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A fuzzy multi-stakeholder socio-optimal model for water and waste load allocation

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Abstract

This study proposes a fuzzy multi-stakeholder socio-optimal methodology for joint water and waste load allocation (WWLA) in river systems while addressing upstream flow uncertainty and different social choice rules (SCRs). QUAL2Kw, as the numerical river water quality model, is executed for various scenarios of water and waste loads to construct a comprehensive dataset of plausible settings, which is in turn used to train a meta-model in the form of multivariate linear regressions. The river upstream flow as the main uncertain parameter is assessed by fuzzy transformation method (FTM). Then, for different confidence levels of fuzzy uncertain input, the meta-model is linked with the non-dominated sorting genetic algorithm (NSGA-II) multi-objective optimization model to generate trade-off curves among the stakeholders’ utility functions. Subsequently, five SCRs are utilized at each confidence level to determine the fuzzy interval solutions for each objective. Next, the possibility degree method is applied to rank the fuzzy interval solutions in each α-cut level. Finally, considering the priorities of all stakeholders, the fallback bargaining method is used to specify the most appropriate SCR in each confidence level. Application of the proposed methodology in Kor River, Iran, shows its efficacy to realize the socio-optimal WWLA scenario(s) among different stakeholders.

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References

  • Afshar, A., & Masoumi, F. (2016). Waste load reallocation in river–reservoir systems: simulation–optimization approach. Environmental Earth Sciences, 75(1), 53.

    Article  Google Scholar 

  • Afshar, A., Masoumi, F., & Sandoval Solis, S. (2018). Developing a reliability-based waste load allocation strategy for river-reservoir systems. Journal of Water Resources Planning and Management, 144(9), 04018052.

    Article  Google Scholar 

  • Aghasian, K., Moridi, A., Mirbagheri, A., & Abbaspour, M. (2019). A conflict resolution method for waste load reallocation in river systems. International journal of Environmental Science and Technology, 16(1), 79–88.

    Article  Google Scholar 

  • Alizadeh, M. R., Nikoo, M. R., & Rakhshandehroo, G. R. (2017). Hydro-environmental management of groundwater resources: a fuzzy-based multi-objective compromise approach. Journal of Hydrology, 551, 540–554.

    Article  Google Scholar 

  • Allam, A., Tawfik, A., Yoshimura, C., & Fleifle, A. (2016a). Multi-objective models of waste load allocation toward a sustainable reuse of drainage water in irrigation. Environmental Science and Pollution Research, 23(12), 11823–11834.

    Article  Google Scholar 

  • Allam, A., Tawfik, A., Yoshimura, C., & Fleifle, A. (2016b). Simulation-based optimization framework for reuse of agricultural drainage water in irrigation. Journal of Environmental Management, 172, 82–96.

    Article  CAS  Google Scholar 

  • Bassett, G. W., & Persky, J. (1999). Robust voting. Public Choice, 99(3–4), 299–310.

    Article  Google Scholar 

  • Brams, S. J., & Kilgour, D. M. (2001). Fallback bargaining. Group Decision and Negotiation, 10, 287–316.

    Article  Google Scholar 

  • Cao Q (2005) A water quantity and quality model of optimal water allocation based on green benefit. Water resource and hydropower engineering. Zhengzhou University, Zhengzhou, Master, 70.

  • Chaudhary, S., Dhanya, C. T., & Kumar, A. (2018). Sequential calibration of a water quality model using reach-specific parameter estimates. Hydrology Research, 49(4), 1042–1055.

    Article  CAS  Google Scholar 

  • Cho, J. H., & Ha, S. R. (2010). Parameter optimization of the QUAL2K model for a multiple-reach river using an influence coefficient algorithm. Science of the Total Environment, 408(8), 1985–1991.

    Article  CAS  Google Scholar 

  • Dai, T., & Labadie, J. W. (2001). River basin network model for integrated water quantity/quality management. Journal of Water Resources Planning and Management, 127(5), 295–305.

    Article  Google Scholar 

  • de Moraes, M. A., Cai, X., Ringler, C., Albuquerque, B. E., Vieira da Rocha, S., & Amorim, C. A. (2010). Joint water quantity-quality management in a biofuel production area—integrated economic-hydrologic modeling analysis. Journal of Water Resources Planning and Management, 136(4), 502–511.

