4.2.2. Results and Analysis of LISA Cluster Map

We also use the LISA to visualize the haze aggregation characteristics of the nine blocks. The autoregressive analysis of the local space of nine blocks, combined with the block information table in Table 1, explains the specific spatial location and the saliency of agglomeration. The saliency is the Z value used in the theoretical introduction. In the experiment of this section, the Geoda tool is used for LISA analysis. We use red for H-H, blue for L-L, pink for H-L, and purple for L-H. The LISA maps of winter, spring, summer, and autumn are shown in Figure 7a–d.

**Figure 7.** LISA map of the nine regions in (**a**) winter. (**b**) spring. (**c**) summer. (**d**) autumn.

From the LISA map of Figure 7a, the low agglomeration area is in northern Beijing in winter, and the high agglomeration area is in the south of Beijing. The low agglomeration area is larger than the high agglomeration area. Thus, the central area of Beijing is the L-H type, where the haze concentration in the winter is far lower than the haze concentration of the surrounding area.

Compared with the winter, the concentration in Block 8 becomes the 'L-H' type, and the 'Fangshan' in Block 7 becomes the 'H-L' type. As a result, the haze pollution in the middle part of the high-concentration area in spring is degraded, so that the 'H-H' agglomeration area disappears in the spring, and the 'L-L' low-concentration area is the same as the winter consisting of the four areas of the northern area.

As shown in Figure 7c, the agglomeration characteristics in summer are apparent, and the northern blocks are still low-concentration areas. However, the haze concentration in southern Beijing begins to rise, forming an H-H agglomeration area.

Figure 7d shows that the central area of Beijing has become a high-aggregation pattern, which further expands into the south. In contrast, the haze concentration in the north has been in the 'L-L' agglomeration type.

The LISA maps for the above four seasons all pass the 5% significance level test, and spatial correlation types of regions in different seasons are shown in Table 5.


**Table 5.** Spatial correlation types of regions in different seasons.

The results in Table 5 are arranged in chronological order from top to bottom. Thus, we can analyze the temporal evolution of haze at the seasonal scale.


#### **5. Discussion**

In this paper, we propose a multi-convolution haze-prediction model to predict the daily haze pollution level in different areas of Beijing. We divide the predictions into nine regions and four seasons to study the fine-grained haze pollution and time characteristics. We use the haze level frequency histograms to present the results. From the degree of haze pollution at the seasonal scale, the intensity of haze pollution in Beijing is in the order:

autumn > winter > spring > summer. From the distribution of the pollution, the overall pollution in northern Beijing is weak, and the seasonal changes are also small. On the other hand, the haze pollution in the southern regions is intense and shows an aggregation trend.

Moreover, we use the global Moran's *I* to measure the correlation between haze and geographical location. The results show that, in general, haze in summer and autumn has regional aggregation characteristics, while in winter and spring the haze distribution is relatively random.

Since the global Moran's *I* can only reflect the overall correlation between the haze and the geographical location, we use the local Moran's *I*, the Moran scatter plot and the Local Indicators of Spatial Association (LISA) to study the spatial characteristics of haze in the vicinity. The results show that there are obvious agglomeration areas in summer and autumn, while the aggregation effects in spring and winter were relatively weak. Thus, the spatial distribution of haze in Beijing is as follows: the southern region presents a high-high agglomeration, while the northern region exhibits a low-low agglomeration. The temporal evolution of haze on the seasonal scale is according to the chronological order of winter, spring, and summer to autumn, the haze gradually becoming agglomerated.
