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The imbalance in global streamflow gauge distribution and regional data scarcity, especially in large transboundary basins, challenge regional water resource management. Effectively utilizing these limited data to construct reliable models is of crucial practical importance. This study employs a transfer learning (TL) framework to simulate daily streamflow in the Dulong-Irrawaddy River Basin (DIRB), a less-studied transboundary basin shared by Myanmar, China, and India. Our results show that TL significantly improves streamflow predictions: the optimal TL model achieves an average Nash-Sutcliffe efficiency of 0.872, showing a marked improvement in the Hkamti sub-basin. Despite data scarcity, TL achieves a mean NSE of 0.817, surpassing the 0.655 of the process-based model MIKE SHE. Additionally, our study reveals the importance of source model selection in TL, as different parts of the flow are affected by the diversity and similarity of data in the source model. Deep learning models, particularly TL, exhibit complex sensitivities to meteorological inputs, more accurately capturing non-linear relationships among multiple variables than the process-based model. Integrated gradients (IG) analysis further illustrates TL’s ability to capture spatial heterogeneity in upstream and downstream sub-basins and its adeptness in characterizing different flow regimes. This study underscores the potential of TL in enhancing the understanding of hydrological processes in large-scale catchments and highlights its value for water resource management in transboundary basins under data scarcity.

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. 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. 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 Machine Learning models outperform regional (physiographic) hydraulic geometry equations for predicting stream width and depth Model performance varies by stream orders and geographical regions, demonstrating the utility of multi‐model machine‐learning approaches The STREAM‐geo data set provides predictions of river width, depth, width‐to‐depth ratio, and river area for the NHDPlus stream reaches

Dissolved oxygen (DO) reflects river metabolic pulses and is an essential water quality measure. Our capabilities of forecasting DO however remain elusive. Water quality data, specifically DO data here, often have large gaps and sparse areal and temporal coverage. Earth surface and hydrometeorology data, on the other hand, have become largely available. Here we ask: can a Long Short-Term Memory (LSTM) model learn about river DO dynamics from sparse DO and intensive (daily) hydrometeorology data? We used CAMELS-chem, a new data set with DO concentrations from 236 minimally disturbed watersheds across the U.S. The model generally learns the theory of DO solubility and captures its decreasing trend with increasing water temperature. It exhibits the potential of predicting DO in “chemically ungauged basins”, defined as basins without any measurements of DO and broadly water quality in general. The model however misses some DO peaks and troughs when in-stream biogeochemical processes become important. Surprisingly, the model does not perform better where more data are available. Instead, it performs better in basins with low variations of streamflow and DO, high runoff-ratio (>0.45), and winter precipitation peaks. Results here suggest that more data collections at DO peaks and troughs and in sparsely monitored areas are essential to overcome the issue of data scarcity, an outstanding challenge in the water quality community.

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. Utilizing the differentiability of the surrogate, a gradient‐based optimizer is used to perform bathymetry inversion. Two physically based constraints on the ranges of both bed elevation and slope have to be added as inversion loss regularizations to contract the solution space. Using the “L‐curve” criterion, a heuristic approach is proposed to determine the regularization parameters. Both the surrogate model and the inversion algorithm show good performance. The bathymetry inversion progresses in two distinctive stages, which resembles the sculptural process of initial broad‐brush calving and final fine detailing. The inversion loss due to flow prediction error and the two regularizations play dominant roles in the initial and final stages, respectively. The surrogate architecture (whether with both velocity and water surface elevation or velocity only as outputs) does not have significant impact on inversion result. The methodology proposed in this work, an example of differentiable parameter learning, can be similarly used in the inversion of other important distributed parameters such as roughness coefficient. Gradient‐based optimization is used to perform inversion with automatic differentiation enabled by the surrogate based on CNN autoencoderPhysically based regularizations on the ranges of bed elevation and slope are crucial for useable inversion resultsThe methodology works for both simple cases and complex real‐world cases Gradient‐based optimization is used to perform inversion with automatic differentiation enabled by the surrogate based on CNN autoencoder Physically based regularizations on the ranges of bed elevation and slope are crucial for useable inversion results The methodology works for both simple cases and complex real‐world cases

