A Multivariate Model and Correlation Study on the Impact of Typical Residential Spatial Forms in the Middle Reaches of the Hanjiang River on the Thermal Environment and Thermal Comfort

Abstract

Different spatial forms affect the indoor thermal environment and human thermal comfort. A good living environment largely depends on the flexibility of spatial forms, and spatial scale and proportion are the key factors affecting these forms. We selected typical residential houses in the middle reaches of the Hanjiang River in the hot summer and cold winter climate area as an example. Through on-site measurements and questionnaire surveys, we studied the impact of residential form indicators on the thermal environment and thermal comfort. We also established a multivariate model to explore the correlation among various parameters. The results showed that the spatial-real ratio of the residential spatial form index in the middle reaches of Hanjiang River was 5–58%. The height from the ground was 2.23–6.92 m. The open-space ratio was 0.04–4.55. The explanatory power of the spatial form index to indoor air temperature was 57.5%, with a strong correlation (R² = 0.675). The explanatory power for humidity was 38.2%, with a weak correlation (R² = 0.525). The explanatory power of SET was 30.6–50.1%, with a weak correlation (R² = 0.466). The explanatory power of PMV was 6.5–31.7%, and PMV1.0 was weakly correlated (R² = 0.474). The explanatory power for PPD was 15.5%, where PPD 1.0 was close to a weak correlation (R² = 0.508). The results of this study provide reference values for the design methods of and decision-making process for green and energy-saving regional buildings.

1. Introduction

In recent years, energy conservation and emission reduction in the construction industry have received increasing attention. According to statistics, the energy consumption of buildings in China is 1 billion tce, accounting for 21% of the national energy consumption. It is predicted that the proportion will reach 29% by 2040 [1,2]. It is of great significance for research on building energy efficiency to solve energy shortage issues, reduce carbon emissions, and promote sustainable development. Previous studies have shown that the energy efficiency of a passive design strategy can be improved by 20% through spatial form regulation in the early stages of building design, and heating energy consumption and cooling energy consumption can also be reduced by 25% and 10–30% [3], respectively, which would significantly reduce costs compared with the selection of high-performance materials and improvement of active measures.

After thousands of years of trial and error, residents have learned to use local materials to live in a comfortable and low-energy manner while also adapting to climate and environmental changes under conditions of limited energy and technology, which reflects the wisdom of ecological construction technology [4,5]. They not only reflect the microcosm of local residents’ production and life styles but also externalize and express diversified spatial forms with regional characteristics [6,7]. Many studies have confirmed that different spatial forms affect the indoor thermal environment and human thermal comfort [8]. A good living environment largely depends on the flexibility of spatial forms, and spatial size, proportion, and orientation [9,10] are the key factors affecting them. We reference previous studies on the applicability of some spatial form indexes to improve the indoor thermal environment and thermal comfort as references for this study. Conclusions about the impact of indicators, such as the virtual-real ratio [11], the height above the ground [12,13], and the open-space ratio [14], on the thermal environment are more applicable to hot and humid climates. The spatial orientation and virtual-real ratio can effectively regulate temperature and wind speed. The causal relationship and proportion between them can also affect people’s use and communication and interaction [15]. For example, Gratia et al. [16] determined that the difference of heat load between the highest and lowest virtual-real ratio (1.24–0.84) was 18.6%. Ourghi [17] found that it was necessary to use surface area and compactness to represent the openness of spatial form.

