Fuzzy chance-constrained linear fractional programming approach for optimal water allocation

A fuzzy chance-constrained linear fractional programming method was developed for agricultural water resources management under multiple uncertainties. This approach improved upon the previous programming methods, and could reflect the ratio objective function and multiple uncertainties expressed as probability distributions, fuzzy sets, and their combinations. The proposed approach is applied to an agricultural water resources management system where many crops are considered under different precipitation years. Through the scenarios analyses, the multiple alternatives are presented. The solutions show that it is applicable to practical problems to address the crop water allocation under the precipitation variation and sustainable development with ratio objective function of the benefit and the irrigation amount. It also provides bases for identifying desired agriculture water resources management plans with reasonable benefit and irrigation schedules under crops.     

A simulation–optimization modeling approach for watershed-scale agricultural N<Subscript>2</Subscript>O emission mitigation under multi-level uncertainties

In this research, an integrated simulation–optimization modeling approach (ISOMA) was developed for supporting agricultural N₂O emission mitigation at the watershed scale. This approach can successfully combine soil N₂O emission simulation and the consequential mitigation management within a general modeling framework. Also, uncertainties associated with the key soil parameter can be effectively reflected and addressed through adoption of Monte Carlo analysis for the simulation results. The Monte Carlo simulated results were then used to generate fuzzy membership functions that can be consequentially used for emission mitigation management, reflecting the combined uncertainties for N₂O emission simulation and mitigation management. The developed ISOMA was then applied to a reservoir watershed in Miyun county of Beijing municipality. In the studying watershed, the simulation model was calibrated and verified. Then, N₂O emission from multiple agricultural land-use patterns were predicted. The amounts of N₂O emission of four land use patterns (i.e., cash tree, orchard, cropland, and natural forest) were (536.9, 590.8, 653.1), (237.7, 254.4, 275.9), (79.5, 100.7, 105.1), (33.0, 47.3, 61.1) kg CO₂ eq ha^?1 year^?1, respectively. Two scenarios (i.e., G₁ and G₂) were set up according to development priorities of local economy and society. Meanwhile, multiple credibility levels were considered according to the risk of N₂O emission. The land use patterns could be adjusted according to solutions of ISOMA. The developed methods could help regional manager choose various production patterns with cost-effective agriculture N₂O emission management schemes in the Miyun reservoir watershed. The manager also can obtain deeply insights into the tradeoffs between agricultural benefits and system reliabilities.     

Risk assessment of agricultural irrigation water under interval functions

In recent years, water shortages and unreliable water supplies have been considered as major barriers to agricultural irrigation water management in China, which are threatening human health, impairing prospects for agriculture and jeopardizing survival of ecosystems. Therefore, effective and efficient risk assessment of agricultural irrigation water management is desired. In this study, an inexact full-infinite two-stage stochastic programming (IFTSP) method is developed. It incorporates the concepts of interval-parameter programming and full-infinite programming within a two-stage stochastic programming framework. IFTSP can explicitly address uncertainties presented as crisp intervals, probability distributions and functional intervals. The developed model is then applied to Zhangweinan river basin for demonstrating its applicability. Results from the case study indicate that compromise solutions have been obtained. They provide the desired agricultural irrigation water-supply schemes, which are related to a variety of tradeoffs between conflicting economic benefits and associated penalties attributed to the violation of predefined policies. The solutions can be used for generating decision alternatives and thus help decision makers to identify desired agricultural irrigation targets with maximized system benefit and minimized system-failure risk. Decision makers can adjust the existing agricultural irrigation patterns, and coordinate the conflict interactions among economic benefit, system efficiency, and agricultural irrigation under uncertainty.     

Use of the MODFLOW 6 Water Mover Package to Represent Natural and Managed Hydrologic Connections

The latest release of MODFLOW 6, the current core version of the MODFLOW groundwater modeling software, debuted a new package dubbed the “mover” (MVR). Using a generalized approach, MVR facilitates the transfer of water among any arbitrary combination of simulated features (i.e., pumping wells, stream, drains, lakes, etc.) within a MODFLOW 6 simulation. Four “rules” controlling the amount of water transferred from a providing feature to a receiving feature are currently available. In this way, MVR can represent natural connections between features, for example, streams entering or exiting lakes, and perhaps more interestingly, it also can transfer water among simulated features to more accurately simulate water management. An example model representative of an agricultural setting demonstrates some of the available MVR connections. For example, an irrigation event that transfers surface water from an irrigation delivery ditch to multiple cropped areas demonstrates a “one-to-many” connection that is possible within MVR. Conversely, irrigation or precipitation runoff from multiple fields may be routed to a particular stream segment using “many-to-one” MVR connections. MVR supports many additional connection types, several of which are demonstrated by the included example problem.     

