# Spatial Structure Characteristics of Slope Farmland Quality in Plateau Mountain Area: A Case Study of Yunnan Province, China

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study area and Data Sources

#### 2.1. Study Area

^{2}, in which the East Asian monsoon and South Asian monsoon converge. For the topography, it is high in the north and low in the south. Moreover, the mountainous area accounts for 84% of the total land area, and the hill accounts for only 10%. The topography gradually develops from mountain land to karst landform. Due to the common influence of ecological environment evolution and human activities, the region with moderate ecological vulnerability accounts for 32.02% of the total area, while the region with strong and extremely strong fragility accounts for 53.63% [37]. There is abundant rainfall and many rivers in Yunnan, but they are unevenly distributed in space and time. The average reference crop evaporation is between 786.3 and 1511.6 mm, with a mean of 1090.4 mm [38].

^{2}, accounting for 69.79% of the farmland area. The agricultural production of slope farmland plays an important role in the agricultural activities in Yunnan [15]. In order to make the SFQ evaluation consistent with the regional agricultural activities, Yunnan is divided into seven regions in this study, according to the comprehensive agricultural partition in Yunnan. The elevation and spatial distribution of slope farmland are shown in Figure 1, and the distribution characteristics of slope farmland in different partitions are listed in Table 1.

#### 2.2. Data Sources

## 3. Methodology

#### 3.1. Quality Evaluation System of Slope Farmland

#### 3.1.1. Evaluation Unit

#### 3.1.2. Construction of Evaluation Index System

#### 3.1.3. Quantification of Evaluation Index

^{2}. In addition, the range of FRAC value is between 1 and 2, and the range of Q value is between 20 and 100. The area threshold of slope farmland is obtained by the natural break point method. Moreover, the minimum threshold is 2.5 hm

^{2}, and the maximum threshold is 78 hm

^{2}.

#### 3.1.4. Membership Function

#### 3.1.5. Index Weight

_{i}is the comprehensive weight of the i-th evaluation index. C

_{i1}is the weight obtained by the calculation of PCA. C

_{i2}is the weight obtained by the calculation of AHP. And C

_{i3}is the weight obtained by the calculation of EWM.

#### 3.1.6. Evaluation Model and Quality Grading

_{i}is the membership value of the i-th evaluation index. C

_{i}is the weight of evaluation index of the ith evaluation index. n is the number of evaluation indexes.

#### 3.2. Research Methods of Spatial Structure Characteristics of SFQ

#### 3.2.1. Geostatistical Analysis Method

_{i}) and Z(x

_{i}+h) are the values of spatial positions x

_{i}and x

_{i}+h, respectively. n(h) is the logarithm of sample with a spatial distance of h.

_{0}can reflect the influence degree of randomness factors on the regional SFQ. Furthermore, the Sill (C

_{0}+C) represents the maximum spatial variation degree of SFQ. The spatial distribution of SFQ indexes is moderately autocorrelated. Nugget coefficient C

_{0}/(C

_{0}+C) represents the proportion of random variation to the total variation of slope farmland. If the proportion is less than 25%, the spatial distribution of SFQ indexes belongs to the strong spatial autocorrelation. If the proportion is between 25% and 75%, the spatial distribution of SFQ indexes belongs to moderate spatial autocorrelation. If the proportion is greater than 75%, the spatial distribution of SFQ indexes belongs to a weak spatial correlation, indicating that the degree of spatial heterogeneity caused by the random part plays a major role [49,50].

#### 3.2.2. Global Spatial Autocorrelation Analysis Method

_{i}is the observed value, and $\overline{X}$ is the mean of X

_{i}. W(i, j) is the spatial connection matrix between the research objects i and j.

#### 3.2.3. Local Spatial Autocorrelation Analysis Method

_{i}is the observed value, and $\overline{X}$ is the mean of X

_{i}. W(i, j) is the spatial connection matrix between the research objects i and j.

#### 3.2.4. Spatial Cold and Hot Spots Analysis Method

#### 3.3. Data Calculation and Analysis

## 4. Results and Discussion

#### 4.1. Spatial Distribution Characteristics of SFQ

^{2}, accounting for 25.74% of the total area of slope farmland. The second one is the fifth-class farmland with a distribution area of 1.1801 million hm

^{2}, accounting for 24.97% of the total area of slope farmland. Likewise, the distribution areas of fourth-class and seventh-class farmland are also larger, with 0.7975 million hm

^{2}and 0.8594 million hm

^{2}, respectively, accounting for 16.88% and 18.19% of the total area of slope farmland, respectively. However, the distribution areas of fourth-class and seventh-class farmland are smaller, with the distribution areas of 0.2477 million hm

^{2}and 0.3306 million hm

^{2}, respectively. Similarly, the distribution areas of first-class, second-class farmland, ninth-class farmland and tenth-farmland have the smaller distribution area, all accounting for less than 2%.

