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For a number of years since their introduction to hydrology, recurrent neural networks like long short-term memory (LSTM) networks have proven remarkably difficult to surpass in terms of daily hydrograph metrics on community-shared benchmarks. Outside of hydrology, Transformers have now become the model of choice for sequential prediction tasks, making it a curious architecture to investigate for application to hydrology. Here, we first show that a vanilla (basic) Transformer architecture is not competitive against LSTM on the widely benchmarked CAMELS streamflow dataset, and lagged especially prominently for the high-flow metrics, perhaps due to the lack of memory mechanisms. However, a recurrence-free variant of the Transformer model can obtain mixed comparisons with LSTM, producing very slightly higher Kling-Gupta efficiency coefficients (KGE), along with other metrics. The lack of advantages for the vanilla Transformer network is linked to the nature of hydrologic processes. Additionally, similar to LSTM, the Transformer can also merge multiple meteorological forcing datasets to improve model performance. Therefore, the modified Transformer represents a rare competitive architecture to LSTM in rigorous benchmarks. Valuable lessons were learned: (1) the basic Transformer architecture is not suitable for hydrologic modeling; (2) the recurrence-free modification is beneficial so future work should continue to test such modifications; and (3) the performance of state-of-the-art models may be close to the prediction limits of the dataset. As a non-recurrent model, the Transformer may bear scale advantages for learning from bigger datasets and storing knowledge. This work lays the groundwork for future explorations into pretraining models, serving as a foundational benchmark that underscores the potential benefits in hydrology. 

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology. 

Accurate hydrologic modeling is vital to characterizing how the terrestrial water cycle responds to climate change. Pure deep learning (DL) models have been shown to outperform process-based ones while remaining difficult to interpret. More recently, differentiable physics-informed machine learning models with a physical backbone can systematically integrate physical equations and DL, predicting untrained variables and processes with high performance. However, it is unclear if such models are competitive for global-scale applications with a simple backbone. Therefore, we use – for the first time at this scale – differentiable hydrologic models (full name δHBV-globe1.0-hydroDL, shortened to δHBV here) to simulate the rainfall–runoff processes for 3753 basins around the world. Moreover, we compare the δHBV models to a purely data-driven long short-term memory (LSTM) model to examine their strengths and limitations. Both LSTM and the δHBV models provide competitive daily hydrologic simulation capabilities in global basins, with median Kling–Gupta efficiency values close to or higher than 0.7 (and 0.78 with LSTM for a subset of 1675 basins with long-term discharge records), significantly outperforming traditional models. Moreover, regionalized differentiable models demonstrated stronger spatial generalization ability (median KGE 0.64) than a traditional parameter regionalization approach (median KGE 0.46) and even LSTM for ungauged region tests across continents. Nevertheless, relative to LSTM, the differentiable model was hampered by structural deficiencies for cold or polar regions, highly arid regions, and basins with significant human impacts. This study also sets the benchmark for hydrologic estimates around the world and builds a foundation for improving global hydrologic simulations. 

Abstract. As a genre of physics-informed machine learning, differentiable process-based hydrologic models (abbreviated as δ or delta models) with regionalized deep-network-based parameterization pipelines were recently shown to provide daily streamflow prediction performance closely approaching that of state-of-the-art long short-term memory (LSTM) deep networks. Meanwhile, δ models provide a full suite of diagnostic physical variables and guaranteed mass conservation. Here, we ran experiments to test (1) their ability to extrapolate to regions far from streamflow gauges and (2) their ability to make credible predictions of long-term (decadal-scale) change trends. We evaluated the models based on daily hydrograph metrics (Nash–Sutcliffe model efficiency coefficient, etc.) and predicted decadal streamflow trends. For prediction in ungauged basins (PUB; randomly sampled ungauged basins representing spatial interpolation), δ models either approached or surpassed the performance of LSTM in daily hydrograph metrics, depending on the meteorological forcing data used. They presented a comparable trend performance to LSTM for annual mean flow and high flow but worse trends for low flow. For prediction in ungauged regions (PUR; regional holdout test representing spatial extrapolation in a highly data-sparse scenario), δ models surpassed LSTM in daily hydrograph metrics, and their advantages in mean and high flow trends became prominent. In addition, an untrained variable, evapotranspiration, retained good seasonality even for extrapolated cases. The δ models' deep-network-based parameterization pipeline produced parameter fields that maintain remarkably stable spatial patterns even in highly data-scarce scenarios, which explains their robustness. Combined with their interpretability and ability to assimilate multi-source observations, the δ models are strong candidates for regional and global-scale hydrologic simulations and climate change impact assessment. 

