A novel black-gray body atmospheric radiation model for accurate long-term radiative cooling performance simulation and analysis

A novel black-gray body atmospheric radiation model for accurate long-term radiative cooling performance simulation and analysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A novel black-gray body atmospheric radiation model for accurate long-term radiative cooling performance simulation and analysis Gang Pei, Lanxin Li, Xianze Ao, Qiangyan Hao, Meiling Liu, Xiansheng Li, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4019641/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Passive radiative cooling spontaneously emits thermal radiation into the cold universe, providing an environment-friendly solution for cooling. Unlike the mature methods for annual performance evaluation of solar energy harvesting, appropriate long-term radiative cooling performance simulation methods that can be used across different cities in the world are still missing. The main reason is that the spectral distribution of atmospheric radiation varies sensitively with sky status (e.g., cloudy, humid, etc.), while the normalized solar radiation spectrum is relatively stable regardless of weather conditions. Currently reported atmospheric radiation models in radiative cooling field, including the effective sky emissivity model and Modtran model, cannot simultaneously meet the spectral, spatial, and temporal requirements. Herein, we propose an accurate long-term radiative cooling simulation method by developing a novel black-gray (BG) body atmospheric radiation model based on the atmospheric spectral properties and the measured atmospheric radiative power. Experimental validation has been performed in cities with different climate styles and results show superior accuracy than reported methods. The proposed radiative cooling simulation method is well-suited for diverse environmental conditions, encompassing different weather conditions, climate styles, and seasons. It is also applicable for both spectral broadband and selective coolers, particularly for recently proposed selective coolers. To further apply the proposed method, we propose a concept of atmospheric spectral energy databases for the first time and provide a demo case study in Hefei, China, which aims to guide the accurate long-term radiative cooling simulation analysis. Physical sciences/Energy science and technology/Renewable energy Physical sciences/Energy science and technology/Energy harvesting Earth and environmental sciences/Climate sciences/Atmospheric science Radiative cooling Atmospheric window Atmospheric radiation Spectral selectivity temporal-spatial resolution Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1 Introduction With the rapid growth of the global population and the skyrocketing rate of industrialization, the global warming issue has become increasingly severe, leading to a significant surge in the demand for cooling. Currently, conventional cooling methods, such as compression-type refrigeration, not only consume vast amounts of electricity but also pose substantial environmental challenges by releasing greenhouse gases and waste heat into the environment. Importantly, the aforementioned waste heat and exhaust emissions exacerbate the global warming phenomenon, creating a vicious cycle that further intensifies the need for cooling. According to the International Energy Agency 1 , air conditioners and electric fans account for nearly 30% of the total electricity consumption in buildings globally only for cooling, exerting serious challenges on the electricity supply and the environment. So, exploring new, green cooling methods is of great importance for the environment and economy and has consistently remained a hot spot in the energy field. Recently, radiative cooling has drawn much attention due to its unique capability to cool terrestrial objects without any extra energy input, behaving as a completely passive cooling method. Radiative cooling harvests the coldness of the universe (~ 3K) by minimizing ingoing heat flux (e.g., solar radiation and heat from the ambient air) and simultaneously maximizing the outgoing thermal radiation to the cold universe mainly through the atmospheric window (8–13µm). The peak thermal radiation of the Earth’s surface with a temperature of approximately 300K is concentrated at a wavelength of 9.6 µm, which coincides with the transparent atmospheric window. Thus, terrestrial radiation can pass through the atmosphere to the universe, and sky-facing coolers can be cooled to below ambient air passively. Many efforts have been dedicated to the development of passive radiative coolers. In the early stage, the radiative cooler can only create a cooling phenomenon during nighttime since the spectral characteristic properties of conventional materials (e.g., black paint) are far from optimum. However, thanks to advances in photonics and micro/nano-fabrication technologies, we have witnessed the emergence of highly efficient radiative coolers very recently with hundreds of innovative designs, including multilayer coatings 2–5 , hierarchically polymers 6–14 , microfibres 15 , and ultra-white paints 16 . On the level of application, radiative cooling has enormous potential for cooling 17 and thermal management in various backgrounds, such as cool roofs and envolops 18 , photovoltaics cooling 19,20 , water harvesting 21,22 , and personal thermal management 15,23,24 . Currently, the progress in radiative cooling remains primarily confined to the laboratory and has yet to be promoted to extensive application in real-world industrial production and daily life. To fully harvest the coldness potential of the universe for us, a major focus is long-term radiative cooling potential assessment under actual climate conditions, which benefits a lot for policy-making and promotes its practical application. Although attention has been devoted to this topic very recently 6,25,26 , appropriate simulation methods have been still missing. The main reason behind this is that the effect of atmospheric radiation on radiative cooling is not fully characterized. The atmosphere, serving as a semi-transparent media between the Earth and the universe, is a complex collection of numerous gases that includes nitrogen, oxygen, carbon dioxide, water vapor, etc, which affects electromagnetic propagation, including solar radiation and infrared thermal radiation. Importantly, the effect of the atmosphere on solar radiation is spectrally nonselective, which means the attenuation of solar radiation is uniform and the normalized solar radiation spectrum remains the same. However, some atmospheric components, such as water vapor, exhibit specific absorption/emission within the atmospheric window that serves as the primary pathway for radiative cooling, which results in the atmospheric radiation power fraction within the atmospheric window varying sensitively with sky status (e.g., clear, cloudy, dry, humid, climate styles, etc.). In most of the reported