To address the impaired condition of the water bodies listed under Section 303(d) of the Clean Wa... more 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 to 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 a that is not explained by the 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.
Stream ecosystem structure and function are strongly influenced by patterns of velocity and depth... more Stream ecosystem structure and function are strongly influenced by patterns of velocity and depth. Simple methods for predicting the spatial distributions of these two variables, as functions of one-dimensional reach and discharge characteristics, have been recently reported in the literature. These studies have provided valuable insight into the fundamental factors influencing stream behaviour and represent a practical alternative to multi-dimensional hydrodynamic models. However, these previous studies have handled velocity and depth separately, while there is evidence that meso-habitats and stream biota are associated with distinct combinations of the two variables. Therefore, we used survey data from 92 stream reaches in New Zealand to develop a model for the joint distribution of depth and velocity. We found that, for each reach, the bivariate distribution of relative velocity and relative depth could be described by a mixture of two end-member distributions, one bivariate normal and the other bivariate lognormal, each with fixed parameters. The relative contribution of each shape for a particular reach at a particular discharge could then be related to the reach mean Froude number, the reach mean relative roughness, and the ratio of the survey discharge to the mean discharge. As these inputs can be readily estimated for changed channel morphology, our model should provide a useful approach for linking river rehabilitation strategies to hydraulics and ecology.
... A combined model of expert opinion was constructed as an influence diagram, and Monte Carlo s... more ... A combined model of expert opinion was constructed as an influence diagram, and Monte Carlo simulation was used to generate predictions of fish ... Extensive areas of low oxygen can also reduce usable habitat, altering fish distribution and increasing competition (Pihl et al. ...
Fundamental to deriving a sustainable supply of cellulosic feedstock for an emerging biofuels ind... more Fundamental to deriving a sustainable supply of cellulosic feedstock for an emerging biofuels industry is understanding how biomass yield varies as a function of crop management, climate, and soils. Here we focus on the perennial switchgrass (Panicum virgatum L.) and compile a database that contains 1190 observations of yield from 39 fi eld trials conducted across the United States. Data include site location, stand age, plot size, cultivar, crop management, biomass yield, temperature, precipitation, and information on land quality. Statistical analysis revealed the major sources of variation in yield. Frequency distributions of yield for upland and lowland ecotypes were unimodal, with mean (±SD) biomass yields of 8.7 ± 4.2 and 12.9 ± 5.9 Mg ha -1 for the two ecotypes, respectively. We looked for, but did not fi nd, bias toward higher yields associated with small plots or preferential establishment of stands on high quality lands. A parametric yield model was fi t to the data and accounted for one-third of the total observed variation in biomass yields, with an equal contribution of growing season precipitation, annual temperature, N fertilization, and ecotype. Th e model was used to predict yield across the continental United States. Mapped output was consistent with the natural range of switchgrass and, as expected, yields were shown to be limited by precipitation west of the Great Plains. Future studies should extend the geographic distribution of fi eld trials and thus improve our understanding of biomass production as a function of soil, climate, and crop management for promising biofuels such as switchgrass.
Canadian Journal of Fisheries and Aquatic Sciences, 2002
The effect of bottom-water hypoxia on the population density of the clam Macoma balthica is estim... more The effect of bottom-water hypoxia on the population density of the clam Macoma balthica is estimated using a survival-based approach. We used Bayesian parameter estimation to fit a survival model to times-to-death corresponding to multiple dissolved oxygen (DO) concentrations assessed from scientific experts. We describe guidelines for ensuring the accuracy of such assessments and claim that elicitation of quantities that pertain to measurable variables of interest, rather than unobservable parameters, should improve the use of judgment-based information in Bayesian analyses. When directly relevant data are lacking, predictions based on subjective assessments can serve as the basis for preliminary management decisions and additional data collection efforts. To inform pending water quality controls for the Neuse River estuary, North Carolina, we combined the survival model with a model describing the time dependence of DO. For current conditions, the mean summer survival rate is predicted to be only 11%. However, if sediment oxygen demand (SOD) is reduced as a result of nutrient management, summer survival rates will increase, reaching 23% with a 25% reduction in SOD and 46% with a 50% SOD reduction. Full model predictions are expressed as probabilities to provide a quantitative basis for risk-based decision-making and experimental design.