Development of an inexact two-stage stochastic model with downside risk control for water quality management and decision analysis under uncertainty

Water quality management along rivers involves making water-allocation plans, establishing water quality goals, and controlling pollutant discharges, which is complicated itself but further challenged by existence of uncertainties. In this study, an inexact two-stage stochastic downside risk-aversion programming (ITSDP) model is developed for supporting regional water resources allocation and water quality management problems under uncertainties. The ITSDP method is a hybrid of interval-parameter programming, two-stage stochastic programming, and downside risk measure to tackle uncertainties described in terms of interval values and probability distributions. A water quality simulation model was provided for reflecting the relationship between the water resources allocation, wastewater discharge, and environmental responses. The proposed approach was applied to a hypothetical case for a shared stream water quality management with one municipal, three industrial and two agricultural sectors. A number of scenarios corresponding to different river inflows and risk levels were examined. The results demonstrated that the model could effectively communicate the interval-format and random uncertainties, and risk-aversion into optimization process, and generate a trade-off between the system economy and stability. They could be helpful for seeking cost-effective management strategies under uncertainties, and gaining an in-depth insight into the water quality management system characteristics, and make cost-effective decisions.     

Risk analysis for water resources management under dual uncertainties through factorial analysis and fuzzy random value-at-risk

Water resources systems are associated with a variety of complexities and uncertainties due to socio-economic and hydro-environmental impacts. Such complexities and uncertainties lead to challenges in evaluating the water resources management alternatives and the associated risks. In this study, the factorial analysis and fuzzy random value-at-risk are incorporated into a two-stage stochastic programming framework, leading to a factorial-based two-stage programming with fuzzy random value-at-risk (FTSPF). The proposed FTSPF approach aims to reveal the impacts of uncertainty parameters on water resources management strategies and the corresponding risks. In detail, fuzzy random value-at-risk is to reflect the potential risk about financial cost under dual uncertainties, while a multi-level factorial design approach is used to reveal the interaction between feasibility degrees and risk levels, as well as the relationships (including curvilinear relationship) between these factors and the responses. The application of water resources system planning makes it possible to balance the satisfaction of system benefit, the risk levels of penalty and the feasibility degrees of constraints. The results indicate that decision makers would pay more attention to the tradeoffs between the system benefit and feasibility degree, and the water allocation for agricultural section contributes most to control the financial loss of water. Moreover, FTSPF can generate a higher system benefit and more alternatives under various risk levels. Therefore, FTSPF could provide more useful information for enabling water managers to identify desired policies with maximized system benefit under different system-feasibility degrees and risk levels.     

Water quality management in a wetland system using an inexact left-hand-side chance-constrained fuzzy multi-objective approach

Water quality management is a significant item in the sustainable development of wetland system, since the environmental influences from the economic development are becoming more and more obvious. In this study, an inexact left-hand-side chance-constrained fuzzy multi-objective programming (ILCFMOP) approach was proposed and applied to water quality management in a wetland system to analyze the tradeoffs among multiple objectives of total net benefit, water quality, water resource utilization and water treatment cost. The ILCFMOP integrates interval programming, left-hand-side chance-constrained programming, and fuzzy multi-objective programming within an optimization framework. It can both handle multiple objectives and quantify multiple uncertainties, including fuzziness (aspiration level of objectives), randomness (pollutant release limitation), and interval parameters (e.g. water resources, and wastewater treatment costs). A representative water pollution control case study in a wetland system is employed for demonstration. The optimal schemes were analyzed under scenarios at different probabilities (p _i , denotes the admissible probability of violating the constraint i). The optimal solutions indicated that, most of the objectives would decrease with increasing probability levels from scenarios 1 to 3, since a higher constraint satisfaction probability would lead to stricter decision scopes. This study is the first application of the ILCFMOP model to water quality management in a wetland system, which indicates that it is applicable to other environmental problems under uncertainties.     

