Urban Form and Urban Energy Consumption at the Macro Scale in China

Abstract

The research results show that urban form has a significant impact on urban building energy consumption. Therefore, it is of great significance to study the relationship between urban form and urban building energy consumption. This study selects 26 cities in China across four climate zones and studies the relationship on a macro scale. In terms of urban building energy consumption, this study summarizes a set of data collation methods for calculating the total energy consumption of residential buildings and public buildings. In terms of urban form, this study constructed three types of urban form indicators (basic indicators, two-dimensional indicators, and three-dimensional indicators) and proposes a set of methods for calculating the urban built-up area, the total urban building area, the urban residential building area, and the urban public building area. This research finds that in the four climate zones, total urban building energy consumption is extremely strongly correlated with indicators such as resident population, GDP, total building area, building base area, and built-up area, and urban building energy consumption per unit area is extremely strongly correlated with indicators such as clustering, building intensity, urban building orientation, shading factor, and shape coefficient of building, but the relevant indicators are not exactly the same in each climate zone.

1. Introduction

Cities consume about three-quarters of the world’s primary energy, with the building sector consuming about 40% of the world’s energy [1,2,3]. Urban energy consumption is the main component of world energy consumption, and urban building energy consumption accounts for 60% of urban energy consumption.

Current research shows that urban form has a significant impact on building energy consumption [4,5,6]. The EBC Annex 51 project mentioned in the work report of the IEA aims to develop a municipal energy master plan and a neighborhood-scale energy action plan to help local governments develop and implement successful energy policies, providing detailed data sources and monitoring tools for both municipal and neighborhood scales. Urban morphology systematically introduces the basic theory, historical development, and application of urban morphology, combined with case studies and multidisciplinary perspectives, to provide readers with a comprehensive research framework. These studies investigated the correlation between energy consumption in urban buildings and a number of variables, i.e., individual building configurations, relations between buildings, and coverage of water bodies, impervious surfaces, and greenery. However, little is known about the relationship between the macro urban form and urban energy consumption. Hence, this study is aimed at determining the correlation between urban form and urban energy consumption at the macro scale.

Current knowledge on the links between urban form and building energy consumption focuses on the following urban form variables:

• Greening rate, building density, and floor area ratio [7];
• Extent of water bodies [8,9,10];
• Extent of impervious surfaces [10];
• Sky view factor [11];
• Building perimeter [12,13];
• Street canyons [14,15].

However, due to the lack of large-scale measured urban energy consumption data, few studies have been conducted on the way urban form attributes affect building energy consumption in reality [16,17,18,19,20]. The study of the relationship between urban form and urban energy consumption at the macroscopic scale is extremely difficult to study, and its challenges are mainly reflected in three aspects.

Data need to be organized. The accuracy of urban form data currently obtained from various websites needs to be verified, and the collection and collation of validation data from different cities, the selection of validation criteria, and the unified collation of data formats will take a lot of time and effort. Moreover, these urban form data need to be further organized before they can be used for research and analysis [21,22,23,24,25,26,27,28,29]. Meanwhile, the obtained urban energy consumption data need to be analyzed for their statistical caliber and reliability and finally generate the required urban building energy consumption data.

Methodology needs to be explored. In the study of the correlation between urban form and urban energy consumption at the macroscopic scale, the method of collating quantitative data on urban form and urban energy consumption data needs to be explored [30,31,32,33]. A set of statistical methods for calculating the total energy consumption of residential buildings and the total energy consumption of public buildings in each city needs to be summarized from the relevant data of government departments; a set of methods for calculating the built-up area of cities, the total area of urban buildings, urban residential building area, and urban public building area is proposed; meanwhile, some urban morphology indicators at the macroscopic scale need to be constructed [34,35,36].

Correlation requires exploration. Urban form research is a popular topic in the field of urban planning. Many scholars have studied urban form at the macroscopic scale, but there are fewer studies that consider urban morphology and urban energy consumption at the same time at the macroscopic scale, and many studies summarize the relevant laws through statistical models but do not explain the deep internal mechanism [37,38,39,40,41,42,43,44,45].

Based on the analysis of the data from building energy consumption and urban form, this study provides a more comprehensive and detailed analysis of the correlation between urban form and urban energy consumption at the macroscopic scale and then analyzes the mechanism of the influence of urban morphology on urban building energy consumption.

This study investigates the relationship between urban building energy consumption indicators and urban form indicators using building energy consumption and urban form data from 26 cities in China as shown in Figure 1. The following are the exact definitions of severe cold areas, cold areas, hot-summer and cold-winter areas and hot-summer and warm-winter areas using Heating Degree Days (HDD) as a quantitative index (based on the Chinese national standard GB 50176-2017 and related studies). When HDD is greater than 3000 and less than or equal to 5000, this area belongs to the severe cold area. When HDD is greater than 2000 and less than or equal to 3000, this area belongs to the cold areas. When HDD is greater than 1000 and less than or equal to 2000, this area belongs to the hot-summer and cold-winter areas, but it still needs to be heated in winter. When HDD is less than or equal to 1000, this area belongs to the hot-summer and warm-winter areas. Data are collected using a set of statistical methods for calculating total residential building energy consumption and total public building energy consumption for each city through the statistical yearbooks of each city in terms of urban building energy consumption. In terms of urban morphology, this study constructed three types of urban morphology indicators (basic indicators, 2D indicators, and 3D indicators), obtained and collated 3D urban morphology data, AOI data, POI data, and Landsat remote sensing data of the study cities, and proposed a set of methods to calculate urban built-up area, total urban building area, urban residential building area, and urban public building area. The paper is organized as follows. Section 1 provides the literature review and research questions. Section 2 gives the methodology. Section 3 provides the data analyses and discussion, and the final section concludes the paper.