#### 4.2. Spatial Variation Characteristics of SFQ

_{0}is 0.5293, indicating that the random factors of spatial distribution of SFQ indexes are larger. The Partial Sill C is 0.4515, and the Sill (C

_{0}+C) is 0.9808. Thus, the Nugget coefficient C

_{0}/(C

_{0}+C) is 53.97%. This suggests that although the spatial variation caused by random factors is higher, the SFQ indexes are in the medium spatial autocorrelation on the whole. The structural factors, such as climatic condition, soil property, moisture condition, spatial morphological characteristic, etc., still play a major role. Furthermore, the influence of random factors on the spatial differentiation of SFQ indexes should not be ignored. This conforms to the great influence of unreasonable cultivation mode, soil erosion aggravation and frequent regional droughts of slope farmland in Yunnan in recent years. The range (A

_{0}) refers to the distance as the variation function reaches the Sill as well as reflects the distance range of spatial autocorrelation of the research object. Here, the A

_{0}value of SFQ index in Yunnan is 17.96 km, which shows that the spatial autocorrelation range of SFQ in Yunnan is within 17.96km.

#### 4.3. Spatial Autocorrelation Characteristics of SFQ

#### 4.3.1. Global Spatial Autocorrelation Analysis

#### 4.3.2. Local Spatial Autocorrelation Analysis

#### 4.4. Characteristics of Space Cold and Hot Spots in SFQ

## 5. Conclusions

- (1)
- The SFQ indexes in Yunnan Province distributes between 0.36 and 0.81, with a mean of 0.59 ± 0.06. The SIFIs of most evaluation units are less than 0.6. The spatial distributions of SFQ indexes are significantly different. Moreover, the SFQ grade is based on sixth-class, fifth-class, seventh-class and fourth-class land. The SFQ grade is relatively higher in the Southern Fringe, central Yunnan, Western Yunnan and Southeastern Yunnan, while the SFQ grade is relatively lower in Northeastern Yunnan and Northwestern Yunnan.
- (2)
- The SFQ indexes present a normal spatial distribution, and the Gaussian model can well fit the semi-variance function of SFQ indexes. The Nugget C
_{0}of spatial distribution of SFQ indexes is 0.5293, and the Nugget coefficient C_{0}/(C_{0}+C) is 53.97%. Furthermore, the spatial distribution of SFQ indexes is moderately autocorrelated. The structural factors, such as climatic conditions, soil property, moisture conditions, spatial morphology, etc., play a major role in the spatial heterogeneity of SFQ indexes, but the influence of random factors should not be ignored. - (3)
- The Moran’s I value of global spatial autocorrelation of SFQ grades is 0.8489. The spatial distribution of SFQ grades has a significant spatial aggregation characteristic. The spatial autocorrelation types of SFQ grades are based on HH aggregation and LL aggregation, as well as the types of their LISA cluster are based on HH aggregation and LL aggregation.
- (4)
- The cold spot and hot spot distributions of SFQ grades display the significantly spatial difference. The hot spot area is mainly distributed in the Central Yunnan and the Southern Fringe, while the cold spot area is mainly distributed in the Northeastern Yunnan, Northwestern Yunnan and Southwestern Yunnan.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Spatial distribution of sloping integrated fertility index (SIFI) (

**a**) and quality grade (

**b**) of slope farmland.

**Figure 3.**Exploratory analysis results of spatial distribution of SFQ index. (

**a**) Density histogram, (

**b**) Cumulative curve, (

**c**) Normal Q-Q plot.

**Figure 5.**Local spatial autocorrelation local indicators of spatial association (LISA) cluster map of SFQ grade.

Partition Name | Arable Land | Dry Land | Slope Farmland | ||||||
---|---|---|---|---|---|---|---|---|---|

Area (×10 ^{4}hm^{2}) | Proportion of Land Area | Average Slope (°) | Area (×10 ^{4}hm^{2}) | Average slope (°) | Proportion of Cultivated Land Area | Area (×10 ^{4}hm^{2}) | Average Slope (°) | Proportion of Cultivated Land Area | |

