Agricultural Productive Carrying Capacity Improve and Water Optimal Allocation under Uncertainty Based on Remote Sensing Data in Lancang County, Southwest China
Abstract
:1. Introduction
2. Overview of the Studying Area
2.1. The Water Resources System in Lancang County
2.2. The Agricultural Resources System in Lancang County
3. Methods
3.1. Type-2 Triangular Fuzzy Sets
- (1)
- Calculate the relative distance matrix D = |dij|t×t, where dij = |hi − hj|;
- (2)
- Calculate the average of relative distances ;
- (3)
- Introduce the pairwise comparison number pij, /, the pairwise matrix P = |pij|t×t;
- (4)
- Calculate the real weight wj of hj, ;
- (5)
- Calculate the core of the fuzzy number, ;
- (6)
- Define the mean deviation σ, choose and calculate to replace σ;
- (7)
- Define η as the distance from the left end to the right end of the fuzzy number, select and calculate /, /, A = {i|hi < a2, i ∈ I}, B = {i|hi > a2, i ∈ I};
- (8)
- Calculate a1 = a2 − 3(1 + η) ησ/(1 + η2), a3 = a2 + 3(1 + η) σ/(1 + η2). From this, the traditional fuzzy number F = (a1, a2, a3) of cij can be obtained.
3.2. Chance-Constrained Programming (CCP)
3.3. Type-2 Fuzzy Chance-Constrained Programming (T2FCCP) Construction and Its Solution
- (1)
- Surface water supply constraints
- (2)
- Groundwater supply constraints
- (3)
- Water demand constraints
- (4)
- Water balance constraints
- (5)
- Water distribution constraints
- (6)
- Cropping area constraints
- (7)
- Food security constraints
- (8)
- Water transfer constraints
- (9)
- Structure constraints
3.4. Harmony Evaluation Method
- (1)
- Single-index quantification. According to the relationship between the changes from small to large indicators and the changes in the harmony degree of their representations, they can be divided into positive indicators and reverse indicators. The positive index harmony degree increases with the increase of the index value; the reverse index harmony degree decreases with the increase of the index value. Suppose a, b, c, d, and e are the worst value, poor value, passing value, better value and optimal value of a positive or negative index, respectively. Using feature points (a, 0), (b, 0.3), (c, 0.6), (d, 0.8), and (e, 1), then the calculation formula of harmony degree of the positive index and the reverse index are, respectively:
- (2)
- Multi-indicator synthesis. Based on the calculation of the harmony degree of a single index, the harmony degree of each subsystem and the water resources–economic society–ecological environment system is calculated separately according to the method of weighted summation. Assume that the value of a quantitative index at time t is , its harmony degree is , then the water resources subsystem harmony degree (WHD), the economic and social subsystem harmony degree (SEHD), and the environmental subsystem harmony degree (EHD) are, respectively:
- (3)
- Multi-criteria integration. Based on the WHD, SEHD, and EHD calculated above, the water resources–economical society–environmental system harmony degree (WSEHD) is calculated by the weighted sum method, and the formula is
4. Application
4.1. Data Preparation
4.2. Result Analysis and Discussions
4.2.1. Water Resources Optimal Allocation in Lancang County
4.2.2. Planting Area Results of Different Crops in Lancang County
4.2.3. The System Costs and Benefits in Lancang County
4.2.4. Harmony Evaluation in Lancang County
4.2.5. Evaluation of Agricultural Production Irrigation Carrying Capacity in Lancang County
- (1)
- Dry year scenario
- (2)
- Wet year scenario
- (3)
- Planning Scenario
4.2.6. Cost Comparison between CCP, FCCP, T2FCCP Model and Status Quo
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Document | Author | Location | Method | How to Use Optimization Model | Index for Water Allocation | Temporal Scale | Spatial Scale | Scenarios |
---|---|---|---|---|---|---|---|---|
An inexact modeling approach for supporting water resources allocation under natural and social complexities in a border city of China and Myanmar | Chen et al., 2021 | Southwest China | ITSFCCP | Reflect the trade-offs between the system benefits and risks | Fuzzy sets, discrete intervals, probability distribution and credibility levels | 2005–2016 | Prefecture-level city | Flow levels |
