# On the Scale Effect of Relationship Identification between Land Surface Temperature and 3D Landscape Pattern: The Application of Random Forest

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data and Preprocessing

#### 2.3. Method

#### 2.3.1. Land Surface Temperature Retrieval

#### 2.3.2. Landscape Metrics

#### 2.3.3. Pearson Correlation Coefficient

#### 2.3.4. Multiple Linear Regression

#### 2.3.5. Random Forest Regression

#### 2.3.6. Coefficient of Rectangle Variation

## 3. Results

#### 3.1. LST Distribution in the Second and the Fourth Ring Road of Beijing

#### 3.2. Pearson Correlation Coefficient between Landscape Metrics and LST

#### 3.2.1. Pearson Correlation Coefficient between Landscape Metrics and LST at 10 m Grain Size

#### 3.2.2. Pearson Correlation Coefficient between Landscape Metrics and LST at 30 m Grain Size

#### 3.3. Multiple Linear Regression between Landscape Metrics and LST

#### 3.3.1. Multiple Linear Regression between Landscape Metrics and LST at 10 m Grain Size

#### 3.3.2. Multiple Linear Regression between Landscape Metrics and LST at 30 m Grain Size

#### 3.4. Random Forest Regression between Landscape Metrics and LST

#### 3.5. The CORV of 3D Landscape Metrics

#### 3.5.1. The CORV of 3D Landscape Metrics at 10 m Grain Size

#### 3.5.2. The CORV of 3D Landscape Metrics at 30 m Grain Size

## 4. Discussion

#### 4.1. Multi-Scale Relationship between 3D Landscape Pattern and LST in the Fourth Ring Road of Beijing

#### 4.2. Advantages and Limitations

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 2.**Landsat 8 image, land cover map and building height of two study areas. (

**a**) Landsat 8 image; (

**b**) land cover map; (

**c**) building height.

**Figure 5.**The distribution of LST and the proportion of land types at different temperature levels in the study area. (

**a**) the second ring road; (

**b**) the fourth ring road.

**Figure 6.**PCC between LST and landscape metrics at 10 m grain size. (

**a**–

**f**) PCC between LST and 3D landscape metrics at 10 m grain size; (

**g**–

**j**) PCC between LST and 2D landscape metrics at 10 m grain size.

**Figure 7.**PCC between LST and landscape metrics at 30 m grain size. (

**a**–

**f**) PCC between LST and 3D landscape metrics at 30 m grain size; (

**g**–

**j**) PCC between LST and 2D landscape metrics at 30 m grain size.

**Figure 8.**The ${R}^{2}$ of the multiple linear regression model between LST and landscape metrics at 10 m grain size.

**Figure 9.**The ${R}^{2}$ of the multiple linear regression model between LST and landscape metrics at 30 m grain size.

**Figure 11.**Feature importance of 3D landscape metrics to LST in RFR. (

**a**,

**b**) are the feature importance of each metrics at 10 m grain size; (

**c**,

**d**) are the feature importance of each metrics at 30 m grain size.

**Figure 12.**Power fitting of the normalized CORV of each 3D landscape metrics at the 10 m grain size.

**Figure 14.**Comparison of LST, land use and building height in some typical areas of the study area. (

**a**) high LST area with more vegetation; (

**b**) high LST area with less vegetation; (

**c**,

**d**) are low LST area.

Metrics | Index Calculation Formula | Description |
---|---|---|

Component Metrics | ||

Largest Patch Index (%) | $\mathrm{LPI}=\frac{max\left({a}_{ij}\right)}{A}\ast 100$ | ${a}_{ij}$ is the 2D/3D area of patch $ij$, $A$ is the total 2D/3D area of a rectangle. LPI measures the proportion of the largest patch in a rectangle. |

Edge Density (m/ha) | $\mathrm{ED}=\frac{E}{A}{10}^{6}$ | $E$ is the total 2D/3D length of all patches’ edges. ED measures the total side length of all patches divided by the 2D/3D area of a rectangle. |

Number of Patches | $\mathrm{NP}=n$ | NP measures the total number of patches in a rectangle. |

Patches Cohesion Index | $\mathrm{COHESION}=\phantom{\rule{0ex}{0ex}}\left[1-\frac{{\sum}_{j=1}^{n}{p}_{ij}}{{\sum}_{j=1}^{n}{p}_{ij}\sqrt{{a}_{ij}}}\right]{\left[1-\frac{1}{\sqrt{A}}\right]}^{-1}\ast 100$ | ${p}_{ij}$ is the 2D/3D perimeter of patch $ij$, ${a}_{ij}$ is the 2D/3D surface area of patch $ij$. COHESION measures the aggregation and dispersion of patches in a rectangle. |