    Article  Google Scholar 

  • Deb, K., Agrawal, S., Pratap, A., & Meyarivan, T. (2000). “A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II”. In International Conference on Parallel Problem Solving From Nature (pp. 849–858). Springer, Berlin, Heidelberg.

  • Estalaki, S. M., Abed-Elmdoust, A., & Kerachian, R. (2015). Developing environmental penalty functions for river water quality management: application of evolutionary game theory. Environmental Earth Sciences, 73(8), 4201–4213.

    Article  Google Scholar 

  • Farhadi, S., Nikoo, M. R., Rakhshandehroo, G. R., Akhbari, M., & Alizadeh, M. R. (2016). An agent-based-nash modeling framework for sustainable groundwater management: A case study. Agricultural Water Management, 177, 348-358.

  • Ghosh, S., & Mujumdar, P. P. (2010). Fuzzy waste load allocation model: a multiobjective approach. Journal of Hydroinformatics, 12(1), 83–96.

    Article  Google Scholar 

  • Hakimi-Asiabar, M., Ghodsypour, S. H., & Kerachian, R. (2010). Deriving operating policies for multi-objective reservoir systems: application of self-learning genetic algorithm. Applied Soft Computing, 10(4), 1151–1163.

    Article  Google Scholar 

  • Hanss, M. (2003). The extended transformation method for the simulation and analysis of fuzzy-parameterized models. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 11(06), 711–727.

    Article  Google Scholar 

  • Hanss, M., & Klimke, A. (2004). On the reliability of the influence measure in the transformation method of fuzzy arithmetic. Fuzzy Sets and Systems, 143(3), 371–390.

    Article  Google Scholar 

  • Huang, X., Chen, X., & Huang, P. (2018). Research on fuzzy cooperative game model of allocation of pollution discharge rights. Water, 10(5), 662.

    Article  Google Scholar 

  • Jamshidi, S., Niksokhan, M. H., Ardestani, M., & Imani, S. (2019). Operation-based uncertainties in river waste load allocation and their impacts on controlling discharges. Civil Engineering and Environmental Systems, 1–18.

  • Karamouz, M., Zahraie, B., & Kerachian, R. (2003). Development of a master plan for water pollution control using MCDM techniques: a case study. Water International, 28(4), 478–490.

    Article  Google Scholar 

  • Karamouz, M., Moridi, A., & FAYAZI, H. (2008). Dealing with conflict over water quality and quantity allocation: a case study.

  • Karamouz, M., Ahmadi, A., & Moridi, A. (2009). Probabilistic reservoir operation using Bayesian stochastic model and support vector machine. Advances in Water Resources, 32(11), 1588–1600.

    Article  Google Scholar 

  • Kerachian, R., & Karamouz, M. (2007). A stochastic conflict resolution model for water quality management in reservoir–river systems. Advances in Water Resources, 30(4), 866–882.

    Article  Google Scholar 

  • Nikoo, M. R., Kerachian, R., Karimi, A., & Azadnia, A. A. (2013). Optimal water and waste-load allocations in rivers using a fuzzy transformation technique: a case study. Environmental Monitoring and Assessment, 185(3), 2483–2502.

    Article  Google Scholar 

  • Labadie, J. W. (2004). Optimal operation of multireservoir systems: state-of-the-art review. Journal of Water Resources Planning and Management, 130(2), 93–111.

    Article  Google Scholar 

  • Li, Y. P., Huang, G. H., Nie, S. L., & Mo, D. W. (2008). Intervalparameter robust quadratic programming for water quality management under uncertainty. Engineering Optimization, 40(7), 613–635.

    Article  Google Scholar 

  • Liu, D., Guo, S., Shao, Q., Jiang, Y., & Chen, X. (2014). Optimal allocation of water quantity and waste load in the Northwest Pearl River Delta, China. Stochastic Environmental Research and Risk Assessment, 28(6), 1525–1542.

    Article  Google Scholar 

  • Madani, K., Sheikhmohammady, M., Mokhtari, S., Moradi, M., & Xanthopoulos, P. (2014a). Social planner’s solution for the Caspian Sea conflict. Group Decision and Negotiation, 23(3), 579–596.

