A database of in situ water temperatures for large inland lakes across the coterminous United States.

Water temperature dynamics in large inland lakes are interrelated with internal lake physics, ecosystem function, and adjacent land surface meteorology and climatology. Models for simulating and forecasting lake temperatures often rely on remote sensing and in situ data for validation. In situ monitoring platforms have the benefit of providing relatively precise measurements at multiple lake depths, but are often sparser (temporally and spatially) than remote sensing data. Here, we address the challenge of synthesizing in situ lake temperature data by creating a standardized database of near-surface and subsurface measurements from 134 sites across 29 large North American lakes, with the primary goal of supporting an ongoing lake model validation study. We utilize data sources ranging from federal agency repositories to local monitoring group samples, with a collective historical record spanning January 1, 2000 through December 31, 2022. Our database has direct utility for validating simulations and forecasts from operational numerical weather prediction systems in large lakes whose extensive surface area may significantly influence nearby weather and climate patterns.

Seasonal overturn and stratification changes drive deep-water warming in one of Earth's largest lakes.

Most of Earth's fresh surface water is consolidated in just a few of its largest lakes, and because of their unique response to environmental conditions, lakes have been identified as climate change sentinels. While the response of lake surface water temperatures to climate change is well documented from satellite and summer in situ measurements, our understanding of how water temperatures in large lakes are responding at depth is limited, as few large lakes have detailed long-term subsurface observations. We present an analysis of three decades of high frequency (3-hourly and hourly) subsurface water temperature data from Lake Michigan. This unique data set reveals that deep water temperatures are rising in the winter and provides precise measurements of the timing of fall overturn, the point of minimum temperature, and the duration of the winter cooling period. Relationships from the data show a shortened winter season results in higher subsurface temperatures and earlier onset of summer stratification. Shifts in the thermal regimes of large lakes will have profound impacts on the ecosystems of the world's surface freshwater.

Seventy-year long record of monthly water balance estimates for Earth's largest lake system.

We develop new estimates of monthly water balance components from 1950 to 2019 for the Laurentian Great Lakes, the largest surface freshwater system on Earth. For each of the Great Lakes, lake storage changes and water balance components were estimated using the Large Lakes Statistical Water Balance Model (L2SWBM). Multiple independent data sources, contributed by a binational community of research scientists and practitioners, were assimilated into the L2SWBM to infer feasible values of water balance components through a Bayesian framework. A conventional water balance model was used to constrain the new estimates, ensuring that the water balance can be reconciled over multiple time periods. The new estimates are useful for investigating changes in water availability, or benchmarking new hydrological models and data products developed for the Laurentian Great Lakes Region. The source code and inputs of the L2SWBM model are also made available, and can be adapted to include new data sources for the Great Lakes, or to address water balance problems on other large lake systems.

The compartment bag test (CBT) for enumerating fecal indicator bacteria: Basis for design and interpretation of results.

For the past several years, the compartment bag test (CBT) has been employed in water quality monitoring and public health protection around the world. To date, however, the statistical basis for the design and recommended procedures for enumerating fecal indicator bacteria (FIB) concentrations from CBT results have not been formally documented. Here, we provide that documentation following protocols for communicating the evolution of similar water quality testing procedures. We begin with an overview of the statistical theory behind the CBT, followed by a description of how that theory was applied to determine an optimal CBT design. We then provide recommendations for interpreting CBT results, including procedures for estimating quantiles of the FIB concentration probability distribution, and the confidence of compliance with recognized water quality guidelines. We synthesize these values in custom user-oriented 'look-up' tables similar to those developed for other FIB water quality testing methods. Modified versions of our tables are currently distributed commercially as part of the CBT testing kit.

Integrating quantitative PCR and Bayesian statistics in quantifying human adenoviruses in small volumes of source water.

Rapid quantification of viral pathogens in drinking and recreational water can help reduce waterborne disease risks. For this purpose, samples in small volume (e.g. 1L) are favored because of the convenience of collection, transportation and processing. However, the results of viral analysis are often subject to uncertainty. To overcome this limitation, we propose an approach that integrates Bayesian statistics, efficient concentration methods, and quantitative PCR (qPCR) to quantify viral pathogens in water. Using this approach, we quantified human adenoviruses (HAdVs) in eighteen samples of source water collected from six drinking water treatment plants. HAdVs were found in seven samples. In the other eleven samples, HAdVs were not detected by qPCR, but might have existed based on Bayesian inference. Our integrated approach that quantifies uncertainty provides a better understanding than conventional assessments of potential risks to public health, particularly in cases when pathogens may present a threat but cannot be detected by traditional methods.

