Exploring the Connection between Urban 3D Form and Building Energy Performance and the Inﬂuencing Mechanism

: Continuous growth of building energy consumption CO 2 emission (BECCE) threatens urban sustainable development. Urban form is an important factor affecting BECCE. Compactness is a signiﬁcant urban morphological characteristic. There is currently a lack of research on the effect of urban three-dimensional (3D) compactness on BECCE. To clarify the research value of 3D compactness, we investigated whether 3D compactness has a stronger impact on BECCE than two-dimensional (2D) compactness. A total of 288 buildings of the People’s Bank of China (PBOC) were divided into 5 zones according to building climate demarcation. As BECCE is affected mainly by four aspects (socioeconomic condition, building features, macroclimate, and urban form), the BECCE driven by urban form (BECCE-f) in each zone was calculated ﬁrstly using the partial least square regression model. Normalized compactness index (NCI) and normalized vertical compactness index (NVCI) were calculated with Python to quantify urban 2D and 3D compactness within a 1 km buffer of PBOC buildings. The mean NCI and NVCI values of each zone were adopted as 2D and 3D compactness of this zone. Gray correlation analysis of the ﬁve zones showed that the connection between the NVCI and BECCE-f is stronger than that between NCI and BECCE-f. Based on this, we believe that the emphasis of later research should be shifted to urban 3D form, not just 2D elements. 3D form can describe the real urban form in a more accurate and detailed manner. Emphasizing 3D morphological characteristics in studies of the relationship between urban form and building energy performance is more meaningful and valuable than only considering 2D characteristics. The impact mechanism of urban form on BECCE-f should also be analyzed from the perspective of 3D form. This study also provides beneﬁcial solutions to building energy saving and low-carbon building construction.


Introduction
The building energy consumption CO 2 emission (BECCE) we studied is CO 2 emission from building operational energy consumption, which refers to energy utilization concerning building heating, cooling, lighting, and other activities [1]. From 2005 to 2018, the energy consumption of building operational activities and relevant CO 2 emission presented a trend of continuous growth [2]. In 2019, building operational energy consumption was responsible for about 22% of the total energy consumption in China, generating 2.2 billion tons of CO 2 emissions [3]. The building sector is the second-largestCO 2 emissions source in China [4]. Therefore, energy conservation and emission reduction of the building sector can make a significant contribution to China's performance in CO 2 mitigation commitments [5]. With the expansion of urban built-up areas, the continued growth of building stock, and

BECCE Calculation and Data Collection
Firstly, the BECCE of each PBOC building was calculated. The necessary data for future research, including building footprint and the condition of nontarget factors, were also collected.

BECCE Calculation
We calculated BECCE based on the consumption data of 4 kinds of energy: electricity (10 4 kW·h), raw coal (t), natural gas (10 4 m 3 ), and heating power (GJ) in 2014. Consumption of these energies is related to the activities of office buildings (such as heating, cooling, and lighting). These activities are influenced by the microclimate created by urban form. The following formula was used to calculate BECCE: where BECCE is the building energy consumption CO2 emission (tCO2), Coni is the consumption of energy i (i = 1, 2, 3, 4), Fi is the CO2 emission coefficient of energy i, and n is the number of types of consumed energy.

Socioeconomic Condition, Building Features, and Macroclimate Data
Based on the literature review [4,5,12,32,[36][37][38], combined with general knowledge, the secondary indicators of three nontarget factors (socioeconomic condition, building features, and macroclimate) were determined. These secondary indicators can better reflect the condition of the corresponding factor.
Education expenditure (EE, 10 4 yuan) and per-capita wage (PW, yuan) in the city municipal districts were selected as indicators of socioeconomic condition. China City Statistical Yearbook 2014 provided us with these data.
Building floor area (FA, m 2 ) and the number of energy users (EUs, person) were chosen as indicators representing building features. The PBOC buildings dataset contained this information.
Cooling degree day (CDD, °C d) based on 26 °C and heating degree day (HDD, °C d) based on 18 °C are quantitative indices reflecting the demand of building cooling and heating. CDD and HDD were used to represent the macroclimate condition in this study. CDD and HDD were calculated according to Formulas (2)

BECCE Calculation and Data Collection
Firstly, the BECCE of each PBOC building was calculated. The necessary data for future research, including building footprint and the condition of nontarget factors, were also collected.

