The rapid growth of data in water resources has created new opportunities to accelerate knowledge discovery with the use of advanced deep learning tools. Hybrid models that integrate theory with ...state‐of‐the art empirical techniques have the potential to improve predictions while remaining true to physical laws. This paper evaluates the Process‐Guided Deep Learning (PGDL) hybrid modeling framework with a use‐case of predicting depth‐specific lake water temperatures. The PGDL model has three primary components: a deep learning model with temporal awareness (long short‐term memory recurrence), theory‐based feedback (model penalties for violating conversation of energy), and model pretraining to initialize the network with synthetic data (water temperature predictions from a process‐based model). In situ water temperatures were used to train the PGDL model, a deep learning (DL) model, and a process‐based (PB) model. Model performance was evaluated in various conditions, including when training data were sparse and when predictions were made outside of the range in the training data set. The PGDL model performance (as measured by root‐mean‐square error (RMSE)) was superior to DL and PB for two detailed study lakes, but only when pretraining data included greater variability than the training period. The PGDL model also performed well when extended to 68 lakes, with a median RMSE of 1.65 °C during the test period (DL: 1.78 °C, PB: 2.03 °C; in a small number of lakes PB or DL models were more accurate). This case‐study demonstrates that integrating scientific knowledge into deep learning tools shows promise for improving predictions of many important environmental variables.
Key Points
Process‐Guided Deep Learning (PGDL) models integrate advanced empirical techniques with process knowledge
We used PGDL to accurately predict lake water temperatures for various conditions
PGDL performance improved significantly when pretraining data included diverse conditions generated by an existing process‐based model
Satellite estimates of inland water quality have the potential to vastly expand our ability to observe and monitor the dynamics of large water bodies. For almost 50 years, we have been able to ...remotely sense key water quality constituents like total suspended sediment, dissolved organic carbon, chlorophyll a, and Secchi disk depth. Nonetheless, remote sensing of water quality is poorly integrated into inland water sciences, in part due to a lack of publicly available training data and a perception that remote estimates are unreliable. Remote sensing models of water quality can be improved by training and validation on larger data sets of coincident field and satellite observations, here called matchups. To facilitate model development and deeper integration of remote sensing into inland water science, we have built AquaSat, the largest such matchup data set ever assembled. AquaSat contains more than 600,000 matchups, covering 1984–2019, of ground‐based total suspended sediment, dissolved organic carbon, chlorophyll a, and SDDSecchi disk depth measurements paired with spectral reflectance from Landsat 5, 7, and 8 collected within ±1 day of each other. To build AquaSat, we developed open source tools in R and Python and applied them to existing public data sets covering the contiguous United States, including the Water Quality Portal, LAGOS‐NE, and the Landsat archive. In addition to publishing the data set, we are also publishing our full code architecture to facilitate expanding and improving AquaSat. We anticipate that this work will help make remote sensing of inland water accessible to more hydrologists, ecologists, and limnologists while facilitating novel data‐driven approaches to monitoring and understanding critical water resources at large spatiotemporal scales.
Key Points
AquaSat contains ∼600,000 paired observations of water quality and Landsat reflectance, the largest such matchup data set
Matchups capture diverse water bodies across the USA for 1984–2019; we see clear water quality/reflectance relationships
AquaSat and open source code developed here will enable better development of models for remote sensing of water quality
Most environmental data come from a minority of well‐monitored sites. An ongoing challenge in the environmental sciences is transferring knowledge from monitored sites to unmonitored sites. Here, we ...demonstrate a novel transfer‐learning framework that accurately predicts depth‐specific temperature in unmonitored lakes (targets) by borrowing models from well‐monitored lakes (sources). This method, meta‐transfer learning (MTL), builds a meta‐learning model to predict transfer performance from candidate source models to targets using lake attributes and candidates' past performance. We constructed source models at 145 well‐monitored lakes using calibrated process‐based (PB) modeling and a recently developed approach called process‐guided deep learning (PGDL). We applied MTL to either PB or PGDL source models (PB‐MTL or PGDL‐MTL, respectively) to predict temperatures in 305 target lakes treated as unmonitored in the Upper Midwestern United States. We show significantly improved performance relative to the uncalibrated PB General Lake Model, where the median root mean squared error (RMSE) for the target lakes is 2.52°C. PB‐MTL yielded a median RMSE of 2.43°C; PGDL‐MTL yielded 2.16°C; and a PGDL‐MTL ensemble of nine sources per target yielded 1.88°C. For sparsely monitored target lakes, PGDL‐MTL often outperformed PGDL models trained on the target lakes themselves. Differences in maximum depth between the source and target were consistently the most important predictors. Our approach readily scales to thousands of lakes in the Midwestern United States, demonstrating that MTL with meaningful predictor variables and high‐quality source models is a promising approach for many kinds of unmonitored systems and environmental variables.
