Search for: All records

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. 

Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. In this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs. 

Accurate prediction of snow water equivalent (SWE) can be valuable for water resource managers. Recently, deep learning methods such as long short-term memory (LSTM) have exhibited high accuracy in simulating hydrologic variables and can integrate lagged observations to improve prediction, but their benefits were not clear for SWE simulations. Here we tested an LSTM network with data integration (DI) for SWE in the western United States to integrate 30-day-lagged or 7-day-lagged observations of either SWE or satellite-observed snow cover fraction (SCF) to improve future predictions. SCF proved beneficial only for shallow-snow sites during snowmelt, while lagged SWE integration significantly improved prediction accuracy for both shallow- and deep-snow sites. The median Nash–Sutcliffe model efficiency coefficient (NSE) in temporal testing improved from 0.92 to 0.97 with 30-day-lagged SWE integration, and root-mean-square error (RMSE) and the difference between estimated and observed peak SWE valuesd_maxwere reduced by 41% and 57%, respectively. DI effectively mitigated accumulated model and forcing errors that would otherwise be persistent. Moreover, by applying DI to different observations (30-day-lagged, 7-day-lagged), we revealed the spatial distribution of errors with different persistent lengths. For example, integrating 30-day-lagged SWE was ineffective for ephemeral snow sites in the southwestern United States, but significantly reduced monthly-scale biases for regions with stable seasonal snowpack such as high-elevation sites in California. These biases are likely attributable to large interannual variability in snowfall or site-specific snow redistribution patterns that can accumulate to impactful levels over time for nonephemeral sites. These results set up benchmark levels and provide guidance for future model improvement strategies.

 

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. 

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.