Thermal performance analysis for roofs with heat mitigation strategies in subtropical hot and humid regions

Abstract

The thermal behavior of roofs significantly impacts the indoor thermal environment. Rooftop mitigation strategies (RMS), as effective measures to reduce cooling load and improve indoor thermal comfort, have been extensively studied. However, the lack of comparative experimental RMS studies and the limitations of simulation software in accurately reproducing RMS thermal performance post-implementation highlight research gaps. This study utilized reduced-size models to investigate the thermal performance of RMSs - cool coating roof, photovoltaic (PV) roof, and PV cool coating roof - across summer, transition season, and winter, and further developed internal roof surface temperature prediction models through theoretical analysis and experimental data calibration. The results demonstrated that all RMSs outperformed a reference roof in reducing both interior and exterior temperatures, with cool coating roof exhibiting the best thermal performance in summer. The ranking of the internal thermal performance of RMS in summer from best to worst was as follows: cool coating roof, PV cool coating roof and PV roof. In transitional season and winter, PV roof had the lowest exterior surface temperature and PV coating roof had the lowest interior surface temperature. The maximum internal surface temperatures of the cool coating roof in summer were 1.6 °C and 1.5 °C lower than those of PV roof and PV cool coating roof, respectively. The combination of PV and cool coatings only provided better cooling effects in terms of interior surface temperature during the transitional season and winter. This study provides insights for decision-making regarding RMS in subtropical hot and humid regions.

Introduction

Building energy consumption accounts for over 30% of global final energy consumption and continues to rise with increasing urbanization rates¹. In the context of climate and energy crises, enhancing thermal comfort for residents while reducing heating and cooling energy consumption²and minimizing lifecycle carbon emissions in the building sector has become a critical issue. Roofs cover approximately 25% of urban areas³, and due to direct exposure to solar radiation, air temperature, and weather conditions such as rain and snow, the indoor thermal environment of buildings is significantly impacted. The rooftop mitigation strategies (RMSs) utilize rooftop technologies to significantly modify the original energy balance of the roof surface, changing the heat transfer between the roof and the indoors and outdoors⁴. Since the introduction of the first RMS - green roofs (GR) - various other RMSs like cool coating roof (CR), photovoltaic roof (PVR), photovoltaic cool coating roof (PVCR), and photovoltaic green roof (PVGR) have been developed. CR reduces indoor heat gain through high-reflectivity surface coatings that reflect a substantial portion of solar radiation. GR are multilayer ecosystems consisting of waterproof membranes, drainage layers, soil layers, and vegetation that shield against direct sunlight. PVR converts solar energy into electricity using PV panels installed on the roof, which can be used, stored, or transmitted for building consumption. New RMSs, such as PVCR and PVGR, have also been developed. PVCR and PVGR are configurations where PV panels are installed on CR and GR, respectively. These hybrid technologies enhance indoor thermal comfort and improve the performance of PV systems. The impact of different RMSs on the thermal performance of building roof has been widely studied and applied^5,6. Due to the high costs associated with the investment and maintenance of GR, along with the significant load demands they place on rooftops⁷, the practicality of CR and the advantages of energy generation through PV capabilities in PVR and PVCR make these three types of roofs more widely used in practice. In this study, the type where PV panels are installed on a roof with a heat transfer coefficient similar to that of a conventional concrete roof coated with gray paint was defined as PVR, while the type where PV panels are installed on a cool coating roof was defined as PVCR.

There are extensive studies on the impact of different RMSs on indoor thermal comfort and building energy efficiency through heat and mass transfer models^8,9, experimental measurements^6,10,11, or simulation^12–14. Additionally, some studies have demonstrated the positive effects of RMSs on mitigating urban heat island effect at the city scale^15,16. However, as the research gaps identified in Sect. 2, systematic comparative studies on the thermal performance of PV systems and cool coating RMSs in subtropical hot and humid regions, as well as prediction tools for the thermal performance of such roofs, remain limited.

In view of the existing challenges and available studies, this study formulates two research objectives to provide a comparison of the thermal performance of RMSs and complement existing knowledge:

• (i)To investigate which RMS of PV systems and cool coating exhibits the best thermal performance in subtropical hot and humid regions, these findings effectively inform the design and renovation of building roof in alignment with the dual carbon goals;
• (ii)To establish internal surface temperature prediction models for roof employing RMSs, these models could help understand the thermal properties of RMSs in various built environments and quantifies the energy-savings of cool roofs in subtropical hot and humid regions.

This study first reviewed thermal performance comparisons of various RMSs with emphasis on subtropical hot and humid regions and identified the research gaps. The research methodology and experiment settings were introduced in Sect. 3. Shenzhen, China was selected as the test site, and reduced-size models were constructed to compare the effects of a reference roof (RR) and three different RMSs - CR, PVR, and PVCR - on both internal and external roof surface temperatures during summer, transitional season, and winter. Combined with theoretical analysis and experimental data, internal roof surface temperature prediction models for CR, PVR, and PVCR were developed based on the Grasshopper platform. Finally, through experimental data, the best performing roof type was identified.

