Field measurement and numerical simulation of the relationship between the vertical wind environment and building morphology in residential areas in Xi’an, China

The inadequate consideration of the impact of building morphology on ventilation efficiency in many urban residential areas has resulted in a series of environmental problems that threaten human health. The purpose of this paper is to establish a predictive model between ventilation efficiency and building forms in residential areas. First, the characteristics of the vertical wind profile in residential areas were measured using unmanned aerial vehicle (UAV). Second, the wind speed ratio (WSR) at different height levels under the impact of morphological index (floor area ratio, building density, average building height, enclosure degree, height fall, and maximum building height) in the residential area was simulated by ENVI-met. Two kinds of prediction formulas were finally obtained: (1) the average ventilation efficiency at the pedestrian level and (2) the prediction formula of WSR at different heights. The results show that the wind speed (WS) in residential area below 35 m is about 0.6 m/s lower than that in green park. The numerical simulation shows that the mean WSR at the pedestrian level is negatively correlated with each index, and the height fall morphological index has the largest impact on the WSR at different heights. The research provides a reference for the optimal planning and design of ventilation efficiency of residential buildings, especially those in static wind areas.


Introduction
The urbanization of China has led to a large increase in the number of urban residential areas, which give rise to many environmental problems while satisfying the housing needs of residents. Insufficient consideration of ventilation efficiency in residential areas can have an adverse impacts on air pollution reduction, high temperature weather mitigation, and human thermal comfort, or even cause the spread of epidemics (Mochida and Lun 2008;Vazquez-Prokopec et al. 2010;Yuan et al. 2014;Hong and Lin 2015;Feng et al. 2021). Urban residents generally spend more than 2/3 of their time in residential area (State Bureau of Technical Supervision 2018). It is therefore of great significance to enhance the ventilation efficiency in residential areas for residents' health and quality of life.
The previous studies on residential wind environment were carried out from two aspects: planning and layout, and building morphology. Some scholars discussed the correlation between building layout and ventilation efficiency of residential areas. Asfour et al. simulated the wind field of different types of residential area layout by CFD. The results showed that the residential buildings arranged around a central space, forming a layout open to the prevailing wind, can make the residential area well-ventilated (S. 2010). Some scholars also paid attention to the relationship between building morphology index and ventilation efficiency of the wind environment. Kubota et al. (2008), for example, found a striking correlation between BD and the WSR at mean pedestrian level from wind tunnel test results in 22 Japanese urban residential areas,. Yang et al. (2013) measured the wind environment of 10 high-rise residential areas in central Shanghai. They found that the ventilation efficiency in the pedestrian area is significantly related to the ED of the buildings and the green space, and that a 10% increase in SVF can raise the WSR by 7~8% (Yang F 2013). Li et al. (2018) studied the correlation of the FAR with the ventilation efficiency of residential areas, and reported that when the FAR rises from 0.63 to 2.32, the mean WSR of residential areas declines by 0.18 (Li et al. 2018). This paper mainly discusses the influence of building morphology index on ventilation efficiency of residential areas, from pedestrian height and vertical direction.
The previous studies mostly focused on the impact of building morphology factors on ventilation efficiency at the pedestrian height, but few of them investigated the impact in the vertical direction (To and Lam 1995;Jones et al. 2004;Du et al. 2017;Mittal et al. 2019). Some scholars have explored the wind profile on the urban scale. In 1981, Landsberg and Helmut proposed that the roughness of the city would affect the surface resistance, WS, and the wind profile of the city (E 1981(E ). NG et al. (2011, after considering the dense urban morphology and the impact on the wind field, made a highresolution map of Hong Kong's urban surface roughness by using a mapping method, which provided guidance for urban planning. Liu et al. (2017) constructed a full-scale urban model with a length of 2-20 km, simulated the urban wind flow via RANS (Reynolds average Navier-Stockes) equation, and compared the differences of wind profiles in the vertical direction with and without building details. In fact, most of the recent studies regarding wind environment are conducted on the urban scale, or from pedestrian level, and few focus on the vertical wind environment on the residential area scale.
The purpose of this paper is to investigate the relationship between the design index of residential buildings and the ventilation efficiency. The research mainly includes the following aspects: (1) to compare the difference of wind profile between open areas and residential areas in the city; (2) to explore the coupling mechanism between the ventilation efficiency and the building morphology of residential areas at different heights; and (3) to establish a predictive model in residential areas at different heights. This paper can provide reference for improving the ventilation efficiency of residential areas, especially those in low WS cities and regions.

