Thermal Resilience of Public Building Atriums Under Different States During Heatwaves

Abstract

Under the influence of climate change, extreme heat events are becoming more frequent and intense. Understanding the response mechanisms of public building spaces, such as atriums, during extreme heat events is of great significance for developing effective design strategies to enhance the thermal resilience of buildings. This study investigated the effect of atrium spaces on the thermal resilience of buildings during heatwaves, focusing on their ability to mitigate high temperatures under two states: closed and open. The research monitored the indoor and outdoor temperature and humidity data of the atrium of a university building in Shanghai during a typical heatwave, and used statistical methods to analyze the relationships between the thermal resilience indicators and various environmental parameters, including the indoor and outdoor temperatures and ventilation states, to evaluate the thermal performance of the atrium. The results indicate that the atrium demonstrated robust thermal resilience under both closed and open conditions. In the closed phase, the indoor temperature was, on average, approximately 7 °C lower than the outdoor temperature, with the maximum difference reaching 11 °C, and the peak temperature delay was up to 4 h. In the open phase, despite exhibiting larger thermal fluctuations and an increase in temperature non-uniformity, the thermal resilience index improved significantly, from 0.231 in the closed phase to 0.047. The analytical framework developed in this study shows great potential for understanding the thermal resilience mechanisms of buildings during extreme heat events. Additionally, the data-driven insights are invaluable for informing the design strategies of public building spaces, especially in regions prone to extreme heat.

1. Introduction

Climate change has led to an increasing frequency of extreme weather events, with heatwaves increasingly threatening both buildings and human health. The intensity and duration of these events are expected to rise further in the foreseeable future [1,2,3]. In China, densely populated cities are particularly vulnerable to extreme heat events [4], as evidenced during the summer of 2022, when over 900 million people endured more than two months of sustained high temperatures [5]. Rising temperatures not only directly impact human health and quality of life, but also pose significant threats to residents’ safety [6,7]. The ability of buildings to effectively respond to extreme heat during heatwaves, mitigate its destructive impacts, and protect occupants from the dangers of high temperatures have become a critical focus in the field of architecture [8,9,10]. The invitability of future heatwaves has brought the concept of “thermal resilience” into the spotlight. The term “resilience” originates from the Latin word resilio, meaning “to jump back” [11]. However, within the context of architecture, there is no universally agreed-upon definition [12,13,14]. Attia et al. conducted an extensive literature review on the term “resilience”, and identified that the most common external pressures affecting buildings are emergencies, particularly power outages and heatwaves [15]. For the purposes of this study, we define thermal resilience as the ability of a building to maintain indoor thermal comfort in the face of extreme climatic conditions, such as heatwaves.

As a core space in public buildings, atriums play a significant role in shaping the overall thermal environment [16,17]. With the growing emphasis on energy efficiency and sustainability in architecture, understanding the thermal resilience of atrium spaces has become increasingly important. Recent studies have highlighted the potential of atriums to mitigate indoor temperature peaks through various passive design strategies. By optimizing the shape and layout of an atrium, direct solar radiation can be minimized, reducing heat absorption. Additionally, a thoughtful geometric design can guide airflow effectively, further enhancing ventilation efficiency [17,18]. Atrium spaces typically feature a substantial height and large openings, enabling effective natural ventilation. Through well-designed openings, such as operable vents positioned at the top or sides of an atrium, airflow can be promoted, accelerating heat dissipation. This approach helps reduce indoor temperatures and enhances the thermal resilience of a building [19,20]. Atrium spaces generally benefit from excellent natural lighting, but are also susceptible to excessive solar radiation. By incorporating effective shading strategies, such as installing louvers or sunshades, the amount of solar heat entering an interior can be significantly reduced, thereby enhancing a building’s thermal resilience [21]. However, there is still a lack of sufficient data and analytical frameworks to fully understand the extent to which atrium spaces in public buildings can demonstrate thermal resilience, particularly in the face of extreme high-temperature weather conditions.

1.1. Literature Review

In recent years, the focus of indoor thermal environment research has gradually turned to the thermal resilience characteristics of buildings. Hong et al., (2023) identified ten core issues in building thermal resilience research through a comprehensive literature review [12]. A key aspect of evaluating thermal resilience is determining the appropriate indicators to use. Burman et al., (2014) employed a framework combining resilience, vulnerability (such as material deterioration and structural stability), and adaptive capacity (such as design adjustments or technological means to cope with high temperatures) to assess overheating in non-residential buildings [22]. Siu et al., (2023) conducted an in-depth review of the methods for quantifying thermal resilience and explored the strategies for integrating them into building codes and standards [14]. However, establishing a comprehensive and generalized system of numerical metrics to evaluate the thermal resilience performance of buildings is complex. Short-term extreme heat events can cause a rapid increase in indoor temperatures, posing immediate health risks to the occupants. Meanwhile, prolonged heat accumulation effects may lead to the thermal fatigue of building structures and an increase in energy consumption. Rahif et al., (2021) provided a comprehensive review of the various methods and standards for assessing overheating [23]. In this context, Hamdy et al., (2017) proposed three key indicators: Indoor Overheating Degree ($IOD$), Ambient Warmth Degree ($AWD$), and Overheating Escalation Factor (${\alpha }_{IOD}$) [24]. These indicators are increasingly considered important tools for quantifying indoor overheating risks and assessing the ability of multi-zone buildings to withstand the impacts of climate change. At the same time, this metric system is currently the more commonly applied standard that allows for a comparison of cooling strategies in different climate zones under common boundary conditions [23]. It can be applied to both long-term assessments (annually or monthly) and short-term evaluations (weekly or daily). It is also not limited to any building type or operation: residential and non-residential, new or existing.

From a research methodology perspective, studies on building thermal resilience have primarily focused on two approaches: simulation and experimental research. Simulation studies predict the performance of buildings under various climatic conditions (including historical or future scenarios) through computer models. For instance, performance simulations of office buildings based on EnergyPlus have been conducted, and lightweight regression models have been developed to quickly assess the thermal resilience of office buildings [25]. However, in the context of extreme heatwaves, indoor thermal environments are influenced by multiple factors, including the health status of the occupants, their economic capacity, and their willingness to adopt adaptive measures [14]. These factors complicate simulation methods and increase their uncertainty. Experimental research, in contrast, gathers data through field monitoring to assess the actual thermal resilience of buildings. For instance, Lomas and Giridharan conducted an environmental monitoring of a naturally ventilated hospital building and demonstrated that even in extreme years, simple measures could significantly enhance a building’s climate change adaptation [26]. A similar approach was used to demonstrate the role of passive cooling roofs for enhancing the climate adaptability of buildings [27].

