A Least Cumulative Ventilation Cost Method for Urban Ventilation Environment Analysis

-e correct urban building layout is an important influencing factor in urban ventilation, and the heat island effect has become an important factor affecting the quality of urban life. Optimization of the urban building layout can play a role in mitigating the heat island effect.-e traditional ventilation corridor analysis method, based on a least-cost path analysis, can only generate a fewmain ventilation corridors. It is difficult to obtain global ventilation results covering the whole study area using this method of analysis. On the basis of urban morphology and a least-cost path analysis, this study proposes a “least cumulative ventilation cost” method for analyzing urban ventilation. Taking Wuhan downtown as a research area, the urban ventilation environment under different wind directions and seasons was analyzed. -is method can effectively express the ventilation conditions throughout the whole study area and can simultaneously express the quality of the generated corridors effectively.-e results show thatWuhan has three levels of ventilation corridor. Moreover, the ventilation conditions in Wuchang (Wuchang, Qingshan, and Hongshan) are better than those in Hankou (Qiaokou, Jianghan, and Jiang’an).


Introduction
e urban heat island (UHI) effect is a phenomenon in which heat accumulates in an urban area due to people's activities and the buildings. It is one of the most prominent characteristics of the urban climate. With rapid urbanization and a continuous increase in population density, the UHI effect has become an important adverse factor affecting the quality of urban life [1][2][3][4][5]. UHI effects caused by highdensity urban buildings have been reported around the world; it has changed the urban thermal environment [6][7][8][9][10]. As a result of its effects on regional climates, urban hydrology, air quality, urban biological distribution and behavior, and many urban ecological processes, the UHI effect has raised a number of ecological and environmental issues [11][12][13][14][15]. Numerous studies have found that the effect is closely related to urban anthropogenic heat release, underlying surface properties and structure, vegetation coverage, population density, and weather conditions. Among many factors, urban ventilation conditions caused by the underlying surface properties and structure have a significant impact on the UHI effect [16][17][18][19][20]. In order for governments and city planners to make planning decisions intuitively, quantitative methods are needed to determine ventilation paths in urban planning [21][22][23]. e most common simulation methods of urban canopy ventilation corridors use wind tunnels, computational fluid dynamics (CFD), and morphological analysis based on GIS technology. Wind tunnels can be used for wind environment simulations at various scales [24][25][26]. Although wind tunnel simulations can objectively and realistically observe the details of changes of air flowing through the observation object, their high experimental costs, limited simulation range, and physical model accuracy requirements limit the popularity of this method. e CFD method is suitable for small-scale, high-resolution fluid simulations [27][28][29]. CFD is often used for industrial component design, building structure design, urban planning environment prediction, pollutant diffusion simulation, and the like. It has high reliability. However, due to the huge number of calculations involved, CFD is often used to simulate the wind environment of single, multibody, or small-scale building groups. is method is not suitable for large-scale urbanlevel wind environment simulations. e numerical simulation method uses GIS technology to analyze urban ventilation environments by calculating the surface roughness of the underlying surface [30][31][32][33][34]. Many studies have shown that this method can quickly and effectively analyze urban ventilation environments and is suitable for large-scale analysis of ventilation environments. Its implementation can be divided into two main approaches, one based on rules and the other based on a leastcost path analysis (hereafter, the LCP-based method) [35][36][37]. e rule-based method is based on the ventilation analysis results of small-scale building groups in wind tunnel experiments or CFD experiments. is method can obtain the relationship between urban morphological parameters (such as the frontal area index, or FAI) and ventilation conditions, establish a rule recognition model, and then use the model to analyze the ventilation environment of the entire city. e FAI is one of many surface roughness indicators. It represents the ratio of the projected area of the building on the normal plane of the wind direction to the projected area of the analysis region. e larger the value is, the greater the wind resistance is. Yuan [38] used the FAI to analyze the ventilation environment of Wuhan and obtained an intuitive result of potential air paths. e rule-based method is simple and easy to understand, which is conducive to implementation in planning, but under this method, it is particularly difficult to analyze the dynamic differences of urban ventilation environments under different background wind conditions. Based on the roughness index, the LCP-based method uses a least-cost path analysis to obtain a more accurate ventilation corridor distribution. is method can dynamically analyze the ventilation corridors of the urban canopy following changes in wind direction. e LCP-based method assumes that the airflow always flows in the direction with the lowest wind resistance, and the path with the least accumulated wind resistance is the ventilation corridor [30]. Many constructive results have been obtained using the LCP-based method, confirming the credibility and correctness of this approach [30][31][32]. However, this method cannot effectively identify corridor width, and it is difficult to evaluate the ventilation conditions of places without leastcost paths (LCPs).
Based on the above analysis, a new ventilation corridor analysis method is urgently needed, which needs to meet the following requirements. First of all, this method should have a lower operating cost to implement the analysis of the urban ventilation environment in large areas. Secondly, this method should have the ability of ventilation environment analysis of dynamic wind direction. en, the analysis results need to reflect the ventilation status of the whole study area, so as to analyze the impact of urban internal structure on ventilation environment. In this study, a ventilation environment analysis method based on the least cumulative ventilation cost (LCVC) is proposed. Taking Wuhan as a case study area, the feasibility and accuracy of the method are verified. e results show that the method can meet the above three requirements and can be used as a new tool for urban ventilation environment analysis.