Field measurements
Xi ) is located in the Guanzhong Basin in the middle of Weihe River Basin. Xi'an has a warm semi humid continental monsoon climate with four distinct seasons and relatively dry air (Jin et al. 2014). The annual dominant wind direction in Xi'an is 67.5°(the north is 0°, and the east is 90°), the wind frequency is 11%, the static wind (0-0.2 m/s), the frequency is 35%, the outdoor mean WS in summers is 1.9 m/s, and the outdoor mean WS in winters is 1.4 m/s (Ministry of Housing and Urban-Rural Development 2012). Located in an area with a low WS, Xi'an faces great challenges in air pollution, heat island effect, and other issues.
In this paper, an outdoor park and a typical residential area in Xi'an are selected to compare the differences of near surface wind profiles of different land use types. The measurement was carried out on August 13, 2017. The information about the measurement points is given in Table 1.
The wind data of the vertical wind environment were measured by the test equipment carried by the UAV at typical points in the selected area within a height range of 1.5-100 m, and the data were collected through a 5-min hovering every 10 m. The vertical wind profiles of the residential area and park were tested.
In order to evaluate and compare the wind environment in various locations, the WSR index was used to evaluate the ventilation efficiency in residential areas at different heights (FL. 2005;Ren Chao et al. 2017).
V ∞ is the wind speed at the top of the boundary layer (where the wind speed is not affected by the urban canopy), m/s; V P is the wind speed at a certain height above the ground, m/s; VRw is the ventilation efficiency at the current level affected by the built-up area.

ENVI-met simulation
The ENVI-met adopted in this paper was a simulation program of urban microclimate developed by Michael Bruce to simulate the wind and thermal environment on a block scale (Bruse et al. 1998). In recent years, ENVI-met has been widely applied in the field of urban wind environment (Jung et al. 2006;Á 2013;Wang et al. 2019).
The simulation study was carried out on a residential area with a length of 400 m and a width of 380 m (Fig. 2). The morphological parameters were changed according to the principle of control variables. When the parameters of each line change, other morphological parameters remain the same as those of the basic model. Thus, the impact of a single design variable on the mean WSR of the whole area was compared by altering it. The design variables included ABH, BD, FAR, ED, HF, and MBH. Table 2 lists the variation range of each design variable.
The data of air temperature, relative humidity, WS, and wind direction on June 21, 2019 were measured by HOBO U23-001 (air temperature: from −40 to 70°C, accuracy: ±0.21°C over 0-50°C; relative humidity: from 0 to 100%, accuracy: ±2.5% over 10-90%), UAV, and on-board equipment, which were used as input values of the simulation software (Table 3). The accuracy of the simulation software is verified by the measured and simulated data of Xi'an Finance and Economics Campus. As shown in Fig. 3, the average relative error between the measured and simulated WS was 13.5%. Figure 4 shows the WS distribution characteristics at different heights of Zishui Park. In general, the mean WS increases with the rising height. Specifically, the minimum and maximum of the mean WS measured at the heights of 1.5 m (the pedestrian level) and 100 m are 1.07 m/s and 3.98m/s, respectively. From 1.5 to 12 m, the WS surges with the rising height,  That is because there are many trees and artificial facilities in Zishui Park, and those obstacles near the ground slow down the WS.

