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Inexact quadratic joint-probabilistic programming for water quality management under uncertainty in the Xiangxi River, China

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Abstract

An inexact quadratic joint-probabilistic programming model for water quality management (IQJWQ) is developed and applied to supporting multiple-point-source waste reduction in the Xiangxi River, China. The IQJWQ is a hybrid of interval quadratic programming, joint probabilistic programming and multi-segment water quality simulation. It has advantages in reflecting uncertainties expressed as joint probabilities of system risk, probability distributions of water quality standards, interval parameters and nonlinearities in the objective function. An interactive and derivative algorithm is employed for solving the IQJWQ model. The results indicate that the Pingyikou chemical plant and Liucaopo chemical plant contribute more to pollution of the main stream in the Xiangxi River, which should be the prior plants to reduce the wastewater discharge and enhance the wastewater treatment efficiencies. Meanwhile, the environmental agencies should choose the joint probability carefully to balance the tradeoff between production development and pollution control. Compared with the conventional chance-constrained programming method, the IQJWQ exhibits an increased robustness in handling the overall system risk in the optimization process. Although this study is the first application of the IQJWQ to water quality management, the proposed methods in the IQJWQ can also be applicable to many other environmental management problems under uncertainty.

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Abbreviations

i :

The name of waste-water-discharge source

j :

The name of stream segment

k :

The period

n :

The river-way number, n = 1 for Gufu River n = 2 for the main river and n = 3 for the Gaolan River

f ± :

The net system benefit over the planning horizon (RMB¥)

q B :

The joint probability of violating constraints of water quality standard of BOD

q D :

The joint probability of violating constraints of water quality standard of DO

ϕB j :

The coefficients for the constraint equations of the maximum allowable BOD discharge for river segment j

ϕD j :

The coefficients for the constraint equations of the maximum allowable DO-deficit discharge for river segment j

δB ij :

The coefficients for the constraint equations of the maximum allowable BOD discharge of source i for river segment j

δD ij :

The coefficients for the constraint equations of the maximum allowable DO-deficit discharge of source i for river segment j

Q r :

The stream flow (103m3/day)

q Bnj :

The individual probability of violating constraint of maximum allowable BOD discharge for river segment j in the n river-way

q Dnj :

The individual probability of violating constraint of maximum allowable DO-deficit for river segment j in the n river-way

\( NB_{{_{ik} }}^{ \pm } \) :

The net benefit per unit product from source i (104RMB¥/unit product)

\( C_{{_{ik} }}^{ \pm } \) :

The BOD concentration of raw wastewater generated at source i in period k (kg/ton)

\( c_{{_{ik} }}^{ \pm } \) :

Treatment cost coefficients for source i during period k

\( d_{{_{ik} }}^{ \pm } \) :

Treatment cost coefficients for source i during period k

\( \eta_{ik}^{ \pm } \) :

BOD treatment efficiency at source i during period k

\( R_{Bnjk} \) :

The designated BOD concentration at the beginning of reach j during period k in the n river-way (g/ml)

R Dnjk :

Allowable DO deficit at the end of reach j during period k in the n river-way (g/ml)

\( R_{Bnjk}^{{q_{Bnj} }} \) :

The CDF values of stream water-quality standards BOD for river segment j during period k in the n river-way (g/ml)

\( R_{Dnjk}^{{q_{Dnj} }} \) :

The CDF values of stream water-quality standards DO deficit during period k in the n river-way (g/ml)

\( w_{{_{ik} }}^{ \pm } \) :

Random wastewater-discharge rate at source i in period k (ton/unit product)

\( S_{{_{ik} }}^{ \pm } \) :

BOD discharge allowance for source i during period k (kg/day)

\( X_{{_{ik} }}^{ \pm } \) :

Production level of source i during period k (unit product/day)

\( X_{{_{ik\hbox{Min} } }}^{ \pm } \) :

The minimum demand for product i during period k (unit product/day)

\( X_{{_{ik\hbox{Max} } }}^{ \pm } \) :

The maximum demands for product i during period k (unit product/day)

References

  • Babaeyan-Koopaei K, Ervine DA, Pender G (2003) Field measurements and flow modeling of over bank flows in River Severn, UK. J Environ Inf 1:28–36

    Article  Google Scholar 

  • Bobba AG, Singh VP, Bengtsson L (2004) Application of first-order and Monte Carlo analysis in watershed water quality models. Water Resour Manage 10(3):219–240

    Article  Google Scholar 

  • Bouwer H (2003) Integrated water management for the 21st century: problems and solutions. Food Agric Environ 1(1):118–127