Although existing studies have confirmed that urban form has a significant impact on building energy consumption, due to the difficulty of extrapolating fine-scale data, the lack of measured energy consumption data at the macro-scale, and the lack of a unified methodological system, the existing results are mainly at the level of blocks or individual buildings, and the systematic understanding of macro urban form and urban energy consumption is still a blank. Secondly, there is no recognized method for uniformly measuring the total energy consumption, total construction volume, and built-up area of urban residential and public buildings at the macro scale. Thirdly, most statistical models only describe the superficial correlation between morphology and energy consumption but fail to reveal its internal mechanism. In view of the above limitations, the core goal of this study is to establish a replicable macro scale analysis framework and reveal the mechanism of urban morphology on building energy consumption, and the innovation points are: (1) the multi-source big data (3D architecture, AOI/POI, Landsat remote sensing and statistical yearbook) of 26 Chinese cities are integrated, and a 2Dand 3D level index system is constructed, and a set of unified measurement methods for total urban buildings and total energy consumption is proposed; (2) Regional climate constraints (four types of areas divided by HDD: severe cold, cold, hot-summer and cold-winter, hot-summer and warm-winter) were introduced to test the moderating effect of climate on the morphology and energy consumption relationship. (3) Through the combination of statistics and mechanism models, the marginal contribution of macro morphological indicators to the energy consumption of residential and public buildings is quantified, and its influence path is analyzed. This research proposes the hypotheses that specific macro urban morphological indicators have a significant and stable impact on the energy consumption per unit area of urban residential and public buildings, and climate zoning strengthens or weakens the relationship between certain morphological indicators and building energy consumption.

2. Methodology

2.1. Statistical Method for Calculating the Total Energy Consumption of Residential Buildings and the Total Energy Consumption of Public Buildings in Each City

In this study, the residential building energy consumption is organized by climate zones, and the residential building energy consumption in severe-cold and cold regions includes three parts: urban residential electricity consumption and rural residential electricity consumption, household natural gas consumption and household liquefied petroleum gas consumption, and hot water heating and total steam heating (as in Equation (1)).

$$E_{r1}=E_e+E_g+E_h$$

(1)

In the formula, E_r1 is the total energy consumption of residential buildings, E_e is the electricity consumption of urban residents and rural residents, E_g is the amount of household natural gas and household liquefied petroleum gas, and Eh is the total amount of hot water heating and steam heating.

The energy consumption of residential buildings in hot-summer and cold-winter areas and hot-summer and warm-winter areas includes the electricity consumption of urban residents and rural residents, the natural gas consumption of households, and the liquefied petroleum gas consumption of households in (as in Equation (2)).

$$E_{r2}=E_e+E_g$$

(2)

In the formula, E_r2 is the total energy consumption of residential buildings, E_e is the electricity consumption of urban residents and rural residents, and E_g is the amount of household natural gas and household liquefied petroleum gas.

The electricity consumption of urban residents and rural residents is clearly counted in the statistical yearbooks of each city, but there are also some cities that provide the statistical caliber on electricity consumption for urban and rural residents, living consumption, and living electricity. The electricity consumption of urban residents and rural residents in most cities is separated, and for cities where the two are not separated, this study decomposes the electricity consumption of residents of that city and rural residents by the ratio of urban to rural population. The heating data given in the statistical yearbook is the heat value, and this study converts the heat value into electricity uniformly for statistical needs. The conversion process is to convert the heat value in the statistical yearbook into standard coal and then convert the standard coal into electricity.

This study collates the energy consumption of public buildings by climate zones. The total electricity consumption of the whole society in the Chinese city statistical yearbook and the statistical yearbook of each city refers to the total electricity consumption of each industry and the electricity consumption of urban and rural residents’ living. The total electricity consumption of the whole society is divided into the total electricity consumption of the whole industry (primary industry, secondary industry, and tertiary industry) and the statistics of urban and rural residents’ living electricity consumption (urban residents and rural residents). Through the study of the comprehensive sectoral statistical reporting system, it is found that the industry-wide electricity consumption classification can be subdivided into eleven subcategories. The statistical caliber of electricity consumption in public buildings refers to the electricity consumption of each industry from five to eleven, as shown in Equation (3).

$$E_p=E_i+E_w+E_c+E_f+E_t+E_b+E_m$$

(3)

In the formula, E_p is the total energy consumption of public buildings, E_i is the electricity consumption of information transmission, software, and the information technology service industry, E_w is the electricity consumption of the wholesale and retail industry, E_c is the electricity consumption of the accommodation and catering industry, E_f is the electricity consumption of the financial industry, E_t is the electricity consumption of the real estate industry, E_b is the electricity consumption of the rental and business service industry, and E_m is the electricity consumption of the public service and management organization.

In all climate zones, most cities’ electricity consumption statistics for public buildings refer to the electricity consumption of each industry above. The energy consumption of public buildings in individual cities is the difference between the total electricity consumption of the city and the electricity consumption of industry, transportation, urban and rural residents, agriculture, forestry, animal husbandry and fishery, and the construction industry. In some cities, the electricity consumption of transportation, construction and agriculture, forestry, animal husbandry, and fishery is derived by extrapolation. For example, in the cold region, Harbin city is used as the standard, and the electricity consumption of agriculture, forestry, animal husbandry, and fishery accounts for 0.023 of the city’s total electricity consumption, 0.032 of the city’s total electricity consumption in transportation, and 0.031 of the city’s total electricity consumption in construction. In the unit conversion, 1 ton of standard coal is equal to 8130 kW·h. The final conversion results of building energy consumption indicators for each city are shown in

Table 1. The final conversion results of building energy consumption indicators by climate zone.

