Design Guidelines for Residential Shape

Design Support Strategies Based on Optimal Solutions under Japan's Thermal Energy Efficiency Regulation System

Abstract

This paper discusses how to reduce the average external thermal insulation value（U_A value） through the method of increasing the residential external area from view of Japanese designers and policy makers. The U_A value is an important residential thermal parameter in Japan, but there is a lack of discussion on its relationship with the shape of the house or the external area. In this research, We categorized two main way of changing external area and used a method of Modular analysis and Comparative analysis with 360 cases ,we find that U_A value is strongly connect to external walls (R²＞0.8) and can be reduced by 10-15% by expanding external walls in normal cases, but a side effect of the sharper increase of total heat loss will appear. Therefore, this paper proposed a guideline of achieve best thermal evaluation in the current regulation and suggests that designers should only consider reducing the U_A value by increasing the external area if the U_A value is close to the requirement of the energy-saving benchmarks, or if it is difficult or costly to change the construction, and that designers should give priority to reducing the U_A value by adjusting the ratio of the area of the upper and lower floors, which is a more economical way to reduce the growth of energy.

Introduction

The thermal insulation performance of residential building envelopes plays a crucial role in energy conservation and maintaining a healthy indoor living environment during the winter (Alamah, 2024; Fang, Homma et al., 2024; Misni, Baird et al., 2013; Sadineni, Madala et al., 2011; Teng, Shen et al., 2025; Teng, Shen et al., 2023; Yao, Costanzo et al., 2018). While there exists a certain correlation between the form of residences and their energy consumption, with more compact housing forms generally be considered to have lower overall heat loss (Ave, 2016; Danielski, Fröling et al., 2012; Institute for Building Environment and Energy Conservation, 2016).

In this context, the Japanese government, in 2013, amended the Building Energy Efficiency Act (Nagata, Takano et al., 2022; Nihei, S, Satoh et al., 2015) and promote energy-efficient housing. This amendment abandoned the concept of the heat loss coefficient (Q' value) and created a more intricate perimeter, average heat transfer coefficient (U_A value) of the building envelope. The U_A value is defined as the ratio of the total heat loss to the sum of the residential external areas. This modification incorporates the surface areas of all parts rather than just the floor area.

However, under this regulation, there is no explicit specification regarding the relationship between residential form (or envelope) and U_A value. Some related studies suggest a lack of a clear correlation between residential form and U_A value setting due to the complexity of the research cases (Hybrid e-house, 2024; Nagata, Takano et al., 2022). Consequently, this study aims to clarify the connection between this artificially set parameter and residential form through an analysis of the calculation principles of U_A values and residential morphology.

Thermal heat loss (Q value) of residential buildings primarily stems from components such as doors & windows, exterior walls, ventilation and etc., while the first three constituting over 75% of the overall heat loss. As the thermal performance of various parts of a residence improves, the proportion of heat loss from exterior walls increases (Ministry of Land, Infrastructure, Transport and Tourism, 2023). Since doors and windows account for a limited proportion of the exterior of residential and the correlation with the U_A value is relatively clear (Sustainable open Innovation Initiative, 2021) . Thus, when considering the influence of residential morphology on the U_A value, the form and area of exterior walls became an important target for the correlation between the two. In this study, the area of exterior walls is utilized as an indicative metric for the form of the residential building envelope.

Moreover, exploring the correlation between U_A values and residential morphology holds significant practical implications. On one hand, the Japanese government plans to implement U_A value requirements for residences nationwide by 2025 (Ministry of Land, Infrastructure, Transport and Tourism, 2013). On the other hand, lower U_A values imply better energy efficiency, enabling residences to achieve higher energy-saving certifications and qualify for certain incentive mechanisms, such as subsidies for zero-energy homes (Nihei, S, Satoh et al., 2015). Therefore, uncovering the relationship between residential morphology and U_A values can assist designers in optimizing U_A values without necessitating changes in construction methods or materials.

From the perspective of passive design in residential architecture, this study conducts a detailed analysis of the following innovations:

a) Clarifying the relationship between the external envelope area and U_A values: Preliminary practice indicates that increasing the external envelope area leads to a reduction in U_A values. However, due to the lack of comprehensive analysis, it is essential to systematically investigate the correlation between these two factors. Therefore, this paper discusses the feasibility and operational range of reducing U_A values by increasing the external wall area. This enables designers to lower U_A values without altering the structure or thermal insulation materials, achieving the expected energy efficiency standards.

b) Discussing potential side effects of reducing U_A values by increasing the envelope area: Since U_A values represent the average thermal insulation performance of various parts of the envelope structure, they can only reflect the total heat loss of a residence to a certain extent. Consequently, increasing the envelope area may unintentionally result in an overall increase in heat loss. To address this issue, specific guidelines are necessary to assist designers in striking a balance between reducing U_A values and potential increases in heat loss.

c) While the method of setting U_A values is specific to Japanese residential buildings, similar issues arise in other countries employing trade-off methods. The adoption of the trade-off approach by policymakers originated from the desire to comprehensively consider the design and management of residential dwellings. This paper also explores the historical origins of this phenomenon and potential future strategies for resolution.

Literature Review

The relationship between U_A value and form shape

The research on the relationship between the residential energy efficiency parameter U_A and the exterior wall area is currently predominantly centered around Japanese scholars. Overall, the existing research is still insufficient, failing to provide a comprehensive theoretical and clear explanation for impact of residential exterior wall area on U_A value. Some typical studies rely on statistical analyses to explore the correlation between these two factors, such as the work conducted by Nihei, S et al (Nihei, S, Satoh et al., 2015). Their study, which analyzed the correlation between U_A values and exterior spatial design elements in 2229 households, concluded that the relationship between U_A values and residential envelope area is relatively weak due to significant sample variations. In their 2020 study (Kadowaki, 2015), the researchers extended their analysis to include openings in residential structures based on the same dataset. Additionally, we employed this methodology, combined cases from the Japanese government's published data of Zero Energy Homes (ZEH) in 2023 (Sustainable open Innovation Initiative, 2023) to create Figure 1. The analysis involved 90 residences in climatically similar regions. Interestingly, when residential areas were similar and the number of floors increased, there was no discernible upward or downward trend in U_A values. Similar research includes Yutaka Sato's study in 2021(SATO, ISHINO et al., 2021).

