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Integrated waste load allocation for river water pollution control under uncertainty: a case study of Tuojiang River, China

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Abstract

This paper presents a bi-level optimization waste load allocation programming model under a fuzzy random environment to assist integrated river pollution control. Taking account of the leader-follower decision-making in the water function zones framework, the proposed approach examines the decision making feedback relationships and conflict coordination between the river basin authority and the regional Environmental Protection Agency (EPA) based on the Stackelberg-Nash equilibrium strategy. In the pollution control system, the river basin authority, as the leader, allocates equitable emissions rights to different subareas, and the then subarea EPA, as the followers, reallocates the limited resources to various functional zones to minimize pollution costs. This research also considers the uncertainty in the water pollution management, and the uncertain input information is expressed as fuzzy random variables. The proposed methodological approach is then applied to Tuojiang River in China and the bi-level linear programming model solutions are achieved using the Karush-Kuhn-Tucker condition. Based on the waste load allocation scheme results and various scenario analyses and discussion, some operational policies are proposed to assist decision makers (DMs) cope with waste load allocation problem for integrated river pollution control for the overall benefits.

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References

  1. Brierley G, Fryirs K, Outhet D, Massey C (2002) Application of the river styles framework as a basis for river management in new South Wales, Australia. Appl Geogr 22(1):91–122

  2. Burn D H, Lence B J (1992) Comparison of optimization formulations for waste load allocations. J Environ Eng 118(4):597–612

  3. Chang H (2008) Spatial analysis of water quality trends in the han river basin, South Korea. Water Res 42 (13):3285

  4. Chen B, Gu C, Wang H, Tao J, Wu Y, Liu Q, Xu H (2012) Research on gini coefficient application in the distribution of water pollution. J Food Agric Environ 10(2):833–838

  5. Chen X J, Huang G H, Zhu H, Suo M Q, Dong C (2016) Inexact inventory theory based waste management planning model for the city of Xiamen, China. J Environ Eng, 142(5)

  6. China Environmental Status Bulletin (2015) China environmental status bulletin 2015. http://www.zhb.gov.cn/hjzl/zghjzkgb/lssj/zxhjzkgb/

  7. Cullis J, Van Koppen B (2007) Applying the Gini coefficient to measure inequality of water use in the Olifants river water management area, South Africa, vol 113. IWMI

  8. Del C S M, Verdiell A, Iglesias Rodrguez R M, Vidal M (2007) A quantitative method for zoning of protected areas and its spatial ecological implications. J Environ Manag 83(2):198–206

  9. Fang S, Guo P, Li M, Zhang L (2013) Bilevel multiobjective programming applied to water resources allocation. Math Probl Eng

  10. Gastwirth J L (1972) The estimation of the lorenz curve and gini index. Rev Econ Stat 54(3):306–16

  11. Gini C, Salvemini T (1912). In: Pizetti E (ed) Variabilità e mutabilità. Reprinted in Memorie di metodologica statistica. Libreria Eredi Virgilio Veschi 1, Rome

  12. Guo X, Hu T, Zhang T, Lv Y (2012) Bilevel model for multi-reservoir operating policy in inter-basin water transfer-supply project. J Hydrol 424:252–263

  13. Helmer R, Hespanhol I, Organization W H (1997) Water pollution control: a guide to use of water quality management principles 2(3-4): 254–261

  14. Hu Z, Chen Y, Yao L, Wei C, Li C (2016a) Optimal allocation of regional water resources: From a perspective of equity efficiency tradeoff. Resour Conserv Recycl 109:102–113

  15. Hu Z, Wei C, Yao L, Li C, Zeng Z (2016b) Integrating equality and stability to resolve water allocation issues with a multiobjective bilevel programming model. Journal of Water Resources Planning & Management 142(7)

  16. Huang F, Wang X, Lou L, Zhou Z, Wu J (2010) Spatial variation and source apportionment of water pollution in Qiantang river (China) using statistical techniques. Water Res 44(44):1562–1572

