The case study was conducted on the subject of Mao Dun's former residence in the Dongcheng District, Beijing, which was listed as a Cultural Relic Protection Unit of Beijing in 1984^[3]. The courtyard complex follows a characteristic north-south orientation, with all doors and windows of the rooms oriented inward toward the courtyard. What’s more, the site features a courtyard layout combining two small and one large courtyard, representing the typical small-to-medium-sized courtyard type found in Beijing. Each demonstrates unique spatial and botanical characteristics. The first courtyard forms a long horizontal rectangle devoid of vegetation. The second courtyard features a large longitudinal rectangle flanked by two small patio courtyards, with central vegetation and a tall banyan tree in the western patio. The third courtyard maintains a long horizontal rectangle form with symmetrical low-canopy trees and entrance-adjacent ornamental plantings.

The research object is geographically situated between 39°30′N and 39°40′N latitude, and 115°30′E to 117°30′E longitude. The region exhibits a temperate continental monsoon climate with semi-humidity and four distinct seasons^[3]. Climate variations follow cyclical patterns, with the key environmental factors such as solar altitude angle, solar radiation, and air temperature fluctuating between the winter solstice and the summer solstice^[25]. Therefore, two solstice dates, June 12, 2012 and December 22, 2020, were selected as the specific research dates from 25-year meteorological data of Beijing, for which exhibits typical Summer Solstice and Winter Solstice meteorological characteristics. The characteristics could be illustrated in the variation of two solstice dates’ specific meteorological factors at Mao Dun's Former Residence, such as air temperature, relative humidity, wind speed and wind direction (Fig. 1).

The microclimate simulation of Mao Dun's former residence was implemented using ENVI-met, incorporating both a three-dimensional (3D) master model and a one-dimensional (1D) boundary model. The 3D master model was established through specifying parameters such as building heights, material properties, vegetation characteristics, and observation point locations based on actual surveying data. There are four types of underlying surfaces in the study area, including building roof, pavement, exposed soil, and vegetation. Primary material properties encompass masonry facades, tiled roofs, gray permeable brick floor, asphalt concrete pavement, and soil floor. The 1D boundary model was constructed through initial simulation parameters (e.g., wind profiles, temperature, humidity gradients)^[26]. Each three-dimensional grid in the study area had a resolution of 1 meter in both horizontal and vertical directions, with a total of 60 × 80 × 20 grids. Following rigorous validation of both grid checks and parameter verification, the microclimate simulation was performed. Post-processing was conducted using BIO-met and Leonardo modules to calculate Physiological Equivalent Temperature (PET) (Fig. 2).

Following model establishment, the meteorological data collected on June 12, 2012, and December 22, 2020, the representative meteorological days, were input into the model for simulation (Table 1). The simulation period (7:00 to 18:00) corresponded to typical outdoor activity hours. During the simulation, key microclimate parameters, like Mean Radiant Temperature (MRT), air temperature, relative humidity, wind speed, and PET, were recorded to characterize the micro-environment characteristics of the Beijing courtyard house. The data were mainly collected from different observation points, which were set at different locations in the courtyard according to the types of data collected.

The collection of MRT relied on five observation points, which were set at a height of 1.5 meters at the entrances of rooms facing different directions in Beijing courtyard houses. Receptor Ⅰ (RⅠ) was located at the entrance of the south-facing room. Similarly, RⅡ was at the entrance of the west-facing room, RⅢ at the entrance of the east-facing room, and RⅣ and RⅤ at the entrance of the north-facing room. Among these, RⅠ, RⅡ, RⅢ, and RⅣ were situated in the larger second courtyard, while RⅤ was located in the smaller first courtyard. Through dynamic simulation using winter and summer meteorological datasets, MRT data collected could be used to investigate solar radiation reception and blockage patterns across differently oriented buildings in Beijing courtyard houses (Fig. 3(a))^[27].