Floodplain lakes represent important aquatic ecosystems, and field‐based estimates of their water budgets are difficult to obtain, especially over multiple years. We examine the hydrological fluxes for an Amazon floodplain lake connected to the Solimões River using a process‐based hydrologic model. Water exchanges between the river and lake agree well with field estimates, including the timing of different hydrological phases. However, beyond available field data, modeling results show that the seven simulated years all differed from each other. These interannual differences were caused by the interplay between phases when water levels were rising with river‐water flowing into the lake (RWRI), versus rising with lake‐water flowing out to the river (RWLO). This exchange determines the river‐water content in the lake (CL). Maximum CLoccurred before river levels peaked because local catchment contributions can be sufficient to push lake‐water out to the river, even as river levels rise. Numerical experiments show that the seasonal distribution of local rainfall, local catchment size, and interannual variability in both climate and river stage can contribute to differing dynamics of CLin a floodplain lake. Their impacts vary among phases: river‐rise dominates the RWRI, whereas local hydrological processes dominate the RWLO and receding‐water phases. Intermediate‐to‐long‐term rainfall accumulation controls CLduring the RWLO phase, whereas annual precipitation accumulation is important for CLduring low water. Our model generalizes beyond limited available field studies and offers potential to better understand floodplain lakes in other areas and how regional versus local changes in climate may affect their hydrological dynamics. Each year of modeled water exchanges between the Solimões and a floodplain lake differed as the river stage interacted with the local runoffPerturbed runs show 10‐month rainfall accumulation and the rate of seasonal river rise as strong controls of river‐water contentClimate type, basin area, and interannual rainfall variability all have important but seasonally varying influences on river‐water content

Recently, rainfall‐runoff simulations in small headwater basins have been improved by methodological advances such as deep neural networks (NNs) and hybrid physics‐NN models—particularly, a genre called differentiable modeling that intermingles NNs with physics to learn relationships between variables. However, hydrologic routing simulations, necessary for simulating floods in stem rivers downstream of large heterogeneous basins, had not yet benefited from these advances and it was unclear if the routing process could be improved via coupled NNs. We present a novel differentiable routing method (δMC‐Juniata‐hydroDL2) that mimics the classical Muskingum‐Cunge routing model over a river network but embeds an NN to infer parameterizations for Manning's roughness (n) and channel geometries from raw reach‐scale attributes like catchment areas and sinuosity. The NN was trained solely on downstream hydrographs. Synthetic experiments show that while the channel geometry parameter was unidentifiable, ncan be identified with moderate precision. With real‐world data, the trained differentiable routing model produced more accurate long‐term routing results for both the training gage and untrained inner gages for larger subbasins (>2,000 km2) than either a machine learning model assuming homogeneity, or simply using the sum of runoff from subbasins. The nparameterization trained on short periods gave high performance in other periods, despite significant errors in runoff inputs. The learned npattern was consistent with literature expectations, demonstrating the framework's potential for knowledge discovery, but the absolute values can vary depending on training periods. The trained nparameterization can be coupled with traditional models to improve national‐scale hydrologic flood simulations. A novel differentiable routing model can learn effective river routing parameterization, recovering channel roughness in synthetic runsWith short periods of real training data, we can improve streamflow in large rivers compared to models not considering routingFor basins >2,000 km2, our framework outperformed deep learning models that assume homogeneity, despite bias in the runoff forcings A novel differentiable routing model can learn effective river routing parameterization, recovering channel roughness in synthetic runs With short periods of real training data, we can improve streamflow in large rivers compared to models not considering routing For basins >2,000 km2, our framework outperformed deep learning models that assume homogeneity, despite bias in the runoff forcings