Abstract We develop a Bayesian probability network model to characterize eutrophication in the Ne... more Abstract We develop a Bayesian probability network model to characterize eutrophication in the Neuse River Estuary, NorthCarolina, and support the estimation of a TMDL for nitrogen. Unlike conventional simulation models, Bayesian network models describe probabilistic dependencies among system variables rather than substance mass balances. Full networks are decomposable into smaller submodels, with structure and quantification that reflect relevant theory, judgment,
... be derived from any combination of process knowledge, statistical correlations, or expert Pag... more ... be derived from any combination of process knowledge, statistical correlations, or expert Page 7. ... Details of the stakeholder elicitation effort are described by Borsuk et al. (2001a). ... ecosystem attributes of policy relevance, the model structure can be best explained by starting ...
A Bayesian uncertainty analysis of 12 parameters of the Bern2.5D climate model is presented. This... more A Bayesian uncertainty analysis of 12 parameters of the Bern2.5D climate model is presented. This includes an extensive sensitivity study with respect to the major statistical assumptions. Special attention is given to the parameter representing climate sensitivity. Using the framework of robust Bayesian analysis, the authors first define a nonparametric set of prior distributions for climate sensitivity S and then update the entire set according to Bayes' theorem. The upper and lower probability that S lies above 4.5°C is calculated over the resulting set of posterior distributions. Furthermore, posterior distributions under different assumptions on the likelihood function are computed. The main characteristics of the marginal posterior distributions of climate sensitivity are quite robust with regard to statistical models of climate variability and observational error. However, the influence of prior assumptions on the tails of distributions is substantial considering the important political implications. Moreover, the authors find that ocean heat change data have a considerable potential to constrain climate sensitivity.
Abstract}We compared patterns of historical watershed nutrient inputs with in-river nutrient load... more Abstract}We compared patterns of historical watershed nutrient inputs with in-river nutrient loads for the Neuse River, NC. Basin-wide sources of both nitrogen and phosphorus have increased substantially during the past century, marked by a sharp increase in the last 10 years resulting from an intensification of animal production. However, this recent increase is not reflected in changes in river loading over the last 20 years. Temporal patterns in river loads more closely parallel short-term changes in point sources and cropland nutrient application despite their overall lower magnitude. Total phosphorus loads have declined at all stations considered, corresponding to a 1988 phosphate detergent ban. Nitrogen load temporal patterns vary by location and the nitrogen fraction considered. The furthest upstream station exhibited nitrogen decreases after the completion of a dam in 1983. At a station just downstream of a rapidly growing urban area, the total nitrogen load has increased since the mid-1980s, primarily as a nitrate concentration increase. This is consistent with concurrent increases in chemical fertilizer use and point source discharges, as well as increased nitrification at treatment plants. This increase in nitrate loading is not reflected at the most downstream station, where no clear nitrogen trends are discernable. The lack of clear downstream nutrient increases suggests that current water quality impairment in the lower river and estuary may result from chronic nutrient overload rather than recent changes in the watershed. If this is true, then the impact of a planned 30% nitrogen loading reduction may not be immediately apparent. We calculate that, given annual variability, detecting a load reduction of this magnitude will take at least four years, and, should nutrients accumulated in the watershed become a significant source, detecting the resulting ecological improvements is likely to take substantially longer. #
A Bayesian probability network has been developed to integrate the various scientific findings of... more A Bayesian probability network has been developed to integrate the various scientific findings of an interdisciplinary research project on brown trout and their habitat in Switzerland. The network is based on a dynamic, age-structured population model, which is extended to include the effect of natural and anthropogenic influence factors. These include gravel bed conditions, water quality, disease rates, water temperature, habitat conditions, stocking practices, angler catch and flood frequency. Effect strength and associated uncertainty are described by conditional probability distributions. These conditional probabilities were developed using experimental and field data, literature reports, and the elicited judgment of involved scientists. The model was applied to brown trout populations at 12 locations in four river basins. Model testing consisted of comparing predictions of juvenile and adult density under current conditions to the results of recent population surveys. The relative importance of the various influence factors was then assessed by comparing various model scenarios, including a hypothetical reference condition. A measure of causal strength was developed based on this comparison, and the major stress factors were analyzed according to this measure for each location. We found that suboptimal habitat conditions are the most important and ubiquitous stress factor and have impacts of sufficient magnitude to explain the reduced fish populations observed in recent years. However, other factors likely contribute to the declines, depending on local conditions. The model developed in this study can be used to provide these site-specific assessments and predict the effect of candidate management measures.