Surface wind profile difference between urban builtup areas and open area
The WS distribution characteristics at different heights of Shijiaxingcheng Community are shown in Fig. 5. In general, the mean WS increases along with the height. Specifically, the minimum and maximum of the mean WS measured at the heights of 1.5 m and 80 m are 0.56 m/s and 2.56 m/s, respectively. In the height range of 1.5-12 m, the WS increases rapidly with the rising height. Each 10 m of increase in the height raises the WS by 1 m/s. In the height range of 12-36 m, the WS dwindles with the rising height. The WS decreases by 0.06 m/s for every 10 m of height increase. In the range of 36-100 m, the WS increases slowly with the height, by 0.19 m/s with every 10 m increase in height.
It can be seen that the WS in the residential area below building heights is significantly lower than those in the park area. The mean WS measured below 35 m in the residential area and park is 1.2 m/s and 1.8 m/s, respectively. Residential buildings reduce WS by about 0.6 m/s.

Single factor correlation between vertical wind environment and morphological index
This part will further explore the influence of building form on the ventilation efficiency at the pedestrian level and in the vertical direction, and summarize the reasons for the difference in vertical wind profile in the residential area through single factor analysis and multi-factor analysis. The results contain two parts: the WSR at the pedestrian level (1.5 m) and the vertical WSR at different heights.

Impact of ABH on WSR
Relationship between WSR and ABH at the pedestrian level As shown in Fig. 6, the area of low WS region gradually increases along with the average height. Specifically, when the average height is 10 m, the average horizontal WSR at the pedestrian level reaches the maximum of 0.609, and then decreases slowly with the increasing ABH. In addition, the maximum WS increases slowly with the increasing average height. When the average height is 60 m, the maximum WS reaches 5.87 m/s; the minimum WS varies from 0.02 to 0.06, but its correlation with the average height is small. It can be seen that the ventilation efficiency at the pedestrian level dwindles with the increasing average height, resulting in accelerated winds.
Relationship between WSR and ABH at different height levels As shown in Fig. 7, the mean WSR at different horizontal heights increases with the rising height. This indicates that built-up area obstructs the mean WSR to different degrees. At the same horizontal height, different ABHs have no obvious correlation with the mean WSR, but when the horizontal height is greater than 20 m, the average height exerts a growing attenuation effect on the mean WSR. In the vertical direction, the increase rate of the mean WSR increases with the rising height, showing a trend of first decreasing and then increasing. Specifically, when the mean WSR is below 0.65, the increase rate of the mean WSR gradually decreases with

Impact of BD on WSR
Relationship between WSR and BD at the pedestrian level As shown in Fig. 8, with the increase of BD, the low WS area at the pedestrian height around the building gradually increases, and gradually approaches the static WS. Specifically, when the BD is 4.9%, the WSR of the average pedestrian height level is 0.592, which then dwindles with the increasing BD. Moreover, the maximum WS increases along with the BD. When the BD is 51.9%, the maximum WS reaches 5.92 m/s, and the minimum WS varies between 0.03 and 0.19. They are insignificantly correlated with the BD. It can be seen that the BD has a negative correlation with the WSR at the average pedestrian height and a positive one with the maximum WS. The increase in the BD reduces the ventilation efficiency at the pedestrian height level, leading to a greater WS.
Relationship between WSR and BD at different height levels It can be seen from Fig. 9 that the mean WSR at different horizontal heights increases along with the height. At the same horizontal height, the increase rate of the mean WSR below 20 m decreases with the rising BD because the building height is 20 m. Below 20 m, owing to the obstruction of the buildings, the smaller the mean WSR and the denser the built-up area, the greater the obstruction to the wind. When the vertical height is over 20 m, the increase rate of the mean WSR has little correlation with the increasing BD, but in the case of a 51.9% BD, the increase rate of the mean WSR is the largest. For every 1 m increase in the vertical height, the mean WSR rises by 0.17.

