3.1. Measurement and Screening of Landscape Spatial Structure Index
The selection of indicators should be careful, as highly correlated indicators may bring the threat of redundant information [
26]. For example, in multivariable regression, the multicollinearity between the independent variables will lead to the larger confidence interval of the parameter and the sign error of parameter fitting, and the wrong result will be obtained by hypothesis testing [
27]. Variance inflation factor (VIF) is an important index to quantify the degree of multicollinearity. The higher the collinearity between independent variables, the larger the VIF value. The empirical judgment method shows that a VIF value greater than 10 indicates that the model has severe multicollinearity [
28]. After obtaining the results of 13 landscape spatial indicators by Fragstats 4.2 software (
Appendix A,
Table A1), multicollinearity test was carried out. According to VIF values in
Table 3, the variables selected in this paper have serious multicollinearity and need to be screened for indicators.
The most common way to solve multicollinearity is to find the explanatory variable that causes multicollinearity and exclude it. Spearman’s rank correlation coefficients (RHOs) are nonparametric indicators that measure the dependence of two variables. Pairwise correlation Spearman rank correlation coefficients were tested for all 13 variables. Among them, the correlation coefficients were ±0.75–1.0 for strong correlation, ±0.5–0.75 for moderate correlation and ±0.25–0.5 and ±0–0.25 for weak correlation and no correlation, respectively. According to the Spearman rank correlation coefficient, the high correlation indicators with large absolute values were sorted from largest to smallest in order to achieve preliminary screening of indicators. The Spearman rank correlation coefficient matrix of all variables is shown in
Table 4, and the variable combinations with higher coefficients are shown in
Table 5.
According to Spearman rank correlation coefficient matrix, landscape spatial form index was eliminated in further analysis, and variables highly correlated with other variables and with high correlation frequency were given priority to be eliminated. Combined with the correlation between the indicators and the applicability of the representation of urban spatial form, four indicators were left: Patch Class Area (CA), Largest patch area (LPI), Patch Density (PD) and Mean Euclidean Nearest Neighbor Distance (ENN-MN). These four indicators represent the four dimensions of urban spatial form: city scale, dominance, compactness and dispersion.
CA is equal to the sum of all the construction land patch areas within the urban cluster. The size of urban patch not only affects the urban productivity but also affects the healthy development of residential environment [
29]. This indicator helps reveal the size of cities, which can reduce vegetation cover and lead to a decrease in carbon sinks. This will have a negative impact on the carbon cycle, resulting in an increase in carbon emissions.
LPI is the area proportion of dominant patch types in the landscape, which can describe the degree to which an urban cluster area is characterized by a single nuclear development pattern on the type scale. The larger the value is, the larger the contiguous area of urban patches is, which directly affects the carbon emission. The stronger the advantages of the core area and the more concentrated the resources, the lower the cost of infrastructure construction connecting the patches, and the increase in round-trip activities and transportation distance will also lead to the increase in carbon emissions.
PD represents the patch area per unit area, and the greater the value, the greater the patch density per unit area in the urban cluster. Compactness is the core concept of urban sustainable development [
30], and its quantitative index is an effective method to evaluate the internal structure of urban spatial clusters. Compact development allows for shorter distances between different parts of the city, and shorter distances reduce the need for car traffic, directly reducing carbon emissions. In addition, urban compactness indirectly affects ecological environment, industrial production, travel choice and other factors, thus affecting carbon emissions.
ENN-MN quantified the average distance between the two closest urban built-up patches, which could be interpreted as the spatial linkage value between urban patches. The larger the value, the higher the degree of urban growth and expansion. This index can measure the spatial correlation between urban patches. The higher the dispersion of urban patches, the higher the cost of infrastructure construction to connect the patches, and the increase in round-trip activities and transportation distance will also lead to the increase in carbon emissions.
After the selection of landscape spatial form, in order to further understand the correlation between landscape spatial form and carbon emission, according to the natural discontinuity method, the spatial distribution map of landscape spatial form index in Zhuhai was obtained (
Figure 3), and the distribution characteristics of variables were analyzed.
As can be seen from
Figure 3a, the overall distribution of large urban clusters in Zhuhai is relatively uniform. Since this index has a large correlation with the total area of urban clusters, the scale of urban clusters in Xiangzhou District (eastern central urban area) is relatively small. As can be seen from
Figure 3b, the urban clusters with high dominance in Zhuhai are mainly located in Xiangzhou District. Due to the long development time within these clusters, the fragmented built-up areas within them have been basically contiguous, and the dominance of large built-up patches is strong. In contrast, the dominance of the western district of Zhuhai is relatively low. As can be seen from
Figure 3c, the areas with high patch density (PD) are mainly distributed in the western suburbs of Zhuhai (Doumen District and Jinwan District), especially the central district of Jinwan, Hezhou high-speed railway Station and Fushan Industrial Zone. The main reason is industrial structure. Due to the large amount of farmland and other ecological land, the patches of construction land are cut into small pieces, resulting in high patch density. On the contrary, the patch density in eastern central city was lower. As can be seen from
Figure 3d, ENN_MN was generally high and evenly distributed, showing a high distribution in the west and low distribution in the east. The high dispersion of most clusters in the western suburbs of Zhuhai reflects that the construction of a large number of new towns and the expansion of construction land in the western suburbs in recent years lead to the high dispersion of built-up areas. The high dispersion of Xiangzhou District (central urban area) is mainly in the east coastal zone. These areas are mainly blocked by terrain, and the patch dispersion is high. The central area of Jinwan in the western suburbs of Zhuhai and the high-tech zone in the north of Xiangzhou District are depressions with group dispersion. The construction land in these places is mainly distributed in the plain, and the built-up areas are basically contiguous with low dispersion.