A Stochastic Optimization Model for Agricultural Irrigation Water Allocation Based on the Field Water Cycle | Yan et al., 2018 | Northwest China | TSCCP | Considering field water cycle process | Different crops and months | 2000–2015 | Irrigation District level | Different flow levels and constraint-violation risk levels |
Efficient and Economical Allocation of Irrigation Water under a Changing Environment: a Stochastic Multi-Objective Nonlinear Programming Model | Yan et al., 2018 | Northwest China | SMONLP | Trade-offs between NEB and IWUE | Different crops and months | From April to September in 2016 | Irrigation District level | weighting factor of objective functions and violating probability |
This study | Zhang et al., 2022 | Southwest China | T2FCCP | Conjunction with the Harmony Evaluation Method | Harmony level | 2021–2025 | County area | Three SSPs |
WSEHD | 0 | (0, 0.2) | [0.2, 0.4) | [0.4, 0.6) | [0.6, 0.8) | [0.8, 1) | 1 |
---|---|---|---|---|---|---|---|
Harmony level | totally discordant | less harmonious | basic dissonance | close to harmony | basic harmony | more harmonious | complete harmony |
2021 | 2022 | 2023 | 2024 | 2025 | ||
---|---|---|---|---|---|---|
Number | Tributaries | WSEHD Harmony Level | WSEHD Harmony Level | WSEHD Harmony Level | WSEHD Harmony Level | WSEHD Harmony Level |
1 | Shangyun River | 0.42 close to harmony | 0.41 close to harmony | 0.48 close to harmony | 0.62 basic harmony | 0.64 basic harmony |
2 | Hei River | 0.43 close to harmony | 0.42 close to harmony | 0.54 close to harmony | 0.63 basic harmony | 0.71 basic harmony |
3 | Mangpa River | 0.46 close to harmony | 0.51 close to harmony | 0.47 close to harmony | 0.65 basic harmony | 0.74 basic harmony |
4 | Nanlang River | 0.36 basic dissonance | 0.38 basic dissonance | 0.42 close to harmony | 0.44 close to harmony | 0.72 basic harmony |
Total Water Resources | Total Amount of Water Resources Is Higher than the Average over the Years | Precipitation Is Higher than the Multi-Year Average | Groundwater Resources | Farmland Irrigation Water Consumption | Non-Farmland Irrigation Water Consumption | Groundwater Supply | Surface Water Supply | Reclaimed Water Volume | Total Water Supply |
---|---|---|---|---|---|---|---|---|---|
125.96 | −28.62% | −35.72% | 108.06 | 110.52 | 115.34 | 118.08 | 78.08 | 12.8 | 260.78 |
Total Surface Water Supply and Reclaimed Water | Non-Agricultural Water Use Exceeds Surface Water | Remaining after Deduction of Groundwater | 60% of the Groundwater Resources of the Year |
---|---|---|---|
80.21 | 70.62 | 135.28 | 64.85 |
Total Water Resources | Total Amount of Water Resources Is Higher than the Average over the Years | Precipitation Is Higher than the Multi-Year Average | Groundwater Resources | Farmland Irrigation Water Consumption | Non-Farmland Irrigation Water Consumption | Groundwater Supply | Surface Water Supply | Reclaimed Water Volume | Total Water Supply |
---|---|---|---|---|---|---|---|---|---|
135.68 | 25.48% | 28.20% | 112.65 | 56.48 | 58.25 | 65.4 | 30.5 | 18.2 | 280.2 |
Total Surface Water Supply and Reclaimed Water | Non-Agricultural Water Use Exceeds Surface Water | Remaining after Deduction of Groundwater | 60% of the Groundwater Resources of the Year |
---|---|---|---|
85.28 | 66.4 | 140.6 | 67.6 |
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Zhang, Y.; Yang, P. Agricultural Productive Carrying Capacity Improve and Water Optimal Allocation under Uncertainty Based on Remote Sensing Data in Lancang County, Southwest China. Water 2022, 14, 3641. https://doi.org/10.3390/w14223641
Zhang Y, Yang P. Agricultural Productive Carrying Capacity Improve and Water Optimal Allocation under Uncertainty Based on Remote Sensing Data in Lancang County, Southwest China. Water. 2022; 14(22):3641. https://doi.org/10.3390/w14223641
Chicago/Turabian StyleZhang, Yunquan, and Peiling Yang. 2022. "Agricultural Productive Carrying Capacity Improve and Water Optimal Allocation under Uncertainty Based on Remote Sensing Data in Lancang County, Southwest China" Water 14, no. 22: 3641. https://doi.org/10.3390/w14223641