works on radiative cooling topics, the EFFECTIVE SKY EMMISSIVITY model and MODTRAN model have been widely recognized to simulate atmospheric radiation under various conditions, but these models do not effectively characterize atmospheric radiation power. The EFFECTIVE SKY EMMISSIVITY model treats the atmosphere as a grey body with an effective emissivity, which cannot capture the spectral distribution of atmospheric radiation across different wavelengths and this is not suitable for radiative cooling evaluation of the selective coolers. Moreover, the effective sky emissivity formulas ( Supplementary note 1 ) in the EFFECTIVE SKY EMMISSIVITY model were developed for specific conditions (e.g., daytime, nighttime, clear sky, etc.) at discrete regions or cities, so their validity conditions are limited and most regions around the world do not have effective sky emissivity formulas. Previous work shows that fifteen empirical sky emissivity formulas under clear-sky conditions are compared and recalibrated using data collected from 7 climatologically diverse weather stations over the United States 27 , revealing the empirical sky emissivity formulas are not universally suitable. The MODTRAN model can output the atmospheric radiation power with a spectrum distribution, but it divides the Earth's latitude into three broad regions (tropical, mid-latitude, polar), behaving with poor space resolution. So, the MODTRAN model is unable to predict the atmospheric radiation power at city scales. Besides, the MODTRAN model can only provide static atmospheric radiation power profiles, failing to achieve real-time response, and cannot be used for long-term radiative cooling simulation. In summary, to better characterize atmospheric radiation for accurate long-term radiative cooling performance simulation, the model needs to simultaneously consider its spectral distribution and transient characteristics at the city scale. Herein, we propose and develop a black-gray body (BG) atmospheric radiation model with a small temporal-spatial scale and corresponding long-term radiative cooling performance (BG-RC) simulation method. A black-gray body hypothesis is applied in the BG atmospheric radiation model, which assumes that the atmosphere is a greybody within the atmospheric window and a blackbody within the remaining mid-infrared wavelength band. In addition, locally measured transient atmospheric radiation power is introduced to capture the dynamic variable of the atmospheric radiation power at a small spatial resolution. To validate the BG-RC simulation method, we conduct comparative experiments in different cities with diverse climate styles under various weather conditions using broadband and selective coolers, whose results show that the proposed simulation method is credible with better accuracy and applicability than EFFECTIVE SKT EMISSIVITY and MODTRAN models-based radiative cooling methods. Finally, we propose a concept of atmospheric spectral energy databases for the first time, just like typical solar radiation databases, to efficiently guide the long-term radiative cooling performance evaluation and provide a demo case study in Hefei, China. In summary, the BG-RC simulation method exhibits city-level accuracy on a spatial scale and is scalable for global applications. On a temporal scale, it allows for precise tracking at the minute level, thereby enhancing the accuracy of year-round simulation forecasts of radiative cooling. 2 Results and discussion 2.1 BG atmospheric radiation model and BG-RC simulation method The fundamental principles of the radiative cooling process can be elucidated by analyzing the heat exchange components of the radiative cooler, as illustrated in Fig. 1 a. Considering a sky-facing radiative cooler at a temperature T , the radiative cooling power of the cooler is expressed by: $${P_{cool}}(T)={P_{rad}}(T) - {P_{atm}}({T_{amb}}) - {P_{non - rad}}(T,\;{T_{amb}})$$ 1 where, T is the temperature of the radiative cooler. T amb is the ambient temperature. P non−rad denotes the non-radiative heat transfer power from the surroundings to the cooler, which can be obtained based on an overall non-radiative heat transfer coefficient, defined as h non−rad , by : $${P_{non - rad}}(T,{T_{amb}})={h_{non - rad}}({T_{amb}} - T)$$ 2 Thermal radiative power of the radiative cooler, defined as P rad ( T ) in Eq. ( 1 ), can be expressed by: $${P_{rad}}\left( T \right)=\int_{0}^{\infty } {\int_{0}^{{2\pi }} {\int_{0}^{{\frac{\pi }{2}}} {{I_{bb}}(\lambda ,T)\varepsilon (\lambda ,\theta ,\varphi )\sin \theta \cos \theta d\theta d\varphi d\lambda } } }$$ 3 where, ε ( λ , θ , φ ) is the cooler’s spectral-angular emissivity/absorptivity. I bb ( λ , T ) is the spectral irradiance of a blackbody at the cooler temperature, which can be calculated by Planck’s law 29 . Absorbed atmospheric radiative power, defined as P atm ( T amb ) in Eq. ( 1 ), is the key to predicting the radiative cooling power. As shown in Figs. 1 b and Supplementary note 2 , the atmosphere behaves like a blackbody outside the atmospheric window and emits dramatically different within the atmospheric window for different conditions. So, we propose a BG atmospheric model to dynamically capture the absorbed atmospheric radiation. First, the BG atmospheric model assumes the atmosphere is a greybody within the atmospheric window (8–13 µm) and serves as a blackbody within the remaining mid-infrared wavelength band (3–8 µm and > 13 µm), which corresponds to a unity emissivity outside the atmospheric window and an energy-weighted average emissivity within the atmospheric window (Fig. 1 b). Second, the total download atmospheric radiation power is dynamically and locally measured for the actual boundary condition. Consequently, P atm ( T amb ) can be calculated by: $${P_{atm}}({T_{amb}}){\text{=}}{P_{atm\_out}}({T_{amb}}){\text{+}}{P_{atm\_in}}({T_{amb}})$$ 4 where, P atm_out ( T amb ) is the absorbed atmospheric radiative power outside the atmospheric window and P atm_in ( T amb ) denotes the absorbed atmospheric radiative power inside the atmospheric window. Based on the BG assumption, P atm_out ( T amb ) can be expressed by: $$\begin{gathered} {P_{atm\_out}}({T_{amb}})=\int_{3}^{8} {\int_{0}^{{2\pi }} {\int_{0}^{{\frac{\pi }{2}}} {{I_{bb}}(\lambda ,{T_{amb}})\alpha (\lambda ,\theta ,\varphi )\sin \theta \cos \theta d\theta d\varphi d\lambda } } } \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;+\int_{{13}}^{\infty } {\int_{0}^{{2\pi }} {\int_{0}^{{\frac{\pi }{2}}} {{I_{bb}}(\lambda ,{T_{amb}})\alpha (\lambda ,\theta ,\varphi )\sin \theta \cos \theta d\theta d\varphi d\lambda } } } \hfill \\ \end{gathered}$$ 5 To further evaluate the P atm_in ( T amb ), locally measured total atmospheric download radiative power is introduced and P atm_in ( T amb ) can be determined by: $${P_{atm\_in}}({T_{amb}})=\left[ \begin{gathered} {E_{amb}} - \int_{3}^{8} {\int_{0}^{{2\pi }} {\int_{0}^{{\frac{\pi }{2}}} {{I_{bb}}(\lambda ,{T_{amb}})\sin \theta \cos \theta d\theta d\varphi d\lambda } } } \hfill \\ \;\; - \int_{{13}}^{\infty } {\int_{0}^{{2\pi }} {\int_{0}^{{\frac{\pi }{2}}} {{I_{bb}}(\lambda ,{T_{amb}})\sin \theta \cos \theta d\theta d\varphi d\lambda } } } \hfill \\ \end{gathered} \right]{\varepsilon _{8 - 13}}$$ 6 where, E amb is locally measured total atmospheric download radiative power, ε 8−13 is the average emissivity of the radiative cooler within the atmospheric window. Maximal radiative cooling power occurs when cooler temperature equals ambient temperature and this is what the BG-RC simulation method aims to obtain. Based on the above solution, the long-term radiative cooling power under different locations and meteorological conditions can be predicted when local ambient temperature and atmospheric radiative power are input. If a radiative cooler works under sunlight, absorbed solar power should be further considered, and this parameter can be easily handled using the incident solar radiation power and effective solar absorptivity of the cooler 5,30 . 