BECCE Calculation
We calculated BECCE based on the consumption data of 4 kinds of energy: electricity (10 4 kW·h), raw coal (t), natural gas (10 4 m 3 ), and heating power (GJ) in 2014. Consumption of these energies is related to the activities of office buildings (such as heating, cooling, and lighting). These activities are influenced by the microclimate created by urban form. The following formula was used to calculate BECCE: where BECCE is the building energy consumption CO 2 emission (tCO 2 ), Con i is the consumption of energy i (i = 1, 2, 3, 4), F i is the CO 2 emission coefficient of energy i, and n is the number of types of consumed energy.

Socioeconomic Condition, Building Features, and Macroclimate Data
Based on the literature review [4,5,12,32,[36][37][38], combined with general knowledge, the secondary indicators of three nontarget factors (socioeconomic condition, building features, and macroclimate) were determined. These secondary indicators can better reflect the condition of the corresponding factor.
Education expenditure (EE, 10 4 yuan) and per-capita wage (PW, yuan) in the city municipal districts were selected as indicators of socioeconomic condition. China City Statistical Yearbook 2014 provided us with these data.
Building floor area (FA, m 2 ) and the number of energy users (EUs, person) were chosen as indicators representing building features. The PBOC buildings dataset contained this information.
Cooling degree day (CDD, • C d) based on 26 • C and heating degree day (HDD, • C d) based on 18 • C are quantitative indices reflecting the demand of building cooling and heating. CDD and HDD were used to represent the macroclimate condition in this study. CDD and HDD were calculated according to Formulas (2) and (3): where t i is the average daily outdoor temperature for i day, D = 1 d. When (t i − 26) or (18 − t i ) is negative, take (t i − 26) and (18 − t i ) = 0. We obtained the daily mean temperature data of 398 Chinese meteorology stations throughout 2014 from the Global Surface Summary of the Day (https://data.noaa.gov/ dataset/dataset/global-surface-summary-of-the-day-gsod, accessed on: 5 January 2020) and calculated their CDD and HDD. A total of 288 PBOC buildings acquired their CDD and HDD value by interpolation, as shown in Figure 2. where ti is the average daily outdoor temperature for i day, D = 1 d. When (ti − 26) or (18 − ti) is negative, take (ti − 26) and (18 − ti) = 0. We obtained the daily mean temperature data of 398 Chinese meteorology stations throughout 2014 from the Global Surface Summary of the Day (https://data.noaa.gov/dataset/dataset/global-surface-summary-of-the-day-gsod, accessed on: 5 January 2020) and calculated their CDD and HDD. A total of 288 PBOC buildings acquired their CDD and HDD value by interpolation, as shown in Figure 2.

Buildings Footprint Data
The influence of urban form on building energy performance and CO2 emission is indirect. As mentioned above, urban form influences BECCE by affecting the building microclimate environment. Hence, research of the effect of urban form on BECCE should be conducted from the perspective of building microclimate, which refers to the local climate within a radius of 1 km around the building, as shown in Figure 3a [39]. 2D and 3D compactness within a 1 km buffer area of individual buildings was selected as an indicator of urban form. Building footprint data we collected contained the building area and height information. Example data in the 2D pattern are shown in Figure 3b, and its corresponding 3D form is shown in Figure 3c.

Calculating BECCE-f
Next, the BECCE and nontarget factors were used to eliminate the effects of nontarget factors on BECCE and calculate BECCE-f by the specific method in this study.

Buildings Footprint Data
The influence of urban form on building energy performance and CO 2 emission is indirect. As mentioned above, urban form influences BECCE by affecting the building microclimate environment. Hence, research of the effect of urban form on BECCE should be conducted from the perspective of building microclimate, which refers to the local climate within a radius of 1 km around the building, as shown in Figure 3a [39]. 2D and 3D compactness within a 1 km buffer area of individual buildings was selected as an indicator of urban form. Building footprint data we collected contained the building area and height information. Example data in the 2D pattern are shown in Figure 3b, and its corresponding 3D form is shown in Figure 3c. where ti is the average daily outdoor temperature for i day, D = 1 d. When (ti − 26) or (18 − ti) is negative, take (ti − 26) and (18 − ti) = 0. We obtained the daily mean temperature data of 398 Chinese meteorology stations throughout 2014 from the Global Surface Summary of the Day (https://data.noaa.gov/dataset/dataset/global-surface-summary-of-the-day-gsod, accessed on: 5 January 2020) and calculated their CDD and HDD. A total of 288 PBOC buildings acquired their CDD and HDD value by interpolation, as shown in Figure 2.

