Bayesian Statistical Analysis in Coastal Eutrophication Models: Challenges and Solutions

Bayesian Statistical Analysis in Coastal Eutrophication Models: Challenges and Solutions by Farnaz Nojavan A. Environment Duke University Date: Approved: Song S. Qian, Co-Supervisor Gabriel Katul, Co-Supervisor Elizabeth A. Albright Marco Marani Craig Stow An abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Environment in the Graduate School of Duke University 2014 Copyright c © 2014 by Farnaz Nojavan A. All rights reserved except the rights granted by the Creative Commons Attribution-Noncommercial Licence Abstract Estuaries interfacing with the land, atmosphere and open oceans can be influenced in a variety of ways by anthropogenic activities. Centuries of overexploitation, habitat transformation, and pollution have degraded estuarine ecological health. Key concerns of public and environmental managers of estuaries include water quality, particularly the enrichment of nutrients, increased chlorophyll a concentrations, increased hypoxia/anoxia, and increased Harmful Algal Blooms (HABs). One reason for the increased nitrogen loading over the past two decades is the proliferation of concentrated animal feeding operations (CAFOs) in coastal areas. This dissertation documents a study of estuarine eutrophication modeling, including modeling of major source of nitrogen in the watershed, the use of the Bayesian Networks (BNs) for modeling eutrophication dynamics in an estuary, a documentation of potential problems of using BNs, and a continuous BN model for addressing these problems. Environmental models have emerged as great tools to transform data into useful information for managers and policy makers. Environmental models contain uncertainty due to natural ecosystems variability, current knowledge of environmental processes, modeling structure, computational restrictions, and problems with data/observations due to measurement error or missingness. Many methodologies capable of quantifying uncertainty have been developed in the scientific literature. Examples of such methods are BNs, which utilize conditional probability tables to describe the relationships among variables. This doctoral dissertation demonstrates ivEstuaries interfacing with the land, atmosphere and open oceans can be influenced in a variety of ways by anthropogenic activities. Centuries of overexploitation, habitat transformation, and pollution have degraded estuarine ecological health. Key concerns of public and environmental managers of estuaries include water quality, particularly the enrichment of nutrients, increased chlorophyll a concentrations, increased hypoxia/anoxia, and increased Harmful Algal Blooms (HABs). One reason for the increased nitrogen loading over the past two decades is the proliferation of concentrated animal feeding operations (CAFOs) in coastal areas. This dissertation documents a study of estuarine eutrophication modeling, including modeling of major source of nitrogen in the watershed, the use of the Bayesian Networks (BNs) for modeling eutrophication dynamics in an estuary, a documentation of potential problems of using BNs, and a continuous BN model for addressing these problems. Environmental models have emerged as great tools to transform data into useful information for managers and policy makers. Environmental models contain uncertainty due to natural ecosystems variability, current knowledge of environmental processes, modeling structure, computational restrictions, and problems with data/observations due to measurement error or missingness. Many methodologies capable of quantifying uncertainty have been developed in the scientific literature. Examples of such methods are BNs, which utilize conditional probability tables to describe the relationships among variables. This doctoral dissertation demonstrates iv how BNs, as probabilistic models, can be used to model eutrophication in estuarine ecosystems and to explore the effects of plausible future climatic and nutrient pollution management scenarios on water quality indicators. The results show interaction among various predictors and their impact on ecosystem health. The synergistic effects between nutrient concentrations and climate variability caution future management actions. BNs have several distinct strengths such as the ability to update knowledge based on Bayes’ theorem, modularity, accommodation of various knowledge sources and data types, suitability to both data-rich and data-poor systems, and incorporation of uncertainty. Further, BNs’ graphical representation facilitates communicating models and results with environmental managers and decision-makers. However, BNs have certain drawbacks as well. For example, they can only handle continuous variables under severe restrictions (1Each continuous variable be assigned a (linear) conditional Normal distribution; 2No discrete variable have continuous parents). The solution, thus far, to address this constraint has been discretizing variables. I designed an experiment to evaluate and compare the impact of common discretization methods on BNs. The results indicate that the choice of discretization method severely impacts the model results; however, I was unable to provide any criteria to select an optimal discretization method. Finally, I propose a continuous variable Bayesian Network methodology and demonstrate its application for water quality modeling in estuarine ecosystems. The proposed method retains advantageous characteristics of BNs, while it avoids the drawbacks of discretization by specifying the relationships among the nodes using statistical and conditional probability models. The Bayesian nature of the proposed model enables prompt investigation of observed patterns, as new conditions unfold. The network structure presents the underlying ecological ecosystem processes and provides a basis for science communication. I demonstrate model development and v temporal updating using the New River Estuary, NC data set and spatial updating using the Neuse River Estuary, NC data set.