  17. Jury W A, Jr H J V (2007) The emerging global water crisis: Managing scarcity and conflict between water users. Adv Agron 95:1–76

  18. Karr J R (1993) Defining and assessing ecological integrity: Beyond water quality. Environ Toxicol Chem 12 (9):1521–1531

  19. Kruse R, Meyer K D (1987) Statistics with Vague Data

  20. Kwakernaak H (1978) Fuzzy random variablesi. definitions and theorems. Inf Sci 15(1):1–29

  21. Laffont J J, Maskin E (1982) The theory of incentives: an overview. Advances in Economic Theory

  22. Li M, Guo P (2015) A coupled random fuzzy two-stage programming model for crop area optimizationa case study of the middle Heihe River basin, China. Agric Water Manag 155:53–66

  23. Liang S, Jia H, Yang C, Melching C, Yuan Y (2015) A pollutant load hierarchical allocation method integrated in an environmental capacity management system for Zhushan Bay, Taihu Lake. Sci Total Environ 533:223–237

  24. Loucks D P, Stedinger J R, Haith D A (1981) Water resource systems planning and analysis

  25. Mahjouri N, Abbasi M R (2015) Waste load allocation in rivers under uncertainty: application of social choice procedures. Environ Monit Assess 187(2):1–15

  26. Meng W, Zhang N, Zhang Y, Zheng B (2007) The study on technique of basin water quality target management I: Pollutant total amount control technique in control unit. Res Environ Sci 20(4):1–8

  27. Murty Y, Bhallamudi S M, Srinivasan K (2006) Non-uniform flow effect on optimal waste load allocation in rivers. Water Resour Manag 20(4):509–530

  28. Ni J R, Zhong D S, Huang Y F, Wang H (2001) Total waste-load control and allocation based on inputcoutput analysis for Shenzhen, South China. J Environ Manag 61(61):37–49

  29. Nikoo M R, Beiglou P H B, Mahjouri N (2016) Optimizing multiple-pollutant waste load allocation in rivers: an interval parameter game theoretic model. Water Resour Manag 30(12):4201–4220

  30. Poorsepahy Samian H, Kerachian R, Nikoo M R (2012) Water and pollution discharge permit allocation to agricultural zones: Application of Game Theory and Min-Max Regret Analysis. Water Resour Manag 26(14):4241–4257

  31. Roghanian E, Aryanezhad M B, Sadjadi S J (2008) Integrating goal programming, kuhnctucker conditions, and penalty function approaches to solve linear bi-level programming problems. Appl Math Comput 195(2):585–590

  32. Shen Z, Zhong Y, Huang Q, Chen L (2015) Identifying non-point source priority management areas in watersheds with multiple functional zones. Water Res 68:563–571

  33. Sichuan Province Bulletin (2015) Sichuan province bulletin 2015. http://www.sc.gov.cn/10462/10464/10465/10574/2016/10/14/10399118.shtml

  34. Sichuan Province Environmental Status Bulletin (2015) Sichuan province environmental status bulletin 2015. http://www.schj.gov.cn/cs/hjjc/zkgg/

  35. Sichuan Statistical Yearbook (2015) Sichuan statistical yearbook 2015. http://www.sc.stats.gov.cn/tjcbw/tjnj/2015/index.htm

  36. Sinha S, Sinha S B (2002) Kkt transformation approach for multi-objective multi-level linear programming problems. Eur J Oper Res 143(1):19–31

  37. Stackelberg H V, Peacock A T (1952) The theory of the market economy. Hodge

  38. Stackelberg H V, Peacock A T (1953) The theory of the market economy. Economica, 4(6)

  39. Su S, Li D, Zhang Q, Xiao R, Huang F, Wu J (2011) Temporal trend and source apportionment of water pollution in different functional zones of Qiantang River, China. Water Res 45(4):1781–95