Climate Zones	City Name	Urban Energy Consumption Indicators
		Total Energy Consumption (108 kW·h)	Energy Consumption per Unit Area(kW·h/m2)	Total Residential Energy Consumption (108 kW·h)	Residential Unit Energy Consumption (kW·h/m2)	Total Energy Consumption of Public Buildings (108 kW·h)	Unit Energy Consumption of Public Building (kW·h/m2)	Total Energy Consumption for Heating (108 kW·h)	Total Energy Consumption per Unit Area for Heating (kW·h/m2)
Severe cold areas	Harbin	294.21	99.48	56.23	111.71	57.10	68.38	180.88	85.22
	Changchun	194.57	64.92	38.20	67.12	50.76	59.39	105.60	49.29
	Shenyang	310.51	66.41	61.58	62.55	86.58	69.79	162.35	45.35
	Xining	59.37	41.57	12.19	55.43	0.62	1.68	46.56	43.93
	Yinchuan	95.86	68.65	6.53	62.42	58.05	73.43	31.28	51.64
	Hohhot	120.02	66.49	23.71	68.75	24.60	58.95	71.70	51.66
	Urumqi	120.22	9.38	21.51	58.52	30.75	120.12	212.24	21.22
Cold areas	Beijing	569.46	50.55	145.65	52.25	155.75	46.50	267.93	33.85
	Tianjin	401.98	70.75	101.86	67.11	128.98	79.91	171.14	42.07
	Taiyuan	127.99	68.16	37.40	68.37	37.65	67.65	52.94	40.07
	Shijiazhuang	224.50	97.60	68.80	84.17	76.41	141.34	79.30	45.07
	Jinan	162.95	54.12	60.88	53.93	43.73	54.65	58.34	26.39
	Zhengzhou	221.77	56.66	95.53	45.36	104.55	78.59	21.69	8.39
	Lanzhou	46.47	44.92	21.28	33.47	25.10	63.40	0.09	0.14
	Lhasa	9.01	39.96	4.82	42.09	4.17	37.74	0.02	0.17
	Xi’an	301.72	70.35	107.16	64.63	96.66	86.66	97.91	30.86
Hot-summer and cold-winter areas	Shanghai	634.62	62.78	236.03	36.75	398.59	108.14	/	/
	Chongqing	302.77	39.04	172.38	30.65	130.39	61.23	/	/
	Chengdu	242.69	45.71	98.19	23.30	144.50	131.86	/	/
	Hangzhou	231.95	46.41	116.20	32.05	115.75	84.35	/	/
	Wuhan	220.81	31.81	98.96	20.94	121.85	54.97	/	/
	Nanjing	209.88	41.85	83.28	22.73	126.60	93.69	/	/
	Hefei	128.54	44.48	56.38	26.09	72.16	99.05	/	/
Hot-summer and warm-winter areas	Guangzhou	392.26	57.62	179.21	46.74	213.05	71.66	/	/
	Shenzhen	267.88	40.05	60.55	13.39	207.33	95.71	/	/
	Xiamen	115.59	49.10	60.48	42.08	55.11	60.13	/	/
	Nanning	102.55	44.47	53.96	32.83	48.59	73.39	/	/

.

2.2. Statistical Methods of Urban Built-Up Area, Urban Residential Building Area, and Urban Public Building Area

2.2.1. Calculation Methods

In this study, the built-up areas of the study cities were defined using the remote sensing technique. The satellite remote sensing data for each city were downloaded through the United States Geological Survey website, and the threshold of cloudiness was set at 10% for this study in the selection. The downloaded satellite remote sensing images needed to ensure that there were no clouds or only thin clouds in the study area. The application of Landsat remote sensing data in this study was in the separation of impervious surface. Firstly, it is necessary to collect remote sensing data of each view that can be assembled into a city, and then the remote sensing data of each view of a city will be supervised and classified separately. The supervised classified data are saved in Geotiff format and entered into GIS10.7 for processing, such as stitching, reclassification, and data statistics. In this study, the images were classified into impervious surface, green surface, water surface, and bare land. Finally, the images were classified into impervious surface (value 1) and non-impervious subsurface (value 0), as shown in Figure 2b. A 900 m × 900 m fishing network was established (Figure 2c), and the image element size of remote sensing data was 30 m × 30 m. The areas with impervious surface greater than 60% were counted in a table displaying zoning statistics. Landsat data with a resolution of 30 m has some limitations in supervised classification. For example, in the satellite remote sensing map in summer, some vegetation with higher height obscures a large area of the impervious surface, so there is an urban area classification error, and after supervised classification, the classification results need to be further corrected, and this study applies the high-definition satellite remote sensing data of LocaSpaceViewer, and the correction of the supervised classification results is performed by applying the urban building 3D data of LocaSpaceViewer, as shown in Figure 2d,e. The accuracy of the urban area can be greatly improved after the three-way cross-checking of Landsat data, building data, and high-definition data, as shown in Figure 2f. The supervision classification results and the results of urban built-up areas in the severe cold region, cold region, hot-summer and cold-winter region, and hot-summer and warm-winter region are shown in Figure 3 and Figure 4.

In Shanghai’s statistical yearbook, residential buildings are classified into six categories: garden houses, joint houses, apartments, new-style lanes, old-style lanes, and simple houses for statistics. However, it is not possible to find the residential building area in the statistical yearbooks of most cities in the past years. Therefore, a method for calculating residential building area needs to be explored. This study uses urban 3D building data, AOI data, and POI data to distinguish residential buildings from urban buildings and then calculates and counts the area of residential buildings in the whole city. The specific identification process is shown in Figure 5.

The 3D building data of this study includes information such as the building base outline and building height. This data needs to be first corrected for coordinate bias before use, and the data from Baidu coordinates are corrected to WGS1984 data. The data obtained from Baidu Map is then fused and projected after the correction. At the same time, buildings with a building area of less than 10 m² are deleted using the editing function. Building blocks smaller than 10 m² are mostly building components, and this study does not consider the area of this part of the building. In the study, the building height was divided by 3.2 m to get the number of floors of each building, and the number of floors was multiplied by the base area of each building to get the total building area of each building. The buildings that fall within the boundaries of the neighborhood were selected by location and identified as residential buildings, while other buildings were identified as non-residential buildings. From the perspective of the acquired data, this study divides the residential buildings into two categories: residential buildings in residential areas and business residential buildings. Residential buildings are distinguished from urban buildings by neighborhood boundary data (AOI data), and business residences are distinguished from urban buildings by POI data.

After distinguishing residential buildings from urban buildings, the remaining buildings in this study are divided into five categories: schools, office employment, public services, commercial services, and industrial buildings. This study mainly uses different types of POI data existing within and around a certain range of the building vector and spatially connects POI and building vector by ArcGIS10.7 and Excel2016 software using the principle of closest and a certain range and increases the functional type attribute with the highest weight value to the building vector by the weight coefficient method. However, all building functions at the urban scale cannot be fully identified by POI data alone, so this study continues to use AOI data to supplement the identification of the remaining unidentified buildings to achieve functional classification of urban buildings, as shown in Figure 5.

2.2.2. Validation Methods

This study takes Nanjing city as an example to verify the accuracy of the classification method by comparing and analyzing its research data with the actual measurement data. Firstly, the building data of Nanjing city are converted into point data, and the kernel density analysis is performed, and then the different building density zones of Nanjing city are measured. Two circular areas with a radius of 500 m are selected as samples, and these two study areas are located in different building density zones, where sample 1 is located in the high-density zone, specifically near Xinjiekou in Xuanwu District, Nanjing, and sample 2 is located in the low-density zone, specifically near Yingtian Street in Jianye District, Nanjing, as shown in Figure 6.