Natural ventilation has proven highly effective for enhancing the cooling capacity of buildings and improving their thermal resilience. The principle behind this lies in the fact that natural ventilation utilizes the differences in temperature and pressure between indoor and outdoor air, and promotes air movement through openings in a building (such as the windows, vents, and atrium) to carry away excess heat from a room. Ahmad et al., (2021) investigated the effectiveness of various natural ventilation systems aimed at improving a building’s adaptability during heatwaves, while considering their feasibility under both current and future climate scenarios [28]. This strategy not only effectively reduced indoor temperatures under current climatic conditions, but also enhanced the long-term resilience of buildings by maintaining their thermal comfort in future warming climates. Zhang et al., (2021) explored the critical role and importance of passive cooling solutions in the event of power outages [29]. Natural ventilation, which has been extensively studied due to its ability to harness the cooling potential of outdoor air, is particularly effective in atrium spaces. These spaces benefit from higher spatial volumes that facilitate natural airflow and, in many cases, their thermal comfort requirements are more flexible. Daniel et al., (2020) confirmed, based on field data from public building atrium spaces, that natural ventilation can significantly reduce a building’s cooling energy demand [30]. Li et al., (2025) developed a design framework for the nighttime natural cooling of the internal thermal mass, which resulted in a substantial reduction in the annual cooling demand [31].

In practical applications, the research on building thermal resilience is primarily used to inform architectural design and optimization. By improving building geometry, structure, and materials, the thermal performance of buildings can be significantly enhanced. Furthermore, the findings are also applied to the development of building standards and codes to address the challenges posed by climate change. The research on building thermal resilience is of great importance to academic fields, as it intersects with multiple disciplines, including architecture, physics, and environmental science, providing a scientific foundation for addressing climate change. By deepening our understanding of building thermal resilience, we can advance the field of architectural science and introduce new theories and methods for future building design.

1.2. Research Gaps and Objectives

Although significant progress has been made in the study of building thermal resilience, most of the research has focused on simulations and theoretical analyses, with relatively little field monitoring data available. Specifically, case studies on the thermal resilience of atrium spaces in public buildings under various conditions during heatwaves have not received widespread attention. In practical applications, the thermal resilience of atrium spaces is critical for improving the overall thermal comfort of buildings [17]. However, there are still insufficient data support and a lack of systematic analytical frameworks to assess the thermal resilience performance of atrium spaces in public buildings under extreme high-temperature conditions. Additionally, in practical applications, the calculation results and interrelationships of the existing thermal resilience indicators require further mathematical interpretation. Notably, limited research has addressed the data analysis of thermal resilience in atrium spaces under different states (such as closed and open) during heatwaves.

This study aims to address this gap by investigating the thermal resilience of atrium spaces under different conditions based on field data. By exploring the interactions between building usage patterns, environmental data, spatial zones, and temporal distributions, this study seeks to develop a comprehensive framework for analyzing the thermal resilience performance of atrium spaces. The findings are expected to provide valuable insights for optimizing atrium design to enhance occupant comfort and energy efficiency, with potential applications for both new construction and renovation projects. The specific research questions addressed in this study include the following:

• Analyzing the temperature variation characteristics of atrium spaces in closed and open states during heatwaves.
• Investigating the differences in thermal resilience across the various regions of the atrium space under different conditions.
• Analyzing the performance of thermal resilience indicators under different states and their interrelationships with various environmental data.

The paper is structured as follows: Introduction, Methodology, Results, Discussion, and Conclusion. Specifically, Section 2, Methodology, provides a detailed overview of the selected case studies, the methods for collecting the environmental data, and the thermal resilience indicator system employed. Section 3, Results, presents the monitored data on heatwaves and indoor environmental conditions, with a visualization of the thermal resilience calculation results. Section 4 introduces various statistical analysis methods to interpret the data comprehensively, offering a scientific analytical framework for understanding the thermal resilience mechanisms of atrium spaces during heatwaves. In Section 5, the Conclusion, the main findings of this study are summarized, along with a discussion of its limitations and potential directions for future research.

2. Materials and Methods

2.1. Building and Climate Description

The building chosen for this case study is a university activity center (as shown in Figure 1d). Completed in 2023, it is located on a university campus in Jiading District, Shanghai, China (121.22° E, 31.28° N), with a total area of 21,750 square meters. Notably, the building employs an assembled concrete structural system. The columns and beams of the main structure are rotated by 45 degrees (as shown in Figure 1b). This design strategy effectively mitigates excessive solar radiation. Particularly in the afternoon, it can efficiently block unfavorable sunlight from entering the interior, reducing indoor heat gain. The rotated structure, combined with the facade elements, also responds intelligently to the prevailing local wind direction, efficiently guiding outdoor natural ventilation into the interior.

The atrium space of interest in this study is located at the southwest corner of the building. The length and width of the first floor are both 21 m, while the length of the second floor is 27.9 m and the width is 24.8 m (as shown in Figure 1a, b). The height of both floors is 5.5 m (as shown in Figure 1c). The design of this space is also based on energy-saving goals, utilizing the building’s inherent passive modulation strategies to maximize the use of the natural environment.

To effectively promote natural ventilation within the building, the doors located on the south side of the first floor are designed to open fully, facilitating airflow throughout the space. This design feature is crucial for improving indoor air quality and maintaining a comfortable environment for the occupants. Additionally, compared to the first floor, the building mass on the second floor extends outward by 4.7 m (as shown in Figure 1c, d). This cantilever not only enhances the building’s aesthetic profile but also significantly reduces the direct solar radiation impacting the first floor. Such a design strategy is vital for minimizing heat gain and improving the overall thermal comfort of the interior space.

In addition to the cantilever, the top of the atrium is equipped with a carefully designed skylight, with beam heights exceeding standard structural requirements (as shown in Figure 1c). This feature helps reduce direct solar radiation entering the interior space while ensuring adequate natural lighting, thereby enhancing thermal performance and energy efficiency. Furthermore, the skylight is equipped with an electric opening mechanism, allowing it to open when necessary to accelerate the dissipation of accumulated heat indoors. This capability is particularly beneficial for maintaining a comfortable indoor temperature during high-temperature periods. Unfortunately, due to operational management requirements imposed by the building’s management, we were not allowed to open the skylight at the top during the experimental measurement process. This limitation underscores the complexities of managing public buildings and highlights the need for its further consideration in future research.

The topography of the Shanghai region is primarily characterized by expansive plains. According to the Köppen climate classification system, the region has a Cfa climate, which is classified as temperate with no distinct dry season and hot summers [32]. Figure 2 displays the dry-bulb temperature and horizontal solar radiation intensity data for a typical year. July and August are the hottest months in Shanghai. The orange line in Figure 2 represents temperature data recorded at Shanghai Hongqiao Airport, with the maximum temperature reaching 41 °C during the selected experimental period (from 28 July to 8 August 2024), significantly exceeding typical annual temperature data. In recent years, numerous studies have documented unusually high temperatures in the Shanghai region [33,34], emphasizing the importance of understanding, analyzing, and enhancing buildings’ thermal resilience during extreme heat events.