Journal of Water Resources Planning and Management-asce, 2003
The North Carolina Division of Water Quality developed a total maximum daily load ͑TMDL͒ to reduc... more The North Carolina Division of Water Quality developed a total maximum daily load ͑TMDL͒ to reduce nitrogen inputs into the Neuse River Estuary to address the problem of repeated violations of the ambient chlorophyll a criterion. Three distinct water quality models were applied to support the TMDL: a two-dimensional laterally averaged model, a three-dimensional model, and a probability ͑Bayesian network͒ model. In this paper, we compare the salient features of all three models and present the results of a verification exercise in which each calibrated model was used to predict estuarine chlorophyll a concentrations for the year 2000. We present six summary statistics to relate the model predictions to the observed chlorophyll values: ͑1͒ the correlation coefficient; ͑2͒ the average error; ͑3͒ the average absolute error; ͑4͒ the root mean squared error; ͑5͒ the reliability index; and ͑6͒ the modeling efficiency. Additionally, we examined each model's ability to predict how frequently the 40 g/L chlorophyll a criterion was exceeded. The results indicate that none of the models predicted chlorophyll concentrations particularly well. Predictive accuracy was no better in the more process-oriented, spatially detailed models than in the aggregate probabilistic model. Our relative inability to predict accurately, even in well-studied, data-rich systems underscores the need for adaptive management, in which management actions are recognized as whole-ecosystem experiments providing additional data and information to better understand and predict system behavior.
AbstractÐWe describe a generalized version of the BOD decay model in which the reaction is allowe... more AbstractÐWe describe a generalized version of the BOD decay model in which the reaction is allowed to assume an order other than one. This is accomplished by making the exponent on BOD concentration a free parameter to be determined by the data. This``mixed-order'' model may be a more appropriate representation of the aggregation of underlying processes that contribute to overall oxygen consumption in organic wastes and therefore has the potential to result in improved model ®t. In order to directly compare the relative plausibility of alternative choices for a reaction order, we adopt a Bayesian approach to parameter estimation. This approach uses Bayes' theorem to develop a joint probability distribution for all parameter values conditional on the observed data. From this joint distribution, we employ a numerical integration method to derive marginal parameter distributions that can be used to directly compare the relative plausibility of competing parameter values. For the data sets we examine, reaction orders other than one are generally much better supported by the data, and the often-proposed second-order model does not appear to be an adequate alternative. For practical use, the mixed-order model formulation results in a better ®t to observations and yields more realistic predictions of ultimate BOD than the ®rst-order expression. In addition, the probabilistic nature of the Bayesian model we describe facilitates explicit consideration of uncertainty in subsequent water quality management and decision-making. #
Catches of brown trout have decreased about 50% in many rivers and streams in Switzerland in the ... more Catches of brown trout have decreased about 50% in many rivers and streams in Switzerland in the past 15 years. Additionally, the health status of numerous brown trout populations has been assessed to be impaired. In order to evaluate the causes for these phenomena, a nationwide interdisciplinary project named "Fischnetz" was launched in 1999. Twelve hypotheses for the fish population declines were proposed and laboratory and field research projects were initiated to investigate these suggested causes. To apply the results of these investigations to the task of discerning the relative causal importance of each of the hypotheses, a Bayesian probability network is being developed. The development of a "Bayes net" begins with eliciting mental models about the cause-and-effect relationships among system variables from subjectmatter experts. Represented as a graphical network, these models imply a set of assumptions about the conditional dependencies among the variables, which simplifies the problem of working with imprecise knowledge. Hard-to-derive joint probability distributions are replaced by a set of conditional distributions, which can be characterized using either: (1) experimental investigation, (2) collected field data, (3) processbased models, or (4) elicited expert opinion. Such information, available as a result of the "Fischnetz" research program and from the scientific literature, will be integrated into the network, thus quantitatively summarizing all relevant information. The quantified network will then be used to assess the historical causal importance of anthropogenic changes, as well as predict the effect of proposed management actions. Analyses will be carried out for individual streams using site-specific information as evidence to update less specific prior beliefs. The results can be used form the basis for preliminary management and to prioritize future research projects based on their ability to reduce uncertainty in model-based assessments. In this paper, a first prototype of the network is presented and the methodology for its construction and application is discussed.
