Reducing bias and quantifying uncertainty in watershed flux estimates: the R package loadflex

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

The metabolic regimes of 356 rivers in the United States

A national-scale quantification of metabolic energy flow in streams and rivers can improve understanding of the temporal dynamics of in-stream activity, links between energy cycling and ecosystem services, and the effects of human activities on aquatic metabolism. The two dominant terms in aquatic metabolism, gross primary production (GPP) and aerobic respiration (ER), have recently become practical to estimate for many sites due to improved modeling approaches and the availability of requisite model inputs in public datasets. We assembled inputs from the U.S. Geological Survey and National Aeronautics and Space Administration for October 2007 to January 2017. We then ran models to estimate daily GPP, ER, and the gas exchange rate coefficient for 356 streams and rivers across the continental United States. We also gathered potential explanatory variables and spatial information for cross-referencing this dataset with other datasets of watershed characteristics. This dataset offers a first national assessment of many-day time series of metabolic rates for up to 9 years per site, with a total of 490,907 site-days of estimates.We thank Jill Baron and the USGS Powell Center for financial support for this collaborative effort (Powell Center Working Group title: "Continental-scale overview of stream primary productivity, its links to water quality, and consequences for aquatic carbon biogeochemistry"). Additional financial support came from the USGS NAWQA program and Office of Water Information. NSF grants DEB-1146283 and EF1442501 partially supported ROH. A post-doctoral grant from the Basque Government partially supported MA. NAG was supported by the U.S. Department of Energy's Office of Science, Biological and Environmental Research. Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for the U.S. Department of Energy under contract DE-AC05-00OR22725. Leah Colasuonno provided expert logistical support of our working group meetings. The developers of USGS ScienceBase were very helpful both in hosting this dataset and in responding to our requests. Randy Hunt and Mike Fienen of the USGS Wisconsin Modeling Center graciously provided access to their HTCondor cluster. Mike Vlah provided detailed and insightful reviews of the data and metadata

Light and flow regimes regulate the metabolism of rivers

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.We thank Ted Stets, Jordan Read, Tom Battin, Sophia Bonjour, Marina Palta, and members of the Duke River Center for their help in developing these ideas. This work was supported by grants from the NSF 1442439 (to E.S.B. and J.W.H.), 1834679 (to R.O.H.), 1442451 (to R.O.H.), 2019528 (to R.O.H. and J.R.B.), 1442140 (to M.C.), 1442451 (to A.M.H.), 1442467 (to E.H.S.), 1442522 (to N.B.G.), 1624807 (to N.B.G.), and US Geological Survey funding for the working group was supported by the John Wesley Power Center for Analysis and Synthesis. Phil Savoy contributed as a postdoc- toral associate at Duke University and as a postdoctoral associate (contractor) at the US Geological Survey

Evaluating deep learning architecture and data assimilation for improving water temperature forecasts at unmonitored locations

Deep learning (DL) models are increasingly used to forecast water quality variables for use in decision making. Ingesting recent observations of the forecasted variable has been shown to greatly increase model performance at monitored locations; however, observations are not collected at all locations, and methods are not yet well developed for DL models for optimally ingesting recent observations from other sites to inform focal sites. In this paper, we evaluate two different DL model structures, a long short-term memory neural network (LSTM) and a recurrent graph convolutional neural network (RGCN), both with and without data assimilation for forecasting daily maximum stream temperature 7 days into the future at monitored and unmonitored locations in a 70-segment stream network. All our DL models performed well when forecasting stream temperature as the root mean squared error (RMSE) across all models ranged from 2.03 to 2.11°C for 1-day lead times in the validation period, with substantially better performance at gaged locations (RMSE = 1.45–1.52°C) compared to ungaged locations (RMSE = 3.18–3.27°C). Forecast uncertainty characterization was near-perfect for gaged locations but all DL models were overconfident (i.e., uncertainty bounds too narrow) for ungaged locations. Our results show that the RGCN with data assimilation performed best for ungaged locations and especially at higher temperatures (>18°C) which is important for management decisions in our study location. This indicates that the networked model structure and data assimilation techniques may help borrow information from nearby monitored sites to improve forecasts at unmonitored locations. Results from this study can help guide DL modeling decisions when forecasting other important environmental variables

Dataset of Observed Suspended Sediment and Particulate Organic Carbon Concentrations and Modeled Long-Term Suspended Sediment and Particulate Organic Carbon Yields (1994-2017) from the Reynolds Creek Experimental Watershed and Critical Zone Observatory in Southwestern Idaho, USA

Long-term datasets of suspended sediment (SS) and particulate organic carbon (POC) are valuable to understand the role the fluvial export plays in the landscape responses to changing climate and disturbance regimes such as fire. Here we report a dataset that includes raw SS and POC concentrations and estimated long-term (\u3e 23 years) SS and POC yields from 4 nested catchments that ranged from \u3c 1 to 54 km2 in area across the Reynolds Creek Experimental Watershed and Critical Zone Observatory (RCEW-CZO) in southwestern Idaho, USA. We also estimated SS and POC yields from a burned catchment in the first two years following fire. The RCEW-CZO is representative of many rangelands in the Intermountain West USA consisting of a mosaic of vegetation including Wyoming big sagebrush (Artemisia tridentata ssp. wyomingensis) and rabbitbrush (Chrysothamnus viscidiflorus) at lower elevations and mountain big sagebrush (Artemisia tridentata ssp. vaseyana), aspen (Populus tremuloides), bitter brush (Purshia tridentata), mountain mahogany (Cercocarpus ledifolius), Utah snowberry (Symphoricarpos oreophilus), and douglas-fir (Pseudotsuga menziesii) at higher elevation areas. Mean annual precipitation across these 4 catchments ranged from 616 to 911 mm yr-1 and mean annual temperature ranged from 7.16-4.75 degrees C. We first developed relationships between SS and POC for the five catchments from two years of data, one dry and one of the wettest water years on record. We then estimated SS yields using a composite model in loadflex that performs residual correction to improve estimates with the exception of burned catchment where we used a linear interpolation. We found strong relationships between log-transformed SS and POC (R2=0.38-0.86) that varied across catchments but did not vary across years, one dry and one of the wettest water years on record. Mean annual SS yields varied from 18-89 g SS m-2 yr-1 and POC from 0.61-11 g C m-2 yr-1 across the four unburned catchments. SS and POC yields were 611 g SS m-2 yr-1 and 35 g C m-2 yr-1, respectively, from the burned catchment in the first year following fire, and yields remained elevated in the second year, at 466 g SS m-2 yr-1 and 27.5 g C m-2 yr-1, owing to the large water year. These datasets are unique because few long-term records are available across nested catchments in rangelands in the Intermountain West US, and these datasets will aid in modeling and understanding linkages between climate, erosion, and carbon

Differentiable modelling to unify machine learning and physical models for geosciences

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

Differentiable modelling to unify machine learning and physical models for geosciences

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.6 month embargo; first published 11 July 2023This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]