2.2. Data Acquisition

2.2.1. Standards for Heatwaves

Table 1. Definitions and criteria for hot weather or heatwaves of different countries and organizations.

Source	Definitions and Criteria for Hot Weather or Heatwaves
Environmental Protection Agency, United States [37]	It is frequently based on how unusually hot and humid it is for an area. Typically, temperatures of 95 °F (35 °C) or higher are considered the standard for extreme heat.
Ministry of the Environment, Japan [38]	Japan uses the Wet-Bulb Globe Temperature (WBGT) as a measure of heat risk. A WBGT value between 25 and 28 is considered to indicate a moderate-to-high risk for daily activities, while a WBGT value greater than 28 is considered dangerous for all life activities.
Bureau of Meteorology, Australian Government [39]	A heatwave is defined as a period during which both the maximum and minimum temperatures are unusually hot for at least three consecutive days, compared to the local climate and past weather patterns. In Australia, the Excess Heat Factor (EHF) is used for monitoring and forecasting heatwaves. The EHF combines a comparison of the average temperatures for a 3-day period with the temperatures that would typically be considered hot for that location, as well as the observed temperatures at that location over the past 30 days.
World Meteorological Organization [40]	A heatwave can be defined as a period where local excess heat accumulates over a sequence of unusually hot days and nights.

presents the definitions and standards for high-temperature weather or heatwaves of various countries and organizations. However, as noted by the World Meteorological Organization (WMO), while there is no universally accepted definition of a heatwave, it is generally characterized as prolonged periods of unusually hot weather, lasting anywhere from several days to months [35]. During such periods, both maximum and minimum temperatures remain consistently higher than normal levels. Since this case study is located in Shanghai, China, we adopted the standards set by the China Meteorological Administration (CMA) to define a heatwave [36]. According to the CMA, a high-temperature event is recognized when the daily maximum temperature reaches or exceeds 35 °C. If this heat persists for more than three days, it is officially classified as a heatwave. Additionally, the standard for extreme high-temperature events stipulates that the maximum temperature must be greater than or equal to 95% of the highest temperatures recorded for the same period over the past 30 years.

In the context of a heatwave, it is equally important to consider minimum temperatures. While maximum temperatures often receive more attention, minimum temperatures are equally significant because lower nighttime temperatures are essential for buildings’ recovery and temperature regulation [41]. When nighttime temperatures remain abnormally high, a building is unable to effectively cool down, leading to higher temperatures being reached earlier in the day and sustained for longer periods. The interaction between maximum and minimum temperatures is key to understanding the overall impact of heatwaves on human health and well-being, especially in urban environments like Shanghai.

2.2.2. Measured Indoor Temperatures

The on-site measurements followed the recommendations of industry standards [42]. However, due to practical constraints and management regulations, we made slight adjustments to the placement of the test points, drawing on relevant similar literature for guidance [43,44]. In Figure 1, the specific locations of the temperature and humidity sensors placed in the atrium space are marked. Four sensors were placed on each floor, identified by their floor and letter designation. The environmental monitoring was conducted in two phases, each lasting six days. The first phase, referred to as the “closed phase”, took place from 28 July to 2 August 2024, during which all doors and windows remained closed. The second phase, the “open phase”, occurred from 3 August to 8 August, with all doors and windows open during the daytime. The opened windows and doors included the folding door on the south side of the first floor, top-hung windows on the east and west sides, as well as top-hung windows on the south and west sides of the second floor. The folding door was fully opened to its maximum position on both sides, while all the top-hung windows were opened to the maximum angle allowed by their limiters. To eliminate the influence of the HVAC (Heating, Ventilation, and Air Conditioning) systems, all air conditioning units in the atrium and surrounding areas were switched off starting from 25 July. During the experimental period, the doors connecting the atrium space to the surrounding areas remained closed to isolate the environment in the atrium from the influence of other spaces. In addition to monitoring the indoor conditions, sensors installed on the building’s second-floor roof recorded outdoor meteorological parameters, providing valuable background data for comparison.

The sensor chips used in this study were Sensirion SHT45, with a temperature accuracy of ±0.1 °C and a relative humidity accuracy of ±1.5%. At each designated sensor location, air temperature and relative humidity were recorded every minute. These measurement points were specifically chosen to be far from any potential heat sources and were placed in areas that were not exposed to direct sunlight, ensuring accurate data collection.

In addition, on 2nd August (during the first phase) and August 8th (during the second phase), thermal images of the atrium space were captured every hour using an FLIR (Teledyne FLIR, Wilsonville, OR, USA) infrared thermal camera from four different angles. This allowed for a comprehensive spatial and temporal understanding of the thermal environment within the atrium. There were two observation points on each floor: T1 and T2 were located on the first floor, while T3 and T4 were on the second floor. T1 and T3 focused on the localized temperature of the west interior facade of the atrium, with T3 providing a view of facade components rotated at a 45-degree angle. Meanwhile, T2 and T4 captured broader spatial thermal images to examine the characteristics of temperature uniformity, with T4 offering a view of the skylight at the top of the atrium. The specific locations of the thermal imaging points are shown in Figure 1. The temperature range of the thermal imaging images was uniformly set at 30–45 °C to provide a more intuitive contrast effect. This image-based monitoring approach provided clear and intuitive evidence for analyzing the thermal resilience of the atrium in different states.

2.3. Building Thermal Resilience Indicators

Upon acquisition of temperature data from various areas within a building, building thermal resilience indicators can be employed to characterize the building’s thermal resilience performance during a heatwave. The key indicators utilized for this purpose include $IOD$, $AWD,$ and ${\alpha }_{IOD}$. Widely used to quantify the risk of overheating in buildings, these indicators have been extensively applied in both simulation-based and empirical studies focused on assessing building thermal resilience [24,29,45].

2.3.1. Indoor Overheating Degree (IOD) Indicator

$IOD$, measured in degrees Celsius (°C), serves to quantify the severity of the indoor thermal environment within a building. The higher the $IOD$ value, the more severe the building’s overheating problem during heatwaves, and the less thermal resilient it is. Conversely, a lower $IOD$ value indicates that the building is more thermal resilient. The formula evaluates the overheating of the entire building during occupancy by comparing the indoor operative temperature of each zone with the comfort temperature limit:

$$IOD={\displaystyle \frac{{\sum }_{z=1}^Z {\sum }_{i=1}^{N_{occ}\left(z\right)} \left[{\left(T_{in,o,z,i}-T_{comf,z,i}\right)}^{+}{t}_{i,z}\right]}{{\sum }_{z=1}^Z {\sum }_{i=1}^{N_{occ}\left(z\right)} t_{i,z}}},$$

(1)

where $t$ is the time step (1 h), $i$ is the number of occupied hours, $z$ is the number of the building zone, $Z$ is the total number of building zones, $T_{in,o,z,i}$ is the zonal indoor operative temperature, and $T_{comf,z,i}$ is the zonal thermal comfort limit. $N_{occ}\left(z\right)$ is the total number of zonal occupied hours.

