A Hybrid Interval-Robust Optimization Model for Water Quality Management

A hybrid land-water-environment model for identification of ecological effect and risk under uncertain meteorological precipitation in an agroforestry ecosystem

In this study, a hybrid land-water-environment (LWE) model is developed for identifying ecological effect and risk under uncertain precipitation in an agroforestry ecosystem. A simulation-based fuzzy-stochastic programming with risk analysis (SFSR) method is used into LWE model to reflect the meteorological impacts; meanwhile, it also can quantify artificial fuzziness (e.g., risk attitude of policymaker) and natural vagueness (e.g., ecological function) in decision-making. The developed LWE model with SFSR method is applied to a practical agroforestry ecosystem in China. Results of optimized planting scale, irrigative water schedule, pollution mitigation scheme, and system benefit under changed rainfall, precise risk-adoption and vague ecological function are obtained; meanwhile their corresponding ecological effects and risks are analyzed. It found that current LWE plans could generate massive water deficits (e.g., 23.22×10⁶m³ in crop irrigation and 26.32×10⁶m³ in forest protection at highest) due to over-cultivation and excessive pollution discharges (e.g., the highest excessive TP and TN discharges would reach 460.64 and 15.30×10³ ton) due to irrational fertilization, which would increase regional ecological risks. In addition, fifteen scenarios associated with withdrawing cultivation and recovering forest based on regional environment heterogeneity (such as soil types) have been discussed to adjust current agriculture-environment policies. It found that, the excessive pollution discharges (TN and TP) could be reduced 12.95% and 18.32% at highest through ecological expansions, which would generate higher system benefits than that without withdrawing farmland and recovering forest. All above can facilitate local policymakers to modulate a comprehensive LWE with more sustainable and robust manners, achieving regional harmony between socio-economy and eco-environment.

Research on the Relationship between Water Diversion and Water Quality of Xuanwu Lake, China

Water diversion is often used to improve water quality to reach the standard of China in the short term. However, this large amount of water diversion can not only improve the water quality, but also lead to a decline in the water quality (total phosphorus, total nitrogen) of Xuanwu Lake. Through theoretical analysis, the relationship between water quality and water diversion is established. We also found that the multiplication of the pollutant degradation coefficient (K) and the water residence time (T) is a constant (N), K⋅T=N. The water quality changed better at first, with the increase of inflow discharge, and then became worse, and the optimal water quality inflow discharge is 180,000 m³/day. By constructing two-dimensional hydrodynamic and water quality models, the optimal diversion water plan is calculated. Through model calculations, it can be seen that reducing the inflow discharge makes the water residence time longer (15.3 days changed to 23.8 days). Thereby, increasing the degradation of pollutants, and thus improving water quality. Compared with other wind directions, the southwest wind makes the water quality of Xuanwu Lake the most uniform. The concentration of water quality first became smaller and then became larger, as the wind speed increased, and eventually became constant. Implementing these results for water quality improvement in small and medium lakes will significantly reduce the cost of water diversion.

An integrated optimization method for river water quality management and risk analysis in a rural system

In this study, an interval-stochastic-based risk analysis (RSRA) method is developed for supporting river water quality management in a rural system under uncertainty (i.e., uncertainties exist in a number of system components as well as their interrelationships). The RSRA method is effective in risk management and policy analysis, particularly when the inputs (such as allowable pollutant discharge and pollutant discharge rate) are expressed as probability distributions and interval values. Moreover, decision-makers' attitudes towards system risk can be reflected using a restricted resource measure by controlling the variability of the recourse cost. The RSRA method is then applied to a real case of water quality management in the Heshui River Basin (a rural area of China), where chemical oxygen demand (COD), total nitrogen (TN), total phosphorus (TP), and soil loss are selected as major indicators to identify the water pollution control strategies. Results reveal that uncertainties and risk attitudes have significant effects on both pollutant discharge and system benefit. A high risk measure level can lead to a reduced system benefit; however, this reduction also corresponds to raised system reliability. Results also disclose that (a) agriculture is the dominant contributor to soil loss, TN, and TP loads, and abatement actions should be mainly carried out for paddy and dry farms; (b) livestock husbandry is the main COD discharger, and abatement measures should be mainly conducted for poultry farm; (c) fishery accounts for a high percentage of TN, TP, and COD discharges but a has low percentage of overall net benefit, and it may be beneficial to cease fishery activities in the basin. The findings can facilitate the local authority in identifying desired pollution control strategies with the tradeoff between socioeconomic development and environmental sustainability.

An inexact mixed risk-aversion two-stage stochastic programming model for water resources management under uncertainty

Uncertainties exist in the water resources system, while traditional two-stage stochastic programming is risk-neutral and compares the random variables (e.g., total benefit) to identify the best decisions. To deal with the risk issues, a risk-aversion inexact two-stage stochastic programming model is developed for water resources management under uncertainty. The model was a hybrid methodology of interval-parameter programming, conditional value-at-risk measure, and a general two-stage stochastic programming framework. The method extends on the traditional two-stage stochastic programming method by enabling uncertainties presented as probability density functions and discrete intervals to be effectively incorporated within the optimization framework. It could not only provide information on the benefits of the allocation plan to the decision makers but also measure the extreme expected loss on the second-stage penalty cost. The developed model was applied to a hypothetical case of water resources management. Results showed that that could help managers generate feasible and balanced risk-aversion allocation plans, and analyze the trade-offs between system stability and economy.

A Fuzzy Robust Optimization Model for Waste Allocation Planning Under Uncertainty

In this study, a fuzzy robust optimization (FRO) model was developed for supporting municipal solid waste management under uncertainty. The Development Zone of the City of Dalian, China, was used as a study case for demonstration. Comparing with traditional fuzzy models, the FRO model made improvement by considering the minimization of the weighted summation among the expected objective values, the differences between two extreme possible objective values, and the penalty of the constraints violation as the objective function, instead of relying purely on the minimization of expected value. Such an improvement leads to enhanced system reliability and the model becomes especially useful when multiple types of uncertainties and complexities are involved in the management system. Through a case study, the applicability of the FRO model was successfully demonstrated. Solutions under three future planning scenarios were provided by the FRO model, including (1) priority on economic development, (2) priority on environmental protection, and (3) balanced consideration for both. The balanced scenario solution was recommended for decision makers, since it respected both system economy and reliability. The model proved valuable in providing a comprehensive profile about the studied system and helping decision makers gain an in-depth insight into system complexity and select cost-effective management strategies.