The Beijing courtyard house is typically arranged as three rectangular courtyards along a central, symmetrical axis. The first courtyard contains only a row of north-facing rooms. The second and largest courtyard, which serves as the primary living area, is centered on the south-facing main room. This main room is flanked by eastern and western wings, with a north-facing room situated directly opposite. The symmetrical layout affects the thermal environment of different rooms in the courtyard houses, as evidenced by the variation of MRT at different observation points during the summer solstice. On a clear and sunny day, the diurnal variation of solar radiation exhibited a noon maximum, decreased with the decrease of solar altitude, and became least (zero) in the morning and evening^[32]. As shown in Fig. 4(a), MRT measured from five observation points exhibited a pattern of initial continuous increase followed by a decline in summer, though with varying peak timing across locations. Under the same northward orientation, the MRT observation data for RⅣ in the second observatory were significantly greater than those for RⅤ in the first observatory. Apparently, the bigger courtyard allows more natural lighting into deeper parts of the building^[33]. Within the same courtyard, MRT variations reflect different heating rates among rooms of different orientations. Notably, RⅢ (east-facing) reached its peak MRT earliest at 9:00, while RⅣ (north-facing) exhibited the slowest heating rate. From 12:00 to 14:00, RⅠ (south-facing) recorded the highest MRT. RⅡ (west-facing) saw its MRT peak after 14:00. The MRT at each receptor exhibits distinct temporal variations, demonstrating that the rooms facing different directions receive varying amounts of sunlight at different times of the day in the Beijing courtyard house^[34].

The mean radiant temperature can be regarded as a weighted sum of all long- and short-wave radiant fluxes (including direct, reflected, and diffuse components) to which a human body is exposed. It is one of the most important meteorological parameters related to human energy balance and human thermal comfort^[35]. The data of PET show similar trends with MRT in Fig. 4, indicating a strong correlation with solar radiation intensity. As shown in Fig. 4 (b), PET values at RⅠ-RⅢ remained below 60℃ despite MRT exceeding 70℃ (Fig. 4(a)). This discrepancy suggests that PET is modulated by other factors, such as air temperature, relative humidity, and wind speed. Notably, although RⅠ, RⅡ, and RⅢ exhibited different heating rates (Fig. 4(b)), their peak PET values were similar (57–59℃), further revealing microclimate homogenization within the same courtyard. The uniformity in PET highlights the integrative role of convective and evaporative processes in stabilizing thermal conditions, which align with prior studies on courtyard thermodynamics, where airflow and humidity buffer radiant heat extremes^[36].

Due to the sun's position, observation points in the courtyard were exposed to direct solar radiation at different times and shaded during certain periods, resulting in varying PET values across observation points with different orientations. Comparison in Fig. 4 revealed that when oriented northward, RⅤ maintained more stable MRT and PET changes relative to RⅣ (ΔPET < 17℃). This thermal stability can be attributed to the narrow layout of the first courtyard, which effectively shields the north-facing room from direct solar exposure, thereby demonstrating its superior summer cooling performance. In contrast, the second courtyard is larger and receives more solar radiation. RⅠ and RⅢ exhibited prolonged thermal conditions, with PET values exceeding 45℃ for approximately 66.7% of the total observation period (Fig. 4(b)). This persistent thermal stress reflects the significant thermal discomfort experienced in south- and east-facing rooms due to prolonged exposure to solar radiation. RⅡ displayed a significant upward trend in PET after 13:00, which could be ascribed to intense afternoon solar radiation. The thermal sensation corresponding to the experimentally calculated PET values is consistent with the extreme heat sensation reported by researchers during on-site investigations, which was caused by west-facing solar radiation.

These results establish that the bigger courtyard allows more natural lighting into deeper parts of the building. However, the accompanying solar radiation elevates ambient temperatures. To mitigate this, vegetation and water pools are crucial, as their strategic integration enhances shading and evaporative cooling^[37]. On the other hand, orientation is a primary factor affecting thermal comfort in courtyard environments, with the south- and west-facing rooms being particularly prone to overheating in summer due to solar radiation. It is recommended to install flexible shading devices on facade openings facing different orientations to block excessive solar radiation at different times of the day. For south-facing rooms, adjustable shading systems effectively reduce midday solar gain^[15], while west-facing spaces may benefit from strategically placed vegetation or architectural elements to block afternoon radiation^[27].

(a) MRT; (b) PET.

Analysis of winter solstice data reveals unimodal MRT patterns across all room entrances (Fig. 5(a)). During peak solar hours (10:00–15:00, solar altitude > 30°), RⅢ (east-facing), RⅠ (south-facing), and RⅡ (west-facing) demonstrated sequential MRT peaks followed by declines, while RⅣ (north-facing) maintained minimal fluctuation. During late afternoon hours (15:00–18:00, solar altitude < 30°), RⅠ, RⅡ, and RⅢ exhibited similar cooling rates (Fig. 5(a)). Under high solar altitude conditions, orientation-dependent MRT variations become pronounced, whereas during low solar altitude periods (< 30°), reduced incident solar radiation leads to thermal homogenization across courtyard spaces.

