Grantee Research Project Results
Final Report: Bayesian Methods for Regional-Scale Stressor-Response Models
EPA Grant Number: R830887Title: Bayesian Methods for Regional-Scale Stressor-Response Models
Investigators: Lamon, E. Conrad
Institution: Louisiana State University - Baton Rouge
EPA Project Officer: Packard, Benjamin H
Project Period: May 14, 2003 through April 13, 2006 (Extended to April 13, 2008)
Project Amount: $389,168
RFA: Developing Regional-Scale Stressor-Response Models for Use in Environmental Decision-making (2002) RFA Text | Recipients Lists
Research Category: Ecological Indicators/Assessment/Restoration , Aquatic Ecosystems
Objective:
To use modern classification and regression trees and other Bayesian hierarchical techniques to link multiple environmental stressors to biological responses and quantify uncertainty in model predictions.
Summary/Accomplishments (Outputs/Outcomes):
- This research uses modern classification and regression trees and other Bayesian hierarchical techniques with lake and reservoir water quality data obtained from the Environmental Protection Agency (U.S. EPA) National Nutrient Criteria Database to link multiple environmental stressors to biological responses and quantify uncertainty in model predictions.The resulting Bayesian multilevel (hierarchical) model allows forecasts for unmonitored or poorly monitored waterbodies, among other advantages.
- A systematic method for identification and estimation of regional scale stressor-response models in aquatic ecosystems will be useful in monitoring and assessment of aquatic resources, determination of TMDL’s and for increased understanding of the differences between regions.These models should be useful to states, tribes and EPA in developing and refining regional nutrient criteria for lakes and reservoirs.
- These models will support development of ecoregion-specific, model based nutrient criteria for lakes and reservoirs, to complement criteria developed using EPA guidance documents.
We demonstrate a Bayesian classification and regression tree (CART) approach to link multiple environmental stressors to biological responses and quantify uncertainty in model predictions. Such an approach can: (1) report prediction uncertainty, (2) be consistent with the amount of data available and (3) be flexible enough to permit updates and improvements. Tree-based methods are a flexible approach useful for variable subset selection and when the analyst suspects global nonlinearity and cannot (or does not want to) specify the functional form of possible interactions a priori. We use the US EPA National Eutrophication Survey data to fit three models demonstrating the methods and to highlight important differences arising from slightly different model specifications. The Bayesian approach offers many advantages, including the estimation of the value of new information and proper probability distributions on the variable of interest as an output, which can be directly used in risk assessment or decision-making.
We develop regional-scale eutrophication models for lakes, ponds, and reservoirs to investigate the link between nutrients and chlorophyll-a. The Bayesian TREED (BTREED) model approach allows association of multiple environmental stressors with biological responses, and quantification of uncertainty sources in the empirical water quality model. Nutrient data for lakes, ponds, and reservoirs across the United States were obtained from the Environmental Protection Agency (USEPA) National Nutrient Criteria Database. The nutrient data consist of measurements for both stressor variables (such as total nitrogen and total phosphorus), and response variables (such as chlorophyll-a), used in the BTREED model. Markov chain Monte Carlo (McMC) posterior exploration guides a stochastic search through a rich suite of candidate trees toward models that better fit the data. The Bayes factor provides a goodness of fit criterion for comparison of resultant models. We randomly split the data into training and test sets; the training data were used in model estimation, and the test data were used to evaluate out of sample predictive performance of the model. An average relative efficiency of 1.02 between the training and test data for the four highest log-likelihood models suggests good performance in out of sample predictive efficiency.
A systematic method for identification and estimation of regional scale stressor-response models in aquatic ecosystems will be useful in monitoring and assessment of aquatic resources, determination of regional nutrient criteria and for increased understanding of the differences between regions. The model response variable is chlorophyll a, a measure of algal density, while the stressors include nutrient concentrations from the US EPA Nutrient Criteria Database (NCD) for lakes/ponds and reservoirs of the continental U.S. The NCD has observations for both stressors and biological responses determined using methods that are not consistently available at the continental scale. In order to link multiple environmental stressors to biological responses and quantify uncertainty in model predictions, we take a multilevel modeling approach to the estimation of a linear model for prediction of log10 Chlorophyll a using predictors log TP10 and log10 TN. The multilevel modeling approach allows us to adjust the impact of covariates at all levels (observation, higher level groups) for the simultaneous operation of contextual and individual variability in the outcome. Here we wish to allow separate regression coefficients for inference regarding similarities and differences between each of 14 ecoregions, and between the 2 water body types, lakes / ponds and reservoirs. We are also interested in the nuisance effects of the categorical variables indicating the type of nitrogen measurements (3 levels) and the type of chlorophyll a measurements (4 levels) used. Model based determination of nutrient criteria points to an apparent incompatibility of criteria developed for nutrient stressors and eutrophication responses using current EPA guidance.