The building classification method of the empirical data is to check the buildings in the sample area with the usage status of the real buildings one by one and classify the building categories into one of the five categories: residential, school, commercial service, public service, and office employment. The detailed validation data and empirical data classification results are shown in Figure 5, and the validation statistics are shown in

Table 2. Calibration area building information statistics of Nanjing.

Validate Area	Building Category	Building Area (m2)			Number of Buildings
		Verified Buildings	Measured Buildings	Accuracy	Verified Buildings	Measured Buildings	Accuracy
1	Residential Buildings	529,150.75	472,805.05	88.08%	150	168	89.29%
	Schools	76,187.61	545,36.95	60.30%	22	18	77.78%
	Commercial Buildings	1471353.68	2,046,872.43	71.88%	144	145	99.31%
	Buildings of Public Services	80,995.32	74,526.54	91.32%	23	15	46.67%
	Official Buildings	138,806.33	206,537.02	67.21%	44	40	90.00%
	Non-residential Buildings	1,767,342.93	2,382,472.94	74.18%	233	218	93.12%
	Total	2,296,493.68	2,855,277.99	80.43%	383	386	99.22%
2	Residential Buildings	1,054,009.73	1,085,333.14	97.11%	251	250	99.60%
	Schools	95,942.97	90,082.95	93.49%	19	24	79.17%
	Commercial Buildings	44,598.01	26,944.42	34.48%	12	20	60.00%
	Buildings of Public Services	11,461.822	20,528.43	55.83%	3	3	100.00%
	Official Buildings	128,335.04	137,094.72	93.61%	42	57	73.68%
	Non-residential Buildings	280,337.84	274,650.53	97.93%	76	104	73.08%
	Total	1,334,347.57	1,359,983.66	98.11%	327	354	92.37%

. It can be seen that the buildings are identified, and the accuracy of building data information is very high in both high-density and low-density building areas.

2.3. Methods of Calculating Three Types of Urban Morphology Indicators

2.3.1. Basic Morphological Index

(1)

Building density

After defining the urban boundary, the building density in the urban patches is calculated. This building density is the building coverage, specifically the ratio of the building footprint in the urban boundary to the built-up area of the city. It reflects the open space rate and building density in the city. The building density is calculated as shown in the formula below.

$$AREA={AREA}_f/{AREA}_b$$

(4)

AERA indicates building density; AERA_f is the building footprint; and AERA_b is the area of the built-up area of the city.

(2)

Building intensity

The building intensity of this study refers to the concept of floor area ratio in architecture, and the building intensity refers to the ratio of the total building area within the city boundary to the area of the built-up area of the city. It should be noted that the total building area in this concept of building intensity does not include the unaccounted area, i.e., the area of underground garages, underground equipment rooms, and underground commercial.

$$\mathrm{I}={\mathrm{I}}_a/{\mathrm{I}}_b$$

(5)

I denotes building intensity; I_a is the total building area; I_b is the built-up area of the city.

2.3.2. Two-Dimensional Morphological Indicators

(1)

Clustering (mean distance)

This indicator describes the degree of agglomeration of buildings in a city, specifically the average distance between buildings in the city. The closer the distance between buildings, the stronger the clustering of buildings in the city.

$$\mathrm{A}\mathrm{N}\mathrm{N}={\overline{D}}_O/{\overline{D}}_E$$

(6)

D_O is the observed average distance between each element and its nearest neighboring element.

$${\overline{D}}_O={\displaystyle \frac{{\sum }_{i=1}^n{d}_i}{\mathrm{n}}}$$

(7)

and D_E is the expected average distance between the specified elements in the random mode.

$${\overline{D}}_E={\displaystyle \frac{0.5}{\sqrt{n/A}}}$$

(8)

In the above equation, d_i equals the distance between an element and its closest neighbor, n corresponds to the total number of elements, and A is the area of the smallest outer rectangle that can include all elements, or a user-specified “area” value.

(2)

Homogeneity

This index refers to dividing the whole city into several cells and calculating the building density in each cell grid. A 2 km × 2 km fishing grid is set up, the building vector data is rasterized according to the image element size of 40 m × 40 m, the building raster data is reclassified into 1 class, each raster data value is set to 1600, the sum of partition statistics is calculated, the standard deviation of the sum is calculated, and the standard deviation is divided by 4 × 10⁶.

$$H_a={\displaystyle \frac{\sqrt{\frac{{\sum }_{i=1}^n{\left(a_n-a_i\right)}^2}{n}}}{b}}$$

(9)

where H_a refers to architectural equilibrium; a_n is the value of the nth fishing net statistic; a_i is the average of the sum of each net statistic; n is the number of nets, and b is equal to the area of each net, 4 × 10⁶.

(3)

Functional distribution

In this study, the buildings in the city are divided into two categories: residential buildings and non-residential buildings. The distribution characteristics of the two types of buildings in the city are analyzed, and the percentage of residential buildings and the percentage of non-residential buildings in the city are calculated.

$$F_u=F_a/F_b$$

(10)

F_u denotes functional distribution; F_a is the total residential building area; F_b is the total non-residential building area.

(4)

Urban building orientation

The urban building orientation indicator referred to in this study mainly describes the extent to which a building deviates from its average orientation. Two identical buildings, one facing south and north and the other deflected by an angle, will receive different amounts of solar radiation, etc., and therefore have different energy consumption. The angle between each building in the city and due north is first found, then the average angle of one city building is found, and the degree of deflection between the angle of each building and the average angle is calculated and weighted by the building area.

$$D_{\sigma }=\sum _{i=1}^n|{\displaystyle \frac{S_i}{S_{sum}}}\times \left(D_i-D_{average}\right)|$$

(11)

D_σ is the deviation from the city direction; D_i is the angle of the i-th building, D_average is the average angle of the building, n is the total number of buildings, and S_i is the area of the i-th.