Life cycle greenhouse gas footprint of shale gas: a probabilistic approach

With the increase in natural gas (NG) production in recent years, primarily from shale gas, some sources, including the US Environmental Protection Agency (EPA), have suggested that upstream methane emissions are increasing. Much of the recent controversy has centered on emissions during well drilling, testing, and completion even though emissions downstream of the wellhead are also of concern. The study critically assessed the current state of knowledge about the life cycle GHG footprint of NG, analyzed the assumptions, data and analysis methodologies used in the existing literature. This study comprehensively analyzed the emission of methane from different stage of the life of well for conventional and unconventional NG using the EPA’s revised 2011 estimates as well as other existing literature and publicly available government data. The study proposed a probabilistic model to estimate the range of total GHG footprint of NG with varying probabilities. Through the bottom up approach starting from the well construction to the delivery of NG to the small user and using Monte Carlo simulation, the study identified the critical sources of fugitive emissions from the NG. As expected, emissions from well completion and periodic emissions (e.g. liquid unloading in the case of onshore conventional wells and workovers in the case of unconventional wells) are significant contributors to the overall GHG footprint of NG, and possess large opportunity for reduction. Finally the application of probabilistic model is demonstrated through a case study using the data from the Montney and Horn River shale gas basins in the Northern British Columbia to estimate the range of total GHG footprint of shale gas with varying probabilities. The study found that the GHG footprint of Montney and Horn River wells are much smaller than that of Barnett shale (which is representative of US shale gas) due to strict flaring regulations followed in BC. The study also undercuts the outcome of Howarth et al. (Clim Chang Lett 106:679–690, 2011), which states that the GHG footprint of shale gas is at least 20 % greater than coal.     

Agricultural effluent control under uncertainty: An inexact double-sided fuzzy chance-constrained model

An inexact double-sided fuzzy chance-constrained programming (IDFCCP) method was developed in this study and applied to an agricultural effluent control management problem. IDFCCP was formulated through incorporating interval linear programming (ILP) into a double-sided fuzzy chance-constrained programming (DFCCP) framework, and could be used to deal with uncertainties expressed as not only possibility distributions associated with both left- and right-hand-side components of constraints but also discrete intervals in the objective function. The study results indicated that IDFCCP allowed violation of system constraints at specified confidence levels, where each confidence level consisted of two reliability scenarios. This could lead to model solutions with high system benefits under acceptable risk magnitudes. Furthermore, the introduction of ILP allowed uncertain information presented as discrete intervals to be communicated into the optimization process, such that a variety of decision alternatives can be generated by adjusting the decision-variable values within their intervals. The proposed model could help decision makers establish various production patterns with cost-effective water quality management schemes under complex uncertainties, and gain in-depth insights into the trade-offs between system economy and reliability.     

典型农业流域不同类型池塘水体CO2排放特征

内陆水体是大气CO₂收支估算的重要组成部分。农业流域分布着大量池塘景观水体,且具备蓄洪抗旱、消纳污染、水产养殖等多种功能。但是,农业流域不同功能的小型池塘CO₂排放特征尚不清楚。本研究以极具农业流域代表性的烔炀河流域为研究对象,选取流域中用于水产养殖(养殖塘)、生活污水承纳(村塘)、农业灌溉(农塘)、蓄水(水塘)的4个功能不同的景观池塘,基于为期1年的野外实地观测,以明确农业流域小型池塘CO₂排放特征。结果表明,不同功能池塘水体CO₂排放差异显著,受养殖活动、生活污水输入和农田灌溉等人类活动影响,养殖塘((80.37±100.39) mmol/(m²·d))、村塘((48.69±65.89) mmol/(m²·d))和农塘((13.50±15.81) mmol/(m²·d))是大气CO₂的热点排放源,其CO₂排放通量分别是自然蓄水塘((4.52±23.26) mmol/(m²·d))的18、11和3倍。统计分析也表明,该流域池塘CO₂排放变化总体上受溶解氧、营养盐等因素驱动。4个不同景观池塘CO₂排放通量全年均值为(37.31±67.47) mmol/(m²·d),是不容忽视的CO₂排放源,其中养殖塘和村塘具有较高的CO₂排放潜力,在未来研究中需要重点关注。     