The environmental parameters based on human thermal comfort include air temperature (Ta), relative humidity (RH), average radiation temperature, standard effective temperature (SET), actual thermal sensation, and thermal discomfort index [18,19,20,21]. These evaluation indicators are closely related to different spatial forms [22]. Several studies have shown that when indoor temperature and humidity are too high or too low, people feel uncomfortable. They can block strong solar radiation by adjusting spatial layout [23], spatial form [24], spatial interface [25], and plant configuration [26], which can reduce discomfort and enhance the vitality of space utilization to improve the level of the living environment. The SET can even be reduced by 6–10 °C by changing the spatial form [27]. Although previous studies have quantified the impact of building types in different climate zones on improving the indoor thermal environment [28], it may apply to one climate zone, but the impact degree and scope of other climate zones remains unknown. At present, most of the relevant studies have focused on cold [29] and mild climate areas [30], and few relevant studies have examined the middle reaches of Hanjiang River in China, which is a typical hot summer and cold winter climate area. Little research has studied the influence of spatial form, thermal environment, and thermal comfort in the middle reaches of Hanjiang River. Some scholars [31] have suggested that the spatial form of buildings should be quantitatively analyzed and optimized in combination with different regions and types. Therefore, it holds great significance and practical value to study the quantitative relationship between the spatial form of residential buildings in different regional environments, thermal environment, and thermal comfort.

In addition, multiple regression models and correlation analysis feature three main parts: data definition, data transformation, and data analysis. Previous studies have used multiple regression models in data analysis for data calculation, and scientifically and rigorously quantified three types of potentially related topics in the field of architecture, mainly distributed in the analysis of public building energy consumption, urban design, and street vitality. Traditional residential spatial forms also have been gradually explored, such as Zhang Qian’s first use of the SPSS software V 23.0 regression method to analyze the correlation between tunnel spatial characteristics and the indoor and outdoor thermal environment; Yang Tao constructed a relevant indicator system for the architectural and courtyard forms of traditional courtyard houses in Hongcun, Hanzhong, and Hancheng, and analyzed their climate adaptability and application strategies using linear correlation analysis in SPSS software. The specific analysis under different regional climate conditions, however, still needs further study. Correlation analysis has usually used the rank correlation coefficient to represent the degree or direction of linear correlation between variables in terms of classification level.

In this study, we focused on these practical problems, taking typical residential buildings in the middle reaches of the Hanjiang River as the research object. Through on-site measurements and questionnaire surveys, we studied the impact of residential form indicators on the thermal environment and thermal comfort. By quantifying statistics and analyzing data, we explored the mechanisms of mutual influence and explored the explanatory forms and strengths between various combinations of indicators and parameters. We also provided a reference value to promote the development of green and energy-saving design from the perspective of architectural space.

2. Materials and Methods

2.1. Research Methods

Statistically, a relationship involving more than two variables is often expressed as a linear relationship [32]. The technology road map of this study is shown in Figure 1.

According to the rank correlation method, two rank sequences are arranged with related relationships in a certain way, and then Spearman’s formula is used to determine the degree of correlation between the two rank orders. Usually, 0 indicates no correlation between the two, −1 indicates negative correlation, and 1 indicates positive correlation. The closer to −1 or 1, the stronger the correlation.

2.2. Regional Climate and Sample Characteristics

We sourced meteorological data for this study from the National Meteorological Information Center (http://data.cma.cn), accessed on 1 January 2024. The basic outdoor meteorological parameters were provided by the China Building Energy Efficiency Design Basic Data Platform. The Hanjiang River basin belongs to a transition zone of subtropical humid monsoon continental climate, and the seasonal temperature changes significantly. The annual average temperature is 16.7 °C, which follows a fluctuating upward trend. Affected by terrain and other factors, different areas in the same climate zone present different climate environments, and the spatial form characteristics of residential buildings are also different. Therefore, in this study, we took full account of the natural geographic characteristics when selecting samples, including the following research objects: the old street of Xiangyang Chenlao Lane, Ruan Xiangtai’s former residence (sample A), and Taiping Old Street Jiangxi Guild Hall (sample B), which were represented by the hilly land and plains; Qiushi residence (sample C) in Qianwan Town, Zaoyang City, which was mainly hilly; and Feng folk house (sample D) in Banqiao Town, Nanzhang County, which was represented by mountainous area. Details are shown in Figure 2 and

Table 1. List of basic information of research objects.

