This study focused on Wuhan, a metropolis in central China with a major PM_2.5 pollution problem and typical metropolitan characteristics. Wuhan is an important industrial base and transportation center in central China, located in the east of Jianghan Plain, at the confluence of the Yangtze River and the Han River. Wuhan has a north subtropical monsoon climate with frequent rain throughout the year and four distinct seasons. PM_2.5 was determined to be the predominant pollutant for 86 days of the year in the Wuhan urban area in 2020, accounting for 32.3% of days in the year (http://hbj.wuhan.gov.cn/fbjd_19/xxgkml/zwgk/hjjc/hjzkgb/). Wuhan was ranked 87th out of 168 cities in the country in terms of monthly average PM_2.5 concentrations in November 2021. Wuhan’s built-up area was 812.39 km² as of 2019, ranking 10th in China (https://www.mohurd.gov.cn/gongkai/fdzdgknr/sjfb/tjxx/index.html).

Windward area ratio: The windward area ratio is the ratio of the front windward area of the building to the plot acreage. The windward area represents the total area of the windward surface blocked by the front of the building in the direction of incoming wind. The calculation method is as follows: λ f θ = A F A T (1)

In the formula, A F represents the sum of the front windward area of the buildings in the plot, which represents the θ direction of incoming wind; and A T represents the area of the plot.

Building volume density: The building volume density is the numerical value of the total building volume divided by the volume value, which multiplies the height of the tallest building in the plot by the plot area. This value reflects the spatial density of the buildings in the plot. The calculation method is as follows: V B = ∑ S i   H i S 0 H max (2)

In the formula, VB stands for building volume density, Si stands for the bottom acreage of the ith building, H_i stands for the ith building’s height, S0 stands for the area of the plot, and H_max stands for the height of the tallest building.

Building density: The building density is the ratio of the total area of the building base in the plot to the total occupied area. The calculation method is as follows: D B = S A S 0 (3)

In the formula, D_B stands for the building density in the plot, S_A stands for the total area of the building base in the plot, and S₀ stands for the area of total occupied plot.

Plot ratio: The plot ratio is the ratio of the gross floor area of the building on land to the net land area. The calculation method is as follows: R a = ∑ S F S L (4)

In the formula, R_a represents the plot ratio, S_F represents the gross floor area of the building on land, and S_L represents the net land area.

Building height standard deviation: The building height standard deviation is the standard deviation of all building height values in the plot and reflects the level of dispersion of the data. It also reflects the degree of difference and the staggering of building heights in the vertical direction of the plot. The calculation method is as follows: S = 1 N ∑ i = 1 N x i − x ¯ 2 (5)

In the formula, S represents the building height standard deviation, N represents the number of buildings in the plot, x i represents the height of the ith building, and x ¯ represents the average height of buildings in the plot.

In recent years, deep learning based methods have been widely used to estimate PM_2.5 concentrations with ground and satellite observations (Meng et al., 2021; Sun et al., 2021; Xu et al., 2021). In this study, the Deep Belief Net (DBN) model was employed to model the complex factors and relationships between the urban PM_2.5 concentration, satellite observations and meteorological data. The DBN model is a kind of Deep Neural Network, and it is composed of multiple restricted Boltzmann machine (RBM) layers and a back-propagation (BP) layer. An RBM is a generative stochastic artificial neural network that can learn a probability distribution over the input data. It is composed of two layers connected by weights. The first is a visible layer and the second is a hidden layer. The hidden layer of the previous RBM is the visible layer of the next RBM. In the experiment, two RBM layers and one BP layer were selected to estimate the ground PM_2.5 concentration. The PM_2.5 estimation model can be presented by P M 2.5 = f T O A , A n g , P B L H , P S , R H , T E M P , W S (6) where A n g denotes the satellite observation angles.

The PM_2.5 concentration annual average value of Wuhan central city in 2018 was obtained through performing inversion according to the above method. The estimated values were also validated by the measurements of ground stations. The RMSE is 6.524 μg/m³, which indicate that the employed estimation method is acceptable. As shown in Figure 3, the distribution of the PM_2.5 concentration in Wuhan showed an overall trend of high in the north and low in the south. Qingshan District and Dongxihu District had obvious high-value PM_2.5 distribution. Even the number of buildings is not much, these two areas are mainly industrial agglomeration areas, which are more likely to produce particulate pollution due to various factors such as industrial production, transportation, and ground dust. These findings show that the overall PM_2.5 pollution in Wuhan is significantly affected by industrial-related emissions. However, there are obvious low-value distribution areas along the Yangtze River and the areas near East Lake and South Lake. These areas are less affected by emissions from human activities, and it is easier for air pollutants to diffuse due to the open terrain and the lack of buildings.

