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.     

Interval-parameter Two-stage Stochastic Nonlinear Programming for Water Resources Management under Uncertainty

Over the past decades, controversial and conflict-laden water allocation issues among competing interests have raised increasing concerns. In this research, an interval-parameter two-stage stochastic nonlinear programming (ITNP) method is developed for supporting decisions of water-resources allocation within a multi-reservoir system. The ITNP can handle uncertainties expressed as both probability distributions and discrete intervals. It can also be used for analyzing various policy scenarios that are associated with different levels of economic consequences when the promised allocation targets are violated. Moreover, it can deal with nonlinearities in the objective function such that the economies-of-scale effects in the stochastic program can be quantified. The proposed method is applied to a case study of water-resources allocation within a multi-user, multi-region and multi-reservoir context for demonstrating its applicability. The results indicate that reasonable solutions have been generated, which present as combined interval and distributional information. They provide desired water allocation plans with a maximized economic benefit and a minimized system-disruption risk. The results also demonstrate that a proper policy for water allocation can help not only mitigate the penalty due to insufficient supply but also reduce the waste of water resources.     

Fuzzy AHP Assessment of Water Management Plans

There are two mainstreams when using the analytic hierarchy process (AHP). One is the standard applications of crisp distributive and ideal mode versions. The other is characterised by fuzzification of the AHP methodology and by attempts to better tackle inherently uncertain and imprecise decision processes with quantitative and qualitative data. The latter is characterised by different approaches to fuzzificating the decision problem; the way of conducting judgment and evaluating process; and finally, in synthesising the results and manipulating fuzzy numbers to devise priorities for the decision alternatives. This paper presents a fuzzy methodology for solving fully structured decision problems with criteria, sub-criteria and alternatives. It follows the logic of AHP in a simple and straightforward manner, efficiently aggregates criteria and sub-criteria into unique hierarchical level and applies a total integral method for comparing decision alternatives. The proposed methodology has been used for the assessment of water management plans in part of the Paraguacu River Basin in Brazil.     

Interval-parameter Two-stage Stochastic Semi-infinite Programming: Application to Water Resources Management under Uncertainty

In this study, an interval-parameter two-stage stochastic semi-infinite programming (ITSSP) method was developed for water resources management under uncertainty. As a new extension of mathematical programming methods, the developed ITSSP approach has advantages in uncertainty reflection and policy analysis. In order to better account for uncertainties, the ITSSP approach is expressed with discrete intervals, functional intervals and probability density functions. The ITSSP method integrates the two-stage stochastic programming (TSP), interval programming (IP) and semi-infinite programming (SIP) within a general optimization framework. The ITSSP has an infinite number of constraints because it uses functional intervals with time (t) being an independent variable. The different t values within the range [0, 90] lead to different constraints. At same time, ITSSP also includes probability distribution information. The ITSSP method can incorporate pre-defined water resource management policies directly into its optimization process to analyze various policy scenarios having different economic penalties when the promised amounts are not delivered. The model is applied to a water resource management system with three users and four periods (corresponding to winter, spring, summer and fall, respectively). Solutions of the ITSSP model provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable interval solutions were generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of stream flow. The obtained solutions are useful for decision makers to obtain insight regarding the tradeoffs between environmental, economic and system reliability criteria.     