We used the Bayesian TREED procedure to determine the efficacy of using an existing trophic status classification scheme for prediction of chlorophyll a in 150 Finnish lakes. Growing season data were log (base e) transformed and averaged by lake and year. We compared regressions of lnTP and lnTN on lnChla based on aggregations of the 9 levels of “Lake Type”, the classification scheme of the Finnish Environment Institute (SYKE), to a new classification scheme identified by the Bayesian TREED regression algorithm that partitioned the data based on geographic, morphometric and chemical properties of the lakes. The classifier identified with the BTREED algorithm had the best resulting model fit as measured by several different metrics. The model identified by the BTREED procedure that was allowed to use the suite of geographic, morphometric and chemical classifiers selected only the morphometric variable mean lake depth as the basis of the classification scheme. This model resulted in separate classes for shallow (<2.6 m), medium (2.6 m < mean depth < 16.3 m) and deep (>16.3 m) lakes corresponding to co-control by N and P (shallow and medium depths) and N-control (deep lakes) of algal productivity as measured by chlorophyll a, as indicated by the regression coefficients for each partition on depth. However, TN:TP ratios indicate clear P limitation in each depth class.
Journal Articles on this Report : 4 Displayed | Download in RIS Format
Other project views: | All 19 publications | 5 publications in selected types | All 4 journal articles |
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Freeman AM, Lamon EC, Stow CA. Nutrient criteria for lakes, ponds, and reservoirs:a Bayesian TREED model approach. Ecological Modelling 2009;220(5):630-639. |
R830887 (Final) |
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Lamon III EC, Stow CA. Bayesian methods for regional-scale eutrophication models. Water Research 2004;38(11):2764-2774. |
R830887 (2003) R830887 (Final) |
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Lamon III EC, Malve O, Pietilainen OP. Lake classification to enhance prediction of eutrophication endpoints in Finnish lakes. Environmental Modelling & Software 2008;23(7):938-947. |
R830887 (Final) |
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Lamon III EC, Qian SS. Regional scale stressor-response models in aquatic ecosystems. Journal of the American Water Resources Association 2008;44(3):771-781. |
R830887 (Final) |
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Supplemental Keywords:
Bayesian analysis; Bayesian TREED model; chlorophyll a; classification and regression trees (CART); decision theory, environmental statistics, eutrophication; lake classification; Markov chain Monte Carlo methods; multilevel models; National Eutrophication Survey; nitrogen; nutrients; Nutrient Criteria Database; nutrient ecoregions; nutrient criteria; regionalization; stressor-response relationships; tree based models; water quality, water quality models,, RFA, Economic, Social, & Behavioral Science Research Program, Scientific Discipline, Water, Ecosystem Protection/Environmental Exposure & Risk, Water & Watershed, Monitoring/Modeling, Regional/Scaling, decision-making, Ecology and Ecosystems, Watersheds, Economics & Decision Making, Social Science, risk assessment, ecosystem modeling, aquatic ecosystem, watershed, ecosystem assessment, Bayesian approach, decision analysis, decision making, environmental decision making, TMDL, ecological variation, regional scale impacts, water quality, assessment endpoint mechanistic research, ecology assessment models, ecosystem stress, watershed assessment, decision support tool, environmental risk assessment, Bayesian classifiers, water monitoring, adaptive implementation modelingRelevant Websites:
http://www.nicholas.duke.edu/people/faculty/reckhow/ConradSelectedPublications.pdf Exit
Progress and Final Reports:
Original AbstractThe perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Conclusions drawn by the principal investigators have not been reviewed by the Agency.