    Google Scholar 

  • Burn DH, Mcbean EA (1985) Optimization modeling of water quality in an uncertain environment. Water Resour Res 21:122–131

    Google Scholar 

  • Cai YP, Huang GH, Wang X, Li GC, Tan Q (2011) An inexact programming approach for supporting ecologically sustainable water supply with the consideration of uncertain water demand by ecosystems. Stoch Environ Res Risk Assess 25:721–735

    Article  Google Scholar 

  • Chen B (2007) Climate change and pesticide loss in watershed systems: a simulation modeling study. J Environ Inf 10(2):55–67

    Article  Google Scholar 

  • Chen MJ, Huang GH (2001) A derivative algorithm for inexact quadratic program-application to environmental decision-making under uncertainty. Eur J Oper Res 128:570–586

    Article  Google Scholar 

  • Jan C, Steven B, Veronique V (2011) Coupling a hydrological water quality model and an economic optimization model to set up a cost-effective emission reduction scenario for nitrogen. Environ Model Softw 26:44–51

    Google Scholar 

  • Costa M, Goncalves AM (2011) Clustering and forecasting of dissolved oxygen concentration on a river basin. Stoch Environ Res Risk Assess 25:151–163

    Article  Google Scholar 

  • Dupa cová J, Gaivoronski A, Kos Z, Szantai T (1991) Stochastic programming in water management: a case study and a comparison of solution techniques. Eur J Oper Res 52:28-44

    Google Scholar 

  • Eckenfelder WW Jr (2000) Industrial water pollution control, 3rd edn. McGraw-Hill, New York

    Google Scholar 

  • Fu DZ, Li YP, Huang GH (2012) A fuzzy-Markov-chain-based analysis method for reservoir operation. Stoch Environ Res Risk Assess 26:375–391

    Article  Google Scholar 

  • Ghosh S, Mujumdar PP (2006) Risk minimization in water quality control problems of a river system. Adv Water Resour 29:458–470

    Article  CAS  Google Scholar 

  • Haith AD (1982) Environmental systems optimization. John & Sons, Inc., New York

    Google Scholar 

  • Hillier FS, Lieberman GJ (1986) Introduction to operations research, 4th edn. Holden-Day, Oakland

    Google Scholar 

  • Hoppe H, Weilandt M, Orth H (2004) A combined water management approach based on river water quality standards. J Environ Inf 3:67–76

    Article  Google Scholar 

  • Huang GH (1998) A hybrid inexact-stochastic water management model. Eur J Oper Res 107:137–158

    Article  Google Scholar 

  • Huang GH, Chang NB (2003) The perspectives of environmental informatics and systems analysis. J Environ Inf 1:1–6

    Article  Google Scholar 

  • Huang GH, Xia J (2001) Barriers to sustainable water-quality management. J Environ Manag 61:1–23

    Article  CAS  Google Scholar 

  • Huang GH, Baetz BW, Patry GG (1995) Grey quadratic programming and its application to municipal waste management planning under uncertainty. Eng Optim 23:210–223

    Article  Google Scholar 

  • Huang GH, Sae-Lim N, Liu L, Chen Z (2001) An interval-parameter fuzzy-stochastic programming approach for municipal solid waste management and planning. Environ Model Assess 6:271–283

    Article  Google Scholar 

  • Huang GH, Sun W, Nie XH, Qin XS, Zhang XD (2010) Development of a decision-support system for rural eco-environmental management in Yongxin County, Jiangxi Province, China. Environ Model Softw 25:24–42

    Article  Google Scholar 

  • Huang JL, Ho MH, Du PF (2011) Assessment of temporal and spatial variation of coastal water quality and source identification along Macau peninsula. Stoch Environ Res Risk Assess 25:353–361

    Article  Google Scholar 

  • Huang Y, Li YP, Chen X, Ma YG (2012) Optimization of the irrigation water resources for agricultural sustainability in Tarim River Basin, China. Agric Water Manag 107:74–85

    Article  Google Scholar 

  • Hwang Y, Clerk MP, Rajagopalan B (2011) Use of daily precipitation uncertainties in streamflow simulation and forecast. Stoch Environ Res Risk Assess 25:957–972

    Article  Google Scholar 

  • Karmakar S, Mujumdar PP (2006) Grey fuzzy optimization model for water quality management of a river system. Adv Water Resour 29:1088–1105