Literature review

This section provided a comprehensive review of RMS thermal performance by comparing different types of RMSs, examining variations across climatic zones, and evaluating research methodologies.

Types and research focuses of RMSs

Extensive and detailed studies have been conducted on the thermal performance of CR, PVR, and GR, while research on PVCR and PVGR has primarily focused on PV generation. Comparisons of thermal performance among different RMSs remain limited, as summaries in Table 1.

Table 1.

Different RMSs types and research focuses.

RMSs Types	Research Focuses	References
GR	Thermal performance	17–21
	Energy efficiency	22,23
PVR	Thermal performance	24–26
	Energy efficiency	27–30
CR	Thermal performance	31–33
	Energy efficiency	34–39
GR, CR	Energy efficiency	40,41
PVR, PVGR	Thermal performance	42,43
	PV power generation	44–46
PVR, PVCR	PV power generation	47,48
PVR, PVCR, PVGR	PV power generation	49,50
CR, GR, PVR, PVCR, PVGR	Thermal performance	16

Research has shown that in hot regions GR reduce the U-value of roofs¹⁸, leading to varying reductions in internal and external surface temperatures and heat flux, thereby saving building energy consumption. GR with moist substrates exhibit better insulation and cooling effects¹⁹. PVR provide more significant shading effects when the solar absorptivity is high and the roof’s R-value is low²⁶, and elevated PV systems show lower indoor temperatures and humidity compared to attached systems²⁵. Light-colored CR reduce building energy consumption more effectively than dark-colored ones³³. PVCR and PVGR, through their synergistic effects, effectively reduce the temperatures of PV modules and the environment⁴³, enhancing PV efficiency^{44,45,47,49,50}, with bifacial PV panels generating higher energy output⁴⁸. Based on existing studies, RMS configurations for measurements can be designed to better compare the energy efficiency and thermal performance of buildings.

RMSs in different climate zones

Table 2 summarizes the research on the thermal performance of RMSs in different climate zones. The thermal performance of RMSs varies under different climatic conditions. Most existing studies focus on Cfa (humid subtropical) and Cfb (oceanic) zones. According to the Köppen climate classification, regions where the hottest month’s temperature exceeds 22 °C and the coldest month’s temperature ranges between 0 and 18 °C are categorized as Cfa climates. Existing research on Cfa regions mainly focuses on the hottest month, with relatively little attention focus on transitional seasons and winter. Consequently, studies on the thermal performance of RMSs from a year-round perspective remain insufficient (Fig. 1). To bridge these research gaps, this study focuses on Shenzhen, China, classified under Cfa, as the experimental site in a hot and humid region. The measurements were conducted continuously for 24 h a day, from August 1, 2023 to April 23, 2024.

Table 2.

RMSs thermal performance in different climates.

Climate Zones	Köppen Climate Classifications	Seasons	References
Tropical Climates	Aw, Am, Af	Summer	28,31,43
		Transitional season	21
		Winter	25
		All year	29,45
Arid Climates	Bwh, Bsk	Summer	38
		Transitional season	47
		All year	39
Temperate Climates	Cfa, Cfb	Summer	17,19,20,23,27,32,36,52
		Summer, Transitional season	34,35
		All year	42,50
	Csa, Csb	Summer	49
		Transitional season	24
		All year	18,22,48
Continental Climates	Dfa	All year	44
Comparisons Across Multiple Climate Zones	Af, Aw, Bsh, Bwh	Summer	33
	Bsh, Bsk, Cfa	All year	30,51
	Bwh, Bsk, Dsa	All year	40
	Cfa, Dwa	All year	41
	Cfa, Cfb, Csa, Dfa	Summer	16
	Bwh, Csa, Dsa	All year	26

Fig. 1.

Global distribution of experimental locations.

RMSs research methods

Table 3summarizes the research methods for the thermal performance of different RMSs. Experimental studies, field measurements, simulation modeling, and theoretical modeling are employed to explore the thermal performance of RMSs. Most studies select heat flux and surface temperatures as thermal performance indicators and simulate building annual energy consumption or cooling load, with a few studies on heat transfer coefficients. In subtropical hot and humid regions, while some studies have compared different RMS types, conflicting conclusions have been drawn. The conflicting results may be due to inconsistencies in building shapes, RMSs parameter settings, weather conditions in the simulations, and the oversimplification in the heat transfer of RMSs, leading to an underestimation of roofs’ role in mitigating energy demand³⁴. Therefore, it is urgent to address the limited availability of systematic comparative studies on the thermal performance of PV systems and cool coating RMSs, as well as to develop prediction tools for the thermal performance of such roofs.

Table 3.

Comparative study of thermal performance of different RMSs.