Water Right Institution and Strategies of the Yellow River Valley

With the rapid economic and social development in China, pressure on water resources in the Yellow River is becoming more and more prominent. For the sustainable social, economic and agricultural development in the Yellow River valley, it is imperative to create the perfect water right institution, which plays a key role in improving the efficiency, equity and sustainability of water use. This article analyzes the problems with the water right institution of the Yellow River valley, which includes unclear definition of water right, ineffective allocation mechanism, low water price, and water pollution. Correspondingly, some measures need taking in order to address these challenges. First of all, the water right, especially tradable water right should be well defined. In the article, water right is defined as a series of water management capabilities and use requirements. Then, water right allocation system should be built up, including examining and approving water usufruct, the paid transfer, and the paid utilization of water right. In the end, based on the well defined tradable water right and the well developed water right allocation system, water right market should be developed, which will promote the transfer to the highest valued water uses. When the water right trade happens, the water right price should be fixed in certain situation. On one hand, the water right price should be raised; on the other hand, the water right price should be determined according to a two-part water price system. Of course, market should not be the only role in the water right institution. The authorities should also be necessarily responsible for water right organizations, which make proper water right law, policy and regulations that assist the smooth going of water right market. There are some other measures for the yellow river, such as a water booklet should be recorded for mastering the detailed situation of water resources in the Valley; the South-to-North Water Diversion Project should be accelerated in order to alleviate the water scarcity. All the above measures will do good to resolve the problems of water resources of the Yellow River valley when they are correctly taken.     

Estimating the Potential Impacts of Irrigation Water Pricing Using Multicriteria Decision Making Modelling. An Application to Northern Greece

A great challenge of the current European water policy is the implementation of volumetric water pricing in the agricultural sector, especially of Mediterranean countries, where irrigation is a necessary precondition of agricultural production and farmers’ income, but also the major consumer of water. The overall aim of the present work is to develop a methodology that will be suitable for the estimation of the potential environmental, economic and social impacts of irrigation water pricing. For this purpose, Multi-Attribute Utility Theory is implemented in order to simulate agricultural decision making at various water pricing scenarios. Water demand functions are then elicited, by means of the best crop and water allocation (farmers’ decisions) in each scenario. The European Water Framework Directive recommends that any issue concerning water resources management (including water pricing policies) should be developed at the river basin level. In this framework, a cluster analysis is performed to partition the river basin area (namely, Loudias River Basin, located in Northern Greece) into a small number of homogeneous sub-regions. The differential impact of water pricing in each region is then analyzed, and finally, an average water demand function is formulated for the whole river basin.     

Optimizing Hydropower Reservoir Operation Using Hybrid Genetic Algorithm and Chaos

Genetic algorithms (GA) have been widely applied to solve water resources system optimization. With the increase of the complexity and the larger problem scale of water resources system, GAs are most frequently faced with the problems of premature convergence, slow iterations to reach the global optimal solution and getting stuck at a local optimum. A novel chaos genetic algorithm (CGA) based on the chaos optimization algorithm (COA) and genetic algorithm (GA), which makes use of the ergodicity and internal randomness of chaos iterations, is presented to overcome premature local optimum and increase the convergence speed of genetic algorithm. CGA integrates powerful global searching capability of the GA with that of powerful local searching capability of the COA. Two measures are adopted in order to improve the performance of the GA. The first one is the adoption of chaos optimization of the initialization to improve species quality and to maintain the population diversity. The second is the utilization of annealing chaotic mutation operation to replace standard mutation operator in order to avoid the search being trapped in local optimum. The Rosenbrock function and Schaffer function, which are complex and global optimum functions and often used as benchmarks for contemporary optimization algorithms for GAs and Evolutionary computation, are first employed to examine the performance of the GA and CGA. The test results indicate that CGA can improve convergence speed and solution accuracy. Furthermore, the developed model is applied for the monthly operation of a hydropower reservoir with a series of monthly inflow of 38 years. The results show that the long term average annual energy based CGA is the best and its convergent speed not only is faster than dynamic programming largely, but also overpasses the standard GA. Thus, the proposed approach is feasible and effective in optimal operations of complex reservoir systems.     

