Do invasive mussels restrict offshore phosphorus transport in Lake Huron?

Dreissenid mussels were first documented in the Laurentian Great Lakes in the late 1980s. Zebra mussels (Dreissena polymorpha) spread quickly into shallow, hard-substrate areas; quagga mussels (Dreissena rostriformis bugensis) spread more slowly and are currently colonizing deep, offshore areas. These mussels occur at high densities, filter large water volumes while feeding on suspended materials, and deposit particulate waste on the lake bottom. This filtering activity has been hypothesized to sequester tributary phosphorus in nearshore regions reducing offshore primary productivity. We used a mass balance model to estimate the phosphorus sedimentation rate in Saginaw Bay, a shallow embayment of Lake Huron, before and after the mussel invasion. Our results indicate that the proportion of tributary phosphorus retained in Saginaw Bay increased from approximately 46-70% when dreissenids appeared, reducing phosphorus export to the main body of Lake Huron. The combined effects of increased phosphorus retention and decreased phosphorus loading have caused an approximate 60% decrease in phosphorus export from Saginaw Bay to Lake Huron. Our results support the hypothesis that the ongoing decline of preyfish and secondary producers including diporeia (Diporeia spp.) in Lake Huron is a bottom-up phenomenon associated with decreased phosphorus availability in the offshore to support primary production.

On the application of multilevel modeling in environmental and ecological studies.

This paper illustrates the advantages of a multilevel/hierarchical approach for predictive modeling, including flexibility of model formulation, explicitly accounting for hierarchical structure in the data, and the ability to predict the outcome of new cases. As a generalization of the classical approach, the multilevel modeling approach explicitly models the hierarchical structure in the data by considering both the within- and between-group variances leading to a partial pooling of data across all levels in the hierarchy. The modeling framework provides means for incorporating variables at different spatiotemporal scales. The examples used in this paper illustrate the iterative process of model fitting and evaluation, a process that can lead to improved understanding of the system being studied.

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 object-oriented Bayesian network approach for establishing swine manure-borne natural estrogenic compounds budget.

A facility-wide estrogen budget model was developed to assess the excretion of natural estrogens by swine in a commercial swine farrowing concentrated animal feeding operations (CAFO) in North Carolina, using an object-oriented Bayesian network (OOBN) approach. The OOBN model is the combination of twelve objects of Bayesian network models, which characterize the estrogen budget flows based on the sow reproductive cycle (i.e., pre-estrus, estrus, and lactation) for the three natural estrogen types [estrone (E1), 17ß-estradiol (E2), and estriol (E3)] within each barn. This OOBN model provides a mechanism to quantify the levels of the natural estrogens and their probabilistic distributions with regard to estrogen type, waste sources such as urine, feces, and recycling lagoon slurry, and animal reproductive status. Moreover, the OOBN model allows us to assess the overall contribution of natural estrogen compounds from each operational unit of the CAFO, while accounting for the uncertainties. Results from the OOBN model indicate a rank order of lactating sows > gestating sows > breeding sows in terms of contribution of estrogen loads to the total natural estrogen budget. As to estrogen type, E1 was found as the major estrogen metabolite with the summed concentrations of urine, feces, and flushing slurry wastes exceeding 3000 ng/l > 90% of the time. As to waste sources, the flushing slurry waste was found to be a major contributor of the estrogen budget compared with urine and feces wastes from barn animals.

Assessment of water quality management with a systematic qualitative uncertainty analysis.

