Computable optimal value bounds for generalized convex programs

It has been shown by Fiacco that convexity or concavity of the optimal value of a parametric nonlinear programming problem can readily be exploited to calculate global parametric upper and lower bounds on the optimal value function. The approach is attractive because it involves manipulation of information normally required to characterize solution optimality. A procedure is briefly described for calculating and improving the bounds as well as its extensions to generalized convex and concave functions. Several areas of applications are also indicated

IMPACTS OF WINDS AND RIVER FLOW ON ESTUARINE DYNAMICS AND HYPOXIA IN CHESAPEAKE BAY

In the stratified rotating estuary of Chesapeake Bay, the driving mechanisms of wind-induced lateral circulation are examined using a three-dimensional hydrodynamic model (ROMS). A new approach based on the streamwise vorticity dynamics is developed, and the analysis reveals a balance among three terms: the conversion of the planetary vorticity by along-channel current shear, baroclinicity due to cross-channel density gradient, and turbulent diffusion. It is found that the lateral flow in the Bay is mainly driven by the Ekman forcing, but the lateral baroclinicity creates asymmetry in the streamwise vorticity between down- and up-estuary winds. The traditional view of wind-driven circulation in estuaries ignores the lateral circulation, but wind-induced lateral flows can affect subtidal estuarine circulation and stratification. Coriolis acceleration associated with the lateral flows is of first-order importance in the along-channel momentum balance, with the sign opposite to the stress divergence in the surface layer and the pressure gradient in the bottom layer, thereby reducing the shear in the along-channel current. Moreover, the lateral straining of the density field by lateral circulation offsets the along-channel straining to control the overall stratification. Regime diagrams are constructed using the dimensionless Wedderburn (W) and Kelvin (Ke) numbers to clarify the net wind effects. A coupled hydrodynamic-biogeochemical model is developed to simulate the seasonal cycle of dissolved oxygen in Chesapeake Bay and investigate key processes which regulate summer hypoxia in the estuary. Diagnostic analysis of the oxygen budget for the bottom water reveals a balance between physical transport and biological consumption. In addition to the vertical diffusive flux, the along-channel and cross-channel advective fluxes are found to be important contributors in supplying oxygen to the bottom water. While the vertical diffusive oxygen flux varies over the spring-neap tidal cycle and is enhanced during wind events, the advective oxygen fluxes show long-term averages due to the gravitational estuarine circulation but display strong oscillations due to wind-driven circulations. It is found that water column respiration comprises about 74% of the total consumption and sediment oxygen demand contributes 26%. Sensitivity-analysis model runs are conducted to further quantify the effects of river flow, winds, water column respiration and sediment oxygen demand on the hypoxic volume in the estuary

Water quality modeling of Lake Diefenbaker

Lake Diefenbaker is one of the most important sources of water in the prairie province of Saskatchewan, Canada. It is a long (181.6 km) and narrow (maximum width 6 km) reservoir formed along the South Saskatchewan River by the construction of the Gardiner and Qu'Appelle River dams in the 1960s. The reservoir has a surface elevation of 556.87 meters above sea level (full supply level) with a maximum depth of 60 m, a surface area of approximately 393 km2 and a volume of 9.03 km3. The reservoir and dams are part of a multipurpose hydraulic project, which provides water for irrigation, drinking water, eco-services, hydropower generation, aquaculture and recreation as well as for flood mitigation. Surface water quality modeling is a useful tool to simulate and predict nutrient dynamics in lakes, reservoirs, and rivers, as well as the fate and transport of sediment and toxic contaminants in freshwater environments. In this study, water quality modeling of Lake Diefenbaker was carried out in order to help understand the mixing regimes and biological processes in the aquatic environment of this strategic reservoir. Based on the study's objectives, the physical and chemical characteristics of the lake and available data, the laterally-averaged two-dimensional model CE-QUAL-W2 hydrodynamic and water quality model was deemed the best model for Lake Diefenbaker. CE-QUAL-W2 was developed by the US Army Corp of Engineers to simulate the hydrodynamics, water quality, aquatic biology and aquatic chemistry in surface waters. On the one hand, this study provided information on temperature and hydrodynamic behaviors of Lake Diefenbaker as well as sediment and nutrient transport, nutrient uptake and algal activities. On the other hand, it addressed some key and limitations in the application of water quality models. Limitations addressed include studying snow cover effects on the ice surface in winter, applying variable algal stoichiometry, using combined local/global optimization for model calibration, and running the model on High-Performance Cluster (HPC) systems

