# Uncovering the Structural Effect Mechanisms of Natural and Social Factors on Land Subsidence: A Case Study in Beijing

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}occurred in undeveloped land-use classes, such as marshland and wetland forests, and the highest rates of 18–20 mm year

^{−1}occurred in a built-up area in the Mekong Delta. In a study of the impact of anthropogenic causes on land subsidence in the Su-Xi-Chang area, Lu [19] confirmed that the main driving factor was deep groundwater exploitation before 2000, whereas the physical loading of the compressible subsurface sediments by city buildings and infrastructure was the dominant factor after the year 2000, owing to the policy of banning groundwater exploitation after this date.

## 2. Materials and Methods

#### 2.1. Study Area and Datasets

^{2}. Following China’s reform and opening-up policy implemented in the 1980s, the process of urbanization in Beijing has significantly accelerated. Based on China’s urban statistics yearbook and data released by the National Bureau of Statistics, the central built-up area increased from 23,816 km

^{2}in 1980 to 71,213 km

^{2}in 1995 (expanding to the northwest of the Summer Palace, the west of Shijingshan, and the south and southeast of the Beijing Economical and Technological Development Zone) and from 83,017 km

^{2}in 2000 to 121,012 km

^{2}in 2005 (expanding to the Fifth Ring Road) [21]. Land subsidence in Beijing has been developing since the 1960s, and the spatial distribution is uneven, especially in Chaoyang District and Tongzhou District, where severe land subsidence has been taking place [22].

^{2}. Level surveying data collected from the Hydrogeology and Engineering Geology Team from Beijing were used to verify the subsidence monitoring results. A total of 14 monitoring points (a total 17 points with leveling surveys and underground water level) (see Figure 2) located in the study area were selected to correspond with the PS pixels. Compared with the annual deformation of the leveling surveys and the monitoring results by PS-InSAR, the differences between the PS-InSAR monitoring results and level measurements hovered within 8 mm; consequently, the PS-InSAR measurement results were validated.

#### 2.2. Methods

#### 2.2.1. Identifying Local Effect Mechanisms Using the GTWR Model

_{i}, u

_{i}, and v

_{i}are the longitude and latitude coordinates of area i, ${X}_{ik}$ represents the value of the k-th explanatory variable at sample I (k is the total number of related explanatory variables), respectively, ${\beta}_{0}\left({u}_{i,}{v}_{i,}{t}_{i}\right)$ is the space-time intercept term of location I, ${\beta}_{k}\left({u}_{i,}{v}_{i,}{t}_{i}\right)$ donates the slope coefficient of the kth variable of sample I, which describes the relationship between the kth variable and land subsidence, and $\epsilon \left({u}_{i,}{v}_{i,}{t}_{i}\right)$ represents the independent random error term. The estimation of each regression coefficient at the monitoring site I can be obtained by using the locally weighted least-square method:

#### 2.2.2. Detecting Structural Effect Mechanisms Using the SCMC Algorithm

^{2}is defined as the following equations:

^{2}value for each variable, which is more effective to divide the study area into clusters of features [32,33]. The larger the R

^{2}value, the better discrimination among those features. In other words, the R

^{2}value reflects how much of the variation in the coefficients of each variable was retained after the clustering process [34]. The R

^{2}value is defined as follows:

## 3. Results

#### 3.1. Identification of Local Effect Mechanisms of Associated Factors on Land Subsidence

^{2}, adjusted R

^{2}, AICC information, and root mean square error (RMSE) (Table 2).

^{2}, or adjusted R

^{2}, can reflect the degree of model fitting: the larger the value is, the higher the fitting degree will be. RMSE reflects the size of model accuracy: the smaller the value is, the higher the accuracy of the model will be, and the AICC is another important criterion to evaluate the goodness of the model fitting: the smaller the value is, the higher the accuracy of the model will be. According to Table 2, the AICC value is reduced from 12.924 of GWR and 13.952 of OLS to 12.730 of GTWR, showing that there are significant differences in performance between these models. The fitting degree (R

^{2}) of the GTWR model is 0.672, which is greatly improved compared with a GWR of 0.524 and OLS of 0.062. The further evaluation of the model performance is executed using out-of-sample validation (80% random samples for modeling and the remaining 20% for validation/prediction analysis). The RMSE value is reduced from 12.355 (GWR) and 17.344 (OLS) to 6.681 (GTWR), indicating that the prediction precision of the GTWR model is relatively higher. From the above comprehensive comparison results, the GTWR model outperforms the GWR and OLS models in describing spatiotemporal variations in land subsidence and other independent variables.

#### 3.2. Identification of Structural Effect Mechanisms of Associated Factors on Land Subsidence

#### 3.2.1. Estimating Number of Clusters

#### 3.2.2. Regression Coefficients and Structural Characteristics

^{2}values for the four variables are shown in Table 4, and these values were listed for the regression coefficients of each variable. The larger the R

^{2}value, the greater the difference that was identified among these features. Overall, underground water and rainfall were the variables that most effectively divided the study area into clusters of features, with an obvious spatial aggregation characteristic, while IBI and population were the variables that less effectively divided the study area into clusters of features. When the analysis was performed for the annual regression coefficients, among the four variables, the highest R

^{2}value was for 2004.

#### 3.2.3. Cluster Membership Likelihood

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Spatial distribution of monitoring points and interpolation results of underground water levels in 2005.

