An interval-parameter waste-load-allocation model for river water quality management under uncertainty

An integrated simulation-optimization approach for combined allocation of water quantity and quality under multiple uncertainties

Multiple uncertainties such as water quality processes, streamflow randomness affected by climate change, indicators' interrelation, and socio-economic development have brought significant risks in managing water quantity and quality (WQQ) for river basins. This research developed an integrated simulation-optimization modeling approach (ISMA) to tackle multiple uncertainties simultaneously. This approach combined water quality analysis simulation programming, Markov-Chain, generalized likelihood uncertainty estimation, and interval two-stage left-hand-side chance-constrained joint-probabilistic programming into an integration nonlinear modeling framework. A case study of multiple water intake projects in the Downstream and Delta of Dongjiang River Basin was used to demonstrate the proposed model. Results reveal that ISMA helps predict the trend of water quality changes and quantitatively analyze the interaction between WQQ. As the joint probability level increases, under strict water quality scenario system benefits would increase [3.23, 5.90] × 109 Yuan, comprehensive water scarcity based on quantity and quality would decrease [782.24, 945.82] × 106 m3, with an increase in water allocation and a decrease in pollutant generation. Compared to the deterministic and water quantity model, it allocates water efficiently and quantifies more economic losses and water scarcity. Therefore, this research has significant implications for improving water quality in basins, balancing the benefits and risks of water quality violations, and stabilizing socio-economic development.

An Optimization Model for Water Management under the Dual Constraints of Water Pollution and Water Scarcity in the Fenhe River Basin, North China

Sustainable watershed development suffers from severe challenges, such as water pollution and water scarcity. Based on an analysis of water quality and water utilization in the Fenhe River Basin, an inexact two-stage stochastic programming model with downside-risk aversion was built for optimal water resource allocations for the four primary water use sectors (industry, domestic use, agriculture, and the environment) in the Fenhe River Basin. The model aims to maximize the comprehensive watershed benefits, including water benefits, water costs, water treatment costs, and downside risks. The constraints are water quality, available water resources, and sectoral demands in different hydrological scenarios. The results show that pollutant emissions decrease as risk-aversion levels increase and show the opposite trend in the midstream and downstream areas. The increase in water resource allocation for agriculture and reduction in ecological water indicate that agriculture suffered the greatest water shortage and risk. Improving water recycling and coordinating the transferred water resources increases the comprehensive benefits and reduces sectoral risks. The model effectively manages rational water allocations under dual constraints and provides support for coordinating socio-economic development and environmental protection in the river basin.

Data-driven interval credibility constrained quadratic programming model for water quality management under uncertainty

Although integrated simulation-optimization modeling can provide a comprehensive and reliable analysis for water quality management (WQM), it is usually not easy to implement in practice. This study proposed a new efficient simulation-optimization modeling approach by leveraging the power of data-driven modeling, to support WQM under various uncertainties. A water quality simulation model is integrated with the optimization model, and then substituted by a series of numerical surrogate models based on inexact linear regression. The transformation can significantly reduce the computational burden and make it possible to implement uncertainty quantification through hybrid inexact programming. The proposed model incorporates interval quadratic programming and credibility constrained programming to deal with nonlinearity and various uncertainties associated with the management system. The proposed approach is applied to a real case study of the Grand River watershed in Canada for controlling phosphorus concentration in river water. The Grand River Simulation Model (GRSM) is employed as the physical simulation model to estimate the total phosphorus concentration in the river. Interval solutions under different confidence levels of violating the effluent standards were obtained, which can be used to generate optimal phosphorus control strategies. The results indicate the proposed data-driven interval credibility constrained quadratic programming (DICCQP) model is able to provide reliable and robust solutions for WQM by considering nonlinearity and various uncertainties while maintaining a high computational efficiency. The proposed new framework can be extended and applied to the other watersheds. The high efficiency of the proposed model makes it possible to solve large-scale complex water quality management and planning problems.

