Inconsistent experiment design leads to systematic bias across the literature on daytime radiative cooling

^a School of Built Environment, Faculty of Arts, Design and Architecture, University of New South Wales, UNSW Sydney, Australia

Teng Xiong^a, Ziao Zheng^{a, b}, Hassan Saeed Khan^{a, c}, Ioannis Kousis^a, Olivia Marie Lucie Julia^{a, d}, Djordje Krajcic^e, Gianluca Ranzi^e, Mattheos Santamouris^{a, f}, Riccardo Paolini^a*

^b Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai, 200240, China

^c School of Engineering and Technology, Central Queensland University, Sydney, Australia

^d Renewable Energy Cluster ENAC, School of Architecture, Civil and Environmental Engineering, EPFL, Lausanne, Switzerland

^e School of Civil Engineering, The University of Sydney, Sydney, Australia

^f Anita Lawrence Chair in High Performance Architecture. School of Built Environment, University of New South Wales, Sydney, Australia

* Corresponding Author: A/Prof Riccardo Paolini: r.paolini@unsw.edu.au

Abstract

Passive Daytime Radiative Coolers (PDRCs) can cool buildings and cities by achieving subambient surface temperatures thanks to high solar reflectance and selectively high infrared emissivity within the atmospheric window. However, their performance is assessed outdoors with often too small samples and inconsistent experimental setups across the literature, which hinders intercomparison. Here, we demonstrate the limitations of current approaches and identify an experimental setup to achieve consistent and comparable results. We measured the surface temperatures of PDRC samples with different setups under both above-ambient and subambient conditions in temperate and desert climates, focusing on the effects of sample size and polyethylene (PE) film cover. Sample size introduced significant measurement uncertainty for air-exposed PDRC, resulting in overestimations of 1.2°C and 1.6°C under above-ambient and sub-ambient conditions, respectively. Further, PE film covers introduced greater deviations, up to + 3.0°C for above-ambient and − 2.7°C for subambient PDRCs. Instead, air-exposed PDRC samples of at least 200 mm, placed over insulation boards with reflectivity comparable to the PDRC, and with surrounding buffering boards, achieve a low measurement uncertainty of ± 0.3°C. Compared to this stable setup, other setups exhibit a large measurement bias, with 90% of this bias being systematic. Our findings underscore the need for consistent outdoor measurement methods to assess PDRC performance and enable quantitative analysis across the literature.

Urban environments are increasingly overheated by the synergy of global climate change and urban development¹. Prolonged extreme heat periods pose severe risks to human life (impairing health, productivity, and well-being²), restrict outdoor activity (by 5% above 30°C and 13% above 35°C³), and decrease the efficiency of urban energy systems, including condensing units of air conditioning⁴ and photovoltaic modules⁵. In International Energy Agency (IEA) member countries, space cooling already constitutes 20–30% of total electricity use in residential buildings^{6, 7}, while it is a larger fraction in commercial buildings⁸. As the planet warms and population growth continues, the market penetration of air conditioning is expected to surge, particularly in hot climates⁹. Widespread use of air conditioning in cities increases energy demand and releases waste heat, which exacerbates the urban heat island (UHI) effect and drives further air conditioning use, creating a vicious cycle¹⁰. Cool roofing materials provide a practical strategy for mitigating urban overheating and reducing reliance on air conditioning¹¹. The last generation of super-cool materials, known as passive daytime radiative coolers (PDRCs), can maintain subambient surface temperatures under direct sunlight without external energy input¹². This capability arises from two key spectral properties: (i) high solar reflectivity in the 0.3–2.5 µm range to minimise solar heat gain¹³; and (ii) high infrared emissivity in the atmospheric window (8–13 µm) to enable radiative heat dissipation to outer space (with extremely low temperatures of ~ − 270°C)¹⁴.

Various types of PDRCs have been developed based on multilayered structures^{15, 16, 17}, metasurfaces^{18, 19}, randomly dispersed particles^{20, 21, 22}, and porous materials^{23, 24, 25}. However, all newly developed PDRCs have been tested outdoors with largely different and often incomparable testing protocols, in terms of setup, substrate, and even sample size (Fig. 1a–c and Supplementary Table 1). To characterise the maximum net cooling performance of PDRCs, it is a widely accepted practice to minimise nonradiative heat exchange (conduction and convection) from surroundings^{26, 27}. To minimise the conduction heat gain, 80% the surveyed studies used insulation foams, while 20% opted for air cavity (Fig. 1d). To minimise the convection heat gain, 71% applied convection shields made of polyethylene (PE) film with high transmittance in both solar and atmospheric window bands (Fig. 1e). In contrast, only 26% tested the PDRCs in the open air. Additional strategies (Fig. 1f), such as enclosures^{16, 18, 28}, solar shields^{15, 17, 29}, radiation shields^{17, 23, 30}, and vacuum chambers^{17, 30, 31}, enabled even greater subambient temperature reductions (up to 42°C¹⁷). However, due to the complexity and high cost of these strategies (e.g., vacuum chambers^{30, 31}), they are neither feasible nor practical for large-scale deployment on cool roofs, which are the main application of PDRCs in urban heat mitigation. Enclosing PDRCs in convection shields can create temperatures and microclimates that differ from those of the ambient air^{23, 32}, potentially leading to inaccurate assessments of their cooling potential on roofs. Moreover, most PE films lack sufficient mechanical strength and weather resistance for long-term use on roofs³³, while rigid wind covers made of ZnSe or Ge are too costly³⁴. Hence, there is a pressing need for reliable methods to assess the performance of PDRCs in the open air, as this configuration more realistically represents roofing conditions.

