# Managing Agricultural Water Considering Water Allocation Priority Based on Remote Sensing Data

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Development of Methodology

#### 2.1. Overview of the Problem

#### 2.2. Water Allocation Priority Evaluation

#### 2.2.1. Spatialization of Statistical Data

#### Remote Sensing Data Preparation

#### Regression Models

^{2}) and the significance test value F [19,36,37].

#### Modification Model

#### Model Validation

#### 2.2.2. Evaluation Index

#### 2.2.3. Evaluation Method

#### Division of Water Supply Response Unit

#### The AHP-TOPSIS Evaluation Approach

#### 2.3. Nonlinear Multi-Objective Optimization Model of Agricultural Land and Water

#### 2.3.1. Crop Water Requirements

_{0}and Kc, and the maximum evapotranspiration of crops can be calculated according to the crop coefficient method recommended by the FAO [43]:

#### 2.3.2. Objectives

#### 2.3.3. Constraints

#### 2.3.4. Solution Method

## 3. Application

#### 3.1. Study Area

^{9}m

^{3}. However, due to the decrease in annual runoff of the Yellow River, the water distribution of HID is reduced, and the gap between supply and demand of irrigation water is widened [49]. Water resources have become the main factor restricting the development of irrigation area. The challenges of the irrigation area are (1) how to manage water use on a canal system scale; (2) how to determine a reasonable priority for water distribution; and (3) how to allocate water resources in consideration of allocation efficiency and fairness.

#### 3.2. Evaluation Index Selection

#### 3.3. Data

## 4. Results and Discussion

#### 4.1. Spatial Results of Statistical Data

#### 4.1.1. Statistical Regression Model

^{2}= 0.7177, F = 25.42). Statistical regression results of grain yield also show that the model established by NDVI is better. Among these models, the quadratic function model and the power function model established by NDVI have better fitting results. In real cases, the agricultural output value and grain yield are not supposed to be negative. However, the linear and quadratic function models are prone to negative values, while the exponential function and power function algorithm would not be negative. Therefore, although the established linear model between NDVI and grain yield has a good fitting effect, we cannot select it due to the existence of negative values. In addition, considering the combined effects of NDVI and potential yield of farmland a multiple linear regression model is proposed. For preventing negative values, this study set the intercept of regression model to zero.

#### 4.1.2. Spatialization Results

#### 4.2. Water Allocation Priority

#### 4.3. Optimization Results Analysis

#### 4.4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. The AHP-TOPSIS Evaluation Approach

_{ij}refers to the initial value of the evaluation index j of the response unit i and R is the standardized evaluation matrix.

^{+}is the maximum value of the jth index in the evaluation data response unit i, which is the positive ideal solution; Y

^{−}is the negative ideal solution, which can be calculated through the opposite method to the positive ideal solution. The calculation method is shown as follows:

_{i}is the proximity of each response unit i, its value range is between 0 and 1, and the closer to 1, the greater the priority weight, otherwise the opposite.

#### Appendix A.2. Statistical Regression Model

**Figure A1.**Statistical relationship between NDVI and agricultural output value: (

**a**) Linear algorithm; (

**b**) quadratic polynomial algorithm; (

**c**) exponential algorithm; (

**d**) power function algorithm.

**Figure A2.**Statistical relationship between potential yield of farmland and agricultural output value: (

**a**) Linear algorithm; (

**b**) quadratic polynomial algorithm; (

**c**) exponential algorithm; (

**d**) power function algorithm.

**Figure A3.**Statistical relationship between NDVI and grain yield. (

**a**) Linear algorithm; (

**b**) quadratic polynomial algorithm; (

**c**) exponential algorithm; (

**d**) power function algorithm.

**Figure A4.**Statistical relationship between potential yield of farmland and grain yield: (

**a**) Linear algorithm; (

**b**) quadratic polynomial algorithm; (

**c**) exponential algorithm; (

**d**) power function algorithm.

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**Figure 4.**Some basic data of the study area. (

**a**) Cultivated land data of Inner Mongolia; (

**b**) NDVI data of Inner Mongolia; (

**c**) potential productivity of farmland data of Inner Mongolia; and (

**d**) population spatial distribution data of HID.

**Figure 7.**Spatial data of agricultural output value and grain yield in HID: (

**a**) Agricultural output value; (

**b**) grain yield.

Parameters | Definition |
---|---|

i | Index of response unit (i = 1, 2, 3…I) |

c | Index of crop type (c = 1, 2, 3…C) |

t | Index of month, from March to October (t = 1, 2, 3…T) |

AP_{p} | The revised grid agricultural output value, CNY |

AP_{r} | The grid agricultural output value estimated by regression model, CNY |

AP_{t} | The agricultural output value counted by city units, CNY |

AP_{s} | The sum of grid agricultural output value estimated by regression model within the scope of city unit, CNY |