    Article  CAS  Google Scholar 

  • Kotti ME, Vlessidis AG, Thanasoulias NC, Evmiridis NP (2005) Assessment of river water quality in Northwestern Greece. Water Resour Manage 19(1):77–94

    Article  Google Scholar 

  • Kuhn HW, Tucker AW (1951) Nonlinear programming. Neyman J (ed) Proceedings of the second Berkeley symposium on mathematical statistics and probability. University of California Press, Berkeley, CA, pp 481–492

  • Lai YC, Yang CP, Hsieh CY, Wu CY, Kao CM (2011) Evaluation of non-point source pollution and river water quality using a multimedia two-model system. J Hydrol 409:583–595

    Article  CAS  Google Scholar 

  • Lamb JC, Hull DB (1985) Current status in use of flexible effluent standards. J Water Pollut Control Fed 57:993–998

    Google Scholar 

  • Lee CS, Chang SP (2005) Interactive fuzzy optimization for an economic and environmental balance in a river system. Water Res 39(1):221–231

    CAS  Google Scholar 

  • Li YP, Huang GH (2009) Two-stage planning for sustainable water-quality management under uncertainty. J Environ Manage 90:2402–2413

    Article  CAS  Google Scholar 

  • Li YP, Huang GH (2010) Inexact joint-probabilistic stochastic programming for water resources management under uncertainty. Eng Optim 42:1023–1027

    Article  Google Scholar 

  • Li YP, Huang GH (2012) A recourse-based nonlinear programming model for stream water quality management. Stoch Environ Res Risk Assess 26:207–223

    Article  Google Scholar 

  • Li YP, Huang GH, Nie SL (2006) An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty. Adv Water Resour 29:776–789

    Article  Google Scholar 

  • Li YP, Huang GH, Nie SL (2007) Mixed interval-fuzzy two-stage integer programming and its application to flood-diversion planning. Eng Optim 39:163–183

    Article  Google Scholar 

  • Li YP, Huang GH, Nie SL, Liu L (2008a) Inexact multistage stochastic integer programming for water resources management under uncertainty. J Environ Manage 88:93–107

    Article  CAS  Google Scholar 

  • Li YP, Huang GH, Nie SL (2008b) Interval-parameter robust quadratic programming for water quality management under uncertainty. Eng Optim 40:613–635

    Article  Google Scholar 

  • Li HZ, Li YP, Huang GH, Xie YL (2012) A simulation-based optimization approach for water quality management of Xiangxihe River under uncertainty. Environ Eng Sci 29:270–283

    Article  Google Scholar 

  • Liu L, Huang GH, Liu Y, Fuller GA, Zeng GM (2003) A fuzzy-stochastic robust programming model for regional air quality management under uncertainty. Eng Optim 35:177–199

    Article  CAS  Google Scholar 

  • Loucks DP, Stedinger JR, Haith DA (1981) Water resource systems planning and analysis. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Luo H, Liu D, Huang Y (2010) Artificial neural network modeling of algal bloom in Xiangxi Bay of three gorges reservoir. IEEE, pp 645–647

  • Lv Y, Huang GH, Li YP, Yang ZF, Sun W (2011) A two-stage inexact joint-probabilistic programming method for air quality management under uncertainty. J Environ Manage 92:813–826

    Article  CAS  Google Scholar 

  • Lv Y, Huang GH, Li YP, Sun W (2012) Managing water resources system in a mixed inexact environment using superiority and inferiority measures. Stoch Environ Res Risk Assess 26:681–693

    Article  Google Scholar 

  • Murty YSR, Bhallamudi SM, Srinivasan K (2006) Non-uniform flow effect on optimal waste load allocation in rivers. Water Resour Manage 20(4):509–530

    Article  Google Scholar 

  • O’Connor DJ, Dobbins WE (1958) Mechanisms of reaeration in natural streams. Trans Am Soc Civ Eng 123:641–684

    Google Scholar 

  • Qin XS (2012) Assessing environmental risks through fuzzy parameterized probabilistic analysis. Stoch Environ Res Risk Assess 26:43–58

    Article  Google Scholar 

  • Qin XS, Huang GH (2009) An inexact chance-constrained quadratic programming model for stream water quality management. Water Resour Manage 23:661–695

    Article  Google Scholar 

  • Qin XS, Huang GH, Zeng GM, Chakma A, Xi BD (2007) A fuzzy composting process model. J Air Waste Manag Assoc 57:535–550

    Article  CAS  Google Scholar 

  • Qin XS, Huang GH, Chakma A (2008) Modeling groundwater contamination under uncertainty: a factorial-design-based stochastic approach. J Environ Inf 11(1):11–20