Research methods	Thermal performance indicators				Other indicators		Conclusions
	Heat transfer coefficient	Heat flux	Internal surface temperature	External surface temperature	Cooling and heating load	Energy consumption
Site measurement		√	√	√		√	GR: average daily external temperature↓1.8 °C17
		√	√			√	GR: the U-value↓55%18
		√	√	√			GR: under normal conditions heat transfer↓81%, and↓40% when the substrate is dry19 GR: external surface temperature↓27.5 °C20
			√	√	√		PVR: daytime cooling load↓37.4%27
				√			PVGR: PV generation↑1.2%49
					√		PVGR: power generation↑1.4%44
			√				PVGR: generation efficiency↑2%45 PVCR: power generation↑5–10%47; PVCR: power generation of bifacial PV↑8.6% than monofacial PV, ground temperature↓3.8℃48
Experimental study	√						GR: Heat transfer coefficient ranges 2.807–5.401 W/m2K53
			√				PVGR: ambient temperature↓3.36%, PV component temperature↓17%43
Simulation			√		√		GR: indoor temperature↓7.2℃23 PVR: cooling load↓23%28
			√	√	√	√	PVR: reduces cooling load and energy consumption29
					√		PVR: heat loss↓4.85%in summer, heat transfer↑5.54% in winter30 GR: annual heat load↓17.8–171.4kWh/m, CR↓5.5–124.0 kWh/m40
						√	With high solar absorptivity and low R-value, PVR provides significant shading effects26 PVGR eases energy demand46
				√	√	√	CR: annual cooling load↓26% in arid climates, energy consumption↓12%39
					√	√	CR and GR: energy↓12.6% and 9.4%41
Theoretical model			√				PVGR and PVCR: power generation↑1.8% and 3.4%50
Site measurement, simulation validation						√	GR: energy consumption↓34.9%22 Combining CR with ventilation: energy consumption↓27%35 Double-layer CR: energy consumption↓66%38
		√	√	√			PVR: internal surface temperature↓2.5 K24
			√	√			PVR: external surface temperature↓2.5℃25
Simulation, site measurement validation					√		Walls are more effective than GR in reducing cooling load51
		√	√	√			PVCR: total heat flux↓55%, PVGR↓42%16
Simulation, experimental study validation			√	√			GR: indoor temperature↓4.7℃21
Theoretical model, site measurement validation				√			CR: performance was underestimated 44–85%34
		√	√	√		√	CR: internal surface temperature↓15.4℃ cooling load↓ 62.7%31 CR: heat flux↓33.3–66.7%32
Theoretical model, experimental study validation	√						PVGR: indoor temperature↓6%, PV surface temperature↓8℃42
Theoretical model, simulation validation		√	√	√			Insulating CR: daily heat gain↓37–56%33
			√			√	Ventilated CR: annual total energy consumption↓16.9%37
Theoretical model, experimental study, simulation			√	√			CR: annual cooling demand↓136.4kWh/m236

The thermal performance of different RMSs has been studied using various methods such as experimental study, field measurement, simulation modeling, and theoretical modeling, according to the reviewed literature. Current research often focuses on one or two strategies, lacking a systematic comparison on the thermal performance of PV systems and cool coating of typical RMSs. Second, the thermal performance of RMSs is significantly influenced by climate, with existing studies mainly focusing on the hottest months in hot and humid climate zones. Few studies measure the annual thermal performance. Additionally, simulation tools or modules have not yet been able to precisely calculate the thermal performance of various RMSs. Therefore, this study, based on theoretical analysis and experimental data, explored the most effective types of typical RMSs in subtropical hot and humid regions.

Methodology

To explore the thermal performance of various RMSs in subtropical hot and humid regions, comparative studies were conducted between RR and three typical RMSs: CR, PVR, and PVCR. Reduced-size models were established to perform experimental analyses throughout the year, including summer, transition season, and winter. Additionally, internal roof surface temperature prediction models for various RMSs were developed. Figure 2 presents the research framework.

Fig. 2.

Research framework.

Experimental platforms setup

Site description and experimental equipment layout

The experimental platforms for this study were established on the rooftop of the south building of the library at Shenzhen University, located at 113°93′E, 22°53′N, with the height of the experimental platforms from the ground level approximately 15 m (Fig. 3a). The site was devoid of obstructions or any other external sources of thermal interference, situated at a considerable distance from surrounding high-rise buildings. Figure 3b shows the layout of the experimental platforms. Platforms I, II, III, and IV correspond to RR, CR, PVR, and PVCR respectively. The experiments utilized four reduced-size models, each constructed from hollow Polyurethane (PU) cubes without any heating or cooling systems. Due to space constraints, the four reduced-size models were arranged non-linearly, ensuring no obstructions or thermal impacts between them. The dimensions of each reduced-size model were as follows: 1900 mm × 1400 mm × 1280 mm (Length × Width × Height). The thickness of the PU foam board on the roof was 80 mm, with the facades at 50 mm and the base at 40 mm thick. A 750 mm × 450 mm window was positioned in the center of the southern side of each reduced-size model, and a 1000 mm × 500 mm wooden door was on the north side. Both the window and the door were kept closed during testing. Considering the application of the reduced-size models in real-world scenarios, the roof heat transfer coefficient of the RR was calculated to meet the energy-saving standards applicable to Shenzhen, China. Based on this foundation, the most common materials for CR, PVR, and PVCR were selected to investigate the thermal performance of different RMSs.