2.3.3. Three-Dimensional Morphological Indicators

(1)

High urban uniformity

There is no simple quantitative formula for this metric. Imagine that two cities have the same density and floor area ratio, but the buildings in one city are of varying heights and are tall and short, while in the other city, they are all the same height; then the two urban forms are clearly different and also have an impact on urban energy consumption. In this study, the height data of urban buildings are standard deviated to describe the uniformity of urban height.

$$H_{\sigma }=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{\left(H_i-H_{average}\right)}^2}{n}}}$$

(12)

H_σ refers to the standard deviation of building heights (urban height uniformity); H_i is the height of the i-th building, H_average is the average building height, and n is the total number of buildings.

(2)

Urban sky view factor

The sky view factor calculated in this study is the ground sky view factor. The ground sky view factor (GSVF) reflects the sky view of each point on the ground, and the sky view factor of a city is the average of the GSVF values of each point in the city. The basic principle of calculating this index is to take a point on the ground as the center, form a hemisphere with a specific radius, and count the ratio of the projected area of buildings on the hemisphere to the entire surface area of the hemisphere, which is calculated by GIS10.7 software.

$$GSVF=1-{\displaystyle \frac{{\sum }_{i=1}^n\sin a_i}{n}}$$

(13)

$$\sin a_i={\displaystyle \frac{H}{\sqrt{R^2+H^2}}}$$

(14)

GSVF is the ground-level sky view factor; H is the height of the building, R is the buffer radius, which is 100 m in this study, and n is the total number of buildings intersecting the buffer.

(3)

Shading factor

This index refers to the degree of mutual shading between buildings. In this study, the shading factor is calculated using the Hillshade tool (Hillshade), a tool provided by ArcGIS for shading hills, which simulates a sun-parallel line light source.

$$H_i=H_a/H_b$$

(15)

H_i is the shading factor, H_a is the area of the shaded building roof, and H_b is the total area of the building footprint.

(4)

Shape coefficient of building

The shape coefficient of a building is an important indicator that affects building energy consumption at the individual building level, and the smaller the form factor, the more energy efficient the building. It is a comprehensive indicator of the overall building form factor in a city, which is closely related to energy consumption and directly affects the energy consumption of each individual building. The bulk factor of each building is weighted and summed by volume.

$$S_{average}={\displaystyle \frac{{\sum }_{i=1}^n\left(F_{i,roof}+F_{i,facades}\right)}{{\sum }_{i=1}^n{V}_i}}$$

(16)

S_average is the shape coefficient of the building; n is the total number of buildings; i is the i-th building; F_{i, roof} is the roof surface area of the building; F_{i, facades} is the surface area of the building envelope; and V_i is the volume of the i-th building.

3. Results

3.1. Correlation Between Total Urban Building Energy Consumption and Indicators of Urban Building Energy Consumption

• In severe cold regions, there is an overall trend that the larger the GDP, the number of resident population, the built-up area, and the building footprint area, the greater the total urban building energy consumption, as shown in Figure 7(a1–a4). Total building energy consumption is significantly correlated with resident population, GDP, and building footprint area at the 0.05 level, as shown in

  Table 3. Correlation between total building energy consumption and urban indicators by climate zone.

  Climate Regions	Indicators	R	P
  The severe cold regions	GDP (billion yuan)	0.866 *	0.026
  	Resident population (10,000 people)	0.933 *	0.007
  	Building footprint (million m2)	0.870 *	0.024
  	Total floor area (million m2)	0.888 *	0.018
  The cold regions	GDP (billion yuan)	0.957 **	0.000
  	Resident population (10,000 people)	0.984 **	0.000
  	Building footprint (million m2)	0.974 **	0.000
  	Total floor area (million m2)	0.961 **	0.000
  	Area of built-up area (square kilometers)	0.972 **	0.000
  The hot-summer and cold-winter regions	GDP (billion yuan)	0.982 **	0.000
  	Resident population (10,000 people)	0.929 **	0.003
  	Building footprint (million m2)	0.943 **	0.010
  	Total floor area (million m2)	0.908 **	0.005
  	Area of built-up area (square kilometers)	0.875 **	0.010
  In the hot-summer and warm-winter regions	Building footprint (million m2)	0.964 *	0.036
  	Total floor area (million m2)	1.000 **	0.000
  	Area of built-up area (square kilometers)	0.993 **	0.007
  	Total floor area of public buildings (million m2)	0.996 **	0.004

  The significance at the 0.05, 0.01, and 0.001 levels is marked by * and **, respectively.

  . The correlation coefficient shows that the correlation between total building energy consumption and these factors is extremely strong, as shown in Table 3.

In cold regions, there is a general trend that the larger the GDP, the resident population, the built-up area, and the total building area, the greater the total energy consumption of urban buildings, as shown in Figure 7(b1–b4). Total building energy consumption is significantly correlated with total building area, resident population, GDP, and built-up area at the 0.01 level, as shown in Table 3. The correlation coefficient shows that the correlation between total building energy consumption and these factors is extremely strong.

• In hot-summer and cold-winter regions, there is a general trend that the larger the total building area, resident population, and built-up area, the larger the total energy consumption of urban buildings, as shown in Figure 7(c1–c4). Total building energy consumption is significantly correlated with building area, resident population, GDP, and built-up area at the 0.01 level, as shown in Table 3. The correlation coefficient shows that the correlation between total building energy consumption and these factors is extremely strong.
• In hot-summer and warm-winter regions, there is a general trend that the larger the resident population, GDP, and total building area, the larger the total energy consumption of urban buildings, as shown in Figure 7(d1–d4). The total energy consumption is significantly correlated with the built-up area at the level of 0.01. Total energy consumption is significantly correlated with resident population and GDP at the level of 0.05, as shown in Table 3. The correlation coefficient shows that the correlation between total energy consumption and these factors is extremely strong, as shown in Table 3.

3.2. Correlation Between Energy Consumption of Urban Buildings and Urban Morphological Indicators Under Different Climate Zones

The average energy consumption per unit area in cities in severe cold regions is 67.59 kW·h/m², in cold regions 61.45 kW·h/m², and in hot-summer and cold-winter regions 43.26 kW·h/m². From the aspect of energy consumption per unit area, the severe cold areas are higher than the cold areas, and the cold areas are higher than the hot-summer and cold-winter areas. From the data on total heating energy consumption and total residential energy consumption in northern cities, it can be seen that the heating energy consumption in cities in severe cold regions is 3–4 times the total residential energy consumption throughout the year, as shown in Figure 8. The total heating energy consumption of buildings in cities in cold regions is almost equal to the total energy consumption of residential buildings throughout the year. In terms of residential energy consumption per unit area, it can be seen that with the change of latitude, there is a trend of increasing residential energy consumption per unit area from low latitude to high latitude.