Journal of The American Water Resources Association, 2007
Abstract: The National Research Council recommended Adaptive Total Maximum Daily Load implementa... more Abstract: The National Research Council recommended Adaptive Total Maximum Daily Load implementation with the recognition that the predictive uncertainty of water quality models can be high. Quantifying predictive uncertainty provides important information for model selection and decision-making. We review five methods that have been used with water quality models to evaluate model parameter and predictive uncertainty. These methods (1) Regionalized Sensitivity Analysis, (2) Generalized Likelihood Uncertainty Estimation, (3) Bayesian Monte Carlo, (4) Importance Sampling, and (5) Markov Chain Monte Carlo (MCMC) are based on similar concepts; their development over time was facilitated by the increasing availability of fast, cheap computers. Using a Streeter-Phelps model as an example we show that, applied consistently, these methods give compatible results. Thus, all of these methods can, in principle, provide useful sets of parameter values that can be used to evaluate model predictive uncertainty, though, in practice, some are quickly limited by the “curse of dimensionality” or may have difficulty evaluating irregularly shaped parameter spaces. Adaptive implementation invites model updating, as new data become available reflecting water-body responses to pollutant load reductions, and a Bayesian approach using MCMC is particularly handy for that task.
Fecal indicator bacteria (FIB) are commonly used to assess the threat of pathogen contamination i... more 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.
The total maximum daily load ͑TMDL͒ concept provides the basis for regulating pollution load from... more The total maximum daily load ͑TMDL͒ concept provides the basis for regulating pollution load from riverine sources to impaired water bodies. However, load is comprised of two components: flow and concentration. These two components may have confounding, or even conflicting, effects on waterbody attributes of concern. This is particularly the case for dynamic, advective systems, such as estuaries. Resolving these components is critical for properly predicting the response of impaired systems to watershed management actions. The Neuse River Estuary in North Carolina is an example of such an impaired system. Nitrogen has been identified as the pollutant of concern, and the process of developing a TMDL for nitrogen is underway. We, therefore, analyze the extensive data that have been collected for the Neuse River and estuary to investigate spatiotemporal relationships between river flow, riverine total nitrogen ͑TN͒ inputs, water temperature, dissolved inorganic nitrogen concentration, algal density, and primary productivity. Results support the belief that phytoplankton in the estuary are under substantial riverine control. However, the riverine TN concentration alone has only a minor role in determining estuarine chlorophyll a គ concentration. River flow has a stronger influence, likely through its effects on down-estuary nitrogen delivery, residence time, salinity, and turbidity. These results imply that using riverine nitrogen load as the metric to evaluate watershed nutrient management may not be appropriate. While nitrogen controls should reduce loads in the long term, in the short term, river flow is the dominant component of load and has the opposite effect of nitrogen on algae at the up-estuary locations.
... this approach may lead to the inclusion of processes about which we have very little informat... more ... this approach may lead to the inclusion of processes about which we have very little information ... m −3 mol −1 ) n−1 d −1 ) and s is the sinking speed (md −1 ... resulting from high temperatures, combined with extended periods of vertical stratification leads to short-term bottom water ...
