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Risk aversion based interval stochastic programming approach for agricultural water management under uncertainty

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Abstract

In this study, a risk aversion based interval stochastic programming (RAIS) method is proposed through integrating interval multistage stochastic programming and conditional value at risk (CVaR) measure for tackling uncertainties expressed as probability distributions and intervals within a multistage context. The RAIS method can reflect dynamic features of the system conditions through transactions at discrete points in time over the planning horizon. Using the CVaR measure, RAIS can effectively reflect system risk resulted from random parameters. When random events are occurred, the adjustable alternatives can be achieved by setting desired targets according to the CVaR, which could make the revised decisions to minimize the economic penalties. Then, the RAIS method is applied to planning agricultural water management in the Zhangweinan River Basin that is plagued by drought due to serious water scarcity. A set of decision alternatives with different combinations of risk levels employed to the objective function and constraints are generated for planning water resources allocation. The results can not only help decision makers examine potential interactions between risks under uncertainty, but also help generate desired policies for agricultural water management with a maximized payoff and a minimized loss.

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Abbreviations

I :

Crop, i = 1, 2, 3, I

j :

Subarea, j = 1, 2,…, 15, J

t :

Planning time period, t = 1, 2,…, 5, T

k :

Scenario of reservoir inflow, k = 1, 2,…, 5 representing very-low, low, medium, high and very-high levels respectively

f ± :

Expected system benefit over the planning horizon (RMB¥)

IB ± ijt :

Irrigation benefit for crop i in subarea j per unit of planting area (RMB¥/ha)

IT ± ijt :

Fixed surface-water irrigation target of crop i in subarea j during period t (ha)

p tk :

Probability level under scenario k during period t

IP ± ijt :

Reduction of benefit (economic penalty) to subarea j planting crop i per unit of area not irrigated during period t (RMB¥/ha)

ISD ± ijtk :

Cropland that cannot be irrigated by the surface water under scenario k (ha)

W ± ijt :

Irrigation quota for crop i in subarea j during period t (m3)

W ± ij(t−1) :

Irrigation quota for crop i in subarea j during period t − 1(m3)

IQ ± tk :

Water available for irrigation in Yuecheng Reservoir under scenario k during period t (m3)

IQ ±(t−1)k :

Water available for irrigation in Yuecheng Reservoir under scenario k during period t − 1 (m3)

ɛ ±(t−1)k :

Surplus flow when water is delivered in period t−1 under scenario k (m3), and assuming no spilling for reservoir

ɛ ±(t−2)k :

Surplus flow when water is delivered in period t − 2 under scenario k (m3), and assuming no spilling for reservoir

IT ± ijtmax :

Maximum area that crop i should be planted in subarea j during period t (ha)

λ :

Weight coefficient between cost and risk

ξ :

The biggest system loss under the given confidence level (RMB¥)

α :

Confidence interval

v ± tk :

Instrumental variables

CWR ± ijt :

Amount of water requirement of crop i in subarea j during period t (m3/ha)

D ± ijt :

Average root depth of crop i in period t (m)

D ± ij(t+1) :

Average root depth of crop i in period t + 1 (m)

θ ± ijt :

Soil moisture content of crop i in subarea j in period t (m3/m)

θ ± ij(t+1) :

Soil moisture content of crop i in subarea j in period t + 1 (m3/m)

θ ± ijtmax :

Maximum soil moisture content of crop i in subarea j (m3/m)

θ ± ijtmin :

Minimum soil moisture content of crop i in subarea j (m3/m)

Ep ± jt :

Amount of effective precipitation of crop i in subarea j in period t (m3/ha)

Ep ±0jt :

Amount of actual precipitation of crop i in subarea j in period t (m3/ha)

Ec ± jt :

Evaporation capacity of crop i in subarea j in period t (m3/ha)

SR ± jt :

Surface runoff of crop i in subarea j in period t (m3/ha)

UR ± jt :

Underground runoff of crop i in subarea j in period t (m3/ha)

DP ± ijt :

Deep percolation for crop i in subarea j during the period t (m)

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Acknowledgements

This research was supported by the National Key Research Development Program of China (2016YFA0601502), the Natural Science Foundation of China (51779008), and the Interdiscipline Research Funds of Beijing Normal University. The authors are grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.

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Authors and Affiliations

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

    Q. Q. Li & C. X. Wang

  2. State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing, 100875, China

    Y. P. Li & G. H. Huang

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

    Y. P. Li & G. H. Huang

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  1. Q. Q. Li
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  2. Y. P. Li
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Correspondence to Y. P. Li.

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Li, Q.Q., Li, Y.P., Huang, G.H. et al. Risk aversion based interval stochastic programming approach for agricultural water management under uncertainty. Stoch Environ Res Risk Assess 32, 715–732 (2018). https://doi.org/10.1007/s00477-017-1490-0

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