Research Object	Sample A	Sample B	Sample C	Sample D
Era build	Qing dynasty	Qing dynasty	Qing dynasty	Qing dynasty
Permanent population	6	4	2	0
Building orientation	West facing east	East facing west	Facing south	Facing south
Floor area	319.92 m2	200.82 m2	244.42 m2	841.51 m2
Building stories	Local layer 2	Local layer 2	Local layer 2	Local layer 2
Architectural structure	Post and panel structure	Post and panel structure	Post and panel structure	Post and panel structure
Building envelope	Blue brick wall; wood doors and windows Slope roof (wood purlin + wood rafters + gray tile)	Blue brick wall; wood doors and windows Slope roof (wood purlin + wood rafters + gray tile)	Blue brick wall; wood doors and windows Slope roof (wood purlin + wood rafters + gray tile)	Blue brick wall wood doors and windows Slope roof (wood purlin + wood rafters + gray tile)
Heat transfer coefficient W/m2·K	1.67	1.54	1.46	1.58
Thermal resistance m2·K/W	0.66	0.37	0.75	0.68
Cooling method	Natural ventilation	Natural ventilation	Natural ventilation	Natural ventilation

.

2.3. Spatial Form Index

The virtual–solid ratio (VSR) was the ratio between the virtual area (doors and windows) and the solid area (walls) of the facade of residential buildings. Height from ground (HFG) was the distance between the top of a space and the ground. The open-space ratio (OSR) was the ratio of the length of the open space to the total perimeter. The formula is given in

Table 2. Definition and calculation formula of residential space interface shape index.

Morphological Index	Definition	Computational Formula
Delivery criterion	The distance between two adjacent transverse positioning axes, m	L
Depth	The actual length between the front and back walls of the building, m	W
Terrain clearance	Height of roof surface (floor) to indoor floor, m	H
Space-solid ratio/virtual-real ratio	Virtual area divided by solid area, m2	Svirtual/Sreal
Open-space ratio	The open length based on the perimeter divided by the total perimeter	Lopen/Ltoal
General perimeter	The sum of the lengths of all sides of the perimeter	Ltotal

.

2.4. Thermal Environment Parameters and Thermal Comfort Indexes

The thermal comfort parameters were temperature (Ta) and relative humidity (RH), and the wind speed in most rooms was almost 0. Therefore, we did not consider the wind speed. Thermal comfort indicators included SET and predicted mean vote (PMV). Considering the fact that comfort varied from place to place, we also used the thermal discomfort index PPD to evaluate the degree of discomfort. According to the survey, the thermal resistance of clothing worn by local residents in summer was 0.3 clo (typical clothing was short sleeves, trousers, and sandals), and the activity level was 1.0 met (such as sitting), 1.5 met (standing), and 2.0 met (such as walking). Therefore, we selected SET, PMV, and PPD for analysis in this study.

2.5. Test Instruments

The test contents included indoor and outdoor air temperature, relative humidity, wind speed, and black sphere temperature required for the calculation of thermal comfort index. The test period was from 25 June to 18 August 2023, and the recording frequency was once every 10 min. Test instruments and parameters are shown in

Table 3. Test instruments and parameters.

Measurement Content	Name	Measuring Range	Precision	Test Cycle
Air temperature and humidity	ONSET HOBO UX100-011 High precision temperature and humidity recorder	−20 °C to 70 °C, 1–95%	0.024 °C, 0.01%	72 h
wind speed	WWFWZY-1 wireless universal wind speed and temperature recorder	−260 °C to 1370 °C	0.04 °C	72 h
Black ball temperature	Heat index HD32.3TC	−5 °C to 50 °C	ClassA 1/3DIN	instantaneous
Subjective evaluation scale

. The thermal comfort questionnaire was based on ASHRAE Standard 55-2013 and GB/T50785-2012 [33,34], “Evaluation Standards for Indoor Thermal and Humid Environment of Civil Buildings”.

3. Results

3.1. Spatial Form Index Distribution Characteristics of Residential Buildings

Based on the field survey and mapping data, the morphological index values of 19 typical spaces of the four sample dwellings are shown in

Table 4. Spatial interface shape index of each typical space of sample residential buildings.