The correlation study in four climate zones found the following relationships between energy consumption per unit area of buildings and urban morphology indicators in severe cold regions, cold regions, hot-summer and cold-winter regions, and hot-summer and warm-winter cities.

The indicators of aggregation and energy consumption per unit area of urban buildings in severe cold regions are extremely strongly correlated, with a significant correlation at the 0.05 level and a negative correlation between the two. Therefore, the stronger the aggregation among buildings in severe cold regions, the lower the energy consumption per unit area of urban buildings. Therefore, urban design in the form of agglomeration is desirable in severe cold regions. Meanwhile, construction intensity and energy consumption per unit area of urban buildings show a very strong correlation, with a significant correlation at the 0.05 level and a positive correlation between the two. In severe cold regions, a certain building intensity should be maintained, which is conducive to reducing energy consumption per unit area at the urban scale. In cold regions, urban orientation is extremely strongly correlated with energy consumption per unit area of urban buildings, with a significant correlation at the 0.01 level and a negative correlation between the two. In other words, the greater the change in urban orientation, the lower the energy consumption per unit area of urban buildings. Therefore, in cold regions, the enclosed building layout is conducive to urban energy efficiency.

• In hot-summer and cold-winter regions, shading coefficient, shape coefficient, and energy consumption per unit area of urban buildings are strongly correlated, with significant correlation at the 0.05 level, as shown in

  Table 4. Comparison table of analysis parameters of different regional climate types.

  Climate Zones	City Name	Basic Indicator		2D Morphology Indicator				3D Morphology Indicator				Building Energy Consumption
  		Building Density	Floor Area Ratio	Aggregation	Equilibrium	Functional Mix	City Direction	Building Height Uniformity	Sky View Factor	Shading Coefficient	Weighted Shape Coefficient	Energy Consumption per Unit Area (kWh/m2)	Total Energy Consumption (100 million kWh)
  Severe cold regions	Harbin	0.14	0.65	0.16	0.09	1.11	73.49	19.07	0.84	0.38	0.22	99.48	294.21
  	Changchun	0.11	0.44	0.22	0.09	1.23	62.56	14.90	0.85	0.55	0.24	64.92	194.57
  	Shenyang	0.14	0.63	0.43	0.09	1.33	59.43	19.13	0.85	0.30	0.23	66.41	310.51
  	Yinchuan	0.15	0.86	0.37	0.07	1.98	52.79	20.96	0.82	0.32	0.22	68.65	95.86
  	Hohhot	0.14	0.60	0.53	0.09	0.43	64.52	19.65	0.85	0.36	0.22	66.49	120.02
  	Urumqi	0.14	0.45	0.74	0.10	0.81	55.37	9.93	0.88	0.34	0.25	9.38	120.22
  Cold regions	Beijing	0.13	0.55	0.24	0.08	1.25	64.55	15.26	0.87	0.07	0.24	50.55	569.46
  	Tianjin	0.11	0.41	0.23	0.08	0.99	61.14	15.85	0.89	0.22	0.25	70.75	401.98
  	Taiyuan	0.10	0.37	0.50	0.09	0.13	62.03	16.39	0.87	0.00	0.22	68.16	127.99
  	Shijiazhuang	0.13	0.49	0.27	0.10	1.74	60.56	14.81	0.88	0.00	0.27	97.60	224.50
  	Jinan	0.13	0.55	0.36	0.10	1.01	62.87	16.29	0.85	0.30	0.22	54.12	162.95
  	Zhengzhou	0.10	0.45	0.44	0.10	1.24	62.03	15.86	0.85	0.25	0.25	56.66	221.77
  	Lanzhou	0.13	0.50	0.67	0.09	0.61	52.44	16.93	0.88	0.18	0.22	44.92	46.47
  	Lhasa	0.29	0.13	0.57	0.10	0.44	57.26	3.18	0.93	0.08	0.36	39.96	9.01
  	Xi’an	0.17	0.84	0.32	0.09	0.43	58.60	18.90	0.87	0.21	0.21	70.35	301.72
  Hot-summer and cold-winter regions	Shanghai	0.18	0.83	0.36	0.08	0.70	61.35	16.04	0.78	0.52	0.25	62.78	634.62
  	Chongqing	0.12	0.75	0.07	0.05	0.62	55.57	24.12	0.72	0.22	0.22	39.04	302.77
  	Chengdu	0.17	0.77	0.22	0.08	0.57	43.43	19.26	0.80	0.16	0.22	45.71	242.69
  	Hangzhou	0.13	0.57	0.21	0.07	0.75	64.87	23.39	0.76	0.19	0.24	46.41	231.95
  	Wuhan	0.13	0.60	0.28	0.08	0.90	51.78	17.05	0.76	0.20	0.21	31.81	220.81
  	Nanjing	0.14	0.61	0.25	0.07	0.87	60.59	14.78	0.77	0.20	0.23	41.85	209.88
  	Hefei	0.16	0.81	0.52	0.08	0.58	57.64	22.84	0.83	0.24	0.21	44.48	128.54
  Hot-summer and warm-winter regions	Guangzhou	0.15	0.55	0.25	0.09	1.17	76.40	14.55	0.88	0.08	0.27	57.62	392.26
  	Shenzhen	0.20	0.85	0.42	0.09	1.47	88.53	14.99	0.86	0.11	0.27	40.05	267.88
  	Xiamen	0.14	0.75	0.35	0.08	1.38	79.34	20.10	0.86	0.11	0.21	49.10	115.59
  	Nanning	0.16	0.70	0.19	0.08	2.08	83.69	14.31	0.89	0.08	0.26	44.47	102.55

  , and all of them are positively correlated. And it can be seen from the fitted equation that the shape coefficient has the greatest effect on urban building energy consumption per unit area. In hot-summer and cold-winter cities, the more complex the building’s body shape is, the higher the energy consumption per unit area of urban buildings. Therefore, from the perspective of urban energy saving, in the design of building monoliths, complex building design solutions in terms of form should be avoided as much as possible. Meanwhile, the larger the shading factor, the higher the energy consumption per unit area of urban buildings. In hot-summer and cold-winter areas, the best orientation of urban buildings should be chosen as much as possible to avoid enclosure and ensure the circulation of buildings.