To address the impaired condition of the water bodies listed under Section 303(d) of the Clean Wa... more 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 to 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 a that is not explained by the 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.
Stream ecosystem structure and function are strongly influenced by patterns of velocity and depth... more Stream ecosystem structure and function are strongly influenced by patterns of velocity and depth. Simple methods for predicting the spatial distributions of these two variables, as functions of one-dimensional reach and discharge characteristics, have been recently reported in the literature. These studies have provided valuable insight into the fundamental factors influencing stream behaviour and represent a practical alternative to multi-dimensional hydrodynamic models. However, these previous studies have handled velocity and depth separately, while there is evidence that meso-habitats and stream biota are associated with distinct combinations of the two variables. Therefore, we used survey data from 92 stream reaches in New Zealand to develop a model for the joint distribution of depth and velocity. We found that, for each reach, the bivariate distribution of relative velocity and relative depth could be described by a mixture of two end-member distributions, one bivariate normal and the other bivariate lognormal, each with fixed parameters. The relative contribution of each shape for a particular reach at a particular discharge could then be related to the reach mean Froude number, the reach mean relative roughness, and the ratio of the survey discharge to the mean discharge. As these inputs can be readily estimated for changed channel morphology, our model should provide a useful approach for linking river rehabilitation strategies to hydraulics and ecology.
... A combined model of expert opinion was constructed as an influence diagram, and Monte Carlo s... more ... A combined model of expert opinion was constructed as an influence diagram, and Monte Carlo simulation was used to generate predictions of fish ... Extensive areas of low oxygen can also reduce usable habitat, altering fish distribution and increasing competition (Pihl et al. ...
Fundamental to deriving a sustainable supply of cellulosic feedstock for an emerging biofuels ind... more Fundamental to deriving a sustainable supply of cellulosic feedstock for an emerging biofuels industry is understanding how biomass yield varies as a function of crop management, climate, and soils. Here we focus on the perennial switchgrass (Panicum virgatum L.) and compile a database that contains 1190 observations of yield from 39 fi eld trials conducted across the United States. Data include site location, stand age, plot size, cultivar, crop management, biomass yield, temperature, precipitation, and information on land quality. Statistical analysis revealed the major sources of variation in yield. Frequency distributions of yield for upland and lowland ecotypes were unimodal, with mean (±SD) biomass yields of 8.7 ± 4.2 and 12.9 ± 5.9 Mg ha -1 for the two ecotypes, respectively. We looked for, but did not fi nd, bias toward higher yields associated with small plots or preferential establishment of stands on high quality lands. A parametric yield model was fi t to the data and accounted for one-third of the total observed variation in biomass yields, with an equal contribution of growing season precipitation, annual temperature, N fertilization, and ecotype. Th e model was used to predict yield across the continental United States. Mapped output was consistent with the natural range of switchgrass and, as expected, yields were shown to be limited by precipitation west of the Great Plains. Future studies should extend the geographic distribution of fi eld trials and thus improve our understanding of biomass production as a function of soil, climate, and crop management for promising biofuels such as switchgrass.
Canadian Journal of Fisheries and Aquatic Sciences, 2002
The effect of bottom-water hypoxia on the population density of the clam Macoma balthica is estim... more The effect of bottom-water hypoxia on the population density of the clam Macoma balthica is estimated using a survival-based approach. We used Bayesian parameter estimation to fit a survival model to times-to-death corresponding to multiple dissolved oxygen (DO) concentrations assessed from scientific experts. We describe guidelines for ensuring the accuracy of such assessments and claim that elicitation of quantities that pertain to measurable variables of interest, rather than unobservable parameters, should improve the use of judgment-based information in Bayesian analyses. When directly relevant data are lacking, predictions based on subjective assessments can serve as the basis for preliminary management decisions and additional data collection efforts. To inform pending water quality controls for the Neuse River estuary, North Carolina, we combined the survival model with a model describing the time dependence of DO. For current conditions, the mean summer survival rate is predicted to be only 11%. However, if sediment oxygen demand (SOD) is reduced as a result of nutrient management, summer survival rates will increase, reaching 23% with a 25% reduction in SOD and 46% with a 50% SOD reduction. Full model predictions are expressed as probabilities to provide a quantitative basis for risk-based decision-making and experimental design.