Uncertainty is an inevitable source of noise in water quality management and will weaken the adequacy of decisions. Uncertainty is derived from imperfect information, natural variability, and knowledge-based inconsistency. To make better decisions, it is necessary to reduce uncertainty. Conventional uncertainty analyses have focused on quantifying the uncertainty of parameters and variables in a probabilistic framework. However, the foundational properties and basic constraints might influence the entire system more than the quantifiable elements and have to be considered in initial analysis steps. According to binary classification, uncertainty includes quantitative uncertainty and non-quantitative uncertainty, which is also called qualitative uncertainty. Qualitative uncertainty originates from human subjective and biased beliefs. This study provides an understanding of qualitative uncertainty in terms of its conceptual definitions and practical applications. A systematic process of qualitative uncertainty analysis is developed for assisting complete uncertainty analysis, in which a qualitative network could then be built with qualitative relationship and quantifiable functions. In the proposed framework, a knowledge elicitation procedure is required to identify influential factors and their interrelationship. To limit biased information, a checklist is helpful to construct the qualitative network. The checklist helps one to ponder arbitrary assumptions that have often been taken for granted and may yield an incomplete or inappropriate decision analysis. The total maximum daily loads (TMDL) program is used as a surrogate for water quality management in this study. 15 uncertainty causes of TMDL programs are elicited by reviewing an influence diagram, and a checklist is formed with tabular interrogations corresponding to each uncertainty cause. The checklist enables decision makers to gain insight on the uncertainty level of the system at early steps as a convenient tool to review the adequacy of a TMDL program. Following the instruction of the checklist, an appropriate algorithm in a form of probability, possibility, or belief may then be assigned for the network. Consequently, the risk or evidence of the success of outcomes will be obtained. The incorporation of the systematic consideration of qualitative uncertainty into water quality management is expected to refine the decision-making process.

A Bayesian approach to retransformation bias in transformed regression.

Ecological data analysis often involves fitting linear or nonlinear equations to data after transforming either the response variable, the right side of the equation, or both, so that the standard suite of regression assumptions are more closely met. However, inference is usually done in the natural metric and it is well known that retransforming back to the original metric provides a biased estimator for the mean of the response variable. For the normal linear model, fit under a log-transformation, correction factors are available to reduce this bias, but these factors may not be generally applicable to all model forms or other transformations. We demonstrate that this problem is handled in a straightforward manner using a Bayesian approach, which is general for linear and nonlinear models and other transformations and model error structures. The Bayesian framework provides a predictive distribution for the response variable so that inference can be made at the mean, or over the entire distribution to incorporate the predictive uncertainty.

Predicting characteristics of rainfall driven estrogen runoff and transport from swine AFO spray fields.

Animal feeding operations (AFOs) have been implicated as potentially major sources of estrogenic contaminants into the aquatic environment due to the relatively minimal treatment of waste and potential mobilization and transport of waste components from spray fields. In this study a Bayesian network (BN) model was developed to inform management decisions and better predict the transport and fate of natural steroidal estrogens from these sites. The developed BN model integrates processes of surface runoff and sediment loss with the modified universal soil loss equation (MUSLE) and the soil conservation service curve number (SCS-CN) runoff model. What-if scenario simulations of lagoon slurry wastes to the spray fields were conducted for the most abundant natural estrogen estrone (E1) observed in the system. It was found that E1 attenuated significantly after 2 months following waste slurry application in both spring and summer seasons, with the overall attenuation rate predicted to be higher in the summer compared to the spring. Using simulations of rainfall events in conjunction with waste slurry application rates, it was predicted that the magnitude of E1 runoff loss is significantly higher in the spring as compared to the summer months, primarily due to spray field crop management plans. Our what-if scenario analyses suggest that planting Bermuda grass in the spray fields is likely to reduce runoff losses of natural estrogens near the water bodies and ecosystems, as compared to planting of soybeans.

Validation and sensitivity of the FINE Bayesian network for forecasting aquatic exposure to nano-silver.

The adaptive nature of the Forecasting the Impacts of Nanomaterials in the Environment (FINE) Bayesian network is explored. We create an updated FINE model (FINEAgNP-2) for predicting aquatic exposure concentrations of silver nanoparticles (AgNP) by combining the expert-based parameters from the baseline model established in previous work with literature data related to particle behavior, exposure, and nano-ecotoxicology via parameter learning. We validate the AgNP forecast from the updated model using mesocosm-scale field data and determine the sensitivity of several key variables to changes in environmental conditions, particle characteristics, and particle fate. Results show that the prediction accuracy of the FINEAgNP-2 model increased approximately 70% over the baseline model, with an error rate of only 20%, suggesting that FINE is a reliable tool to predict aquatic concentrations of nano-silver. Sensitivity analysis suggests that fractal dimension, particle diameter, conductivity, time, and particle fate have the most influence on aquatic exposure given the current knowledge; however, numerous knowledge gaps can be identified to suggest further research efforts that will reduce the uncertainty in subsequent exposure and risk forecasts.