An Improved Inexact Two-Stage Stochastic with Downside Risk-Control Programming Model for Water Resource Allocation under the Dual Constraints of Water Pollution and Water Scarcity in Northern China

Water resource allocation aimed at sustainable watershed development suffers from prominent challenges such as water pollution and scarcity, especially in water-deprived regions. Based on analysis of water quality, use, and sectoral demands during the planning period in the Fenhe River Basin, an improved inexact two-stage stochastic programming model with downside risk control was built for optimal resource allocations for the four primary sectors (industry, domestic use, agriculture, and the environment) in the basin. The principal constraints are river water quality and available water resources under the three hydrological scenarios (low, medium, and high). The results show that industrial, domestic, and agricultural water use in the middle and lower reaches were significantly reduced by requiring improved water quality; agriculture suffered the greatest water shortage and risk. As the level of risk control improved, the comprehensive watershed benefits and agricultural risks were gradually reduced. Improving water reuse significantly reduces the risk and increases the benefits. The model can effectively manage rational water allocations under the dual constraints of water quality and quantity, meanwhile alleviating water competition caused by different water benefits to provide support for coordinating the improvement of water quality and socio-economic development in the basin.

Simulation-based interval chance-constrained quadratic programming model for water quality management: A case study of the central Grand River in Ontario, Canada

Effective river water quality management and planning is a complex issue challenged by various complexities and uncertainties. A simulation-based interval chance-constrained quadratic programming (ICCQP) model is developed for the seasonal planning of water quality management (WQM) under various uncertainties. The proposed model incorporates interval quadratic programming, chance-constrained programming, and a seasonal water quality simulation model within a general framework for WQM. Uncertainties associated with the objective and the coefficients in the left-hand sides of the constraints are tackled as intervals. Meanwhile, parameter uncertainties on the right-hand sides are characterized using probability distributions. Nonlinearities in the cost function are reflected by quadratic programming. A multi-segment water quality model is used to simulate the dynamic interactions between wastewater discharges and river water quality. The proposed ICCQP-WQM model is applied in a real case study for the control of total phosphorus (TP) in the central Grand River in Ontario, Canada. The results demonstrate that the proposed model is able to incorporate uncertainties expressed as intervals and probability information into an optimization framework and provide interval solutions. Thus, different cost-effective schemes for seasonal WQM could be generated. The results show the Kitchener wastewater treatment plant (WWTP) affects the value of the objective function more than the other WWTPs in the study area. It is also found that the Kitchener WWTP's cost accounts for the highest proportion (approximately 35.1-37.9%) of the total annual cost, which implies the control of TP at the Kitchener plant is the most important to the system. Moreover, river water TP standards in spring and autumn are usually difficult to meet, indicating different TP control strategies are needed in these two seasons. The generated results are valuable for local decision makers to generate TP control strategies, and also to identify optimized solutions under various uncertainties. The proposed ICCQP-WQM model can be extended to other watersheds to support effective water quality management and planning.

Trade-off between equity and efficiency for allocating wastewater emission permits in watersheds considering transaction

As the management of wastewater emission permits in watershed has become a growing worldwide concern, a substantial challenge has been created in balancing the social stability, economic construction, and ecological function. Therefore, the equitable and efficient allocation of wastewater emission permits in watershed integrating sustainability is vital for environmental management. Considering the wastewater discharge permits transaction between subareas, a multi-objective model is proposed to analyze the allocation of wastewater emission permits in a watershed. The first objective function is to maximize the allocation equity using the environmental Gini coefficient, and the second is to maximize the economic efficiency for the sustainable development of a watershed as the constraint. In this study, the trade-off between the equity and economic efficiency of allocation is balanced. A case study of the Tuojiang River Basin in China is conducted to demonstrate the feasibility, rationality and practicality of the model. The multi-principle and multi-objective allocation model was found to be more reliable and feasible than the previous models, indicating that the equity and efficiency should be balanced to mitigate the water scarcity and deteriorating water quality when managing the basin, and trading is an effective measure for ensuring the equity.

How did the bacterial community respond to the level of urbanization along the Yangtze River?