Fig. 1

Literature review on outdoor testing of passive daytime radiative coolers (PDRCs). Three commonly used experimental setups for PDRCs: (a) Sample on insulation foam; (b) Sample on insulation foam with polyethylene (PE) film; (c) Suspended sample in thermally insulated enclosure with PE film. (d) Strategies for reducing heat conduction. (e) Strategies for reducing heat convection. (f) Additional strategies for reducing parasitic heat gain. (g) Distribution of sample sizes. Analysis is based on 70 studies summarised in Supplementary Table 1.

Sample size is another critical yet underexplored factor for performance measurement of PDRCs. 82% of the surveyed studies used samples smaller than 100 mm (46% between 50 and 100 mm, and 36% even smaller than 50 mm), while only 3% used samples of no less than 200 mm (Fig. 1g). Despite the inconsistent sample size across the literature, to our knowledge, little attention has been given to whether such variations introduce uncertainty in measuring the surface temperatures of PDRCs and, therefore, evaluating their performance. A recent study³⁵ reported the size effect of PDRCs under subambient conditions, but it neither explored its underlying cause nor considered above-ambient conditions. Also, no study was found in the literature that addressed and explained whether PDRCs can maintain uniform surface temperatures in the open air, or whether temperature variations take place that need to be considered for effective placement of temperature sensors. In most cases, the surface temperatures of PDRCs were measured using centrally fixed K-type or T-type thermocouples (Supplementary Table 1), which have relatively low accuracy³⁶ (Supplementary Table 2). Further, no published research quantified the measurement uncertainty of the whole experimental setup; most only provided the nominal accuracy or the type of temperature sensor used. However, the nominal accuracy does not account for uncertainties related to sensor adhesion to the sample, signal transmission, and data logging noise, which, combined, may largely exceed the nominal measurement uncertainty due to the sensor only. Often^{37, 38, 39, 40, 41, 42}, the reported temperature reductions are close to the nominal accuracy of the sensors used, especially for K-type thermocouples. Under these conditions, it can be challenging to confirm subambient cooling effects for air-exposed PDRCs. Finally, to our knowledge, no study has quantified systematic (consistent deviations from the reference) and random (unpredictable fluctuations) biases introduced by improper setups. As the cooling performance of PDRCs depends strongly on boundary conditions and is usually benchmarked against ambient air temperature, the lack of consensus in testing methods hinders comparison between different materials on a common baseline, preventing quantitative reviews with meta-analyses across studies^{43, 44}.

In this context, we aim to identify the minimum experimental setup necessary to achieve repeatable and comparable results for outdoor testing of PDRCs. Firstly, we investigated how varying sample sizes influenced centre temperature measurements for air-exposed PDRCs. The size effect resulted in overestimations of 1.2°C for above-ambient PDRCs and 1.6°C for subambient PDRCs. Mitigation of this effect required a minimum sample size of 200 mm. The experimental work was complemented by modelling based on a two-dimensional computational fluid dynamics (CFD) model. The results indicated that the size effect is largely driven by the mismatch in solar reflectance between the exposed surface area of the holding board and the samples, regardless of whether the samples are above- or subambient. Secondly, we examined measurement deviations between PE-covered and air-exposed PDRCs. Using PE cover led to an overestimation of up to 3.0°C for above-ambient PDRCs and an underestimation of up to 2.7°C for subambient PDRCs. Further, the PE cover caused deviations > 1°C between two identical PDRC samples, likely due to irregular natural convection in the air cavity. Thirdly, we proposed a cost-effective approach to achieve repeatable measurements for air-exposed PDRCs by surrounding them with buffering boards, which achieved a low measurement uncertainty of ± 0.3°C. Using the buffered PDRCs as a reference, we quantified both systematic and random biases produced by other setups. For most setups, over 90% of the measurement bias was systematic, and solar radiation was the main contributor to the deviations across different setups. To expose the samples to distinct meteorological conditions we conducted the PDRC field tests with different setups in Blacktown (Fig. 2, see Methods for details) and Alice Springs (Supplementary Fig. 1), Australia. To our knowledge, this is the first systematic investigation of measurement bias in outdoor testing of PDRCs. By establishing the minimum sample size, clarifying the impact of PE cover, and proposing a stable experimental setup, this study provides a practical framework for consistent and comparable evaluation of PDRC performance, enabling comparisons across the literature.

Fig. 2

Overview of the outdoor test conducted in Blacktown. (a) Spectral properties of the materials in the 0.3–40 µm waveband. (b) Configuration of R-50, R-100, R-150, R-200, R-250, R-300, and two R-200-PE samples; the inset shows the schematic cross section of R-200-PE. (c) Configuration of R-200-X and R-100-E. (d) Configuration of mixed samples; the inset shows the positions and labels of nine 100-mm samples. (e) Configuration of two R-200-S samples; the red dashed rectangle indicates the surrounding 400-mm expanded polystyrene (EPS) buffering boards. (f) Photographs of the experimental setup. Note: In (b)–(e), R, W, and B denote PDRC, White, and Black emitters, respectively. The black dashed rectangles indicate the boundaries of the stands. The same testing configuration used for the PDRC was applied to the White and Black emitters. Red spots indicate RTD sensors.

Results

Effects of sample size

To assess the effects of sample size, we placed square PDRC samples with side lengths of 50–300 mm on 400-mm square expanded polystyrene (EPS) boards (R-50 to R-300, Fig. 2b). We also included White and Black emitters to compare the thermal effects of PDRC and non-PDRC materials (see Methods for details). These materials’ spectral properties are shown in Fig. 2a. For ease of discussion, we defined the exposed surface area of the holding board surrounding the samples as the “mask”. The surface–air temperature differences of PDRC, White, and Black samples and the corresponding meteorological parameters were measured in Blacktown (Fig. 3, see Methods for details) and Alice Springs (Supplementary Fig. 2). Statistical significance tests were performed to analyse the size effects observed during 12:00–13:00 (Fig. 4a–f, see Methods for details). In addition, thermal images were taken to provide insight into the observed size effects (Fig. 4g–i).