Influence of Mercury-Dissolved Organic Matter (DOM) Complexation on Toxicity in Natural Waters

Global industrialization, coupled with a large biogeochemical cycle that moves mercury through the environment, has resulted in higher mercury concentrations being detected in many environmental compartments. Although the presence of mercury in each compartment has the potential to elicit toxicity, mercury found in natural waters provides the greatest risk, due to the various reactions it can undergo, resulting in a plethora of different species. Due to the fact that mercury contamination in aquatic systems has the potential to bioaccumulate and biomagnify up the food chain and cause toxicity, understanding the behavior of mercury in these systems is imperative in the protection of both organisms and humans. Although much research has focused on the human health effects of mercury contamination, little research has examined the environmental implications of mercury contamination. This research attempts to bridge the gap in understanding of mercury toxicity in the presence of natural organic matter (NOM) to aquatic organisms in natural waters. Whole water samples were collected from seven sites along the length of the Ogeechee River in southeastern Georgia. Physiochemical parameters of each water sample, including hardness, alkalinity, pH, conductivity, and ion concentrations, were measured to obtain a more comprehensive understanding of the sites. Due to the fact that organic matter collected from waters can be varied in both concentration and nature, measurements were also performed in an effort to construct profiles for the dissolved organic matter (DOM) in each water sample. These profiles were later used in the quantification of accurate metal concentrations for toxicity experiments. The results from the physiochemical analysis of the Ogeechee River water samples show that while the DOM is relatively similar with regards to both molecular weight and size distribution, there are differences observed in the molecular weight polydispersity values as well as the concentration of reduced sulfur associated with the DOM at each site. The Ogeechee River site water was used in mercury toxicity experiments to assess the role that DOM complexation plays in the amelioration of metal toxicity. The original whole water and a variety of manipulations to the original water were used to quantify the reduction in mercury toxicity. Results indicated that although a reduction in mercury toxicity was observed in the presence of Ogeechee River DOM, the observed reduction in toxicity was independent of DOM concentration in all experiments. To confirm the mercury toxicity results using the Ogeechee River waters, Suwannee River DOM was obtained from the International Humic Substances Society and used in similar experiments. In addition to mercury, copper toxicity experiments were also conducted to compare results. These experiments showed that although copper toxicity was systematically decreased with higher concentrations of organic matter, mercury toxicity was again independent of DOM concentration. The toxicity results observed between the two metals was hypothesized to be due to the differences in binding strengths between the metals and various ligands present in DOMs. Due to the fact that such different toxicity reductions were observed between copper and mercury using the same organic matter source, the kinetic lability of various metal complexes was quantified using competitive ligand-exchange reactions. The complexation strengths of each metal were assessed using a variety of simple organic ligands. These ligands were used separately to determine rate constants for individual metal-simple ligand complexes. Results show that, although both copper and mercury share similar rate constants to simple ligands, the metal\u27s dependence on the ligand concentration is equally important. In the copper simple ligand experiments, an independence is observed, minimizing the importance of the disjunctive mechanistic pathway. Mercury, on the other hand, shows a dependence on ligand concentration, resulting in the disjunctive pathway playing a larger role. The simple ligand relationships were then used as a model to predict the expected binding strength of each metal when complexed to dissolved organic matter, a much more complicated and complex ligand. Results show that copper is much more kinetically stable when complexed to DOM, which is a result of its stronger complexation to both oxygen and nitrogen ligands, which are predominantly found on DOM. Mercury complexed to DOM results in a much more labile complex, due to the fact that it does not strongly bind to wither oxygen or nitrogen ligands. Therefore, mercury bound to DOM is much more likely to be bioavailable for organismal uptake in the water column, supporting the hypothesis of kinetic lability to explain the toxicity results obtained using both metals