A study of anthropogenic and climatic disturbance of the New River Estuary using a Bayesian belief network.

The present paper utilizes a Bayesian Belief Network (BBN) approach to intuitively present and quantify our current understanding of the complex physical, chemical, and biological processes that lead to eutrophication in an estuarine ecosystem (New River Estuary, North Carolina, USA). The model is further used to explore the effects of plausible future climatic and nutrient pollution management scenarios on water quality indicators. The BBN, through visualizing the structure of the network, facilitates knowledge communication with managers/stakeholders who might not be experts in the underlying scientific disciplines. Moreover, the developed structure of the BBN is transferable to other comparable estuaries. The BBN nodes are discretized exploring a new approach called moment matching method. The conditional probability tables of the variables are driven by a large dataset (four years). Our results show interaction among various predictors and their impact on water quality indicators. The synergistic effects caution future management actions.

A Bayesian network model for assessing natural estrogen fate and transport in a swine waste lagoon.

Commercial swine waste lagoons are regarded as a major reservoir of natural estrogens, which have the potential to produce adverse physiological effects on exposed aquatic organisms and wildlife. However, there remains limited understanding of the complex mechanisms of physical, chemical, and biological processes that govern the fate and transport of natural estrogens within an anaerobic swine lagoon. To improve lagoon management and ultimately help control the offsite transport of these compounds from swine operations, a probabilistic Bayesian network model was developed to assess natural estrogen fate and budget and then compared against data collected from a commercial swine field site. In general, the model was able to describe the estrogen fate and budget in both the slurry and sludge stores within the swine lagoon. Sensitivity analysis within the model demonstrated that the estrogen input loading from the associated barn facility was the most important factor in controlling estrogen concentrations within the lagoon slurry storage, whereas the settling rate was the most significant factor in the lagoon sludge storage. The degradation reactions were shown to be minor in both stores based on prediction of average total estrogen concentrations. Management scenario evaluations demonstrated that the best possible management options to reduce estrogen levels in the lagoon are either to adjust the estrogen input loading from swine barn facilities or to effectively enhance estrogen bonding with suspended solids through the use of organic polymers or inorganic coagulants.

Assessment of sources of human pathogens and fecal contamination in a Florida freshwater lake.

We investigated the potential for a variety of environmental reservoirs to harbor or contribute fecal indicator bacteria (FIB), DNA markers of human fecal contamination, and human pathogens to a freshwater lake. We hypothesized that submerged aquatic vegetation (SAV), sediments, and stormwater act as reservoirs and/or provide inputs of FIB and human pathogens to this inland water. Analysis included microbial source tracking (MST) markers of sewage contamination (Enterococcus faecium esp gene, human-associated Bacteroides HF183, and human polyomaviruses), pathogens (Salmonella, Cryptosporidium, Giardia, and enteric viruses), and FIB (fecal coliforms, Escherichia coli, and enterococci). Bayesian analysis was used to assess relationships among microbial and physicochemical variables. FIB in the water were correlated with concentrations in SAV and sediment. Furthermore, the correlation of antecedent rainfall and major rain events with FIB concentrations and detection of human markers and pathogens points toward multiple reservoirs for microbial contaminants in this system. Although pathogens and human-source markers were detected in 55% and 21% of samples, respectively, markers rarely coincided with pathogen detection. Bayesian analysis revealed that low concentrations (<45 CFU × 100 ml(-1)) of fecal coliforms were associated with 93% probability that pathogens would not be detected; furthermore the Bayes net model showed associations between elevated temperature and rainfall with fecal coliform and enterococci concentrations, but not E. coli. These data indicate that many under-studied matrices (e.g. SAV, sediment, stormwater) are important reservoirs for FIB and potentially human pathogens and demonstrate the usefulness of Bayes net analysis for water quality assessment.