Abstract We develop a Bayesian probability network model to characterize eutrophication in the Ne... more Abstract We develop a Bayesian probability network model to characterize eutrophication in the Neuse River Estuary, NorthCarolina, and support the estimation of a TMDL for nitrogen. Unlike conventional simulation models, Bayesian network models describe probabilistic dependencies among system variables rather than substance mass balances. Full networks are decomposable into smaller submodels, with structure and quantification that reflect relevant theory, judgment,
... be derived from any combination of process knowledge, statistical correlations, or expert Pag... more ... be derived from any combination of process knowledge, statistical correlations, or expert Page 7. ... Details of the stakeholder elicitation effort are described by Borsuk et al. (2001a). ... ecosystem attributes of policy relevance, the model structure can be best explained by starting ...
A Bayesian uncertainty analysis of 12 parameters of the Bern2.5D climate model is presented. This... more A Bayesian uncertainty analysis of 12 parameters of the Bern2.5D climate model is presented. This includes an extensive sensitivity study with respect to the major statistical assumptions. Special attention is given to the parameter representing climate sensitivity. Using the framework of robust Bayesian analysis, the authors first define a nonparametric set of prior distributions for climate sensitivity S and then update the entire set according to Bayes' theorem. The upper and lower probability that S lies above 4.5°C is calculated over the resulting set of posterior distributions. Furthermore, posterior distributions under different assumptions on the likelihood function are computed. The main characteristics of the marginal posterior distributions of climate sensitivity are quite robust with regard to statistical models of climate variability and observational error. However, the influence of prior assumptions on the tails of distributions is substantial considering the important political implications. Moreover, the authors find that ocean heat change data have a considerable potential to constrain climate sensitivity.
Abstract}We compared patterns of historical watershed nutrient inputs with in-river nutrient load... more Abstract}We compared patterns of historical watershed nutrient inputs with in-river nutrient loads for the Neuse River, NC. Basin-wide sources of both nitrogen and phosphorus have increased substantially during the past century, marked by a sharp increase in the last 10 years resulting from an intensification of animal production. However, this recent increase is not reflected in changes in river loading over the last 20 years. Temporal patterns in river loads more closely parallel short-term changes in point sources and cropland nutrient application despite their overall lower magnitude. Total phosphorus loads have declined at all stations considered, corresponding to a 1988 phosphate detergent ban. Nitrogen load temporal patterns vary by location and the nitrogen fraction considered. The furthest upstream station exhibited nitrogen decreases after the completion of a dam in 1983. At a station just downstream of a rapidly growing urban area, the total nitrogen load has increased since the mid-1980s, primarily as a nitrate concentration increase. This is consistent with concurrent increases in chemical fertilizer use and point source discharges, as well as increased nitrification at treatment plants. This increase in nitrate loading is not reflected at the most downstream station, where no clear nitrogen trends are discernable. The lack of clear downstream nutrient increases suggests that current water quality impairment in the lower river and estuary may result from chronic nutrient overload rather than recent changes in the watershed. If this is true, then the impact of a planned 30% nitrogen loading reduction may not be immediately apparent. We calculate that, given annual variability, detecting a load reduction of this magnitude will take at least four years, and, should nutrients accumulated in the watershed become a significant source, detecting the resulting ecological improvements is likely to take substantially longer. #
A Bayesian probability network has been developed to integrate the various scientific findings of... more A Bayesian probability network has been developed to integrate the various scientific findings of an interdisciplinary research project on brown trout and their habitat in Switzerland. The network is based on a dynamic, age-structured population model, which is extended to include the effect of natural and anthropogenic influence factors. These include gravel bed conditions, water quality, disease rates, water temperature, habitat conditions, stocking practices, angler catch and flood frequency. Effect strength and associated uncertainty are described by conditional probability distributions. These conditional probabilities were developed using experimental and field data, literature reports, and the elicited judgment of involved scientists. The model was applied to brown trout populations at 12 locations in four river basins. Model testing consisted of comparing predictions of juvenile and adult density under current conditions to the results of recent population surveys. The relative importance of the various influence factors was then assessed by comparing various model scenarios, including a hypothetical reference condition. A measure of causal strength was developed based on this comparison, and the major stress factors were analyzed according to this measure for each location. We found that suboptimal habitat conditions are the most important and ubiquitous stress factor and have impacts of sufficient magnitude to explain the reduced fish populations observed in recent years. However, other factors likely contribute to the declines, depending on local conditions. The model developed in this study can be used to provide these site-specific assessments and predict the effect of candidate management measures.
