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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 δ HBV-globe1.0-hydroDL, shortened to δ HBV here) to simulate the rainfall–runoff processes for 3753 basins around the world. Moreover, we compare the δ HBV models to a purely data-driven long short-term memory (LSTM) model to examine their strengths and limitations. Both LSTM and the δ HBV 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 FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Predicting the response of hydrologic systems to modified driving forces beyond patterns that have occurred in the past is of high importance for estimating climate change impacts or the effect of management measures. This kind of prediction requires a model, but the impossibility of testing such predictions against observed data makes it difficult to estimate their reliability. Metamorphic testing offers a methodology for assessing models beyond validation with real data. It consists of defining input changes for which the expected responses are assumed to be known, at least qualitatively, and testing model behavior for consistency with these expectations. To increase the gain of information and reduce the subjectivity of this approach, we extend this methodology to a multi-model approach and include a sensitivity analysis of the predictions to training or calibration options. This allows us to quantitatively analyze differences in predictions between different model structures and calibration options in addition to the qualitative test of the expectations. In our case study, we apply this approach to selected conceptual and machine learning hydrological models calibrated for basins from the CAMELS data set. Our results confirm the superiority of the machine learning models over the conceptual hydrologic models regarding the quality of fit during calibration and validation periods. However, we also find that the response of machine learning models to modified inputs can deviate from the expectations and the magnitude, and even the sign of the response can depend on the training data. In addition, even in cases in which all models passed the metamorphic test, there are cases in which the quantitative response is different for different model structures. This demonstrates the importance of this kind of testing beyond and in addition to the usual calibration–validation analysis to identify potential problems and stimulate the development of improved models. [ABSTRACT FROM AUTHOR]

Photosynthesis plays an important role in carbon, nitrogen, and water cycles. Ecosystem models for photosynthesis are characterized by many parameters that are obtained from limited in situ measurements and applied to the same plant types. Previous site-by-site calibration approaches could not leverage big data and faced issues like overfitting or parameter non-uniqueness. Here we developed an end-to-end programmatically differentiable (meaning gradients of outputs to variables used in the model can be obtained efficiently and accurately) version of the photosynthesis process representation within the Functionally Assembled Terrestrial Ecosystem Simulator (FATES) model. As a genre of physics-informed machine learning (ML), differentiable models couple physics-based formulations to neural networks (NNs) that learn parameterizations (and potentially processes) from observations, here photosynthesis rates. We first demonstrated that the framework was able to correctly recover multiple assumed parameter values concurrently using synthetic training data. Then, using a real-world dataset consisting of many different plant functional types (PFTs), we learned parameters that performed substantially better and greatly reduced biases compared to literature values. Further, the framework allowed us to gain insights at a large scale. Our results showed that the carboxylation rate at 25 ∘ C (Vc,max25) was more impactful than a factor representing water limitation, although tuning both was helpful in addressing biases with the default values. This framework could potentially enable substantial improvement in our capability to learn parameters and reduce biases for ecosystem modeling at large scales. [ABSTRACT FROM AUTHOR]

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 FROM AUTHOR]

Hybrid hydroclimatic forecasting systems employ data-driven (statistical or machine learning) methods to harness and integrate a broad variety of predictions from dynamical, physics-based models – such as numerical weather prediction, climate, land, hydrology, and Earth system models – into a final prediction product. They are recognized as a promising way of enhancing the prediction skill of meteorological and hydroclimatic variables and events, including rainfall, temperature, streamflow, floods, droughts, tropical cyclones, or atmospheric rivers. Hybrid forecasting methods are now receiving growing attention due to advances in weather and climate prediction systems at subseasonal to decadal scales, a better appreciation of the strengths of AI, and expanding access to computational resources and methods. Such systems are attractive because they may avoid the need to run a computationally expensive offline land model, can minimize the effect of biases that exist within dynamical outputs, benefit from the strengths of machine learning, and can learn from large datasets, while combining different sources of predictability with varying time horizons. Here we review recent developments in hybrid hydroclimatic forecasting and outline key challenges and opportunities for further research. These include obtaining physically explainable results, assimilating human influences from novel data sources, integrating new ensemble techniques to improve predictive skill, creating seamless prediction schemes that merge short to long lead times, incorporating initial land surface and ocean/ice conditions, acknowledging spatial variability in landscape and atmospheric forcing, and increasing the operational uptake of hybrid prediction schemes. [ABSTRACT FROM AUTHOR]