**Figure 3.**Methodological flowchart and results of IBI (static load) extraction using the Landsat TM5 image: (

**a**) Landsat TM5 satellite image in 2006, (

**b**) flowchart of extracting IBI index (static load), (

**c**) results of extracting IBI index (static load) of Beijing in 2006 by Landset TM5 satellite image.

**Figure 4.**Spatial distribution of all variable values (except IBI and underground water level) in 2006: (

**a**) land subsidence, (

**b**) annual average rainfall, (

**c**) population, and (

**d**) nighttime light.

**Figure 6.**Spatial distribution of the regression coefficient for the underground water level in: (

**a**) 2004 (p-values = 0.0032), (

**b**) 2007 (p-values = 0.0025), and (

**c**) 2010 (p-values = 0.0041).

**Figure 7.**Spatial distribution of the regression coefficient for the static load (IBI) in: (

**a**) 2004 (p-values = 0.0022), (

**b**) 2007 (p-values = 0.0017), and (

**c**) 2010 (p-values = 0.0008).

**Figure 8.**Spatial distribution of the regression coefficient for the annual average rainfall in: (

**a**) 2004 (p-values = 0.0012), (

**b**) 2007 (p-values = 0.0020), and (

**c**) 2010 (p-values = 0.0032).

**Figure 9.**Spatial distribution of the regression coefficient for the population in: (

**a**) 2004 (p-values = 0.0142), (

**b**) 2007 (p-values = 0.0233), and (

**c**) 2010 (p-values = 0.0086).

**Figure 10.**Pseudo-F statistic (optimal number of clusters) for (

**a**) underground water, (

**b**) IBI, (

**c**) rainfall, and (

**d**) population.

**Figure 11.**Spatial distribution of clusters and parallel box plots showing a summary of the analysis (interquartile range, median values, and outliers from each variable regression coefficients) for underground water (

**a**), IBI (

**b**), rainfall (

**c**), and population (

**d**).

**Note:**the lines across box plots represent each cluster determined in our analysis; the variation in these lines is based on the median values from each variable; the color from each line is in agreement with the colors displayed in the maps (each color represents one cluster group).

**Figure 12.**Distribution of membership probability for (

**a**) underground water, (

**b**) IBI, (

**c**) rainfall, and (

**d**) population.

Category | Year | Spatial Scale | Source |
---|---|---|---|

Annual average subsidence rate | 2003–2010 | 30 m | https://earth.esa.int/ (accessed on 8 December 2021) |

Nighttime satellite images | 2003–2010 | 1 km | http://earthdata.nasa.gov/ (accessed on 8 December 2021) |

Land static load | 2003–2010 | 30 m | http://www.gscloud.cn/ (accessed on 8 December 2021) |

Annual average rainfall | 2003–2010 | 204 blocks (Beijing) | http://www.cma.gov.cn/ (accessed on 8 December 2021) |

Block population | 2003–2010 | 204 blocks (Beijing) | https://www.worldpop.org/ (accessed on 8 December 2021) |

Underground water | 2003–2010 | 204 blocks (Beijing) | http://www.cigem.cgs.gov.cn/ (accessedon 8 December 2021) |

Index | GTWR | GWR | OLS |
---|---|---|---|

AICC | 12,730 | 12,924 | 13,952 |

R^{2} | 0.672 | 0.524 | 0.062 |

Adjusted R^{2} | 0.671 | 0.523 | - |

RMSE | 6.681 | 12.355 | 17.344 |

Variable | Descriptive Statistics of Regression Coefficients | ||||
---|---|---|---|---|---|

Min | Max | Mean | Std. | CV | |

Underground water level (m) | −1.682 | 1.188 | 0.106 | 0.486 | 4.585 |

Static load (IBI) | −1.800 | 0.604 | 0.126 | 0.309 | 2.452 |

Annual average rainfall (mm) | −9.720 | 14.401 | −1.361 | 3.089 | −2.270 |

Population (10 thousand) | −0.917 | 1.734 | 0.027 | 0.322 | 11.926 |

**Table 4.**R

^{2}values (the effectiveness of each variable coefficient to divide the features into clusters).

Variable | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 |
---|---|---|---|---|---|---|---|---|

Underground water | 0.754 | 0.847 | 0.714 | 0.626 | 0.762 | 0.750 | 0.610 | 0.563 |

IBI | 0.440 | 0.670 | 0.335 | 0.292 | 0.481 | 0.325 | 0.301 | 0.364 |

Rainfall | 0.635 | 0.843 | 0.599 | 0.550 | 0.561 | 0.674 | 0.601 | 0.539 |

Population | 0.274 | 0.727 | 0.255 | 0.248 | 0.261 | 0.302 | 0.330 | 0.360 |

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**MDPI and ACS Style**

Zhao, B.; Yang, X.; Wu, Q.; Xiao, W.; Yang, W.; Deng, M.
Uncovering the Structural Effect Mechanisms of Natural and Social Factors on Land Subsidence: A Case Study in Beijing. *Sustainability* **2022**, *14*, 10139.
https://doi.org/10.3390/su141610139

**AMA Style**

Zhao B, Yang X, Wu Q, Xiao W, Yang W, Deng M.
Uncovering the Structural Effect Mechanisms of Natural and Social Factors on Land Subsidence: A Case Study in Beijing. *Sustainability*. 2022; 14(16):10139.
https://doi.org/10.3390/su141610139

**Chicago/Turabian Style**

Zhao, Bin, Xuexi Yang, Qianhong Wu, Weifeng Xiao, Wentao Yang, and Min Deng.
2022. "Uncovering the Structural Effect Mechanisms of Natural and Social Factors on Land Subsidence: A Case Study in Beijing" *Sustainability* 14, no. 16: 10139.
https://doi.org/10.3390/su141610139