Differentiating Enterococcus concentration spatial, temporal, and analytical variability in recreational waters.

Monitoring recreational waters for fecal contamination is an important responsibility of water resource management agencies throughout the world, yet fecal indicator bacteria (FIB)-based recreational water quality assessments rarely distinguish between analytical, spatial, and temporal variability. To address this gap in water resources research and management protocol, we compare two methods for quantifying FIB concentration variability at a frequently-used beach on Lake Huron (Michigan, USA). The first method calculates differences between most probable number (MPN) and colony-forming unit (CFU) values derived from conventional analysis procedures. The second method uses the "raw data" from these analysis procedures in a Bayesian hierarchical model to explicitly acknowledge analytical variability and subsequently infer the relative significance of the effect of sampling location and time on in situ FIB concentrations. Results of the Bayesian analysis indicate that in situ FIB concentrations do not vary significantly over small spatial and temporal scales, and that observed differences in MPN and CFU values over these same spatial and temporal scales are due almost entirely to intrinsic variability introduced by laboratory analysis procedures. Our findings underscore potential opportunities for incorporating Bayesian statistical models directly into routine recreational water quality assessments and for advancing the state of the art in methods for protecting humans from waterborne disease.

Addressing uncertainty in fecal indicator bacteria dark inactivation rates.

Assessing the potential threat of fecal contamination in surface water often depends on model forecasts which assume that fecal indicator bacteria (FIB, a proxy for the concentration of pathogens found in fecal contamination from warm-blooded animals) are lost or removed from the water column at a certain rate (often referred to as an "inactivation" rate). In efforts to reduce human health risks in these water bodies, regulators enforce limits on easily-measured FIB concentrations, commonly reported as most probable number (MPN) and colony forming unit (CFU) values. Accurate assessment of the potential threat of fecal contamination, therefore, depends on propagating uncertainty surrounding "true" FIB concentrations into MPN and CFU values, inactivation rates, model forecasts, and management decisions. Here, we explore how empirical relationships between FIB inactivation rates and extrinsic factors might vary depending on how uncertainty in MPN values is expressed. Using water samples collected from the Neuse River Estuary (NRE) in eastern North Carolina, we compare Escherichia coli (EC) and Enterococcus (ENT) dark inactivation rates derived from two statistical models of first-order loss; a conventional model employing ordinary least-squares (OLS) regression with MPN values, and a novel Bayesian model utilizing the pattern of positive wells in an IDEXX Quanti-Tray®/2000 test. While our results suggest that EC dark inactivation rates tend to decrease as initial EC concentrations decrease and that ENT dark inactivation rates are relatively consistent across different ENT concentrations, we find these relationships depend upon model selection and model calibration procedures. We also find that our proposed Bayesian model provides a more defensible approach to quantifying uncertainty in microbiological assessments of water quality than the conventional MPN-based model, and that our proposed model represents a new strategy for developing robust relationships between environmental factors and FIB inactivation rates, and for reducing uncertainty in water resource management decisions.

Improving water quality assessments through a hierarchical Bayesian analysis of variability.

Water quality measurement error and variability, while well-documented in laboratory-scale studies, is rarely acknowledged or explicitly resolved in most model-based water body assessments, including those conducted in compliance with the United States Environmental Protection Agency (USEPA) Total Maximum Daily Load (TMDL) program. Consequently, proposed pollutant loading reductions in TMDLs and similar water quality management programs may be biased, resulting in either slower-than-expected rates of water quality restoration and designated use reinstatement or, in some cases, overly conservative management decisions. To address this problem, we present a hierarchical Bayesian approach for relating actual in situ or model-predicted pollutant concentrations to multiple sampling and analysis procedures, each with distinct sources of variability. We apply this method to recently approved TMDLs to investigate whether appropriate accounting for measurement error and variability will lead to different management decisions. We find that required pollutant loading reductions may in fact vary depending not only on how measurement variability is addressed but also on which water quality analysis procedure is used to assess standard compliance. As a general strategy, our Bayesian approach to quantifying variability may represent an alternative to the common practice of addressing all forms of uncertainty through an arbitrary margin of safety (MOS).