While the framework for evaluating indoor thermal conditions recommends the use of the Predicted Mean Vote (PMV) and Predicted Percentage Dissatisfied (PPD) models to estimate $T_{comf}$, it is imperative to recognize that the selection of the indoor ambient temperature threshold should be made with careful consideration of the health risks, rather than the comfort, faced by occupants during heatwave events [29]. For extreme heat events, such a calculation may result in an overestimation of the $IOD$ values. This is because thermal comfort indices reflect the temperature that people ideally consider comfortable, rather than the threshold temperature that they can endure. The Heat Index (HI) combines air temperature and relative humidity to measure the equivalent temperature perceived by humans. Originally developed to assess the outdoor thermal environment during hot summer conditions, HI is also applicable for evaluating indoor thermal resilience during extreme heat events [46]. There are four levels of heat stress based on the HI, including Caution, Extreme Caution, Danger, and Extreme Danger. In light of this, this study advocates for the use of the HI as a more appropriate method for estimating the thermal comfort threshold $T_{comf}$, a method that has been validated by other scholars [45]. The HI calculation integrates multiple regression analyses of air temperature and relative humidity, offering a more nuanced understanding of the thermal comfort experienced by building occupants. When the impact of high temperatures poses a threat to human health, the HI classification moves into the “warning” category. Based on the hourly average relative humidity values measured during this experimental study, the corresponding critical air temperature threshold values were calculated. Figure 3 shows the variations in this parameter over different time periods. During this study, the highest $T_{comf}$ is 27.0 °C, while the lowest is 25.4 °C, showing a negative correlation with humidity changes. This threshold serves as a critical indicator for assessing the potential health risks associated with indoor thermal conditions during extreme heat events. Therefore, accurately understanding and applying these indicators is crucial for architectural design and assessment, especially in the face of climate challenges, to prioritize the health and well-being of occupants.

2.3.2. Ambient Warmness Degree (AWD) Indicator

$AWD$ (°C) quantifies the severity of the outdoor thermal conditions. A higher $AWD$ value indicates a more severe outdoor thermal environment during a heatwave. This formula evaluates the outdoor thermal environment of the entire building during occupancy by comparing the outdoor air temperature to a base temperature:

$$AWD={\displaystyle \frac{{\sum }_{i=1}^N {\left(T_{out,i}-T_b\right)}^{+}{t}_i}{{\sum }_{i=1}^N t_i}},$$

(2)

where $T_{out,i}$ is the outdoor air temperature, $T_b$ is the base temperature, and $N$ is the total number of building occupied hours.

A base temperature ($T_b$) of 18 °C has been employed as a reference point for evaluating thermal conditions within buildings in several studies [23,24,29], as this value ensures that both the $IOD$ and $AWD$ calculations remain positive during heatwave periods. However, it is important to note that utilizing a lower base temperature during extreme heat events may result in a misleading and inaccurate assessment of the $IOD$. Given the critical implications of this measurement for understanding thermal comfort and resilience, we propose that, in the context of this study, the base temperature should be set equal to the thermal comfort temperature ($T_b=T_{comf}$) [45]. This recommendation is predicated on the imperative to ensure that the calculations more precisely reflect the actual conditions faced by occupants during periods of elevated temperatures. In doing so, it aims to bolster the reliability and applicability of our findings within the realm of building resilience.

2.3.3. Overheating Escalation Factor (α_IOD)

The quantitative assessment of a building’s thermal resilience must inherently consider the interplay between both the outdoor and indoor environmental conditions. A crucial metric in this context is the Overheating Escalation Factor (${\alpha }_{IOD}$), which serves to quantify a building’s capacity to maintain comfortable indoor conditions despite the fluctuations and variances inherent in the external climatic environment. This factor has garnered significant attention and has been extensively employed in numerous quantitative evaluation studies aimed at assessing the thermal resilience of buildings [6,24,45].

In order to construct a robust analytical framework, it is assumed that there exists a linear relationship between the $IOD$, which is considered as the dependent variable, and the $AWD$, which is treated as the independent variable. Under this assumption, the ${\alpha }_{IOD}$ can be effectively calculated as the slope of the linear regression line. This linear relationship serves a dual purpose. Firstly, it enables a more in-depth comprehension of how varying outdoor conditions impact indoor thermal comfort; secondly, it facilitates the development of strategies aimed at enhancing the resilience of buildings in the face of climate variability:

$${\alpha }_{IOD}={\displaystyle \frac{\Delta IOD}{\Delta AWD}}={\displaystyle \frac{{\sum }_{Sc=1}^{Sc=M} \left(IO{D}_{Sc}-\overline{IOD}\right)\times \left(AW{D}_{Sc}-\overline{AWD}\right)}{{\sum }_{Sc=1}^{Sc=M} {\left(AW{D}_{Sc}-\overline{AWD}\right)}^2}},$$

(3)

where $Sc$ is the number of different weather scenarios, and $M$ is the total number of weather scenarios.

Theoretically, an ${\mathsf{\alpha }}_{\mathit{I}\mathit{O}\mathit{D}}$ value of less than 1 indicates that a building is thermally resilient and can effectively cope with thermal stresses caused by fluctuations in the external climatic environment. This indicates that the building is capable of maintaining comfortable indoor conditions even in the face of variable outdoor temperatures. On the contrary, an ${\alpha }_{IOD}$ value greater than 1 indicates that a building exhibits poor thermal resilience, suggesting an inability to adequately mitigate the adverse effects of thermal stress resulting from changes in the outdoor climate. This situation may lead to uncomfortable indoor conditions, which ultimately affect the health of the occupants and the overall thermal resilience performance of the building. Therefore, understanding and accurately measuring ${\alpha }_{IOD}$ is essential for assessing and improving the thermal resilience of architectural designs in response to varying climatic challenges.

3. Results

3.1. The Detected Heatwave

Figure 4 shows the trend for the outdoor temperature and humidity during the monitoring period, with the temperature data recorded at Shanghai Hongqiao Airport attached as a reference. Although the sensor-recorded temperatures were consistently higher than those from the airport, which may have been due to the different geographical location and environment, both sets of data show that from 28 July to 8 August, the maximum daily temperatures exceeded 35 °C, aligning with the CMA’s definition of a heatwave. The highest temperature during the 12-day-long heatwave occurred on 2 August, reaching 42.4 °C. The average temperature followed an upward trend before decreasing, peaking on August 2 as well. The last two days of the first phase had daily mean temperatures exceeding 35 °C, and only the last day of the second phase had daily mean temperatures below 35 °C. In terms of daily fluctuations, the outdoor temperatures generally fell to their minimum around 7 A.M., before rising quickly. This rapid increase generally occurred about two hours after sunrise (sunrise in Shanghai during the experimental period was around 05:15 a.m.) and peaked around 2–3 P.M. The relative humidity (RH) showed a negative correlation with the temperature, with the highest RH, near 80%, occurring on the night of 28 July when the daily temperature was at its lowest. The lowest RH, approximately 30%, was recorded on the afternoon of 6 August.