Impact of FAR on WSR
Relationship between WSR and FAR at the pedestrian level As shown in Fig. 10, when the FAR is 0.403, the mean WSR at the pedestrian level reaches the maximum of 0.609, and then decreases slowly as the FAR increases. The maximum WS rises with the increasing FAR. When the FAR is 2.684, the maximum WS is 5.87 m/s, and the minimum WS varies between 0.02 and 0.06. Furthermore, with the increasing FAR, the mean WSR at the pedestrian height level gradually declines, which will lead to a greater WS.
Relationship between WSR and FAR at different height levels As shown in Fig. 11, the mean WSR increases along with the vertical height, which indicates that in built-up areas, WS is hindered. At the same height, the correlation between different FARs and the mean WSR is slight. Additionally, the mean WSR decreases first and then increases with the change of height. When the mean WSR is below 0.7, the increase rate of the mean WSR decreases with the rising height. But after the mean WSR reaches 0.7, the increase rate of the mean WSR in different FAR scenarios rises gradually with the vertical height.

Impact of ED on WSR
The relationship between mean WSR and the ED at the pedestrian level As shown in Fig. 12, as the ED rises, the area of low WS in the center of the site increases gradually. Specifically, when the closure is 0.092, the mean WSR is 0.630, which then dwindles with the increasing ED. In addition, when the ED is 0.378, the maximum WS drops to the minimum of 5.74 m/s, and the minimum WS ranges between 0.03 and 0.05. Furthermore, the ED is negatively correlated with the mean WSR at the pedestrian level. This indicates that the increase in the ED will reduce the ventilation performance at the pedestrian height level in the residential areas.
Relationship between WSR and ED at different height levels It can be seen from Fig. 13 that the mean WSR of each scene increases along with the vertical height. When the vertical height is smaller than 30 m, at the same horizontal height, the larger the ED, the smaller the mean WSR. In the vertical direction, the increase rate of the mean WSR declines with the increasing ED. The increase rate of the mean WSR is the largest at the ED of 0.092. When the vertical height increases by 1 m, the increase rate of the mean WSR is about 0.0104 and it is the smallest when the ED is 0.533. Every 1 m increase in the vertical height raises the mean WSR by about 0.00775. Under 30 m, the larger the ED, the greater the wind blocking effect. The increase in ED will lead to a general reduction in the ventilation efficiency around residential buildings.

Impact of HF on WSR
Relationship between the mean WSR and HF at the pedestrian level As shown in Fig. 14, mean WSR decreases with the rising HF at the pedestrian level. When the HF is 10, the ratio of mean WS at the pedestrian height level is 0.560, which then decreases slowly with the increasing HF. The maximum WS increases slowly with the rising HF. When the HF is 70, the maximum WS reaches the maximum of 5.57 m/s, and the minimum WS always ranges between 0.03 and 0.09, showing a descending trend. It can be seen that the HF has a negative correlation with the mean WSR at the pedestrian level and the minimum WS, and a positive relationship with the maximum WS. It shows that high-rise residential buildings will reduce the ventilation efficiency at the pedestrian level, and result in a high WS. Figure 15 shows that the mean WSR of each scene increases with the rising vertical height, except for the scene with an HF of 10 m. When the vertical height is below 20 m, the correlation between different HF and the mean WSR at the same horizontal height is weak. For every 1 m increase in vertical height, the mean WSR corresponding to different HF increases by about 0.018. When the vertical height is greater than 20 m, the increase in the HF will cause a reduction in the mean WSR. When the HF is 70, the increase rate of the mean WSR is the largest. Each 1 m increase in the vertical height will lead to an increase of 0.0027 in the mean WSR. The possible reason is that the wind is hindered by four high-rise buildings. Thus, it can be concluded that the variation of the HF impacts the mean WSR mostly in the area above the average height of the site. The larger the HF, the more obvious the blocking effect of highrise buildings on the wind.