Fig. 3.

(a) Aerial photograph of the library with the locations of experiment stations indicated in red, (b) experimental platforms setup.

The main equipment employed for the experiment included temperature sensors, spectrally flat class B pyranometer, spectrally flat pyranometer, and data loggers. Two types of data loggers were used to record thermocouple data and data from other experimental equipment, respectively. The specifications of experiment equipment are listed in Table 4.

Table 4.

The specifications of experiment equipment.

Instrument	Type	Range	Accuracy
Temperature sensor	Kapson K-type Thermocouple	−20-200℃	0.5℃
Spectrally flat class B pyranometer	Delta Ohm LPPYRA02	0–2000 W/m2	<5%
Spectrally flat pyranometer	Delta Ohm LPPYRA-Lite	0–2000 W/m2	<3%
Data logger	Logger Net CR1000	-	0.04%
Data logger	Yugen technology RR-1048	-	0.05%

The outdoor air temperature, wind speed, solar radiation intensity, as well as internal and external roof surface temperatures were continuously measured and logged at one-minute intervals over a 24-hour period. A weather station equipped with spectrally flat pyranometers, shown in Fig. 3b, was positioned on the roof 5 m away from the experimental reduced-size models, with no obstructions around. To minimize the systematic error in the measurements, the equipment was calibrated before the formal experiment. The thermocouple placement positions were polished and leveled, and adhesive was applied to secure them in place, reducing errors caused by air gaps during data collection. To evaluate the uncertainty of the measured values, the relative uncertainty propagation formula was used for calculation⁵⁴. The formula is as follows:

1

Here, ΔT/T represents the relative uncertainty of the measured value T, ΔT1/T1 is the sensor accuracy error, Δl/l is the error related to the sensor size and installation position, and ΔT2/T2 is the data acquisition reading error. In this study, the temperature sensor accuracy was ± 0.5 °C, the sensor length was 7 mm, and the data acquisition device accuracy was 0.04%. During summer testing, the average interior surface temperature of the RR roof was 45.3 °C. Based on the calculations, the temperature uncertainty U_T was 1.16%. Generally, temperature uncertainty within 10% is deemed acceptable⁵⁵, demonstrating that the measurements are feasible and accurate.

The temperatures of the internal and external roof surfaces were measured at four equally spaced points along the mid-line of the roof surface, resulting in a total of 24 measurement points. To minimize experimental error, the data from the measured points were averaged. The layout of the measured points is illustrated in Fig. 4. RR featured gray paint with a solar reflectance of 0.5, while CR used a coating with a solar reflectance of 0.65. PVR consisted of three PV panels, each measuring 1000 mm × 500 mm and inclined at 40° south, with a working voltage of 20.4 V.

Fig. 4.

Schematic of measurement points.

Testing periods and weather conditions

The measurement period spanned from August 1, 2023, to April 23, 2024, with data recorded at 1-minute intervals, and the analysis conducted using data averaged every 10 min. Days with typically representative solar radiation intensity and temperature were selected from the entire experimental period to identify characteristic days for analysis. To minimize the impact of extreme weather events, such as heavy rainstorms and typhoons, and to ensure data continuity, accuracy, and comparability, testing days were selected based on stable and representative meteorological conditions for at least three consecutive days, starting one day before the testing period. For summer, the periods from August 24 to August 27 were selected; for transitional season, December 27 to December 30 were selected; for winter, January 8 to January 10 were selected. Table 5 details the experimental study on the selected dates.

Table 5.

Comparative testing of experimental platforms.

Seasons	Test periods	Platform 1	Platform 2	Platform 3	Platform 4
Summer	24.8.2023–27.8.2023	RR	CR	PVR	PVCR
Transition season	27.12.2023–30.12.2023	RR	CR	PVR	PVCR
Winter	8.1.2024–10.1.2024	RR	CR	PVR	PVCR

August represents typical summer days in Shenzhen. Data from four consecutive days, from August 24 to August 27, were used for the analysis of RR, CR, PVR and PVCR (Fig. 5a). The four consecutive measurement days were characterized by cloudy weather with significant fluctuations in solar radiation intensity, but the peak values of solar radiation exceeded 1200 W/m², and the maximum temperature was above 40℃, which was typical. The transition seasons in subtropical hot and humid regions are relatively short, with slightly reduced solar radiation intensity and shorter duration of high temperatures compared to summer. Data from four days, December 27 to December 30, were selected for the comparative analysis (Fig. 5b). The weather was cloudy, with peak solar radiation intensity exceeding 800 W/m² and maximum air temperatures above 25℃. Winter conditions are similar to the transition seasons, with the lowest average temperature remaining above 10 °C. Due to weather conditions, only three days from January 8 to January 10 were selected for the winter comparison of RR, CR, PVR, and PVCR (Fig. 5c).

Fig. 5.

Solar radiation intensity and air temperature during the testing period.