Central Yunnan | 187.76 | 21.32% | 9.70 | 132.16 | 11.69 | 70.39% | 114.80 | 13.20 | 61.14% |

Western Yunnan | 91.94 | 18.13% | 12.28 | 62.71 | 15.02 | 68.21% | 58.10 | 16.09 | 63.20% |

Southeastern Yunnan | 95.73 | 19.02% | 10.90 | 67.06 | 11.97 | 70.05% | 58.55 | 13.46 | 61.16% |

Southwestern Yunnan | 109.20 | 18.46% | 16.31 | 96.15 | 17.00 | 88.05% | 93.60 | 17.41 | 85.71% |

Southern Fringe | 99.03 | 15.90% | 12.61 | 77.89 | 14.39 | 78.66% | 71.32 | 15.58 | 72.03% |

Northeastern Yunnan | 62.95 | 27.61% | 16.08 | 55.68 | 16.45 | 88.46% | 52.80 | 17.25 | 83.88% |

Northwestern Yunnan | 30.40 | 5.95% | 18.01 | 25.74 | 19.14 | 84.66% | 23.34 | 20.97 | 76.77% |

Total | 676.99 | 17.61% | 12.68 | 517.39 | 14.41 | 76.42% | 472.55 | 15.62 | 69.79% |

Target Layer (A) | Criterion Level (B) | Index Level (C) | ||
---|---|---|---|---|

Code | Classification | Code | Index | |

Slope farmland quality (A) | B1 | Soil profile properties | C1 | Effective soil layer thickness (cm) |

C2 | Thickness of cultivated-layer (cm) | |||

B2 | Physicochemical properties | C3 | Bulk density (g/cm^{3}) | |

C4 | Soil texture (Dimensionless) | |||

C5 | pH value (Dimensionless) | |||

C6 | Organic matter (g/kg) | |||

B3 | soil nutrient | C7 | Available phosphorus (mg/kg) | |

C8 | Available potassium (mg/kg) | |||

B4 | Site conditions | C9 | ≥10 °C accumulated temperature (°C) | |

B5 | Spatial form | C10 | Field regularity (Dimensionless) | |

C11 | Degree of continuity (Dimensionless) | |||

B6 | Moisture condition | C12 | Rainfall (mm) | |

C13 | Irrigation assurance rate (%) | |||

B7 | Soil erosion | C14 | Slope (°) |

Index Code | Index | Membership Function Type | Formula of Membership Function | Parameters | |
---|---|---|---|---|---|

a | b | ||||

C1 | Effective soil layer | S-type | $\mu (x)=\{\begin{array}{c}1,x\ge b\\ 0.9(x-a)/(b-a)+0.1,a<x<b\\ 0.1,x\le a\end{array}$ | 30.0 | 120.0 |

C2 | Thickness of cultivated-layer | S-type | 14.03 | 20.00 | |

C6 | Organic matter | S-type | 15.0 | 40.0 | |

C7 | Available phosphorus | S-type | 5.70 | 53.83 | |

C8 | Available potassium | S-type | 40.00 | 216.06 | |

C9 | ≥10 °C accumulated temperature | S-type | 3000.0 | 5500.0 | |

C11 | Degree of continuity | S-type | 20.0 | 100.0 | |

C12 | Rainfall | S-type | 800.0 | 1200.00 | |

C13 | Irrigation assurance rate | S-type | 40.0 | 100.0 | |

C3 | Soil bulk density | Anti-S-type | $\mu (x)=\{\begin{array}{c}1,x\le a\\ 0.9(x-b)/(a-b)+0.1,a<x<b\\ 0.1,x\ge b\end{array}$ | 1.15 | 1.50 |

C10 | Field regularity | Anti-S-type | 1.00 | 1.34 | |

C14 | Slope | Anti-S-type | 3.00 | 25.00 |

Index Code | Index | Membership Function Type | Formula of Membership Function | Parameters | |||
---|---|---|---|---|---|---|---|

a_{1} | b_{1} | b_{2} | a_{2} | ||||

C5 | pH value | Parabolic-type (Peak type) | $\mu (x)=\{\begin{array}{c}1,{b}_{2}\ge x\ge {b}_{1}\\ \begin{array}{l}0.9(x-{a}_{1})/({b}_{1}-{a}_{1})+0.1,{a}_{1}<x<{b}_{1}\\ 0.9(x-{a}_{2})/({b}_{2}-{a}_{2})+0.1,{a}_{2}>x>{b}_{2}\end{array}\\ 0.1,x\le {a}_{1}\mathrm{or}x\ge {a}_{2}\end{array}$ | 5.5 | 6.5 | 7.5 | 8.5 |

_{1}and b

_{2}are the lower limit and upper limit of the critical value of the index, respectively, the minimum value and the maximum value of the measured value are taken in this study; b

_{1}and b

_{2}are the upper and lower boundary points of the most suitable value, and their values are determined according to the comprehensive comparison of the measured results in the study area.