Buildings Footprint Data
The influence of urban form on building energy performance and CO2 emission is indirect. As mentioned above, urban form influences BECCE by affecting the building microclimate environment. Hence, research of the effect of urban form on BECCE should be conducted from the perspective of building microclimate, which refers to the local climate within a radius of 1 km around the building, as shown in Figure 3a [39]. 2D and 3D compactness within a 1 km buffer area of individual buildings was selected as an indicator of urban form. Building footprint data we collected contained the building area and height information. Example data in the 2D pattern are shown in Figure 3b, and its corresponding 3D form is shown in Figure 3c.

Calculating BECCE-f
Next, the BECCE and nontarget factors were used to eliminate the effects of nontarget factors on BECCE and calculate BECCE-f by the specific method in this study.

Calculating BECCE-f
Next, the BECCE and nontarget factors were used to eliminate the effects of nontarget factors on BECCE and calculate BECCE-f by the specific method in this study.

Basic Principle
The 288 PBOC buildings were divided into 5 zones according to the building climate demarcation depicted in Figure 4: hot summer/warm winter zone (HSWW), hot summer/cold winter zone (HSCW), mild zone (ML), cold zone (CL), and severe cold zone (SC).
To obtain the BECCE-f of each zone, the nontarget factors' interference should be eliminated, including socioeconomic condition, building features, and macroclimate. That means the three factors of the 5 zones should be kept consistent with each other. In each zone, taking BECCE as the dependent variable and EE, PW, FA, EU, CDD, and HDD as independent variables, we first set up the regression model between them. When keeping the other three factors as the average level-a standardized unit-the BECCE of this standardized unit should be the same in every zone because the three driving factors are the same. The fact is there are differences between the zones when this standardized unit is put into a different zone. These differences were believed to be driven by the fourth driving factor, i.e., the target factor-urban form. Hence, the respective mean value of EE, PW, FA, EU, CDD, and HDD of all 288 buildings was then put into 5 regression models to calculate BECCE driven by the urban form of each zone. Considering the collinearity of independent variables, the partial least square regression (PLSR) method was chosen to calculate BECCE-f.

PLSR
The partial least square method combines the advantages of both principal component analysis and canonical correlation analysis. It is applicable to the data characterized by collinearity. The basic theory can be summarized as follows [40,41].
Assuming there are independent variables matrix X = [x1, x2, …, xm] and dependent variable y. X can be decomposed as Formula (4): where T is a latent factor matrix, P is a loading vector matrix, and E is the residual matrix of X. The basis for the PLSR is that the relation between X and y can be conveyed by the latent factors. This means that y can also be decomposed as: To obtain the BECCE-f of each zone, the nontarget factors' interference should be eliminated, including socioeconomic condition, building features, and macroclimate. That means the three factors of the 5 zones should be kept consistent with each other. In each zone, taking BECCE as the dependent variable and EE, PW, FA, EU, CDD, and HDD as independent variables, we first set up the regression model between them. When keeping the other three factors as the average level-a standardized unit-the BECCE of this standardized unit should be the same in every zone because the three driving factors are the same. The fact is there are differences between the zones when this standardized unit is put into a different zone. These differences were believed to be driven by the fourth driving factor, i.e., the target factor-urban form. Hence, the respective mean value of EE, PW, FA, EU, CDD, and HDD of all 288 buildings was then put into 5 regression models to calculate BECCE driven by the urban form of each zone.
Considering the collinearity of independent variables, the partial least square regression (PLSR) method was chosen to calculate BECCE-f.

