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A Bayesian-based two-stage inexact optimization method for supporting stream water quality management in the Three Gorges Reservoir region

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Abstract

In this study, a Bayesian-based two-stage inexact optimization (BTIO) method is developed for supporting water quality management through coupling Bayesian analysis with interval two-stage stochastic programming (ITSP). The BTIO method is capable of addressing uncertainties caused by insufficient inputs in water quality model as well as uncertainties expressed as probabilistic distributions and interval numbers. The BTIO method is applied to a real case of water quality management for the Xiangxi River basin in the Three Gorges Reservoir region to seek optimal water quality management schemes under various uncertainties. Interval solutions for production patterns under a range of probabilistic water quality constraints have been generated. Results obtained demonstrate compromises between the system benefit and the system failure risk due to inherent uncertainties that exist in various system components. Moreover, information about pollutant emission is accomplished, which would help managers to adjust production patterns of regional industry and local policies considering interactions of water quality requirement, economic benefit, and industry structure.

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Acknowledgments

This research was supported by the Major Science and Technology Program for Water Pollution Control and Treatment (2014ZX07104-005-03) and the National Natural Science Foundation for Distinguished Young Scholar (51225904). The authors are grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.

Author information

Authors and Affiliations

  1. Sino-Canada Resources and Environmental Research Academy, North China Electric Power University, Beijing, 102206, China

    X. H. Hu, Y. P. Li, G. H. Huang, X. W. Zhuang & X. W. Ding

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

    Y. P. Li & G. H. Huang

Authors
  1. X. H. Hu
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  2. Y. P. Li
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  3. G. H. Huang
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  4. X. W. Zhuang
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  5. X. W. Ding
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Corresponding author

Correspondence to Y. P. Li.

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Responsible editor: Marcus Schulz

Appendix

Appendix

i :

Number of chemical plant

j :

Number of phosphorus mining company

s :

Number of river segment

t :

Planning period: t = 1 nonflood season and t = 1 flood season

k :

Maximum allowable loading levels: k = 1 low level, k = 2 medium level, and k = 3 high level

L t :

Length of planning period (day)

CB ± it :

Net benefit from chemical plant i in period t (RMB¥/t)

PB ± jt :

Net benefit from phosphorus mining company j in period t (RMB¥/t)

TB ± st :

Net benefit from town water supply on segment s in period t (RMB¥/m3)

AB ± st :

Net benefit from agricultural zone on segment s in period t (RMB¥/ha)

LB ± st :

Net benefit from livestock husbandry on segment s in period t (RMB¥/unit of equivalent pig)

RB ± st :

Net benefit from rural water supply on segment s in period t (RMB¥/m3)

X ± it :

Production level of chemical plant i in period t (t/day)

P ± jt :

Production level of phosphorus mining company j in period t (t/day)

WT ± st :

Production level of town water supply on segment s in period t (m3/day)

Z ± st :

Planting area of agricultural zone on segment s in period t (ha/t)

Y ± st :

Equivalent pig number of livestock husbandry on segment s in period t (t−1)

WR ± st :

Production level of rural water supply on segment s in period t (m3/day)

p kt :

Probability of maximum allowable loading levels in period t

CC ± it :

Economic penalty when the predefined pollutant load targets for chemical plant i in period t are not met (RMB¥/t)

CP ± jt :

Economic penalty when the predefined pollutant load targets for phosphorus mining company j in period t are not met (RMB¥/t)

CT ± st :

Economic penalty when the predefined pollutant load targets for town water supply on segment s in period t are not met (RMB¥/m3)

CA ± st :

Economic penalty when the predefined pollutant load targets for agricultural zone on segment s in period t are not met (RMB¥/ha)

CL ± st :

Economic penalty when the predefined pollutant load targets for livestock husbandry on segment s in period t are not met (RMB¥/unit of equivalent pig)

CR ± st :

Economic penalty when the predefined pollutant load targets for rural water supply on segment s in period t are not met (RMB¥/m3)

XD ± ikt :

The production amount of chemical plant i by which production target is not met when the probability of maximum loading level is k (t/day)

PD ± jkt :

The production amount of phosphorus mining company j by which production target is not met when the probability of maximum loading level is k (t/day)

TD ± skt :

The amount by which town water supply target is not met when the probability of maximum loading level is k (m3/day)

AD ± skt :

The amount by which planting area target is not met when the probability of maximum loading level is k (ha/t)

LD ± skt :

The amount by which livestock husbandry target is not met when the probability of maximum loading level is k (t−1)

RD ± skt :

The amount by which rural water supply target is not met when the probability of maximum loading level is k (m3/day)

CLP ± it :

TP load of per unit production from chemical plant i in period t (t/t)

PLP ± jt :

TP load of per unit production from phosphorus mining company j in period t (t/t)

TLP ± st :

TP load of per m3 wastewater from urban sewage treatment plant on segment s in period t (t/m3)

ALP ± st :

TP load of per ha cropped land from agricultural zone on segment s in period t (t/ ha)

LLP ± st :

TP load of per equivalent pig from livestock husbandry on segment s in period t (t)

RLP ± st :

TP load of per m3 rural wastewater from rural life on segment s in period t (t/m3)

CLO ± it :

COD load of per unit production from chemical plant i in period t (t/t)

PLO ± jt :

COD load of per unit production from phosphorus mining company j in period t (t/t)

TLO ± st :

COD load of per m3 wastewater from urban sewage treatment plant on segment s in period t (t/m3)

ALO ± st :

COD load of per ha cropped land from agricultural zone on segment s in period t (t/ha)

LLO ± st :

COD load of per equivalent pig from livestock husbandry on segment s in period t (t)

RLO ± st :

COD load of per m3 rural wastewater from rural life on segment s in period t (t/ m3)

RTW ± st :

Generation rate of urban wastewater on segment s in period t (m3/m3)

RRW ± st :

Generation rate of rural wastewater on segment s in period t (m3/m3)

ω ± st :

Proportion of agricultural effluent discharged into the river on segment s in period t (%)

η ± st :

Proportion of livestock husbandry effluent discharged into the river on segment s in period t (%)

δ ± st :

Proportion of rural life effluent discharged into the river on segment s in period t (%)

MALP ± skt :

Maximum allowable loading of TP with probability k on segment s in period t (t)

MALO ± skt :

Maximum allowable loading of COD with probability k on segment s in period t (t)

SL ± st :

Average soil loss from agricultural zone on segment s in period t (t/ha)

ML ± st :

Maximum allowable soil loss agricultural zone on segment s in period t (t/ha)

X min i , X max i :

The minimum and maximum production amount of chemical plant i (t/day).

P min j , P max j :

The minimum and maximum production amount of phosphorus mining company j (t/day)

WT min st , WT max st :

The minimum and maximum amount of town water supply on segment s in period t (m3/day)

WR min st , WR max st :

The minimum and maximum amount of rural water supply on segment s in period t (m3/day)

Y min st , Y max st :

The minimum and maximum amount of equivalent pig on segment s in period t

Z min st , Z max st :

The minimum and maximum cropped area on segment s in period t (ha)

TS ±min , TS ±max :

The minimum and maximum treatment amount of urban sewage treatment plant on segment s in period t (m3/day)

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Hu, X.H., Li, Y.P., Huang, G.H. et al. A Bayesian-based two-stage inexact optimization method for supporting stream water quality management in the Three Gorges Reservoir region. Environ Sci Pollut Res 23, 9164–9182 (2016). https://doi.org/10.1007/s11356-016-6106-6

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