Comparative analysis reveals greater similarity in MRT and PET curves in winter compared to summer, indicating a stronger dominant influence of MRT on winter thermal comfort. As shown in Fig. 5, the minimum PET at all observation points is 8–10℃ higher than the minimum MRT. During winter, deciduous vegetation in the courtyard has a limited influence on ambient temperature and humidity. Moreover, when wind speeds are low, the moderating effect of airflow and humidity on radiant heat becomes significantly weaker than in summer^[33]. Figure 5(a) shows a significant increase in MRT at observation points RⅢ, RⅠ, and RⅡ between 10:00 and 15:00, indicating that the larger second courtyard receives more solar radiation but also loses more heat. Consequently, the maximum PET values at RⅢ, RⅠ, and RⅡ decreased by 3–6°C relative to the maximum MRT values, while the change at RⅤ in the first courtyard was negligible. Despite comparable solar exposure in the same courtyard, RⅡ and RⅢ exhibited distinct peak times in PET (RⅡ: 10:00–11:00; RⅢ: 13:00–14:00), which was caused by the different solar azimuth angles (Fig. 5(b)). This reveals orientation-dependent effects on solar utilization efficiency, with PET showing a strong positive correlation with radiation intensity during winter conditions^[38].

The analysis demonstrates that solar radiation constitutes the dominant factor governing courtyard thermal comfort in both summer solstice and winter solstice, with notably stronger influence during winter conditions. Driven by heat loss concerns in exposed courtyards, courtyard dimensions are limited. As a result, courtyards in cold climates tend to adopt a more compact, inward-looking form. However, the building needs natural heating during winter and also natural lighting all year. In contrast, the narrow courtyard space would significantly block sunlight in a real-life situation due to the low solar altitude angle in winter^[39]. Therefore, the reasonable dimensions of the courtyard (such as its area, length, and width) and the appropriate building height are suggested, ensuring that each room can receive sufficient solar radiation in winter to enhance the thermal comfort of the residential environment^[40].

(a) MRT; (b) PET.

The first and third courtyards in Mao Dun's former residence share the same width and similar areas. While the first courtyard remains unvegetated, the third courtyard contains centrally positioned low trees and ornamental plantings. The second courtyard, covered with vegetation and divided by a crisscross stone path, is twice the size of the first and third courtyards, with a tall banyan tree in the northwest corner. The shape and vegetation of the courtyard would affect the air temperature and relative humidity.

Figure 6 shows that during summer solstice conditions, air temperatures ranged from 25℃ to 35℃, while the relative humidity varied between 30% and 62% across the study sites. The air temperature and relative humidity in different courtyards maintain a similar level, which could be attributed to the air exchange among different courtyards through the interconnected doorways. As depicted in Fig. 6 (a), an initial increase followed by a decrease was observed in all observation points, which reach zenith at approximately 14:00. Figure 6 (b) reveals a characteristic diurnal humidity pattern across all observation points, exhibiting three distinct phases: (1) an initial transient increase, (2) followed by a gradual decline, and (3) a subsequent recovery. The relative humidity peaked at approximately 08:00 hours before decreasing to its minimum value around 15:00 hours. It is shown in Fig. 6(a, c) that a single peak with a trend of rising and then falling is present in the spectrum of air temperature and PET, confirming a strong positive correlation between the two factors. Moreover, the variation of PET at different observation points was significantly greater than that of air temperature, primarily attributable to differential solar radiation exposure. Comparative analysis revealed significantly lower PET values at RA (center of the first courtyard) and RC (center of the third courtyard) relative to RB (center of the second courtyard), indicating markedly cooler thermal conditions. This could be put down to the elongated and narrow geometries of first and third courtyards with limited depth, reducing solar radiation exposure and offering a relatively more comfortable thermal environment. Conversely, the second courtyard, which featured a wider layout and lacked significant shading elements, was highly susceptible to solar radiation, with rapid PET escalation (9:00–17:00) and prolonged thermal discomfort. This result is consistent with the conclusions of Kumar, R., who demonstrated the efficacy of shading measures in temperature reduction^[41]. It further demonstrates that the amount of sunshine directly affects the changes in air temperature within the courtyard.