3.2. The Results of Social Spatial Structure Measurement
The social space indicators in urban spatial form are calculated, and the results are divided into five levels according to the natural discontinuity method, as shown in
Figure 4. Social spatial index factors are few, and there is no high correlation between each other, so it does not need to be screened.
As can be seen from
Figure 4a, the densely populated areas of Zhuhai are mainly distributed in Xiangzhou (the central area of Zhuhai), especially Qianshan Cluster and Shishan Cluster. Jingan Cluster, as the central urban area of Doumen District (western suburb) and one of the sub-centers of Zhuhai, has a high population density too. In contrast, the population density of other clusters is lower, and there is still a large room for population growth. As can be seen from
Figure 4b, there are more high-value areas of residential building area and relatively dispersed areas. For example, Xiangzhou District, aviation industrial Park in the western suburbs and Doumen Center and other clusters of residential buildings are relatively high, which is basically consistent with the distribution of densely populated areas. In the southwest of Zhuhai, the residential area of the cluster is small. This area is an industrial intensive area, which is dominated by industrial land. As can be seen from
Figure 4c, there is a large gap between the east and west of Zhuhai in terms of commercial building area. Xiangzhou district in the east is generally higher, while Doumen District and Jinwan District in the west is generally lower. It reflects the commercial development gap between the East and west of Zhuhai. As can be seen from
Figure 4d, different from the commercial building area, the industrial building area of Zhuhai is generally higher in the west and lower in the east. The industrial layout of Zhuhai is mainly in the western district, especially the booming development of Gaolan Industrial zone and Fushan Industrial Zone, which result in the large industrial building area of these two clusters. The industry in the east has basically completed the relocation, and the industrial structure is dominated by the tertiary industry.
3.3. The Influence of Urban Spatial Form on Carbon Emission
The carbon emissions of each cluster in Zhuhai are obtained by adding the values obtained by the direct and indirect measurement methods, as shown in
Figure 5. Zhuhai’s carbon emissions totaled 6.16 million tons. According to China’s county-level carbon dioxide emission inventory [
31], Zhuhai’s carbon dioxide emission in 2017 was about 16.13 million tons. Since one ton of carbon completely burned in oxygen produces about 3.67 tons of carbon dioxide, the resulting carbon emission from the inventory is about 4.4 million tons. Considering that the carbon emission in 2020 is calculated in this paper, the result is not much different from that calculated in this paper, which is considered to be basically reasonable.
As can be seen from
Figure 5, The high-value area of Zhuhai carbon emission is the aviation industrial park and Nanhu Cluster in the south of the western suburbs, which are basically consistent with the distribution area of heavy industry. In addition, Nanping Town in the west of Xiangzhou District, the high-tech zone in the north of Xiangzhou District and the west of Doumen District also have high carbon emissions.
In order to investigate the influence of urban spatial form on carbon emission, CA, LPI, PD, ENN-MN in landscape spatial form index and population density, residential building area, commercial building area and industrial building area in social spatial form index were taken as explanatory variables, and urban carbon emission was taken as explained variables. The least square regression model was used to conduct multiple regression analysis for the two clusters, respectively. The regression results of landscape spatial form and carbon emission of urban clusters are shown in
Table 6, and the regression results of social spatial form and carbon emission of urban clusters are shown in
Table 7.
In the regression of landscape spatial form and carbon emission, the overall R2 of model regression is 0.713, with good regression accuracy. It can be found that the four variables all have significant effects on carbon emissions (significance is 0).
According to the comparison of standardization coefficient values, city scale has the greatest influence on carbon emissions of each cluster (0.630), followed by city compactness (−0.498), city dispersion (−0.418) and dominance has the least influence (−0.388). The size of a city plays a role in promoting carbon emissions; that is, the bigger the city, the higher the carbon emissions. Compactness, dispersion and dominance have an inhibitory effect on carbon emissions; that is, the more compact the city is, the stronger the urban expansion is, the more dominant the core is, and the less carbon emissions will be. In addition to the dispersion, the results of the other three variables are consistent with our hypothesis. Considering the actual situation of Zhuhai, the cluster with high dispersion is generally the area with more construction land such as farmland and mountain forest, which makes the built-up area distributed scattered. These areas, however, emit less carbon because of the smaller amount of construction land, such as industrial land and residential land.
The inner land of the urban cluster tends to be saturated, so the urban scale can only be increased by outward expansion to obtain new land resources. However, it is of great significance to avoid excessive expansion of construction land to reduce carbon emissions. In addition, for each large cluster, enhancing the inner compactness of the city in a planned way and enhancing the advantage of the core area are also an effective way to reduce the carbon emissions of each urban cluster.
In the regression of social spatial form and carbon emission, the overall R2 of model regression is 0.709, with good regression accuracy. The residential building area and the industrial building area have significant influence on urban carbon emission.
According to the comparison of standardized coefficient values, industrial building area has the greatest impact on carbon emissions of each cluster (0.751), followed by residential building area (0.405). Both industrial and residential building area play a role in promoting carbon emissions; that is, the larger the industrial and residential building area, the higher the carbon emissions. Industrial carbon emissions and domestic carbon emissions are important sources of carbon emissions, and industrial carbon emissions account for a larger proportion, so it is necessary to prioritize emissions reduction in the industrial sector.