GY_{p} | The revised grid grain yield, kg |

GY_{r} | The grid grain yield estimated by regression model, kg |

GY_{t} | The grain yield counted by administrative units, kg |

GY_{s} | The sum of grid grain yield estimated by regression model within the scope of each city unit, kg |

O_{g} | Measured value of the county g (provinces govern cities and cities govern counties) |

S_{g} | Simulation value of the county g |

ET_{0} | Reference evapotranspiration, mm |

Δ | Slope of the saturated vapor pressure and air temperature curve, kPa/°C |

R_{n} | Net radiation, MJ/(m^{2}·d) |

G | Soil heat flux, MJ/(m^{2}·d) |

γ | Hygrometer constant, kPa/°C |

T | Average air temperature, °C |

u_{2} | Wind speed at a height of 2 m above the ground, m/s |

e_{s} | Air saturated vapor pressure, kPa |

e_{a} | Actual vapor pressure, kPa |

K_{c} | Crop coefficient |

ET_{ict} | Actual evapotranspiration of crop c in the t month of response unit i, mm |

ET_{mct} | Maximum evapotranspiration of crop c in the t month, mm; |

λ_{ict} | Water sensitivity parameters of crop c in the t month of response unit i |

A_{ic} | Irrigated area of crop c in response unit i, ha |

B_{c} | The unit price of crop c, CNY |

GPm_{ic} | Maximum yield per unit area of crop c in response unit i, kg/ha |

M_{ai} | Actual water consumption of response unit i, m^{3} |

Ma_{ei} | The amount of water required by response unit i, m^{3} |

M_{ak} | Actual water consumption of response unit k, m^{3} |

M_{ek} | The amount of water required by response unit k, m^{3} |

h_{ict} | Available water in root zone of crop c in the month t of response unit i, mm |

m_{ict} | Irrigation water of crop c in the month t of response unit i |

p_{t} | Effective precipitation of month t, mm |

Ge_{ict} | Groundwater recharge of crop c in the month t of response unit i |

h_{m} | Maximum available water in root zone, mm |

Q_{t} | Available water in month t, m^{3} |

η | Irrigation water utilization coefficient |

A_{maxic}, A_{minic} | Maximum and minimum irrigation area, respectively, of crop c in response unit i, ha. |

ZY_{minc} | Minimum yield of crop c, kg |

Ge | Total groundwater recharge, m^{3} |

p | Total effective precipitation, m^{3} |

α, σ | Proportional fairness coefficient, the degree of proportional fairness |

x_{1}, x_{2} | Potential yield of farmland, kg/ha, NDVI |

Irrigation Districts | Length of Main Canal (km) | Design Discharge of Canal (m^{3}/s) | Number of Branch Canals |
---|---|---|---|

YG | 17 | 65 | 17 |

WLH | 53.4 | 27.4 | 15 |

YJH | 58.5 | 53 | 25 |

HJ | 81.4 | 58 | 34 |

YJ | 49.4 | 106 | 39 |

FJ | 105 | 60 | 36 |

ZH | 52 | 29.2 | 23 |

SH | 80 | 31.4 | 20 |

YH | 83 | 33 | 24 |

TJ | 67.9 | 31 | 24 |

CJ | 53.5 | 24 | 20 |

TB | 44.5 | 22 | 21 |

Month | ETm (mm) | Effective Precipitation (mm) | Available Water (10^{8} m^{3}) | ||
---|---|---|---|---|---|

Wheat | Corn | Sunflower | |||

3 | 35.99 | 0 | 0 | 0 | 0 |

4 | 103.55 | 0 | 0 | 0 | 2.16 |

5 | 199.95 | 114.70 | 0 | 0 | 10.67 |

6 | 112.00 | 147.20 | 155.20 | 7.65 | 4.17 |

7 | 0 | 179.30 | 151.59 | 4.59 | 5.37 |

8 | 0 | 90.35 | 68.11 | 17.13 | 2.02 |

9 | 0 | 0 | 48.48 | 0 | 1.46 |

Crop | Local Crop Prices (CNY/kg) | Crop Minimum Yield (10^{4} kg) |
---|---|---|