Figure 1. The scatter plot depicting the distribution of U_A values and residential areas for 90 selected Zero Energy Homes (ZEH) in zones 5-6, as stipulated by the Japanese government regulations

A commonality among these studies lies in the fact that due to various variables in different cases, such as floor plans, elevations, and construction methods, the results of correlation analyses lack specificity. Consequently, the conclusions are limited to descriptive interpretations of the outcomes and struggle to offer substantive guidance at the design level. Moreover, factors such as variations in external thermal insulation performance and window areas across different building components may diminish the overall evaluative correlation between U_A and various design elements. Therefore, this study contends that it is necessary to conduct a more focused correlation analysis under controlled variable conditions. Specifically, the influence of the building envelope and U_A should be examined within the confines of structural parameters. This analytical approach has garnered substantial support in the field of residential energy consumption research.

There is substantial research on parameters related to residential form, such as the shape coefficient (Rs), as specified in the Japanese government's regulations for the one-time energy consumption of residences (JFE Holdings, Inc, 2019). Japanese scholars have also proposed the "Plan Shape Complexity " Index (Kadowaki, 2015; Nihei, Shimon, Satoh et al., 2020). Additionally, in regulations and related studies in other countries, parameters like aspect ratio (Shi, Tian et al., 2016), heat loss shape coefficient (National House-Building Council, 2016), form factor (Depecker, Menezo et al., 2001) and compactness index (Pacheco, Ordóñez et al., 2012) have been introduced. These parameters are typically described in terms of the ratios or combinations of perimeter, floor area, surface area, and volume to characterize the shape of buildings.

In this paper, to simplify and align with current standards, we consider the following 2 situations in Figure 2: when upper and lower floors of the residence are entirely consistent of a residence, the external wall area is equal to the product of the perimeter (C value) and the floor height. Given the generally limited range of variation in residential floor heights, we choose the perimeter as an indicator of the shape of the residence. In cases where the residence exhibits irregularities, we adopt the concept of the Shape coefficient (Rs) as stipulated by the Japanese government to maintain consistency with existing regulations.

Figure 2. The schematic diagrams for the two scenarios discussed in this paper are as follows: (a) case 1: where the upper and lower floors of the residence are entirely consistent, choosing perimeter (C value) as the indication of external area;(b) case 2: where the upper and lower floors of the residence are inconsistent, choosing Shape coefficient (Rs) as the indication of external area

Furthermore, it is noteworthy that, although the concept of the shape coefficient (Rs) has been employed by the Japanese government in the regulation of energy-efficient residences, it has not been utilized to restrict residential designs that may impact the overall U_A value. Instead, it is employed in the parallel "construction method” evaluation approach (JFE Holdings,Inc, 2019; Ministry of Land, Infrastructure, Transport and Tourism, 2013), and is not a mandatory concept (Council for Promotion of Architecture that Utilizes Wood, 2021a; Japan Sustainable Building Council, 2013; JFE Holdings,Inc, 2016). Overall, there is currently insufficient research and regulation for the design support of U_A values.

Generative Logic of Residential Forms

Despite the current lack of research on the relationship between residential U_A values and envelope morphometrics, extensive discussions on the logic of residential form generation have taken place in studies related to residential form and energy consumption. Some typical methods include: Using multiple existing buildings or typical residential forms (Danielski, Fröling et al., 2012; Depecker, Menezo et al., 2001; Lylykangas, 2009; Mahdavi, Gurtekin et al., 2002; Pessenlehner and Mahdavi, 2003), generating residential forms through modular geometric systems or shape grammars (Çaǧdaş, 1996; Mahdavi, Gurtekin et al., 2002; Pessenlehner and Mahdavi, 2003). In these studies, residential forms are often transformed into a series of spatial prototypes, and various variable parameters are introduced based on study scenarios (such as climate zones, exterior structures, etc.) for classification and discussion.

From the aforementioned research, it is evident that common approaches in studying residential form and energy consumption involve simplifying external spatial details, transforming them into a series of spatial prototypes for comparison and analysis. Similarly, for the analysis of U_A values, the same methodology can be employed. By combining dependent variables C and Rs, representative building forms or modular geometric systems can be generated, and a series of residential forms can be analyzed with different scenarios to examine the relationship between residential envelopes and U_A values.

As residential design often begins with floor plans and is often constrained by building area limitations, this study primarily considers methods to control residential area and alter residential forms to adjust the surface area of residential envelopes. Through this approach, we aim to explore the feasibility of reducing U_A values by increasing area without altering structural methods and discuss its operability. Subsequently, by conducting morphological analysis to identify relevant patterns, we aim to strike a balance between reducing U_A values and increasing overall heat loss. We propose some recommendations to guide designers in residential form design and thermal performance.

Materials and Methods

Research Framework

Figure 3 shows the main research process. Firstly, by drawing the plan outlines of residences and utilizing Grasshopper, modular residential masses was established. Secondly, according to the 2 cases (in Figure 2), 3 building area was set and each have 20 residential samples, with three different sets of envelope parameters, a total of 360 samples were generated. Based on these samples, the U_A value and Q value were calculated for specific cases under two cases using the C and Rs value. Through statistical analysis, the correlation between residential envelope design and U_A and Qall values was examined. Guiding strategies were extracted, and an economic analysis was conducted to determine the cost-effectiveness of this approach. Finally, the study validates the conclusions introducing other cases and samples, with summarizing optimization strategies for the overall thermal performance of Japanese residences through residential envelope design.

Figure 3. Flowchart with all the research process

Thermal Insulation Performance and Shape Indicators

Thermal Performance Indicators：U_A Value and Q Value

The thermal performance analysis in this study includes the residential U_A value and Q value. The U_A value represents the average heat transfer rate of the residence, focusing on describing the insulation design of the residence from the perspective of overall average thermal performance. The calculation formula for U_A is as follows:

Formula 1:

  

$$U_A=\frac{Q_f}{A_{env}}$$

$Q_f={\sum }_i^{}（Ai*Ui*Hi）+{\sum }_i^{}（Lj*\phi j*Hj）$ ………………(1)