Impact of MBH on WSR
Relationship between mean WSR and MBH at the pedestrian level It can be seen from Fig. 16  Relationship between WSR and MBH at different height levels Figure 17 shows that, in general, the mean WSR of each scene increases along with the vertical height, and the correlation between the maximum height and the mean WSR is weak at any horizontal height. When the vertical height is below 20 m, the increase rate of the mean WSR in different scenes tends to be equal. For every 1 m increase in the vertical height, the mean WSR of each scene increases by about 0.014. When the maximum height is 100 m, the mean WSR is relatively large. When the vertical height is above 20 m, the maximum height is weakly correlated with the mean WSR. When the maximum height is 80 m, the increase rate of the mean WSR is the lowest. Every 1 m increase in vertical height raises the mean WSR by about 0.012. Thus, there is no significant correlation between the maximum height and the mean WSR, and the ABH of the site is the dividing line that affects the change rate of the mean WSR in the vertical direction.

Multi-factor correlation between vertical wind environment and morphological index
The single factor analysis of wind environment in residential area is insufficient. Therefore, based on the previous sections, the prediction formulas for the mean WSR at the pedestrian level and vertical wind environment are established respectively.
Multiple linear regression formula for WSR at the pedestrian level The results of the 37 scenarios simulated above are integrated (according to Table 2), and the regression equation of the average pedestrian horizontal mean WSR is obtained through the SPSS software. Due to the differences in the order of magnitude and unit of each index, the following regression equation and R 2 are finally obtained by standardizing the data: In Formula (1), U1 is the mean WSR at the pedestrian level in the residential area under the specific form combination. It can be seen that R 2 is 0.855, indicating that the sample regression effect is good; F test statistic f = 28.565, and associated probability p < 0.001, which indicates that there is a linear Fig. 7 Correlation between the ABH and the mean WSR in the vertical direction Fig. 8 Correlation between the mean WSR at the pedestrian level and the BD R 2 ¼ 0:855 À Á regression relationship between the independent variable and the dependent variable; the independent variables with an associated probability p below 0.05 include average height (P < 0.013), BD (P < 0.001), HF (P < 0.005), and maximum height (P < 0.015). This implies that the WSR at the pedestrian level has a significant linear relationship with the average height, BD, HF, and the maximum height. The influence degree of each index in descending order is as follows: the HF > the MBH > the ABH > the BD > the FAR > the ED.

Multiple linear regression formula for vertical WSR prediction
The simulation results of the above 381 scenarios are taken as the basic data and standardized to obtain the following regression equation and R 2 : In Formula (2), U2 is the mean WSR at any horizontal height in the residential area under the specific combination of forms, and VH is the vertical height. It can be seen that the coefficient R 2 is 0.801, which indicates that the regression effect of the sample is good; the statistic of F test is f = 212.42, and the associated probability is p < 0.001, indicating that there is a linear regression relationship between the independent variable and the dependent variable. Furthermore, the vertical height (P < 0.001) is only the independent variable with an associated probability (p) of below 0.05, which indicates that there is a significant linear relationship between the vertical height and the WSR of any horizontal plane. The relationship between other building shape indexes and vertical WSR is insignificant. The influence degree of each index in decreasing order is VH > HF > MBH > ABH > FAR > BD > ED.