The air temperature at each observation point increased significantly between 8:00 and 15:00, while the relative humidity dropped sharply after 8:00 (Fig. 6(b)). Relative humidity represents the ratio of actual water vapor pressure to saturation vapor pressure at identical air temperature^[28]. As the temperature rose, the saturation vapor pressure gradually increased, leading to a decrease in relative humidity with actual water vapor pressure remaining unchanged. At the identical air temperature, RA and RC exhibited marginally higher relative humidity than RB prior to 10:00, attributable to greater water vapor content in the narrow courtyard. Furthermore, Fig. 6 demonstrates an inverse temperature-humidity relationship with coupled PET variations. Prior to, rising temperatures coincided with decreasing humidity and increasing PET. Subsequently, declining temperatures were accompanied by rising humidity and falling PET values. It indicates that the elevated temperature, coupled with reduced humidity, exacerbates thermal discomfort in summer by intensifying heat perception. Conversely, the environment with low temperature and high humidity in summer is conducive to improving human comfort. Notably, while summer solstice air temperature and relative humidity trends were consistent across courtyards, PET variations differed significantly (Fig. 6(c)). This divergence primarily reflects vegetation differences: although RA and RC shared similar air temperatures, RC exhibited lower PET values. The third courtyard's greenery attenuated solar radiation, reducing ground and building heat absorption and MRT compared to the unvegetated first courtyard.

The observed PET variations among courtyards in summer result from differential solar radiation and vegetation greenery. Specifically, the expansive, unshaded second courtyard received greater solar radiation, yielding higher PET values. In contrast, the more compact first and third courtyards with better shading conditions experienced reduced solar radiation and consequently lower PET values. Therefore, installing sunshades or planting tall greenery in large courtyard spaces is suggested to reduce the impact of solar radiation and improve the comfort of the courtyard living environment^[42]. Using deciduous plants is a very effective strategy to reduce the temperature through their shading and evaporative cooling function. Because of this evaporation and evapotranspiration, the humidity in the courtyard is increased as well^[37].

(a) Air temperature; (b) Relative humidity; (C) PET.

During the observation period on the winter solstice, air temperature ranged from − 4℃ to 4℃, while relative humidity fluctuated between 62% and 85%. Figure 7(a) demonstrates that receptors C, A, and B exhibited unimodal air temperature trends, peaking at 16:00 before gradually declining. Figure 7(b) illustrates that relative humidity followed a unimodal trend, reaching its minimum at 15:00. Similarly, PET exhibited a single peak pattern, peaking at 13:00 (Fig. 7(c)).

Figure 7(a) demonstrates subzero temperatures (< 0℃) at all three receptors from 7:00 to 10:00, with RC and RA exhibiting similar thermal trends and marginally higher values than RB. The thermal pattern primarily results from the second courtyard's expansive layout, promoting greater heat dissipation under winter's low solar altitude, compared to the first courtyard's narrow configuration. From 10:00 to 17:00, RA and RB maintained comparable temperatures marginally below RC's values, which could be interpreted from the airflow between the first and second courtyards, and the enclosed layout of the third courtyard. The relative humidity at different observation points during the winter solstice exhibited distinct characteristics (Fig. 7(b)). RB maintained higher humidity than RA before 10:00, with values converging thereafter. For that, the air humidity in courtyards with vegetation is higher when the solar altitude angle is relatively small. As solar radiation increased, the second courtyard's larger scale enhanced its solar heat gain relative to the first courtyard, demonstrating scale-dependent thermal responses. In contrast to the relative humidity observed at RA and RB, RC recorded the lowest relative humidity throughout the observation. This can be attributed to two primary factors. Firstly, the third courtyard has a more enclosed layout, effectively restricting the ingress of cold and humid air, thereby reducing the absolute humidity^[26]. Secondly, as shown in Fig. 7(a), Receptor C's elevated air temperatures (Fig. 7(a)) increase saturation vapor pressure, resulting in a lower relative humidity.

Figure 7(C) reveals that RB (the second courtyard) recorded the highest PET value, followed by RA, while RC showed the lowest value during the 9:00–15:00. It is inferred that larger-scaled courtyards have a greater surface area exposed to solar radiation, which increases the amount of solar energy absorbed, leading to an increase in PET values as a result. This confirms PET’s strong dependence on solar altitude angle and the direction of sunlight in winter. Therefore, the PET of different courtyards is predominantly related to courtyard dimensions under stronger solar radiation. Conversely, observation points in different courtyards experienced weaker solar radiation during 7:00–9:00 and 15:00–18:00 (corresponding to sunrise and sunset hours). During these periods, the air temperature of RC was slightly higher than at other observation points, and the corresponding PET was also higher, which shows that air temperature is a key factor affecting the thermal environment of courtyards in the absence of sufficient solar radiation^[43].

The analysis confirms that the changes in air temperature and relative humidity have a definite impact on PET. High temperatures coupled with low-humidity environments promote higher PET values, whereas cooler temperatures with increased humidity depress PET. Consequently, high temperatures and drier conditions are advocated in winter to improve environmental thermal comfort. The analysis further identifies limitations in traditional courtyard design. Specifically, the second courtyard's open layout exacerbates winter heat loss due to reduced thermal mass effectiveness. This could be mitigated through adaptive solar management strategies, such as flexible insulation facilities to minimize heat loss. The tall trees in the third courtyard block a significant amount of solar radiation in winter, resulting in the highest relative humidity. Therefore, pruning the tree crowns in winter is recommended to increase solar radiation for passive heating.