Journal of Water Resources Planning and Management-asce, 2003
The North Carolina Division of Water Quality developed a total maximum daily load ͑TMDL͒ to reduc... more The North Carolina Division of Water Quality developed a total maximum daily load ͑TMDL͒ to reduce nitrogen inputs into the Neuse River Estuary to address the problem of repeated violations of the ambient chlorophyll a criterion. Three distinct water quality models were applied to support the TMDL: a two-dimensional laterally averaged model, a three-dimensional model, and a probability ͑Bayesian network͒ model. In this paper, we compare the salient features of all three models and present the results of a verification exercise in which each calibrated model was used to predict estuarine chlorophyll a concentrations for the year 2000. We present six summary statistics to relate the model predictions to the observed chlorophyll values: ͑1͒ the correlation coefficient; ͑2͒ the average error; ͑3͒ the average absolute error; ͑4͒ the root mean squared error; ͑5͒ the reliability index; and ͑6͒ the modeling efficiency. Additionally, we examined each model's ability to predict how frequently the 40 g/L chlorophyll a criterion was exceeded. The results indicate that none of the models predicted chlorophyll concentrations particularly well. Predictive accuracy was no better in the more process-oriented, spatially detailed models than in the aggregate probabilistic model. Our relative inability to predict accurately, even in well-studied, data-rich systems underscores the need for adaptive management, in which management actions are recognized as whole-ecosystem experiments providing additional data and information to better understand and predict system behavior.
AbstractÐWe describe a generalized version of the BOD decay model in which the reaction is allowe... more AbstractÐWe describe a generalized version of the BOD decay model in which the reaction is allowed to assume an order other than one. This is accomplished by making the exponent on BOD concentration a free parameter to be determined by the data. This``mixed-order'' model may be a more appropriate representation of the aggregation of underlying processes that contribute to overall oxygen consumption in organic wastes and therefore has the potential to result in improved model ®t. In order to directly compare the relative plausibility of alternative choices for a reaction order, we adopt a Bayesian approach to parameter estimation. This approach uses Bayes' theorem to develop a joint probability distribution for all parameter values conditional on the observed data. From this joint distribution, we employ a numerical integration method to derive marginal parameter distributions that can be used to directly compare the relative plausibility of competing parameter values. For the data sets we examine, reaction orders other than one are generally much better supported by the data, and the often-proposed second-order model does not appear to be an adequate alternative. For practical use, the mixed-order model formulation results in a better ®t to observations and yields more realistic predictions of ultimate BOD than the ®rst-order expression. In addition, the probabilistic nature of the Bayesian model we describe facilitates explicit consideration of uncertainty in subsequent water quality management and decision-making. #
Catches of brown trout have decreased about 50% in many rivers and streams in Switzerland in the ... more Catches of brown trout have decreased about 50% in many rivers and streams in Switzerland in the past 15 years. Additionally, the health status of numerous brown trout populations has been assessed to be impaired. In order to evaluate the causes for these phenomena, a nationwide interdisciplinary project named "Fischnetz" was launched in 1999. Twelve hypotheses for the fish population declines were proposed and laboratory and field research projects were initiated to investigate these suggested causes. To apply the results of these investigations to the task of discerning the relative causal importance of each of the hypotheses, a Bayesian probability network is being developed. The development of a "Bayes net" begins with eliciting mental models about the cause-and-effect relationships among system variables from subjectmatter experts. Represented as a graphical network, these models imply a set of assumptions about the conditional dependencies among the variables, which simplifies the problem of working with imprecise knowledge. Hard-to-derive joint probability distributions are replaced by a set of conditional distributions, which can be characterized using either: (1) experimental investigation, (2) collected field data, (3) processbased models, or (4) elicited expert opinion. Such information, available as a result of the "Fischnetz" research program and from the scientific literature, will be integrated into the network, thus quantitatively summarizing all relevant information. The quantified network will then be used to assess the historical causal importance of anthropogenic changes, as well as predict the effect of proposed management actions. Analyses will be carried out for individual streams using site-specific information as evidence to update less specific prior beliefs. The results can be used form the basis for preliminary management and to prioritize future research projects based on their ability to reduce uncertainty in model-based assessments. In this paper, a first prototype of the network is presented and the methodology for its construction and application is discussed.