PLSR
The partial least square method combines the advantages of both principal component analysis and canonical correlation analysis. It is applicable to the data characterized by collinearity. The basic theory can be summarized as follows [40,41].
Assuming there are independent variables matrix X = [x 1 , x 2 , . . . , x m ] and dependent variable y. X can be decomposed as Formula (4): where T is a latent factor matrix, P is a loading vector matrix, and E is the residual matrix of X. The basis for the PLSR is that the relation between X and y can be conveyed by the latent factors. This means that y can also be decomposed as: where q is the loading value of y, and f is the residual vector of y. Predicted dependent variableŷ is computed through the following linear equation: where b is an array of regression coefficients. In our study, PLSR models were established in R software and tested with the method of leave-one-out cross-validation.

2D and 3D Compactness
The compactness index (CI) is based on Newton's law of gravitation [42]. It quantifies the urban 2D compactness by gridding the construction land and calculating the average gravitation of the spatial interaction of urban land use. CI is significantly affected by the scale of an urban built-up area. To offset this shortcoming, the normalized compactness index (NCI) was developed [43]. It assumes that a round city has the greatest compactness because the urban space is fully occupied by construction land. NCI is defined as the ratio of the actual urban construction land to its equivalent circular land, whose area is equal to the target city's construction area. The compactness of equivalent circular land is used as a normalized factor in the NCI to normalize CI between 0 and 1, which makes it convenient to compare the urban 2D compactness among different cities. The NCI is given by: where CI is the average gravity of urban spatial interaction, (i.e., the compactness of urban spatial form), CI round is the compactness of the round city, N is the total number of grids of construction land, M is the total number of grids of the round city, Z i and Z j represent the urban construction land area (i = j) in any two grids i and j, d (i, j) is the geometric distance between grid i and grid j, and S i ' and S j ' are construction land areas of grids i ' and j ' in the round city. The normalized vertical compactness index (NVCI) indicates the compactness of urban 3D spatial form by the strength of the spatial gravitation between urban buildings [44,45]. A sphere is the most compact 3D spatial form in the universe because of gravity. The equivalent sphere of a city refers to the sphere whose volume is equal to the urban buildings' volume. NVCI is defined as the ratio of actual 3D urban spatial form to its equivalent sphere. The equivalent sphere was taken as the normalized factor in the NVCI to eliminate errors caused by city scale differences. The NVCI calculation formula is: where VCI is vertical compactness index, VCI max is the compactness of the equivalent sphere, P is the total number of cubes that the equivalent sphere occupies, Q is the number of all cubes, V i and V j are the volume of urban buildings in urban cube i and cube j (i = j), d(i, j) is the geometric distance between centroids of urban cube i and j, and V' i and V' j are the volumes of the equivalent sphere in the cube i' and j' ( Figure 5). The value of NVCI is between 0 and 1, and the spatial form is more compact as the value approximates 1.

Gray Relationship Analysis
Gray relationship analysis is based on the geometric corresponding relationship between factors, and gray correlation degree (GCD) can describe the strength and extent of the connection between factors [46].
Assuming there is a reference sequence X0 = {x0(k), k = 1, 2, …, n}, and a factor sequence Xi = {xi(k), k = 1, 2, …, n}, (i = 1, 2, …, m). The GCD between X0 and Xi is defined as: where ρ is the distinguishing coefficient, and ρ∈[0, 1], normally ρ = 0.5. The matrix of GCD can be obtained by sorting the GCD in descending order. Then, the strength of the connection between X0 and factors Xi can be judged. Gray relationship analysis is applicable for the data with a small number of representative samples. Taking the BECCE-f as a reference sequence and the NCI and NVCI as factor sequences, we calculated GCD in a data processing system (DPS) to investigate the connections between urban 2D and 3D compactness and BECCE-f among the 5 zones.

BECCE of PBOC Buildings
As depicted in Figure 6, high BECCE bars were primarily concentrated in the north and east of China, while low bars mainly appeared in south and west China. The result implies that, on the whole, the buildings in north and east China consume more energy and generate more CO2 than the buildings in south and west China. This trend is similar to the conclusion of previous research [47][48][49]. CO2 released from electricity consumption is dominant in most buildings' BECCE structure, especially in south China. Electricity is the main energy used in their daily activities, while in the north, CO2 generated from heating power and raw coal consumption accounts for a considerable proportion. Because heating power and raw coal are important heating energy sources in the cold and severe cold zones, building heat load plays a dominant role, and the heating period is long [50]. For batch processing and convenient computation, two programs calculating the NCI and NVCI, respectively, were developed with Python and ArcGIS.