2.2 Experimental device for method validation To validate the proposed method for radiative cooling assessment, a radiative cooling power measurement system is developed (Fig. 2 ). The radiative cooler is fixed in an enclosing cavity. An electric heater is attached at the back of the cooler and a thermocouple is attached at the back side of the heater. The cavity is structured by thermally insulated sheets with low thermal conductivity. To obtain the maximal cooling power of the cooler, the cooler temperature is dynamically controlled to be the same as the ambient air temperature by adjusting the power supplied to the heater based on the temperature control system. Thus, the power supplied to the heater is the radiative cooling power of the cooler. Pretesting results show the temperature can be controlled to the target with a difference of ± 0.5°C ( Supplementary note 3 ). During testing, the highly reflective aluminum tape is affixed to the outside of the cavity except for the bottom of the cooler to control the temperature of the cavity to be consistent with the ambient temperature, as well as reduce the effect of the heat transfer process between the cavity and ambient air. Polyethylene film with high transmittance (~ 0.9) at all wavelengths is selected as the wind cover and placed above the cavity to reduce the convective heat transfer process between the cooler and ambient air while allowing the thermal radiation from the cooler to the sky. The experiment system also contains a meteorological sub-system, as shown in Fig. 2 a. Relative humidity is measured by a portable weather station and wind speed is measured by a three-cup anemometer. Besides, a pyrgeometer is horizontally fixed to monitor the download atmospheric radiative power E amb . Details of the pyrgeometer are shown in Supplementary note 4 . The portable weather station and three-cup anemometer are powered by a power supply (MS-305D, MAISHENG) with a voltage of approximately 16 V. All the above data is recorded by a data logger (LR8450, HIOKI). Two kinds of radiative coolers, including broadband cooler and selective cooler, are selected for testing in this work. The broadband cooler has high emissivity in the whole mid-infrared wavelength band, while the selective cooler only exhibits high emissivity in the atmospheric window. Notably, the absorbed atmospheric radiative power is the key to radiative cooling prediction and the verification experiments were conducted at night, so spectral property in the solar band is not required in this work. The broadband cooler is a metamaterial 7 that consists of a particle-doped polymer and silver reflective film and the selective cooler is a multilayer photonic cooler that is composed of four layers of aluminum oxide, vanadium dioxide, aluminum oxide, and aluminum. Measured spectral emissivity of broadband and selective cooler are shown in Fig. 2 c, the weighted emissivity of the broadband cooler and selective cooler within the atmospheric window is 0.941 and 0.664, respectively. 2.3 Experiment validation under various weather conditions To verify the accuracy of the proposed BG-RC method under different seasons and weather conditions, a considerable amount of experiments were designed and performed on the rooftop at University of Science and Technology of China, Hefei (31°N, 117 E), China. Figure 3 illustrates the validation results of the broadband radiative cooler under different seasons and weather conditions, which include measured maximal cooling power ( P exp ), predicted maximal cooling power by the BG-RC simulation method ( P sim _ new ), predicted cooling power by the EFFECTIVE SKY EMISSIVITY model-based radiative cooling simulation method ( P sim _ E ) and predicted cooling power by the MODTRAN model-based radiative cooling simulation method ( P sim _ M ). Here, we abbreviate the EFFECTIVE SKY EMISSIVITY model-based radiative cooling simulation method as the ESE-RC simulation method, and the MODTRAN model-based radiative cooling simulation method as the MODTRAN-RC simulation method. The details of the ESE-RC simulation method and MODTRAN-RC simulation method are presented in Supplementary notes 5 and 6 . In summer clear weather conditions, the predicted cooling power P sim _ new and P sim_M are close to the measured cooling power P exp (Fig. 3 a), but the predicted cooling power P sim _ E is far away from them and this may be because the selected empirical correlation of the effective sky emissivity is obtained at specific conditions (e.g., locations and weather styles) but such a correlation is not valid at Hefei. In summer cloudy weather conditions, the predicted cooling power P sim _ new still agrees well with the measured cooling power P exp , while the predicted cooling power P sim _ E and P sim_M significantly deviate from the measured power (Fig. 3 b). Specifically, in the beginning (Fig. 3 b), the sky was pretty cloudy and the transient sky condition was fluctuant, which can be directly reflected by the measured download atmospheric radiative power and measured radiative cooling power. After 2:00 AM, the sky changed to be clear with a relatively stable download atmospheric radiative power. Under such a dynamic atmosphere, the predicted cooling power P sim _ new always closely matches the measured cooling power P exp , demonstrating good robustness. As for the P sim_M , the prediction accuracy is relatively poor due to that the transient sky condition cannot be captured by the MODTRAN atmospheric radiation model. To further demonstrate the applicability of the proposed BG-RC simulation method for different seasons, we conducted experiments validation in the winter season, as shown in Figs. 3 c and d . It is obvious that the temperature and humidity in winter are lower than those in summer, which accounts for the relatively low atmospheric radiative power. Under winter conditions, the predicted cooling power P sim _ new also agrees well with the measured cooling power P exp regardless of weather conditions, but the accuracy of the predicted