Encoding	Room Name	Space-Solid Ratio/Virtual-Real Ratio	Terrain Clearance	Open-Space Length	General Perimeter	Open-Space Ratio
A-1	Lobby	0.13	6.92	7.78	23.54	0.33
A-2	Courtyard 1	0.13	5.73	4	16	0.25
A-3	Courtyard 2	0.58	6.28	12.6	16.45	0.77
A-4	Three halls	0.22	4.04	8.28	18.6	0.45
B-1	Lobby	0.29	3.6	9.1	35	0.26
B-2	Courtyard	0.32	4.2	5.4	26.8	0.2
B-3	Wing-room	0.19	2.21	1.23	12.1	2.65
B-4	Principal room	0.18	4.56	1.52	17.56	21.6
C-1	Lobby	0.47	2.7	5.94	10.8	0.55
C-2	Courtyard	0.13	5	5.68	21.8	1.55
C-3	Second hall	0.13	2.55	2.96	19.89	2.55
C-4	Wing-room	0.23	2.93	1.66	18.52	3.55
C-5	Second floor	0.05	2.23	1.64	16.74	4.55
D-1	West to east wing	0.09	2.59	0.7	17.38	0.04
D-2	West to the second-floor west wing	0.12	2.75	0.7	17.38	0.04
D-3	West to the second floor	0.12	3.8	1.4	19.7	0.07
D-4	Two halls west	0.22	4.96	4.22	21.8	0.19
D-5	East into the second floor	0.12	2.76	1.43	18.85	0.08
D-6	East into the first floor	0.31	3.3	2.56	19.2	0.072

.

Figure 3 shows the numerical values of various morphological indicators of the spatial interface of the sample residential buildings.

As shown in Figure 3, the values for the morphological indicators were as follows: the average value of the virtual-real ratio was 20%, which ranged from 5% to 58%; the average height above the ground was 3.9 m, which ranged from 2.23 m to 6.92 m; and the average OSR was 1.07, which ranged from 0.04 to 4.55. The results showed that to block the summer radiation and sunshine, the window area of each space was small, the height of the first floor and the attic space of the second floor were appropriately increased, and the local open space was strengthened to improve the air convection to cope with the local environment’s high temperature and high humidity.

3.2. Influence of Spatial Form Index on Indoor and Outdoor Thermal Environment

3.2.1. Measured Thermal Environment on Site

The summer thermal environment characteristics of traditional residential houses in the Hanjiang River Basin are shown in

Table 5. Measured values of outdoor thermal environment.

Numerical Value	Solar Radiation	Outdoor Air Temperature	Outdoor Relative Humidity	Outdoor Wind Speed
Mean value	203.73	28.17	74.16%
Maximum value	926.85	42.15	97.8%	12.67
Minimum value	0	15.94	35.1%	0.08

.

As shown in Table 5, traditional dwellings in the Hanjiang River Basin have the characteristics of high temperature, high humidity, strong radiation, and low wind speed in the summer in a typical climate area with a hot summer and cold winter. Under the action of outdoor climate conditions, 19 typical spatial forms also affected the temperature and humidity changes of the indoor thermal environment. The changing trends in air temperature and relative humidity are shown in Figure 4 and Figure 5, respectively.

We tested samples A–C in August and sample D in June, which showed differences in temperature and humidity as a result of seasonal factors. According to the results shown in Figure 4 and Figure 5, the temperature and humidity range in different spaces was 17.7–35.14 °C, and the temperature difference between the indoor and outdoor space was −2.46 °C–5.47 °C. The relative humidity was 36.07–88.97%. The indoor heterodyne value was between −15.86% and 13.46%.