The calculation results of each building form index are shown in Figure 4. Figure 4A shows the distribution of building volume density in Wuhan, revealing that the overall volume density distribution in Wuhan is relatively evenly, and only some areas in Hanyang District have higher volume density values. Because the buildings in these areas are densely distributed and their heights are relatively similar, the distribution characteristics of such buildings are less correlated with the diffusion of air pollutants, so they have no reference value. Figure 4B shows the distribution of building density. The closer to the city center, the higher the building density. On the contrary, the closer to the city edge, the lower the building density value. This distribution is consistent with common knowledge. The areas with lower building density in the south of Wuhan are far from emission sources, and their relatively open surfaces are more conducive to the diffusion of atmospheric pollutants, resulting in relatively lower PM_2.5 concentrations. However, the same factors were considered in the siting of high-emission industrial areas. This also makes the air particulate pollution in the north easier to diffuse. The densely built area in the middle of the city has become a buffer zone to a certain extent, absorbing and blocking the spread of near-surface particles. Figure 4C shows the plot ratio distribution. The spatial distribution pattern is basically consistent with the building density, and these two architectural form indices also indicated a similar situation. Figure 4D shows the distribution of the standard deviation of building heights. The standard deviation of building heights showed that most areas with large building standard deviations had lower PM_2.5 concentrations. This is because areas with large building standard deviations are usually located on the banks of rivers and lakes, which not only have lower building density, but are also more conducive to the diffusion of air pollutants. Figures 4E, F shows the windward area ratios in the north–south and east–west directions, respectively. Among them, the high windward area ratio values mostly appeared in areas with more significant PM_2.5 concentration changes. It can be speculated that when the windward area of a building is relatively large, the diffusion of PM_2.5 is affected to a certain extent.

The influence of building form on the diffusion of air pollution in Wuhan was further analyzed. Figure 5 shows the correlation between the building form indices and PM_2.5 concentration. Considering the windward area ratio is in different directions, the change of PM_2.5 concentration in corresponding directions is used instead of PM_2.5 concentration. The change of PM_2.5 concentration is calculated by PM_2.5 concentration value of each grid minus the corresponding value in corresponding direction, and then take the absolute value. In Figures 5A–D, the correlation coefficients are 0.056, 0.018, −0.061 and −0.158 respectively, and the p values are all larger than 0.05. It can be found that the four building form indices are not significantly correlated with PM_2.5 concentration. As can be seen from Figure 5E, the correlation between the change of PM_2.5 concentration in the east–west direction and the windward area ratio of buildings in Wuhan was not significant. The overall distribution was relatively uniform, and the correlation coefficient was 0.276, and p-value less than 0.001. As shown in Figure 5F, the change of PM_2.5 concentration in Wuhan in the north–south direction had an obvious correlation with the windward area ratio of the building, and the correlation coefficient reached 0.483 and the p-value less than 0.001. This phenomenon reveals that the diffusion of PM_2.5 concentrations in Wuhan is more significantly affected by the blocking effect of buildings. High-density north–south buildings can slow the spread of near-surface particulate pollution. These conclusions provide a reference for subsequent architectural planning.

To further explore the blocking effect of buildings in different seasons, the correlation coefficients between fine particulate matter concentration change and windward area ratio are calculated. As shown in Figures 6A–D, the correlation coefficients between fine particulate matter concentration and east-west windward area ratio are 0.164, 0.118, 0.188 and 0.184 respectively. It means that the blocking effect of buildings in east-west direction is not significant. However, the blocking effect is still slightly better in autumn than other seasons. Meanwhile, as shown in Figures 6E–H, the correlation coefficients are 0.494, 0.452, 0.497 and 0.437 respectively, and the p values are all less than 0.001. It is indicated that the building form is in favor of the diffusion of air pollutants in spring and autumn. It can also be found that the fine particulate matter concentration change is less related with windward area ratio in winter. It may because that the main wind direction in winter of Wuhan is north wind, while the steel factories and chemical factories are mostly located in northern Wuhan. The combined effect of weather and location makes the impact of building forms less significant.