    Article  Google Scholar 

  • Madani, K., Zarezadeh, M., & Morid, S. (2014b). A new framework for resolving conflicts over transboundary rivers using bankruptcy methods. Hydrology and Earth System Sciences, 18(8), 3055–3068.

    Article  Google Scholar 

  • Mahjouri, N., & Abbasi, M. R. (2015). Waste load allocation in rivers under uncertainty: application of social choice procedures. Environmental Monitoring and Assessment, 187(2), 5.

    Article  Google Scholar 

  • Mahjouri, N., & Ardestani, M. (2011). Application of cooperative and non-cooperative games in large-scale water quantity and quality management: a case study. Environmental Monitoring and Assessment, 172(1–4), 157–169.

    Article  Google Scholar 

  • Mahjouri, N., & Bizhani-Manzar, M. (2013). Waste load allocation in rivers using fallback bargaining. Water Resources Management, 27(7), 2125–2136.

    Article  Google Scholar 

  • Mallakpour, I., Sadegh, M., & AghaKouchak, A. (2018). A new normal for streamflow in California in a warming climate: Wetter wet seasons and drier dry seasons. Journal of Hydrology, 567, 203–211.

    Article  Google Scholar 

  • Meng, C., Wang, X., & Li, Y. (2017). An optimization model for waste load allocation under water carrying capacity improvement management, a case study of the Yitong River, Northeast China. Water, 9(8), 573.

  • Mesbah, S. M., Kerachian, R., & Nikoo, M. R. (2009). Developing real time operating rules for trading discharge permits in rivers: application of Bayesian networks. Environmental Modelling & Software, 24(2), 238–246.

    Article  Google Scholar 

  • Moridi, A. (2019). A bankruptcy method for pollution load reallocation in river systems. Journal of Hydroinformatics, 21(1), 45–55.

    Article  Google Scholar 

  • Mousavi, S. J., Karamouz, M., & Menhadj, M. B. (2004). Fuzzy-state stochastic dynamic programming for reservoir operation. Journal of Water Resources Planning and Management, 130(6), 460–470.

    Article  Google Scholar 

  • Naeini, M. R., Yang, T., Sadegh, M., AghaKouchak, A., Hsu, K. L., Sorooshian, S., et al. (2018). Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL) optimization framework. Environmental Modelling & Software, 104, 215–235.

    Article  Google Scholar 

  • Nafarzadegan, A. R., Vagharfard, H., Nikoo, M. R., & Nohegar, A. (2018). Socially-optimal and Nash Pareto-based alternatives for water allocation under uncertainty: an approach and application. Water Resources Management, 32(9), 2985–3000.

    Article  Google Scholar 

  • Nikoo, M. R., Kerachian, R., Malakpour-Estalaki, S., Bashi-Azghadi, S. N., & Azimi-Ghadikolaee, M. M. (2011). A probabilistic water quality index for river water quality assessment: a case study. Environmental Monitoring and Assessment, 181(1–4), 465–478.

    Article  Google Scholar 

  • Nikoo, M. R., Kerachian, R., & Karimi, A. (2012a). A nonlinear interval model for water and waste load allocations in river basins. Water Resources Management, 26, 2911–2926.

    Article  Google Scholar 

  • Nikoo, M. R., Kerachian, R., & Niksokhan, M. H. (2012b). Equitable waste load allocation in rivers using fuzzy bi-matrix games. Water Resources Management, 26(15), 4539–4552.

    Article  Google Scholar 

  • Nikoo, M. R., Varjavand, I., Kerachian, R., Pirooz, M. D., & Karimi, A. (2014). Multi-objective optimum a design of double-layer perforated-wall breakwaters: application of NSGA-II and bargaining models. Applied Ocean research, 47, 47–52.

    Article  Google Scholar 

  • 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 Resources Management, 30(12), 4201–4220.

    Article  Google Scholar 

  • Niksokhan, M. H., Kerachian, R., & Karamouz, M. (2009). A game theoretic approach for trading discharge permits in rivers. Water Science and Technology, 60(3), 793–804.

    Article  Google Scholar 

  • Ning, S. K., Chang, N. B., Yang, L., Chen, H. W., & Hsu, H. Y. (2001). Assessing pollution prevention program by QUAL2E simulation analysis for the Kao-Ping River Basin, Taiwan. Journal of Environmental Management, 61(1), 61–76.