Although deep learning models for stream temperature (Ts) have recently shown exceptional accuracy, they have limited interpretability and cannot output untrained variables. With hybrid differentiable models, neural networks (NNs) can be connected to physically based equations (called structural priors) to output intermediate variables such as water source fractions (specifying what portion of water is groundwater, subsurface, and surface flow). However, it is unclear if such outputs are physically meaningful when only limited physics is imposed, and if structural priors have enough impacts to be identifiable from data. Here, we tested four alternative structural priors describing basin‐scale water temperature memory and instream heat processes in a differentiable stream temperature model where NNs freely estimate the water source fractions. We evaluated models’ abilities to predict Tsand baseflow ratio. The four priors exhibited noticeably different behaviors in these two metrics and their tradeoffs, with some dominating others. Therefore, the better structural priors can be identified. Moreover, testing different priors yielded valuable insights: having a separate shallow subsurface flow component better matches observations, and a recency‐weighted averaging of past air temperature for calculating source water temperature resulted in better Tsand baseflow prediction than traditionally employed simple averaging. However, we also highlight the limitations when insufficient physical constraints are implemented: the internal variables (water source fractions) may not be adequately constrained by a single target variable (stream temperature) alone. To ensure the physical significance of the internal fluxes, one can either employ multivariate data for model selection, or include more physical processes in the priors. A new framework called differentiable modeling combines the benefits from neural networks (NNs) and process‐based models. This framework can learn from big data while the process‐based model components (called prior knowledge, or priors) are intended to output intermediate physical variables. However, do such priors matter, can we tell if one set of priors is better than another, and do the intermediate outputs represent the intended physical concepts? We explore these questions with a differentiable stream temperature model where the NN replaces the hydrologic component and estimates parameters pertaining to the stream temperature module. The strong optimizing capability of NNs allows us to avoid some complexities and attribute the differences in model outcomes to the assumed priors. Testing different priors thus yielded many important lessons, for example, the need for having a separate shallow groundwater “bucket,” the benefit of placing more importance on recent air temperature when estimating groundwater temperature, and the importance of describing in‐stream temperature. The results show lots of untapped potential with differentiable modeling and the data we have available. We can identify better structural priors (process equations) using differentiable models, circumventing intertwined parameter issuesConsidering a separate bucket for shallow subsurface water improves both stream temperature and baseflow simulationThe models selected by the multivariate evaluation produce physically meaningful estimates of water source fractions We can identify better structural priors (process equations) using differentiable models, circumventing intertwined parameter issues Considering a separate bucket for shallow subsurface water improves both stream temperature and baseflow simulation The models selected by the multivariate evaluation produce physically meaningful estimates of water source fractions

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 interdisciplinarity, 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, transdisciplinary 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 subdiscipline 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. Deep learning (DL) is transforming many scientific disciplines, but its adoption in hydrology is gradualDL can help tackle interdisciplinarity, data deluge, unrecognized linkages, and long‐standing challenges such as scaling and equifinalityThe new field of AI neuroscience opens up many opportunities for scientists to use DL as an exploratory tool for scientific advancement

Interannual changes in low, median, and high regimes of streamflow have important implications for flood control, irrigation, and ecologic and human health. The Gravity Recovery and Climate Experiment (GRACE) satellites record global terrestrial water storage anomalies (TWSA), providing an opportunity to observe, interpret, and potentially utilize the complex relationships between storage and full‐flow‐regime streamflow. Here we show that utilizable storage‐streamflow correlations exist throughout vastly different climates in the continental US (CONUS) across low‐ to high‐flow regimes. A panoramic framework, the storage‐streamflow correlation spectrum (SSCS), is proposed to examine macroscopic gradients in these relationships. SSCS helps form, corroborate or reject hypotheses about basin hydrologic behaviors. SSCS patterns vary greatly over CONUS with climate, land surface, and geologic conditions. Data mining analysis suggests that for catchments with hydrologic settings that favor storage over runoff, e.g., a large fraction of precipitation as snow, thick and highly‐permeable permeable soil, SSCS values tend to be high. Based on our results, we form the hypotheses that groundwater flow dominates streamflows in Southeastern CONUS and Great Plains, while thin soils in a belt along the Appalachian Plateau impose alimit on water storage. SSCS also suggests shallow water table caused by high‐bulk density soil and flat terrain induces rapid runoff in several regions. Our results highlight the importance of subsurface properties and groundwater flow in capturing flood and drought. We propose that SSCS can be used as a fundamental hydrologic signature to constrain models and to provide insights thatlead usto better understand hydrologic functioning. Water storage on land is the sum of surface water, soil moisture, and groundwater. Rainfall can partition into direct runoff and infiltration into the ground. The direction runoff part leaves no signal in water storage, while the part that infiltrates and exfiltrates does. By looking at the correlations between storage and streamflow and combining it with other information, we can infer a great deal about how a basin partitions and processes precipitation. With the GRACE satellites, which measure water storage on land, we now have the opportunity to observe, interpret and possibly utilize storage‐streamflow relationships. We propose a novel framework, the storage‐streamflow correlation spectrum (SSCS), to synthesize these relationships. SSCS patterns present important clues about hydrology, e.g., storage on the Appalachian Plateau is limited by thin soils, compacted soils in northern Ohio lead to shallow water table that limits storage, and northern Great Plains and Southeast Atlantic regions are groundwater‐dominated. SSCS provides a new observation dimension to understanding hydrology. In addition, it points out key dynamics for models to capture to predict streamflow accurately. Utilizable full‐flow‐regime streamflow‐storage correlations exist under diverse climates, but the patterns vary with environmental settingsSSCS provides novel observational dimensions that can corroborate or reject hypotheses about how hydrologic systems functionSSCS shows the importance of soil bulk density, soil thickness, water table depth, and groundwater flow in capturing floods and droughts

