produce catastrophic results. However, model generalizability was further meaningfully improved by compiling an ensemble based on models with different input selections.

Wen-Ping Tsai, Dapeng Feng, Ming Pan et al.

The behaviors and skills of models in many geosciences (e.g., hydrology and ecosystem sciences) strongly depend on spatially-varying parameters that need calibration. A well-calibrated model can reasonably propagate information from observations to unobserved variables via model physics, but traditional calibration is highly inefficient and results in non-unique solutions. Here we propose a novel differentiable parameter learning (dPL) framework that efficiently learns a global mapping between inputs (and optionally responses) and parameters. Crucially, dPL exhibits beneficial scaling curves not previously demonstrated to geoscientists: as training data increases, dPL achieves better performance, more physical coherence, and better generalizability (across space and uncalibrated variables), all with orders-of-magnitude lower computational cost. We demonstrate examples that learned from soil moisture and streamflow, where dPL drastically outperformed existing evolutionary and regionalization methods, or required only ~12.5% of the training data to achieve similar performance. The generic scheme promotes the integration of deep learning and process-based models, without mandating reimplementation.

Dapeng Feng, Kuai Fang, Chaopeng Shen

Recent observations with varied schedules and types (moving average, snapshot, or regularly spaced) can help to improve streamflow forecasts, but it is challenging to integrate them effectively. Based on a long short-term memory (LSTM) streamflow model, we tested multiple versions of a flexible procedure we call data integration (DI) to leverage recent discharge measurements to improve forecasts. DI accepts lagged inputs either directly or through a convolutional neural network (CNN) unit. DI ubiquitously elevated streamflow forecast performance to unseen levels, reaching a record continental-scale median Nash-Sutcliffe Efficiency coefficient value of 0.86. Integrating moving-average discharge, discharge from the last few days, or even average discharge from the previous calendar month could all improve daily forecasts. Directly using lagged observations as inputs was comparable in performance to using the CNN unit. Importantly, we obtained valuable insights regarding hydrologic processes impacting LSTM and DI performance. Before applying DI, the base LSTM model worked well in mountainous or snow-dominated regions, but less well in regions with low discharge volumes (due to either low precipitation or high precipitation-energy synchronicity) and large inter-annual storage variability. DI was most beneficial in regions with high flow autocorrelation: it greatly reduced baseflow bias in groundwater-dominated western basins and also improved peak prediction for basins with dynamical surface water storage, such as the Prairie Potholes or Great Lakes regions. However, even DI cannot elevate high-aridity basins with one-day flash peaks. Despite this limitation, there is much promise for a deep-learning-based forecast paradigm due to its performance, automation, efficiency, and flexibility.

Kuai Fang, Chaopeng Shen, Daniel Kifer

Soil moisture is an important variable that determines floods, vegetation health, agriculture productivity, and land surface feedbacks to the atmosphere, etc. Accurately modeling soil moisture has important implications in both weather and climate models. The recently available satellite-based observations give us a unique opportunity to build data-driven models to predict soil moisture instead of using land surface models, but previously there was no uncertainty estimate. We tested Monte Carlo dropout (MCD) with an aleatoric term for our long short-term memory models for this problem, and asked if the uncertainty terms behave as they were argued to. We show that the method successfully captures the predictive error after tuning a hyperparameter on a representative training dataset. We show the MCD uncertainty estimate, as previously argued, does detect dissimilarity.

Chaopeng Shen

Deep learning (DL), a new-generation of artificial neural network research, has transformed industries, daily lives and various scientific disciplines in recent years. DL represents significant progress in the ability of neural networks to automatically engineer problem-relevant features and capture highly complex data distributions. I argue that DL can help address several major new and old challenges facing research in water sciences such as inter-disciplinarity, data discoverability, hydrologic scaling, equifinality, and needs for parameter regionalization. This review paper is intended to provide water resources scientists and hydrologists in particular with a simple technical overview, trans-disciplinary progress update, and a source of inspiration about the relevance of DL to water. The review reveals that various physical and geoscientific disciplines have utilized DL to address data challenges, improve efficiency, and gain scientific insights. DL is especially suited for information extraction from image-like data and sequential data. Techniques and experiences presented in other disciplines are of high relevance to water research. Meanwhile, less noticed is that DL may also serve as a scientific exploratory tool. A new area termed 'AI neuroscience,' where scientists interpret the decision process of deep networks and derive insights, has been born. This budding sub-discipline has demonstrated methods including correlation-based analysis, inversion of network-extracted features, reduced-order approximations by interpretable models, and attribution of network decisions to inputs. Moreover, DL can also use data to condition neurons that mimic problem-specific fundamental organizing units, thus revealing emergent behaviors of these units. Vast opportunities exist for DL to propel advances in water sciences.

Kuai Fang, Chaopeng Shen, Daniel Kifer et al.

The Soil Moisture Active Passive (SMAP) mission has delivered valuable sensing of surface soil moisture since 2015. However, it has a short time span and irregular revisit schedule. Utilizing a state-of-the-art time-series deep learning neural network, Long Short-Term Memory (LSTM), we created a system that predicts SMAP level-3 soil moisture data with atmospheric forcing, model-simulated moisture, and static physiographic attributes as inputs. The system removes most of the bias with model simulations and improves predicted moisture climatology, achieving small test root-mean-squared error (<0.035) and high correlation coefficient >0.87 for over 75\% of Continental United States, including the forested Southeast. As the first application of LSTM in hydrology, we show the proposed network avoids overfitting and is robust for both temporal and spatial extrapolation tests. LSTM generalizes well across regions with distinct climates and physiography. With high fidelity to SMAP, LSTM shows great potential for hindcasting, data assimilation, and weather forecasting.