    Article  CAS  Google Scholar 

  • Nurmi, H. (1999). Voting paradoxes and how to deal with them. Berlin: Springer Verlag.

    Book  Google Scholar 

  • Paredes-Arquiola, J., Andreu-Álvarez, J., Martín-Monerris, M., & Solera, A. (2010). Water quantity and quality models applied to the Jucar River Basin, Spain. Water Resources Management, 24(11), 2759–2779.

    Article  Google Scholar 

  • Pelletier, G. J., Chapra, S. C., & Tao, H. (2006). QUAL2Kw–a framework for modeling water quality in streams and rivers using a genetic algorithm for calibration. Environmental Modelling & Software, 21(3), 419–425.

    Article  Google Scholar 

  • 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 Resources Management, 26(14), 4241–4257.

    Article  Google Scholar 

  • Qin, X., Huang, G., Chen, B., & Zhang, B. (2009). An intervalparameter waste-load-allocationmodel for riverwater quality management under uncertainty. EnvironmentalManagement, 43, 999–1012.

    Google Scholar 

  • Raei, E., Nikoo, M. R., & Pourshahabi, S. (2017). A multi-objective simulation-optimization model for in situ bioremediation of groundwater contamination: application of bargaining theory. Journal of Hydrology, 551, 407–422.

    Article  CAS  Google Scholar 

  • Reynolds, A., Reilly, B., & Ellis, A. (2008). Electoral system design: the new international IDEA handbook. International Institute for Democracy and Electoral Assistance.

  • Saadatpour, M., Afshar, A., & Khoshkam, H. (2019). Multi-objective multi-pollutant waste load allocation model for rivers using coupled archived simulated annealing algorithm with QUAL2Kw. Journal of Hydroinformatics.

  • Saberi, L., & Niksokhan, M. H. (2017). Optimal waste load allocation using graph model for conflict resolution. Water Science and Technology, 75(6), 1512–1522.

    Article  Google Scholar 

  • Sadegh, M., & Kerachian, R. (2011). Water resources allocation using solution concepts of fuzzy cooperative games: fuzzy least core and fuzzy weak least core. Water Resources Management, 25(10), 2543–2573.

    Article  Google Scholar 

  • Sadegh, M., Mahjouri, N., & Kerachian, R. (2010). Optimal inter-basin water allocation using crisp and fuzzy Shapley games. Water Resources Management, 24, 2291–2310.

    Article  Google Scholar 

  • Sadegh, M., Ragno, E., & AghaKouchak, A. (2017). Multivariate C opula A nalysis T oolbox (MvCAT): describing dependence and underlying uncertainty using a B ayesian framework. Water Resources Research, 53(6), 5166–5183.

    Article  Google Scholar 

  • Sadegh, M., Moftakhari, H., Gupta, H. V., Ragno, E., Mazdiyasni, O., Sanders, B., & AghaKouchak, A. (2018). Multi-hazard scenarios for analysis of compound extreme events. Geophysical Research Letters., 45, 5470–5480.

    Article  Google Scholar 

  • Sadegh, M., Majd, M. S., Hernandez, J., & Haghighi, A. T. (2018b). The quest for hydrological signatures: effects of data transformation on Bayesian inference of watershed models. Water Resources Management, 32(5), 1867–1881.

    Article  Google Scholar 

  • Sedghamiz, A., Nikoo, M. R., Heidarpour, M., & Sadegh, M. (2018). Developing a non-cooperative optimization model for water and crop area allocation based on leader-follower game. Journal of Hydrology, 567, 51–59.

    Article  Google Scholar 

  • Sheikhmohammady, M., & Madani, K. (2008). Bargaining over the Caspian Sea—the largest lake on the earth. In World environmental and water resources congress 2008: Ahupua’a (pp. 1–9).

  • Sheikhmohammady, M., Kilgour, D. M., & Hipel, K. W. (2010). Modeling the Caspian Sea negotiations. Group Decision and Negotiation, 19(2), 149–168.