Bacterial communities in the sediment of the Yangtze River influenced by rapid urbanization have thus far been under-investigated despite the importance of microorganisms as mass transporters. Here, the response patterns of the bacterial community along the Yangtze River to different levels of urbanization were generated using 16S rRNA Miseq sequencing. The results reveal that economic aspects have made the largest contribution (41.8%) to the urbanization along the Yangtze River. A clear declining tendency in the abundance of Chloroflexi and Acidobacteria and a significant increase in the abundance of Bacteroidetes were observed with an elevated urbanization level gradient. Bacterial diversity showed a negative relevance (P < 0.01) to the demographic, economic and social urbanization index. Per capita gross domestic product (GDP) (PCGDP) and the GDP of tertiary industry (GDP3) exhibited significantly (P < 0.05) negative correlations with the bacterial diversity, while a positive relationship between the pH and α-diversity (P < 0.05) was observed. Redundancy analysis revealed that PCGDP was significantly correlated (13.9%, P < 0.01) with the overall bacterial compositions, followed by temperature (10.8%, P < 0.01) and GDP3 (8.4%, P < 0.05). Meanwhile, the GDP3 (35.9%), the ratio of total nitrogen and total phosphorus (N/P) (12.9%) and the PCGDP (8.8%) were revealed to be most significantly related to the metabolic bacteria (P < 0.05). The metabolic functions of the bacteria related to the N-cycle and S-cycle were significant in the sediment of the Yangtze River. The variations of the bacterial community and metabolic function responding to the rapid urbanization were related to the economic development via the influence of the 'mass effect'. In brief, the tertiary industry was significantly correlated with the variations in the composition of the metabolic community and the variations in the overall bacteria were both related to the tertiary and secondary industry.

A simulation-based bi-level multi-objective programming model for watershed water quality management under interval and stochastic uncertainties

A simulation-based interval stochastic bi-level multi-objective programming (SISBLMOP) model was proposed in this research, through integrating the global nutrient export from watersheds model, interval parameter programming and stochastic chance-constrained programming into a general bi-level multi-objective programming framework. The SISBLMOP model can handle multiple uncertainties expressed as discrete intervals and probability density functions in both the simulation and optimization processes. System complexities, including the hierarchy structure of upper- and lower-level decision makers, can also be addressed in the model. The proposed model is applied to a real-world case study of the Xinfengjiang Reservoir Watershed in South China to identify the satisfactory implementation levels of multiple best management practices (BMPs). The model results show that multiple BMP schemes for water quality management can be obtained under different upper- and lower-level decision-making and risk-violation scenarios, reflecting the cooperation and gaming results of the two-level decision makers. Consequently, the corresponding BMP implementation costs are acceptable to both the upper- and lower-level decision makers. The model is widely applicable and can be effectively used for water quality management under multiple uncertainties and complexities.

Managing the uncertainty problems of municipal solid waste disposal

In waste management systems, several parameters such as the rate of waste production, disposal facility, treatment cost, and their relations may be uncertain and can influence the associated optimization processes. These uncertainty problems in waste management were addressed by using various inexact programming methods. For example, fuzzy, stochastic programming, and interval programming techniques were generally used for solving the uncertainty-related waste management problems. The analysis revealed that the efficiency of waste management system can be maximized by the proper use of these optimization techniques. In this approach, an uncertainty problem is reduced into several subproblems with sureness by using the minimax regret optimization technique. And these subproblems are focused on a calculation where the lament of not getting the goal is minimized. The analysis also revealed that the fuzzy-stochastic method was increasingly used for dealing with the waste management system uncertainty in recent times. This paper gives an overview of dealing with the uncertainty problems of waste disposal in urban areas. An indication of the solid waste disposal problems and its management in conjunction with the repercussion of the investigation is described. The rationale and setting of the uncertainty issues in proper waste management are detailed. The applications of fuzzy analysis approach and integrated waste management in dealing with the uncertainty problems are presented. The applications of these techniques in diverse case studies worldwide are discussed and finally, the conclusions of the literature analysis are summarized.

