Recent studies of Chesapeake Bay hypoxia suggest higher susceptibility to hypoxia in years after the 1980s. We used two simple mechanistic models and Bayesian estimation of their parameters and prediction uncertainty to explore the nature of this regime shift. Model estimates show increasing nutrient conversion efficiency since the 1980s, with lower DO concentrations and large hypoxic volumes as a result. In earlier work, we suggested a 35% reduction from the average 1980-1990 total nitrogen load would restore the Bay to hypoxic volumes of the 1950s-1970s. With Bayesian inference, our model indicates that, if the physical and biogeochemical processes prior to the 1980s resume, the 35% reduction would result in hypoxic volume averaging 2.7 km(3) in a typical year, below the average hypoxic volume of 1950s-1970s. However, if the post-1980 processes persist the 35% reduction would result in much higher hypoxic volume averaging 6.0 km(3). Load reductions recommended in the 2003 agreement will likely meet dissolved oxygen attainment goals if the Bay functions as it did prior to the 1980s; however, it may not reach those goals if current processes prevail.
Applications using simulation-optimization approaches are often limited in practice because of the high computational cost associated with executing the simulation-optimization analysis. This research proposes a nonlinearity interval mapping scheme (NIMS) to overcome the computational barrier of applying the simulation-optimization approach for a waste load allocation analysis. Unlike the traditional response surface methods that use response surface functions to approximate the functional form of the original simulation model, the NIMS approach involves mapping the nonlinear input-output response relationship of a simulation model into an interval matrix, thereby converting the original simulation-optimization model into an interval linear programming model. By using the risk explicit interval linear programming algorithm and an inverse mapping scheme to implicitly resolve nonlinearity in the interval linear programming model, the NIMS approach efficiently obtained near-optimal solutions of the original simulation-optimization problem. The NIMS approach was applied to a case study on Wissahickon Creek in Pennsylvania, with the objective of finding optimal carbonaceous biological oxygen demand and ammonia (NH4) point source waste load allocations, subject to daily average and minimum dissolved oxygen compliance constraints at multiple points along the stream. First, a simulation-optimization model was formulated for this case study. Next, a genetic algorithm was used to solve the problem to produce reference optimal solutions. Finally, the simulation-optimization model was solved using the proposed NIMS, and the obtained solutions were compared with the reference solutions to demonstrate the superior computational efficiency and solution quality of the NIMS.
Hypoxia is a critical issue in the Gulf of Mexico that has challenged management efforts in recent years by an increase in hypoxia sensitivity to nitrogen loads. Several mechanisms have been proposed to explain the recent increase in sensitivity. Two commonly cited mechanisms are bottom-water reducing conditions preventing nitrification and thus denitrification, leading to more N recycling and production of oxygen-consuming organic matter, and carryover of organic matter from previous years increasing oxygen demand, making the system more sensitive. We use models informed by these mechanisms and fit with Bayesian inference to explore changes in Gulf of Mexico hypoxia sensitivity. We show that a model including an annually fit parameter representing variation in the fraction of nutrient loading and recycling contributing to bottom water oxygen demand provides a good fit to observations and is not improved by explicit inclusion of organic matter carryover to subsequent years. Both models support two stepwise increases in system sensitivity during the period of record. This change in sensitivity has greatly increased the nutrient reduction needed to achieve the established hypoxia goal. If the Gulf remains at the current state of sensitivity, our analysis suggests a roughly 70% reduction of spring TN loads from the 1988-1996 average of 6083 ton/day may be required.
The civil and environmental decision-making processes are plagued with uncertain, vague, and incomplete information. Interval linear programming (ILP) is a widely applied mathematical programming method in assisting civil and environmental decision making under uncertainty. However, the existing ILP decision approach is found to be ineffective in generating operational schemes for practical decision support due to a lack of linkage between decision risk and system return. In addition, the interpretation of the ILP solutions represented as the lower and upper bounds of decision variables can cause problems of infeasibility and nonoptimality in the resulted implementation schemes. This study proposed a risk explicit ILP (REILP) approach to overcome the limitations of existing ILP approaches. The REILP explicitly reflects the tradeoffs between risk and system return for a decision-making problem under an interval-type uncertainty environment. A risk function was defined to enable finding solutions which maximize system return while minimizing system risk, hence leading to crisp solutions that are feasible and optimal for practical decision making. A numerical experiment on land-use decision making under total maximum daily load was conducted to illustrate the REILP approach. The model results show that the REILP approach is able to efficiently explore the interval uncertainty space and generate an optimal decision front that directly reflects the tradeoff between decision risks and system return, allowing decision makers to make effective decision based on the risk-reward information generated by the REILP modeling analysis.
A multivariate statistical approach integrating the absolute principal components score (APCS) and multivariate linear regression (APCS-MLR), along with structural equation modeling (SEM), was used to model the influence of water chemistry variables on chlorophyll a (Chl a) in Lake Qilu, a severely polluted lake in southwestern China. Water quality was surveyed monthly from 2000 to 2005. APCS-MLR was used to identify key water chemistry variables, mine data for SEM, and predict Chl a. Seven principal components (PCs) were determined as eigenvalues > 1, which explained 68.67% of the original variance. Four PCs were selected to predict Chl a using APCS-MLR. The results showed a good fit between the observed data and modeled values. with R(2) = 0.80. For SEM, Chl a and eight variables were used: NH(4)-N (ammonia-nitrogen), total phosphorus (TP), Secchi disc depth (SD), cyanide (CN), arsenic (As), cadmium (Cd), fluoride (F), and temperature (T). A conceptual model was established to describe the relationships among the water chemistry variables and Chl a. Four latent variables were also introduced: physical factors, nutrients, toxic substances, and phytoplankton. In general, the SEM demonstrated good agreement between the sample covariance matrix of observed variables and the model-implied covariance matrix. Among the water chemistry factors, T and TP had the greatest positive influence on Chl a, whereas SD had the largest negative influence. These results will help researchers and decision-makers to better understand the influence of water chemistry on phytoplankton and to manage eutrophication adaptively in Lake Qilu. (C) 2009 Elsevier B.V. All rights reserved.