Key Points
Meta‐transfer learning (MTL) learns from models trained on data‐rich systems to inform predictions in systems where no observations exist
We use MTL with process‐based and process‐guided deep learning models to accurately predict lake temperatures in the Midwest United States
The most important predictor of transfer model success is the difference in maximum depth between the data‐rich and unmonitored lake
The foundational ecosystem processes of gross primary production (GPP) and ecosystem respiration (ER) cannot be measured directly but can be modeled in aquatic ecosystems from subdaily patterns of ...oxygen (O2) concentrations. Because rivers and streams constantly exchange O2 with the atmosphere, models must either use empirical estimates of the gas exchange rate coefficient (K600) or solve for all three parameters (GPP, ER, and K600) simultaneously. Empirical measurements of K600 require substantial field work and can still be inaccurate. Three‐parameter models have suffered from equifinality, where good fits to O2 data are achieved by many different parameter values, some unrealistic. We developed a new three‐parameter, multiday model that ensures similar values for K600 among days with similar physical conditions (e.g., discharge). Our new model overcomes the equifinality problem by (1) flexibly relating K600 to discharge while permitting moderate daily deviations and (2) avoiding the oft‐violated assumption that residuals in O2 predictions are uncorrelated. We implemented this hierarchical state‐space model and several competitor models in an open‐source R package, streamMetabolizer. We then tested the models against both simulated and field data. Our new model reduces error by as much as 70% in daily estimates of K600, GPP, and ER. Further, accuracy benefits of multiday data sets require as few as 3 days of data. This approach facilitates more accurate metabolism estimates for more streams and days, enabling researchers to better quantify carbon fluxes, compare streams by their metabolic regimes, and investigate controls on aquatic activity.
Key Points
We introduce a flexible tool to estimate metabolism from multiday time series by Bayesian inference
Representing both process and observation error in metabolism models improves accuracy of estimates
Hierarchical partial pooling of gas exchange rates reduces bias and noise in metabolism estimates
Ecosystems globally are undergoing rapid changes in elemental inputs. Because nutrient inputs differently impact high- and low-fertility systems, building a predictive framework for the impacts of ...anthropogenic and natural changes on ecological stoichiometry requires examining the flexibility in stoichiometric responses across a range of basal nutrient richness. Whether organisms or communities respond to changing conditions with stoichiometric homeostasis or flexibility is strongly regulated by their species-specific capacity for nutrient storage, relative growth rate, physiological plasticity, and the degree of environmental resource availability relative to organismal demand. Using a meta-analysis approach, we tested whether stoichiometric flexibility following nutrient enrichment correlates with the relative fertility of terrestrial and aquatic systems or with the initial stoichiometries of the organism or community. We found that regardless of limitation status, N-fertilization tended to significantly reduce biota C:N and increase N:P, and P fertilization reduced C:P and N:P in both terrestrial and aquatic systems. Further, stoichiometric flexibility in response to fertilization tended to decrease as environmental nutrient richness increased in both terrestrial and aquatic systems. Positive correlations were also detected between the initial biota C:nutrient ratio and stoichiometric flexibility in response to fertilization. Elucidating these relationships between stoichiometric flexibility, basal environmental and biota fertility, and fertilization will increase our understanding of the ecological consequences of ongoing nutrient enrichment across the world.
Mean annual temperature and mean annual precipitation drive much of the variation in productivity across Earth's terrestrial ecosystems but do not explain variation in gross primary productivity ...(GPP) or ecosystem respiration (ER) in flowing waters. We document substantial variation in the magnitude and seasonality of GPP and ER across 222 US rivers. In contrast to their terrestrial counterparts, most river ecosystems respire far more carbon than they fix and have less pronounced and consistent seasonality in their metabolic rates. We find that variation in annual solar energy inputs and stability of flows are the primary drivers of GPP and ER across rivers. A classification schema based on these drivers advances river science and informs management.
Many ecological insights into the function of rivers and watersheds emerge from quantifying the flux of solutes or suspended materials in rivers. Numerous methods for flux estimation have been ...described, and each has its strengths and weaknesses. Currently, the largest practical challenges in flux estimation are to select among these methods and to implement or apply whichever method is chosen. To ease this process of method selection and application, we have written an R software package called loadflex that implements several of the most popular methods for flux estimation, including regressions, interpolations, and the special case of interpolation known as the period-weighted approach. Our package also implements a lesser-known and empirically promising approach called the "composite method," to which we have added an algorithm for estimating prediction uncertainty. Here we describe the structure and key features of loadflex, with a special emphasis on the rationale and details of our composite method implementation. We then demonstrate the use of loadflex by fitting four different models to nitrate data from the Lamprey River in southeastern New Hampshire, where two large floods in 2006-2007 are hypothesized to have driven a long-term shift in nitrate concentrations and fluxes from the watershed. The models each give believable estimates, and yet they yield different answers for whether and how the floods altered nitrate loads. In general, the best modeling approach for each new dataset will depend on the specific site and solute of interest, and researchers need to make an informed choice among the many possible models. Our package addresses this need by making it simple to apply and compare multiple load estimation models, ultimately allowing researchers to estimate riverine concentrations and fluxes with greater ease and accuracy.