Historical Accountability for Equitable, Efficient, and Sustainable Allocation of the Right to Emit Wastewater in China

Establishing policies for controlling water pollution through discharge permits creates the basis for emission permit trading. Allocating wastewater discharge permits is a prerequisite to initiating the market. Past research has focused on designing schemes to allocate discharge permits efficiently, but these schemes have ignored differences among regions in terms of emission history. This is unfortunate, as fairness may dictate that areas that have been allowed to pollute in the past will receive fewer permits in the future. Furthermore, the spatial scales of previously proposed schemes are not practical. In this article, we proposed an information entropy improved proportional allocation method, which considers differences in GDP, population, water resources, and emission history at province spatial resolution as a new way to allocate waste water emission permits. The allocation of chemical oxygen demand (COD) among 30 provinces in China is used to illustrate the proposed discharge permit distribution mechanism. In addition, we compared the pollution distribution permits obtained from the proposed allocation scheme with allocation techniques that do not consider historical pollution and with the already established country plan. Our results showed that taking into account emission history as a factor when allocating wastewater discharge permits results in a fair distribution of economic benefits.

Industrial water resources management based on violation risk analysis of the total allowable target on wastewater discharge

To improve the capabilities of conventional methodologies in facilitating industrial water allocation under uncertain conditions, an integrated approach was developed through the combination of operational research, uncertainty analysis, and violation risk analysis methods. The developed approach can (a) address complexities of industrial water resources management (IWRM) systems, (b) facilitate reflections of multiple uncertainties and risks of the system and incorporate them into a general optimization framework, and (c) manage robust actions for industrial productions in consideration of water supply capacity and wastewater discharging control. The developed method was then demonstrated in a water-stressed city (i.e., the City of Dalian), northeastern China. Three scenarios were proposed according to the city’s industrial plans. The results indicated that in the planning year of 2020 (a) the production of civilian-used steel ships and machine-made paper & paperboard would reduce significantly, (b) violation risk of chemical oxygen demand (COD) discharge under scenario 1 would be the most prominent, compared with those under scenarios 2 and 3, (c) the maximal total economic benefit under scenario 2 would be higher than the benefit under scenario 3, and (d) the production of rolling contact bearing, rail vehicles, and commercial vehicles would be promoted.

Waste load equilibrium allocation: a soft path for coping with deteriorating water systems

Waste load allocation is always regarded as another efficient approach comparing with the technology-based approach to improve the water quality. This paper proposes a bi-level multi-objective optimization model for optimally allocating the waste load of a river basin incorporating some concerns (i) the allocation equity from the regional authority, (ii) maximal benefits from the subareas along the river, and (iii) the Stackelberg-Nash-Cournot equilibrium strategy between the upper and lower decision makers. Especially, a novel Gini coefficient for measuring the load allocation equity is defined by considering the economic level and waste water quantity. The applicability and effectiveness of the proposed model is demonstrated through a practical case based on the Tuojiang River, which is a typical basin with diversified industrial waste discharges in western China. Some operational suggestions are developed to assist the decision makers' cope with deteriorating water systems.

A Bayesian-based two-stage inexact optimization method for supporting stream water quality management in the Three Gorges Reservoir region

In this study, a Bayesian-based two-stage inexact optimization (BTIO) method is developed for supporting water quality management through coupling Bayesian analysis with interval two-stage stochastic programming (ITSP). The BTIO method is capable of addressing uncertainties caused by insufficient inputs in water quality model as well as uncertainties expressed as probabilistic distributions and interval numbers. The BTIO method is applied to a real case of water quality management for the Xiangxi River basin in the Three Gorges Reservoir region to seek optimal water quality management schemes under various uncertainties. Interval solutions for production patterns under a range of probabilistic water quality constraints have been generated. Results obtained demonstrate compromises between the system benefit and the system failure risk due to inherent uncertainties that exist in various system components. Moreover, information about pollutant emission is accomplished, which would help managers to adjust production patterns of regional industry and local policies considering interactions of water quality requirement, economic benefit, and industry structure.