Journal of The American Water Resources Association, 2007
Abstract: The National Research Council recommended Adaptive Total Maximum Daily Load implementa... more Abstract: The National Research Council recommended Adaptive Total Maximum Daily Load implementation with the recognition that the predictive uncertainty of water quality models can be high. Quantifying predictive uncertainty provides important information for model selection and decision-making. We review five methods that have been used with water quality models to evaluate model parameter and predictive uncertainty. These methods (1) Regionalized Sensitivity Analysis, (2) Generalized Likelihood Uncertainty Estimation, (3) Bayesian Monte Carlo, (4) Importance Sampling, and (5) Markov Chain Monte Carlo (MCMC) are based on similar concepts; their development over time was facilitated by the increasing availability of fast, cheap computers. Using a Streeter-Phelps model as an example we show that, applied consistently, these methods give compatible results. Thus, all of these methods can, in principle, provide useful sets of parameter values that can be used to evaluate model predictive uncertainty, though, in practice, some are quickly limited by the “curse of dimensionality” or may have difficulty evaluating irregularly shaped parameter spaces. Adaptive implementation invites model updating, as new data become available reflecting water-body responses to pollutant load reductions, and a Bayesian approach using MCMC is particularly handy for that task.
Fecal indicator bacteria (FIB) are commonly used to assess the threat of pathogen contamination i... more 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.
The total maximum daily load ͑TMDL͒ concept provides the basis for regulating pollution load from... more The total maximum daily load ͑TMDL͒ concept provides the basis for regulating pollution load from riverine sources to impaired water bodies. However, load is comprised of two components: flow and concentration. These two components may have confounding, or even conflicting, effects on waterbody attributes of concern. This is particularly the case for dynamic, advective systems, such as estuaries. Resolving these components is critical for properly predicting the response of impaired systems to watershed management actions. The Neuse River Estuary in North Carolina is an example of such an impaired system. Nitrogen has been identified as the pollutant of concern, and the process of developing a TMDL for nitrogen is underway. We, therefore, analyze the extensive data that have been collected for the Neuse River and estuary to investigate spatiotemporal relationships between river flow, riverine total nitrogen ͑TN͒ inputs, water temperature, dissolved inorganic nitrogen concentration, algal density, and primary productivity. Results support the belief that phytoplankton in the estuary are under substantial riverine control. However, the riverine TN concentration alone has only a minor role in determining estuarine chlorophyll a គ concentration. River flow has a stronger influence, likely through its effects on down-estuary nitrogen delivery, residence time, salinity, and turbidity. These results imply that using riverine nitrogen load as the metric to evaluate watershed nutrient management may not be appropriate. While nitrogen controls should reduce loads in the long term, in the short term, river flow is the dominant component of load and has the opposite effect of nitrogen on algae at the up-estuary locations.
... this approach may lead to the inclusion of processes about which we have very little informat... more ... this approach may lead to the inclusion of processes about which we have very little information ... m −3 mol −1 ) n−1 d −1 ) and s is the sinking speed (md −1 ... resulting from high temperatures, combined with extended periods of vertical stratification leads to short-term bottom water ...
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Papers by Mark Borsuk