In the above formula, Ai*Ui*Hi and Lj*φj*Hj respectively represent the designed surface heat flow and designed line heat flow ( In the context of calculating heat loss in residential buildings, the term $𝐀𝐢*𝐔𝐢*𝐇𝐢$ corresponds to each part of the building's: [Area] × [Thermal Transmittance (U-value)] × [Temperature Difference Coefficient]. Meanwhile, $𝐋𝐣*𝛗𝐣*𝐇𝐣$ refers to the foundation insulation and slab-on-grade sections, calculated as [Perimeter Length] × [Linear Thermal Transmittance] × [Temperature Difference Coefficient]. This calculation method is relatively unique and detailed). The U_A value is the ratio of the sum of these two values (designed heat flow loss (Qf)) to the residential envelope area (A_env). Here, H refers to the temperature difference coefficient, a constant value based on the component, with coefficients between 0.7 and 1 for different components (JFE Holdings，Inc, 2019).( For the specific H values corresponding to different components, please refer to Table 4 in this paper)

Additionally, another crucial parameter in this study is the Q value. Because emphasis of the heat flow loss is to discuss the overall residential design from the perspective of winter energy consumption. It is noteworthy that designed ventilation heat loss (Q_v) and Q_f together constitute the Q value, and its calculation formula is as follows:

Formula 2:

  

$$Q=Q_f+Q_v$$

$Q_v=A_{env}*h*N_{air}*U_{air}$ ………………(2)

$U_{air}$ : Represents the heat capacity per cubic meter of air (volumetric specific heat), calculated as 0.35 Wh/m³·K, which is the product of the specific heat capacity of air and its density.

$N_{air}$ : Represents the ventilation rate, expressed in air changes per hour (ACH), indicating how many times the air within a building is completely replaced in one hour.

$h：Representstheheightofinsidespace$

From formula 1 and 2, we can deduce that when there is a variation in the external wall area of the residence, both the numerator and denominator of the mathematical formula, representing Q_f value and A_env value, will change. As a result, the variation in U_A value may exhibit a nonlinear state, while Q_f and Q_v value will show a linear increase with the enlargement of the external wall area. This implies that simultaneously analyzing the changes in U_A value and Q value with variations in the external wall area allows for achieving a balance between residential thermal performance evaluation (U_A) and the actual growth in heat loss (Q). Consequently, increasing the area to reduce U_A value becomes more practically meaningful.

Form Factor of Detached House

In order to elucidate the impact of changes in residential envelope area on U_A values, we take the perimeter (C) and the shape coefficient (Rs) of the residence to express variations in the external wall area. The residential envelope area is constituted by the product of the perimeter (C) and the floor height. Considering that the floor height typically remains within a relatively stable numerical range, controlling for floor height allows variations in the perimeter (C) to reflect the trend of changes in the envelope area.

Another parameter Rs, is defined by the Japanese government (JFE Holdings, Inc, 2019), serves as an indicator representing the ratio of the envelope surface area to the total building area. Its calculation formula is as follows:

Formula 3：

$R_S=A_{env}/S_{Basefloor}=\frac{S_{wall}+S_{patio}+S_{totalfloor}}{S_{totalfloor}}$ …………(3)

According to the definition of this parameter, more dispersed the residences are, the larger the Rs. In the Japanese government's regulations for one-time energy consumption, if the "Structural method" evaluation method is used, Rs should be no more than 2.9. When it exceeds 2.9, the energy efficiency of the residence should be evaluated using alternative methods. Therefore, this parameter is not a mandatory value, and its consideration is only necessary when assessing the thermal performance compliance of a residence that utilizes the "Structural method" without calculating U_A values.

The advantage of Rs lies in its ability to evaluate more complex residences, particularly those with irregular forms. Additionally, both Rs and C can represent the morphology of a residence. We chose to use these two parameters for two reasons: firstly, the C value is more direct, especially during the design process, allowing designers to visually understand the trend of changes in U_A values and residential design. Secondly, Rs is a parameter stipulated by the Japanese government, facilitating compliance with relevant regulations.

Moreover, in cases where the upper and lower floors of a residence are inconsistent, variations in protruding parts due to irregularities and their corresponding H values differ. Hence, C values cannot be used, and Rs values should be adopted for describing the morphology of the residence. Therefore, it is necessary to separately discuss situations where the upper and lower floors of the residence are consistent and inconsistent.

Selecting & Modelling of Research Target

Setting of The Modeling Cases

The residential parameters analyzed in this study primarily include the total building area, the thermal insulation parameters of the exterior walls, and the thermal insulation areas of each component of the residence. Regarding the values for the area of the residence, based on the data of 1490 Zero Energy Homes (ZEH) published in October 2023 using the Japan Single Family House Case Study Search Tool (Sustainable open Innovation Initiative, 2023), this study examined the floor area of the mentioned cases.

As depicted in Figure 4, the median area of the residences in the dataset is 115 m², with quartiles at 100 m² and 125 m², indicating that 50% of the cases have residence areas within the range of 100-125 m². Simultaneously, the distribution of residence areas in Japan is broad, with the majority falling between 65 m² and 160 m². Considering the long-time use of traditional Japanese measurement concepts, such as "shaku" (3 shaku = 910 mm) and "tsubo" (3.3 m², representing the area of a square with sides measuring 1.82 m) in the design and construction of wooden residences in Japan, three residence areas were selected: 99 m², 118.8 m², and 132 m². These areas correspond to 30/36/40 square of 1.82 m × 1.82 m, respectively, representing the typical range of residence areas in Japan. Furthermore, according to statistical data from the Ministry of Internal Affairs and Communications (Statistics Bureau of Japan, n.d.) in 2018, the average area of a single-family residence is 126.63 m², falling within this selected range.

Figure 4. The distribution of total building areas for the disclosed 1490 Zero Energy Homes (ZEH)

Morphological Generation Logic

Simplification of Residential Forms

In the calculation rules for U_A values, the regulations regarding the insulation form of the roof simplify the analysis. According to the calculation rules set by the Japanese government, the calculation of the roof area depends on the installation method of the roof insulation material. When choosing the "patio insulation" option, the patio area is considered as the roof area (Figure 5b); alternatively, if the insulation material is laid underneath the roof, the calculation is based on the actual roof area (excluding the eaves portion) (Figure 5a).

Under this regulation, all cases in this study use patio insulation. Therefore, in the calculation of U_A values, the roof can be considered as a flat roof. When calculating Rs, the roof area is taken as 1.1 times the building's one-story area (Sharetech Co .,Ltd., n.d.). This implies that there is no need to consider the impact of the roof shape on the calculation, effectively simplifying the morphology of the study objects.

Simultaneously, to further simplify the analysis, this paper only analyzes the type of detached houses with two stories.

