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Simulation-Based Inexact Rough-Interval Programming for Agricultural Irrigation Management: A Case Study in the Yongxin County, China

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Abstract

A simulation-based inexact rough-interval programming approach is proposed for agricultural irrigation management in a China’s rural region. The conjunctive use of multiple water sources is examined under a set of land-area, water-availability, environmental-standard, capital, and technical constraints. The formulated model presents capability in interpreting implication of various water-supply means on agricultural water-allocation plans, as well as handling highly-uncertain parameters existing in many real-world practices. A case study in the central-south China demonstrates the applicability of the proposed model. The modelling inputs of economy-related parameters are identified as conventional intervals based on the statistical data, while those of water availability are characterized as rough intervals by converting the predicted values from a distributed hydrological model. Scenarios of groundwater supplementation rates being 0, 20, 30 and 40 %, respectively are considered to generate optimal irrigation plans. Reasonable results are obtained, which are then used to analyze the impact of water-supplier variation on planning sustainable development strategies.

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Abbreviations

A ℝ, B ℝ :

two sets of rough intervals, and \( {A^{\mathbb{R}}} \in {R^{{\mathbb{R}\left( {m \times n} \right)}}} \) and \( {B^{\mathbb{R}}} \in {R^{{\mathbb{R}\left( {m \times n} \right)}}} \)

C ±∈{Π}p and Π :

denotes a set of interval parameters

X ℝ :

a set of decision variables

f ℝ :

denotes objective function value

SNB ℝ :

system net benefit (¥)

\( U{B_j}^{\pm } \) :

unit benefit for crop j ($/ha)

\( CROPA_{{ijt}}^{\mathbb{R}} \) :

allocated crop area for crop j in zone i at time t (ha)

USWC ± :

unit surface water cost for delivering ($/tonne)

\( SW{S_{{ijt}}}^{\mathbb{R}} \) :

allocated surface water amount for crop j in zone i at time t (tonne)

UGWC ± :

unit groundwater cost for pumping and delivering ($/tonne)

\( GW{S_{{ijt}}}^{\mathbb{R}} \) :

allocated groundwater amount for crop j in zone i at time t (tonne)

i :

index of agricultural zones

j :

index of crops

t :

index of planning horizon

I, J, T :

total number of zones, types of crops, and planning periods

\( SW{A_t}^{\Re } \) :

surface water availability in period t (m3)

\( GW{A_t}^{\Re } \) :

groundwater availability in period t (m3)

RPSW t :

defined rate of surface water use

RPGW t :

defined rate of groundwater use, equal to (1 − RPSW t )

PR ℜ :

precipitation (mm)

IF ℜ :

inflow (mm)

RC ℜ :

recharge (mm)

AET ℜ :

actual evaportranspiration (mm), which is function of precipitation, temperature, and solar radiation

OF ℜ :

outflow (mm)

IN ℜ :

inflow of the aquifer (mm)

ES ℜ :

evaporation of the aquifer (mm)

OUT ℜ :

outflow of the aquifer (mm)

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

unit water demand for irrigating crop j in period t (m3/ha)

ESWU ± :

efficiency of surface water use

EGWU ± :

efficiency of groundwater use

TCWU ± :

maximum investment for water allocation over the planning horizon (¥)

ALA t :

maximum allowable area for planting crops in period t (ha)

RLA t :

minimum allowable area for planting crops in period t (ha)

\( RCROPA_{{ijt}}^{\pm } \) :

is regulated minimum area for planting crop j in zone i in period t (ha)

\( UNL_{{ij}}^{\pm } \) :

unit nitrogen loss (tonne/ha)

\( ATND_t^{\pm } \) :

allowable maximum total nitrogen discharge (tonne)

\( UPL_{{ij}}^{\pm } \) :

unit phosphorous loss (tonne/ha)

\( TPD_t^{\pm } \) :

allowable maximum total phosphorous discharge (tonne)

\( UPCL_{{ij}}^{\pm } \) :

unit pesticide loss (tonne/ha)

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

allowable maximum total pesticide discharge (tonne).

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (Grant No. 51222906 and 41271540), and, the Fundamental Research Funds for the Central Universities. The authors are grateful to the editor 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, China, 102206

    H. W. Lu, G. H. Huang & L. He

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  1. H. W. Lu
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  2. G. H. Huang
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  3. L. He
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Correspondence to H. W. Lu.

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Lu, H.W., Huang, G.H. & He, L. Simulation-Based Inexact Rough-Interval Programming for Agricultural Irrigation Management: A Case Study in the Yongxin County, China. Water Resour Manage 26, 4163–4182 (2012). https://doi.org/10.1007/s11269-012-0138-6

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