Gray Relationship Analysis
Gray relationship analysis is based on the geometric corresponding relationship between factors, and gray correlation degree (GCD) can describe the strength and extent of the connection between factors [46].
Assuming there is a reference sequence X 0 = {x 0 (k), k = 1, 2, . . . , n}, and a factor sequence X i = {x i (k), k = 1, 2, . . . , n}, (i = 1, 2, . . . , m). The GCD between X 0 and X i is defined as: where ρ is the distinguishing coefficient, and ρ∈[0, 1], normally ρ = 0.5. The matrix of GCD can be obtained by sorting the GCD in descending order. Then, the strength of the connection between X 0 and factors X i can be judged. Gray relationship analysis is applicable for the data with a small number of representative samples. Taking the BECCE-f as a reference sequence and the NCI and NVCI as factor sequences, we calculated GCD in a data processing system (DPS) to investigate the connections between urban 2D and 3D compactness and BECCE-f among the 5 zones.

BECCE of PBOC Buildings
As depicted in Figure 6, high BECCE bars were primarily concentrated in the north and east of China, while low bars mainly appeared in south and west China. The result implies that, on the whole, the buildings in north and east China consume more energy and generate more CO 2 than the buildings in south and west China. This trend is similar to the conclusion of previous research [47][48][49]. CO 2 released from electricity consumption is dominant in most buildings' BECCE structure, especially in south China. Electricity is the main energy used in their daily activities, while in the north, CO 2 generated from heating power and raw coal consumption accounts for a considerable proportion. Because heating power and raw coal are important heating energy sources in the cold and severe cold zones, building heat load plays a dominant role, and the heating period is long [50].  Figure 7 displays the minimum, mean, and maximum values of independent variables in each zone. For education expenditure, there are three extremely high values in CL, HSCW, and HSWW. They are 7,184,218, 6,773,006, and 3,308,000 (10 4 yuan), which, respectively, belong to Beijing, Shanghai, and Shenzhen, three megacities of China. It can be seen that the mean values of education expenditure of CL, HSCW, and HSWW are also relatively higher than the other two zones. The three regions spent more on education. There are few differences between mean values of the per-capita wage of the five zones. The highest per-capita wage appeared in HSCW (Tongren, 116,925.52 yuan), and the lowest exists in SC (Yichun, 24,631.43 yuan). ML has the least gap of per-capita wage between the maximum and minimum.

Description of Nontarget Factors
The differences in floor area and energy user among zones show the same trend, regardless of maximum, minimum, and mean values. PBOC buildings in ML have a relatively smaller floor area and fewer employees. PBOC buildings in regions with a high level of economic development usually have a larger floor area and more employees.
The macroclimate factors show a certain regularity among different zones. The SC has the lowest cooling degree day (i.e., the lowest cooling load), while the HSWW has the highest cooling degree day. On the contrary, HSWW has the lowest heating degree day (i.e., the lowest heating load), while SC has the highest heating degree day. There is a certain cooling load in CL and a certain heating load in HSCW. This regularity is associated with the location and the altitude. For example, ML is a low-latitude area, but its high altitude results in a lower cooling degree day and higher heating degree day.  Figure 7 displays the minimum, mean, and maximum values of independent variables in each zone. For education expenditure, there are three extremely high values in CL, HSCW, and HSWW. They are 7,184,218, 6,773,006, and 3,308,000 (10 4 yuan), which, respectively, belong to Beijing, Shanghai, and Shenzhen, three megacities of China. It can be seen that the mean values of education expenditure of CL, HSCW, and HSWW are also relatively higher than the other two zones. The three regions spent more on education. There are few differences between mean values of the per-capita wage of the five zones. The highest per-capita wage appeared in HSCW (Tongren, 116,925.52 yuan), and the lowest exists in SC (Yichun, 24,631.43 yuan). ML has the least gap of per-capita wage between the maximum and minimum.