3.2. Measured Indoor Environment

3.2.1. Indoor Air Temperature

Figure 5 presents the hourly average indoor and outdoor air temperatures at each sensor test point, highlighting the significant differences in the daily temperature variations between the two environments and two phases. In the first phase, the indoor temperature gradually increases as the outdoor temperature climbs day by day. The temperature difference between the two floors gradually expands, with the increase on the second floor being slightly greater than on the first floor, indicating a higher sensitivity to external temperature changes under the closed condition. From 28 July to 31 July, the outdoor minimum nighttime temperature is lower than the indoor temperatures in most areas, whereas on 2 August, the outdoor nighttime temperature exceeds the indoor temperature across all areas. In the second phase, after the windows and doors were opened, although the outdoor average temperature gradually decreases, the indoor temperature does not show a significant downward trend. Notably, the daily maximum temperature on the second floor consistently exceeds 35 °C. It is worth mentioning that the fluctuation range of the indoor temperatures during the second phase is much larger compared to the first phase, especially on the first floor, where the temperature variation increases by approximately 2 °C (as also evidenced in Figure 6). The temperature differences between different the test points on the first floor also grow larger. This suggests that the thermal unevenness in the lower-floor areas of the atrium might be more pronounced. Regarding the nighttime low temperatures, from 4 August onwards, the outdoor minimum nighttime temperature is always between the indoor temperatures of the first and second floors.

To further illustrate the thermal unevenness of the atrium space in both the vertical and horizontal directions, Figure 6 presents the statistical results after grouping the data by plane location for the two phases. Based on the results in Figure 5, throughout the entire experiment, the indoor air temperature on the first floor is consistently 2–4 °C lower than on the second floor, particularly at points A and B. This vertical temperature gradient can be partially attributed to the upward movement of warm air, a phenomenon typically associated with buoyancy-driven ventilation. In the horizontal direction, the temperature data from both phases show similar distribution patterns: B < A < C < D. The smallest values for both the mean and median temperatures at point B can be well explained, as it is the farthest from direct sunlight and climatic boundaries. Points C and D, located near the south side of the atrium, received the most solar radiation for the longest duration, thus exhibiting higher temperatures.

3.2.2. Thermal Images

The thermal imaging data further emphasize these results (Figure 7), and also present some new findings. On 2 August, during the first phase, the glass at T3 on the second floor begins to heat up significantly from 3:00 P.M., while the corresponding position at T1 on the first floor does not show significant changes until 5:00 P.M. This indicates that the overhang of the second floor greatly delays the adverse effects of sunlight on the first floor. On 8 August, during the second phase, the peak temperature at T1 occurs noticeably earlier and is nearly synchronized with that at T3. This suggests that in a naturally ventilated state, the building is more sensitive to changes in the external environmental temperature. At the same time, it is noteworthy that, compared to the image from 2 August, the peak temperature in the 8 August image is significantly decreased, providing some evidence for the passive regulation potential of natural ventilation. The images from both phases also exhibit some common points:

• The images for T2 show that the indoor temperature peaks around 2:00–3:00 P.M., consistent with the previous conclusion.
• The surface temperature of the wall at T3 reaches its minimum when the outdoor temperature reaches its maximum, which is contrary to the general pattern.
• The images at T4 demonstrate a clear vertical temperature unevenness: the temperature at the top of the atrium is significantly higher than that at the bottom.

3.3. Building Thermal Resilience Analysis

The $IOD$ and $AWD$ are derived from the measured data, as shown in Figure 8. Due to the inherent limitations and potential errors of the experimental instruments, the calculated data may contain some inaccuracies, which are reflected in the figure. Since the experiment was conducted during the university’s summer break, the occupancy time used for the calculation of the $IOD$ and $AWD$ was simplified. During this period, the space was occupied from 9:00 A.M. to 5:00 P.M. on weekdays (the same applied to weekends).

The analysis of the ${\alpha }_{IOD}$ calculation data revealed two important conclusions: First, even with a relatively limited number of experimental days, the $IOD$ generally did not exceed the $AWD$. This indicates that the courtyard space demonstrated strong thermal resilience in both states. Second, there was a clear positive correlation between the $IOD$ and $AWD$ values in both states, though the thermal resilience performance varied. In the first phase, under closed conditions, the courtyard space exhibited relatively weak thermal resilience. However, a noteworthy anomaly was observed upon a detailed examination of Figure 8 and

Table 2. Building resilience indicators calculated from detected temperatures.

Phase 1
Date	28 Jul	29 Jul	30 Jul	31 Jul	01 Aug	02 Aug
$\mathit{A}\mathit{W}\mathit{D}$	9.05	9.61	9.99	10.71	11.87	12.98
$\mathit{I}\mathit{O}\mathit{D}$	5.25	5.36	5.76	6.00	6.06	6.15
Phase 2
Date	03 Aug	04 Aug	05 Aug	06 Aug	07 Aug	08 Aug
$\mathit{A}\mathit{W}\mathit{D}$	12.27	11.69	11.66	11.50	11.31	10.72
$\mathit{I}\mathit{O}\mathit{D}$	7.37	7.36	7.77	7.38	7.44	7.34

: during the six days of the closed first phase, the outdoor daily average temperature increased progressively, and both the $AWD$ and $IOD$ followed suit. This is easily understandable, as a hotter outdoor environment naturally leads to indoor overheating. However, this monotonic change was disrupted during the second phase, during which the outdoor daily average temperature decreased progressively, and the $AWD$ followed a similar trend, which resembled the first phase results. Yet, the variation in the $IOD$ was different. For instance, on 3 August, when the highest outdoor daily average temperature occurred within that phase, the $IOD$ ranked fourth, while its peak value occurred on the third day of the second phase, 5 August. The cause of this anomalous phenomenon is likely to be multifaceted. Firstly, the indoor environment in the open phase was significantly less stable than in the closed phase (even though the closed phase could be more prone to overheating). The large-scale openings in the windows and doors allowed local winds to bring in outdoor air, which could be relatively hotter or colder, causing fluctuations in the indoor air temperature. Secondly, another potential cause could be that the indoor thermal environment in the second phase was influenced by various factors, including the gradually decreasing $AWD$ of the outdoors, as well as the accumulated heat from the first phase and over several days. Moreover, as time progressed, the uncertainty of these disturbances became more complex in the open phase. Additionally, during the experimental period, we also observed periods of cloudy weather, which led to unstable direct sunlight exposure indoors. This, in turn, directly affected the fluctuations in the indoor air temperature.