From this analysis, the following conclusions were drawn: the courtyard was the first gradient to reduce the indoor and outdoor temperature difference; interior walls and shading components were the second gradient; the stratification of the longitudinal space layout caused the temperature difference to gradually increase—that is, the lower the indoor temperature was 1–2 °C. The influence of building height led to higher temperature in the front hall of Jiangxi Guild Hall and the second floor of Qiu family residence. It was obvious that the height, location, and open area of the indoor space was affected by temperature and humidity. For example, the humidity of the wing room was greater (the level of the floor), the humidity of the main room was greater than that of the second floor (the height of the floor was higher), the contact area between the front room and the outside was large, and the entrance was more open.

3.2.2. Multiple Regression Model

We conducted multiple linear regression analysis with VSR, HFG, and OSR as the independent variables, and average air temperature and relative humidity for each of the typical spaces as the dependent variables. The results are shown in

Table 6. Coefficients of typical space and temperature and humidity.

Indoor Thermal Environment	Model	Nonnormalized Coefficient		Standardization Coefficient (Beta)	p-Value (p)	Variance Inflation Factor (VIF)
		(B)	(Std. Dev.)
Air temperature	(constant)	16.712	2.694		0.000
	Virtual–solid ratio/air–solid ratio (VSR)	9.557	5.665	0.317	0.122	1.085
	Ground clearance m-OSR	1.246	0.576	0.431	0.056	1.225
	More open space than m-HFG	2.476	0.601	0.798	0.002 *	1.155
Relative humidity	(constant)	89.265	7.203	-	0.000
	Virtual–solid ratio/air–solid ratio (VSR)	−18.023	15.117	−0.271	0.261	1.085
	Ground clearance m-OSR	−2.05	1.540	−0.321	0.213	1.225
	More open space than m-HFG	−4.973	1.607	−0.725	0.011 *	1.155

Note: VIF results are all ≤ 10, indicating that the data basically conforms to the hypothesis of multiple linear analysis, that is, there is no multicollinearity problem. Therefore, all data in this case meet the requirements and can be used for multiple linear regression operation. * is significant correlation (p < 0.05).

.

The descriptive statistics showed that the average indoor air temperature was 26.15 °C, and the average relative humidity was 72.33%. The abstract of the regression model of air temperature showed that R² = 0.675, which can be interpreted to mean that the three shape indexes of virtual-real ratio, OSR, and HFG can explain the change in air temperature from 57.8% to 67.5%, which indicated that the change of the shape index had a significant influence on air temperature. The regression model of relative humidity showed that R² = 0.525, which can be interpreted to mean that the three morphological indexes of VSR, OSR, and HFG can explain 38.2% to 52.5% of the change in air temperature, which indicated that the change in the morphological index had a certain influence on the relative humidity. The results of the significance test showed that the F value = 6.94, p = 0.008 (p-value < 0.05 indicates that a linear correlation between the dependent variable and the independent variable), which indicated that there was a linear correlation between the independent variable of the three morphological indicators and the dependent variable of air temperature. The results of the significance test showed that the F value = 3.679, p-value = 0.051. The regression model can be assumed as follows:

$$\mathrm{Typical}\mathrm{mean}\mathrm{air}\mathrm{temperature}=B0\left(\mathrm{constant}\right)+B1\ast VSR+B2\ast 0SR+B3\ast HFG$$

$$\mathrm{Typical}\mathrm{mean}\mathrm{air}\mathrm{temperature}=0.798\ast HFG$$

The significance test results of the respective variables in the model showed that p < 0.005, which was statistically significant. Because the OSR was p < 0.005, the regression model in this case (no constant was added when the standardized coefficient is used) was as follows:

$$\mathrm{Typical}\mathrm{spatial}\mathrm{mean}\mathrm{relative}\mathrm{humidity}=B0+B1\ast VSR+B2\ast OSR+B3\ast HFG$$

$$\mathrm{Typical}\mathrm{spatial}\mathrm{mean}\mathrm{relative}\mathrm{humidity}=1.607\ast HFG$$

The results of multiple regression analysis of the three indexes of spatial morphology and thermal environment parameters showed that the air temperature increased with an increase in the VR-real area, while the relative humidity decreased. This result showed that the larger the window area of indoor space in the summer, the higher the possibility of outdoor heat flow into the room, and the lower humidity could avoid certain indoor humidity. The HFG was negatively correlated with air temperature and was positively correlated with relative humidity, which indicated that the average temperature of the indoor space decreased and humidity increased with an increase in height. The OSR was positively correlated with mean temperature and relative humidity, which indicated that the more open the space, the stronger the convection and heat transfer effect.