Water Environmental Capacity Analysis of Taihu Lake and Parameter Estimation Based on the Integration of the Inverse Method and Bayesian Modeling

An integrated approach using the inverse method and Bayesian approach, combined with a lake eutrophication water quality model, was developed for parameter estimation and water environmental capacity (WEC) analysis. The model was used to support load reduction and effective water quality management in the Taihu Lake system in eastern China. Water quality was surveyed yearly from 1987 to 2010. Total nitrogen (TN) and total phosphorus (TP) were selected as water quality model variables. Decay rates of TN and TP were estimated using the proposed approach. WECs of TN and TP in 2011 were determined based on the estimated decay rates. Results showed that the historical loading was beyond the WEC, thus, reduction of nitrogen and phosphorus input is necessary to meet water quality goals. Then WEC and allowable discharge capacity (ADC) in 2015 and 2020 were predicted. The reduction ratios of ADC during these years were also provided. All of these enable decision makers to assess the influence of each loading and visualize potential load reductions under different water quality goals, and then to formulate a reasonable water quality management strategy.

An integrated GIS-based interval-probabilistic programming model for land-use planning management under uncertainty--a case study at Suzhou, China

A large number of mathematical models have been developed for supporting optimization of land-use allocation; however, few of them simultaneously consider land suitability (e.g., physical features and spatial information) and various uncertainties existing in many factors (e.g., land availabilities, land demands, land-use patterns, and ecological requirements). This paper incorporates geographic information system (GIS) technology into interval-probabilistic programming (IPP) for land-use planning management (IPP-LUPM). GIS is utilized to assemble data for the aggregated land-use alternatives, and IPP is developed for tackling uncertainties presented as discrete intervals and probability distribution. Based on GIS, the suitability maps of different land users are provided by the outcomes of land suitability assessment and spatial analysis. The maximum area of every type of land use obtained from the suitability maps, as well as various objectives/constraints (i.e., land supply, land demand of socioeconomic development, future development strategies, and environmental capacity), is used as input data for the optimization of land-use areas with IPP-LUPM model. The proposed model not only considers the outcomes of land suitability evaluation (i.e., topography, ground conditions, hydrology, and spatial location) but also involves economic factors, food security, and eco-environmental constraints, which can effectively reflect various interrelations among different aspects in a land-use planning management system. The case study results at Suzhou, China, demonstrate that the model can help to examine the reliability of satisfying (or risk of violating) system constraints under uncertainty. Moreover, it may identify the quantitative relationship between land suitability and system benefits. Willingness to arrange the land areas based on the condition of highly suitable land will not only reduce the potential conflicts on the environmental system but also lead to a lower economic benefit. However, a strong desire to develop lower suitable land areas will bring not only a higher economic benefit but also higher risks of violating environmental and ecological constraints. The land manager should make decisions through trade-offs between economic objectives and environmental/ecological objectives.

Simulation and evaluation of pollution load reduction scenarios for water environmental management: a case study of inflow river of Taihu Lake, China

In the beginning of the 21st century, the deterioration of water quality in Taihu Lake, China, has caused widespread concern. The primary source of pollution in Taihu Lake is river inflows. Effective pollution load reduction scenarios need to be implemented in these rivers in order to improve the water quality of Taihu Lake. It is important to select appropriate pollution load reduction scenarios for achieving particular goals. The aim of this study was to facilitate the selection of appropriate scenarios. The QUAL2K model for river water quality was used to simulate the effects of a range of pollution load reduction scenarios in the Wujin River, which is one of the major inflow rivers of Taihu Lake. The model was calibrated for the year 2010 and validated for the year 2011. Various pollution load reduction scenarios were assessed using an analytic hierarchy process, and increasing rates of evaluation indicators were predicted using the Delphi method. The results showed that control of pollution from the source is the optimal method for pollution prevention and control, and the method of “Treatment after Pollution” has bad environmental, social and ecological effects. The method applied in this study can assist for environmental managers to select suitable pollution load reduction scenarios for achieving various objectives.

