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

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Abstract

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.

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Abbreviations

t :

Planning horizon; t = 1 for period 1, t = 2 for period 2

i :

Water users; i = 1 for municipal, i = 2 for food processing plant, i = 3 for thermal power plant, and i = 4 for paper mill

r :

Agricultural sector; r = 1 for agricultural region I, and r = 2 for agricultural region II

j :

Type of crops; j = 1 for cotton, j = 2 for rice, j = 3 for maize, j = 4 for soybean, j = 5 for peanut, j = 6 for wheat, and j = 7 for rape

h :

Stream inflow level; h = 1 for low level, h = 2 for medium level, and h = 3 for high level

n :

Agricultural pollutants; n = 1 for total nitrogen (TN), n = 2 for total phosphorus (TP)

m :

River pollutants; m = 1 for BOD, m = 2 for COD

\( W_{it}^{ \pm } \) :

Allocation target of water that is promised to user i (106 m3)

\( DW_{iht}^{ \pm } \) :

Amount of water deficit in scenario h during period t (106 m3)

\( NB_{it}^{ \pm } \) :

Net benefit of user i per unit of water allocated (million$/106 m3)

\( CS_{it}^{ \pm } \) :

Reduction of net benefit to user i per unit of water not delivered during period t (million$/106 m3)

\( CT_{it}^{ \pm } \) :

Costs of wastewater treatment of user i during period t (million$/106 m3)

\( \varphi_{it}^{ \pm } \) :

Wastewater emissions of per water consumption during period t

p ht :

Probability of occurrence for scenario h during period t

\( S_{jrt}^{ \pm } \) :

Surface water irrigation target of crop j in agricultural region r (ha)

\( SD_{jrht}^{ \pm } \) :

Area by which surface water irrigation target \( S_{jrt}^{ \pm } \) is not met under inflow h (ha)

\( CA_{jt}^{ \pm } \) :

Reduction of net benefit of crop j per unit of yields during period t ($/kg)

\( BC_{jt}^{ \pm } \) :

Net benefit of crop j per unit of yields ($/kg)

\( Y_{j}^{ \pm } \) :

Crop yields (kg/ha)

\( CF_{n}^{ \pm } \) :

Cost of fertilizer n ($/kg)

\( FD_{jnt}^{ \pm } \) :

Fertilizer application amount of crop j during period t (kg/ha)

x 1, x 2, x 3, x 4, x 5, x 6, x 7, x 8 and x 9 :

Length of reach 1, 2, 3, 4, 5, 6, 7, 8 and 9, with the value of 2.2, 3.6, 3.2, 2.5, 3.5, 2.5, 2.0, 2.8 and 3.2 km, respectively

\( S_{jrt\hbox{max} }^{ \pm } \) :

Maximum allowable plant area for crop j (ha)

\( R_{1m}^{ \pm } ,\;R_{2m}^{ \pm } ,\;R_{3m}^{ \pm } ,\;R_{4m}^{ \pm } ,\;R_{5m}^{ \pm } ,\;R_{6m}^{ \pm } ,\,R_{7m}^{ \pm } ,\,R_{8m}^{ \pm } \,{\text{and}}\,R_{9m}^{ \pm } \) :

Designated pollutant (m) concentration at the beginning of 1, 2, 3, 4, 5, 6, 7, 8 and 9, respectively (mg/L)

\( B_{jnt}^{ \pm } \) :

Demand of fertilizer n during the whole plant growing period (kg/ha)

\( TN_{jnt}^{ \pm } \) :

Maximum loss tolerance of fertilizer n of each crop in period t (kg/ha)

\( \zeta_{jt}^{ \pm } \) :

Irrigation quota for crop j (103 m3/ha)

\( q_{ht}^{ \pm } \) :

Available water resources in scenario h during period t (106 m3)

\( W_{it\hbox{max} }^{ \pm } \) :

Maximum allowable allocation amount for user i during period t (106 m3)

\( C_{imt}^{ \pm } \) :

Concentration of pollutant m in raw wastewater generated at source i in period t (mg/L)

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

Pollutant treatment efficiency at source i during period t (%)

\( GB_{im}^{ \pm } \) :

Pollutant concentration of wastewater discharge in emission standard of sewage (mg/L)

\( C_{0m} \) :

Pollutant concentration at the head of reach 1 (mg/L)

\( \varepsilon_{jnt}^{ \pm } \) :

Volatilization loss of fertilizer n during the whole plant growing period (%)

\( Q_{ht}^{ \pm } \) :

Stream inflow in scenario h during period t (106 m3)

v :

Average flow velocity (5.5 km/day)

λ :

A control factor to acquire a more stringent limitation of risk, λ ∈ [0, 1]

\( \Omega_{it}^{ \pm } ,\,\Omega_{rt}^{ \pm } \text{ } \) :

Expected benefit of municipal, industrial and agricultural sectors

\( \psi_{it}^{ \pm } ,\,\psi_{rt}^{ \pm } \) :

Expected downside risk value

A r :

Agricultural acreage of region r (ha)

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Acknowledgments

This research was supported by the Fundamental Research Funds for the Central Universities (13XS20), the Major Project Program of the Natural Sciences Foundation (51190095), and the Program for Innovative Research Team in University (IRT1127). The authors are extremely grateful to the editor and the anonymous editors and reviewers for their insightful comments and suggestions.

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

    Y. L. Xie & G. H. Huang

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  1. Y. L. Xie
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  2. G. H. Huang
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Correspondence to G. H. Huang.

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Xie, Y.L., Huang, G.H. Development of an inexact two-stage stochastic model with downside risk control for water quality management and decision analysis under uncertainty. Stoch Environ Res Risk Assess 28, 1555–1575 (2014). https://doi.org/10.1007/s00477-013-0834-7

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