Calibrating and validating bacterial water quality models: a Bayesian approach.

Water resource management decisions often depend on mechanistic or empirical models to predict water quality conditions under future pollutant loading scenarios. These decisions, such as whether or not to restrict public access to a water resource area, may therefore vary depending on how models reflect process, observation, and analytical uncertainty and variability. Nonetheless, few probabilistic modeling tools have been developed which explicitly propagate fecal indicator bacteria (FIB) analysis uncertainty into predictive bacterial water quality model parameters and response variables. Here, we compare three approaches to modeling variability in two different FIB water quality models. We first calibrate a well-known first-order bacterial decay model using approaches ranging from ordinary least squares (OLS) linear regression to Bayesian Markov chain Monte Carlo (MCMC) procedures. We then calibrate a less frequently used empirical bacterial die-off model using the same range of procedures (and the same data). Finally, we propose an innovative approach to evaluating the predictive performance of each calibrated model using a leave-one-out cross-validation procedure and assessing the probability distributions of the resulting Bayesian posterior predictive p-values. Our results suggest that different approaches to acknowledging uncertainty can lead to discrepancies between parameter mean and variance estimates and predictive performance for the same FIB water quality model. Our results also suggest that models without a bacterial kinetics parameter related to the rate of decay may more appropriately reflect FIB fate and transport processes, regardless of how variability and uncertainty are acknowledged.

An assessment of fecal indicator bacteria-based water quality standards.

Fecal indicator bacteria (FIB) are commonly used to assess the threat of pathogen contamination in coastal and inland waters. Unlike most measures of pollutant levels however, FIB concentration metrics, such as most probable number (MPN) and colony-forming units (CFU), are not direct measures of the true in situ concentration distribution. Therefore, there is the potential for inconsistencies among model and sample-based water quality assessments, such as those used in the Total Maximum Daily Load (TMDL) program. To address this problem, we present an innovative approach to assessing pathogen contamination based on water quality standards that impose limits on parameters of the actual underlying FIB concentration distribution, rather than on MPN or CFU values. Such concentration-based standards link more explicitly to human health considerations, are independent of the analytical procedures employed, and are consistent with the outcomes of most predictive water quality models. We demonstrate how compliance with concentration-based standards can be inferred from traditional MPN values using a Bayesian inference procedure. This methodology, applicable to a wide range of FIB-based water quality assessments, is illustrated here using fecal coliform data from shellfish harvesting waters in the Newport River Estuary, North Carolina. Results indicate that areas determined to be compliant according to the current methods-based standards may actually have an unacceptably high probability of being in violation of concentration-based standards.

Modeling the relationship between most probable number (MPN) and colony-forming unit (CFU) estimates of fecal coliform concentration.

Most probable number (MPN) and colony-forming-unit (CFU) estimates of fecal coliform bacteria concentration are common measures of water quality in coastal shellfish harvesting and recreational waters. Estimating procedures for MPN and CFU have intrinsic variability and are subject to additional uncertainty arising from minor variations in experimental protocol. It has been observed empirically that the standard multiple-tube fermentation (MTF) decimal dilution analysis MPN procedure is more variable than the membrane filtration CFU procedure, and that MTF-derived MPN estimates are somewhat higher on average than CFU estimates, on split samples from the same water bodies. We construct a probabilistic model that provides a clear theoretical explanation for the variability in, and discrepancy between, MPN and CFU measurements. We then compare our model to water quality samples analyzed using both MPN and CFU procedures, and find that the (often large) observed differences between MPN and CFU values for the same water body are well within the ranges predicted by our probabilistic model. Our results indicate that MPN and CFU intra-sample variability does not stem from human error or laboratory procedure variability, but is instead a simple consequence of the probabilistic basis for calculating the MPN. These results demonstrate how probabilistic models can be used to compare samples from different analytical procedures, and to determine whether transitions from one procedure to another are likely to cause a change in quality-based management decisions.