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, 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 can be improved via coupled NNs. We present a novel differentiable routing model 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, n can 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 n parameterization trained on short periods gave high performance in other periods, despite significant errors in runoff inputs. The learned n pattern 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 n parameterization can be coupled with traditional models to improve national-scale flood simulations.

In this article, we consider the scenario where remotely sensed images are collected sequentially in temporal batches, where each batch focuses on images from a particular ecoregion, but different batches can focus on different ecoregions with distinct landscape characteristics. For such a scenario, we study the following questions: (1) How well do DL models trained in homogeneous regions perform when they are transferred to different ecoregions, (2) Does increasing the spatial coverage in the data improve model performance in a given ecoregion (even when the extra data do not come from the ecoregion), and (3) Can a landslide pixel labelling model be incrementally updated with new data, but without access to the old data and without losing performance on the old data (so that researchers can share models obtained from proprietary datasets)? We address these questions by a framework called Task-Specific Model Updates (TSMU). The goal of this framework is to continually update a (landslide) semantic segmentation model with data from new ecoregions without having to revisit data from old ecoregions and without losing performance on them. We conduct extensive experiments on four ecoregions in the United States to address the above questions and establish that data from other ecoregions can help improve the model’s performance on the original ecoregion. In other words, if one has an ecoregion of interest, one could still collect data both inside and outside that region to improve model performance on the ecoregion of interest. Furthermore, if one has many ecoregions of interest, data from all of them are needed.

Accurate global river discharge estimation is crucial for advancing our scientific understanding of the global water cycle and supporting various downstream applications. In recent years, data-driven machine learning models, particularly the Long Short-Term Memory (LSTM) model, have shown significant promise in estimating discharge. Despite this, the applicability of LSTM models for global river discharge estimation remains largely unexplored. In this study, we diverge from the conventional basin-lumped LSTM modeling in limited basins. For the first time, we apply an LSTM on a global 0.25° grid, coupling it with a river routing model to estimate river discharge for every river reach worldwide. We rigorously evaluate the performance over 5332 evaluation gauges globally for the period 2000-2020, separate from the training basins and period. The grid-scale LSTM model effectively captures the rainfall-runoff behavior, reproducing global river discharge with high accuracy and achieving a median Kling-Gupta Efficiency (KGE) of 0.563. It outperforms an extensively bias-corrected and calibrated benchmark simulation based on the Variable Infiltration Capacity (VIC) model, which achieved a median KGE of 0.466. Using the global grid-scale LSTM model, we develop an improved global reach-level daily discharge dataset spanning 1980 to 2020, named GRADES-hydroDL. This dataset is anticipated to be useful for a myriad of applications, including providing prior information for the Surface Water and Ocean Topography (SWOT) satellite mission. The dataset is openly available via Globus.

Some machine learning (ML) methods such as classification trees are useful tools to generate hypotheses about how hydrologic systems function. However, data limitations dictate that ML alone often cannot differentiate between causal and associative relationships. For example, previous ML analysis suggested that soil thickness is the key physiographic factor determining the storage-streamflow correlations in the eastern US. This conclusion is not robust, especially if data are perturbed, and there were alternative, competing explanations including soil texture and terrain slope. However, typical causal analysis based on process-based models (PBMs) is inefficient and susceptible to human bias. Here we demonstrate a more efficient and objective analysis procedure where ML is first applied to generate data-consistent hypotheses, and then a PBM is invoked to verify these hypotheses. We employed a surface-subsurface processes model and conducted perturbation experiments to implement these competing hypotheses and assess the impacts of the changes. The experimental results strongly support the soil thickness hypothesis as opposed to the terrain slope and soil texture ones, which are co-varying and coincidental factors. Thicker soil permits larger saturation excess and longer system memory that carries wet season water storage to influence dry season baseflows. We further suggest this analysis could be formalized into a novel, data-centric Bayesian framework. This study demonstrates that PBM present indispensable value for problems that ML cannot solve alone, and is meant to encourage more synergies between ML and PBM in the future.