Abstract. Climate change threatens our ability to grow food for an ever-increasing population. There is aneed for high-quality soil moisture predictions in under-monitored regionslike Africa. However, it is unclear if soil moisture processes are globallysimilar enough to allow our models trained on available in situ data tomaintain accuracy in unmonitored regions. We present a multitask longshort-term memory (LSTM) model that learns simultaneously from globalsatellite-based data and in situ soil moisture data. This model is evaluated inboth random spatial holdout mode and continental holdout mode (trained onsome continents, tested on a different one). The model compared favorably tocurrent land surface models, satellite products, and a candidate machinelearning model, reaching a global median correlation of 0.792 for the randomspatial holdout test. It behaved surprisingly well in Africa and Australia,showing high correlation even when we excluded their sites from the trainingset, but it performed relatively poorly in Alaska where rapid changes areoccurring. In all but one continent (Asia), the multitask model in theworst-case scenario test performed better than the soil moisture activepassive (SMAP) 9 km product. Factorial analysis has shown that the LSTM model'saccuracy varies with terrain aspect, resulting in lower performance for dryand south-facing slopes or wet and north-facing slopes. This knowledgehelps us apply the model while understanding its limitations. This model isbeing integrated into an operational agricultural assistance applicationwhich currently provides information to 13 million African farmers. 

Abstract. Photosynthesis plays an important role in carbon,nitrogen, and water cycles. Ecosystem models for photosynthesis arecharacterized by many parameters that are obtained from limited in situmeasurements and applied to the same plant types. Previous site-by-sitecalibration approaches could not leverage big data and faced issues likeoverfitting or parameter non-uniqueness. Here we developed an end-to-endprogrammatically differentiable (meaning gradients of outputs to variablesused in the model can be obtained efficiently and accurately) version of thephotosynthesis process representation within the Functionally AssembledTerrestrial Ecosystem Simulator (FATES) model. As a genre ofphysics-informed machine learning (ML), differentiable models couplephysics-based formulations to neural networks (NNs) that learn parameterizations(and potentially processes) from observations, here photosynthesis rates. Wefirst demonstrated that the framework was able to correctly recover multiple assumedparameter values concurrently using synthetic training data. Then, using areal-world dataset consisting of many different plant functional types (PFTs), welearned parameters that performed substantially better and greatly reducedbiases compared to literature values. Further, the framework allowed us togain insights at a large scale. Our results showed that the carboxylationrate at 25 ∘C (Vc,max25) was more impactful than a factorrepresenting water limitation, although tuning both was helpful inaddressing biases with the default values. This framework could potentiallyenable substantial improvement in our capability to learn parameters andreduce biases for ecosystem modeling at large scales. 

Abstract Hydroelectric power (hydropower) is unique in that it can function as both a conventional source of electricity and as backup storage (pumped hydroelectric storage and large reservoir storage) for providing energy in times of high demand on the grid (S. Rehman, L M Al-Hadhrami, and M M Alam), (2015Renewable and Sustainable Energy Reviews,44, 586–98). This study examines the impact of hydropower on system electricity price and price volatility in the region served by the New England Independent System Operator (ISONE) from 2014-2020 (ISONE,ISO New England Web Services API v1.1.”https://webservices.iso-ne.com/docs/v1.1/, 2021. Accessed: 2021-01-10). We perform a robust holistic analysis of the mean and quantile effects, as well as the marginal contributing effects of hydropower in the presence of solar and wind resources. First, the price data is adjusted for deterministic temporal trends, correcting for seasonal, weekend, and diurnal effects that may obscure actual representative trends in the data. Using multiple linear regression and quantile regression, we observe that hydropower contributes to a reduction in the system electricity price and price volatility. While hydropower has a weak impact on decreasing price and volatility at the mean, it has greater impact at extreme quantiles (>70th percentile). At these higher percentiles, we find that hydropower provides a stabilizing effect on price volatility in the presence of volatile resources such as wind. We conclude with a discussion of the observed relationship between hydropower and system electricity price and volatility. 

Basin-centric long short-term memory (LSTM) network models have recently been shown to be an exceptionally powerful tool for stream temperature (Ts) temporal prediction (training in one period and making predictions for another period at the same sites). However, spatial extrapolation is a well-known challenge to modeling Ts and it is uncertain how an LSTM-based daily Ts model will perform in unmonitored or dammed basins. Here we compiled a new benchmark dataset consisting of >400 basins across the contiguous United States in different data availability groups (DAG, meaning the daily sampling frequency) with or without major dams and studied how to assemble suitable training datasets for predictions in basins with or without temperature monitoring. For prediction in unmonitored basins (PUB), LSTM produced an RMSE of 1.129 °C and R2 of 0.983. While these metrics declined from LSTM's temporal prediction performance, they far surpassed traditional models' PUB values, and were competitive with traditional models' temporal prediction on calibrated sites. Even for unmonitored basins with major reservoirs, we obtained a median RMSE of 1.202°C and an R2 of 0.984. For temporal prediction, the most suitable training set was the matching DAG that the basin could be grouped into, e.g., the 60% DAG for a basin with 61% data availability. However, for PUB, a training dataset including all basins with data is consistently preferred. An input-selection ensemble moderately mitigated attribute overfitting. Our results indicate there are influential latent processes not sufficiently described by the inputs (e.g., geology, wetland covers), but temporal fluctuations are well predictable, and LSTM appears to be a highly accurate Ts modeling tool even for spatial extrapolation.