IFTSQP: An Inexact Optimization Model for Water Resources Management under Uncertainty

Abstract

An interval-fuzzy two-stage quadratic programming (IFTSQP) method is developed for water resources management under uncertainty. The methodincorporates techniques of interval-parameter programming, two-stage stochastic programming, and fuzzy quadratic programming within a general optimization framework to tackle multiple uncertainties presented as intervals, fuzzy sets and probability distributions. In the model formulation, multiple control variables are adopted to handle independent uncertainties in the model's right-hand sides; fuzzy quadratic terms are used in the objective function to minimize the variation in satisfaction degrees among the constraints. Moreover, the method can support the analysis of policy scenarios that are associated with economic penalties when the promised targets are violated. The developed method is then applied to a case study of water resources management planning. The results indicate that reasonable solutions have been obtained. They can help provide bases for identifying desired water-allocation plans with a maximized system benefit and a minimized constraint-violation risk.     

模糊评价在水闸工程管理考核中的应用

针对目前水闸工程管理考核评价中存在的问题，研究了水闸工程管理的模糊评价方法。在确定评价指标、权重分配的基础上，构建了2层模糊评价模型，利用专家定性评价结果计算各项2级指标的隶属度，采用模糊运算，依据最大隶属度原则确定评价结果。实例计算表明，水闸工程管理模糊评价得出的结果合理。因此，构建的水闸工程管理模糊评价模型是正确的。     

Fuzzy Multiobjective and Linear Programming Based Management Models for Optimal Land-Water-Crop System Planning

In this article, linear programming and fuzzy optimization models are developed for planning and management of available land-water-crop system of Mahanadi-Kathajodi delta in eastern India. The models are used to optimize the economic return, production and labour utilization, and to search the related cropping patterns and intensities with specified land, water, fertilizer and labour availability, and water use pattern constraints. Due to extreme backwardness of the study area, it has been decided to keep all the three objectives of the linear programming models at the same priority level to obtain the compromised solution in a fuzzy environment that incorporates the imprecision in fuzzy goals and fuzzy constraints. These non-structural models facilitate the conjunctive use of available surface water and groundwater resources. A comparative evaluation along with the benefit-cost ratios of the existing and proposed farming systems is also presented.     

An Inexact Chance-constrained Quadratic Programming Model for Stream Water Quality Management

Water quality management is complicated with a variety of uncertainties and nonlinearities. This leads to difficulties in formulating and solving the resulting inexact nonlinear optimization problems. In this study, an inexact chance-constrained quadratic programming (ICCQP) model was developed for stream water quality management. A multi-segment stream water quality (MSWQ) simulation model was provided for establishing the relationship between environmental responses and pollution-control actions. The relationship was described by transformation matrices and vectors that could be used directly in a multi-point-source waste reduction (MWR) optimization model as water-quality constraints. The interval quadratic polynomials were employed to reflect the nonlinearities and uncertainties associated with wastewater treatment costs. Uncertainties associated with the water-quality parameters were projected into the transformation matrices and vectors through Monte Carlo simulation. Uncertainties derived from water quality standards were characterized as random variables with normal probability distributions. The proposed ICCQP model was applied to a water quality management problem in the Changsha section of the Xiangjiang River in China. The results demonstrated that the proposed optimization model could effectively communicate uncertainties into the optimization process, and generate inexact solutions containing a spectrum of wastewater treatment options. Decision alternatives could then be obtained by adjusting different combinations of the decision variables within their solution intervals. Solutions from the ICCQP model could be used to analyze tradeoffs between the wastewater treatment cost and system-failure risk due to inherent uncertainties. The results are valuable for supporting decision makers in seeking cost-effective water management strategies.     

Hydrogeographical Regionalisation: An Approach for Evaluating the Effects of Land Cover Change in Watersheds. A Case Study in the Cuitzeo Lake Watershed, Central Mexico