Figure 5. Forms of thermal insulation on residential roofs and areas of roof area included in U_A calculations (diagonal area above) :(a) area of roof area included in the calculation of U_A in case of thermal insulation on the roof;(b) area of roof area included in the calculation of U_A in case of thermal insulation under the patio

Modular Configuration of Residential Spaces

The residential areas of 99 m², 118.8 m², and 132 m² are visualized as housing arrangements with 30/36/40 square modules (1.82m x 1.82m each). Considering the construction of two stories with 30 modules, theoretically, there are 4*314 (19131876) possible configurations. However, not all permutations, due to internal space constraints, may be meaningful. To overcome this, the study employs modular geometric systems and shape grammars (Çaǧdaş, 1996; Pessenlehner and Mahdavi, 2003).

Here, we categorized residential spatial forms into three types as listed in Figure 6. On one hand, residences often have irregularities in their spatial configurations, such as porches and balconies. On the other hand, due to differences in calculation coefficients for openings, basement and et.al in the U_A calculation method in Japan (refer to Table 3) when changing the house shape, we classified them into three common types: residences with consistent areas for both upper and lower floors（case1）, residences with a smaller area on the second floor than on the first floor（case(2a), and residences with a larger area on the second floor than on the first floor. Figure 7 illustrates some representative spatial forms for each of these three categorized types.

Figure 6. Classification of residential morphogenesis

Figure 7. Schematic representation of the residential case generated

By classifying them into three types and then generating residential forms based on square modules for comparative analysis, the purpose is to analyze which spatial design for residences can effectively reduce U_A values by increasing the external wall area while achieving a balance between total heat loss.

Range of Perimeters of Dwellings

Although it is not possible to list all the possible forms of a dwelling by exhaustive enumeration, it is possible to exhaust the perimeter of a dwelling by combining it with python's combinations command when the upper and lower floors are consistent.

Figure 8. flow chart of python code used for exhaust the boundary of perimeters

Figure 8 shows a flow chart of code used in this study. The code exhaustively explores the range of residential perimeters for the three aforementioned cases. Given our assumption of a two-story residence, the modules (1.82*1.82m each) are set to 15/18/20 for each floor. The distribution of perimeters is illustrated in Figure 8(a), where the minimum value, Q1, median, Q3, and maximum value of perimeters are marked. Taking a 99 m² residence as an example, 50% of residences have perimeters in the range of 32.76-43.68m. The fluctuation range of perimeter varies between 36% and 76% (ratios of the differences between the maximum and minimum values, Q3, and Q1). In this study, we control the height of the residence to remain constant, implying that the residential envelope area is also within a similar fluctuation range. Calculating the fluctuation range of the residential perimeter helps us determine the interval where the U_A value of the residence can be influenced by the perimeter.

However, it's essential to note that the results in Figure 9(a) may be larger than perimeters in actual designs. In practical design, designers tend to avoid extremely unusual residential forms, and the 1.82*1.82m units are typically used for small areas like entrances and bathrooms. Usually, more than two units are combined to form a room. Therefore, in Figure 9(a), the value of C may be slightly larger than the actual design. As demonstrated in Figure 8(b), We expanded the unit by 1.2 times, and the range of perimeter became smaller compared to Figure 9(a). Overall, the residential perimeter has a considerable degree of flexibility depending on the design. In the subsequent analysis, we integrated the perimeter ranges (mainly Figure 9(b)) derived from these two calculation methods as the basis for discussion.

Figure 9. Exhausted perimeters of 3 building area:(a) take a modular of 1.82m square; (b) take a modular of 2.184m(1.2 times of 1.82m) square.

Simulation and Calculation

Insulation Performance Parameter

The insulation performance parameters in this study includes the heat transfer coefficients (U-values) for each component of the residence (shown in Table 1). The approaches and U-values for each component are referenced from the “Guidelines for design, construction, and maintenance regarding the rationalization of energy use related to housing.”(Ministry of Land, Infrastructure, Transport and Tourism, 2013) under standard construction. In the study, we categorized these parameters into three sets based on the thermal insulation effects of the residence (Parameter 1, 2, and 3 refer to residence with high-performance insulation materials, standard insulation materials, and low-performance insulation materials, they are taken from commonly used building material databases) . We established three analysis scenarios and combined them with the proposed 40 residential morphologies and 3 building area situations, resulting in a total of 360 samples representing the thermal performance of the building envelope for the residences.

Table 1. Thermal performance parameters of each component in simulation

	Parameter 1 （W/m2・k）	Parameter 2 （W/ m2・k）	Parameter 3 （W/ m2・k）
Patio	0.17	0.24	0.24
External walls	0.35	0.53	0.92
Basement walls	0.37	0.76	1.80
Opening (door)	2.33	2.91	4.65
Opening (Window)	2.91	3.49	4.07
Floor	0.24	0.34	0.48
Basement	1.80	1.80	1.80

The following Table 2 lists the residential design parameters required for the analysis, primarily including the orientation of the residence, the areas of each component, and the number of floors in the residence. Here, we also referred to the “ Specific contents and calculation method of the 2013 energy conservation standards” (JFE Holdings,Inc, 2019) and the " Housing Energy Saving Technology Training Text Standards/Evaluation Methods Edition 2nd ed "(Council for Promotion of Architecture that Utilizes Wood, 2021b). The height of the residence is set to a common value of 2.8m. The area of the openings in the residence is calculated based on the opening ratio, with Japanese regulations stipulating that it should not be less than 1/7 of the building area (Government of Japan, n.d.).We set it at 20% of the residence area based on the median of the statistically gathered opening ratios(Housing Performance Evaluation and Display Association, no date).

Table 2. Residential design parameters of the modelling cases

Residential design parameters	Value	Explanation
Location	4-7 region	This region encompasses most of Japan except for the northeastern and southernmost parts of the country.
Layers	2 floors	In Japan, one-family houses are often built with 1-3 floors, with 2 floors being the most common.
Floor height	2.8m	Common floor heights of dwellings
Total building area	99 m2，118.8 m2，132 m2	Module setting according to the residence
Door area	2 m2	One entrance
Window area	S*20%	Take a normal count
Soil area	3.3 m2	Generally, Japanese houses have an entrance hall, the size of which affects the area of the foundation wall and the perimeter of the foundation.
Basement length	9.1m	Assuming that the first floor has an entrance for 1.82 * 1.82m square, toilet and bathroom bit 1.82 * 3.64m rectangle, so the perimeter of the outside air side = entrance outside air side + bathroom outside air side = 9.1m, inside the air side of the same thing
Basement area	3.2 m2	Assuming the same as above, outside air side area = outside air side perimeter * outside air side protruding from the ground floor height, here take the common value of 0.35m

Calculation Process and Determination Formula

The calculation of U_A values offers various methods, and this study employs the standard calculation method (Council for Promotion of Architecture that Utilizes Wood, 2021a). Despite its relatively high computational complexity, it is regarded as the most accurate approach and can be used to all the cases (Japan Sustainable Building Council, 2013). One of its notable advantages is its feasibility for computation using Excel (Housing Performance Evaluation and Display Association, n.d.). The Table 3 below illustrates the calculation table used in this paper. Given the specified conditions, we alter the residential perimeter/shape while keeping the residence area constant. Consequently, in cases where the upper and lower floors of the residence are consistent, the exterior wall area and window area undergo changes (shown in yellow). In situations where the upper and lower floors differ, the patio, floor area, exposed area, exterior wall area, and window area also experience variations (shown in yellow and green).