Climate change threatens our ability to grow food for an ever-increasing population. There is a need for high-quality soil moisture predictions in under-monitored regions like Africa. However, it is unclear if soil moisture processes are globally similar enough to allow our models trained on available in situ data to maintain accuracy in unmonitored regions. We present a multitask long short-term memory (LSTM) model that learns simultaneously from global satellite-based data and in situ soil moisture data. This model is evaluated in both random spatial holdout mode and continental holdout mode (trained on some continents, tested on a different one). The model compared favorably to current land surface models, satellite products, and a candidate machine learning model, reaching a global median correlation of 0.792 for the random spatial holdout test. It behaved surprisingly well in Africa and Australia, showing high correlation even when we excluded their sites from the training set, but it performed relatively poorly in Alaska where rapid changes are occurring. In all but one continent (Asia), the multitask model in the worst-case scenario test performed better than the soil moisture active passive (SMAP) 9 km product. Factorial analysis has shown that the LSTM model's accuracy varies with terrain aspect, resulting in lower performance for dry and south-facing slopes or wet and north-facing slopes. This knowledge helps us apply the model while understanding its limitations. This model is being integrated into an operational agricultural assistance application which currently provides information to 13 million African farmers. [ABSTRACT FROM AUTHOR]

Recently, deep learning (DL) has emerged as a revolutionary and versatile tool transforming industry applications and generating new and improved capabilities for scientific discovery and model building. The adoption of DL in hydrology has so far been gradual, but the field is now ripe for breakthroughs. This paper suggests that DLbased methods can open up a complementary avenue toward knowledge discovery in hydrologic sciences. In the new avenue, machine-learning algorithms present competing hypotheses that are consistent with data. Interrogative methods are then invoked to interpret DL models for scientists to further evaluate. However, hydrology presents many challenges for DL methods, such as data limitations, heterogeneity and co-evolution, and the general inexperience of the hydrologic field with DL. The roadmap toward DL-powered scientific advances will require the coordinated effort from a large community involving scientists and citizens. Integrating process-based models with DL models will help alleviate data limitations. The sharing of data and baseline models will improve the efficiency of the community as a whole. Open competitions could serve as the organizing events to greatly propel growth and nurture data science education in hydrology, which demands a grassroots collaboration. The area of hydrologic DL presents numerous research opportunities that could, in turn, stimulate advances in machine learning as well. [ABSTRACT FROM AUTHOR]

Machine learning methods can serve as highly efficient and more objective generators for data-consistent hypotheses that explain how hydrologic systems function. However, they alone cannot differentiate between causal and associative relationships. The hypotheses, however, can be further assessed by the physics and causal relationships encoded in process-based models in a data-centric Bayesian learning framework, as opposed to the typical model-centric one. As a demonstration case, we show how a classification tree algorithm generated competing hypotheses explaining the gradients in storage-streamflow correlation relationships found in basins in the eastern continental US. With the help of numerical experiments using a process-based model, we then rejected soil texture and terrain slope and validated large soil thickness as the factor that causes high correlations between streamflow and storage. Based on our work in soil moisture modeling with deep learning and a trans-disciplinary literature review, we then provide an outlook of how this framework could be migrated to deep-learning-based effort, opening up a new research avenue. [ABSTRACT FROM AUTHOR]

Recently, recurrent deep networks have been shown to be a powerful tool in harnessing newly available big data for accurate long-term soil moisture predictions. However, to be useful in forecasting applications, they need more than just accuracy - the deep networks must provide model uncertainty estimates as well. Uncertainty for statistical and machine learning models can be classified into two categories: aleatoric and epistemic. Aleatoric uncertainty is the inherent uncertainty due to measurement error and noise in the data - it can be thought of like the error obtainable by a correctly specified model with infinite training data. Epistemic uncertainty results from insufficient training data and/or model misspecification. In this study, we adapt and evaluate an efficient uncertainty estimation framework that was recently proposed in the deep learning community. This method simultaneously estimates both aleatoric and epistemic uncertainty. The aleatoric estimate is provided directly by the deep network by adding an additional output unit. The epistemic component is estimated by Monte Carlo Dropout (MCD), which has two interpretations: the variability observed in an ensemble of deep networks, and an uncertainty estimate derived from a Gaussian Process trained with variational inference. Neither interpretation is exact (both rely on approximations whose errors are not quantified); however, Monte Carlo dropout has shown promise in estimating uncertainty in computer vision tasks for non-recurrent deep networks. Here, we carefully evaluate the quality of the aleatoric and epistemic uncertainty measures through a series of controlled experiments for soil moisture prediction. Using recurrent deep learning models trained on regional soil moisture time series, we show that the estimated uncertainties are indeed predictive of model errors. The MCD estimate of epistemic uncertainty clearly rises in response to cases that are different from the training data. Thus it can be used to detect when a model is being applied to a dataset for which the training data were not representative. Meanwhile, the aleatoric uncertainty estimate is accurate for representative training data, but, as expected, can be flawed if training data are not representative (a situation that can be detected Monte Carlo Dropout). However, we found that the two uncertainty estimates are not independent, suggesting that the network's aleatoric uncertainty estimate is also correlated with true epistemic uncertainty, e.g., the network learns not to trust its own predictions for cases that differ from the majority of the training data. [ABSTRACT FROM AUTHOR]