Description of Nontarget Factors
The differences in floor area and energy user among zones show the same trend, regardless of maximum, minimum, and mean values. PBOC buildings in ML have a relatively smaller floor area and fewer employees. PBOC buildings in regions with a high level of economic development usually have a larger floor area and more employees.
The macroclimate factors show a certain regularity among different zones. The SC has the lowest cooling degree day (i.e., the lowest cooling load), while the HSWW has the highest cooling degree day. On the contrary, HSWW has the lowest heating degree day (i.e., the lowest heating load), while SC has the highest heating degree day. There is a certain cooling load in CL and a certain heating load in HSCW. This regularity is associated with the location and the altitude. For example, ML is a low-latitude area, but its high altitude results in a lower cooling degree day and higher heating degree day.

PLSR Models and BECCE-f
PLSR models are listed in Table 1. For each zone, FA and EU have a positive effect on BECCE, and the coefficients are relatively stable. The larger the floor area and the more energy consumed, the greater the BECCE. The higher HDD means a higher heating load, which can result in more BECCE in SC and CL. In HSWW, more cooling load can promote BECCE; thus, CDD has a positive correlation with BECCE. A cooler environment with higher HDD can reduce cooling energy consumption in HSWW. In HSCW, although the cooling load accounts for a large proportion of building air conditioning load, the heating load in winter also cannot be ignored. Therefore, both CDD and HDD have a positive effect on BECCE in HSCW. However, the negative effect of CDD and the positive effect of HDD on BECCE in ML might be due to the higher altitude. The higher the income, the greater the climate sensitivity of the energy consumed, which can cause more building energy consumption [51]. Strangely, the income has a negative effect on BECCE in SC, which needs further discussion. Income is often positively associated with education level, so the education level expressed by EE also has a positive effect on BECCE [52,53]. The

PLSR Models and BECCE-f
PLSR models are listed in Table 1. For each zone, FA and EU have a positive effect on BECCE, and the coefficients are relatively stable. The larger the floor area and the more energy consumed, the greater the BECCE. The higher HDD means a higher heating load, which can result in more BECCE in SC and CL. In HSWW, more cooling load can promote BECCE; thus, CDD has a positive correlation with BECCE. A cooler environment with higher HDD can reduce cooling energy consumption in HSWW. In HSCW, although the cooling load accounts for a large proportion of building air conditioning load, the heating load in winter also cannot be ignored. Therefore, both CDD and HDD have a positive effect on BECCE in HSCW. However, the negative effect of CDD and the positive effect of HDD on BECCE in ML might be due to the higher altitude. The higher the income, the greater the climate sensitivity of the energy consumed, which can cause more building energy consumption [51]. Strangely, the income has a negative effect on BECCE in SC, which needs further discussion. Income is often positively associated with education level, so the education level expressed by EE also has a positive effect on BECCE [52,53].   Table 2.

Urban 2D and 3D Compactness
Using Python programs, we calculated the NCI and NVCI values for each PBOC building.