In Blacktown, strong solar radiation and high humidity prevented all PDRC samples from reaching subambient conditions during 10:00–16:00 (Fig. 3a, b), whereas in Alice Springs most PDRC samples maintained subambient throughout the day under a drier atmosphere (Supplementary Fig. 2a). Our results show that sample size significantly influenced centre temperature measurements at both sites, which is summarised into two opposing effects: (i) micro cool island effect, in which larger samples exhibited lower centre temperatures; and (ii) micro heat island effect, in which larger samples exhibited higher centre temperatures. In Blacktown, the PDRC samples exhibited a micro cool island effect, whereas the White and Black samples exhibited a micro heat island effect. Smaller PDRC samples (R-50 to R-150) also showed reduced temperature fluctuations compared to their larger counterparts (R-200 to R-300). After 16:00, as the sky turned overcast, the size effects in all samples reduced significantly. In Alice Springs, the PDRC and White samples exhibited a micro cool island, while the Black samples consistently exhibited a micro heat island. At both testing sites, the size effect was minor for samples larger than 200 mm.

Fig. 3

Temperature profiles and meteorological conditions in Blacktown. Surface–air temperature differences for (a, b) PDRC samples, (c, d) White samples, and (e, f) Black samples. Meteorological parameters: (g) air temperature (T_a), dew point (T_d), and absolute humidity (AH); (h) direct solar radiation (SR), diffuse solar radiation (DSR), and infrared radiation (IR); (i) wind speed (WS) and wind direction (WD). [Data collected from 10:00 to 18:00, 21 January 2025].

In Blacktown, the centre temperature tended to decrease with increasing PDRC sample size (Fig. 4a), although the trend was not strictly monotonic (a more monotonic size effect was confirmed in a follow-up test,

see Supplementary Note 1 for details). Pairwise comparisons confirmed significant differences (p < 0.001) for most sizes, except for R-150 vs. R-300 and R-200 vs. R-250. The average temperature (T_avg) decreased with increasing sample size for R-50 (32.5°C) > R-100 (32.0°C) > R-150 (31.1°C). However, the differences among R-200 (31.6°C), R-250 (31.5°C), and R-300 (31.3°C) were within the measurement uncertainty (± 0.3°C, see Supplementary Note 2 for details), indicating a diminished size effect beyond 200 mm. The average temperature difference (ΔT_avg) between R-50 and R-300 was 1.2°C, well above the measurement uncertainty. In contrast, the White and Black samples showed higher centre temperatures with increasing sample size up to 200 mm (Fig. 4b, c).

In Alice Springs, the PDRCs exhibited a stronger micro cool island effect (ΔT_avg = 1.6°C between R-100 and R-300, Fig. 4d). All pairwise comparisons were statistically significant (p < 0.001), except for R-200 vs. R-300. T_avg decreased with increasing sample size up to 200 mm (R-100 (28.6°C) > R-150 (27.9°C) > R-200 (27.0°C)), beyond which the differences were within the measurement uncertainty. The White samples also exhibited a micro cool island effect (~ 2°C between small and large samples, Fig. 4e), whereas the Black samples retained a significant micro heat island effect (Fig. 4f). In Alice Springs, the size effects in the White and Black samples were less consistent than in Blacktown, likely due to the mixed placement of PDRC and non-PDRC samples on the same holding board with 60–75 mm spacing (Supplementary Fig. 1b, c), which may have led to thermal interference between the adjacent samples (See Supplementary Note 3 for discussions).

Thermal images taken in Blacktown reveal non-uniform surface temperatures across the samples. R-50 showed a warmer centre than R-100 (Fig. 4g), possibly due to stronger thermal interference from the surrounding EPS mask. The lower solar reflectance (R_sol) and infrared emissivity (ε_IR) of EPS compared to PDRC (Fig. 2a) may have led to the formation of a warmer surface boundary layer around R-50 and R-100, with the smaller R-50 more affected by lateral heat gain than the larger R-100. In contrast, the White and Black samples were subject to a cooling effect from their EPS masks (Fig. 4h, i), likely because the EPS had a higher R_sol than the emitters, thereby resulting in a cooler surface boundary layer. Moreover, due to differences in wind direction during measurements, the direction of thermal interference from the EPS masks differed among the samples. Similarly, the samples in Alice Springs exhibited non-uniform surface temperatures during peak solar hours, with 200-, 250-, and 300-mm PDRC samples showing irregular deviations of 0.5–0.9°C across different sensor positions (Supplementary Fig. 3a–c).

Mechanisms underlying the size effects

In the field tests, the PDRCs consistently exhibited the micro cool island effect (Fig. 4a, d), whereas the White emitters showed opposing size effects at the two testing sites (Fig. 4b, e). Hence, whether the emitters are above- or subambient is not the determining factor for the type of size effect produced. To elucidate the mechanisms underlying the observed size effects, we developed a two-dimensional CFD model (Fig. 5a, see Methods for details). Between 08:00 and 18:00, the transient-state simulation showed good agreement with the experimental data for R-200 in Blacktown (Fig. 5b,c). The slight discrepancy may be due to the simplified wind direction in the two-dimensional model and the omission of the angular dependence of R_sol and ε_IR⁴⁵.