The Budyko hypothesis provides a first‐order estimate of water partitioning into runoff (Q) and evapotranspiration (E). Observations, however, often show significant departures from the Budyko curve; moreover, past improvements to Budyko curve tend to lose predictive power when migrated between regions or to small scales. Here to estimate departures from the Budyko curve, we use hydrologic signatures extracted from Gravity Recovery And Climate Experiment (GRACE) terrestrial water storage anomalies. The signatures include GRACE amplitude as a fraction of precipitation (A/P), interannual variability, and 1‐month lag autocorrelation. We created a group of linear models embodying two alternate hypotheses that departures can be predicted by (a) Taylor series expansion based on the deviation of physical characteristics (seasonality, snow fraction, and vegetation index) from reference conditions and (b) surrogate indicators covarying with E, e.g., A/P. These models are fitted using a mesoscale USA data set (HUC4) and then evaluated using world data sets and USA basins <1 ×105km2. The model with A/Pcould reduce error by 50% compared to Budyko itself. We found that seasonality and fraction of precipitation as snow account for a major portion of the predictive power of A/P, while the remainder is attributed to unexplained basin characteristics. When migrated to a global data set, type b models performed better than type a. This contrast in transferability is argued to be due to data set limitations and catchment coevolution. The GRACE‐based correction performs well for USA basins >1000 km2and, according to comparison with other global data sets, is suitable for data fusion purposes, with GRACE error as estimates of uncertainty. GRACE amplitude can predict departure of water partitioning from the Budyko curveGRACE‐based models have better transferability than physical‐factor‐based modelsOur global product is comparable to other ET products and can be useful in data fusion

The critically important at‐a‐station hydraulic geometry (AHG) relationships relate hydraulic variables (depth, width, or velocity) to discharge in power law form. The recently discovered at‐many‐stations hydraulic geometry (AMHG) states that AHG exponents and coefficients are strongly correlated, removing one parameter and lending AMHGs to remote sensing discharge estimation. Despite the excitement, there is an urgent need to clarify AMHG's geomorphological significance for different hydraulic variables. Using data from 57 rivers in the U.S. and perturbation experiments, we show that the width‐AMHG is weak, arising mainly from the mathematical construct involving the exponent in both the regressor and the regressand. In contrast, the depth‐AMHGs result from geomorphological coevolution. The similar‐time‐mean condition, as argued for in the literature, is sufficient but not necessary for rating curve convergence and in turn AMHG, for depth and velocity. The predictive accuracy of AMHGs, whose coefficient of determination is unit dependent, is similar to the flow percentile‐based downstream hydraulic geometry. The width‐AMHG is a weak relation arising mainly from the mathematical constructThe depth and velocity AMHGs arise from coevolution, with no need for the similar‐time‐mean conditionThe predictive power of unit‐dependent AMHG is similar to the traditional downstream hydraulic geometry