An inexact programming method for agricultural irrigation systems under parameter uncertainty

Rapid population growth and economy development have led to increasing reliance on water resources. It is even aggravated for agricultural irrigation systems where more water is necessary to support the increasing population. In this study, an inexact programming method based on two-stage stochastic programming and interval-parameter programming is developed to obtain optimal water-allocation strategies for agricultural irrigation systems. It is capable of handling such problems where two-stage decisions need to be suggested under random- and interval-parameter inputs. An interactive solving procedure derived from conventional interval-parameter programming makes it possible for the impact of lower and upper bounds of interval inputs to be well reflected in the resulting solutions. An agricultural irrigation management problem is then provided to demonstrate the applicability, and reasonable solutions are obtained. Compared to the solutions from a representative interval-parameter programming model where only one decision-stage exists, the interval of optimized objective-function value is narrow, indicating more alternatives could be provided when water-allocation targets are rather high. However, chances of obtaining more benefits exist in association with a risk of paying more penalties; such a relationship becomes apparent when the variation of water availability is much intensive.     

水库温室气体净通量评估模型(G-res Tool)及在长江上游典型水库初步应用

目前准确量化温室气体排放量已成为气候变化研究和政策制定的关键.在IPCC水库温室气体净通量的概念性框架下,国际水电协会汇总分析了全球223座水库的CO₂和CH₄研究成果,构建了G-res Tool,其可以用于评估已建或待建水库在长时间尺度下的温室气体净通量.本文介绍了G-res Tool模型的基本原理与模型框架,利用模型内置数据库中所涉及的中国长江上游12座典型水库数据进行初步应用分析,12座水库温室气体净通量平均值为88.17 g CO₂e/（m²·a）,在全球约7000座水库中所处水平为11.67%,处于低阈值范围.在水库温室气体净通量分析结果中,其他非相关人类活动产生的水库温室气体通量（UAS）在蓄水后总通量（Post）中所占比重远高于蓄水前温室气体通量（Pre）.长江上游水库蓄水后的CH₄和CO₂通量对于温室效应的贡献量相当.通过将G-res Tool模型蓄水后的温室气体通量评估结果和所涉及到的12座水库中已发表的数据对比分析发现,G-res Tool具有简便、适用面广等特点.但G-res Tool毕竟仍为经验性模型,其基本原理和模块设计上的内在缺陷在很大程度上限制了其应用范围并造成了一定的不确定性.对个案水库而言,长期跟踪观测与机理研究仍是未来减少水库温室气体净通量不确定性的关键.     

A stochastic rough-approximation water management model for supporting sustainable water-environment strategies in an irrigation district of arid region

In this study, a stochastic rough-approximation water management model (SRAWM) associated with optimistic and pessimistic options is proposed for supporting regional sustainability in an irrigation system (IS) of an arid region with uncertain information. SRAWM can not only handle conventional stochastic variations in objective functions or constraints, but also tackle objective and subjective (i.e., risk performance of the decision maker) fuzziness through rough-approximation model based on measure Me. The developed model would be applied to a real case study of an irrigation district (ID) in Kaidu-kongque River Basin, China, which is encountering challenges in economic development and a serious environmental crisis (e.g., drought, water deficit, land deterioration, stalinization, soil erosion and water pollution) synchronously. Simulation technical (i.e., support vector regression) is put into SRAWM framework to reflect dynamic prediction of water demand in the future. Results of optimized irrigation area, water allocation, water deficit, pollution reduction, water and soil erosion and system benefit under various water-environmental policies (corresponding to various ecological effects) are obtained. Tradeoffs between ecological and irrigative water usages can facilitate the local decision makers rectifying the current irrigation patterns and ecological protection polices. Moreover, compromises between systemic benefit and failure risk can help policymakers to generate a robust risk-control plan under uncertainties. These detections are beneficial to achieve conjunctive goals of socio-economic development and eco-environmental sustainability in such an arid IS.     