Study Area
Wuhan is the capital city of Hubei Province with an area of 8589 km 2 , located at 29°58′-31°22′ N and 113°41′-115°05′ E ( Figure 1). Wuhan is located in the east of the Jianghan Plain and the middle reaches of the Yangtze River. e world's third-largest river, the Yangtze, and its largest tributary, the Han River, meet in the city, dividing Wuhan's central urban area into three parts. ese are Hankou (including Jianghan District, Jiang'an District, and Qiaokou District), Wuchang (including Wuchang District, Qingshan District, and Hongshan District), and Hanyang. e rivers and lakes (such as the East Lake, Tangxun Lake, South Lake, and Sand Lake) are intricately woven into the fabric of the city. e water area occupies a quarter of the city's total area, providing the city with a lot of open spaces along the lakes and rivers.
Wuhan has a long history. In recent years, because it is a strategic development city in central China, the scale of its built-up areas has expanded rapidly. e mix of old and new urban areas has brought great difficulties to urban planning and environmental protection, however. Wuhan's UHI effect is gradually increasing, with the highest surface temperature (heat source center) reaching 58.7°C and the maximum surface temperature difference between cities and suburbs reaching 20°C. e problem of UHIs is an increasingly important issue that plagues urban development. erefore, it is very important to research and solve the problems of urban ventilation in Wuhan.

Data
e fundamental geographic information database (including land use data, road network data, and 3D building data) and point of interest (POI) database were provided by the Wuhan Natural Resources and Planning Bureau (Table 1). e building coordinates, ground graphics, and building height information are contained in a 3D database that is used to calculate the ventilation resistance coefficient of buildings. Daily wind data for 2018 were provided by the China Meteorological Administration. Landsat 8 imagery for land surface temperature (LST) inversion was obtained from the United States Geological Survey (USGS).

Methods for the Determination of Roughness Parameters.
In air quality and meteorological models, surface roughness is used to express the drag effect of rough surfaces. Use of the morphometric method, which is based on surface roughness, for calculating wind profiles in urban boundary layers (UBLs), has been extensively studied [39,40]. Using a current modeling method based on a 3D building database, Gal and Unger [41] studied the roughness (Z 0 ) of urban areas to analyze the urban wind environment. In order to make the assessment of urban air permeability more practical and to provide urban planners with computable geometric parameters of the city, many indices have been developed to assess urban permeability, such as the frontal area index λ f and the site coverage ratio λ p [30,38,42]. In this study, the frontal area index λ f was selected as the roughness measurement index.