Establishing internal roof surface temperature prediction models

Internal roof surface temperature prediction models for the roof with RMS were established based on the existing EnergyPlus roof heat transfer models through theoretical analysis and experimental data. EnergyPlus was developed by the U.S. Department of Energy, and it has been widely used in building design and energy consumption assessment. It improves upon DOE-2 by enhancing the flexibility and accuracy of simulations. Ladybug Tools is an environmental performance analysis plugin for Rhino/Grasshopper. Within this suite, Honeybee is used for analyzing building energy consumption and comfort and interfaces with EnergyPlus as its simulation engine.

In this study, based on the integration of Honeybee with EnergyPlus, the internal surface temperatures of the roof with RMS were first simulated. These simulated temperatures were then calibrated by fitting them to the experimental data. Figure 6 shows the detailed process employed in this work. Based on the experimental material performance parameters, Ladybug Tools were used to construct four types of roof models, with the main physical performance parameters detailed in Sect. 3.2.2. The experimental weather data were used to simulate the internal roof surface temperatures, and the iterative least squares method was employed to fit the simulation data to the experimental data, with the goodness of fit evaluated using the R-squared value. Through data analysis, the correlation between the simulation data and the experimental data was determined, resulting in empirical equations. The internal roof surface temperature prediction models for RMSs are described in Sect. 4.3.

Fig. 6.

Research process for the internal roof surface temperature prediction models.

Surface heat balance algorithm in EnergyPlus

In EnergyPlus, the calculation of roof energy balance involves the thermal exchange between the internal and external surfaces of the building and the internal heat conduction. The heat balance equations for the external and internal surfaces define the external and internal boundary conditions for heat conduction calculations. The conduction equation calculates the process of heat transfer from the external surface to the internal surface and updates the node temperatures through numerical iteration, computing the new temperature distribution. The external surface heat balance equation is as follows:

2

Where, q_asol represents the absorbed solar shortwave radiation flux, q_LWR is the net longwave radiation exchange flux, q_conv is the external air convection heat flux, and q_ko is the heat flux conducted to the surrounding structure. Surface convection is calculated using the conductive transfer function (CTF), which is modeled based on the DOE-2 algorithm, taking into account the effects of surface temperature and air velocity. The convection equation is as follows:

3

Where, Q_c represents the conductive heat flux, and h_c denotes the conductive heat transfer coefficient. The internal surface heat balance equation is coupled by four components of heat transfer: heat conduction through the enclosure, air convection, absorption and reflection of shortwave radiation, and longwave radiation exchange. Internal conduction is also calculated using the CTF formula, and internal convection uses an adaptive convection algorithm. The internal surface heat balance equation is as follows:

4

Here, q_LWX represents the net longwave radiation exchange flux between the interior space and the internal surface, q_SW is the net shortwave radiation flux from lighting to the internal surface, q_LWS is the longwave radiation flux from internal space equipment, q_ki is the conductive flux through the enclosure, q_sol is the transmitted solar radiation flux, and q_conv is the internal air convection heat flux. In this study, both q_SW and q_LWS were considered to be zero.

The PV model predicts the part of the solar radiation and solar thermal calculations, and it operates continuously when the total incident solar energy is greater than 0.3 W; below 0.3 W, it does not generate electricity. This study used a simplified model for predicting PV electricity generation, which can specify the efficiency of converting incident solar radiation on the PV surface into electrical energy. The formula for calculating the usable electric power produced on the PV surface is:

5

Here, A_surf is the net surface area, f_activ is the fraction of the active solar cell surface area, G_T is the total incident solar radiation,η_cell is the module conversion efficiency, and η_invert is the DC to AC conversion efficiency. Table 6 summarizes the heat transfer calculation principles of different RMSs in EnergyPlus.

Table 6.

The heat transfer calculation principles of different RMSs in EnergyPlus.

RMS types	Heat transfer principles
CR	- Thermal exchange between internal and external surfaces - Conduction through the building enclosure - Numerical iteration for updating temperature distributions
PVR	- Predicts solar radiation and thermal calculations - Operates based on the threshold of solar energy incident - Efficiency of converting solar radiation to electrical energy
PVCR	- Combines features of PV roofs and cool coating roofs - Aspects of solar energy conversion - Improved thermal performance through reflective or emissive surfaces

As identified in Sect. 2.3, the heat transfer and exchange process for the roof with RMS is oversimplified in current simulation modules. For instance, PV is typically modeled solely as a shading element, disregarding the influence of long-wave radiation and air convection occurring between the PV system and the roof. Consequently, discrepancies exist between the simulation results and the experimental data of RMSs. It is necessary to advance the internal roof surface temperature prediction for RMSs in subtropical hot and humid regions.

Modeling for roofs with RMSs

EnergyPlus simulations require the configuration of building files and weather data files. The building file outlines the building’s geometry, material construction, internal loads, occupancy schedules, and HVAC settings. 1:1 scale models of the experimental platforms were created in Rhino. Based on the experimental material parameters, four roof models were created: RR, CR, PVR, and PVCR. Internal loads, occupancy schedules, and HVAC settings were all set to none.

