# Spatial Non-Stationarity-Based Landslide Susceptibility Assessment Using PCAMGWR Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Dataset

#### 2.1. Overview of the Study Area

^{2}. It has a complex topography mainly composed of mountains, hills, tablelands, valleys, and small flat dams, and the relative elevation is between 500 m and 3820 m.

^{3}, and the water energy reserves are larger than 1 million kW. The soil types are diverse, including yellow loam, yellow-brown loam, dark brown loam, and subalpine meadow soil. The dominant lithology is magmatic rocks, metamorphic rocks, and clastic rocks. Three fault zones are distributed in parallel, from northeast to southwest.

#### 2.2. Dataset Preparation

## 3. Materials and Methods

#### 3.1. Flowchart

- Three spatial neighborhood expressions were constructed in GIS—Moore neighborhoods, slope-unit-based neighborhoods, and hexagonal neighborhoods. The segmentation metric function proposed by Espindola [46] was then used for the prime spatial proximity expression and the extracted LCF was used as the input of the PCAMGWR model.
- Based on the geoenvironmental condition of the study area, LCFs were selected, and thematic layers of LCFs were prepared. Then, the LCFs were analyzed using Pearson correlation analysis and multicollinearity test.
- ESDA was used to investigate the validity of global regression, and the residual obtained by Ordinary Least Squares (OLS) was analyzed based on Moran’s I autocorrelation.
- PCAMGWR model was established for exploring the influence of spatial non-stationarity and factor correlation on LSM.
- The accuracy of the proposed model was verified using statistical measures, and the spatial non-stationarity scale effect was analyzed and compared.

#### 3.2. Expression of Spatial Proximity Selection Method

#### 3.3. Factor Analysis

#### 3.3.1. Correlation Analysis

#### 3.3.2. Multicollinearity Test

#### 3.4. ESDA

#### 3.5. Validation Method

## 4. PCAMGWR Modeling

#### 4.1. Principal Component Analysis (PCA)

#### 4.2. MGWR

## 5. Results

#### 5.1. Expression of Spatial Proximity

#### 5.2. Correlation Analysis and Multicollinearity Test

#### 5.3. ESDA

#### 5.4. LSMs Based on PCAMGWR Model

#### 5.5. Analysis and Comparison of Spatial Non-Stationarity Scale Effect

#### 5.6. Validation and Accuracy Assessment

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Zoning map of (

**a**) elevation, (

**b**) terrain relief, (

**c**) slope, (

**d**) aspect, (

**e**) lithology, (

**f**) distance to fault zones, (

**g**) distance to stream, (

**h**) distance to settlement, (

**i**) vegetation coverage types, and (

**j**) precipitation.

**Figure 4.**Schematic diagram of spatial proximity in Qingchuan county: (

**a**) Moore neighborhoods, (

**b**) slope-unit-based neighborhoods, (

**c**) hexagonal neighborhoods.

**Figure 6.**Elliptical diagram of Pearson correlation of LCFs. L—lithology; DSt—distance to stream; DSe—distance to settlement; DFZ—distance to fault zones; A—aspect; S—slope; TR—terrain relief; VCT—vegetation cover type; Pre—precipitation; E—elevation.

**Figure 7.**Diagram of ESDA: (

**a**) residual distribution diagram based on OLS, (

**b**) Moran’s index analysis of residual values.

**Figure 11.**Iterative process of bandwidths based on the back-fitting algorithm: (

**a**) LCFs for MGWR, (

**b**) PCs for PCAMGWR.

**Figure 13.**Area under the ROC for different models. Figure 14a shows the convergence of SOC-f during the fitting of the back-fitting algorithm for the MGWR model and PCAMGWR model. The speedy convergence rate means that bandwidth was not chosen at each iteration step, and the optimization stopped at convergence inversely. It can be seen from Figure 14b that the optimal bandwidth was selected based on AICc at a slow convergence, and the AICc value did not continue to decline. It is hard to differentiate the SOC-f of PCAMGWR and MGWR models in detail, and the PCAGWR model represented by the black dot plot was better than the GWR model regarding the convergence of AICc values.

**Figure 14.**Parameter variation diagram of bandwidth judgment criterion: (

**a**) SOC-f for MGWR and PCAMGWR, (

**b**) AICc for GWR and PCAGWR.

LCFs | VIF | TOL |
---|---|---|

Lithology | 1.328 | 0.753 |

Distance to stream | 1.109 | 0.901 |

Distance to settlement | 2.255 | 0.443 |

Distance to fault zones | 2.195 | 0.456 |

Aspect | 1.025 | 0.975 |

Slope | 1.540 | 0.650 |

Terrain relief | 1.719 | 0.582 |

Vegetation cover type | 1.019 | 0.981 |

Precipitation | 1.052 | 0.950 |

Elevation | 2.861 | 0.350 |

LCFs | PC1 | PC2 | PC3 | PC4 | PC5 | PC6 |
---|---|---|---|---|---|---|

Lithology | 0.500 | −0.448 | −0.160 | 0.109 | −0.211 | 0.176 |

Distance to stream | 0.272 | 0.322 | 0.542 | 0.156 | 0.071 | −0.621 |

Distance to settlement | 0.782 | −0.267 | 0.120 | −0.018 | −0.012 | −0.065 |

Distance to fault zones | 0.803 | −0.291 | 0.097 | 0.003 | −0.084 | 0.163 |

Aspect | 0.058 | 0.396 | 0.031 | 0.509 | −0.740 | 0.088 |

Slope | 0.483 | 0.630 | −0.337 | 0.027 | 0.182 | 0.171 |

Terrain relief | 0.604 | 0.528 | −0.286 | −0.042 | 0.227 | 0.075 |

Vegetation cover type | −0.034 | −0.277 | −0.190 | 0.819 | 0.450 | −0.058 |

Precipitation | −0.012 | 0.164 | 0.740 | 0.109 | 0.232 | 0.592 |

Elevation | 0.865 | −0.086 | 0.112 | −0.084 | 0.000 | −0.147 |

Model | AIC | AICc | BIC | AUC |
---|---|---|---|---|

PCAMGWR | 78,228.039 | 78,291.042 | 85,829.127 | 0.89773 |

MGWR | 78,232.004 | 78,295.213 | 85,845.297 | 0.89771 |

PCAGWR | 78,682.364 | 78,696.459 | 82,307.355 | 0.83198 |

GWR | 78,785.304 | 78,794.218 | 81,672.072 | 0.81701 |

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**MDPI and ACS Style**

Li, Y.; Huang, S.; Li, J.; Huang, J.; Wang, W.
Spatial Non-Stationarity-Based Landslide Susceptibility Assessment Using PCAMGWR Model. *Water* **2022**, *14*, 881.
https://doi.org/10.3390/w14060881

**AMA Style**

Li Y, Huang S, Li J, Huang J, Wang W.
Spatial Non-Stationarity-Based Landslide Susceptibility Assessment Using PCAMGWR Model. *Water*. 2022; 14(6):881.
https://doi.org/10.3390/w14060881

**Chicago/Turabian Style**

Li, Yange, Shuangfei Huang, Jiaying Li, Jianling Huang, and Weidong Wang.
2022. "Spatial Non-Stationarity-Based Landslide Susceptibility Assessment Using PCAMGWR Model" *Water* 14, no. 6: 881.
https://doi.org/10.3390/w14060881