Calculation of the Frontal Area Index.
Windward building walls obstruct airflow. e frontal area index is a measurement of the building frontal area facing into the wind. e frontal area index was first approximated by the product of the average height, width, and density of the buildings [39]: where L y is the average width of the buildings perpendicular to the wind direction, H is the average height of buildings, and ρ d is the density of buildings per unit area. Burian [40] calculated the frontal area index in any wind direction directly using ArcView Avenus script and an improved formula: where λ f(θ) represents the frontal area index of buildings facing into the wind θ, A proj represents the total projected area of buildings on a plane perpendicular to the wind direction, and A T represents the plan area.
ere is some ambiguity about the minimum distance between two adjacent buildings that divides them into two separate buildings. e problem is that as the two buildings get closer, the upwind building may begin to obscure the facade of the leeward building. Analyzing the exposed front area (shown in Figure 2) may be more important than analyzing the total front area [40]. Wong [30] eliminated the area blocked by buildings upwind of the blocked area of the leeward buildings by setting incremental projection lines (with an interval of 5 meters). In this study, a program was developed that was based on the ArcGIS 10.2 in the NET 4.0 environment. e projected areas of the buildings were directly integrated through a graphic method to calculate the frontal area index. e average frontal area index λ f is obtained by weighting λ f(θ) with annual frequency P θ of wind direction θ. n is the collection of wind direction. In this paper, there are 16 wind directions, so n � 16. e equation is as follows:

Resolution.
Recent studies have mainly used two aggregation methods. One is to aggregate buildings based on building blocks, which treats buildings as a unit. e other is to use a regular grid to process the building data, which is  often used for spatial data analysis. Open space is a key factor in assessing urban ventilation, but it cannot be expressed well using the building block aggregate method. erefore, in this study, a regular grid was selected to divide the urban space [31]. Due to the scale effect, analyzing the same data at different scales will lead to different results. e selection of the grid scale should consider the correlation between the calculated value of the frontal area index and the actual ventilation capacity of the study area, as well as the ability of the frontal area index to express the details of ventilation [42]. Hsieh [31] conducted an urban ventilation study in Tainan using 100 m grids. e Hong Kong Planning Department found 100 m grids to be compatible with various variables for the thermal environment in urban climate research [30]. e correlation between the frontal area index and UHI intensity was analyzed using a grid scale from 400 m to 40 m in Hong Kong, and it was found that the two showed the highest correlation on the 100 m grid scale [30,43]. A 100 m grid has been used to study the ventilation environment of Wuhan central urban area [38], which has the same research area as this study. In light of these research results, a 100 m regular grid was used to divide the research area in this study.

Zero Displacement Height.
e morphometric method based on surface roughness for calculating wind profiles in UBLs has been studied extensively. Current morphology models, such as those of MacDonald [44] and Bottema [45], assume that wake interference between surface obstacles is negligible and that the average wind speed approaching each obstacle is logarithmic. Given these assumptions, these models are only valid when the frontal area index λ f is less than 0.3-0.5. In other words, as the roughness increases, the average wind profile approaching each building becomes nonlogarithmic because the interference between buildings promotes air turbulence near the ground. is is why it is necessary to introduce zero displacement height (Z d ) into the logarithmic velocity profile.
MacDonald [44] proposed that the frontal area index above the displacement height (λ * f ) can estimate Z 0 better than λ f and proposed that the average wind speed below the displacement height be assumed to be zero. Ng [42]suggested that wind speed below Z d might depend on building geometries such as λ f ′ (frontal area density below Z d ) and used 15 m as the value of Z d . Wong [30] further simplified the frontal area index under the displacement height. Z d was set as 20 m indirectly by setting the lowest level interval of λ f as (0, 0.2) within 100 m grids. e 3D building data used in this study do not include information on overpasses, large traffic billboards, and large green vegetation, and these are important details for calculating λ f ′ . erefore, this study extends Wang's method to set different Z d values for different land types (Z b d � 10 m for built-up areas and Z w d � 1 m for water bodies).