Recently, runoff simulations in small, headwater basins have been improved by methodological advances such as deep learning (DL). Hydrologic routing modules are typically needed to simulate flows in stem rivers downstream of large, heterogeneous basins, but obtaining suitable parameterization for them has previously been difficult. It is unclear if downstream daily discharge contains enough information to constrain spatially-distributed parameterization. Building on recent advances in differentiable modeling principles, here we propose a differentiable, learnable physics-based routing model. It mimics the classical Muskingum-Cunge routing model but embeds a neural network (NN) to provide parameterizations for Manning’s roughness coefficient (n) and channel geometries. The embedded NN, which uses (imperfect) DL-simulated runoffs as the forcing data and reach-scale attributes as inputs, was trained solely on downstream hydrographs. Our synthetic experiments show that while channel geometries cannot be identified, we can learn a parameterization scheme for n that captures the overall spatial pattern. Training on short real-world data showed that we could obtain highly accurate routing results for both the training and inner, untrained gages. For larger basins, our results are better than a DL model assuming homogeneity or the sum of runoff from subbasins. The parameterization learned from a short training period gave high performance in other periods, despite significant bias in runoff. This is the first time an interpretable, physics-based model is learned on the river network to infer spatially-distributed parameters. The trained n parameterization can be coupled to traditional runoff models and ported to traditional programming environments.

There is a drastic geographic imbalance in available global streamflow gauge and catchment property data, with additional large variations in data characteristics, so that models calibrated in one region cannot normally be migrated to another. Currently in these regions, non-transferable machine learning models are habitually trained over small local datasets. Here we show that transfer learning (TL), in the sense of weights initialization and weights freezing, allows long short-term memory (LSTM) streamflow models that were trained over the Conterminous United States (CONUS, the source dataset) to be transferred to catchments on other continents (the target regions), without the need for extensive catchment attributes. We demonstrate this possibility for regions where data are dense (664 basins in the UK), moderately dense (49 basins in central Chile), and where data are scarce and only globally-available attributes are available (5 basins in China). In both China and Chile, the TL models significantly elevated model performance compared to locally-trained models. The benefits of TL increased with the amount of available data in the source dataset, but even 50-100 basins from the CONUS dataset provided significant value for TL. The benefits of TL were greater than pre-training 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 significant synergies can be had with a simple modification of the currently predominant workflows, greatly expanding the reach of existing big data. Finally, this work diversified existing global streamflow benchmarks.

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 dataset. 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, the two uncertainty terms are correlated. This approach has promise, but care is needed to interpret the results.

Stream water temperature (T) is a variable of critical importance and decision-making relevance to aquatic ecosystems, energy production, and human’s interaction with the river system. Here, we propose a basin-centric stream water temperature model based on the long short-term memory (LSTM) model trained over hundreds of basins over continental United States, providing a first continental-scale benchmark on this problem. This model was fed by atmospheric forcing data, static catchment attributes and optionally observed or simulated discharge data. The model achieved a high performance, delivering a high median root-mean-squared-error (RMSE) for the groups with extensive, intermediate and scarce temperature measurements, respectively. The median Nash Sutcliffe model efficiency coefficients were above 0.97 for all groups and above 0.91 after air temperature was subtracted, showing the model to capture most of the temporal dynamics. Reservoirs have a substantial impact on the pattern of water temperature and negative influence the model performance. The median RMSE was 0.69 and 0.99 for sites without major dams and with major dams, respectively, in groups with data availability larger than 90%. Additional experiments showed that observed or simulated streamflow data is useful as an input for basins without major dams but may increase prediction bias otherwise. Our results suggest a strong mapping exists between basin-averaged forcings variables and attributes and water temperature, but local measurements can strongly improve the model. This work provides the first benchmark and significant insights for future effort. However, challenges remain for basins with large dams which can be targeted in the future when more information of withdrawal timing and water ponding time were accessible.