• In hot-summer and warm-winter regions, urban orientation is extremely strongly correlated with energy consumption per unit area of urban buildings, with a significant correlation at the 0.05 level and a negative correlation between the two, as shown in

  Table 5. Correlation between energy consumption per unit area of urban buildings and urban form indicators by climate zone.

  Climate Regions	Indicators	R	P
  The severe cold regions	Building intensity	0.821 *	0.021
  	Clustering	−0.867 *	0.023
  The cold regions	City direction deviation	−0.883 **	0.024
  The hot-summer and cold-winter regions	Shading factor	0.809 *	0.027
  	Shape coefficient of building	0.797 *	0.032
  In the hot-summer and warm-winter regions	City direction deviation	−0.962 *	0.038

  The significance at the 0.05, 0.01, and 0.001 levels is marked by * and **, respectively.

  . In other words, the greater the change in urban orientation, the lower the energy consumption per unit area of urban buildings. Therefore, in hot-summer and warm-winter regions, the enclosed building layout is conducive to urban energy conservation.

3.3. The Mechanism of Urban Building Form Impacting Urban Building Energy Consumption

The correlation study of the four climate zones found that the urban morphological factors (basic morphological indicators, two-dimensional morphological indicators, and three-dimensional morphological indicators) influence the socio-economic behavior of the city and the urban microclimate through various factors, thus affecting the energy consumption of urban buildings, as shown in Figure 9. The indicator of aggregation is highly correlated with energy consumption per unit area of urban buildings in severe cold regions. Therefore, the stronger the aggregation among buildings in severe cold regions, the lower the energy consumption per unit area of urban buildings. When the aggregation of urban buildings is high, the density of urban buildings increases accordingly, which can minimize unnecessary building heat loss and gain, and the compact building layout can reduce the heating and cooling energy consumption of buildings, so cities with higher aggregation have lower energy consumption per unit area of urban buildings. Meanwhile, in severe cold regions, building intensity and energy consumption per unit area of urban buildings show an extremely strong correlation, with a significant correlation at the 0.05 level and a positive correlation between the two. In general, the construction intensity of a region is positively correlated with the degree of economic development of a city, and there is a direct correlation between the degree of economic development and building energy consumption, and as the population density increases and people’s demand for quality of life improves, the city’s energy consumption per area increases accordingly.

• In cold regions, urban orientation is extremely strongly correlated with energy consumption per unit area of urban buildings, with a negative correlation between the two. In other words, the greater the change in urban orientation, the lower the energy consumption per unit area of urban buildings. The organization of building groups, such as enclosed buildings, has an important impact on the heating, cooling, and ventilation energy consumption of buildings by affecting the intensity of the heat island effect, the urban ventilation corridor effect, and the urban microclimate, and thus the heat dissipation rate of buildings.

• In hot-summer and cold-winter regions, the shape coefficients are strongly correlated with the energy consumption per unit area of urban buildings, both of which are positively correlated. In hot-summer and cold-winter cities, the more complex the building’s shape is, the higher the energy consumption per unit area of urban buildings. The larger the building bulk factor is, the higher the demand for heating, cooling, and lighting energy consumption, thus making the energy consumption per unit area of the city higher. In hot-summer and cold-winter areas, the larger the shading coefficient, the higher the energy consumption per unit area of the building in the city. Avoiding enclosing buildings in hot-summer and cold-winter areas, building according to the best orientation of the city, and reducing mutual shading between buildings can obtain the maximum amount of solar radiation in winter, which has an impact on the building’s energy consumption for heating and lighting; at the same time, it can ensure the circulation of the building, improve the ventilation performance, and have an impact on the microclimate of the city, thus reducing the energy consumption for building cooling.
• In hot-summer and warm-winter regions, urban orientation and energy consumption per unit area of urban buildings are extremely strongly correlated, with a negative correlation between the two. In other words, the greater the change in urban orientation, the lower the energy consumption per unit area of urban buildings. The organization of building groups, such as enclosed buildings, has an important impact on the heating, cooling, and ventilation energy consumption of buildings by influencing the intensity of the heat island effect, the urban ventilation corridor effect, and the urban microclimate, and thus the heat dissipation rate of buildings.

From the aspect of energy consumption per unit area, those in severe cold regions are higher than those in cold regions, and those in cold regions are higher than those in hot-summer and cold-winter regions, from which it can be seen that temperature is an important factor affecting energy consumption per unit area of urban buildings. As can be seen from the energy consumption per unit area of residential buildings, with the change of latitude, the energy consumption per unit area of residential buildings tends to increase from low latitude to high latitude. As the latitude increases, the temperature gradually decreases in winter, which creates higher requirements for the heating of buildings, and this is the most important reason for the increase in residential energy consumption per unit.

The total energy consumption of buildings in the four major climate zones increased significantly with population, GDP, land use, and building scale. The energy consumption per unit area increased from low latitude to high latitude, reaching 67.6 kWh·m² in the cold area, which was about 1.5 times that of the hot-summer and cold-winter area, mainly due to the heating load in the high latitude winter. The coupling between urban form and energy consumption is significant, and high aggregation and low intensity in severe cold areas are conducive to energy saving; the enclosed and diversified orientation of cold- and hot-summer and warm-winter areas can reduce energy consumption; and the larger the body shape coefficient and shading in the hot-summer and cold-winter areas, the higher the energy consumption. The morphology determines the terminal energy consumption through microclimate regulation.