From the calculation formula for the $IOD$, it can be observed that different time factors may lead to different results. Although we used a unified simplified occupancy time for the calculation, if there was a prolonged period of high temperature during the occupancy hours, it could lead to an increase in the $IOD$. To further support this hypothesis, we performed a statistical analysis of the daily indoor temperatures exceeding 35 °C (Figure 9). The results indicate that during the first phase, the duration of indoor temperatures exceeding 35 °C was negligible, occurring only in the last two days for approximately 9 min and 25 min, respectively. In contrast, the second phase saw a significant increase in the duration of indoor temperatures above 35 °C, with an average of around 3 h per day. On 5 August, the proportion of time with indoor temperatures exceeding 35 °C was the highest, reaching 14.2%. This indicates that the high temperatures concentrated during the occupancy period, contributing to the excessive $IOD$ on that day, aligning with the results shown in Table 2. A comparison of the statistics for the two phases reveals that natural ventilation substantially increased the duration of temperatures exceeding 35 °C during the occupancy hours in the open phase. At first glance, this would seem to contribute to a higher $IOD$, potentially implying a decline in thermal resilience. However, this is not the case. It is important to note that the duration of outdoor temperatures exceeding 35 °C also generally increased during the second phase, despite a decrease in the average outdoor temperature. This indicates that the impact of natural ventilation on the $IOD$ is less pronounced compared to the $AWD$, resulting in a reduction in the ${\alpha }_{IOD}$ rather than an increase. Additionally, Figure 9 provides a reasonable explanation for the smaller $IOD$ on 3 August: there was a lower distribution of high temperatures compared to the other days during the occupancy period.

The inconsistency between the $IOD$ and $AWD$, especially during prolonged periods of high temperatures, suggests that the relationship between these indicators is more complex than initially anticipated. While a general positive correlation holds, the dynamic changes in temperature data over time may introduce some uncertainty between the two. These anomalies indicate that short-term temperature fluctuations and the temporal distribution of heat have a significant impact on the calculation of resilience indicators like the $IOD$ and $AWD$. The results emphasize that when evaluating a building’s thermal resilience, it is crucial not only to consider the daily average temperature but also to examine the importance of the time patterns and duration of thermal exposure.

4. Discussion

4.1. Data Analysis and Comparison

Section 3.2 provided a preliminary overview of the thermal heterogeneity reflected by the data measured within the atrium space. However, the overall distribution of the data within each stage does not effectively illustrate the differences between the groups. It remains necessary to apply more quantitative statistical methods, based on the time series data, to describe the thermal environmental differences at various locations under both conditions. Additionally, the previous results have already highlighted that the uneven distribution of the temperature data over time significantly impacts the evaluation of a building’s thermal resilience. Therefore, it is essential to further explore the specific statistical characteristics of these data to establish a more solid foundation for the analysis and assessment of building thermal resilience.

4.1.1. Euclidean Distance

The Euclidean distance is suitable for comparing two sets of data in terms of their overall differences. To further explore the variability in the data in the two states at different locations, we employ it to calculate the magnitude of the differences between the data in the two states at corresponding time points during the heatwave:

$$d=\sqrt{{\sum }_{i=1}^n (x_i-y_i{)}^2},$$

(4)

where $x_i$ and $y_i$ are the $i$th value of the two sets of data, respectively, and $n$ is the number of data points. The result of the calculation, $d$, indicates the overall difference between the temperature data for the atrium space in the closed and open states. Larger values of $d$ indicate greater differences in the temperature data between the two states, and vice versa.

Table 3. Euclidean distance of different positions in two states.

Sensors Position	1A	1B	1C	1D	2A	2B	2C	2D
d	82.8	81.8	118.2	162.2	150.4	188.7	173.8	203.5

presents the calculation results of the Euclidean distances. It can be observed that the differences in the planar location within the same heatwave period may introduce uncertainty into the results. For example, at test points A and B on the first floor, the differences between the two sets of data are relatively small. The opening status of the building’s doors and windows does not significantly affect the temperature at these points. This suggests that areas on the first floor, far from large open windows and doors, may be more conducive to maintaining stable indoor temperatures. This aligns with the conclusions that can be drawn from the research by Yin et al., (2024) [47]. Moreover, on the first floor, the Euclidean distances maintain the same pattern as before: B < A < C < D. However, the situation on the second floor is slightly different. The B point, which should exhibit the smallest value, shows a relatively large increase. This contradicts the conclusion from Figure 6, but can still be explained. While the Euclidean distance can measure the differences between two sets of parallel data, the calculation is based on corresponding features. In other words, when the peak positions of the two sets of data differ, it leads to a larger distance (d value). The time inconsistency of the peak positions can be influenced by various objective factors, particularly short-term and accidental environmental fluctuations that may occur during the monitoring period. Therefore, further analysis of the distribution patterns of the time series data is necessary.

4.1.2. Excess Kurtosis

Kurtosis is an important statistical measure used to describe the shape of a data distribution, primarily indicating the sharpness or the thickness of the tails of the distribution. In this study, kurtosis reflects the “sharpness” of the temperature data distribution and the likelihood of extreme high-temperature occurrences. By calculating the kurtosis, we can determine whether the indoor temperature data are more concentrated around the mean or whether there are more extreme values, thereby providing further insights for the analysis of thermal resilience. Kurtosis is calculated based on the fourth central moment of the data, and its specific definition is as follows:

$$Kurtosis={\displaystyle \frac{\frac{1}{n}{\sum }_{i=1}^n{\left(x_i-\mu \right)}^4}{{\sigma }^4}},$$

(5)

$$Excess Kurtosis=Kurtosis-3,$$

(6)

where $x_i$ is the $i$th value of the data set, $\mu$ is the arithmetic mean of all the values in the data set, $\sigma$ is the standard deviation of the data set, and $n$ is the number of data points. For comparison, the kurtosis is usually subtracted by three (the base value of the normal distribution), and when the excess kurtosis > 0, the distribution is more sharply peaked and thick-tailed than the normal distribution. When the excess kurtosis < 0, the distribution is more gently thin-tailed than normal.

Figure 10 presents the calculated standardized kurtosis of the temperature data for different positions throughout the day. The results indicate that most of the monitoring data are flatter than that of a normal distribution, with only a few test points showing sharper distribution patterns on certain days. Although the trends in the standardized kurtosis calculations are generally consistent, the following two phenomena are noteworthy:

• In the closed state during the first phase, the kurtosis of the second floor is generally 0.5 lower than that of the first floor. In contrast, during the second phase when the space is open, the situation is reversed. The kurtosis of the first floor is typically 0.5 lower than that of the second floor. This suggests that after normalizing the data fluctuations, in the absence of natural ventilation during a heatwave, the temperature data distribution on the second floor of the atrium is much flatter, with a thinner tail and a lower probability of extreme values compared to the first floor. However, once the doors and windows are opened in the second phase, the temperature data distribution on the second floor becomes steeper, with a higher probability of extreme values compared to the first floor. In other words, natural ventilation causes the temperature data on the upper floors of the atrium to become more unstable.
• In the first phase, the data from points A and B on the first floor show positive standardized kurtosis values on three separate days. This suggests that in the closed state, positions closer to the interior (further from the boundaries) on the bottom floor of the atrium are more likely to experience extreme values. It is important to note that this does not contradict the conclusions from Section 4.1.1. While the positions of A and B on the plan help maintain stability, they also make these points somewhat more vulnerable. A more uniform temperature data distribution is more sensitive to sudden environmental changes, which can significantly impact the kurtosis values. A similar situation is observed at point C in the second phase, which further supports the previous discussion on thermal unevenness.