Wheat | 3.00 | 28,862.22 |

Corn | 1.70 | 98,154.24 |

Sunflower | 6.30 | 42,126.28 |

Impact Factors | Cultivated Land Area | NDVI | Potential Yield of Farmland | |
---|---|---|---|---|

Statistical Data | ||||

Agricultural output value | 0.93 ** | 0.78 ** | 0.65 * | |

Grain yield | 0.87 ** | 0.86 ** | 0.73 ** |

Factor | Algorithm | Agricultural Output Value | Grain Yield | ||
---|---|---|---|---|---|

R^{2} | F | R^{2} | F | ||

NDVI | Linear algorithm | 0.61 | 15.37 | 0.74 | 28.203 |

Quadratic polynomial algorithm | 0.61 | 6.92 | 0.8 | 18.56 | |

Exponential algorithm | 0.65 | 18.23 | 0.73 | 27.10 | |

Power function algorithm | 0.72 | 25.42 | 0.77 | 33.124 | |

Potential yield of farmland | Linear algorithm | 0.42 | 7.223 | 0.53 | 11.18 |

Quadratic polynomial algorithm | 0.44 | 3.619 | 0.73 | 12.22 | |

Exponential algorithm | 0.56 | 12.64 | 0.61 | 15.41 | |

Power function algorithm | 0.63 | 16.87 | 0.56 | 12.56 | |

Multiple linear regression | 0.81 | 20.86 | 0.74 | 13.94 |

Factor | Algorithm | MAPE | RMSE |
---|---|---|---|

Agricultural output value (10^{4} CNY) | Area weighted algorithm | 28.37% | 60,183 |

NDVI power function algorithm | 12.18% | 40,283 | |

Multiple linear regression | 25.54% | 48,252 | |

Grain yield (kg) | NDVI power function algorithm | 16.69% | 62,953 |

NDVI quadratic polynomial algorithm | 14.92% | 61,161 | |

Multiple linear regression | 14.66% | 60,101 |

Objective | Weight | CR |
---|---|---|

Economic benefit | 0.18 | 0.04 |

Water allocation priority satisfaction | 0.24 | |

Grain yield | 0.37 | |

Equity | 0.21 |

County | Grain Yield (10^{3} kg) | Agricultural Output Value (10^{4} CNY) | ||||
---|---|---|---|---|---|---|

Statistical Data | Estimation Results | MAPE (%) | Statistical Data | Estimation Results | MAPE (%) | |

Linhe | 557,750.00 | 517,682.00 | 7.18 | 346,934.50 | 280,051.00 | 19.28 |

Wuyuan | 419,200.00 | 494,521.00 | 17.96 | 244,794.50 | 298,946.00 | 22.12 |

Hangjing Houqi | 420,180.00 | 417,076.00 | 0.74 | 248,715.20 | 225,567.00 | 9.31 |

Urat Qianqi | 500,225.00 | 413,854.00 | 17.23 | 317,690.50 | 305,545.00 | 3.82 |

Dengkou | 191,000.00 | 248,555.00 | 30.13 | 78,170.99 | 83,150.00 | 6.37 |

Attribute | Gini | Minimum Envy Fairness |
---|---|---|

p | 0.39 | 0.47 |

Grain yield (10^{8} kg) | 18.07 | 21.83 |

Economic benefit (10^{8} CNY) | 74.43 | 80.98 |

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## Share and Cite

**MDPI and ACS Style**

Luo, B.; Zhang, F.; Liu, X.; Pan, Q.; Guo, P.
Managing Agricultural Water Considering Water Allocation Priority Based on Remote Sensing Data. *Remote Sens.* **2021**, *13*, 1536.
https://doi.org/10.3390/rs13081536

**AMA Style**

Luo B, Zhang F, Liu X, Pan Q, Guo P.
Managing Agricultural Water Considering Water Allocation Priority Based on Remote Sensing Data. *Remote Sensing*. 2021; 13(8):1536.
https://doi.org/10.3390/rs13081536

**Chicago/Turabian Style**

Luo, Biao, Fan Zhang, Xiao Liu, Qi Pan, and Ping Guo.
2021. "Managing Agricultural Water Considering Water Allocation Priority Based on Remote Sensing Data" *Remote Sensing* 13, no. 8: 1536.
https://doi.org/10.3390/rs13081536