cooling power P sim_M and P sim_E is poor even in clear sky conditions. The above results are based on the broadband cooler, Figs. 3 e and f demonstrate the validation results of the selective cooler under different weather conditions, which also confirms that the proposed BG-RC simulation method can accurately predict the radiative cooling power and the prediction accuracy is better than other two traditional models. Importantly, the consideration of spectral properties in the proposed BG-RC simulation method is more targeted towards selective coolers, as selective coolers have a high emissivity only within the atmospheric window bands. To quantitatively represent the deviation between predicted cooling power and measured cooling power, mean biased error (MBE) is implemented to assess the accuracy of two models: $${\text{MBE=}}\frac{1}{K}\sum\limits_{{k=1}}^{K} {\left( {\frac{{\left| {{P_{sim}} - {P_{exp}}} \right|}}{{{P_{exp}}}}} \right)}$$ 7 where, K represents the total available data points. Figures 3 g,h and i show the MBE of three methods under different conditions for broadband and selective cooler, respectively. We can find that the MBE of the proposed BG-RC simulation method among all weather conditions is always low (< 0.1), while the MBE of the other two traditional methods is very high in most of the tested conditions, demonstrating the proposed BG-RC simulation method can reflect the effect of the transient condition of a local location on radiative cooling and has potential to behaves as a universal radiative cooling prediction method that can be used for long-term radiative cooling performance simulation at city scales. 2.4 Experiment validation under different cities The experiment validation in Section 2.3 was conducted in Hefei, China, we also performed outdoor experiment verifications in Haikou, China, and Lhasa, China to demonstrate the applicability of the proposed BG-RC simulation method under different cities with various climate styles. The detailed information and climate types of Hefei, Haikou, and Lasa are shown in Supplementary note 7 . Based on the given data, it is observed that Hefei and Lhasa have similar latitudes but differ significantly in terms of climate and average humidity. Consequently, the performance of a specific radiative cooling system may vary considerably between these two cities. Herein, we have selected Lhasa as an experimental site to validate the proposed BG-RC simulation method that aims to improve the accuracy of radiative cooling performance analysis across diverse regions. To further verify its accuracy, we have also selected Haikou, which belongs to the tropical zone, for experimental validation. As indicated in Fig. 4 and Supplementary note 8 , we conducted field experiments by using the selective (Fig. 4 ) and broadband cooler ( Supplementary note 8 ) in Lhasa and Haikou under different weather conditions, which reveals several important pieces of information. First, the predicted cooling power P sim _ new always agrees well with the measured cooling power P exp regardless of cities and weather conditions, but the MODTRAN-RC simulation method and ESE-RC simulation method can not achieve this point. Second, although Lhasa and Hefei have similar latitudes, the sky condition is different for radiative cooling since the level of measured cooling power is different in Lhasa and Hefei, indicating the currently popular solution that uses mid-latitude winter/summer conditions in MODTRAN to evaluate the atmospheric transmittance for the regions with similar latitudes can not fully reflect the real conditions. Third, the advantage of the proposed BG-RC simulation method is more prominent when there are transient changes in the weather, such as dynamic changes in cloud cover, which can also be demonstrated by the MBE value (Fig. 4 d and Figure S4d ). Next, radiative cooling performance is sensitive to climate styles because the measured cooling power of the same cooler in dry Lhasa and humid Haikou are quite different, revealing that long-term radiative cooling potential evaluation at a large scale can contribute to objective recommendations for carbon-neutral policy development. 3 Long-term atmospheric spectral energy database In the solar energy field, the normalized solar radiation spectrum is regarded as a stable spectrum, so solar radiation data is summarized as a database for references, such as solar radiation data included in typical meteorological year database, which provides many benefits when quantifying the effects of solar irradiance at long-term scale. However, in the field of radiative cooling, there is currently no similar database available for reference since the normalized atmospheric radiation spectrum differs dramatically, especially within the atmospheric window. So, we intend to develop a long-term atmospheric spectral energy database based on the BG atmospheric radiation model and locally measured atmospheric radiation power to promote the performance prediction of radiative cooling. Herein, the atmosphere wavelength region is first divided into three band regions, including Region I (3–8 µm), Region II (8–13 µm), and Region III (> 13 µm). According to the BG assumption, the atmosphere is a blackbody within bands of Regions I and III and the atmospheric radiative power can be calculated based on the transient local ambient temperature. Then, the atmospheric radiative power within Region II is determined by subtracting the above-calculated power from the measured atmospheric radiative power. So, the absorbed atmospheric radiative power can be expressed by $${P_{atm}}={\alpha _{Region\;I}} \times {E_{Region\;I}}+{\alpha _{Region\;II}} \times {E_{Region\;II}}+{\alpha _{Region\;III}} \times {E_{Region\;III}}$$ 8 where, E Region I , E Region II , and E Region III are atmospheric radiative power within the band of Region I, Region II, and Region III, which can be introduced to the long-term atmospheric spectral energy database. α Region I , α Region II , and α Region III denote the effective absorptivity of the radiative cooler within the corresponding bands. To preliminary demonstrate such an idea, we conducted a demo based on Hefei meteorological data (Fig. 5a). We obtained the long-wave atmospheric radiative power data and universal meteorological data (e.g., ambient temperature and solar radiation power) based on field measurement (From March 2023 to September 2023). As shown in Fig. 5a , the variation in atmospheric radiative power is relatively small in the bands of Region I and Region III, and it changes consistently with changes in ambient air temperature. However, the atmospheric radiative power within the atmospheric window shows significant fluctuations, which is closely influenced by local meteorological conditions, such as dynamic humidity and cloud cover. Finally, the long-term maximum radiative cooling power of the broadband cooler is evaluated and presented in Fig. 5b , which provides a convenient way for performance evaluation of radiative cooling and will contribute to the development of passive radiative cooling. 