A stochastic rough-approximation water management model for supporting sustainable water-environment strategies in an irrigation district of arid region

  • X. T. Zeng
  • G. H. Huang
  • J. L. Zhang
  • Y. P. Li
  • L. You
  • Y Chen
  • P. P. Hao
Original Paper
  • 117 Downloads

Abstract

In this study, a stochastic rough-approximation water management model (SRAWM) associated with optimistic and pessimistic options is proposed for supporting regional sustainability in an irrigation system (IS) of an arid region with uncertain information. SRAWM can not only handle conventional stochastic variations in objective functions or constraints, but also tackle objective and subjective (i.e., risk performance of the decision maker) fuzziness through rough-approximation model based on measure Me. The developed model would be applied to a real case study of an irrigation district (ID) in Kaidu-kongque River Basin, China, which is encountering challenges in economic development and a serious environmental crisis (e.g., drought, water deficit, land deterioration, stalinization, soil erosion and water pollution) synchronously. Simulation technical (i.e., support vector regression) is put into SRAWM framework to reflect dynamic prediction of water demand in the future. Results of optimized irrigation area, water allocation, water deficit, pollution reduction, water and soil erosion and system benefit under various water-environmental policies (corresponding to various ecological effects) are obtained. Tradeoffs between ecological and irrigative water usages can facilitate the local decision makers rectifying the current irrigation patterns and ecological protection polices. Moreover, compromises between systemic benefit and failure risk can help policymakers to generate a robust risk-control plan under uncertainties. These detections are beneficial to achieve conjunctive goals of socio-economic development and eco-environmental sustainability in such an arid IS.

Keywords

Rough-approximation Stochastic programming Support-vector-regression (SVR) Irrigation system (IS) Uncertainty Risk sensitive analysis 

List of symbols

f

System benefit from an ecological irrigation system (US $)

BmjA

Net benefit for agricultural crop in district j per volume of water being delivered (US $/m3)

DAmj

Irrigation area target for agricultural crop in district j (ha)

RAmj

Water consumption per unit area for agricultural crop in district j (m3/ha)

SAkmj

Water shortage for agricultural plant n in district j (m3)

CmjA

Loss of water shortage for agricultural plant in district j per volume of water not being delivered (US $/m3)

BnjE

Net benefit for ecological plant in district j per volume of water being delivered (US $/m3)

DEnj

Planting area target for ecological plant in district j (ha)

REnj

Water consumption per unit area for ecological plant in district j (m3/ha)

SEknj

Water shortage for ecological plant n in district j (m3)

CnjE

Loss of water shortage for ecological plant in district j per volume of water not being delivered (US $/m3)

BjM

Net benefit for farmer living water in district j per volume of water being delivered (US $/m3)

CkmjA

Loss of water shortage for agricultural crop m in district j per volume of water not being delivered (US $/m3)

FnjEC

Net benefits from pollution discharges retreated through ecological mechanism in district j (US $/m3)

TnjEC

Water delivering costs for ecological plant in district j volume of water being polluted (US $/m3)

FnjECS

Net benefits from soil intention through ecological mechanism in district j (US $/m3)

FnjECW

Net benefits from water conservation through ecological mechanism in district j (US $/m3)

TmjAC

Water delivering costs for agricultural crop in district j volume of water being polluted (US $/m3)

FmjAC

Pollution discharge treatment costs for agricultural crop in district j volume of water being polluted (US $/m3)

FmjACS

Soil intention costs for agricultural crop in district j volume of water being polluted (US $/m3)

FmjACW

Water conservation costs for agricultural crop in district j volume of water being polluted (US $/m3)

SMkj

Water shortage for farmer living water in district j (m3)

CjM

Loss of water shortage for farmer living water in district j per volume of water not being delivered (US $/m3)

TjMC

Water delivering costs for farmer living water in district j volume of water not being polluted (US $/m3)

FjMC

Environmental treatment costs for farmer living water in district j volume of water not being polluted (US $/m3)

phj

Probability of random water availability Q ij ± under level h (%)

Qkj

Water availability from river and underground of district j under probabilityp j (m3)

Rkj

Water flow from river of district j in period t under probabilityp j (m3)

Ej

Evaporation and infiltration loss of water from river of district j (m3)

Hj

Normal water requirement of watercourse of district j (m3)

QUj

Water availability from underground water of district j (m3)

AXMj

The minimum water demand for farmer living water in district j (m3)

XDAmj

The maximum land utilization area for agricultural crop in district j (ha)

XDEnj

The maximum land utilization area for ecological plant in district j (ha)

SCMhj

The maximum water supply capacity in district j under level h (106 m3)

EAmj

The maximum soil erosion for agricultural crop in district j (ton)

EEnj

The maximum soil erosion for ecological plant in district j (ton)

NAmj

Nitrogen discharge for agricultural crop in district j per unit water consumption (ton/m3)

PAmj

Phosphorus discharge for agricultural crop in district j per unit water consumption (ton/m3)

BAmj

BOD discharge for agricultural crop in district j per unit water consumption (ton/m3)

γN

The purification capacity coefficient of Nitrogen discharge for ecological plant in district j per unit water consumption (ton/m3)

γP

The purification capacity coefficient of Phosphorus discharge for ecological plant in district j per unit water consumption (ton/m3)

γB

The purification capacity coefficient of BOD discharge for ecological plant in district j per unit water consumption (ton/m3)

αmj

The erosion coefficient for agricultural crop in district j per unit water consumption

βnj

The erosion coefficient for ecological plant in district j per unit water consumption

NMj

Nitrogen discharge for farmer living water in district j per unit water consumption (ton/m3)

PMj

Phosphorus discharge for farmer living water in district j per unit water consumption (ton/m3)

BMj

BOD discharge for farmer living water in district j per unit water consumption (ton/m3)

NAPj

The maximum nitrogen discharge in district j per unit water consumption (ton/m3)

PAPj

The maximum phosphorus discharge in district j per unit water consumption (ton/m3)

BAPj

The maximum BOD discharge in district j per unit water consumption (ton/m3)

Subscript

j

District: j = 1 Kuerle, j = 2 Yanqi, j = 3 Hejing, j = 4 Heshuo, j = 5 Bohu j = 6 Luntai and j = 7 Yuli

m

Agriculture crop: m = 1 Wheat, m = 2 Cotton, m = 3 Oil plants, m = 4 Vegetable

n

Ecological plant: n = 1 Medicago, n = 2 Populus, n = 3 Tarmaik, n = 4 Alhagl, n = 5 other,

k

Water level: k = 1 Low, k = 2 Medium, k = 3 High

Notes

Acknowledgements

This research was supported by the Start Project of Young Teacher of CUEB (Grant No. 00291762791008) and National Key Research Development Program of China (2016YFC0502803 and 2016YFA0601502). The authors are grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • X. T. Zeng
    • 1
    • 2
  • G. H. Huang
    • 3
    • 5
  • J. L. Zhang
    • 4
  • Y. P. Li
    • 5
  • L. You
    • 6
  • Y Chen
    • 1
  • P. P. Hao
    • 1
  1. 1.Capital University of Economics and BusinessBeijingChina
  2. 2.Institute for Energy, Environment and Sustainable CommunitiesUniversity of ReginaReginaCanada
  3. 3.Faculty of Engineering and Applied SciencesUniversity of ReginaReginaCanada
  4. 4.College of Environmental Science and EngineeringQingdao UniversityQingdaoChina
  5. 5.Beijing Normal UniversityBeijingChina
  6. 6.Research Center for Eco-Environmental Sciences, Chinese Academy of SciencesBeijingChina

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