Fig. 5

Numerical results for explaining the observed size effects. (a) Model description and structured mesh. Model validation: (b) comparison between experimental and numerical results for R-200; (c) linear regression analysis for R-200. Surface temperature distributions along the x-direction for (d–f) PDRC, White, and Black emitters under clear-sky conditions. Centre temperatures of (g–i) PDRC, White, and Black emitters under clear-sky and overcast sky conditions. Effects of various mask materials on centre temperatures of (j–l) PDRC, White, and Black emitters under clear-sky conditions.

Based on meteorological data at 13:00, steady-state simulations were performed to analyse surface temperature distributions along the x-direction for PDRC, White, and Black emitters of varying sizes (Fig. 5d–f). In all cases, the EPS mask surface temperature increased along the x-direction (up to 150 mm), indicating that a larger mask area (smaller sample size) resulted in higher temperatures at the mask–sample interface. Beyond this interface, the surface temperature dropped sharply in the PDRCs (Fig. 5d), whereas it continued to rise in the White and Black emitters (Fig. 5e, f). These opposing results indicate that the EPS mask formed a warmer surface boundary layer around the PDRCs but a cooler one around the White and Black emitters, which are consistent with the thermal patterns observed in Fig. 4g–i. Consequently, the centre temperature at x = 200 mm decreased with increasing emitter size for the PDRCs but increased for the White and Black emitters. Further, centre temperature differences were minimal for emitters beyond 200 mm, which is consistent with the experimental results (Fig. 4a–f).

The magnitude of the size effects strongly depended on solar irradiance. At 13:00 (solar irradiance of 990 W/m²), the centre temperature differences between 50-mm and 300-mm emitters were 0.9°C for PDRC, − 2.1°C for White, and − 16.9°C for Black (Fig. 5g–i). These results are consistent with the averaged measurements between 12:00 and 13:00 (1.2°C for PDRC, − 1.7°C for White, and − 16.8°C for Black, Fig. 4a–c). In contrast, at 17:00 (solar irradiance of 115 W/m²), the differences substantially reduced to 0.3°C for PDRC, − 0.2°C for White, and − 2.2°C for Black, which also agree with the averaged measurements between 16:00 and 17:00 (Supplementary Fig. 4). The diminished size effects under low solar irradiance suggest that they are mainly driven by the mismatch in R_sol between the emitters and the surrounding EPS mask (Fig. 2a). This mechanism is supported by two additional tests (see Supplementary Note 4 for details).

To further validate the proposed mechanism, EPS, silver tape, and extruded polystyrene (XPS) were used as mask materials (Fig. 5j–l). Masking with PDRC rendered R-50 to R-300 equivalent to a full 400-mm PDRC, thereby showing no size effect (Fig. 5j). Among the masks, EPS with the highest R_sol (0.89) produced the smallest size effect. Replacing EPS with XPS (R_sol of 0.68) strongly increased the difference between R-50 and R-300 from 0.9°C to 6.0°C. In contrast, the difference between EPS and silver tape (R_sol of 0.83) was moderate: R-200-EPS was 0.5°C cooler than R-200-Silver tape, which is consistent with the experimental results (R-200 and R-200-X in Supplementary Fig. 5a). For the White emitters, masking with XPS produced the micro cool island effect, while masking with EPS or silver tape produced the micro heat island effect (Fig. 5k). This partially explains the opposing size effects of the White emitters at the two testing sites (see Supplementary Note 5 for discussions). For the Black emitters, the size effect reduced with decreasing R_sol of the mask (Fig. 5l).

Effects of PE film cover

To access the effects of PE film cover (often referred to in the literature as a wind cover), we tested two identical PE-covered 200-mm PDRC samples (R-200-PE-1 and R-200-PE-2, Fig. 2b) and reported their average. The same setup was also applied to the White and Black emitters. Our results show that the thermal effect of PE cover depended on whether the emitters were above- or subambient in the open air. In Blacktown, all samples remained above-ambient between 10:00 and 15:00, with R-200-PE about 3.0°C warmer than R-200 (Fig. 6a) and W-200-PE and B-200-PE showing stronger overheating effects (Fig. 6b, c). After 16:00, as the sky turned overcast, both R-200-PE and R-200 turned subambient, with R-200-PE becoming cooler than R-200. A weaker overcooling effect was also observed in W-200-PE. In Alice Springs, both R-200 and R-200-PE remained subambient throughout the day, with R-200-PE consistently cooler than R-200 (Fig. 6d). At 12:00, R-200-PE was 0.3°C cooler than R-200, but the difference gradually increased to 2.7°C by 16:00. W-200-PE showed a similar trend, remaining cooler than W-200 under subambient conditions (Fig. 6e). In contrast, B-200-PE remained consistently hotter than B-200 (Fig. 6f). In summary, using PE film cover led to overheating in above-ambient samples and overcooling in subambient samples.

Fig. 6

Effects of PE film cover on centre temperature measurements of the samples. Surface–air temperature difference profiles of samples with and without PE film cover in Blacktown: (a–c) PDRC, White, and Black samples in Blacktown; (d–f) PDRC, White, and Black samples in Alice Springs. For each emitter, the temperature profile represents the average of two identical samples (R-200-PE-1 and R-200-PE-2 in Fig. 2), in order to reduce random measurement variability.

The thermal effects of PE film cover arise from the insulating air cavities above the samples, which suppress convective heat exchange with the ambient air³¹. Moreover, temperature discrepancies > 1°C were observed between R-200-PE-1 and R-200-PE-2 at both sites (Supplementary Fig. 6). In a follow-up test, we evaluated PE and polyethylene terephthalate (PET) wind covers of varying thicknesses to ascertain if cover deflection could lead to non-uniform air cavity thicknesses and thereby introduce variability in thermal resistance (Supplementary Fig. 7). With the PE film used at both sites, the deflection was less than 1 mm for a 10-mm air cavity. However, no significant effect of this deflection was observed, as thicker, more rigid PE or PET covers showed variability similar to Supplementary Fig. 6. Therefore, irregular natural convection in the air cavities was the more likely source of the observed discrepancies⁴⁵.