(a) Air temperature; (b) Relative humidity; (C) PET.

During the observation period on the summer solstice, the air temperature at the center of different courtyards ranged from 24℃ to 36℃ with wind speeds of 0-1.2 m/s. All observation points displayed similar unimodal temperature patterns, peaking at approximately 14:00 (Fig. 8(a)). Figure 8(b) demonstrates consistent wind speed patterns across observation points with stable temporal variations. R1, located at the southeastern main gate, recorded the highest wind speed from the southeast due to its direct exposure to prevailing southeasterly summer winds in Beijing. R3 recorded the lowest wind speed of approximately 0.1 m/s at the second courtyard's center. The second courtyard’s broad wind tunnel cross-sections, significantly larger than those of the first and third courtyards, explain the lowest wind speed under the condition of a fixed total wind volume in the courtyard. This shows a gradual decline in the efficiency of the windshield with an increase in the yard area^[43].

As shown in Fig. 8(c), all receptors follow a unimodal PET pattern peaking around 13:00. R1 maintained the lowest PET value between 8:00 and 16:00 due to its elevated wind speeds, which enhanced convective heat loss through accelerated evaporative cooling. Although R2 (center of the first courtyard), R3 (center of the second courtyard), and R4 (center of the third courtyard) showed similar air temperature variations, significant variations emerged in both wind speed and PET values across these locations. R3 recorded the lowest wind speed and the highest PET value, indicating the uncomfortable thermal environment in summer. Despite comparable wind speeds and air temperatures at R2 and R4, R4 exhibited significantly lower PET values. It can be attributed to two aspects: the trees in the third courtyard block part of the solar radiation, and the wind speed is significantly higher than that in the first courtyard. Higher wind speeds accelerate the evaporation of sweat, leading to a cooling sensation^[44].

In summary, summer PET distributions exhibit significant spatial variations mediated by courtyard ventilation efficiency. The main gate recorded the highest wind speed and the lowest PET, while the second courtyard recorded the lowest wind speed and the highest PET. Therefore, two ventilation optimization strategies are recommended: (1) enhancing air circulation within the courtyard in summer through the principle of thermal pressure; (2) installing shallow water pools to generate convective airflow via temperature-induced pressure differentials with surrounding areas.

(a)Air temperature; (b)Windspeed; (c)PET.

Figure 9(a) suggests a consistent diurnal pattern in air temperature across multiple observation points during winter, characterized by a single peak occurring at 16:00. Figure 9(b) documents speeds ranging from 0 m/s to 1.7 m/s with slight spatial variations. R5 at the northwest exterior recorded the highest wind speed (1.4 m/s-1.7 m/s) due to direct exposure to prevailing northwest winds. Contrasting with R1 regulated airflow (0.3 m/s-0.5 m/s) at the main gate, R2, R3, and R4, located in the first, second, and third courtyards, respectively, recorded the minimal airflow (~ 0.1 m/s). This demonstrates that the courtyard wall can effectively resist the cold wind and create a relatively stable internal wind environment within the courtyard. Especially, the exterior walls and buildings can act as barriers to reduce the direct impact of strong northwesterly winds on the internal courtyard in winter. Notably, the location of the main entrance ensures summer ventilation while preventing winter winds from invading, providing residents with relatively comfortable and stable indoor activity spaces^[23].

Figure 9(a) reveals consistent air temperature patterns across different areas, while PET values exhibit significant spatial variations influenced by wind speed. As depicted in Fig. 9, R5 (northwest exterior) recorded both peak wind speed and minimum PET values. Moreover, exterior PET values remained systematically lower than interior measurements due to wind-driven heat dissipation. In comparison, the enclosed courtyard effectively shields the interior from the influence of strong winds, maintaining consistently low wind speeds (< 0.2 m/s) with minimal spatial variation. This wind reduction significantly decreases convective heat loss, resulting in elevated interior PET values^[45].

In conclusion, the northwestern exterior (R5) experienced the highest wind speed in winter, driving convective heat loss that yields minimum PET values and pronounced thermal discomfort. In contrast, the courtyard interior maintains a pleasant living environment through effective wind speed attenuation (around 0.1 m/s). Moreover, the comfort level of the courtyard environment can be further improved by increasing the courtyard thermal insulation performance to reduce wind speed and increase PET.

(a)Air temperature; (b)Wind speed; (c)PET.