Predictions of hydrologic variables across the entire water cycle have significant value for water resources 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 δmodels 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's modules. Without using an ensemble or post‐processor, δmodels can obtain a median Nash‐Sutcliffe efficiency of 0.732 for 671 basins across the USA for the Daymet forcing data set, compared to 0.748 from a state‐of‐the‐art LSTM model with the same setup. For another forcing data set, the difference is even smaller: 0.715 versus 0.722. Meanwhile, the resulting learnable process‐based models can output a full set of untrained variables, for example, soil and groundwater storage, snowpack, evapotranspiration, and baseflow, and can 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. Recently, deep neural networks like long short‐term memory (LSTM) have received a lot of attention for producing high‐accuracy simulations in hydrology, but they do not respect physical laws and remain difficult to understand. However, what if you can have a model with similar accuracy, but with clarity about physical processes? What if at the same time the model respects physical laws like mass conservation and produces interpretable outputs (like soil moisture, groundwater storage, evapotranspiration and baseflow), with which you can tell a whole story to stakeholders? What if the same framework allows you to ask precise questions about different parts of hydrology and re‐examine your understanding of some parts of the physical system or check if your past equations are correct? This paper delivers a system that achieves these grand goals and opens many avenues for further exploration. Differentiable (δ) hydrologic models show that process clarity and a performance approaching deep learning (DL) can be both attainedUnlike DL, δmodels can output untrained physical variables, which agreed well with alternative estimatesDynamic parameterization has a moderate impact but is needed to narrow the gap to DL, suggesting that current model states are inadequate Differentiable (δ) hydrologic models show that process clarity and a performance approaching deep learning (DL) can be both attained Unlike DL, δmodels can output untrained physical variables, which agreed well with alternative estimates Dynamic parameterization has a moderate impact but is needed to narrow the gap to DL, suggesting that current model states are inadequate

Evaluated relative controls on hydrologic and vegetation fluxes and statesEvaluated the coupling strengths between biogeochemical and hydrologic cyclesElucidated patterns of hydrology and vegetation dynamics in a Great Lakes basin Understanding key controls on hydrologic dynamics is important for effectively allocating resources for data collection, reducing model dimensionality, and making modeling decisions. This work seeks to elucidate the physical factors responsible for the observed hydrologic patterns of a watershed in Michigan using an integrated hydrologic model, Process‐based Adaptive Watershed Simulator and Community Land Model (PAWS+CLM). The model is tested using observed data for streamflows, soil temperature, groundwater table depths, and satellite‐based observations of evapotranspiration (ET) and leaf area index (LAI). Numerical experiments are carried out to lump the effects of key controls, including land use types, nitrogen levels, groundwater redistribution, and soil texture, into different process indices. Using analysis of variance (ANOVA), we quantitatively determine the strengths of these controls on ET, net primary production (NPP), and other important variables. Groundwater flow is found to be the major control on runoff and infiltration, with soil texture ranking next, while vegetation type and nitrogen levels are found to dominate NPP, top soil temperature, and transpiration. Soil texture and groundwater are found to have comparable influence on soil moisture, which is in agreement with analysis of field data in the literature. All controls are found to colimit ET, which serves as the nexus for ecosystem‐hydrology interactions. From the simulation results, we find that nitrogen significantly controls transpiration, through which it influences other hydrologic fluxes. While there is room for improving descriptions of the nitrogen cycle in the current version of CLM, these novel results call for an understanding of the interplay between hydrology and biogeochemistry. Additional analysis shows that the relative strengths of the controls examined in this work are fairly robust with respect to changes in parameters and spatial resolution.