4 Summary and conclusion In summary, this work propose an accurate long-term radiative cooling simulation method by developing a black-gray (B-G) body atmospheric radiation model based on the atmospheric spectral properties and the locally measured transient atmospheric radiative power. Validation experiments were carried out in various cities (Heife, Lhasa, and Haikou, China) under different weather conditions (clear and cloudy sky) and seasons (winter and summer) using spectral broadband and selective coolers. The results confirm that on a spatial scale the BG-RC simulation method exhibits city-level accuracy and is scalable for global applications; On a temporal scale, it allows for precise tracking at the minute level, thereby enhancing the accuracy of long-term simulation forecasts of radiative cooling. To further apply the proposed method and facilitate accurate long-term radiative cooling simulation analysis we introduce the concept of atmospheric spectral energy databases for the first time and provide a demo case study in Hefei, China. This approach allows for the rapid and straightforward assessment of the accurate long-term radiative cooling power potential, thereby fostering the widespread application of radiative cooling technology. Declarations Acknowledgements This work was supported by the National Natural Science Foundation of China (NSFC 52106276 and 52130601), USTC Research Funds of the Double First-Class Initiative (YD2090002014), Young Elite Scientists Sponsorship Program by CAST (2023QNRC001), the research center for multi-energy complementation and conversion of USTC, and the USTC Center for Micro and Nanoscale Research and Fabrication. References ( Ao, X. et al. Self-adaptive integration of photothermal and radiative cooling for continuous energy harvesting from the sun and outer space. Proc Natl Acad Sci U S A 119 , e2120557119, doi:10.1073/pnas.2120557119 (2022). Chen, Z., Zhu, L., Raman, A. & Fan, S. Radiative cooling to deep sub-freezing temperatures through a 24-h day-night cycle. Nat Commun 7 , 13729, doi:10.1038/ncomms13729 (2016). Jeong, S. Y. et al. Field investigation of a photonic multi-layered TiO2 passive radiative cooler in sub-tropical climate. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4019641","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":277087623,"identity":"ed692f96-2d26-47b5-83dc-4777d75c2aef","order_by":0,"name":"Gang Pei","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIie3OMQuCQBTA8ScHulizS/UVLhxC/DIeDi7V3GByILypaO5bNDYqgi2Gq1tES0tgY0ORYfN5Y9D94R08eD84AJXqJ9P45x1+NyJP7O+1FGljXJpMjDi+PvbLYFeWaQ0Ll3HjmAiJs0rRWReH2a7yiQVFwLg594SEVgxpD/OGEB00zBi3TCompzOOn5gHtMwa8pIhlRZfehh6NPEbwiWIs2JIBpiMt5VvW14e2GhOxWRiHC73G0ajfpme6zp0Bxuj6PgYgG4BZO3mNaML71tCaoCo606lUqn+uTdqcEjDZe6yTwAAAABJRU5ErkJggg==","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":true,"prefix":"","firstName":"Gang","middleName":"","lastName":"Pei","suffix":""},{"id":277087624,"identity":"f5d1eefe-942a-4d70-a459-e901962a603f","order_by":1,"name":"Lanxin Li","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Lanxin","middleName":"","lastName":"Li","suffix":""},{"id":277087625,"identity":"a5615047-9f88-4b00-871a-035280d900ad","order_by":2,"name":"Xianze Ao","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Xianze","middleName":"","lastName":"Ao","suffix":""},{"id":277087626,"identity":"ef343047-b6f0-4ba6-9697-032093e51a79","order_by":3,"name":"Qiangyan Hao","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Qiangyan","middleName":"","lastName":"Hao","suffix":""},{"id":277087627,"identity":"fb9caed2-5761-4a5a-83bb-dc7a2719e45a","order_by":4,"name":"Meiling Liu","email":"","orcid":"https://orcid.org/0009-0005-5714-4640","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Meiling","middleName":"","lastName":"Liu","suffix":""},{"id":277087628,"identity":"8db591f9-7ef4-4094-8bb4-e7c232e3c75b","order_by":5,"name":"Xiansheng Li","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Xiansheng","middleName":"","lastName":"Li","suffix":""},{"id":277087629,"identity":"5d27e83a-24c2-4e01-8354-002be195c31b","order_by":6,"name":"Kegui Lu","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Kegui","middleName":"","lastName":"Lu","suffix":""},{"id":277087630,"identity":"36a16ac3-541b-44c0-83e9-adbe00ea3185","order_by":7,"name":"Bin Zhao","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Bin","middleName":"","lastName":"Zhao","suffix":""}],"badges":[],"createdAt":"2024-03-06 06:50:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4019641/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4019641/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":53507247,"identity":"63f1b6be-1092-4adc-8abc-5d9ea4b595a6","added_by":"auto","created_at":"2024-03-26 20:36:39","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":184411,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEnergy balance process of radiative cooling and atmospheric radiation power profile\u003c/strong\u003e. \u003cstrong\u003ea\u003c/strong\u003e. Heat transfer process of a radiative cooler. \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eatm \u003c/em\u003e\u003c/sub\u003edenotes the absorbed atmospheric radiative power, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003erad\u003c/em\u003e\u003c/sub\u003e is the thermal radiative power of the cooler. \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003enon-rad\u003c/em\u003e\u003c/sub\u003e denotes the non-radiative heat transfer power from the surroundings to the cooler. \u003cstrong\u003eb\u003c/strong\u003e. Spectral irradiance of the blackbody and atmosphere \u003csup\u003e28\u003c/sup\u003e, and the equivalent emissivity of the atmosphere.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-4019641/v1/3f6cd08162f6cbdd90c4f31b.png"},{"id":53507626,"identity":"503716bc-1e72-42bd-917f-3ef6f7fd245a","added_by":"auto","created_at":"2024-03-26 20:44:39","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":548481,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRadiative cooling power measurement device. a\u003c/strong\u003e. Experimental setup for measuring maximal cooling power. \u003cstrong\u003eb\u003c/strong\u003e. Schematic of the testing system. \u003cstrong\u003ec. \u003c/strong\u003eMeasured spectral emissivity of the broadband and selective cooler.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-4019641/v1/1fa0f391d55cf516a43e0cd9.png"},{"id":53507248,"identity":"5c149047-01ec-428d-9375-792bb52d68bf","added_by":"auto","created_at":"2024-03-26 20:36:39","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":255546,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of measured and predicted cooling power.