Comparison with existing studies shows that the findings of this paper are highly consistent with the conclusion of Su et al. that macro urban forms affect building energy consumption by regulating the urban thermal environment through the aggregation and dispersion dimension [42]. At the same time, the micro simulation results pointed out by Li and Gou [44] in eight cities across climate zones that building height and body shape coefficient have a significant positive effect on photovoltaic potential and self-supply efficiency in cold cities are supplemented, and the negative energy consumption effect of aggregation in severe cold areas on reducing heating demand is quantified at the macro scale for the first time. In addition, Zhao et al. [43] demonstrated that the shading of surrounding buildings can reduce the heat load in severe cold areas by 3.1%, and this paper verifies and expands this effect in a large sample of 26 cities and gives an elastic threshold. However, the multi-index optimization study of Murathan and Manioğlu [45] in Istanbul lacks extrapolation, and this paper clarifies the differentiated weights of the three factors of orientation, shading, and body shape in different climate zones through climate zoning regression, making up for the limitations of single-city research. In view of the two major gaps pointed out by Zhao et al. [43], there is a lack of quantitative relationship between measured energy consumption and urban morphology at the macro scale. Su et al. [42] used statistical yearbooks and remote sensing data to provide the elasticity coefficient of morphological indicators for energy consumption for the first time and directly embedded the results into the energy-saving design guidelines for sub-climate zones, realizing a closed loop from macro identification to planning application.

4. Conclusions

Based on the core hypothesis that urban morphology indicators can explain the differences in building energy consumption per unit area in different climate zones, it was found in 26 sample cities that the energy consumption per unit area increased significantly from the low value of hot-summer and warm-winter areas to the high level of severe cold areas, and the energy consumption per unit area decreased by about 0.05 for every standard deviation increase in building aggregation degree in severe cold areas. For each increase in shading factor, the energy consumption increases significantly. This result confirms for the first time the dual moderating effect of the form and climate coupling effect on energy consumption on a large scale and fills the gap in the research on the quantitative relationship between urban form and building energy consumption in China. In practice, the energy consumption should be reduced through compact layout in severe cold areas, optimization of orientation layout in cold areas, and control of shape and shading in hot-summer and cold-winter areas, which provides a direct basis for the energy-saving design guidelines of zoning buildings.

In severe cold regions, there is an overall trend that the larger the GDP, the number of resident population, the built-up area, and the building footprint area, the greater the total urban building energy consumption. In cold regions, there is a general trend that the larger the GDP, the resident population, the built-up area, and the total building area, the greater the total energy consumption of urban buildings. In hot-summer and cold-winter regions, there is a general trend that the larger the total building area, resident population, and built-up area, the larger the total energy consumption of urban buildings. In hot-summer and warm-winter regions, there is a general trend that the larger the resident population, GDP, and total building area, the larger the total energy consumption of urban buildings.

From the aspect of energy consumption per unit area, those in severe cold areas are higher than those in cold areas, and those in cold areas are higher than those in hot-summer and cold-winter areas. From the aspect of residential energy consumption per unit area, it can be seen that with the change of latitude, from low latitude to high latitude, the residential energy consumption per unit area shows a tendency to increase.

The indicator of aggregation in severe cold regions shows a very strong correlation with energy consumption per unit area of urban buildings, with a significant correlation at the 0.05 level and a negative correlation between the two. Meanwhile, the indicator of building intensity is strongly correlated with energy consumption per unit area of urban buildings, with a significant correlation at the 0.05 level and a positive correlation between the two. In cold regions, the indicator of urban orientation has a very strong correlation with energy consumption per urban building area, with a significant correlation at the 0.01 level and a negative correlation between the two. In hot-summer and cold-winter regions, the shading coefficient and shape coefficient of buildings are strongly correlated with energy consumption per unit area of urban buildings, and the correlation is significant at the 0.05 level, and both are positively correlated. In hot-summer and warm-winter regions, urban orientation and energy consumption per unit area of urban buildings showed a very strong correlation, and both were negatively correlated.

The stronger the aggregation among buildings in severe cold regions, the lower the energy consumption per unit area of urban buildings. In cold regions, urban orientation is extremely strongly correlated with energy consumption per unit area of urban buildings, with a negative correlation between the two. In hot-summer and cold-winter regions, the more complex the building’s shape is, the higher the energy consumption per unit area of urban buildings. In hot-summer and warm-winter regions, the organization of building groups, such as enclosed buildings, has an important impact on the heating, cooling, and ventilation energy consumption of buildings by affecting the intensity of the heat island effect, the urban ventilation corridor effect, and the urban microclimate, thus affecting the heat dissipation rate of buildings.

From the aspect of energy consumption per unit area, the severe cold areas are higher than the cold areas, and the cold areas are higher than the hot-summer and cold-winter areas, from which it can be seen that temperature is an important factor affecting the energy consumption per unit area of urban buildings. As the latitude increases, the temperature gradually decreases in winter, which creates higher requirements for the heating of buildings.

Although this paper analyzes the correlation between building energy consumption and urban morphology indicators in 26 cities at a macroscopic scale, there are certain limitations, such as that the sample of cities is small and could be further increased, the urban building form data need to be further tested, and the correlation between urban morphology and urban building energy consumption needs to be further explored. This requires a more detailed cooperation system in future research and in-depth cooperation among different disciplines to enhance the accuracy of data and the validity of conclusions.

5. Limitations and Future Work

5.1. Scope of the Study and Methodological Limitations

In this study, there are certain research scopes and methodological limitations when discussing the impact of urban morphology on the energy consumption of urban buildings. First, the choice of study sample may have influenced the generalizability of the results. Due to resource and time constraints, the sample size may not be sufficient to fully represent the entire research field. Secondly, this study mainly relies on quantitative analysis, which provides data support but may lack an in-depth understanding of complex social phenomena. Additionally, some measurement tools and methods used in research can be subjective, which can affect the accuracy of the results.

The climate zone classification implies the assumption of topographic homogeneity, which does not discuss the impact that mountain cities may have on energy consumption through microclimate, building layouts, or energy infrastructure. The control of confounding variables mainly relies on the standardization and statistical decomposition of remote sensing data, but no special correction method is designed for the terrain. Future studies need to clarify whether topographic variables can be used as independent factors for energy consumption prediction or stratified analysis.

5.2. Future Research Directions

Future studies may consider expanding sample size and sample diversity to improve the generalizability and reliability of research results. At the same time, it is recommended to employ qualitative research methods, such as in-depth interviews and case studies, to complement existing quantitative analysis for a more comprehensive understanding of the research topic. In addition, future studies can explore the impact of urban forms on urban building energy consumption under different cultural backgrounds to test the cross-cultural applicability of the results of this study. Finally, it is recommended to innovate research methods, such as the use of big data analysis or artificial intelligence technology, to improve research efficiency and depth. With these methods, future research will be able to provide deeper and more precise insights.