Efficient natural resources management, including continental water at watershed level, requires understanding the arrangement of landscape attributes in a region. The geographical analysis of landscape attributes is a useful approach to delineate relatively homogeneous watersheds or regions. This research was carried out in order to evaluate the effect of land cover through time on regionalisation modelling in the poorly-gauged Cuitzeo Lake Watershed, and to develop models to create two hydrogeographical regionalisations for the years 1975 and 2000. The inputs required by the regionalisation methodology were integrated in a GIS and validated before carrying out statistical regionalisation procedures (cluster analysis and PCA). GIS operations were done in Arc View 3.2 and statistical analyses in PC-ORD. Median Euclidean distances with mean distance linkage methods were used. A 75% of similarity was chosen as the threshold to generate regions. Importance rankings of regions were obtained using multicriteria evaluation methods. Based on the analysis, 38 of the 52 subwatersheds belonging to the Cuitzeo Lake Watershed were clustered; eight groups were defined in 1975 and nine in 2000. According to PCA, the strongest positive variables are associated to morphometric, geologic, land cover and soil attributes. Fourteen subwatersheds were never clustered. Four subwatersheds changed of cluster between 1975 and 2000. This change is explained because of rainfed agricultural parcel abandonment, and subsequent shrubland growth. This means that the hydrogeographical regionalisation is sensitive to land cover change processes. The methodological approach applied in this research is a low-cost and fast alternative for evaluating the impact of land cover and land use change on hydrogeographical regionalisation; in consequence, data and information generated during the analysis were made available to local authorities so that they can improve both water resources planning and their informational baseline for decision making and for development of environmental policies in the Cuitzeo Lake Watershed.     

Optimal Land-Use Management for Surface Source Water Protection Under Uncertainty: A Case Study of Songhuaba Watershed (Southwestern China)

The water supply to Chinese cities is increasingly degrading from pollution due to watershed activities. Consequently, water source protection requires urgent action using optimal land-use management efforts. An inexact linear programming model for optimal land-use management of surface water source area was developed. The model was proposed to balance the economic benefits of land-use development and water source protection. The maximum net economic benefit (NEB) was chosen as the objective of land-use management. The total environmental capacity (TEC) of rivers and the minimum water supply (MWS) were considered key constraints. Other constraints included forest coverage, government requirements concerning the proportions of various land-use types, soil loss, slope lands, and technical constraints. A case study was conducted for the Songhuaba Watershed, a reservoir supplying water to Kunming City, the third largest city in southwestern China. A 15-year (2006 to 2020) optimal model for land-use management was developed to better protect this water source and to gain maximum benefits from development. Ten constraints were involved in the optimal model, and results indicated that NEB ranged between 893 and 1,459 million US$. The proposed model will allow local authorities to better understand and address complex land-use systems and to develop optimal land-use management strategies for balancing source water protection and local economic development.     

An Interactive Fuzzy Satisfying Approach for Sustainable Water Management in the Yellow River Delta,China

This paper proposes using an interactive fuzzy satisfying method to solve multi-objective optimization problems in integrated water management of the Yellow River Delta, China. The approach involves economic, social and ecological objectives represented by net returns, water deficiency and ecological water requirements, respectively. It considers the decision-maker’s preferences in terms of fuzzy satisfying of each objective and holistic satisfying of all objectives based on Euclid distance. The method avoids the subjectivity of having decision-makers assigning weights to the multiple objectives to some degree. The method is applied to the Yellow River Delta, China. Results indicate that considerably more water should be allocated to ecological uses of water in the Yellow River than currently occurs. An interactive fuzzy satisfying approach for the multi-objective optimization problems has significant potential in the field of integrated water management.     

乌东德水电站原生植物资源移栽创新管理模式

为保护和利用施工区原生植物,乌东德水电站通过开展施工区原生植物资源分布情况调查,编制施工区树木移栽规划设计,利用市场竞争机制和招投标管理手段,提出了乌东德水电站现有原生植物移栽的创新管理模式,成功地实施施工区可利用原生植物移栽,保护了自然资源,节约了绿化工程投资,应用前景广阔。     

An Investigation of Spinal Deformity of Trout (Salmo sp.) in the Brule River,Wisconsin

An unusually high incidence of spinal deformity in migratory trout from the Brule River, Wisconsin, was investigated to determine its probable cause and extent. Incidence in rainbow trout (Salmo gairdneri) and brown trout (Salmo trutta) was determined by external examination and x-ray. The total incidence of deformity in x-rayed and externally examined lake-run rainbow trout was 50 and 26 percent, respectively. No vertebral anomalies were found by x-ray in 75 Brule River juvenile rainbow trout which had not yet emigrated to Lake Superior, nor in 25 lake-run rainbow trout from the French River, Minnesota. Examination of 25 lake-run brown trout from the Brule River showed external deformity (8 percent) and internal vertebral abnormalities (16 percent). The absence of spinal deformity in juvenile rainbow trout from the Brule River and in lake-run trout from the French River suggest that the electric lamprey control weir on the Brule was affecting fish which migrated downstream. The lower incidence of injury in brown trout reflects the difference in the time of their migration which was not coincident with weir operation. It is apparent that the electric lamprey weir has had a greater total impact on recruitment of trout to Lake Superior than previously thought.