EnergyPlus uses historical meteorological data to provide Typical Meteorological Year (TMY) data files (EPW) for different regions, which include annual hourly values for dry bulb temperature, wet bulb temperature, relative humidity, atmospheric pressure, wind speed, wind direction, and solar radiation. The direct radiation, dry bulb temperature, relative humidity, wind speed, and wind direction in the EPW file for Shenzhen were calibrated using actual meteorological station data, while other meteorological parameters were kept at typical values.

Due to the significant fluctuations in the external roof surface temperature curve caused by external radiation, wind speed, and other factors, the internal roof surface temperature was selected to better reflect the delay and attenuation of thermal performance resulting from different RMSs. Table 7 lists the thermal performance parameter values of roofs with RMSs.

Table 7.

Thermal performance parameters of roofs with RMSs.

	PU insulation board	Gray ordinary paint	High reflective coating	PV panel
Thickness (m)	0.08	0.005	0.005	-
Thermal Conductivity (W/m·k)	0.018	0.45	0.16	-
Solar reflectance	0.75	0.5	0.35	-
Infiltration rate (m)	-	-	-	-
Drainage layer (m)	-	-	-	-
Conversion efficiency	-	-	-	0.2

Fitting and validation of internal roof surface temperature prediction models

EnergyPlus was used to simulate the internal surface temperature of roofs under measured weather conditions. The simulated temperature curves were compared with experimental data to evaluate the accuracy of the models. These datasets were organized such that each time step had corresponding simulated and measured temperature values. Various mathematical models, such as linear, polynomial, exponential, and power function, were tested to determine the most suitable fitting equation form, based on the fundamental physical principles of heat transfer and data trends. The iterative least squares method was employed to minimize the differences between the simulated and measured data points. The parameters of the fitting curve were adjusted iteratively to achieve the best fit.

After curve fitting, the goodness of fit was evaluated using the R-squared value and residual analysis. The coefficient of determination (R²) explained the proportion of variance in the measured data that can be explained by the simulated data. A higher R² value indicated a better fit of the model to the data. Residuals represented the differences between the observed and fitted values, ideally, residuals should be randomly distributed with no apparent patterns, and these models were subsequently validated using experimental data to ensure their accuracy and reliability. The validated models can be used to predict and supplement the internal surface temperatures of roofs during unmeasured phases.

Results and analysis

Comparison of the measured external roof surface temperatures

The temperature of the external roof surface (T_ext) is significantly influenced by solar radiation intensity and air temperature. After removing outliers, the thermocouple data for the external surface temperatures from the three measurements were averaged every 30 minutes. Figure 7 shows the T_ext curves for different RMSs on measurement days in summer, transitional season, and winter. Specifically, Fig. 7a, c, and e illustrate the temperature variations on the measurement days. The minute-by-minute data from these days were averaged to determine the daily temperature variation trends for different RMSs, shown in Fig. 7b, d, and f.

Fig. 7.

T_ext and daily average temperature of various roofs.

Compared to RR, it can be observed that all the investigated RMSs reduced the T_ext during the daytime throughout the year. During summer, the T_ext from lowest to highest were: CR, PVR, and PVCR. The maximum T_ext−RR reached 81.5 °C, which was 25.2 °C, 22 °C, and 20.7 °C higher than T_ext−CR, T_ext−PVR, and T_ext−PVCR. Since the ambient temperature and solar radiation intensity were similar during the transitional season and winter, the T_ext of RMSs exhibited the same variation pattern, with the order of T_ext from lowest to highest being PVR, PVCR, and CR. In the transitional season, the maximum T_ext−RR reached 56.3 °C, which was 14.1 °C, 21.7 °C, and 20.4 °C higher than T_ext−CR, T_ext−PVR, and T_ext−PVCR. In winter, the maximum T_ext−RR was 60.9 °C, which was 13.4 °C, 23.9 °C, and 21.8 °C higher than T_ext−CR, T_ext−PVR, and T_ext−PVCR. At night, the low heat capacity and high radiative cooling ability of RR caused its temperature to drop to the lowest, followed by CR, while PVR has the highest night-time temperature throughout the year.

CR outperformed PVR and PVCR in summer, while PVR and PVCR demonstrated better thermal performance during the transitional season and winter. The different thermal behaviors of RMSs across seasons showed that for the T_ext, when ambient air temperatures exceeded 30 °C or dropped below 25 °C with solar radiation under 300 W/m², the reflective effect of CR surpassed the shading effect of PV panels. Conversely, when ambient air temperatures ranged between 25 and 30 °C, or were below 25 °C with solar radiation exceeding 300 W/m², the shading benefits of PV panels proved more effective.

Comparison of the measured internal roof surface temperatures

The internal surface temperature of the roof (T_int) is of significant reference value for the indoor thermal environment and thermal comfort of buildings. Figure 8 shows the temperature variation trends of the internal surface of different RMSs. Specifically, Fig. 8a, c, and e illustrate the temperature variation curves on measurement days in summer, transitional season, and winter. Figure 8b, d, and f present the daily average temperature variation trends of the RMSs.

Fig. 8.

T_int and daily average temperature of various roofs.