Evaluation of measurement bias

Considering the thermal boundary conditions of real roofs, we established a stable experimental setup that involved surrounding two identical 200-mm PDRC samples with EPS buffering boards to form a 500-mm cornice (R-200-S-1 and R-200-S-2, Fig. 2e). Due to its large surface area (5.1 m²), this setup had a low perimeter-to-area ratio and thus minimal edge disturbance⁴⁶. The PDRC samples did not exhibit thermal interference from the adjacent non-PDRC samples, demonstrating good repeatability: the MAE of R-200-S-1 and R-200-S-2 was only 0.09°C during 06:00–18:00 (Supplementary Fig. 6a). In a follow-up test, simultaneous measurements of ten identical 200-mm PDRC samples with buffering boards yielded a standard deviation of ± 0.3°C, which was taken as the measurement uncertainty (see Supplementary Note 2 for details). Hence, R-200-S (the average of R-200-S-1 and R-200-S-2) was used as the reference for evaluating measurement bias, including setups R-50, R-300, R-200-PE, R-200-X, R-100-E (Fig. 2c), and R-100-M (Fig. 2d) (see Methods for details).

Under clear sky (12:00–13:00), nearly all data points fell below the 1:1 lines in Fig. 7a–c, indicating that the samples were warmer than R-200-S. R-50 showed a regression slope of 0.46 and an MAE of 1.56°C, suggesting temperature overestimation due to the size effect. In contrast, R-300 agreed most closely with R-200-S (MAE of 0.35°C). Although R-200-PE had a slope near 1, it showed the largest MAE (3.45°C), indicating considerable overestimation by using PE film cover. This was followed by R-100-M (2.35°C), due to thermal interference from the adjacent non-PDRC samples (see Supplementary Note 3 for details). Moderate deviations were observed in R-200-X (0.95°C) and R-100-E (0.80°C). Under overcast sky (16:00–17:00), R-300 nearly matched R-200-S. The MAEs of R-50 and R-200-X were reduced to below 0.5°C (Fig. 7d, e), while R-200-PE still showed the largest MAE (1.33°C). Further, R-200-PE shifted from an overheated to an overcooled state relative to R-200-S, reflecting a reversal of PE cover-induced measurement bias. R-100-E and R-100-M exhibited moderate MAEs of 0.98°C and 0.70°C, respectively (Fig. 7f). The deviation in R-100-E was likely due to the absence of an EPS mask to stabilise its surface boundary layer, while R-100-M remained affected by thermal interference from the adjacent non-PDRC samples.

Fig. 7

Bias analysis using R-200-S as the reference. Scatter plots comparing R-200-S with other PDRC samples under clear-sky conditions: (b) R-50 and R-300; (c) R-200-X and R-200-PE; (d) R-100-E and R-100-M. Scatter plots comparing R-200-S with other PDRC samples under overcast sky conditions: (e) R-50 and R-300; (f) R-200-X and R-200-PE; (g) R-100-E and R-100-M. (h) Systematic bias and (i) unsystematic bias of the PDRC samples under clear-sky and overcast sky conditions.

The measurement bias was further divided into systematic bias (RMSD_s) and unsystematic bias (RMSD_u), with RMSD_s representing consistent deviations from R-200-S and RMSD_u reflecting random uncertainty (see Methods for details). Under clear sky, R-50 showed the largest RMSD_s (1.61°C), while R-300 had only 0.35°C (Fig. 7g, Supplementary Table 3). Across R-50 to R-300, the RMSD_u remained below 0.3°C (Fig. 7h). Hence, increasing sample size effectively reduced the proportion of systematic bias (from 98% for R-50 to 77% for R-300). The PE film cover introduced a much larger systematic bias, as R-200-PE exhibited an RMSD_s of 3.45°C but an RMSD_u of only 0.21°C, making its bias nearly 100% systematic. Likewise, other samples also showed > 90% systematic bias. Under overcast sky, most samples exhibited marked reductions in both RMSD_s and RMSD_u, indicating that the systematic and random biases were mainly driven by solar radiation. This interpretation is supported by factor analysis of the relative relevance of meteorological variables (see Methods and Supplementary Fig. 8 for details).

Discussion

We measured the centre temperatures of PDRC samples with different experimental setups, focusing on the effects of sample size and PE film cover under both subambient and above-ambient conditions. Moreover, we evaluated the measurement uncertainty of the most stable setup (R-200-S), which served as the reference to quantify systematic and random biases produced by other setups. Our findings highlight several key experimental aspects to be considered in future outdoor testing:

(1) For air-exposed PDRCs, the size effect can introduce non-negligible uncertainty in monitoring their centre temperatures. In this study, the size effect led to overestimations of up to 1.2°C for above-ambient PDRCs and up to 1.6°C for subambient PDRCs (Fig. 4a, d). These deviations are significant, given that the literature reports subambient temperature reductions in 1.5–6.2°C range for air-exposed PDRCs^{20, 29, 37, 47, 48}. Further, small samples (≤ 100 mm) introduce a predominantly systematic measurement bias (98% for R-50 and 97% for R-100). Numerical simulations indicate that, both in above- or subambient conditions, the size effect primarily arises from the mismatch in R_sol between the mask and the emitters, and smaller samples with larger perimeter-to-area ratios are more affected by lateral heat gain from the surroundings. The size effect cannot be mitigated by using metal substrates with high thermal conductivity (see Supplementary Note 4 for details). To minimise the size effect, the mask material should have R_sol close to that of the samples, with a minimum sample size of 200 mm. However, only 3% of the surveyed papers used samples larger than 200 mm, and no predominant sample size was identified across the literature (Fig. 1d). This lack of size uniformity can be attributed to lab-scale fabrication of PDRCs, as smaller samples reduce fabrication and testing costs⁴⁹. Due to the measurement uncertainty introduced by the size effect, results obtained from testing small PDRC samples do not represent their cooling performance when applied to full-scale roofs. The opposing size effects of PDRC and non-PDRC materials can also lead to systematic underestimation of their performance difference (by up to 2.8°C in this study, Supplementary Fig. 9).