LCVC Analysis.
e LCP-based method has been considered feasible for identifying urban ventilation corridors. e LCP-based method assumes that the air always flows in the direction of least resistance, thus determining the path from the starting point to the end point on the ventilation resistance grid [30,46]. In the LCP-based method, the Z d value is defined as the resistance value. e higher the Z d value is, the higher the resistance value is. In  addition, n starting points and m ending points are determined in order to represent the air inlets and air outlets, respectively. e LCP-based method is then used to generate n * m LCPs between the start and end points. Finally, the LCP frequency of each grid is calculated. e higher the frequency is, the better the ventilation conditions are, and vice versa.
is method can effectively identify the main ventilation corridors, but the disadvantages are also obvious, namely, the lack of estimation of corridor width and the inestimability of the grids with zero LPC frequency.
is study proposes a new approach, namely, the LCVC. For any ventilation resistance surface, let s be the air inlet, d be the air outlet, and m be a point on an LCP between s and d. en, the LCVC from s to d through m can be written as the following formula: According to the calculation formula of λ f(θ) , the calculated values are equal when the difference of θ is π: erefore, the values of LCVC from m to d and from d to m are equal, which can be expressed by the following formula: Combining equation (4) and equation (6) gives e smaller the value of C s⟶d|m is, the lower the cost of airflow passing through the m point is, and the better the ventilation condition is. Using equation (7), the cumulative ventilation cost values at any point to the air outlet and air inlet can easily be calculated, and the LCVC at that point can be obtained by superposition of the two. e average ventilation cost can be obtained by weighting the LCVC values with wind direction frequencies.

Ventilation Potential and Urban Functional Units.
Different types of urban functional units are usually accompanied by different building structures and building heights. For example, residential areas are usually accompanied by middle-or high-rise buildings, and public areas are usually accompanied by low-or middle-level buildings. It is predicted that different urban functional units can be characterized by λ f and ventilation cost. In this study, the urban functional unit information was obtained from the urban POI database.

Validation of Ventilation Cost.
e LST is considered to be related to the urban ventilation environment [33]. In Qiao's research, LST was used to verify the results of the corridor analysis. is study uses LST inversed from Landsat 8 data to verify the results. Retrieve processing includes three main steps: from digital numbers to spectral radiation, from spectral radiation to sensor brightness temperature, and from sensor brightness temperature to LST. In this study, the retrieve processing was implemented by using the Landsat 8 Surface Temperature Inversion System (V2.0) developed by Ren Huazhong from the Institute of Remote Sensing and GIS, Peking University.

Spatial Distribution of the Wind Resistance Coefficient.
ere are 101,328 buildings in the study area ( Figure 3 and Table 2). e building height range is between 0 m and 204 m, with 57,720 buildings less than 10 m, accounting for 48.91% of the total building area. As the height increases, the number and area of the buildings gradually decrease. Buildings with a height between 10 m and 24 m account for 33.38% of the total number of buildings and 38.46% of the total building area. ere are 9,663 buildings with a height between 24 m and 100 m, accounting for 12.48% of the total building area. ere are 120 buildings higher than 100 m, accounting for only 0.12% of the total number of buildings. e wind resistance coefficient obtained according to the method described in Section 4 is shown in Figure 4. e spatial distribution of the wind resistance coefficient is positively related to building height. e average wind resistance coefficient of all grids is 0.153. e number of grids containing high-rise buildings (height greater than 24 m) accounts for 30.26%, and the average wind resistance coefficient is 0.299. Qiaokou, Jianghan, Jiang'an, and Wuchang are the old urban areas of Wuhan. e average wind resistance coefficient of these districts is 0.177, and 0.298 for the grid containing high-rise buildings. Qingshan is an important heavy industry base. ere are many single-story factories and middle-rise residential buildings in this area, so its average wind resistance coefficient is only 0.113. Hanyang and Hongshan are development zones, with an average wind resistance coefficient of 0.138.
In order to determine the wind resistance formed by different urban functional units and to prepare for the ventilation cost analysis, the resistance coefficients of 12 types of urban functional elements were calculated, as shown in Table 3. e urban functional units were obtained from the Wuhan POI database, which contains 155,421 POI points. e ventilation resistance coefficient of outdoor open spaces (parks, green spaces, and squares) was 0.111, which is significantly lower than that of other urban functional units. Next came public management and social organization units, with an average ventilation resistance coefficient of 0.199. Public services and companies had the highest ventilation resistance coefficients, with 0.251 and 0.243, respectively. ese two types of units are usually accompanied by a strong financial correlation, which results in a higher spatial distribution consistency.