Table 3. Calculation table（provided by Japanese government）

Components		Area	length	U value	H value	Through-flow heat loss
Patio		A		U	1	A * U * H
External wall		A		U	1	A * U * H
Basement wall	Outer side	A		U	1	A * U * H
	Next to floor Side	A		U	0.7	A * U * H
Openings	door	A		U	1	A * U * H
	window	A		U	1	A * U * H
Site floor	Exposed floor	A		U	1	A * U * H
	Others	A		U	0.7	A * U * H
Soil area	area	A
Basement	Outer side （perimeter）		L	U	1	L * U * H
	Next to floor Side （perimeter）		L	U	0.7	L * U * H
Total exterior skin area＝		Σ A	External heat loss per unit temperature difference Qf＝			Σ Q
UA =	Σ Q/Σ A

With the data provided in the table and our set of 360 samples, we can proceed with the calculation of U_A values and analyze the trends in their variations under different C and Rs conditions, taking the 4-7 climate zone as an example. In the building energy standard, the required value for this zone is 0.87 W/㎡・K (2013 Energy Efficiency Standard), while the ZEH (Zero Energy House) standard demands a value of 0.6 W/㎡・K. This allows us to determine whether increasing the envelope area can reduce UA values.

Results and Analysis

Case 1：When upper and lower floors are complete consistency

When the upper and lower floors of the residence are entirely consistent, the exterior wall area of the residence can be expressed in terms of C to illustrate the trend. In this study, we computed nine scenarios, corresponding to 20 residential shapes under this premise. These scenarios cover three residential envelope thermal parameters (table 2) and three residential areas (table 3, total building area). Scatter plots in Figures 9 and 10 respectively depict the trends in U_A under different areas and parameters.

Impact of The External Wall Increasing on U_A Value

Overall, when controlling the growth of the exterior wall area (with the increase of C), U_A values show a decreasing trend. Lower U_A values indicate better thermal insulation capabilities of the residence of the evaluation. Figure 10 illustrates the situations for three residential area segments. The U_A values exhibit a certain linear trend with the increase in C, indicating a reduction in U_A values as C values grow. This implies that, for U_A values, within the specified common residential area segments and typical residential thermal parameters, larger exterior areas lead to better U_A values for residences.

Figure 10. The decline trend of UA value with the C increasing in different building area situation:(a) when the building area is 99m²; (b) when the building area is 118.8m2; (c) when the building area is 132m²

Furthermore, from Figure 10, it can be observed that the impact of residential area on U_A values is relatively small. Comparing the three graphs in the horizontal direction in the upper chart, when C is similar, the calculated U_A values are close. Taking parameter 1(the blue curve in the upper chart) as an example, for scenarios with areas of 99 m², 118.8 m², and 132 m², when the perimeter is 36.4 m, the U_A values are 0.552 W/㎡・K, 0.557 W/㎡・K, and 0.560 W/㎡・Which is quite near. This indicates that, when considering the impact of increasing the exterior wall area on U_A, the residential area segment has a relatively minor factor.

Sensitivities

The line chart in Figure 11 reflects the decreasing trend of U_A values with the increase in C under different parameter conditions. Comparing the three charts horizontally, it can be observed that under different parameters, there are variations in the rate of decrease and results of U_A values with the growth of C. This implies that the residence parameters have an impact on this trend, requiring an assessment of the magnitude of the influence. Therefore, the concept of △U_A is introduced, where △U_A is used to represent the percentage change in residential U_A values. Its calculation formula is as follows:

Figure 11. The decline trend of UA value with the C increasing in different building area situation:(a) when taken the parameter 1; (b) when taken the parameter 2; (c) when taken the parameter 3

Formula 4：

$△U_A（\%）=\left\{\frac{U_{AMAX}-U_{Asqu}}{U_{Asqu}}\right\}*100\%$ …………(4)

The term U_{A squ} refers to the U_A value calculated when the residence is a square. This is based on the reasoning that when the residence is a square, its perimeter is the smallest among polygons, and therefore, it can be considered that C is at its minimum. U_{A MAX} refers to the U_A value calculated under the scenario where C has its maximum value, as calculated from Figure 8.

Based on the computation results from Figure 10 and Formula 4, △ U_A has been calculated and shown in Figure 12. From Figure 11, it is evident that the maximum decrease in U_A values varies under different parameters. When the residence itself has good thermal performance (parameter 1), the rate of decrease in U_A values with the increase in the external wall area is the fastest. Conversely, the rate is slower when the residence's thermal performance is poorer. In situations where the residence itself has poor thermal performance (parameter 3, for example), it is challenging to reduce U_A values significantly by increasing the external wall area (U_A values decrease by only 3% as the perimeter increases from 30m to 55m).

Additionally, the average △ U_A for parameter 2 is -7.98%, indicating that by increasing the external wall area, the U_A value of the residence can decrease from 0.74 W/㎡·k to 0.68 W/㎡·k. The value of 0.7 W/㎡·k is an important threshold in many regions or specifications. This suggests that increasing the external surface area is a viable method to meet energy-saving standard evaluation requirements. However, this method has limited effectiveness (around 8-12%) and is not applicable to residences with poor thermal performance (initially judged UA values exceeding 0.8 W/㎡·k).

Figure 12. Range of change of ∆ U_A for different parameters

Side Effect

As the overall heat loss of the residence increases with the growth of the external surface area, it is essential to consider the side effects of the increase in total heat loss, even when U_A values are reduced. Formula 5 defines △Q, which is similar to△U_A, expresses the increase in overall heat loss of the residence as the external surface area increases. It represents the ratio of the rates at which both △Q and △ U_A increase (or decrease).