(2) Using PE film covers introduces inconsistent thermal effects: it lowers the temperature of subambient emitters (e.g., PDRCs in dry, low-radiation climates) but increases the temperature of above-ambient emitters (e.g., PDRCs in humid, high-radiation climates, coloured PDRCs^{50, 51}, and non-PDRC materials). Similar to the size effect, this introduces a bias in the comparison between PDRC and non-PDRC materials. In this study, the PE film cover led to an overestimation of up to 3.0°C for above-ambient PDRCs and an underestimation of up to 2.7°C for subambient PDRCs (Fig. 6a, d). These deviations are significant, given that previous studies^{21, 52, 53, 54, 55} have reported subambient temperature differences of 4.1–11.5°C for PE-covered PDRCs. To achieve a promising cooling performance, most studies tested PE-covered PDRCs under optimal weather conditions (Fig. 1e). However, despite advances in materials science that have made near-ideal PDRCs more accessible, achieving subambient cooling under unfavourable weather conditions remains challenging^{32, 56}. PE films with lower infrared transmittance (T_IR) can also exacerbate overheating of PDRCs, particularly in climates with a less open atmospheric window. In this study, the PE film (T_IR = 0.89, comparable to those reported in the literature³⁴) caused a stronger influence of infrared radiation on measurement deviations in Blacktown than in Alice Springs (Supplementary Fig. 8). In unfavourable climates, PE covers can deteriorate the cooling performance of PDRCs³¹. For roofing applications, results obtained from PE-covered PDRCs could lead to unreliable calculations of cooling power, which should not be used to assess the urban cooling effect of PDRCs (e.g., in climate modelling using long-term weather data). Beyond performance concerns, using PE cover introduced measurement uncertainty > 1°C in this study (Supplementary Fig. 6). Hence, experiments using PE cover would require multiple replicates to control for greater variability compared to those with buffering boards. Finally, PE films are unrealistic in real-world roofing applications: they deteriorate quickly under UV exposure and weathering³³, cannot be walked over (e.g., for maintenance access), and are easily damaged by birds, hail, and strong winds. Taken together, PE film covers should be used only to assess the maximum cooling power of PDRCs, rather than as a practical or standardised measurement setup.

(3) For air-exposed PDRCs, achieving a uniform surface temperature is difficult due to limited thermal conductivity and variations in the surface boundary layer (Fig. 4g, Supplementary Fig. 3). Previous studies have extensively used K-type and T-type thermocouples to measure the surface temperatures of PDRCs (Supplementary Table 1). However, their standard accuracy (± 2.2°C for K-type and ± 1.0°C for T-type thermocouples, Supplementary Table 2) is significantly poorer than that of the 4-wires RTD Pt100 DIN Class A sensors used in this study (± 0.15°C). Moreover, RTD Pt100 sensors provide better stability and are less prone to signal noise problems compared to thermocouples³⁶. On the other hand, no prior study has quantified the measurement uncertainty of the whole experimental setup, which is determined by a combination of factors: sensor accuracy, sensor adhesion to the sample, signal noise, datalogger noise, and sample size and boundary effect. Therefore, some previous studies may have reported results that fall within an unspecified combined measurement uncertainty. Our test shows that the measurement uncertainty of the whole setup is always greater than the nominal accuracy of the sensors, due to sensor positioning and other factors. In our case, it is twice the nominal accuracy of the sensors (± 0.30°C vs. ±0.15°C). However, to our best knowledge, no studies have reported or accounted for this combined uncertainty in their analysis, which may lead to overinterpretation of small temperature differences.

(4) While a few studies^{15, 23, 47, 53} have tested the same PDRCs in different climates, the use of varying measurement setups makes quantitative comparisons unreliable. Further, we found no studies that tested PDRCs with similar spectral properties in similar climates while varying only a single setup parameter (e.g., with or without PE cover, or different sample sizes). In all cases, more than two setup parameters were varied (Supplementary Table 1), making it impossible to assess the individual effects of sample size and PE cover from existing studies. The absence of standardized conditions for experimental testing results in misleading information from manufacturers commercializing PDRC products. This misinformation compromises the performance of large-scale projects, leading to incorrect sizing and dimensioning. Moreover, the fundamental scientific principle of reproducibility is not upheld. Significant errors in reported measurements distort the true scientific value of these products and diminish their innovative potential. Such practices propagate false and inaccurate claims about the actual contribution of the materials and components used, steering researchers toward misguided and unnecessary experimental and theoretical efforts. In this study, we propose a stable setup, which involves using RTD Pt100 DIN Class A sensors and 200-mm air-exposed samples, surrounded by white EPS buffering boards to form a 500-mm cornice. This distance from the leading edge stabilises the surface boundary layer around the samples⁴⁶, which better represents real-word roofing conditions compared to other setups. Moreover, it enables consistent measurements between identical samples, achieving a low measurement uncertainty of ± 0.3°C.