The use of Bayesian networks for nanoparticle risk forecasting: model formulation and baseline evaluation.

We describe the use of Bayesian networks as a tool for nanomaterial risk forecasting and develop a baseline probabilistic model that incorporates nanoparticle specific characteristics and environmental parameters, along with elements of exposure potential, hazard, and risk related to nanomaterials. The baseline model, FINE (Forecasting the Impacts of Nanomaterials in the Environment), was developed using expert elicitation techniques. The Bayesian nature of FINE allows for updating as new data become available, a critical feature for forecasting risk in the context of nanomaterials. The specific case of silver nanoparticles (AgNPs) in aquatic environments is presented here (FINE(AgNP)). The results of this study show that Bayesian networks provide a robust method for formally incorporating expert judgments into a probabilistic measure of exposure and risk to nanoparticles, particularly when other knowledge bases may be lacking. The model is easily adapted and updated as additional experimental data and other information on nanoparticle behavior in the environment become available. The baseline model suggests that, within the bounds of uncertainty as currently quantified, nanosilver may pose the greatest potential risk as these particles accumulate in aquatic sediments.

A Bayesian changepoint-threshold model to examine the effect of TMDL implementation on the flow-nitrogen concentration relationship in the Neuse River basin.

In-stream nutrient concentrations are well known to exhibit a strong relationship with river flow. The use of flow measurements to predict nutrient concentrations and subsequently nutrient loads is common in water quality modeling. Nevertheless, most adopted models assume that the relationship between flow and concentration is fixed across time as well as across different flow regimes. In this study, we developed a Bayesian changepoint-threshold model that relaxes these constraints and allows for the identification and quantification of any changes in the underlying flow-concentration relationship across time. The results from our study support the occurrence of a changepoint in time around the year 1999, which coincided with the period of implementing nitrogen control measures as part of the TMDL program developed for the Neuse Estuary in North Carolina. The occurrence of the changepoint challenges the underlying assumption of temporal invariance in the flow-concentrations relationship. The model results also point towards a transition in the river nitrogen delivery system from a point source dominated loading system towards a more complicated nonlinear system, where non-point source nutrient delivery plays a major role. Moreover, we use the developed model to assess the effectiveness of the nitrogen reduction measures in achieving a 30% drop in loading. The results indicate that while there is a strong evidence of a load reduction, there still remains a high level of uncertainty associated with the mean nitrogen load reduction. We show that the level of uncertainty around the estimated load reduction is not random but is flow related.

Phosphorus load estimation in the Saginaw River, MI using a Bayesian hierarchical/multilevel model.

We propose the use of Bayesian hierarchical/multilevel ratio approach to estimate the annual riverine phosphorus loads in the Saginaw River, Michigan, from 1968 to 2008. The ratio estimator is known to be an unbiased, precise approach for differing flow-concentration relationships and sampling schemes. A Bayesian model can explicitly address the uncertainty in prediction by using a posterior predictive distribution, while in comparison, a Bayesian hierarchical technique can overcome the limitation of interpreting the estimated annual loads inferred from small sample sizes by borrowing strength from the underlying population shared by the years of interest. Thus, by combining the ratio estimator with the Bayesian hierarchical modeling framework, long-term loads estimation can be addressed with explicit quantification of uncertainty. Our study results indicate a slight decrease in total phosphorus load early in the series. The estimated ratio parameter, which can be interpreted as flow-weighted concentration, shows a clearer decrease, damping the noise that yearly flow variation adds to the load. Despite the reductions, it is not likely that Saginaw Bay meets with its target phosphorus load, 440 tonnes/yr. Throughout the decades, the probabilities of the Saginaw Bay not complying with the target load are estimated as 1.00, 0.50, 0.57 and 0.36 in 1977, 1987, 1997, and 2007, respectively. We show that the Bayesian hierarchical model results in reasonable goodness-of-fits to the observations whether or not individual loads are aggregated. Also, this modeling approach can substantially reduce uncertainties associated with small sample sizes both in the estimated parameters and loads.