\u003c/strong\u003e \u003cstrong\u003ea-d:\u003c/strong\u003e Measured and predicted cooling power under different seasons and weather conditions using broadband cooler with measured atmospheric radiative power and relative humidity plotted as references (\u003cstrong\u003ea\u003c/strong\u003e. summer clear(15.09.2022), \u003cstrong\u003eb\u003c/strong\u003e. summer cloudy(16.09.2022), \u003cstrong\u003ec. \u003c/strong\u003ewinter clear(03.11.2022), \u003cstrong\u003ed\u003c/strong\u003e. winter cloudy(04.11.2022)). \u003cstrong\u003ee,f\u003c/strong\u003e: Measured and predicted cooling power under different weather conditions using selective cooler with measured atmospheric radiative power and relative humidity plotted as references (\u003cstrong\u003ee\u003c/strong\u003e. winter clear(15.3.2023), \u003cstrong\u003ef\u003c/strong\u003e. winter cloudy(16.3.2023)). \u003cstrong\u003eg-i.\u003c/strong\u003e Mean biased error of the predicted results obtained by the proposed BG-RC simulation method, MODTRAN-RC simulation method and ESE-RC simulation method, based on the broadband and selective cooler.(\u003cstrong\u003eg\u003c/strong\u003e.broadband cooler in summer, \u003cstrong\u003eh\u003c/strong\u003e. broadband cooler in winter, \u003cstrong\u003ei\u003c/strong\u003e.selective cooler in winter).\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-4019641/v1/bf013635af44866f21e2f08f.png"},{"id":53507250,"identity":"3c44e302-7df2-4659-9002-4758c32c25f4","added_by":"auto","created_at":"2024-03-26 20:36:40","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":242533,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental validation in Lhasa, China, and Haikou, China. a-c. \u003c/strong\u003eMeasured and predicted maximal cooling power under different cities and weather conditions using the selective cooler with measured atmospheric radiative power and relative humidity plotted as references (\u003cstrong\u003ea\u003c/strong\u003e. Lhasa clear sky(06.04.2023), \u003cstrong\u003eb\u003c/strong\u003e. Lhasa cloudy sky(15.04.2023), \u003cstrong\u003ec\u003c/strong\u003e. Haikou cloudy sky(25.04.2023)). \u003cstrong\u003ed\u003c/strong\u003e. Mean biased error of the predicted results obtained by the proposed BG-RC simulation method, MODTRAN-RC simulation method and ESE-RC simulation method, based on the selective cooler.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-4019641/v1/eccdaa0a2f989fa5138f1a48.png"},{"id":53507627,"identity":"d3ecb551-59b5-4c10-97b8-3612c3e69052","added_by":"auto","created_at":"2024-03-26 20:44:40","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":192090,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDemonstration of atmospheric radiative power database concept. a. \u003c/strong\u003eAtmospheric radiative power in different wavelength ranges, including 3-8 μm, 8-13 μm, and 13-20 μm. \u003cstrong\u003eb.\u003c/strong\u003e Predicted maximal radiative cooling power at a long-term scale.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-4019641/v1/f610e189771d254dac67ddd5.png"},{"id":53508354,"identity":"dfe686a8-bb66-48f6-a0c0-7ad575a0d7d7","added_by":"auto","created_at":"2024-03-26 20:52:41","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2507787,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4019641/v1/d010952e-dd56-4cb8-b900-19467d2f7e68.pdf"},{"id":53507252,"identity":"fa379ff1-6d27-4277-8010-ac4fc91cf299","added_by":"auto","created_at":"2024-03-26 20:36:40","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":1643129,"visible":true,"origin":"","legend":"\u003cp\u003esupplementary information\u003c/p\u003e","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-4019641/v1/64c6962c8810117d8af013e1.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"A novel black-gray body atmospheric radiation model for accurate long-term radiative cooling performance simulation and analysis","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eWith the rapid growth of the global population and the skyrocketing rate of industrialization, the global warming issue has become increasingly severe, leading to a significant surge in the demand for cooling. Currently, conventional cooling methods, such as compression-type refrigeration, not only consume vast amounts of electricity but also pose substantial environmental challenges by releasing greenhouse gases and waste heat into the environment. Importantly, the aforementioned waste heat and exhaust emissions exacerbate the global warming phenomenon, creating a vicious cycle that further intensifies the need for cooling. According to the International Energy Agency\u003csup\u003e1\u003c/sup\u003e, air conditioners and electric fans account for nearly 30% of the total electricity consumption in buildings globally only for cooling, exerting serious challenges on the electricity supply and the environment. So, exploring new, green cooling methods is of great importance for the environment and economy and has consistently remained a hot spot in the energy field.\u003c/p\u003e \u003cp\u003eRecently, radiative cooling has drawn much attention due to its unique capability to cool terrestrial objects without any extra energy input, behaving as a completely passive cooling method. Radiative cooling harvests the coldness of the universe (~\u0026thinsp;3K) by minimizing ingoing heat flux (e.g., solar radiation and heat from the ambient air) and simultaneously maximizing the outgoing thermal radiation to the cold universe mainly through the atmospheric window (8\u0026ndash;13\u0026micro;m). The peak thermal radiation of the Earth\u0026rsquo;s surface with a temperature of approximately 300K is concentrated at a wavelength of 9.6 \u0026micro;m, which coincides with the transparent atmospheric window. Thus, terrestrial radiation can pass through the atmosphere to the universe, and sky-facing coolers can be cooled to below ambient air passively. Many efforts have been dedicated to the development of passive radiative coolers. In the early stage, the radiative cooler can only create a cooling phenomenon during nighttime since the spectral characteristic properties of conventional materials (e.g., black paint) are far from optimum. However, thanks to advances in photonics and micro/nano-fabrication technologies, we have witnessed the emergence of highly efficient radiative coolers very recently with hundreds of innovative designs, including multilayer coatings\u003csup\u003e2\u0026ndash;5\u003c/sup\u003e, hierarchically polymers\u003csup\u003e6\u0026ndash;14\u003c/sup\u003e, microfibres\u003csup\u003e15\u003c/sup\u003e, and ultra-white paints\u003csup\u003e16\u003c/sup\u003e. On the level of application, radiative cooling has enormous potential for cooling \u003csup\u003e17\u003c/sup\u003e and thermal management in various backgrounds, such as cool roofs and envolops \u003csup\u003e18\u003c/sup\u003e, photovoltaics cooling\u003csup\u003e19,20\u003c/sup\u003e, water harvesting\u003csup\u003e21,22\u003c/sup\u003e, and personal thermal management\u003csup\u003e15,23,24\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eCurrently, the progress in radiative cooling remains primarily confined to the laboratory and has yet to be promoted to extensive application in real-world industrial production and daily life. To fully harvest the