Deep learning (DL) models trained on hydrologic observations can perform extraordinarily well, but they can inherit deficiencies of the training data, such as limited coverage of in situ data or low resolution/accuracy of satellite data. Here we propose a novel multiscale DL scheme learning simultaneously from satellite and in situ data to predict 9 km daily soil moisture (5 cm depth). Based on spatial cross‐validation over sites in the conterminous United States, the multiscale scheme obtained a median correlation of 0.901 and root‐mean‐square error of 0.034 m3/m3. It outperformed the Soil Moisture Active Passive satellite mission's 9 km product, DL models trained on in situ data alone, and land surface models. Our 9 km product showed better accuracy than previous 1 km satellite downscaling products, highlighting limited impacts of improving resolution. Not only is our product useful for planning against floods, droughts, and pests, our scheme is generically applicable to geoscientific domains with data on multiple scales, breaking the confines of individual data sets. High‐resolution soil moisture data can be of great value for many practical applications, for example, flood forecasting, drought monitoring, crop management, weather forecasting, and better understanding the world's ecosystems. Recently, deep learning (DL) models directly learning patterns from observations have shown strong performance in modeling soil moisture and other environmental factors. Used directly, however, they inherit certain limitations of their training data such as low resolution and low accuracy; in other words, these models are students that cannot exceed their teacher (the data source). For soil moisture, just as for many other environmental variables of interest, observations are available on multiple scales, for example, probes in the ground and satellite‐based data. Here we show that learning from multiple data sources on different scales at the same time can allow DL models to overcome limitations of every single source: the student model can then outperform each teacher. Our multiscale model reported the best metrics for daily soil moisture prediction compared to alternatives and is no longer limited by poor satellite sensing capability in certain regions. This multiscale scheme is broadly applicable to many areas of environmental study. We propose a novel multiscale soil moisture model (5 cm depth) learning from both satellite and in situ data, resulting in high accuracyIn situ data provides more information than satellite data, but if used together, they can overcome the limitations of each data sourceThe impacts of input resolution waned below the 9 km grid, and the results established the upper error bound (RMSE ∼0.034) due to resolution We propose a novel multiscale soil moisture model (5 cm depth) learning from both satellite and in situ data, resulting in high accuracy In situ data provides more information than satellite data, but if used together, they can overcome the limitations of each data source The impacts of input resolution waned below the 9 km grid, and the results established the upper error bound (RMSE ∼0.034) due to resolution

When fitting statistical models to variables in geoscientific disciplines such as hydrology, it is a customary practice to stratify a large domain into multiple regions (or regimes) and study each region separately. Traditional wisdom suggests that models built for each region separately will have higher performance because of homogeneity within each region. However, each stratified model has access to fewer and less diverse data points. Here, through two hydrologic examples (soil moisture and streamflow), we show that conventional wisdom may no longer hold in the era of big data and deep learning (DL). We systematically examined an effect we call data synergy, where the results of the DL models improved when data were pooled together from characteristically different regions. The performance of the DL models benefitedfrom modest diversity in the training data compared to a homogeneous training set, even with similar data quantity. Moreover, allowing heterogeneous training data makes eligible much larger training datasets, which is an inherent advantage of DL. A large, diverse data set is advantageous in terms of representing extreme events and future scenarios, which has strong implications for climate change impact assessment. The results here suggest the research community should place greater emphasis on data sharing. Traditionally with statistical methods used in hydrology, we split the domain into relatively homogeneous regimes, for each of which we can create a simple model, that is, a local model. However, in the era of big data machine learning, we show that this is often the opposite of what should be done. With deep learning models, we should compile a large and heterogeneous data set and compare the local model to a model trained with all the data (global model). Including heterogeneous training samples may improve the results compared to the local model. We call this the data synergy effect, and it results from two main factors. First, deep learning models are complex enough to accommodate different training instances, inherently permitting larger training datasets with more extreme events and changing trends. Second, with a heterogeneous training data set, deep learning models may be able to learn both the underlying similarities and factors contributing to differences between regions. We introduced data synergy, where deep learning performance in a local region improves when including samples from other regionsData synergy is apparent with modestly diverse training data, partly because a larger and more diverse data set contains more extreme eventsThis work highlighted the value of samples outside a region of interest, emphasizing the need for community data sharing We introduced data synergy, where deep learning performance in a local region improves when including samples from other regions Data synergy is apparent with modestly diverse training data, partly because a larger and more diverse data set contains more extreme events This work highlighted the value of samples outside a region of interest, emphasizing the need for community data sharing