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.

Combining model results and monitoring data for water quality assessment.

A Bayesian approach is used to update and improve water quality model predictions with monitoring data. The objective of this work is to facilitate adaptive management by providing a framework for sequentially updating the assessment of water quality status, to evaluate compliance with water quality standards, and to indicate if modification of management strategies is needed. Currently, most water quality or watershed models are calibrated using historical data that typically reflect conditions different from those being forecast. In part because of this, predictions are often subject to large errors. Fortunately, in many instances, postmanagement implementation monitoring data are available, although often with limited spatiotemporal coverage. These monitoring data support an alternative to the one-time prediction: pool the information from both the initial model prediction and postimplementation monitoring data. To illustrate this approach, a watershed nutrient loading model and a nitrogen-chlorophyll a model for the Neuse River Estuary were applied to develop a nitrogen total maximum daily load program for compliance with the chlorophyll a standard. Once management practices were implemented, monitoring data were collected and combined with the model forecast on an annual basis using Bayes Theorem. Ultimately, the updated posterior distribution of chlorophyll a concentration indicated that the Neuse River Estuary achieved compliance with North Carolina's standard.

Evaluation of the current state of mechanistic aquatic biogeochemical modeling: citation analysis and future perspectives.

We examined the factors that determine the citations of 153 mechanistic aquatic biogeochemical modeling papers published from 1990 to 2002. Our analysis provides overwhelming evidence that ocean modeling is a dynamic area of the current modeling practice. Models developed to gain insight into the ocean carbon cycle/marine biogeochemistry are most highly cited, the produced knowledge is exported to other cognitive disciplines, and oceanic modelers are less reluctant to embrace technical advances (e.g., assimilation schemes) and more critically increase model complexity. Contrary to our predictions, model application for environmental management issues on a local scale seems to have languished; the pertinent papers comprise a smaller portion of the published modeling literature and receive lower citations. Given the critical planning information that these models aim to provide, we hypothesize that the latter finding probably stems from conceptual weaknesses, methodological omissions, and an evident lack of haste from modelers to adopt new ideas in their repertoire when addressing environmental management issues. We also highlight the lack of significant association between citation frequency and model complexity, model performance, implementation of conventional methodological steps during model development (e.g., validation, sensitivity analysis), number of authors, and country of affiliation. While these results cast doubt on the rationale of the current modeling practice, the fact that the Fasham et al. (1990) paper has received over 400 citations probably dictates what should be done from the modeling community to meet the practical need for attractive and powerful modeling tools.

Predicting the frequency of water quality standard violations: a probabilistic approach for TMDL development.

To address the impaired condition of the water bodies listed under Section 303(d) of the Clean Water Act, over 40 000 total maximum daily loads (TMDLs) for pollutants must be developed during the next 10-15 years. Most of these will be based on the results of water quality simulation models. However, the failure of most models to incorporate residual variability and parameter uncertainty in their predictions makes them unsuitable for TMDL development. The percentile-based standards increasingly used by the EPA and the requirement for a margin of safety in TMDLs necessitate that model predictions include quantitative information on uncertainty. We describe a probabilistic approach to model-based TMDL assessment that addresses this issue and is suitable for use with any type of mathematical model. To demonstrate our approach, we employ a eutrophication model for the Neuse River Estuary, North Carolina, and evaluate compliance with the state chlorophyll a standard. Any observed variability in chlorophyll athatis notexplained bythe model is explicitly incorporated via a residual error term. This probabilistic term captures the effects of any processes that are not considered in the model and allows for direct assessment of the frequency of standard violations. Additionally, by estimating and propagating the effects of parameter uncertainty on model predictions, we are able to provide an explicit basis for choosing a TMDL that includes a margin of safety. We conclude by discussing the potential for models currently supported by the EPA to be adapted to provide the type of probabilistic information that is necessary to support TMDL decisions.