3.2.3. Correlation Analysis

Figure 6 shows the Spearman correlation between spatial form indicators and the indoor thermal environment.

The test results of the Spearman correlation analysis in Figure 6 showed that the significance probability levels of the virtual-real ratio, HFG, OSR, and average temperature were 0.43, −0.0071, and 0.59, respectively; the significance probability levels with relative humidity were −0.092, 0.13, and 0.87, respectively. The significance probability level of the OSR was higher and the other variables were lower.

3.3. Influence of Spatial Form Index on Indoor Thermal Comfort Evaluation Index

3.3.1. Results of Questionnaire Survey

The thermal response of the human body to SETs and the calculation results are shown in Figure 7, Figure 8 and Figure 9.

According to results shown in Figure 7, Figure 8 and Figure 9, the SET was 18.5–36.7 °C, the actual thermal sensation PMV was −2.5 to 4.7, and the thermal discomfort index PPD was 5–100%. With the change in spatial form and the increase in activity frequency, the thermal sensation of the respondents changed from slightly cool and neutral (normal health state, no obvious sweating) to slightly warm and further transitioning to very hot and uncomfortable. Most respondents were in the medium and above category, that is, from a normal state of health to an uncomfortable state, with vasoconstriction and increased sweating. Additionally, the thermal comfort differences in different spaces were significantly affected by morphological changes.

3.3.2. Multiple Regression Model

The results of multiple linear regression analysis are shown in

Table 7. Coefficients of each typical space and thermal comfort index SET.

Thermal Comfort Parameter	Model	Nonnormalized Coefficient		Standardization Coefficient (Beta)	p-Value (p)	VIF
		B	Std. Dev.
SET	SET 1.0 met
	(constant)	27.838	1.413		0
	Virtual–solid ratio/air–solid ratio (VSR)	2.398	2.966	0.195	0.438	1.085
	Ground clearance m-OSR	0.183	0.302	0.155	0.557	1.225
	More open space than m-HFG	−0.69	0.315	−0.544	0.054 *	1.155
	SET 1.5 met
	(constant)	28.699	1.531
	Virtual–solid ratio/air–solid ratio (VSR)	4.318	3.212	0.285	0.209	1.085
	Ground clearance m-OSR	0.185	0.327	0.128	0.584	1.225
	More open space than m-HFG	−0.938	0.342	−0.602	0.021 *	1.155
	SET 2.0 met
	(constant)	29.422	1.449		0
	Virtual–solid ratio/air–solid ratio (VSR)	4.146	3.041	0.278	0.203	1.085
	Ground clearance m-OSR	0.182	0.31	0.128	0.569	1.225
	More open space than m-HFG	−0.964	0.323	−0.628	0.014 *	1.155
PMV	PMV 1.0 met
	(constant)	0.822	0.461		0.105
	Virtual–solid ratio/air–solid ratio (VSR)	1.047	0.968	0.258	0.305	1.085
	Ground clearance m-OSR	0.094	0.099	0.241	0.364	1.225
	More open space than m-HFG	−0.188	0.103	−0.45	0.097	1.155
	PMV 1.5 met
	(constant)	0.844	0.333		0.03
	Virtual–solid ratio/air–solid ratio (VSR)	0.716	0.699	0.286	0.33	1.085
	Ground clearance m-OSR	0.046	0.071	0.193	0.53	1.225
	More open space than m-HFG	−0.069	0.074	−0.268	0.375	1.155
	PMV 2.0 met
	(constant)	0.863	0.288		0.013
	Virtual–solid ratio/air–solid ratio (VSR)	0.704	0.605	0.298	0.271	1.085
	Ground clearance m-OSR	0.043	0.062	0.189	0.503	1.225
	More open space than m-HFG	−0.095	0.064	−0.39	0.172	1.155
PPD	PPD 1.0 met
	(constant)	0.304	0.174		0.112
	Virtual–solid ratio/air–solid ratio (VSR)	0.443	0.366	0.28	0.254	1.085
	Ground clearance m-OSR	0.026	0.037	0.172	0.499	1.225
	More open space than m-HFG	−0.084	0.039	−0.517	0.056 *	1.155
	PPD 1.5 met
	(constant)	0.276	0.12		0.045
	Virtual–solid ratio/air–solid ratio (VSR)	0.291	0.253	0.306	0.275	1.085
	Ground clearance m-OSR	0.009	0.026	0.1	0.732	1.225
	More open space than m-HFG	−0.04	0.027	−0.405	0.17	1.155
	PPD 2.0 met
	(constant)	0.266	0.107		0.033
	Virtual–solid ratio/air–solid ratio (VSR)	0.295	0.225	0.322	0.22	1.085
	Ground clearance m-OSR	0.01	0.023	0.111	0.681	1.225
	More open space than m-HFG	−0.045	0.024	−0.474	0.091	1.155