**Table 5.**Distribution area statistics of slope farmland quality (SFQ) grades in different regions of Yunnan Province.

Quality Grade | Area Proportion of Different Zones (%) | Total | |||||||
---|---|---|---|---|---|---|---|---|---|

Central Yunnan | Western Yunnan | Southeastern Yunnan | Southwestern Yunnan | Southern Fringe | Northeastern Yunnan | Northwestern Yunnan | Area (×10 ^{4}hm^{2}) | Proportion (%) | |

1 | 0.00 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.09 |

2 | 0.18 | 3.74 | 0.01 | 0.11 | 0.60 | 0.00 | 0.00 | 3.07 | 0.65 |

3 | 5.05 | 11.98 | 4.74 | 2.59 | 8.78 | 0.00 | 0.03 | 24.77 | 5.24 |

4 | 19.34 | 27.06 | 22.86 | 9.18 | 25.41 | 0.09 | 2.00 | 79.75 | 16.88 |

5 | 23.35 | 24.88 | 36.03 | 20.16 | 46.01 | 1.97 | 7.96 | 118.01 | 24.97 |

6 | 26.82 | 21.76 | 27.96 | 28.83 | 16.67 | 29.49 | 33.72 | 121.63 | 25.74 |

7 | 17.22 | 8.47 | 6.76 | 25.46 | 2.42 | 50.64 | 28.39 | 85.94 | 18.19 |

8 | 6.49 | 1.33 | 1.61 | 12.35 | 0.10 | 16.13 | 19.17 | 33.06 | 7.00 |

9 | 1.49 | 0.08 | 0.03 | 1.30 | 0.00 | 1.68 | 7.90 | 5.61 | 1.19 |

10 | 0.06 | 0.00 | 0.00 | 0.02 | 0.00 | 0.00 | 0.83 | 0.27 | 0.06 |

Theoretical Model | Error Prediction Parameters | ||||
---|---|---|---|---|---|

Mean | Mean Square Root | Standardized Mean | Root-Mean-Square Standardized | Mean Standard Error | |

Circular model | −0.000158 | 0.0362 | −0.00323 | 0.7959 | 0.0455 |

Spherical model | −0.000151 | 0.0362 | −0.00308 | 0.7953 | 0.0456 |

Exponential model | −0.000105 | 0.036 | −0.0021 | 0.7889 | 0.0457 |

Gaussian model | −0.000219 | 0.0364 | −0.00452 | 0.8038 | 0.0454 |

Inspection Parameters | Central Yunnan | Western Yunnan | Southeastern Yunnan | Southwestern Yunnan | Southern Fringe | Northeastern Yunnan | Northwestern Yunnan |
---|---|---|---|---|---|---|---|

Moran’s I | 0.8684 | 0.8440 | 0.9364 | 0.8263 | 0.8847 | 0.6293 | 0.8279 |

Z-score | 307.13 | 187.77 | 234.60 | 243.20 | 306.89 | 80.79 | 168.25 |

p-value | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, Z.; Shi, D.
Spatial Structure Characteristics of Slope Farmland Quality in Plateau Mountain Area: A Case Study of Yunnan Province, China. *Sustainability* **2020**, *12*, 7230.
https://doi.org/10.3390/su12177230

**AMA Style**

Chen Z, Shi D.
Spatial Structure Characteristics of Slope Farmland Quality in Plateau Mountain Area: A Case Study of Yunnan Province, China. *Sustainability*. 2020; 12(17):7230.
https://doi.org/10.3390/su12177230

**Chicago/Turabian Style**

Chen, Zhengfa, and Dongmei Shi.
2020. "Spatial Structure Characteristics of Slope Farmland Quality in Plateau Mountain Area: A Case Study of Yunnan Province, China" *Sustainability* 12, no. 17: 7230.
https://doi.org/10.3390/su12177230