Methods

Testing sites

Two major field tests were carried out in Australia: in Blacktown, NSW on 21 January 2025, and in Alice Springs, NT on 8 April 2024. Blacktown, located in the Greater Sydney region (Latitude: −33.77, Longitude: 150.90, Elevation: 50 m), has a hot and temperate climate with humid nights during the summer. Moderate humidity and elevated precipitable water reduce the atmospheric transmittance, resulting in a less open atmospheric window and limiting the potential of PDRCs to achieve subambient temperatures. To evaluate PDRC performance under more favourable climate conditions, a preliminary test was conducted in Alice Springs, located in the Northern Territory (Latitude: −23.70, Longitude: 133.87, Elevation: 545 m). The region’s hot desert climate, marked by low humidity and clear skies, enables a more open atmospheric window, making it an ideal location for testing PDRCs under subambient conditions⁵¹. Insights gained from the Alice Springs campaign informed the design and implementation of the subsequent main campaign in Blacktown.

Materials and spectral characterisation

Three materials were tested outdoors in Blacktown: (i) a 0.15-mm PDRC film (Ningbo Radi-Cool Advanced Energy Technologies), and conventional (ii) 0.30-mm white and (iii) 0.30-mm black films. The white and black films were prepared by sandwiching an aluminium foil between two layers of vinyl sheet, which were intrinsically coloured (black or white). The three materials are referred to as PDRC, White, and Black, respectively. Likewise, the PDRC, White, and Black polycarbonate painted samples (1 mm thick) were tested outdoors in the first campaign in Alice Springs (in the second campaign, in Blacktown, the vinyl films simplified sample preparation to achieve opacity). The selected PDRC has been shown to achieve subambient cooling in prior studies^{57, 58}. The White emitter, representing a conventional cool material, was included to provide a benchmark for comparing partial radiative cooling effects. The Black emitter was included as a reference that is expected to remain above-ambient during daytime testing.

Solar reflectance (R_sol) in the 0.3–2.5 µm wavelength range was measured using a UV-Vis-NIR spectrometer (Lambda 1050, PerkinElmer, USA) equipped with a 150-mm integrating sphere. Reflectance values in the UV, Vis, and NIR bands were computed according to ASTM E903⁵⁹, using the spectral irradiance distribution of AM1.5 Global Tilt (37°) defined in ASTM G173-03⁶⁰. Infrared emissivity was measured using a Fourier transform infrared spectrometer (FTIR, VERTEX 80, Bruker, USA) equipped with an Infragold integrating sphere. Broadband emissivity was calculated according to ASTM E408⁶¹ for the whole thermal range (ε_IR, 4–40 µm) and for the atmospheric window band (ε_AW, 8–13 µm). For the Blacktown samples, the R_sol are 0.90 for PDRC, 0.79 for White, and 0.05 for Black (Fig. 2a). The ε_IR are 0.92 for PDRC, 0.93 for White, and 0.94 for Black; the ε_AW are 0.96 for PDRC, 0.97 for White, and 0.96 for Black. The samples tested in Alice Springs and Blacktown had very similar spectral properties (Supplementary Fig. 1a), differing only in the thickness of the White and Black emitters (1.0 mm in Alice Springs vs. 0.3 mm in Blacktown).

Experimental setup

After subsequent development in the selection of the substrate and setup, the PDRC samples were placed on 400 mm × 400 mm × 100 mm expanded polystyrene (EPS) boards (R_sol of 0.89, ε_IR of 0.78, and ε_AW of 0.79, Fig. 2a). The spectral properties of the EPS boards enabled a relatively cooler surface boundary layer around the samples as compared to those of the aluminium taped extruded polystyrene (XPS) boards used in Alice Springs. Figure 2b–e illustrate the setups. The centre temperatures of the samples were recorded using RTD Class A sensors (SA1-RTD 4-wires by Omega). Each sensor was verified against calibrated references in the laboratory to confirm its nominal accuracy (± 0.15°C) and to rule out malfunction. Prior to and following the field test, all instrumented samples were placed side by side in the laboratory to inspect for sensor displacement or transport-related damage.

Information on the tested samples is detailed in Supplementary Table 4. To evaluate the effect of sample size on air-exposed PDRCs, square PDRC samples with side lengths of 50–300 mm were prepared (R-50 to R-300, Fig. 2b). Two identical 200-mm PE-covered samples (R-200-PE-1 and R-200-PE-2) were placed among the air-exposed samples. The PE-covered samples were placed on 400 mm × 400 mm × 100 mm XPS boards covered with silver tape (R_sol of 0.83, ε_IR of 0.79, and ε_AW of 0.88, Fig. 2a), with the PE film covers installed 10 mm above the samples. The solar transmittance (T_sol), T_IR, and atmospheric window transmittance (T_AW) of the PE film were 0.92, 0.89, and 0.91, respectively (Fig. 2a). To compare PDRCs masked with different materials (EPS vs. silver tape), a 200-mm PDRC sample was placed on a 400 mm × 400 mm × 100 mm silver taped XPS board, referred to as R-200-X (Fig. 2c). To compare PDRCs with and without EPS mask, a 100-mm PDRC sample was placed on a 100 mm × 100 mm × 100 mm EPS board, referred to as R-100-E (Fig. 2c). In several studies^{21, 62, 63}, PDRC and non-PDRC samples with distinct spectral properties were placed very close to each other, which may have caused thermal interference. To assess this potential issue, nine 100-mm samples (three each of PDRC, White, and Black) were placed on a 400 mm × 400 mm × 100 mm EPS board (Fig. 2d). Two 200-mm PDRC samples (R-200-S-1 and R-200-S-2) were surrounded by EPS buffering boards to form a 500-mm cornice (Fig. 2e). This setup was to evaluate whether the buffering boards could stabilise the surface boundary layer around the samples. The same measurement setup used for the PDRC samples was applied to the White and Black samples. The effects of sample size, PE film cover, and buffering boards were also investigated in the preliminary campaign in Alice Springs, with the detailed experimental setup provided in Supplementary Note 6.