Predicting discharge in contiguously data‐scarce or ungauged regions is needed for quantifying the global hydrologic cycle. We show that prediction in ungauged regions (PUR) has major, underrecognized uncertainty and is drastically more difficult than previous problems where basins can be represented by neighboring or similar basins (known as prediction in ungauged basins). While deep neural networks demonstrated stellar performance for streamflow predictions, performance nonetheless declined for PUR, benchmarked here with a new stringent region‐based holdout test on a US data set with 671 basins. We tested approaches to reduce such errors, leveraging deep network's flexibility to integrate “soft” data, such as satellite‐based soil moisture product, or daily flow distributions which improved low flow simulations. A novel input‐selection ensemble improved average performance and greatly reduced catastrophic failures. Despite challenges, deep networks showed stronger performance metrics for PUR than traditional hydrologic models. They appear competitive for geoscientific modeling even in data‐scarce settings. Large areas of land exist on all continents where we do not have access to daily streamflow rate measurements, but predictions are still needed to plan for a changing climate. In such a scenario, if we apply hydrologic models calibrated elsewhere, how reliable are they? Previously, hydrologists studied the problem of prediction in ungauged basins (PUB), where a basin needing predictions can be represented by neighboring or similar basins. There has not been ample recognition that prediction in large, contiguously data‐sparse regions, which we call prediction in ungauged regions (PUR), is a substantially more difficult problem than PUB. Using a new benchmark problem with 671 US basins, we highlight this danger using machine learning models: performance dropped significantly from PUB to PUR scenarios. We proposed multiple approaches to improve model robustness, including a novel input‐selection ensemble method which combines models with different input options, as well as assimilating more widely available data. Despite the challenges with PUR, the machine learning model appears to be the best available tool for PUB and PUR applications. Perhaps counterintuitively, deep networks seem to be highly competitive even in data‐scarce settings, and geoscientific domains should carefully consider the extrapolation performance of their models. We highlight increased model error with predictions in contiguously data‐scarce (or ungauged) regions (PUR) and propose a streamflow benchmarkWe introduce methods to mitigate error, including an input‐selection ensemble and integrating satellite data or flow distributionsWith these methods, our machine learning PUR model presents metrics competitive with basin‐by‐basin calibrated hydrologic models in the conterminous United States We highlight increased model error with predictions in contiguously data‐scarce (or ungauged) regions (PUR) and propose a streamflow benchmark We introduce methods to mitigate error, including an input‐selection ensemble and integrating satellite data or flow distributions With these methods, our machine learning PUR model presents metrics competitive with basin‐by‐basin calibrated hydrologic models in the conterminous United States

There is a drastic geographic imbalance in available global streamflow gauge and catchment property data, with additional large variations in data characteristics. As a result, models calibrated in one region cannot normally be migrated to another without significant modifications. Currently in these regions, non‐transferable machine learning models are habitually trained over small local data sets. Here we show that transfer learning (TL), in the senses of weight initialization and weight freezing, allows long short‐term memory (LSTM) streamflow models that were pretrained over the conterminous United States (CONUS, the source data set) to be transferred to catchments on other continents (the target regions), without the need for extensive catchment attributes available at the target location. We demonstrate this possibility for regions where data are dense (664 basins in Great Britain), moderately dense (49 basins in central Chile), and scarce with only remotely sensed attributes available (5 basins in China). In both China and Chile, the TL models showed significantly elevated performance compared to locally trained models using all basins. The benefits of TL increased with the amount of available data in the source data set, and seemed to be more pronounced with greater physiographic diversity. The benefits from TL were greater than from pretraining LSTM using the outputs from an uncalibrated hydrologic model. These results suggest hydrologic data around the world have commonalities which could be leveraged by deep learning, and synergies can be had with a simple modification of the current workflows, greatly expanding the reach of existing big data. Finally, this work diversified existing global streamflow benchmarks. We introduced a method to utilize available big data to better start and warm up a machine learning streamflow model that is later fine‐tuned for prediction in basins on other continents (Asia, South America and Europe). This procedure noticeably improved streamflow volume prediction for different scenarios with varying amounts of data in the target basins (in terms of time period, length of collected data, and number of basins having data). This allows thousands of basins across the world with only a few years’ worth of streamflow observations to benefit from improved modeling and accuracy resulting from the use of deep learning. Basins around the world can be better modeled by applying transfer learning (TL) to a deep network trained in the US, and tuning it locallyThe benefits of TL increased with the amount and diversity of the source data, and were larger than from pretraining with a hydrologic modelThis work greatly expands the reach of deep learning, adds to the value of existing big data, and calls for synergy of global data sets Basins around the world can be better modeled by applying transfer learning (TL) to a deep network trained in the US, and tuning it locally The benefits of TL increased with the amount and diversity of the source data, and were larger than from pretraining with a hydrologic model This work greatly expands the reach of deep learning, adds to the value of existing big data, and calls for synergy of global data sets