Note: VIF results are all ≤ 10, indicating that the data basically conform to the hypothesis of multiple linear analysis, that is, there is no multicollinearity problem. Therefore, all data in this case meet the requirements and can be used for multiple linear regression operation. * is significant correlation (p < 0.05).

, with the three morphological indexes of virtual-real ratio (VSR), HFG, and OSR as the independent variables, and the thermal comfort indexes SET, PMV, and PPD (1.0 met, 1.5 met, and 2.0 met) at different active metabolic rates as dependent variables.

As shown in Table 7, the SET_avg of the sample dwellings was 28.29–29.92 °C. PMV_avg was 1.19–1.07; and PPD_avg was 40.36–31.43%. The explanatory degree of the SET variation was 30.6–61.6%, that of actual thermal sensation PMV variation was 6.5–47.4%, and that of thermal discomfort index variation was 27.5–36%. The regression model summary was as follows: SET1.0 met, 1.5 met, and 2.0 met (R² = 0.466, 0.585, 0.616); PMV1.0 met, 1.5 met, and 2.0 met (R² = 0.474, 0.281, 0.395); and PPD1.0 met, 1.5 met, and 2.0 met (R² = 0.508, 0.35, 0.442). The results of the significance test were as follows: SET1.0 met, 1.5 met, and 2.0 met (F value = 2.907, 4.694, 5.349; p = 0.088, 0.027, 0.019), and p-value < 0.05, which indicated that there was a linear correlation between the dependent variable and the independent variable. The results showed that there was a linear correlation between the independent variables of the three morphological indicators and the SET1.5 met/SET2.0 met dependent variables. PMV1.0 met (F = 3.009, p = 0.081), PMV1.5 met (F = 1.3, p = 0.327), and PMV2.0 met (F = 2.174, p = 0.154, p < 0.05), which indicated that there was a linear correlation between the dependent variable and the independent variable. The results showed that there was no linear correlation between the independent variables and PMV dependent variables. PPD1.0 met (F = 3.435, p = 0.06), PPD1.5 met (F = 1.3, p = 0.327), PPD2.0 met (F = 2.644, p = 0.107), and p < 0.05, which indicated that there was a linear correlation between the dependent variable and the independent variable. The results showed that there was no linear correlation between the independent variables and the PPD dependent variables. The regression model can be assumed as follows:

$$\mathrm{Typical}\mathrm{space}SET=B0\left(\mathrm{constant}\right)+B1\ast VSR+B2\ast 0SR+B3\ast HFG$$

$$\mathrm{Typical}\mathrm{space}PPD=B0\left(\mathrm{constant}\right)+B1\ast VSR+B2\ast 0SR+B3\ast HFG.$$