Identification of optimal strategies for agricultural nonpoint source management in Ulansuhai Nur watershed of Inner Mongolia,China

In this study, an environmental-friendly modeling system was developed and applied to an agriculture nonpoint source (AGNPS) management in Ulansuhai Nur watershed. In this system, water environmental capacity, credibility-based chance-constrained programming (CCCP), and AGNPS optimization models were integrated into a general modeling framework. It could be used to calculate water environmental capacity of total nitrogen and total phosphorus in Ulansuhai Nur watershed, which could consequentially provide input data for the developed AGNPS optimization model. Also, the inherent uncertainties in estimating water environmental capacities that can be expressed as possibilistic distributions were reflected and addressed based on computational results of three widely used methods. Such uncertainties were consequentially transferred to the proposed CCCP model based on the adoption of multiple credibility satisfactory levels, significantly facilitating objectivity reflection of decision alternatives. The developed modeling system was then applied to Ulansuhai Nur watershed of Inner Mongolia, a semi-arid river basin in northwestern China. Optimal strategies for AGNPS management in Ulansuhai Nur watershed were generated with consideration of the maximum total agricultural income under multiple policy scenarios. The results showed that the total agricultural income would increase with point source pollution being cut down, and would decrease with rising credibility levels, representing decreasing system violation risks. It was indicated that the higher of total nitrogen/phosphorus discharge being less than water environmental capacity of Ulansuhai Nur, the lower the total agriculture incomes. The proposed methods could help decision makers establish various production patterns with cost-effective agriculture nonpoint source management schemes in the basin of Ulansuhai Nur, and gain in-depth insights into the trade-offs between total agricultural incomes and system reliabilities.     

Dynamics of suspended sediment transport at field‐scale drain channels of irrigation‐dominated watersheds in the Sonoran Desert,southeastern California

Suspended sediment is a major source of pollution in irrigation‐dominated watersheds. However, little is known about the process and mechanisms of suspended sediment transport in drain channels directly connected to agricultural fields. This paper explains sediment dynamics using averaged 5 min flow discharge Q (m³ s^?1) and suspended sediment concentration C (mg l^?1) collected during one crop season in a small catchment containing a first‐order drain channel and its connected six agricultural fields within the Salton Sea watershed. The statistical properties and average trends of Q and C were investigated for both early (i.e. November) and late (i.e. January) stages of a crop season. Further in‐depth analysis on sediment dynamics was performed by selecting two typical single‐field irrigation events and two multiple‐field irrigation events. For each set of irrigation events, the process of suspended sediment transport was revealed by examining hydrograph and sediment graph responses. The mechanisms underlying suspended sediment transport were investigated by analysing the types of corresponding hysteresis loop. Finally, sediment rating curves for both hourly and daily data at early and late stages and for the entire crop season were established to seek possible sediment‐transport predictive model(s). The study suggests that the complicated processes of suspended sediment transport in irrigation‐dominated watersheds require stochastic rather than deterministic forecasting. Copyright © 2007 John Wiley & Sons, Ltd.     

An inexact fuzzy-random-chance-constrained air quality management model

An inexact fuzzy-random-chance-constrained programming model (IFRCCMM) was developed for supporting regional air quality management under uncertainty. IFRCCMM was formulated through integrating interval linear programming within fuzzy-random-chance-constrained programming framework. It could deal with parameter uncertainties expressed as not only fuzzy random variables but also discrete intervals. Based on the stochastic and fuzzy chance-constrained programming algorithms, IFRCCMM was solved when constraints was satisfied under different satisfaction and violation levels of constraints, leading to interval solutions with different risk and cost implications. The proposed model was applied to a regional air quality management problem for demonstration. The obtained results indicated that the proposed model could effectively reflect uncertain components within air quality management system through employing multiple uncertainty-characterization techniques (in random, fuzzy and interval forms), and help decision makers analyze trade-offs between system economy and reliability. In fact, many types of solutions (i.e. conservative solutions with lower risks and optimistic solutions with higher risks) provided by IFRCCMM were suitable for local decision makers to make more applicable decision schemes according to their understanding and preference about the risk and economy. In addition, the modeling philosophy is general and applicable to many other environmental problems that may be complicated with multiple forms of uncertainties.     