Compactness Characteristics
For an intuitive comparison, Figure 8 depicts urban form in a 1 km buffer with the highest and lowest NCI and NVCI values. 3.4.2. NCI and NVCI of the 5 Zones Figure 9 shows the ranking of the NCI and NVCI of the five zones. The ML zone has the maximum NCI but the minimum NVCI. This means that the 2D form is the most compact in the ML zone, the layout of the buildings surrounding the PBOC building is denser. As depicted in Figure 8a,b, the higher the NCI is, the denser the distribution of the buildings, and the more compact the urban form on a two-dimensional space, while a less compact form presents a relatively sparser distribution of the buildings. According to the principle of the NCI, a less 2D compact form signifies the interaction strength and connection among buildings is weaker [54]. The reasons for the formation of different urban compact forms are complex, including topography, hydrology, and social and economic conditions [54,55]. For example, as shown in Figure 8a, the strip-shaped blank area in the buffer of the Guangzhou PBOC building is the river. Without this river, it is estimated that the NCI will be higher.
It has been proven by a previous case study that the NVCI is positively correlated with building height and building density [44]. Similarly, in our study, the correlation coefficient between the NVCI and average buildings height is 0.35, and the correlation coefficient between the NVCI and buildings density is 0.45. However, the correlation coefficient between the NVCI and plot ratio (combining buildings density and average buildings height) reaches 0.63. Correspondingly, as shown in Figure 8c,d, buildings with a greater NVCI are denser and taller, and the urban form is more compact in a 3D space. The buildings with a lower NVCI showed a fewer, sparser, and lower pattern on the whole. Figure 9 shows the ranking of the NCI and NVCI of the five zones. The ML zone has the maximum NCI but the minimum NVCI. This means that the 2D form is the most compact in the ML zone, the layout of the buildings surrounding the PBOC building is denser. However, when the vertical attribute of buildings is taken into account, its form is the least compact. Urban form with the highest NCI does not necessarily has the highest NVCI because the vertical characteristics, such as building height and plot ratios of building, are different from each other.  Figure 9 shows the ranking of the NCI and NVCI of the five zones. The ML zone has the maximum NCI but the minimum NVCI. This means that the 2D form is the most compact in the ML zone, the layout of the buildings surrounding the PBOC building is denser. However, when the vertical attribute of buildings is taken into account, its form is the least compact. Urban form with the highest NCI does not necessarily has the highest NVCI because the vertical characteristics, such as building height and plot ratios of building, are different from each other.

Connection between BECCE-f and Urban Compactness
The NCI, NVCI, and BECCE-f of the five zones are listed in Table 3. Based on Table 3, we can calculate that the GCD between the BECCE-f and NCI is 0.51, and the GCD between the BECCE-f and NVCI is 0.69. This shows that the connection between the NVCI and BECCE-f was relatively stronger than the connection between NCI and BECCE-f. The results imply that, after the other factors' effects were eliminated, the NVCI had a more notable impact on BECCE-f. Compared to the NCI, the NVCI is a more applicable and more comprehensive index reflecting the effect of urban form on BECCE. More comprehensive morphological information was taken into account in urban 3D form. Thus, 3D compactness is closer to the actual morphological characteristics of cities and can describe the real urban compact form in a more accurate and detailed manner than 2D compactness [44]. The impact mechanism of urban form through microclimate on BECCE can be reflected more comprehensively by urban 3D form than by 2D form. Therefore, the NVCI has a closer connection with BECCE-f than NCI. It can be inferred that emphasizing the 3D morphological characteristics in the study of the relationship between urban form and BECCE is more meaningful than considering 2D characteristics only.

Impact Mechanism of 3D Compactness on BECCE-f
As mentioned above, urban form can affect BECCE by influencing the urban microclimate environment, such as urban thermal environment, ventilation, reflection and absorption of solar radiation, etc. The study demonstrated that there is a positive relationship between land surface temperature and building density and building expandability, which refers to the utilization intensity of buildings to the space over the city [56]. The urban heat island (UHI) will be intensified in the area with high 3D compactness, where the larger building bodies absorb more solar shortwave radiation and store more heat. Moreover, the radiation is reflected multiple times among taller building façades that are closer to each other. The taller the buildings are, and the less uniform the building height is, the lower the albedo is [57]. Therefore, more solar radiation is captured at the top of the deep urban canyon. This abnormal absorption can lead to an increase in temperature inside the canyon [58]. The heat gain of buildings facades is thus increased, and the longwave radiation leaving the urban canopy is decreased [59,60].
In addition, the ventilation can also be affected by urban form. As tall and dense buildings result in less sky visible from the ground, higher 3D compactness will obviously cause a lower sky view factor (SVF). Lower site coverage and higher SVF can lead to a building's effective energy performance by enhancing urban ventilation [61,62]. Nevertheless, high-rise and high-density buildings will reduce the air ventilation channel and the speed of turbulent heat transport, resulting in hot air trapped between buildings [59,63]. Consequently, a kind of microclimate with a relatively higher temperature is created in the urban canyon. In hot regions where the cooling load dominates, such as HSWW and HSCW in this study, the cooling energy demand will increase considerably. In HSCW, the relatively higher temperature had a certain influence on their heating energy demand reduction in winter. In SC and CL, this microclimate will cause the reduction of heating energy consumption, especially in winter. Considering that the cooling demand is not strong in SC in summer, this microclimate has limited influence on building cooling in SC. However, the cooling demand in CL might increase. In ML, where the climate is moderate, the influence of urban form on BECCE is not very strong.
Dense high-rise buildings can shade the urban land surface and other buildings, creating more shadows in urban space. The shaded area usually has a lower temperature than the area directly shined on by the sun. Mutual shading can make a cooler microclimate environment. This is conducive to the reduction in building cooling energy consumption, especially in HSWW and HSCW in summer, but is adverse to the heating energy saving, especially in CL and SC in winter, where the solar gains are particularly limited and heating load plays a dominant role [64]. However, research has shown that mutual shading can cause the heating energy demand to increase even greater than the decrease in the cooling energy demand [65].
Increasing the area of urban green space and water body (GS&WB) and dispersing them are conducive to building energy saving [28,66]. However, GS&WB are facing space competition in compact cities, resulting in the loss of GS&WB area and the centralization of GS&WB [67]. This competition weakens the GS&WB ability of microclimatic regulation and energy saving advancement in compact cities.
Furthermore, there will be less sunlight accessibility in the area of high coverage of tall buildings, which can bring about more lighting requirements in buildings at afternoon or nightfall, particularly in cities at high latitude where light is scarce [64,68].