  40. Tao S, Zhang H W, Yuan W, Meng X M, Wang C W (2010) The application of environmental gini coefficient (egc) in allocating wastewater discharge permit: the case study of watershed total mass control in Tianjin, China. Resour Conserv Recycl 54(9):601– 608

  41. Tfekci N, Sivri N, Toroz I (2007) Pollutants of textile industry wastewater and assessment of its discharge limits by water quality standards. Turk J Fish Aquat Sci 7(2):97–103

  42. Tung Y K (1992) Multiple-objective stochastic waste load allocation. Water Resour Manag 6(2):117–133

  43. Wang F, Li Y, Yang J, Sun Z (2014) Application of wasp model and gini coefficient in total mass control of water pollutants: a case study in Xicheng Canal, China. Desalin Water Treat 57(7):1– 14

  44. Wang X J, Zhang J Y, Shahid S, Elmahdi A, He R M, Wang X G, Ali M (2012) Gini coefficient to assess equity in domestic water supply in the Yellow River. Mitig Adapt Strateg Glob Chang 17(1):65– 75

  45. Water Pollution Control Planning (2013) Water pollution prevention and control planning in key river basins in sichuan province. http://www.schj.gov.cn/xxgk/auto355/201305/t20130521_1992.html

  46. Wei S, Hong Y, Abbaspour K, Mousavi J, Gnauck A (2010) Game theory based models to analyze water conflicts in the middle route of the South-to-North water transfer project in China. Water Res 44(8):2499–2516

  47. Wen U P, Hsu S T (1991) Linear bi-level programming problems: a review. J Oper Res Soc 42(2):125–133

  48. Weng Q (2007) A historical perspective of river basin management in the Pearl River Delta of China. J Environ Manag 85(4):1048–1062

  49. Wu B, Zheng Y (2012) Assessing the value of information for water quality management: a watershed perspective from China. Environ Monit Assess 185(4):3023–3035

  50. Xu J, Zhou X (2011) Fuzzy-like multiple objective decision making, vol 263, Springer

  51. Xu J, Tu Y, Zeng Z (2012) Bilevel optimization of regional water resources allocation problem under fuzzy random environment. J Water Resour Plan Manag 139(3):246–264

  52. Xu J, Lv C, Zhang M, Yao L, Zeng Z (2015a) Equilibrium strategy-based optimization method for the coal-water conflict: A perspective from China. J Environ Manag 160:312

  53. Xu J, Zhang M, Zeng Z (2015b) Hybrid nested particle swarm optimization for a waste load allocation problem in river system. Journal of Water Resources Planning & Management

  54. Xue P, Zeng W (2011) Trends of environmental accidents and impact factors in China. Front Environ Sci Eng China 5(2):266– 276

  55. Yao L, Xu J, Zhang M, Lv C, Li C (2016) Waste load equilibrium allocation: a soft path for coping with deteriorating water systems. Environ Sci Pollut Res 23(15):1–21

  56. Yu S, Jiang H Q, Chang M (2015) Integrated prediction model for optimizing distributions of total amount of water pollutant discharge in the Songhua River watershed. Stoch Env Res Risk A 30(8):2179–2187

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Acknowledgements

The work is supported by the National Natural Science Foundation for Young Scholars of China (Grant No. 71301109), Soft Science Program of Sichuan Province (Grant No. 2017ZR0154), the Research Foundation of Ministry of Education for the Doctoral Program of Higher Education of China (Grant No. 20130181110063), and Key Program of National Natural Science Foundation of China (Grant No. 70831005).

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Correspondence to Jiuping Xu.

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Xu, J., Hou, S., Yao, L. et al. Integrated waste load allocation for river water pollution control under uncertainty: a case study of Tuojiang River, China. Environ Sci Pollut Res 24, 17741–17759 (2017). https://doi.org/10.1007/s11356-017-9275-z

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Keywords

  • Waste load allocation
  • Bi-level optimization model
  • Stackelberg-Nash game
  • Uncertainty
  • Integrated