Hypoxia is a long-standing threat to the integrity of the Chesapeake Bay ecosystem. In this study, we introduce a Bayesian framework that aims to guide the parameter estimation of a Streeter-Phelps model when only hypoxic volume data are available. We present a modeling exercise that addresses a hypothetical scenario under which the only data available are hypoxic volume estimates. To address the identification problem of the model, we formulated informative priors based on available literature information and previous knowledge from the system. Our analysis shows that the use of hypoxic volume data results in reasonable predictive uncertainty, although the variances of the marginal posterior parameter distributions are usually greater than those obtained from fitting the model to dissolved oxygen (DO) profiles. Numerical experiments of joint parameter estimation were also used to facilitate the selection of more parsimonious models that effectively balance between complexity and performance. Parameters with relatively stable posterior means over time and narrow uncertainty bounds were considered as temporally constant, while those with time varying posterior patterns were used to accommodate the interannual variability by assigning year-specific values. Finally, our study offers prescriptive guidelines on how this model can be used to address the hypoxia forecasting in the Chesapeake Bay area.
Previous optimization-based watershed decision making approaches suffer two major limitations. First of all, these approaches generally do not provide a systematic way to prioritize the implementation schemes with consideration of uncertainties in the watershed systems and the optimization models. Furthermore, with adaptive management, both the decision environment and the uncertainty space evolve (1) during the implementation processes and (2) as new data become available. No efficient method exists to guide optimal adaptive decision making, particularly at a watershed scale. This paper presents a guided adaptive optimal (GAO) decision making approach to overcome the limitations of the previous methods for more efficient and reliable decision making at the watershed scale. The GAO approach is built upon a modeling framework that explicitly addresses system optimality and uncertainty in a time variable manner, hence mimicking the real-world decision environment where information availability and uncertainty evolve with time. The GAO approach consists of multiple components, including the risk explicit interval linear programming (REILP) modeling framework, the systematic method for prioritizing implementation schemes, and an iterative process for adapting the core optimization model for updated optimal solutions. The proposed approach was illustrated through a case study dealing with the uncertainty based optimal adaptive environmental management of the Lake Qionghai Watershed in China. The results demonstrated that the proposed GAO approach is able to (1) efficiently incorporate uncertainty into the formulation and solution of the optimization model, and (2) prioritize implementation schemes based on the risk and return tradeoff. As a result the GAO produces more reliable and efficient management outcomes than traditional non-adaptive optimization approaches. (C) 2011 Elsevier Ltd. All rights reserved.
Water quality management is subject to large uncertainties due to inherent randomness in the natural system and vagueness in the decision-making process. For water quality management optimization models, this means that some model coefficients can be represented by probability distributions, while others can be expressed only by ranges. Interval linear programming (ILP) and risk explicit interval linear programming (REILP) models for optimal load reduction at the watershed scale are developed for the management of Lake Qionghai Watershed, China. The optimal solution space of an ILP model is represented using intervals corresponding to the lower and upper bounds of each decision variable. The REILP model extends the ILP model through introducing a risk function and aspiration levels (lambda(pre)) into the model formulation. The REILP model is able to generate practical solutions and trade-offs through solving a series of submodels, minimizing the risk function under different aspiration levels. This is illustrated in the present study by solving 11 submodels corresponding to different aspiration levels. The results show that the ILP model suffers severe limitations in practical decision support, while the REILP model can generate solutions explicitly relating system performance to risk level. Weighing the optimal solutions and corresponding risk factors, decision makers can develop an efficient and practical implementation plan based directly on the REILP solution.