Supplementary Table 5 lists the instruments used in the field test. Meteorological parameters were determined by averaging measurements from two identical instrument sets. Solar radiation (SR) and infrared radiation (IR) were measured using two net radiometers (NR01 by Hukseflux). Air temperature (T_a), relative humidity (RH), dew point (T_d), wind speed (WS), and wind direction (WD) were measured by two weather stations with radiation shields (MetPakPro by Gill). All data were logged every 15 s using four dataloggers (DT85 and DT80 by Lontek). Absolute humidity (AH) was calculated from T_a and RH, as described in Supplementary Note 6.

Statistical significance test

To determine whether the observed size effects represented statistically robust differences rather than random variability, statistical significance tests were performed for the samples under clear (12:00–13:00) and overcast skies (16:00–17:00). As the data were not normally distributed, significance was assessed using the Kruskal–Wallis test with Dunn’s post hoc test⁶⁴ for pairwise comparisons, with a significance level of p < 0.05. The statistical test results are detailed in Supplementary Note 7.

Numerical simulation

To explain the mechanisms underlying the observed size effects, we developed a two-dimensional CFD model in COMSOL Multiphysics based on the sample–mask configuration. The model comprises a 400 mm × 50 mm fluid region and a 400 mm × 100 mm solid region, with an airflow along the x-direction. The 2D model simultaneously resolved the fluid (air) and the solid (EPS board and sample) domains. Given the low air velocity (< 3 m/s), a laminar flow model was applied. Details of the thermal and fluid boundary conditions, governing equations, and numerical procedures are provided in Supplementary Note 8.

Bias analysis

The most consistent experimental setup identified in the field tests was 200-mm PDRC samples surrounded by EPS buffering boards at a cornice of 500 mm (R-200-S in Fig. 2e). Taking the average of R-200-S-1 and R-200-S-2 as the reference, the systematic and unsystematic (random) biases in centre temperature measurements for other sample setups were calculated as⁶⁵:

${\text{RMS}}{{\text{D}}_{\text{s}}}={[{N^{ - 1}}\sum\limits_{1}^{N} {{{(y' - x)}^2}} ]^{0.5}}{\text{, and MS}}{{\text{D}}_{\text{s}}}={N^{ - 1}}\sum\limits_{1}^{N} {{{(y' - x)}^2}}$

${\text{RMS}}{{\text{D}}_{\text{u}}}={[{N^{ - 1}}\sum\limits_{1}^{N} {{{(y - y')}^2}} ]^{0.5}}{\text{, and MS}}{{\text{D}}_{\text{u}}}={N^{ - 1}}\sum\limits_{1}^{N} {{{(y - y')}^2}}$

where RMSD and MSD are the Root Mean Square Deviation and Mean Square Deviation, respectively, and the subscripts 's' and 'u' denote the systematic and unsystematic components, respectively. y' represents the value obtained from linear least squares regression, computed as:

$y'=ax+b$

To obtain the linear least squares regression equation, we used the data from the average of R-200-S-1 and R-200-S-2 as the reference variable (y) and the data from the other PDRC sample setups as the observed variable (x).

Factor analysis

We employed symbolic regression based on genetic algorithms to analyse the relative relevance of meteorological factors (input variables), including SR, IR, T_a, AH, and WS. The analysis was implemented in HeuristicLab 3.3, a software environment for heuristic and evolutionary computation. An Age-Layered Population Structure (ALPS) Genetic Programming–Symbolic Regression approach was applied, using a dataset split of 66% for training and 34% for testing, with a total of 1500 generations. Six target variables were analysed over a 24-hour period from 18:00 to 18:00, with each pairwise comparison designed to isolate the effect of a single variable: (i) sample size—the temperature difference (ΔT) between R-50 and R-300; (ii) PE film cover—the ΔT between R-200 and R-200-PE; (iii) mask material—the ΔT between R-200 and R-200-X; (iv) EPS mask—the ΔT between R-100 and R-100-E; (v) thermal interference—the ΔT between R-100 and R-100-M; (vi) buffering board—the ΔT between R-200 and R-200-S.

Acknowledgments

This research was supported by the Australian Research Council with the Discovery Project DP230103050: “Adaptive daytime radiative cooling and heating for buildings”. We acknowledge the UNSW Design Futures Lab for the custom accessories for the scientific equipment. We express gratitude to the Northern Territory Government of Australia, the Arid Zone Research Institute (AZRI), Alice Springs, and Blacktown City Council for permission to conduct the field measurements at Blacktown International Sports Park (BISP). The equipment used in the field campaign and for the lab characterisation was supported by UNSW with Research Infrastructure Grants (2020, 2023, and 2024).

Author contributions

T.X. conducted the formal analysis, investigation, data curation, prepared the original draft, and created the visualizations. Z.Z. performed the numerical simulations and contributed to the investigation and manuscript review and editing. H.S.K. contributed to the methodology, resources, and manuscript review and editing. I.K. contributed to the investigation and manuscript review and editing. O.M.L.J. contributed to the methodology and manuscript review and editing. D.K. contributed to the investigation and manuscript review and editing. G.R. supervised the work, contributed to project administration, funding acquisition, and manuscript review and editing. M.S. contributed resources, supervision, and manuscript review and editing. R.P. conceived the research, contributed to methodology, validation, investigation, supervision, resources, project administration, funding acquisition, and manuscript review and editing.

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