Statistics on Wind Direction and Frequency.
When analyzing the urban ventilation conditions, the results for each standard wind direction need to be linearly weighted according to the actual wind direction frequency. e wind direction and frequency were thus plotted on a radar chart according to the daily meteorological statistics of Wuhan in   Figure 5). e main wind direction is northerly (including N, NE, NW, NNW, and WNW), followed by southeasterly (including E, SE, SSE, and ESE). Affected by the monsoon climate, the dominant wind direction varies from season to season. e prevailing winds affected by the northern cold in the autumn and winter are mainly north winds (including N, NE, NW, and NNE), followed by a few east winds (including E, NE, ENE, and SE). e meteorological changes in spring are complicated, and the prevailing winds are still mainly northerly, followed by southeasterly (including ESE and SSE). In summer, the northerly and southwesterly winds (SW, WSW, and SSW) are similar in frequency and accompanied by a few southeasterly winds.

Results of LCVC Analysis.
e difference in wind direction frequency indicates the variation in the influence of the LCVC in each wind direction. Given a time interval, the average LCVC is obtained by weighting the LCVC of each wind direction with the corresponding frequency. Figure 6 shows the results for the LCVC analysis of 16 wind directions in the urban center of Wuhan. In order to maintain comparability, the calculation results of different wind directions use the same classifications and map colors. Two islands with high ventilation costs, centered on Hankou and Wuchang, are formed along the east and west sides of the Yangtze River. e areas of the two are equivalent, but the Hankou side presents a single-core model and the area of high-value areas is large. By contrast, the Wuchang side presents a multicore model, and the area of high-value areas is small and scattered. e East Lake has become another important urban ventilation corridor due to its large water area and its distribution deep into the city's hinterland.
ere are also some differences in the distributions of LCVCs in different seasons. In summer, due to the high wind frequency in an N-S direction, the ventilation corridor formed by the Yangtze River is more obvious than in other seasons. In winter, the width of the ventilation corridor in the north of the East Lake is slightly narrower than in other seasons. At the same time, the width of the ventilation corridors formed by the middle-level LCVC area (from 5 to 7) was also narrower than in other seasons or even disappeared. In the spring and autumn, when the frequency of the south wind is slightly higher than in winter and summer, the ventilation corridors running in an S-N is more obvious.
Summarized below are the details of the spatial distribution pattern of ventilation costs and the three levels of ventilation corridors identified, namely, the main, secondary, and capillary levels.
e main ventilation corridors lay the foundation for urban ventilation. e distribution of the main ventilation corridors has a high spatial correlation with natural geographical features (such as rivers and lakes). e results show that there are two main ventilation corridors in central Wuhan. One is the NE-SW corridor formed by the Yangtze River, and the other is the S-N and NW-SE corridor formed by the East Lake. e secondary ventilation corridors are mostly connected to the main ventilation corridors, and their distribution is affected by the main ventilation corridors. e secondary ventilation corridors spatially divide the high ventilation cost area into several subareas, which play an important part in promoting urban ventilation. Depending on the main ventilation corridors of the East Lake, many N-S or SE-NW secondary ventilation corridors are formed in Wuchang District, Qingshan District, and Hongshan District. ese ventilation corridors promote ventilation in these three areas. e secondary ventilation corridor formed by the Han River connects to the main ventilation corridor formed by the Yangtze River, which promotes the ventilation conditions in Hanyang.