Water and waste load allocation in rivers with emphasis on agricultural return flows: application of fractional factorial analysis

In this paper, a new methodology is developed to handle parameter and input uncertainties in water and waste load allocation (WWLA) in rivers by using factorial interval optimization and the Soil, Water, Atmosphere, and Plant (SWAP) simulation model. A fractional factorial analysis is utilized to provide detailed effects of uncertain parameters and their interaction on the optimization model outputs. The number of required optimizations in a fractional factorial analysis can be much less than a complete sensitivity analysis. The most important uncertain inputs and parameters can be also selected using a fractional factorial analysis. The uncertainty of the selected inputs and parameters should be incorporated real time water and waste load allocation. The proposed methodology utilizes the SWAP simulation model to estimate the quantity and quality of each agricultural return flow based on the allocated water quantity and quality. In order to control the pollution loads of agricultural dischargers, it is assumed that a part of their return flows can be diverted to evaporation ponds. Results of applying the methodology to the Dez River system in the southwestern part of Iran show its effectiveness and applicability for simultaneous water and waste load allocation in rivers. It is shown that in our case study, the number of required optimizations in the fractional factorial analysis can be reduced from 64 to 16. Analysis of the interactive effects of uncertainties indicates that in a low flow condition, the upstream water quality would have a significant effect on the total benefit of the system.

Simulation-based inexact chance-constrained nonlinear programming for eutrophication management in the Xiangxi Bay of Three Gorges Reservoir

Although integrated simulation and optimization approaches under stochastic uncertainty have been applied to eutrophication management problems, few studies are reported in eutrophication control planning where multiple formats of uncertainties and nonlinearities are addressed in forms of intervals and probabilistic distributions within an integrated framework. Since the impounding of Three Gorges Reservoir (TGR), China in 2003, the hydraulic conditions and aquatic environment of the Xiangxi Bay (XXB) have changed significantly. The resulting emergence of eutrophication and algal blooms leads to its deteriorated water quality. The XXB becomes an ideal case study area. Thus, a simulation-based inexact chance-constrained nonlinear programming (SICNP) model is developed and applied to eutrophication control planning in the XXB of the TGR under uncertainties. In the SICNP, the wastewater treatment costs for removing total phosphorus (TP) are set as the objective function; effluent discharge standards, stream water quality standards and eutrophication control standards are considered in the constraints; a steady-state simulation model for phosphorus transport and fate is embedded in the environmental standards constraints; the interval programming and chance-constrained approaches are integrated to provide interval decision variables but also the associated risk levels in violating the system constraints. The model results indicate that changes in the violating level (q) will result in different strategy distributions at spatial and temporal scales; the optimal value of cost objective is from [2.74, 13.41] million RMB to [2.25, 13.08] million RMB when q equals from 0.01 to 0.25; the required TP treatment efficiency for the Baisha plant is the most stringent, which is followed by the Xiakou Town and the Zhaojun Town, while the requirement for the Pingyikou cement plant is the least stringent. The model results are useful for making optimal policies on eutrophication control planning and water quality improvement in the XXB.

Waste management under multiple complexities: inexact piecewise-linearization-based fuzzy flexible programming

To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP's solutions demonstrate its effectiveness for providing more satisfactory interval solutions than IPFP3. Following its first application to waste management, the IPFP can be potentially applied to other environmental problems under multiple complexities.