Energy and GHG emissions management of agricultural systems using multi objective particle swarm optimization algorithm: a case study

In the recent centuries, one of the most important ongoing challenges is energy consumption and its environmental impacts. As far as agriculture is concerned, it has a key role in the world economics and a great amount of energy from different sources is used in this sector. Since researchers have reported a high degree of inefficiency in developing countries, it is necessary for the modern management of cropping systems to have all factors (economics, energy and environment) in the decision-making process simultaneously. Therefore, the aim of this study is to apply Multi-Objective Particle Swarm Optimization (MOPSO) to analyze management system of an agricultural production. As well as MOPSO, two other optimization algorithm were used for comparing the results. Eventually, Taguchi method with metrics analysis was used to tune the algorithms’ parameters and choose the best algorithms. Watermelon production in Kerman province was considered as a case study. On average, the three multi-objective evolutionary algorithms could reduce about 30 % of the average Greenhouse Gas (GHG) emissions in watermelon production although as well as this reduction, output energy and benefit cost ratio were increased about 20 and 30 %, respectively. Also, the metrics comparison analysis determined that MOPSO provided better modeling and optimization results.     

Factorial two-stage stochastic programming for water resources management

This study presents a factorial two-stage stochastic programming (FTSP) approach for supporting water resource management under uncertainty. FTSP is developed through the integration of factorial analysis and two-stage stochastic programming (TSP) methods into a general modeling framework. It can handle uncertainties expressed as probability distributions and interval numbers. This approach has two advantages in comparison to conventional inexact TSP methods. Firstly, FTSP inherits merits of conventional inexact two-stage optimization approaches. Secondly, it can provide detailed effects of uncertain parameters and their interactions on the system performance. The developed FTSP method is applied to a hypothetical case study of water resources systems analysis. The results indicate that significant factors and their interactions can be identified. They can be further analyzed for generating water allocation decision alternatives in municipal, industrial and agricultural sectors. Reasonable water allocation schemes can thus be formulated based on the resulting information of detailed effects from various impact factors and their interactions. Consequently, maximized net system benefit can be achieved.     

Total consumption controlled water allocation management for multiple sources and users with inexact fuzzy chance-constrained programming: a case study of Tianjin,China

Environmental and ecological issues caused by water resources crisis have brought enormous challenges to the sustainable development of water-deficient area. Water resources allocation management balancing the relationship between the social-economic development and the ecological environment has become a hot topic in recent years. In this paper, an inexact fuzzy chance-constrained programming (IFCCP) approach is proposed for regional water resource allocation optimization with the aim of promoting the harmonious development of the social economic and the ecological environment, improving water utilization efficiency, and realizing water resources consumption control under uncertainties. The method is incorporated with interval parameter programming, fuzzy programming, and chance-constrained programming, for handling system uncertainties and balancing the optimal objectives with the risk of violating system constraints. Under this framework, an IFCCP model for water resources allocation management was successfully formulated and applied to a typical water-deficit area, Tianjin, China, for obtaining a better water resources plan among multiple users under resources and environmental limitation. Different total water consumption control policies are designed for assessing regional water allocation schemes. The results indicated that the gap of supply and demand will only be solved by foreign water, the transferred water from Luan River and Changjiang River would still be the main supplier in planning horizon. Moreover, the strict total water consumption control policy would guarantee the water requirement of ecological environment, lead to changes in the structure of water supply, actively guide on water conservation, and promote the large-scale utilization of desalted water and recycle water.     

Optimal reduction of anthropogenic emissions for air pollution control and the retrieval of emission source from observed pollutants Ⅰ. Application of incomplete adjoint operator

The ultimate solution to anthropogenic air pollution depends on an adjustment and upgrade of industrial and energy structures. Before this process can be completed, reducing the anthropogenic pollutant emissions is an effective measure. This is a problem belonging to “Natural Cybernetics”, i.e., the problem of air pollution control should be solved together with the weather prediction; however, this is very complicated. Considering that heavy air pollution usually occurs in stable weather conditions and that the feedbacks between air pollutants and meteorological changes are insufficient, we propose a simplified natural cybernetics method. Here, an off-line air pollution evolution equation is first solved with data from a given anthropogenic emission inventory under the predicted weather conditions, and then, a related “incomplete adjoint problem” is solved to obtain the optimal reduction of anthropogenic emissions. Usually, such solution is sufficient for satisfying the air quality and economical/ social requirements. However, a better solution can be obtained by iteration after updating the emission inventory with the reduced anthropogenic emissions. Then, this paper discusses the retrieval of the pollutant emission source with a known spatio-temporal distribution of the pollutant concentrations, and a feasible mathematical method to achieve this is proposed. The retrieval of emission source would also help control air pollution.