The thermal inertia and buffering effect of the roof materials on heat conduction resulted in a smoother variation of the T_int curves. In summer, during the hottest hours of the day (11:00–15:00), the thermal performance ranking from highest to lowest was: CR, PVCR, and PVR. The maximum T_int−RR reached 45.3 °C, which was 2.7 °C, 1.2 °C, and 1.3 °C higher than T_int−CR, T_int−PVR, and T_int−PVCR. During the transitional season and winter, the peak T_int during the hottest hours (11:00–15:00) from lowest to highest were: PVCR, CR, and PVR. In the transitional season, the peak T_int−RR was 40.7 °C, higher than T_int−CR, T_int−PVR, and T_int−PVCR by 2.1 °C, 1.5 °C, and 2.7 °C. During winter, the peak T_int−RR was 41.7 °C, which was 2.1 °C, 1.7 °C, and 3 °C higher than T_int−CR, T_int−PVR, and T_int−PVCR. At night, the thermal performance ranking of RMSs in summer was: CR, PVCR, and PVR. In the transitional season and winter, RR still had the lowest temperature, followed by PVCR, while PVR had the highest T_int. However, due to the need for HVAC systems to provide heating in subtropical hot and humid regions during the transitional season and winter, a higher T_int has better practical significance.

CR reflected heat through the surface coating, achieving better thermal performance in summer. PVCR reduced the roof’s heat absorption through shading by the PV panels, while the secondary heat release during the conversion of solar energy to electricity created complex heat exchanges among the PV panels, the air gap, and the roof surface. Additionally, the cool coating reflected heat, resulting in the lowest T_int among RMSs during the transitional season and winter. In contrast, T_int−PVR exhibited the highest throughout summer, the transitional season, and winter.

The internal roof surface temperature prediction models for the roof with RMS

Through the fitting of simulation data to experimental data, the internal roof surface temperature prediction models for roofs with RMSs in subtropical hot and humid regions were developed to calibrate the simulation results. The best empirical equation follows a power function form. The fitting equation is as follows:

6

Where T_C represents the calculated temperature, T_S is the simulated surface temperature, and and are the fitted coefficients that vary depending on the specific rooftop configuration.

Figure 9 illustrates the fitted curves of the RMSs, showing that as the temperature increased, the data points exhibited a linear upward trend along the fitted curves, demonstrating that the internal roof surface temperature prediction models of the RMSs had good fitting accuracy under different temperature conditions. After calibration, the coefficients of determination (R²) for the temperature curves were greater than 0.93.

Fig. 9.

Fitted curves of each RMS.

The following Eqs. (7–9) were used to represent the internal roof surface temperature prediction models for different RMSs:

7

8

9

Here, the temperature is measured in degrees Celsius, T_C is the calibrated internal roof surface temperature, and T_S is the simulated temperature.

Discussion

This study demonstrates the effectiveness of three RMSs - CR, PVR, and PVCR - in cooling the exterior and interior roof surfaces temperatures. Through experimental study and internal roof surface temperature prediction modeling, it was demonstrated that in subtropical hot and humid regions CR has the best thermal performance in summer, while in transitional season and winter PVR had the lowest T_ext and PVCR had the lowest T_int, bridging the gap in comparative studies of the thermal performance of various RMSs in such climate regions. Shenzhen, as a representative city with high energy-saving demands in China, has established more stringent building energy-saving standards, making the experimental measurements of RMSs in this region particularly valuable for research. Additionally, the interior roof surface temperature prediction models developed in this study provide a calibration basis and play a key role in assessing the energy-saving benefits of RMSs. Furthermore, the experimental results and prediction models developed in this study offer valuable insights for evaluating the energy-saving performance of different RMSs and advancing the contribution of roofs toward achieving zero-energy buildings. It is anticipated that the methodologies proposed in this study can be further extended to a broader range of RMSs and applied across diverse climate zones, providing a solid foundation for future research.

This study primarily focuses on the impact of RMSs on indoor temperatures. The internal roof surface temperature plays a crucial role in regulating and stabilizing indoor air temperature through its impact on heat conduction and radiation, thus directly relating to indoor thermal comfort and energy efficiency. Three RMSs impact the indoor thermal environment through different mechanisms. CR reduces heat absorption through its coating’s high reflectivity. PVR reduces direct solar exposure through physical shading and uses an air layer between the PV and the roof for insulation. To maximize solar energy absorption, PV panels have low albedo. However, limited by the current stage of power conversion efficiency, most of the unconverted heat is released back into the environment, which increases the difficulty of dissipating accumulated heat beneath the panels and affects the surrounding airflow. PVCR combines the effects of PVR with the reflective impact of the cool coating. According to experimental data, during summer, when ambient air temperatures exceed 30 °C, the high reflectivity of the CR coating performed better. The high-reflective coating reduced heat absorption, allowing CR to exhibit optimal thermal performance, effectively lowering building temperatures and potentially enhancing indoor thermal comfort. The shading effect of PV panels reduced heat absorption on the roof surface. However, due to the temperature-dependent electronic properties of PV materials, the output of voltage and current varies, making PV conversion efficiency negatively correlated with air temperature in different seasons under this climatic condition (Fig. 10). Nevertheless, due to the high solar radiation intensity in summer, the annual PV conversion efficiency still performed best in the summer. During the summer testing period, the average PV conversion efficiencies of PVR and PVCR were 11.4% and 10.9% respectively, while in the transitional season they were 10.5% and 8.3%, and in winter, 9.1% and 8.3% respectively. As a result, PVR exhibiting the highest T_int throughout the year. The varying thermal performance observed in different seasons indicates that in subtropical hot and humid regions, the combination of cool coating and PV in PVCR only demonstrated better thermal performance during the winter and transitional seasons, compared to PVR and CR. In the next phase, it is necessary to further clarify the mechanisms of various RMSs and combine them with urban climatic conditions to select the most suitable RMS strategy for urban rooftops.