Discussion
This paper aims to establish the relationship between ventilation efficiency and building morphology of residential areas. The following will be further discussed in combination with relevant research.
The present study shows that, the mean WSR at the pedestrian height level has a significant linear correlation with the average height, BD, HF, and the MBH. Some scholars also studied the relationship between the WSR at the pedestrian level and the building morphology. Kubota et al. (2008), in a wind tunnel experimental study on the relationship between WS and BD in Japanese detached houses, concluded that the higher the BD, the smaller the mean WSR. According to Feng et al. (2021), the WSR at the pedestrian level is negatively correlated with the average height. Yang et al. (2020) found that the increase in ED is not conducive to the diffusion of air Fig. 9 Variation curve between different BD and mean WSR in the vertical direction Fig. 10 Correlation between mean WSR at the pedestrian level and FAR pollutants in the built-up areas. The results of this paper also demonstrate that the increase in ED will reduce the ventilation efficiency of residential area, which is not conducive to the air circulation in residential area or blocks. Yang et al. (2016) simulated the summer monsoon environment in Xinjiekou area of Nanjing, and, through multiple linear regression analysis, found that the WSR at the pedestrian level has a negative correlation with BD and ED, but a significant, positive linear correlation with the average height. Nonetheless, the results of this study show that the mean WSR at the pedestrian level will be affected by the blocking of buildings. This may be ascribed to the different building geometries, building densities, building intervals, WS, and directions adopted in Yang's simulation and this study. Adamek et al. (2017) pointed out that the high-rise buildings in urban spaces will increase the near-surface WS. It can be concluded that the WSR at the pedestrian height level is negatively Fig. 11 Correlation between the change of FAR with the average height and the mean WSR Fig. 12 Correlation between the mean pedestrian level WSR and ED Fig. 13 Correlation between the mean WSR and different ED in the vertical direction correlated with the BD, the average height, and the ED, yet positively related to the MBH. In practice, planners and designers can refer to these research results to improve the safety and comfort of the wind environment in residential areas.
In terms of the vertical wind profile, the single factor analysis results show that the increase in each single indicator of building morphology will lead to a reduction in ventilation efficiency. The results of multi-factor analysis demonstrate that the mean WSR has a significant positive correlation with the vertical height, and an insignificant linear one with other building morphology indicators. The relevant studies focus mostly on the scale of the city. The research results of Liu (2011) proved that the wind profiles in urban center and rural areas are quite different, so are the degrees to which WS increases with the height from the ground. Grimmond and Oke (1999) reported that the horizontal component of wind profile becomes smaller due to the blocking of urban built-up areas. In the present study, by observing the shape of the wind profile, it can be seen that the wind in the area with buildings is greatly blocked and the ventilation efficiency is reduced, while the WS in the area without buildings is significantly increased. Yuan et al. (2012) studied the ways to improve the ventilation in high-density cities, and, by comparing the Fig. 14 Correlation between the mean WSR at the pedestrian level and HF Fig. 15 Correlation between the mean WSR and different HFs in the vertical direction Fig. 16 Correlation between the mean WSR at the pedestrian level and MBH differences in vertical wind profiles, proposed to improve the ventilation at the pedestrian level by separating single buildings and reducing the overall building coverage of the site. This strategy is consistent with the principle of reducing the BD and ED of residential areas in this paper, because the increase in these two indicators will reduce the WSR at any height level (Yuan et al. 2014). To sum up, the existence of urban built-up areas inevitably reduces the near-surface ventilation efficiency. Thus, planners and architects need to fully consider the regional meteorological conditions and building morphology.

Conclusion
Based on one typical determinant residential area, the present paper, through field measurement and numerical simulation methods, discusses the influencing factors of the ventilation efficiency at different height levels in the residential area. The main conclusions are as follows: 1) The mean WS measured below 35 m in residential areas and park areas are 1.2 m/s and 1.8 m/s, respectively. Residential buildings reduce WS by about 0.6 m/s. This shows that the presence of residential buildings greatly reduces the inflow of wind. Thus, it is particularly important to optimize the layout of residential buildings to let more winds in.
2) The results of single factor analysis show that the mean WSR at the pedestrian height level has a negative correlation with each of the indicators studied.
3) The results of multi-factor analysis show that the ventilation performance at different heights is positively related to the building height and the MBH. The HF has the greatest influence on the WSR at all heights in the residential area. This indicates that to improve the ventilation efficiency among buildings, the height difference should be minimized.

4)
The research can provide data support for the establishment and improvement of wind environment standards in residential areas, and provide a reference method for optimizing the ventilation efficiency in different regions, especially in static wind areas.
This study discusses the quantitative relationship between residential block form and ventilation efficiency. It should be pointed out that there are some limitations. First, this study only discusses aligned communities. Future studies should be carried out on other layout of blocks so as to further compare the differences among layout. Second, this study focuses on the summer situation. The differences between the different seasons are to be analyzed in the future. It is hoped that an integrated prediction model can be established eventually. Data availability Data will be sent based on request.

Declarations
Ethics approval and consent to participate Not applicable.

Consent for publication Not applicable.
Competing interests The authors declare no competing interests.