    Article  Google Scholar 

  • Rauch W et al (1998) River water quality modeling—I. Proceedings of the IAWQ biennial international conference, Vancouver, British Columbia, Canada, June, State of the art, pp 21–26

  • Saadatpour M, Afshar A (2006) Waste load allocation modeling with fuzzy goals: simulation-optimization approach. Water Resour Manage 21(7):1207–1224

    Article  Google Scholar 

  • SEPA (State Environmental Protection Administration) (1996) Industrial wastewater discharge standard (GB8978-1996), Beijing

  • SEPA (State Environmental Protection Administration) (2002) Environmental quality standard for surface water (GB3838-2002), Beijing

  • Thomann RV, Mueller JA (1987) Principles of surface water quality modeling and control. Harper & Row, New York

    Google Scholar 

  • Van Gils JAG, Argiropoulos D (2004) Axios river basin water quality management. Water Resour Manage 5(3–4):271–280

    Google Scholar 

  • Xie YL, Li YP, Huang GH, Li YF, Chen LR (2011) An inexact chance-constrained programming model for water quality management in Binhai New Area of Tianjin, China. Sci Total Environ 409:1757–1773

    Article  CAS  Google Scholar 

  • Xu Y, Qin XS (2010) Agricultural effluent control under uncertainty: an inexact double-sided fuzzy chance-constrained model. Adv Water Resour 33(9):997–1014

    Article  Google Scholar 

  • Xu HM, Richard G Taylor, Daniel G Kingston (2010) Hydrological modeling of river Xiangxi using SWAT2005: a comparison of model parameterizations using station and girded meteorological observations. Quat Int 226:54–59

  • Yang ZJ, Liu DF, Ji DB, Xiao SB (2010) Influence of the impounding process of the Three Gorges Reservoir up to water level 172.5 m on water eutrophication in the Xiangxi Bay. Sci China Ser E-Tech 53:1114–1125

    Article  CAS  Google Scholar 

  • Zeng XK, Wang D, Wu JC (2012) Sensitivity analysis of the probability distribution of groundwater level series based on information entropy. Stoch Environ Res Risk Assess 26:345–356

    Article  Google Scholar 

  • Zhang Y, Monder D, Forbes JF (2002) Real-time optimization under parametric uncertainty: a probability constrained approach. J Process Control 12:373–389

    Article  CAS  Google Scholar 

  • Zhang Q, Singh VP, Chen XH (2012) Influence of Three Gorges Dam on streamflow and sediment load of the middle Yangtze, China. Stoch Environ Res Risk Assess 26:569–579

    Article  Google Scholar 

  • Zheng TG, Mao JQ, Dai HC, Liu DF (2011a) Impacts of water release operations on algal blooms in a tributary bay of Three Gorges Reservoir. Sci China Technol Sci 154:1588–1598

    Article  Google Scholar 

  • Zheng Y, Wang WM, Han F, Ping J (2011b) Uncertainty assessment for watershed water quality modeling: a probabilistic collocation method based approach. Adv Water Resour 34:887–898

    Article  Google Scholar 

  • Zhu H, Huang GH (2009) A fuzzy robust nonlinear programming model for stream water quality management. Water Resour Manage 23:2913–2940

    Article  Google Scholar 

  • Zhu XF, Wang JD, Solo-Gabriele HM, Fleming LE (2011) A water quality modeling study of non-point sources at recreational marine beaches. Water Res 45:2985–2995

    Article  CAS  Google Scholar 

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Acknowledgments

This research was supported by the Major Science and Technology Program for Water Pollution Control and Treatment (2009ZX07104-004). We are deeply grateful to the reviewers for their insightful and careful suggestion, which has greatly helped to improve the quality of manuscript.

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Authors and Affiliations

  1. MOE Key Laboratory of Regional Energy Systems Optimization, S&C Academy of Resources and Environmental Research, North China Electric Power University, Beijing, 102206, China

    Ming Hu, Guo H. Huang & Yongping P. Li

  2. Environmental Systems Engineering Program, Faculty of Engineering and Applied Science, University of Regina, Regina, SK, S4S 0A2, Canada

    Wei Sun

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  1. Ming Hu
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Correspondence to Guo H. Huang.

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Hu, M., Huang, G.H., Sun, W. et al. Inexact quadratic joint-probabilistic programming for water quality management under uncertainty in the Xiangxi River, China. Stoch Environ Res Risk Assess 27, 1115–1132 (2013). https://doi.org/10.1007/s00477-012-0648-z

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