The significance test results of the respective variables in the model showed that p < 0.005 was statistically significant (PMV regression model was not valid). Because only the OSR was p < 0.005, the regression model in this case (no constant was added when the standardized coefficient is used) was as follows:

$$\mathrm{Typical}\mathrm{space}SET=-(0.69—0.938)\ast HFG$$

$$\mathrm{Typical}\mathrm{space}\mathit{PPD}=-0.084\ast \mathit{HFG}$$

The results of multiple regression analysis of the three indices of spatial form on the evaluation index of thermal comfort showed that changes in the three indices of virtual-real ratio, OSR, and HFG had a great influence on SET and had some effect on PMV. It had a certain degree of influence on PPD. The results of the significance test showed that there was a linear correlation between the independent variables of the three morphological indicators and the dependent variables of SET and PMV, but there was no linear correlation between the dependent variables of PPD.

3.3.3. Correlation Analysis

Figure 10 shows the Spearman correlation between spatial form indicators and thermal comfort parameters.

The test results of the Spearman correlation analysis shown in Figure 10 indicated that the significance probability levels of the virtual-real ratio, HFG, OSR, and SET were 0.29–0.41, 0.32–0.44, and −0.0.3 to −0.38. The significance probability levels of PMV were 0.29–0.4, 0.33–0.39, and 0.33–0.39. The significance probability levels of PPD and PPD were 0.31–0.4, 0.33–0.39, and −0.21 to −0.29. The SET was positively correlated with the actual thermal sensation PMV, whereas the thermal discomfort PPD was negatively correlated.

4. Conclusions

In this study, we used the Spearman-grade correlation coefficient to explore the influence of the residential spatial form on indoor thermal environment and thermal comfort in the middle reaches of the Hanjiang River, which was helpful to explore the internal correlation between spatial form and environmental parameters. The main conclusions are as follows:

• We quantified the range value of the key spatial form index and the variation interval of thermal environment and thermal comfort through field measurement of typical residential buildings and questionnaire users, in which the virtual-real ratio was 5–58%; the HFG was 2.23–6.92 m; and the OSR was 0.04–4.55.
• We established regression models for the three spatial form indexes, thermal environment parameters, and thermal comfort indexes. Among them, the explanatory power of the spatial form index to indoor air temperature was 57.5%, with strong correlation (R² = 0.675). The explanatory power for humidity was 38.2%, with weak correlation (R² = 0.525). The explanatory power of SET was 30.6–50.1%, with weak correlation (R² = 0.466). The explanatory power of PMV ranged from 6.5% to 31.7%, and PMV1.0 was weakly correlated (R² = 0.474). The explanatory power for PPD was 15.5%, where PPD1.0 was close to a weak correlation (R² = 0.508).
• Based on the correlation analysis of the indicator variables, we obtained the correlation coefficient between indicator parameters. When the permeability ratio of space form was larger, the air temperature and SET also increased, the humidity decreased, and the thermal sensation and thermal discomfort were significantly affected. The higher the altitude was from the ground, the lower the air temperature and SET; the higher the humidity was, the more general thermal sensation and thermal discomfort were affected. The more open the space was, the higher the air temperature and SET; the lower the humidity was, the more significant the influence of thermal sensation and thermal discomfort.

The discovery of these results was based on measured data of the thermal environment and thermal comfort in different spatial forms, which can realistically reflect a clear understanding of the mutual influence of these indicators. These results can serve as guiding principles in the design process, intuitively indicating passive cooling strategies in different spatial form combinations under different time states.

Note, however, that the correlation results among the different spatial forms, thermal environments, and thermal comfort analysis under humid and hot climate conditions may not necessarily be suitable under other climate conditions. Additional research is needed to apply these analytical methods to other climate zones and experimental data to further enrich the existing knowledge on the response mechanism of different spatial forms to the indoor thermal environment comfort and the design guidelines derived from these findings.