Stream water temperature is considered a “master variable” in environmental processes and human activities. Existing process-based models have difficulties with defining true equation parameters, and sometimes simplifications like assuming constant values influence the accuracy of results. Machine learning models are a highly successful tool for simulating stream temperature, but it is challenging to learn about processes and dynamics from their success. Here we integrate process-based modeling (SNTEMP model) and machine learning by building on a recently developed framework for parameter learning. With this framework, we used a deep neural network to map raw information (like catchment attributes and meteorological forcings) to parameters, and then inspected and fed the results into SNTEMP equations which we implemented in a deep learning platform. We trained the deep neural network across many basins in the conterminous United States in order to maximize the capturing of physical relationships and avoid overfitting. The presented framework has the ability of providing dynamic parameters based on the response of basins to meteorological conditions. The goal of this framework is to minimize the differences between stream temperature observations and SNTEMP outputs in the new platform. Parameter learning allows us to learn model parameters on large scales, providing benefits in efficiency, performance, and generalizability through applying global constraints. This method has also been shown to provide more physically-sensible parameters due to applying a global constraint. This model improves our understanding of how to parameterize the physical processes related to water temperature.

Dissolved oxygen (DO) sustains aquatic life and is an essential water quality measure. Our capabilities of forecasting DO levels, however, remain elusive. Unlike the increasingly intensive earth surface and hydroclimatic data, water quality data often have large temporal gaps and sparse areal coverage. Here we ask the question: can a Long Short-Term Memory (LSTM) deep learning model learn the spatio-temporal dynamics of stream DO from intensive hydroclimatic and sparse DO observations at the continental scale? That is, can the model harvest the power of big hydroclimatic data and use them for water quality forecasting? Here we used data from CAMELS-chem, a new dataset that includes sparse DO concentrations from 236 minimally-disturbed watersheds. The trained model can generally learn the theory of DO solubility under specific temperature, pressure, and salinity conditions. It captures the bulk variability and seasonality of DO and exhibits the potential of forecasting water quality in ungauged basins without training data. It however often misses concentration peaks and troughs where DO level depends on complex biogeochemical processes. The model surprisingly does not perform better where data are more intensive. It performs better in basins with low streamflow variations, low DO variability, high runoff-ratio (> 0.45), and precipitation peaks in winter. This work suggests that more frequent data collection in anticipated DO peak and trough conditions are essential to help overcome the issue of sparse data, an outstanding challenge in the water quality community.

The relationships and seasonal-to-annual variations among evapotranspiration (ET), precipitation (P), and groundwater dynamics (total water storage anomaly, TWSA) are complex across the Amazon basin, especially the water and energy limitation mechanism for ET. To analyze how ET is controlled by P and TWSA, we used wavelet coherence analysis to investigate the effects of P and TWSA on ET at sub-basin, kilometer, regional, and whole basin scales in the Amazon basin. The Amazon-scale averaged ET has strong correlations with P and TWSA at the annual periodicity. The phase lag between ET and P (ϕ_(ET-P)) is ~1 to ~4 months, and between ET and TWSA (ϕ_(ET-TWSA)) is ~3 to ~7 months. The phase pattern has a south-north divide due to the significant variation in climatic conditions. The correlation between ϕ_(ET-P) and ϕ_(ET-TWSA) is affected by the aridity index, of each sub-basin, as determined using the Budyko framework at the sub-basin level. In the southeast Amazon during a drought year (e.g., 2010), both phases decreased, while in the subsequent years, ϕ_(ET-TWSA) increased. The area of places where ET is limited by water continues to decrease over time in the southern Amazon basin. These results suggest immediate strong groundwater subsidy to ET in the following dry years in the water-limited area of Amazon. The water storage has more control on ET in the southeast but little influence in the north and southwest after a drought. The areas of ET limited by energy or water are switched due to the variability in weather conditions.