An integrated multi-level watershed-reservoir modeling system for examining hydrological and biogeochemical processes in small prairie watersheds

Eutrophication of small prairie reservoirs presents a major challenge in water quality management and has led to a need for predictive water quality modeling. Studies are lacking in effectively integrating watershed models and reservoir models to explore nutrient dynamics and eutrophication pattern. A water quality model specific to small prairie water bodies is also desired in order to highlight key biogeochemical processes with an acceptable degree of parameterization. This study presents a Multi-level Watershed-Reservoir Modeling System (MWRMS) to simulate hydrological and biogeochemical processes in small prairie watersheds. It integrated a watershed model, a hydrodynamic model and an eutrophication model into a flexible modeling framework. It can comprehensively describe hydrological and biogeochemical processes across different spatial scales and effectively deal with the special drainage structure of small prairie watersheds. As a key component of MWRMS, a three-dimensional Willows Reservoir Eutrophication Model (WREM) is developed to addresses essential biogeochemical processes in prairie reservoirs and to generate 3D distributions of various water quality constituents; with a modest degree of parameterization, WREM is able to meet the limit of data availability that often confronts the modeling practices in small watersheds. MWRMS was applied to the Assiniboia Watershed in southern Saskatchewan, Canada. Extensive efforts of field work and lab analysis were undertaken to support model calibration and validation. MWRMS demonstrated its ability to reproduce the observed watershed water yield, reservoir water levels and temperatures, and concentrations of several water constituents. Results showed that the aquatic systems in the Assiniboia Watershed were nitrogen-limited and sediment flux played a crucial role in reservoir nutrient budget and dynamics. MWRMS can provide a broad context of decision support for water resources management and water quality protection in the prairie region.

An inexact fuzzy-chance-constrained air quality management model

Regional air pollution is a major concern for almost every country because it not only directly relates to economic development, but also poses significant threats to environment and public health. In this study, an inexact fuzzy-chance-constrained air quality management model (IFAMM) was developed for regional air quality management under uncertainty. IFAMM was formulated through integrating interval linear programming (ILP) within a fuzzy-chance-constrained programming (FCCP) framework and could deal with uncertainties expressed as not only possibilistic distributions but also discrete intervals in air quality management systems. Moreover, the constraints with fuzzy variables could be satisfied at different confidence levels such that various solutions with different risk and cost considerations could be obtained. The developed model was applied to a hypothetical case of regional air quality management. Six abatement technologies and sulfur dioxide (SO2) emission trading under uncertainty were taken into consideration. The results demonstrated that IFAMM could help decision-makers generate cost-effective air quality management patterns, gain in-depth insights into effects of the uncertainties, and analyze tradeoffs between system economy and reliability. The results also implied that the trading scheme could achieve lower total abatement cost than a nontrading one.

An interval-parameter stochastic robust optimization model for supporting municipal solid waste management under uncertainty

A stochastic robust interval linear programming model (IPRO) was developed for supporting municipal solid waste management under uncertainty. The model improves upon the existing stochastic robust optimization (SRO) and interval linear programming (ILP) methods by allowing evaluations of trade-offs among expected costs, cost variability, and risk of violating relax constraints simultaneously, as well as reflections of complex uncertainties through both interval and stochastic theories. A long-term waste management problem was used to demonstrate the applicability of IPRO model. The results indicated that IPRO normally led to interval solutions, where waste-management alternatives could be generated by adjusting the decision-variable values within their intervals. The model could also help waste managers to identify desired policies that under various environmental, economic, system-feasibility and system-reliability constraints.

A genetic-algorithm-aided stochastic optimization model for regional air quality management under uncertainty

A genetic-algorithm-aided stochastic optimization (GASO) model was developed in this study for supporting regional air quality management under uncertainty. The model incorporated genetic algorithm (GA) and Monte Carlo simulation techniques into a general stochastic chance-constrained programming (CCP) framework and allowed uncertainties in simulation and optimization model parameters to be considered explicitly in the design of least-cost strategies. GA was used to seek the optimal solution of the management model by progressively evaluating the performances of individual solutions. Monte Carlo simulation was used to check the feasibility of each solution. A management problem in terms of regional air pollution control was studied to demonstrate the applicability of the proposed method. Results of the case study indicated the proposed model could effectively communicate uncertainties into the optimization process and generate solutions that contained a spectrum of potential air pollutant treatment options with risk and cost information. Decision alternatives could be obtained by analyzing tradeoffs between the overall pollutant treatment cost and the system-failure risk due to inherent uncertainties.