Recently, recurrent deep networks have shown promise to harness newly available satellite‐sensed data for long‐term soil moisture projections. However, to be useful in forecasting, deep networks must also provide uncertainty estimates. Here we evaluated Monte Carlo dropout with an input‐dependent data noise term (MCD+N), an efficient uncertainty estimation framework originally developed in computer vision, for hydrologic time series predictions. MCD+N simultaneously estimates a heteroscedastic input‐dependent data noise term (a trained error model attributable to observational noise) and a network weight uncertainty term (attributable to insufficiently constrained model parameters). Although MCD+N has appealing features, many heuristic approximations were employed during its derivation, and rigorous evaluations and evidence of its asserted capability to detect dissimilarity were lacking. To address this, we provided an in‐depth evaluation of the scheme's potential and limitations. We showed that for reproducing soil moisture dynamics recorded by the Soil Moisture Active Passive (SMAP) mission, MCD+N indeed gave a good estimate of predictive error, provided that we tuned a hyperparameter and used a representative training data set. The input‐dependent term responded strongly to observational noise, while the model term clearly acted as a detector for physiographic dissimilarity from the training data, behaving as intended. However, when the training and test data were characteristically different, the input‐dependent term could be misled, undermining its reliability. Additionally, due to the data‐driven nature of the model, data noise also influences network weight uncertainty, and therefore the two uncertainty terms are correlated. Overall, this approach has promise, but care is needed to interpret the results. With proper hyperparameters and training data, Monte Carlo Dropout with a data noise term can effectively estimate prediction errorThe network‐predicted data noise term clearly responds to added noise while the network weight uncertainty term reacts to dissimilarityThe quality of both the data noise term and the network weight uncertainty term can be lowered by biased training data

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 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 convolutional neural network 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 interannual 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 performance in high‐aridity basins with 1‐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. We propose flexible data integration (DI), which can use various types of observations to improve discharge forecast at continental scalesAdding a convolutional neural network unit to LSTM reduces overfitting but cannot outperform directly accepting lagged discharge as inputsBenefits of DI are strong in regions with high autocorrelation in streamflow, due to either groundwater dominance or surface water storage

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 schedules. 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 moisture product with atmospheric forcings, 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‐square errors (<0.035) and high‐correlation coefficients >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 environmental settings. With high fidelity to SMAP, LSTM shows great potential for hindcasting, data assimilation, and weather forecasting. Soil moisture is the water content in soil, and it is a critical component of the water cycle. It controls whether crops or wild vegetation can function properly, the risk of wildfire, and the likelihood of floods. The NASA satellite SMAP, launched in 2015, measures soil moisture near the ground surface over Earth at high accuracy. SMAP data are of great value to global communities to which soil moisture is relevant. However, since it was launched only recently, there is only little overlap with other data sets, which limits its use. To extend SMAP's observations in time, we employ a “deep learning” technology called Long Short‐Term Memory (LSTM), which is one of the pillars of artificial intelligence and is bringing revolutionary changes in many scientific fields and our daily lives. We use LSTM to learn patterns of soil moisture dynamics and where physics‐based models make mistakes in describing moisture changes. This approach shows great promise for projecting SMAP observations into the long past: because soil moisture has a short memory, 2 years of data seem sufficient to train LSTM to successfully capture its dynamics. Because LSTM can handle large and diverse data, it offers valuable alternatives to older statistical methods. With 2 years of data, SMAP L3 data can be extended at high fidelity using a deep learning network (LSTM), showing potential for hindcastingDespite significant, spatially varying bias in Land Surface Models, LSTM can remove bias, correct moisture climatology, and capture extremesLSTM is more generalizable than simpler methods, and its strength seems to derive from its memory and ability to accommodate large data