Formula 5：

$△Q（\%）=\left\{\frac{Q_{MAX}-Q_{squ}}{Q_{squ}}\right\}*100\%$ …………(5)

Table 4 discusses the side effects of this method. It can be observed that the average values of the ratio under the three parameter sets are 1.308, 2.259, and 8.016, respectively. Since this value is greater than 1, it implies that the rate of increase in overall heat loss of the residence is higher than the rate of reduction in U_A values. From this perspective, solely increasing the external surface area to reduce U_A values has certain uneconomical side effects. This ratio increases as the thermal insulation performance of the residences constructed under parameter sets 1, 2, and 3 decreases successively. It suggests that the practice of increasing the area to reduce U_A values may not be very economical when the residence itself has poor thermal insulation performance, considering the background of overall heat loss. However, it holds practical value when the residence has relatively better thermal insulation performance.

Table 4. △U_A decrease ratio vs △Q, total heat loss increase ratio

	Parameters1			Parameters2			Parameters3
Area	△UA	△Q	△Q/△UA	△UA	△Q	△Q/△UA	△UA	△Q	△Q/△UA
99m2	-9.76%	12.16%	(1.25)	-7.28%	15.53%	(2.13)	-3.05%	21.23%	(6.95)
118.8m2	-11.05%	14.62%	(1.32)	-8.18%	18.73%	(2.29)	-3.15%	25.78%	(8.18)
132m2	-11.51%	15.59%	(1.35)	-8.49%	19.99%	(2.36)	-3.10%	27.64%	(8.92)
Average			(1.308)			(2.259)			(8.016)

Case 2：When Upper and Lower Floors are Not Complete Consistency

In the design process of residential, due to the presence of balconies, entrance spaces and cantilever etc., there are certain irregularities that results into non-identical floor plans for the upper and lower levels. In such situations, the exposed site floor, and other factors related to U_A value calculation will change. Therefore, in this scenario, with the variation of the external wall area, the calculation of U_A involves multiple sets of independent variables, and its trend may exhibit a certain degree of non-linearity. In this study, we mainly categorized it into two states: "upper floor area greater than lower floor area" (case2(a)) and "lower floor area greater than upper floor area." (case2(b)) In addition, we considered three different residential area sizes and three thermal insulation parameters, resulting in a total of 20 different housing shapes.

Impact of The External Wall Increasing on U_A Value

Figure 13 illustrates the variation trends of R_S and U_A values resulting from the increase in the external wall area. The blue, red, and green trend lines represent the calculation results for parameters 1, 2, and 3, respectively. Since a larger R_S implies a more dispersed residential layout, it indicates that the housing maintains a decreasing trend in U_A as the external wall area increases. This trend is consistent with the observations made in section 4.1.

Figure 13. The decline trend of U_A value with the Rs increasing in different building area situation:(a) when the building area is 99m²; (b) when the building area is 118.8m²; (c) when the building area is 132m²

However, the relative difference lies in the lower values of the coefficient of determination (R²), and its correlation with the overall thermal insulation performance parameters of the housing. As evident from Figure 13, the three colored lines indicate that when the housing has a better thermal insulation performance (blue and red lines, corresponding to Parameter 1 and 2 in Table 1), U_A values exhibit a strong correlation. In contrast, when the housing has retaliative poorer thermal insulation performance (green line, corresponding to Parameter 3 in Table 1), the R² value is lower, indicating a weaker correlation in U_A values. Correspondingly, Table 6 calculates the association between the C value and U_A values for the case of inconsistent upper and lower levels. From the computational results, only in the case of 99m², parameters 1 and 2 (blue and orange lines) exhibit a strong correlation. Therefore, in situations where the upper and lower levels of the residence are not entirely consistent, R_S is relatively more useful in describing the variation trend of U_A values compared to C values.

Table 5. Coefficient of determination (R²) between U_A value and C & R_S

R2	With C			With RS
	99m2	118.8m2	132m2	99m2	118.8m2	132m2
Parameter 1	0.830	0.022	0.623	0.938	0.909	0.950
Parameter 2	0.697	0.021	0.463	0.843	0.798	0.896
Parameter 3	0.032	0.152	0.035	0.131	0.281	0.639

Comparison of The Effect of Balconies and Cantilever Design on U_A Values.

In addition to the aforementioned variations, balconies and cantilever in residential design are essential components that may also influence U_A values. Thus, within the previously introduced residential spatial types, we categorize them into two types: cases 2(a) where the first-floor area is greater than the second floor, and case 2(b) where the second-floor area is greater than the first, corresponding to balconies and cantilever in residential design. In Section 4.2.1, we observed a relatively weak correlation between U_A and R_S values using parameter 3, so here we focus on comparing the trends in U_A values for the other two parameters.

Figure 14 compares the relationship between R_S and U_A values for cases2(a) where the first-floor area is greater than the second floor (blue line) and cases2(b) where the second-floor area is greater than the first (red line). Among the six scenarios considered, it was observed that cantilever elements tend to have a disadvantageous impact on the evaluation of U_A values, while balconies elements show some improvement in the evaluation results for U_A values. However, the difference on U_A values for both scenarios is relatively minor. Across the six scenarios, when “R_S=3”, the average difference of U_A is 0.86% (refer to Table S10 in Supplement materials). Therefore, contrary to initial assumptions, the influence of the convex-concave features on the facade of the residence appears to have a relatively minor impact on U_A values.

Figure 14. The difference between the case2(a) and case2(b) by reveal the relative relation between U_A and Rs ;(a) when the building area is 99m²，taken parameter 1; (b) when the building area is 118.8m² ，taken parameter 1; (c) when the building area is 132m² ,taken parameter 1; (d) when the building area is 99m²，taken parameter 2; (e) when the building area is 118.8m², taken parameter 2; (f) when the building area is 132m², taken parameter 2;

Sensitivities

In this section, we maintain consistency with Section 4.1.2 and compare it with the case when the residence is square-shaped. The calculation process is based on the 20 simulated results, and used the trend lines fitted in Figure 12 for assessment. However, as we cannot determine the maximum value of R_S at this point, we make an assumption based on the endpoint of Figure 13. We hypothesize the scenario where R_S max is 1.3 times R_S Square and examine the trend in U_A values. The calculated results are presented in the following table.