4.2. Correlation Analysis

In order to further analyze the possible causes of changes in the thermal resilience of the atrium space, we listed nine different parameters (Figure 11). We incorporated suggestions from several references, to consider not only the outdoor air temperature of the current day but also that of the previous day [45]. Additionally, the impact of the nighttime low temperatures on building thermal resilience was taken into account [31]. Since the measured indoor temperature data did not pass the normality test, we used Spearman’s Rank Correlation for the correlation analysis. It is a nonparametric statistical method that does not require the data to follow a normal distribution, making it applicable to a wider range of data types. Figure 11 presents the results of the correlation analysis for both phases. The numbers in Figure 11 are the results of the correlation analysis, which range from −1 to 1. A value of 1 means a perfect positive correlation, −1 means a perfect negative correlation, and 0 means no correlation.

In the first phase, the $IOD$ shows a significant positive correlation with all parameters at the 0.05 level. This is consistent with the monotonic variations presented in Figure 4, Figure 5 and Figure 8. This indicates that the atrium space in the closed state exhibits strong environmental adaptability and maintains a relatively stable internal environment. Regarding the key indicator of thermal resilience, ${\alpha }_{IOD}$, most of the parameters display significant negative correlations, except for two parameters, C and I, which do not meet the 0.05 significance threshold. This suggests that as environmental temperatures increase—whether in terms of the average temperature or nighttime lows—the thermal resilience of the atrium tends to decline. An anomalous observation is the significant negative correlation between the ${\alpha }_{IOD}$ and G. This implies that in the closed state, the theoretically beneficial cooling effect from lower nighttime outdoor temperatures on the previous day may not necessarily enhance the thermal resilience of the atrium space. This is because the ${\alpha }_{IOD}$, which should decrease, tends to increase as the nighttime outdoor low temperature decreases (cooling capacity increases). In the second phase, significant changes are observed. The correlation trends between the $IOD$ and all parameters are different, and none reach the 0.05 significance level. This indicates that, in the open state, the $IOD$ of the atrium space exhibits strong randomness and is less stable. The correlation of the ${\alpha }_{IOD}$ also differs significantly, with parameters B and F showing a significant negative correlation. In other words, as the average outdoor temperature of the current and previous days rises, the thermal resilience of the atrium space in the open state increases. This finding is promising, as it suggests that the design of the building (particularly in response to extreme heat environments) is successful. However, due to the case-specific nature and the limited sample size of the data, we cannot yet confirm whether this conclusion is universally applicable. Another noticeable phenomenon lies in the relationship between the ${\alpha }_{IOD}$ and parameter I, as this relationship is entirely opposite between the open and closed phases (despite neither phase meeting the 0.05 significance threshold). In the open phase, the ${\alpha }_{IOD}$ exhibits a positive correlation with parameter I, with a correlation coefficient of 0.78. This indicates that under natural ventilation, as the previous day’s indoor minimum temperature decreases, the thermal resilience of the atrium may improve. This further confirms the beneficial effects of natural ventilation, particularly nighttime cooling, on enhancing thermal resilience.

4.3. Peak Clipping and Delayed Effects

Using the ${\alpha }_{IOD}$ to quantify the thermal resilience of the atrium space during heatwaves is indeed an accurate method. However, there are more direct ways to quantify thermal resilience, such as calculating the peak temperature difference between indoor and outdoor environments during a heatwave. In the absence of mechanical temperature control, the greater the peak temperature difference, the more pronounced the peak clipping effect, which similarly indicates better thermal resilience. Figure 12 shows the indoor and outdoor temperature differences recorded at various locations under both conditions. The atrium maintained a commendable performance during both phases, with the indoor peak temperatures averaging about 7 °C lower than the outdoor peak temperatures. The peak clipping effect on the first floor was notably stronger than that on the second floor, exceeding it by approximately 3 °C on average. Additionally, the peak clipping effect also exhibited spatial non-uniformity: areas away from the climatic boundaries showed better performance. In the first phase, the peak clipping effect at all points generally increased, despite the gradual rise in the average outdoor temperature (Figure 4). On August 2, the day with the highest average outdoor temperature, the peak clipping effect reached its maximum. This indicates the atrium’s remarkable capacity to withstand progressively harsh outdoor conditions in a closed state. At location 1A, the peak temperature difference between the indoor and outdoor environments reached as high as 11 °C. This further confirms the strong thermal resilience of the atrium space. As the outdoor temperatures increased during this phase, the variation in the peak reduction effects between the different measurement points slightly widened. In the second phase, the peak clipping effect showed slight fluctuations and a decline, but still demonstrated a good passive cooling effect. Notably, the differences in the peak reduction effects among the measurement points on the first floor became significantly larger than in the first phase, and the lines representing the second-floor measurement points occasionally intersected. This further corroborates the conclusion that natural ventilation increases the unpredictability of indoor environmental fluctuations. Overall, the peak clipping effect on the ground floor was noticeably stronger than that on the second floor. The peak clipping performance at different locations on the floor plan consistently followed the pattern B < A < C < D. This once again confirms the conclusion that locations closer to the interior of the building exhibit better thermal resilience.

The previous analysis has preliminarily demonstrated that the time distribution of high indoor and outdoor temperatures during a heatwave significantly affects the ${\mathsf{\alpha }}_{\mathit{I}\mathit{O}\mathit{D}}$ results. Although the direct analysis of the peak clipping effect reveals the atrium space’s excellent buffering performance against external high temperatures to some extent, it overlooks the time difference between the indoor and outdoor peak temperatures. In general, a longer time delay indicates a better thermal retention performance, while a shorter time delay suggests more efficient heat dissipation. To address this, we further analyzed the time difference between the peak indoor temperatures at each test point and the outdoor peak temperature on the same day (Figure 13). In the first phase, the time delay effects at the various test points did not show as obvious a monotonic variation as some of the previous results. The first three days displayed significant delay effects, generally exceeding 2 h. The longest delay occurred at location 1B on 29 July, reaching approximately 4 h. This suggests that during this phase, the atrium space exhibited strong thermal retention properties, with the closed atrium effectively isolating the interior from external environmental fluctuations. In contrast, the last three days showed relatively lower delay effects, but they remained between 0.5 and 1 h. The differences between the various locations were also irregular. In the second phase, no clear daytime differences appeared over the six days. The delay effects generally remained between 0.5 and 1 h. There was a decline in the retention performance during the open phase. It is noteworthy that on August 4, locations 1B and 1C exhibited a noticeable negative delay effect, where the indoor peak temperatures occurred earlier than outdoor peak temperatures. This may have been caused by local, incidental wind conditions. This aligns with the earlier discussion that natural ventilation tends to exacerbate indoor environmental instability.