Capillary ventilation corridors are distributed in areas with high ventilation costs, and the areas with maximum ventilation costs are divided into several subregions. Capillary ventilation corridors cannot determine the overall conditions of regional ventilation but can effectively reduce the distribution of the maximum value of ventilation costs and can be used as a supplementary means for secondary ventilation corridors. Due to the large amount of capillary ventilation corridors, their locations are not marked on the map. It is easy to determine that the number of capillary ventilation corridors in Hankou (Wuchang District, Qingshan District, and Hongshan District) is significantly less than in Wuchang (Qiaokou District, Jianghan District, and Jiang'an District). e ventilation cost distribution map enables the visualization of urban ventilation conditions. For example, blue indicates a low ventilation cost area, and red indicates a high ventilation cost area. Relatively low-cost areas between high costs are potential ventilation corridors. is facilitates a better understanding of urban ventilation conditions on both local and global scales. e frontal area index λ f was performed on a local scale. When considering the entire urban area, due to the complexity of the buildings and the road network, it will be difficult to achieve the identification of ventilation corridors by visual inspection of the buildings and the windward index map [30]. e results of the LCVC method cover the entire research area, thus solving the problem of no-path passages in some areas in the traditional LCP method.  8 Complexity inversion was performed on the Landsat 8 data (Figure 8). By combining the LST map with the summer urban ventilation analysis results (Figure 7(b)), the LST values for different levels of ventilation costs were calculated (Table 4). e results show that the average LST of the area with the best ventilation conditions is 34.19°C, significantly lower than that of other areas. e average LST in the area with the worst ventilation conditions is 40.53°C. In addition, the area with the worst ventilation conditions has less heterogeneity than other areas do, and the LST standard deviation is 1.71. As ventilation conditions improve, the LST standard deviation continues to increase.  10 Complexity residential areas should be strengthened to improve the ventilation environment.

Discussion and Conclusion
Using the urban morphological characteristics identified by GIS technology, this study established an LCVC method to describe quantitatively the urban ventilation environment at the city scale. First, the frontal area index of three-dimensional urban buildings representing the ventilation resistance coefficient was calculated using a morphological method. Second, the minimum cumulative ventilation cost algorithm was applied to draw the urban ventilation cost maps under different wind directions. en, the wind frequency weighting was used to explore the urban ventilation environment in different seasons, and the urban ventilation corridors of different levels were analyzed. Finally, the results of the summer ventilation analysis were verified using the LST retrieved from Landsat 8 data. e analysis of the urban ventilation environment based on the morphology and GIS technology has the advantage of high calculation efficiency. In addition, the results of the analysis are highly compatible with other spatial analysis and mapping technologies.
is study proposes that the cumulative costs of ventilation can better reflect the differences in urban ventilation conditions than the ventilation resistance coefficient can. In contrast to the corridor extraction method based on empirical rules, the proposed method can directly observe the dynamic characteristics of urban ventilation under different wind directions and frequencies. In contrast to the least-cost path analysis method, the results of the LCVC method cover the whole study area, and the corridor width and area can also be measured. However, several issues require further study. e urban wind environment is affected not only by ground roughness but also by atmospheric environment and local temperature factors.
erefore, it is difficult to achieve an accurate analysis of local wind speeds and directions from an analysis of building form alone. In addition, it is difficult to obtain internal high-density real-time wind speed data, especially wind speed measurements in a vertical direction.
is makes it difficult to improve the model parameters. ese issues will be further studied.

Data Availability
e data used to support the findings of the study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.