    Article  Google Scholar 

  • Shojaeezadeh, S. A., Nikoo, M. R., McNamara, J. P., AghaKouchak, A., & Sadegh, M. (2018). Stochastic modeling of suspended sediment load in alluvial rivers. Advances in Water Resources, 119, 188–196.

    Article  Google Scholar 

  • Shojaei, M., Nazif, S., & Kerachian, R. (2015). Joint uncertainty analysis in river water quality simulation: a case study of the Karoon River in Iran. Environmental Earth Sciences, 73(7), 3819–3831.

    Article  Google Scholar 

  • Singh, A. P., Ghosh, S. K., & Sharma, P. (2007). Water quality management of a stretch of river Yamuna: an interactive fuzzy multi-objective approach. International Journal of Water Resources Management, 21, 515–532.

    Article  Google Scholar 

  • Soltani, M., & Kerachian, R. (2018). Developing a methodology for real-time trading of water withdrawal and waste load discharge permits in rivers. Journal of Environmental Management, 212, 311–322.

    Article  CAS  Google Scholar 

  • Tavakoli, A., Kerachian, R., Nikoo, M. R., Soltani, M., & Estalaki, S. M. (2014). Water and waste load allocation in rivers with emphasis on agricultural return flows: application of fractional factorial analysis. Environmental Monitoring and Assessment, 186(9), 5935–5949.

    Article  Google Scholar 

  • Xia, B., Qian, X., & Yao, H. (2017). An improved risk-explicit interval linear programming model for pollution load allocation for watershed management. Environmental Science and Pollution Research, 24(32), 25126–25136.

    Article  CAS  Google Scholar 

  • Xu, J., Zhang, M., & Zeng, Z. (2016). Hybrid nested particle swarm optimization for a waste load allocation problem in river system. Journal of Water Resources Planning and Management, 142(7), 04016014.

    Article  Google Scholar 

  • Xu, J., Hou, S., Yao, L., & Li, C. (2017). Integrated waste load allocation for river water pollution control under uncertainty: a case study of Tuojiang River, China. Environmental Science and Pollution Research, 24(21), 17741–17759.

    Article  Google Scholar 

  • Yao, L., Xu, J., Zhang, M., Lv, C., & Li, C. (2016). Waste load equilibrium allocation: a soft path for coping with deteriorating water systems. Environmental Science and Pollution Research, 23(15), 14968–14988.

    Article  Google Scholar 

  • Yu, S., & Lu, H. (2018). Integrated watershed management through multi-level and stepwise optimization for allocation of total load of water pollutants at large scales. Environmental Earth Sciences, 77(10), 373.

    Article  Google Scholar 

  • Zhang, W., Wang, Y., Peng, H., Li, Y., Tang, J., & Wu, B. (2010). A coupled water quantity–quality model for water allocation analysis. Journal of Water Resources Planning and Management, 24, 485–511.

    Article  Google Scholar 

  • Zhang, R., Qian, X., Li, H., Yuan, X., & Ye, R. (2012). Selection of optimal river water quality improvement programs using QUAL2K: a case study of Taihu Lake Basin, China. Science of the Total Environment, 431, 278–285.

    Article  CAS  Google Scholar 

  • Zhu, W., Niu, Q., Zhang, R., Ye, R., Qian, X., & Qian, Y. (2015). Application of QUAL2K model to assess ecological purification technology for a polluted river. International Journal of Environmental Research and Public Health, 12(2), 2215–2229.

    Article  CAS  Google Scholar 

  • Zolfagharipoor, M. A., & Ahmadi, A. (2016). A decision-making framework for river water quality management under uncertainty: application of social choice rules. Journal of Environmental Management, 183, 152–163.

    Article  Google Scholar 

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  1. School of Engineering, Dept. of Civil and Environmental Engineering, Shiraz University, Shiraz, Iran

    Mehrdad Ghorbani Mooselu & Mohammad Reza Nikoo

  2. Department of Civil Engineering, Boise State University, Boise, ID, USA

    Mojtaba Sadegh

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  1. Mehrdad Ghorbani Mooselu
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Ghorbani Mooselu, M., Nikoo, M.R. & Sadegh, M. A fuzzy multi-stakeholder socio-optimal model for water and waste load allocation. Environ Monit Assess 191, 359 (2019). https://doi.org/10.1007/s10661-019-7504-2

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