Regional Frequency Distribution Type of Low Flow in North of Iran by L-moments

A regional low flow frequency analysis in the north of Iran using L-moments was carried out. Low flow events have been represented by the 7-day annual minimum series and the L-moments approach was used to assign these data into homogenous regions. According to the homogeneity measure and climatic properties, two subdivisions were found – one in the west of the study area having a homogenous assemblage of sites, and one in the east in which the sites were found to be heterogeneous. The regional low flow frequency distribution was derived for the western division using L-moments and goodness of fit tests were used to evaluate which of a number of possible distributions best represented this. The evaluation suggested that the Generalized Logistic distribution gives the best overall result. For heterogeneous subdivision, the performance of the 2-parameter distribution such as 2-parameter Log Normal, Normal and Gamma distributions gave the best result for the majority of sites. Regional and at-site frequency curves were also compared for the western division, which showed that the quantile estimates could be very different in the upper and lower tails of the distribution. The influence on flow regime and watershed properties on the type of the best fit distribution was investigated which showed that the 2 and 3 parameter distributions do not have a clear relationship with climatic and physiographic characteristics of the watersheds except the watershed area. This may result in simple scaling laws of low flows.     

Regional Flood Frequency Analysis in Tunisia: Identification of Regional Distributions

Best-fit distributions of floods in Tunisia are determined based on L-moment diagram and statistical tests. GEV and GLO distributions provided the best fit to seven and three regions of Tunisia respectively. In each homogeneous region, hierarchical approaches and regression models were developed for gauged and ungauged watersheds. The first two parameters of the distributions (GEV and GLO) were estimated from measured data while the third parameter was represented by the regional average value weighted by the record length of all stations in the region. The obtained parameters were correlated to the catchment size. Quantiles obtained by the proposed models were compared with those obtained using local conventional models. Statistical tests showed that the proposed models provided a much better agreement with observed floods than any of the conventional methods generally used in Tunisia.     

Study of Drawdown–Drain Discharge Relationship and its Application in Design of Cost Effective Subsurface Drainage System in Mugogo Swamp, Busogo, Rwanda

Mostly the swamps in Rwanda are surrounded by volcanic hills with small streams flowing to discharge runoff and seepage water. Mugogo swamp is located in Busogo sector, Musanze district, North province. Total area of the swamp is approximately 50 ha. The swamp is surrounded by hills and elevated volcanic rocky terrains. Potato is the main crop cultivated in the swamp. The average production rate of potato is 7 MT/ha which is very low compared to 12 MT/ha in well drained areas. During rainy season seepage water and runoff water from the surrounding hills cause the waterlogged condition of the swamp and affecting the potato cultivation and land productivity. The remedial measure for this swamp is to divert separately the runoff and seepage water from surrounding catchment area and then remove the recharge water by pumping through a system of subsurface drains. Hydraulic head–drain discharge relationship can be fitted with quadratic equation. Equivalent drainable porosity and equivalent hydraulic conductivity are determined as 0.105 m/day and 0.34% respectively for drain depth of 40 cm from soil surface. Effective hydraulic conductivity in the soil profile shows that its average value in the top 15 cm of soil layer is 0.17 m/day and that in the remaining depth up to impermeable layer is 0.015 m/day. Third degree polynomial expressions are made for Head–hydraulic conductivity and head–drainable porosity relationships. The nonlinear relation of hydraulic conductivity and drainable porosity with drawdown shows that the proximity of Kinoni stream does not affect drainage parameters of the area because of less seepage from the stream. The study also reveals that adoption of 7 m drain spacing is very less if crop parameter is not considered and will result higher drain cost. Drainage coefficient of 5 mm/day is arrived considering the rainfall distribution, infiltration rate of soil, allowable water logging tolerance of potato crop. Required drain spacings are calculated for different drainage coefficients of 1, 2, 3, 4 and 5 mm/day under different drawdown conditions to plot subsurface drainage characteristic curves of the swamp. These curves are useful to directly read the drain spacing and drain depth for the required drainage coefficient without going for tedious calculations. Cost analysis shows that the ratio of drain spacing to drain depth can be a decisive factor to select best combination of drain depth and drain spacing. For drainage coefficient of 5 mm/day, optimum drain spacing-depth ratio is found as 7.2 with a cost of 0.689 million Frw/ha. For different drainage coefficients in the swamp, the drain depth of 1.5 m is crucial and optimum cost occurs at this depth. It is also found that any increase in drawdown beyond the drawdown at critical drain depth will not reduce the cost significantly.