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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 (calledδmodels 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.

 

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

 

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.

 

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.

 

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.

 

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. 

Nowcasts, or near-real-time (NRT) forecasts, of soil moisture based on the Soil Moisture Active and Passive (SMAP) mission could provide substantial value for a range of applications including hazards monitoring and agricultural planning. To provide such a NRT forecast with high fidelity, we enhanced a time series deep learning architecture, long short-term memory (LSTM), with a novel data integration (DI) kernel to assimilate the most recent SMAP observations as soon as they become available. The kernel is adaptive in that it can accommodate irregular observational schedules. Testing over the CONUS, this NRT forecast product showcases predictions with unprecedented accuracy when evaluated against subsequent SMAP retrievals. It showed smaller error than NRT forecasts reported in the literature, especially at longer forecast latency. The comparative advantage was due to LSTM’s structural improvements, as well as its ability to utilize more input variables and more training data. The DI-LSTM was compared to the original LSTM model that runs without data integration, referred to as the projection model here. We found that the DI procedure removed the autocorrelated effects of forcing errors and errors due to processes not represented in the inputs, for example, irrigation and floodplain/lake inundation, as well as mismatches due to unseen forcing conditions. The effects of this purely data-driven DI kernel are discussed for the first time in the geosciences. Furthermore, this work presents an upper-bound estimate for the random component of the SMAP retrieval error.

 

The Soil Moisture Active Passive (SMAP) mission measures important soil moisture data globally. SMAP's products might not always perform better than land surface models (LSM) when evaluated against in situ measurements. However, we hypothesize that SMAP presents added value for long-term soil moisture estimation in a data fusion setting as evaluated by in situ data. Here, with the help of a time series deep learning (DL) method, we created a seamlessly extended SMAP data set to test this hypothesis and, importantly, gauge whether such benefits extend to years beyond SMAP's limited lifespan. We first show that the DL model, called long short-term memory (LSTM), can extrapolate SMAP for several years and the results are similar to the training period. We obtained prolongation results with low-performance degradation where SMAP itself matches well with in situ data. Interannual trends of root-zone soil moisture are surprisingly well captured by LSTM. In some cases, LSTM's performance is limited by SMAP, whose main issue appears to be its shallow sensing depth. Despite this limitation, a simple average between LSTM and an LSM Noah frequently outperforms Noah alone. Moreover, Noah combined with LSTM is more skillful than when it is combined with another LSM. Over sparsely instrumented sites, the Noah-LSTM combination shows a stronger edge. Our results verified the value of LSTM-extended SMAP data. Moreover, DL is completely data driven and does not require structural assumptions. As such, it has its unique potential for long-term projections and may be applied synergistically with other model-data integration techniques. 

Abstract. Recently, deep learning (DL) has emerged as a revolutionary andversatile tool transforming industry applications and generating new andimproved capabilities for scientific discovery and model building. Theadoption of DL in hydrology has so far been gradual, but the field is nowripe for breakthroughs. This paper suggests that DL-based methods can open up acomplementary avenue toward knowledge discovery in hydrologic sciences. Inthe new avenue, machine-learning algorithms present competing hypotheses thatare consistent with data. Interrogative methods are then invoked to interpretDL models for scientists to further evaluate. However, hydrology presentsmany challenges for DL methods, such as data limitations, heterogeneityand co-evolution, and the general inexperience of the hydrologic field withDL. The roadmap toward DL-powered scientific advances will require thecoordinated effort from a large community involving scientists and citizens.Integrating process-based models with DL models will help alleviate datalimitations. The sharing of data and baseline models will improve theefficiency of the community as a whole. Open competitions could serve as theorganizing events to greatly propel growth and nurture data science educationin hydrology, which demands a grassroots collaboration. The area ofhydrologic DL presents numerous research opportunities that could, in turn,stimulate advances in machine learning as well.