From Table 6, it can be observed that when the residential form is diversified through balconies, cantilever and similar features, resulting in a 30% increase in R_S, the average reduction in U_A values is approximately 10.12%. However, it is crucial to note that this result is an estimate and is contingent on the inherent thermal performance parameters of the residence. This method may not be applicable when the residence has poor intrinsic thermal insulation performance.

Table 6. Judgment of the change range of U_A value in the case of inconsistency

	Rs max=1.3* RS Squ			Rs max=1.5* RS Squ
	RS max	UA max	△UA%	RS max	UA max	△UA%
99m2(Parameter 1)	3.606	0.515	-11.93%	4.161	0.486	-16.93%
99m2(Parameter 2)	3.606	0.685	-9.39%	4.161	0.659	-12.88%
118.8m2(Parameter 1)	3.193	0.513	-11.11%	3.684	0.473	-17.94%
118.8m2(Parameter 2)	3.193	0.677	-9.45%	3.684	0.634	-15.14%
132m2(Parameter 1)	3.096	0.514	-10.32%	3.572	0.481	-15.97%
132.8m2(Parameter 2)	3.096	0.68	-8.53%	3.572	0.648	-12.88%
Average			-10.12%			-15.29%

Discussion

Validation of Calculation Results

In the fourth section, two common methods for reducing U_A values by changing the exterior wall area of a residence were discussed. It can be concluded that:

•    Increasing the perimeter of the residence and introducing staggered elements to enlarge the envelope area are both effective means to reduce U_A values. When the perimeter of a residence is enlarged, while maintaining identical upper and lower portions, the U_A values can be reduced by approximately 8-10%, compared to a residence with a square plan that generally implies the minimum perimeter of a quadrilateral house. Additionally, incorporating staggered elements such as balconies and cantilever can result in a reduction of U_A values by around 10-15%.
•    The above considerations assume that the thermal performance parameters of various parts of the residence are not excessively low (e.g., with a preliminary calculated U_A value of 1.0 W/m²K).
•    Increasing the envelope area to lower U_A values will result in an overall increase in heat loss. The rate of heat loss will increase at a higher rate than the rate of U_A value reduction, and this rate will rise as the thermal performance parameters of different parts of the residence decrease. Therefore, when using envelope expansion to reduce U_A values, it is crucial to take into account the possible side effects of an overall increase in heat loss.

To validate the results mentioned above, this study proposes using new residential cases for assessment. In the following research cases, we aim to reduce the U_A value to 0.6 W/m²K, which complies with the Zero Energy House (ZEH) standard (ZEH Roadmap Follow-up Committee, 2019). The case is set as a residence with an area of 125.4 m² (composed of 38 basic units, each measuring 3.3 m²). The study references the thermal performance parameters of each element from parameter2. In the baseline case of a square-shaped residence, the U_Asqu is calculated to be 0.746 W/m²K. Therefore, a 19.5% reduction in the U_A value is required. To achieve this reduction, we simultaneously employ two methods: enlarging the perimeter of the residence and adding balcony area. The text includes 20 validation cases (refer to Figure S7 in Supplement materials) that employ these two methods individually.

Figure 15 illustrate the reduction in ΔU_A under two different scenarios, both compared to the baseline sample. In the left graph, we observe that by increasing the perimeter of the residence to enlarge the envelope area, under given thermal performance parameters, a growth of 70% in the residence perimeter effectively reduces U_A values by approximately 8%. On the other hand, using the staggered method to increase the envelope area and a 30% or 50% increase in the residence form factor, a reduction of approximately 12% or 14.5% is achieved. Additionally, as the form factor increases, U_A values consistently decrease, which aligns with the earlier inference.

Figure 15. Reduction in ∆U_A (compared to U_Asqu) for each of the 10 cases presented under the two methods (a) case 1: Increasing the perimeter of the residence (b) case 2: introducing staggered elements

It is noteworthy that, in the simulated cases, the minimum U_A value is 0.614 W/m²K, which does not quite reach the target value of 0.6 W/m²K. However, the decrease in U_A values validates the feasibility of this approach.

Figure 16 compares the ratio of the rate of decrease in total heat loss (ΔQ) to the rate of decrease in U_A (ΔU_A) with the increase in envelope area. For the left graph, as the form factor (C value) increases, the ratio of ΔQ/ΔU_A shows a decreasing trend. When the residence perimeter increases by 70%, the ratio of ΔQ/ΔU_A is -225%. This indicates that increasing the perimeter of the residence to reduce U_A values leads to a significant increase in heat loss. In the right graph, as R_S increases, the ratio of ΔQ/ΔU_A shows a linear trend and wilder range. When R_S increases by 30%, the ratio of ΔQ/ΔU_A is -111%, and for smaller changes in R_S, the ratio is less than -100%. This suggests that using the staggered method to reduce U_A values, particularly when R_S changes are small, can achieve a balance between reducing U_A values and avoiding a sharp increase in overall heat loss.

Figure 16. Reduction in the ratio of ∆Q/ ∆U_A (compared to U_A squ) for each of the 10 cases presented under the two methods (a) case 1: Increasing the perimeter of the residence (b) case 2: introducing staggered elements

Figure 17. An example of choosing Residential patterns(partly)and corresponding ∆U_A, ∆Q and their ratios for selected cases of validation

Figure 17 illustrates the U_A and ∆Q values for selected validation cases, along with two auxiliary lines: △Q/△U_A =-1 and △Q/△U_A =-2, representing the rates of increase in total heat loss and decrease in U_A value, respectively. From the figure, it can be observed that compared to the square case at the origin, increasing the perimeter of the residence using Case 1 generally results in a smaller reduction in U_A value and a faster overall increase in heat loss. Conversely, with Case 2, a balance between △Q and △U_A can be achieved with a smaller increase in RS. However, when aiming for a larger range of △U_A, △Q also increases rapidly, rendering this method uneconomical.

We believe this approach can provide architects with considerations during the initial design phase. By comparing with the square case, a balance can be struck between design flexibility and achieving optimal evaluation results under current regulations.

Therefore, through the aforementioned validation, we have confirmed the earlier inference. Both increasing the perimeter of the residence(case1) and employing the staggered method(case2) to alter the residence form and increasing external area can effectively reduce U_A values but may also lead to a sharper increase in total heat loss. Overall, using the staggered method while controlling the degree of dispersion of the residence form can effectively mitigate the aforementioned side effects. Another point to note is that this method is only suitable for residences with relatively good intrinsic thermal insulation performance. In cases where the residence is square-shaped with two floors and the U_A value is close to 1.0 W/m²K, this method is not applicable.