Effective Mesh Size (ha) | $\mathrm{MESH}=\frac{{\sum}_{i=1}^{m}{\sum}_{j=1}^{n}{a}_{ij}^{2}}{A}$ | MESH measures the sum of squares of patch area divided by the total rectangle area. |

Configuration Metrics | ||

Landscape Shape Index | $\mathrm{LSI}=\frac{0.25E{A}_{surf}}{\sqrt{A}{A}_{prj}}$ | ${A}_{surf}$ represents the 3D area and ${A}_{prj}$ is the projected plane area of ${A}_{surf}$. $E$ is the total 3D edge length of all patches. |

Landscape Division Index | $\mathrm{DIVISION}=1-{\displaystyle {\displaystyle \sum}_{i=1}^{m}}{\displaystyle {\displaystyle \sum}_{j=1}^{n}}{\left(\frac{{a}_{ij}}{A}\right)}^{2}$ | DIVISION measures the degree of division of a rectangle. DIVISION equals 0 when the landscape consists of single patch. DIVISION achieves its maximum value (1) when the landscape is maximally subdivided. |

Euclidean Nearest-Neighbor Distance (m) | $\mathrm{ENN}-\mathrm{MN}=\frac{{\sum}_{j=1}^{n}{x}_{ij}}{{n}_{i}}$ | ${x}_{ij}$ is the 2D/3D closest distance between the same patch $ij$, and ${n}_{i}$ represents the total number of class $i$. ENN-MN measures the distance to the nearest neighboring patch of the same type. |

Shannon’s Diversity Index | $\mathrm{SHDI}=-{\displaystyle {\displaystyle \sum}_{k=1}^{n}}{P}_{k}ln\left({P}_{k}\right)$ | ${P}_{k}$ equals the 2D/3D area of class $k$, divided by the area of 2D/3D surface. SHDI measures the diversity of a rectangle. |

Shannon’s Evenness Index | $\mathrm{SHEI}=\frac{-{\sum}_{i=1}^{m}\left({P}_{i}ln{P}_{i}\right)}{lnm}$ | ${P}_{i}$ equals the 2D/3D area of class $i$, divided by the area of 2D/3D surface. SHEI measures the evenness of a rectangle. |

Roughness Metrics | ||

Root Mean Square Deviation of a Surface | $\mathrm{SQ}=\sqrt{\frac{1}{N}{{\displaystyle \sum}}_{i=1}^{N}{\left[{h}_{i}-u\right]}^{2}}$ | ${h}_{i}$ is the pixel height of class $i$, $N$ is the total number of pixels in a rectangle, $u$ is the mean height of all pixels. SQ measures the degree to the building deviates from the plane of a rectangle. |

Skewness of Surface Height Distribution | $\mathrm{SKU}=\frac{1}{N{S}_{q}^{3}}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}{\left[{h}_{i}-u\right]}^{3}$ | SKU measures the skewness of the buildings in a rectangle. |

Mean Height (m) | $\mathrm{MEAN}=\frac{H}{A}$ | $H$ is the sum of all pixels in a rectangle. MEAN is the mean height of a rectangle. |

Maximum Height (m) | $\mathrm{MAX}={h}_{max}$ | MAX is the maximum height of a rectangle. |

Sky View Factor | $\mathrm{SVF}=1-\frac{{\sum}_{i=1}^{n}\mathrm{sin}{\gamma}_{i}}{n}$ | $n$ stands for the number of directions used to estimate the vertical elevation angle of the relief horizon. The vertical elevation angle ${\gamma}_{i}$ can be computed from the horizontal distance and the elevation difference between the horizon and the vantage point. SVF measures the sky visibility. |

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**MDPI and ACS Style**

Wu, Q.; Li, Z.; Yang, C.; Li, H.; Gong, L.; Guo, F.
On the Scale Effect of Relationship Identification between Land Surface Temperature and 3D Landscape Pattern: The Application of Random Forest. *Remote Sens.* **2022**, *14*, 279.
https://doi.org/10.3390/rs14020279

**AMA Style**

Wu Q, Li Z, Yang C, Li H, Gong L, Guo F.
On the Scale Effect of Relationship Identification between Land Surface Temperature and 3D Landscape Pattern: The Application of Random Forest. *Remote Sensing*. 2022; 14(2):279.
https://doi.org/10.3390/rs14020279

**Chicago/Turabian Style**

Wu, Qiong, Zhaoyi Li, Changbao Yang, Hongqing Li, Liwei Gong, and Fengxiang Guo.
2022. "On the Scale Effect of Relationship Identification between Land Surface Temperature and 3D Landscape Pattern: The Application of Random Forest" *Remote Sensing* 14, no. 2: 279.
https://doi.org/10.3390/rs14020279