Deep learning (DL) models are increasingly used to make accurate hindcasts of management‐relevant variables, but they are less commonly used in forecasting applications. Data assimilation (DA) can be ...used for forecasts to leverage real‐time observations, where the difference between model predictions and observations today is used to adjust the model to make better predictions tomorrow. In this use case, we developed a process‐guided DL and DA approach to make 7‐day probabilistic forecasts of daily maximum water temperature in the Delaware River Basin in support of water management decisions. Our modeling system produced forecasts of daily maximum water temperature with an average root mean squared error (RMSE) from 1.1 to 1.4°C for 1‐day‐ahead and 1.4 to 1.9°C for 7‐day‐ahead forecasts across all sites. The DA algorithm marginally improved forecast performance when compared with forecasts produced using the process‐guided DL model alone (0%–14% lower RMSE with the DA algorithm). Across all sites and lead times, 65%–82% of observations were within 90% forecast confidence intervals, which allowed managers to anticipate probability of exceedances of ecologically relevant thresholds and aid in decisions about releasing reservoir water downstream. The flexibility of DL models shows promise for forecasting other important environmental variables and aid in decision‐making.
Stream temperature is a fundamental control on ecosystem health. Recent efforts incorporating process guidance into deep learning models for predicting stream temperature have been shown to ...outperform existing statistical and physical models. This performance is in part because deep learning architectures can actively learn spatiotemporal relationships that govern how water and energy propagate through a river network. However, exploration of how spatiotemporal awareness and process guidance influence a model's generalizability under shifting environmental conditions such as climate change is limited. Here, we use Explainable Artificial Intelligence (XAI) to interrogate how differing deep learning architectures affect a model's learned spatial and temporal dependencies, and how those learned dependencies affect a model's ability to maintain high accuracy when applied to unseen environmental conditions. Using the Delaware River Basin in the northeastern United States as a test case, we compare two spatiotemporally aware process‐guided deep learning models for predicting stream temperature (a recurrent graph convolution network—RGCN, and a temporal convolution graph model—Graph WaveNet). Both models achieve equally high predictive performance when testing data are well represented in the training data (test root mean squared errors of 1.64°C and 1.65°C); however, Graph WaveNet significantly outperforms RGCN in 4 out of 5 experiments where test partitions represent different types of unseen environmental conditions. XAI results show that the architecture of Graph WaveNet leads to learned spatial relationships with greater fidelity to physical processes, and that this fidelity improves the generalizability of the model when applied to shifting and/or unseen environmental conditions.
Plain Language Summary
In a river network, the temperature of the water at a given point depends on a suite of information that spans space and time. Downstream reaches are influenced by upstream reaches, and an event such as rain today will influence the water temperature tomorrow. Certain types of deep learning models are capable of learning how this type of information moves through a river network to influence stream temperature. Existing work shows that using models that incorporate this information improves overall model performance, but little is known about how the differences between deep learning models lead to differences in learned spatial and temporal relationships. Here, we apply a variety of techniques to inspect how two different models learn spatial and temporal relationships. Our results show that one model learns relationships that intuitively match how we would expect information to move through a river network. This more accurate representation of the river system leads to improved model results when using the model to predict stream temperature in new environmental conditions that were not seen during training.
Key Points
Deep learning model architecture influences the fidelity of learned spatial and temporal relationships
Explainable Artificial Intelligence provides both detailed and high‐level insight into learned spatiotemporal dependencies
Spatiotemporal awareness can boost neural network accuracy, but only when training data adequately represent spatiotemporal relationships
The global decline of water quality in rivers and streams has resulted in a pressing need to design new watershed management strategies. Water quality can be affected by multiple stressors including ...population growth, land use change, global warming, and extreme events, with repercussions on human and ecosystem health. A scientific understanding of factors affecting riverine water quality and predictions at local to regional scales, and at sub‐daily to decadal timescales are needed for optimal management of watersheds and river basins. Here, we discuss how machine learning (ML) can enable development of more accurate, computationally tractable, and scalable models for analysis and predictions of river water quality. We review relevant state‐of‐the art applications of ML for water quality models and discuss opportunities to improve the use of ML with emerging computational and mathematical methods for model selection, hyperparameter optimization, incorporating process knowledge into ML models, improving explainablity, uncertainty quantification, and model‐data integration. We then present considerations for using ML to address water quality problems given their scale and complexity, available data and computational resources, and stakeholder needs. When combined with decades of process understanding, interdisciplinary advances in knowledge‐guided ML, information theory, data integration, and analytics can help address fundamental science questions and enable decision‐relevant predictions of riverine water quality.
Machine learning (ML) is being increasingly used for hydrological applications and has the potential to improve predictive capabilities and decipher complex, diverse human‐natural processes impacting water quality. In this paper, we review relevant state‐of‐the art models and present considerations for using ML and its limitations when applied for water quality problems. We then discuss opportunities to improve ML models using emerging computational and mathematical methods for model selection, hyperparameter optimization, incorporating process knowledge and complex data, explainable AI, uncertainty quantification, and model‐data integration.
PDF