Conclusions
This study applied a regression method to eliminate the nontarget factors' effects on BECCE and calculated BECCE driven by urban form. Then, the NCI and NVCI of each zone were calculated. Finally, we explored the connection between urban 3D compactness and BECCE-f. Results of gray correlation analysis demonstrated that 3D compactness had a stronger connection with BECCE-f than 2D compactness. The analysis of the impact mechanism of 3D compactness on BECCE-f implied that urban 3D form surrounding an individual building significantly affects the overall building energy performance. This is the result of the influence of urban 3D compact form on building microclimate environment, including ventilation, thermal environment, and radiation environment.
Our studies proved that 3D form deserves more attention in research on the relationship between urban form and building energy consumption and CO 2 emission [69,70]. Urban 3D form takes into account more comprehensive morphological information. 3D form can describe the real urban compact form in a more accurate and detailed manner than 2D compactness. When investigating the impact mechanism of urban form on BECCE, considering 3D elements can definitely reflect the influencing mechanism more comprehensively than only considering 2D elements. It can be inferred that emphasizing the 3D morphological characteristics in the study of the relationship of urban form and building energy performance is more meaningful and valuable than considering 2D characteristics only. Currently, more eyes are being cast on 2D form (such as buildings floor area, building density, 2D layout and pattern, etc.), and research on the effect of urban 3D form on BECCE is still lacking. We believe that the emphasis of later research should be shifted to urban 3D form, not just 2D elements.
As we analyzed the influencing mechanism of 3D compact form on BECCE-f from the perspective of building microclimates, we believe this research can also provide guidance for city planners and building designers for the construction of low-carbon buildings and cities. Some directional measures promoting building energy conservation and emission reduction can be proposed accordingly. For instance, large and dispersed GS&WB was proven to be a feasible way of UHI mitigation [71]. Because of the limited land resources, GS&WB should integrate into compact cities in a new way. Roof greening and wall greening are practicable modes [72,73]. As for the building itself, the insulation performance of the exterior walls should be improved for a relatively constant indoor temperature and comfort. Albedo is a significant explanatory factor of urban land surface temperature [74]. The high reflection coating, which can reduce the heat gain of buildings, should be an increasing concern in the field of building materials and energy saving.
This study was based on building zoning, and one of the limitations is that we just calculated the BECCE-f of each zone. Future work should calculate the BECCE-f of each building using other methods, such as the downscaling method. Then, we simply demonstrated that the 3D compactness had a stronger connection with BECCE-f than 2D compactness. However, considering that the effect of urban 3D compactness on building energy performance displays a complicated pattern on a large scale, the potential linear or nonlinear relationship between urban 3D compact form and BECCE-f needs further exploration. Furthermore, a moderately compact form can be consequently discussed. Acknowledgments: The authors would like to thank the editor, associate editor, and anonymous reviewers for processing our manuscript.

Conflicts of Interest:
On behalf of all authors, the authors declare no conflict of interest.