Sewage Discharging in a Line: Global Optimization and Grand Cooperation

Players cooperating in a line is a special while essential phenomenon in real life collaborating activities such as assembly line production, pipeline supply chain management and other streamlining operational settings. In this paper, we study the scenario of cooperative sewage discharge with multiple participants positioning in a line along a river such that the optimization decision and cooperation strategy are mutually affected by both upstream and downstream players. We make three main contributions accordingly: Firstly, we formalize the sewage discharge problem (SDP) for different groups of players, and use greedy strategy and dynamic programming to design the optimal algorithms to solve the SDP in polynomial time. Secondly, we show that the cooperative game defined on sewage discharge problem, referred to as SDG, has a non-empty core due to its special line-positioning structure. Therefore, a grand stable cooperation is guaranteed. Furthermore, inspired by the fact that the SDG is core non-empty while non-convex, we successfully identify a relaxed concept of convexity -- directional-convexity, which can also serve as a sufficient condition for a cooperative game having a non-empty core

Integrated Environmental Modelling Framework for Cumulative Effects Assessment

Global warming and population growth have resulted in an increase in the intensity of natural and anthropogenic stressors. Investigating the complex nature of environmental problems requires the integration of different environmental processes across major components of the environment, including water, climate, ecology, air, and land. Cumulative effects assessment (CEA) not only includes analyzing and modeling environmental changes, but also supports planning alternatives that promote environmental monitoring and management. Disjointed and narrowly focused environmental management approaches have proved dissatisfactory. The adoption of integrated modelling approaches has sparked interests in the development of frameworks which may be used to investigate the processes of individual environmental component and the ways they interact with each other. Integrated modelling systems and frameworks are often the only way to take into account the important environmental processes and interactions, relevant spatial and temporal scales, and feedback mechanisms of complex systems for CEA. This book examines the ways in which interactions and relationships between environmental components are understood, paying special attention to climate, land, water quantity and quality, and both anthropogenic and natural stressors. It reviews modelling approaches for each component and reviews existing integrated modelling systems for CEA. Finally, it proposes an integrated modelling framework and provides perspectives on future research avenues for cumulative effects assessment

An evaluation of a severe smog episode in the Eastern U.S. using regional modeling and satellite measurements

An ensemble of regional chemical modeling (WRF/Chem with RADM2) simulations, satellite, ozonesonde, and surface observations during July 7-11, 2007 was used to examine the horizontal and vertical signature of one of the worst smog events in the eastern U.S. in the past decade. The general features of this event -- a broad area of high pressure, weak winds and heavy pollution, terminated by the passage of a cold front -- were well simulated by the model. Average 8-hr maximum O3 has a mean (±Σ) bias of 0.59 (±11.0) ppbv and a root mean square error of 11.0 ppbv. WRF/Chem performed the best on poor air quality days, simulating correctly the spatial pattern of surface O3. Yet the model underpredicted O3 maxima by 5-7 ppbv in the Northeast and overpredicted by 8-11 ppbv in the Southeast. High O3 biases in the Southeast are explained by overpredicted temperatures in the model (>1.5°C). Sensitivity simulations with 1) accelerated O3 dry deposition velocity and 2) suppressed multiphase nitric acid formation pushed the model closer to observations. Simulated O3 vertical profiles over Beltsville, MD showed good agreement with ozonesonde measurements, but the modeled boundary layer depth was overpredicted on July 9, contributing to the low bias over this region. During this severe smog episode, space-borne TES detected high total tropospheric column ozone (TCO) over the Western Atlantic Ocean off the coast near North and South Carolina. The standard product (OMI/MLS) missed the magnitude of these local maxima, but the level-2 ozone profile (OMI) confirmed the TES observations. HYSPLIT back trajectories from these O3 maxima intersected regions of strong convection over the Southeast and Great Lakes regions. When lightning NO emissions were implemented in WRF/Chem, the high concentrations of NOx and O3 off the coast were well reproduced, showing that the exported O3 was produced by a combination of natural NO and pollutants lofted from the lower atmosphere. Lastly, WINTER MONEX O3 data from 1978 are presented for the first time here in discussion of open cell convection over Indonesia

Beyond "The limits to peat bog growth'': Cross-scale feedback in peatland development

Copyright by the Ecological Society of America 2006, for personal or educational use only. Article is available at <http://dx.doi.org/10.1890/0012-9615(2006)076[0299:BTLTPB]2.0.CO;2