Significance of This Research

Although U_A values are specifically designed for managing the thermal performance of wooden structures in Japan, similar evaluation methods such as trade-off or alternative evaluation are employed globally, including in countries like the United States, Canada, and India. The essence of these methods is fundamentally similar, aiming to flexibly consider the thermal performance of various components in residential buildings to provide a comprehensive assessment. The primary goal is to strike a balance between thermal constructions in different parts, allowing for design flexibility.

However, residential structures are intricate entities, and the exterior walls, constituting a significant proportion of the building envelope, might not be the most heat-loss-prone element. Consequently, altering the residential form or increasing the building perimeter could potentially enhance the overall thermal performance assessment from a holistic perspective. This aligns with practical residential designs, as evidenced by numerous irregularly shaped residences in Japan's "Japan Eco-House Award." This study originates from real-world design cases, combining common residential constructions, and discusses the possibility, extent, and associated side effects of reducing U_A values by enlarging exterior walls.

The identified side effects in this study should also be considered as issues requiring further attention from policymakers. This consideration is applicable to countries worldwide adopting the trade-off evaluation method, particularly in light of the contradictions inherent in these regulations. The association between residential form, exterior walls, and thermal assessment deserves particular attention.

Applicability, Validity, and Limitations of Results

This research suggests that increasing the size of exterior walls to reduce U_A values can achieve a balance between overall evaluation results and heat loss growth under certain conditions. For designers, assuming an initial design of a square-shaped residence and achieving better U_A values with Rs approximately 1-1.3 times of R_ssqu can be done with minimal side effects.

Figure 18. Guidelines on the Relationship between Housing Forms and UA Values for thermal evaluation in Japan

Figure 18 presents design guidelines based on the simulations conducted in this study. Specifically, we recommend that designers first consider the U_A value range for square residences when using current thermal insulation materials. When the U_A value exceeds 0.9-1W/m²K, it is not advisable to reduce the U_A value by enlarging the external walls (increasing C) or introducing staggered layers (increasing R_S). Additionally, depending on the thermal insulation level goals of the residence and when material substitution is not feasible, designers can utilize this method in conjunction with the ranges of △U_A and △_Q variations.

However, given the diverse forms and sizes of residences, this study, to obtain broader applicability, restricts the research scope to two-story houses with an area concentrated in the common range of 100-150 m². This limitation introduces certain constraints, necessitating further exploration of the practical implications under different thermal parameters and residential area scenarios to confirm the study's applicability. Despite these limitations, this study discusses the relationship between U_A values and residential form and area within common size segments and typical thermal performance, offering theoretical and practical value applicable to common Japanese residences.

While this study primarily focuses on the most common two-story residences and typical residential area ranges, it also does not address one-story or three-story and above residences or residences with areas greater than 150 square meters. Additionally, the study does not delve into scenarios where residences have double-height spaces indoors. These aspects can be explored in further simulations using the same methods.

Furthermore, the study identifies that, despite U_A involving the ratio of the sum of thermal performances across multiple components to the area, U_A exhibits a favorable linear relationship with C values and Rs values in scenarios with good thermal performance. This is attributed to the substantial proportion of residential exterior wall area contributing significantly to overall heat loss. Additionally, when the overall thermal performance of the residence is poor, increasing the proportion of heat loss from exterior walls has minimal impact on the overall evaluation results, leading to the observed non-linear relationship in some of the samples in parameter 3.

Conclusion

This study primarily analyzes potential drawbacks in U_A values during the design process, focusing on variations in U_A values and the analysis of total heat loss (Q) when altering residential exterior wall area or design. To assess the impact of increasing the building envelope area on residential thermal performance, simulations were conducted, and the results were analyzed based on specific cases. The following conclusions were derived and shown in Table 9:

[1] There is a significant correlation between U_A values and residential form and exterior wall area. Increasing the perimeter of the dwelling or introducing staggered layers to enhance the skin area can effectively reduce the U_A value.

[2] Assuming an equivalent area square residence as a reference, when the top and bottom of the house are consistent, increasing the perimeter of the house can reduce the U_A value by approximately 8-10%. Introducing staggered floors, such as cantilevers or balconies, can result in a reduction of the U_A value by about 10-15%.

[3] The prerequisite for using this method is that the thermal performance of the residence itself should not be too poor (U_Asqu > 0.8 W/m²K is an ideal scenario). However, this method comes with the side effect of an increase in total heat loss. Therefore, solely reducing U_A values by increasing the area is not economically viable. Consideration of increasing the building envelope area to adjust U_A values should only be made when the original design is close to Zero Energy Home (ZEH) standards (within 10%) or when using higher thermal performance materials has a significant cost impact. It should also be considered when making minor changes to the residential form (Rs = 1-1.5 * R_ssqu).

Appendix A

List of abbreviations in the text:

C value: perimeter of the residential[m];

Q value: Total thermal heat loss[W/K];

Q' value: heat loss coefficient, the parameter has been abandoned by Japanese government since 2013;

Q_f: designed heat flow loss[W/K];

Q_v: designed ventilation heat loss[W/K];

△Q: Percentage of declining Q values (compared to the square case)

Rs: shape coefficient;

R_{S squ}: the calculated value of R_S When the residential plan form is square;

U_A value: average heat transfer coefficient[W/m²K];

U_{A max}: the predicted value of U_A when C or Rs value is the largest;

U_{A squ}: the calculated value of U_A When the residential plan form is square;

U：The heat transfer coefficient[W/mK], which is related to the thermal resistance of the material, R

△U_A : Percentage of declining U_A values (compared to the square case)

Author Contributions

Conceptualization, Tianqi Ge, Xiao Teng, and Zhenjiang Shen.; methodology, Xiao Teng, and Zhenjiang Shen.; software, Tianqi Ge.; validation, Tianqi Ge, Xiao Teng, and Zhenjiang Shen.; writing—original draft preparation, Tianqi Ge.; writing—review and editing, Xiao Teng, and Zhenjiang Shen.; visualization, Tianqi Ge.; supervision, Xiao Teng, and Zhenjiang Shen. All authors have read and agreed to the published version of the manuscript.

Ethics Declaration

The authors declare that they have no conflicts of interest regarding the publication of the paper.

Acknowledgments

This study was supported by Kanazawa University - Urban Planning Lab

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