Fig. 10.

PV efficiency and exterior surface temperature of PVR and PVCR.

Although the research results demonstrate that in summer CR has the best thermal performance in subtropical hot and humid regions, it should be noted that this study only tested one type of typical cool coating. Moreover, since in subtropical hot and humid regions do not have centralized heating, the ranking of thermal performance during the winter and transitional seasons should be determined based on building type and energy consumption needs. Furthermore, the internal roof surface temperature prediction models developed in this study focus solely on the calibration of T_int of typical RMS roofs and can serve as a reference to the climatic conditions of subtropical hot and humid regions.

Finally, it should be noted that this study did not conduct experimental study on GR and PVGR. Existing studies indicate that selecting roof configurations with trees²³, increasing soil thickness⁵and combining with wall greening⁵¹can more effectively reduce cooling loads; PVGR through the positive synergistic effects of PV and vegetation, increases PV power generation^44–46and has a positive impact on reducing carbon emissions and lowering energy demand^56,57. Additionally, the role of GR and PVGR in mitigating urban heat island effects and responding to extreme weather events caused by climate change deserves discussion. The ecological and social benefits, economic and operational costs associated with GR and PVGR, and other related issues require the engagement and efforts of various stakeholders. Future study will incorporate a comparison of the thermal performance of GR and PVGR, and conduct in-depth research on the impact of different greening configurations on thermal performance. Furthermore, it needs explore the performance and optimization strategies of different RMSs in building energy consumption in subtropical hot and humid regions.

Conclusions

Due to the lack of systematic comparative studies on the thermal performance of PV systems and cool coating RMSs in subtropical hot and humid regions, and the challenges faced by simulation models to accurately calculate heat transfer of roofs with RMSs, this study conducted an experimental study on the internal and external surface temperatures of three types of RMSs - CR, PVR, and PVCR - across summer, transition season, and winter using reduced-size models. Additionally, the internal roof surface temperature prediction models for these RMSs were developed to provide a calibration basis and a calculation tool for assessing the energy-saving benefits of cooling roofs. The main findings are as follows:

• The internal roof temperature ranking from lowest to highest in summer was CR, PVCR, and PVR, while during the transitional season and winter, PVR had the lowest T_ext and PVCR had the lowest T_int. In summer, the maximum T_int−CR was 1.6 °C and 1.5 °C lower than T_int−PVR and T_int−PVCR, corresponding to reductions of 3.8% and 3.5%, respectively. In the transitional season, the maximum T_int−PVCR was 0.6 °C and 1.2 °C higher than T_int−CR and T_int−PVR, indicating reductions of 1.5% and 3.1%, respectively. In winter, the maximum T_int−PVCR was 0.9 °C and 1.3 °C higher than Tint-CR and T_int−PVR, indicating reductions of 2.3% and 3.3%, respectively.

• The external roof temperature ranking from lowest to highest in summer was: CR, PVR, and PVCR, while during the transitional season and winter the T_ext from lowest to highest was PVR, PVCR, and CR. The combination of PV and cool coatings only provided better cooling effects in terms of T_int during the transitional season and winter. This is particularly evident when the air temperature rises above 30 °C or falls below 25 °C with solar radiation intensity under 300 W/m², where T_ext−CR consistently outperforms T_ext−PVR in thermal efficiency.

The thermal performance of PVR and PVCR in different seasons has reference significance for the large-scale application of PV in subtropical hot and humid regions, optimizing system PV efficiency, and mitigating adverse impacts on the thermal environment. Future experimental studies will be conducted on GR and PVGR, incorporating different greening configurations to further explore the impact of RMSs on thermal performance. Based on these studies, and considering factors such as PV power generation, a comprehensive analysis of the significance of RMSs for energy use in buildings in subtropical hot and humid regions will be performed.

Author contributions

Yueer He: Conceptualization, Methodology, Formal analysis, Writing - Review & Editing, Funding acquisition, Supervision. Ziyin Yang: Writing - Original Draft, Visualization. Yue Fan: Writing - Review & Editing, Funding acquisition.

Data availability

Data will be made available on request. Requests for data should be directed Yueer He (email: heyueer@szu.edu.cn) for further assistance.

Declarations

Competing interests

The authors declare no competing interests.