5. Conclusions

This study investigates the thermal resilience of an atrium space during a heatwave in both closed and open states, using field monitoring data. The indoor and outdoor temperature and humidity data were collected from the atrium of a student activity center at a university in Shanghai, in combination with thermal imaging technology. The thermal resilience indicators, including the $IOD$, $AWD$, and ${\alpha }_{IOD}$, were calculated, and statistical analyses were conducted to explore the temporal distribution characteristics of the thermal environment and their impacts. This study provides a comprehensive analytical approach for evaluating a building’s response to extreme weather, and yields the following findings:

• The thermal resilience of the atrium space shows significant differences under different conditions, with distinct vertical and horizontal temperature distribution non-uniformity:
  • In the closed state, the temperature distribution within the atrium remains relatively stable, but the thermal resilience is relatively weak. For example, from 28 July to 2 August, as the outdoor daily average temperature gradually increased, both the $IOD$ and $AWD$ in the atrium followed an upward trend, indicating a limited buffering capacity against high temperatures. Specifically, when the outdoor temperature peaked on 2 August, the $IOD$ in the atrium was 12.98 °C and the $AWD$ was 6.15 °C. Moreover, the temperature increase on the second floor was greater than that on the first floor, and the temperature difference between the two floors gradually increased, with the second floor experiencing a slightly higher temperature rise, showing a stronger sensitivity to external temperature changes in the closed state.
  • In the open state, natural ventilation significantly enhanced the thermal resilience of the atrium, but also increased the temperature distribution non-uniformity. From August 3 to August 8, the outdoor average temperature decreased daily; however, the $IOD$ and $AWD$ in the atrium did not follow the same trend as the closed state. For instance, on 5 August, the $IOD$ reached its maximum value of 11.66 °C, even though the outdoor average temperature was not the highest. This suggests that in the natural ventilation state, indoor temperature fluctuations are influenced by various factors, including outdoor temperature, ventilation effects, and the thermal inertia of the indoor space. Additionally, the thermal imaging data showed that, in the natural ventilation state, the temperature at the top of the atrium was significantly higher than at the bottom, with higher temperatures near the southern side, further confirming the distinct vertical and horizontal temperature distribution irregularities in the atrium under different states.
• The calculation of the thermal resilience indicators is dynamic and complex, with a significant correlation with the environmental data:
  • This study finds that the relationship between the $IOD$ and $AWD$ is not a simple linear relationship and is influenced by various factors. In the open state, the relationship between the $IOD$ and $AWD$ became more complex. Although natural ventilation enhanced the thermal resilience of the atrium to some extent, the changing trends between the $IOD$ and the environmental data became complicated. For instance, the maximum $IOD$ of 7.77 °C on 5 August occurred when the outdoor average temperature was not the highest, suggesting that in the natural ventilation state, indoor temperature fluctuations are influenced by various factors, including fluctuations in outdoor temperature, ventilation effects, and the thermal inertia of the space.
  • Additionally, this study reveals that the thermal resilience indicators have a significant correlation with the environmental data. For example, the Spearman correlation analysis showed that in the closed state, the $IOD$ exhibited a significant positive correlation with the daily maximum outdoor temperature, average outdoor temperature, and the previous day’s minimum outdoor temperature. In the open state, this correlation was weakened, indicating that the indoor temperature fluctuations were influenced by more factors in the natural ventilation state, and the interactions between these factors became more complex.
• The impact of natural ventilation on the thermal resilience of the atrium space is significant but may lead to localized temperature non-uniformity:
  • Natural ventilation showed a marked effect at improving the thermal resilience of the atrium space. The ${\alpha }_{IOD}$ improved from 0.23 (closed state) to 0.05 (open state), confirming natural ventilation’s effectiveness. However, the open state introduced variability. For instance, the statistical analysis revealed that in the open state, the temperature data distribution at different locations in the atrium became steeper, with the probability of extreme values increasing. In particular, the temperature fluctuation on the second floor was more severe, with an increase of about 1 °C, and the local temperature instability was more prominent.
  • These results suggest that when designing and managing atrium spaces, it is essential to fully consider the pros and cons of natural ventilation. On the one hand, optimizing ventilation design can enhance the thermal resilience of an atrium space; on the other hand, appropriate measures should be taken to minimize the localized temperature non-uniformity and instability caused by natural ventilation, thereby improving indoor thermal comfort. For instance, shading devices can be reasonably set, and the location and size of ventilation openings can be optimized to improve the thermal environmental performance of an atrium space.

While this study makes significant contributions to understanding and assessing the thermal resilience of atrium spaces in public buildings during heatwaves, it has certain limitations. Firstly, although the supplementary statistical analyses somewhat address the insensitivity of the thermal resilience indicators to the time distribution, the calculation and analysis of the related indicators are not fully unified, which affects the comprehensiveness of the results. Secondly, while this study explores the thermal resilience performance of the atrium space under different states, it does not delve deeply into the specific effects of various ventilation strategies. Furthermore, the experimental data used in this study are based on a single building case with a short sampling period, which may limit the generalizability of the findings.

The findings of this study provide valuable data support and an analytical framework for future research on and design optimization for building thermal resilience. The results highlight that natural ventilation can significantly mitigate the impact of high temperatures on building interiors during heatwaves, though attention must be given to potential issues of thermal unevenness. This underscores the importance of incorporating passive strategies with dynamic control mechanisms in building design to achieve a balanced and optimized thermal environment. Moving forward, future research could focus on the following areas to address the current limitations:

• Standardizing and unifying the thermal resilience indicators: A more unified approach to calculating and analyzing the various thermal resilience indicators is needed. This would involve ensuring methodological consistency and exploring the relationships among the various indicators to provide a more comprehensive understanding of building thermal resilience.
• Examining the impact of ventilation strategies: Further research could explore the effects of different ventilation strategies (e.g., natural ventilation, mechanical ventilation, and hybrid systems) on thermal resilience, as these strategies could significantly influence the thermal comfort and resilience of buildings under extreme heat conditions.
• Expanding case studies and monitoring periods: To improve the generalizability of the findings, future studies could consider a broader set of case studies across different building types and locations, with a longer monitoring period. This would help assess how thermal resilience may vary across different contexts and provide stronger insights for optimizing building designs.

By addressing these issues, future research could provide more comprehensive and practical recommendations for improving the thermal resilience of public buildings, particularly in light of increasing heatwaves and climate change.