coldness potential of the universe for us, a major focus is long-term radiative cooling potential assessment under actual climate conditions, which benefits a lot for policy-making and promotes its practical application. Although attention has been devoted to this topic very recently\u003csup\u003e6,25,26\u003c/sup\u003e, appropriate simulation methods have been still missing. The main reason behind this is that the effect of atmospheric radiation on radiative cooling is not fully characterized. The atmosphere, serving as a semi-transparent media between the Earth and the universe, is a complex collection of numerous gases that includes nitrogen, oxygen, carbon dioxide, water vapor, etc, which affects electromagnetic propagation, including solar radiation and infrared thermal radiation. Importantly, the effect of the atmosphere on solar radiation is spectrally nonselective, which means the attenuation of solar radiation is uniform and the normalized solar radiation spectrum remains the same. However, some atmospheric components, such as water vapor, exhibit specific absorption/emission within the atmospheric window that serves as the primary pathway for radiative cooling, which results in the atmospheric radiation power fraction within the atmospheric window varying sensitively with sky status (e.g., clear, cloudy, dry, humid, climate styles, etc.).\u003c/p\u003e \u003cp\u003eIn most of the reported works on radiative cooling topics, the EFFECTIVE SKY EMMISSIVITY model and MODTRAN model have been widely recognized to simulate atmospheric radiation under various conditions, but these models do not effectively characterize atmospheric radiation power. The EFFECTIVE SKY EMMISSIVITY model treats the atmosphere as a grey body with an effective emissivity, which cannot capture the spectral distribution of atmospheric radiation across different wavelengths and this is not suitable for radiative cooling evaluation of the selective coolers. Moreover, the effective sky emissivity formulas (\u003cb\u003eSupplementary note 1\u003c/b\u003e) in the EFFECTIVE SKY EMMISSIVITY model were developed for specific conditions (e.g., daytime, nighttime, clear sky, etc.) at discrete regions or cities, so their validity conditions are limited and most regions around the world do not have effective sky emissivity formulas. Previous work shows that fifteen empirical sky emissivity formulas under clear-sky conditions are compared and recalibrated using data collected from 7 climatologically diverse weather stations over the United States\u003csup\u003e27\u003c/sup\u003e, revealing the empirical sky emissivity formulas are not universally suitable. The MODTRAN model can output the atmospheric radiation power with a spectrum distribution, but it divides the Earth's latitude into three broad regions (tropical, mid-latitude, polar), behaving with poor space resolution. So, the MODTRAN model is unable to predict the atmospheric radiation power at city scales. Besides, the MODTRAN model can only provide static atmospheric radiation power profiles, failing to achieve real-time response, and cannot be used for long-term radiative cooling simulation. In summary, to better characterize atmospheric radiation for accurate long-term radiative cooling performance simulation, the model needs to simultaneously consider its spectral distribution and transient characteristics at the city scale.\u003c/p\u003e \u003cp\u003eHerein, we propose and develop a black-gray body (BG) atmospheric radiation model with a small temporal-spatial scale and corresponding long-term radiative cooling performance (BG-RC) simulation method. A black-gray body hypothesis is applied in the BG atmospheric radiation model, which assumes that the atmosphere is a greybody within the atmospheric window and a blackbody within the remaining mid-infrared wavelength band. In addition, locally measured transient atmospheric radiation power is introduced to capture the dynamic variable of the atmospheric radiation power at a small spatial resolution. To validate the BG-RC simulation method, we conduct comparative experiments in different cities with diverse climate styles under various weather conditions using broadband and selective coolers, whose results show that the proposed simulation method is credible with better accuracy and applicability than EFFECTIVE SKT EMISSIVITY and MODTRAN models-based radiative cooling methods. Finally, we propose a concept of atmospheric spectral energy databases for the first time, just like typical solar radiation databases, to efficiently guide the long-term radiative cooling performance evaluation and provide a demo case study in Hefei, China. In summary, the BG-RC simulation method exhibits city-level accuracy on a spatial scale and is scalable for global applications. On a temporal scale, it allows for precise tracking at the minute level, thereby enhancing the accuracy of year-round simulation forecasts of radiative cooling.\u003c/p\u003e"},{"header":"2 Results and discussion","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 BG atmospheric radiation model and BG-RC simulation method\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe fundamental principles of the radiative cooling process can be elucidated by analyzing the heat exchange components of the radiative cooler, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea. Considering a sky-facing radiative cooler at a temperature \u003cem\u003eT\u003c/em\u003e, the radiative cooling power of the cooler is expressed by:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${P_{cool}}(T)={P_{rad}}(T) - {P_{atm}}({T_{amb}}) - {P_{non - rad}}(T,\\;{T_{amb}})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, \u003cem\u003eT\u003c/em\u003e is the temperature of the radiative cooler. \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eamb\u003c/em\u003e\u003c/sub\u003e is the ambient temperature. \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003enon\u0026minus;rad\u003c/em\u003e\u003c/sub\u003e denotes the non-radiative heat transfer power from the surroundings to the cooler, which can be obtained based on an overall non-radiative heat transfer coefficient, defined as \u003cem\u003eh\u003c/em\u003e\u003csub\u003e\u003cem\u003enon\u0026minus;rad\u003c/em\u003e\u003c/sub\u003e, by :\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${P_{non - rad}}(T,{T_{amb}})={h_{non - rad}}({T_{amb}} - T)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThermal radiative power of the radiative cooler, defined as \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003erad\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003eT\u003c/em\u003e) in Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), can be expressed by:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$${P_{rad}}\\left( T \\right)=\\int_{0}^{\\infty } {\\int_{0}^{{2\\pi }} {\\int_{0}^{{\\frac{\\pi }{2}}} {{I_{bb}}(\\lambda ,T)\\varepsilon (\\lambda ,\\theta ,\\varphi )\\sin \\theta \\cos \\theta d\\theta d\\varphi d\\lambda } } }$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, \u003cem\u003eε\u003c/em\u003e(\u003cem\u003eλ\u003c/em\u003e,\u003cem\u003eθ\u003c/em\u003e,\u003cem\u003eφ\u003c/em\u003e) is the cooler\u0026rsquo;s spectral-angular emissivity/absorptivity. \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003ebb\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003eλ\u003c/em\u003e,\u003cem\u003eT\u003c/em\u003e) is the spectral irradiance of a blackbody at the cooler temperature, which can be calculated by Planck\u0026rsquo;s law \u003csup\u003e29\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAbsorbed atmospheric radiative power, defined as \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eatm\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eamb\u003c/em\u003e\u003c/sub\u003e) in Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), is the key to predicting the radiative cooling power. As shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb and \u003cb\u003eSupplementary note 2\u003c/b\u003e, the atmosphere behaves like a blackbody outside the atmospheric window and emits dramatically different within the atmospheric window for different conditions. So, we propose a BG atmospheric model to dynamically capture the absorbed atmospheric radiation. First, the BG atmospheric model assumes the atmosphere is a greybody within the atmospheric window (8\u0026ndash;13 \u0026micro;m) and serves as a blackbody within the remaining mid-infrared wavelength band (3\u0026ndash;8 \u0026micro;m and \u0026gt;\u0026thinsp;13 \u0026micro;m), which corresponds to a unity emissivity outside the atmospheric window and an energy-weighted average emissivity within the atmospheric window (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). Second, the total download atmospheric radiation power is dynamically and locally measured for the actual boundary condition. Consequently, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eatm\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eamb\u003c/em\u003e\u003c/sub\u003e) can be calculated by:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$${P_{atm}}({T_{amb}}){\\text{=}}{P_{atm\\_out}}({T_{amb}}){\\text{+}}{P_{atm\\_in}}({T_{amb}})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eatm_out\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eamb\u003c/em\u003e\u003c/sub\u003e) is the absorbed atmospheric radiative power outside the atmospheric window and \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eatm_in\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eamb\u003c/em\u003e\u003c/sub\u003e) denotes the absorbed atmospheric radiative power inside the atmospheric window. Based on the BG assumption, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eatm_out\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eamb\u003c/em\u003e\u003c/sub\u003e) can be expressed by:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\begin{gathered} {P_{atm\\_out}}({T_{amb}})=\\int_{3}^{8} {\\int_{0}^{{2\\pi }} {\\int_{0}^{{\\frac{\\pi }{2}}} {{I_{bb}}(\\lambda ,{T_{amb}})\\alpha (\\lambda ,\\theta ,\\varphi )\\sin \\theta \\cos \\theta d\\theta d\\varphi d\\lambda } } } \\hfill \\\\ \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;+\\int_{{13}}^{\\infty } {\\int_{0}^{{2\\pi }} {\\int_{0}^{{\\frac{\\pi }{2}}} {{I_{bb}}(\\lambda ,{T_{amb}})\\alpha (\\lambda ,\\theta ,\\varphi )\\sin \\theta \\cos \\theta d\\theta d\\varphi d\\lambda } } } \\hfill \\\\ \\end{gathered}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eTo further evaluate the \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eatm_in\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eamb\u003c/em\u003e\u003c/sub\u003e), locally measured total atmospheric download radiative power is introduced and \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eatm_in\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eamb\u003c/em\u003e\u003c/sub\u003e) can be determined by:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$${P_{atm\\_in}}({T_{amb}})=\\left[ \\begin{gathered} {E_{amb}} - \\int_{3}^{8} {\\int_{0}^{{2\\pi }} {\\int_{0}^{{\\frac{\\pi }{2}}} {{I_{bb}}(\\lambda ,{T_{amb}})\\sin \\theta \\cos \\theta d\\theta d\\varphi d\\lambda } } } \\hfill \\\\ \\;\\; - \\int_{{13}}^{\\infty } {\\int_{0}^{{2\\pi }} {\\int_{0}^{{\\frac{\\pi }{2}}} {{I_{bb}}(\\lambda ,{T_{amb}})\\sin \\theta \\cos \\theta d\\theta d\\varphi d\\lambda } } } \\hfill \\\\ \\end{gathered} \\right]{\\varepsilon _{8 - 13}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eamb\u003c/em\u003e\u003c/sub\u003e is locally measured total atmospheric download radiative power, \u003cem\u003eε\u003c/em\u003e\u003csub\u003e8\u0026minus;13\u003c/sub\u003e is the\u003c/p\u003e \u003cp\u003eaverage emissivity of the radiative cooler within the atmospheric window.\u003c/p\u003e \u003cp\u003eMaximal radiative cooling power occurs when cooler temperature equals ambient temperature and this is what the BG-RC simulation method aims to obtain. Based on the above solution, the long-term radiative cooling power under different locations and meteorological conditions can be predicted when local ambient temperature and atmospheric radiative power are input. If a radiative cooler works under sunlight, absorbed solar power should be further considered, and this parameter can be easily handled using the incident solar radiation power and effective solar absorptivity of the cooler\u003csup\u003e5,30\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Experimental device for method validation\u003c/h2\u003e \u003cp\u003eTo validate the proposed method for radiative cooling assessment, a radiative cooling power measurement system is developed (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The radiative cooler is fixed in an enclosing cavity. An electric heater is attached at the back of the cooler and a thermocouple is attached at the back side of the heater. The cavity is structured by thermally insulated sheets with low thermal conductivity. To obtain the maximal cooling power of the cooler, the cooler temperature is dynamically controlled to be the same as the ambient air temperature by adjusting the power supplied to the heater based on the temperature control system. Thus, the power supplied to the heater is the radiative cooling power of the cooler. Pretesting results show the temperature can be controlled to the target with a difference of \u0026plusmn;\u0026thinsp;0.5\u0026deg;C (\u003cb\u003eSupplementary note 3\u003c/b\u003e). During testing, the highly reflective aluminum tape is affixed to the outside of the cavity except for the bottom of the cooler to control the temperature of the cavity to be consistent with the ambient temperature, as well as reduce the effect of the heat transfer process between the cavity and ambient air. Polyethylene film with high transmittance (~\u0026thinsp;0.9) at all wavelengths is selected as the wind cover and placed above the cavity to reduce the convective heat transfer process between the cooler and ambient air while allowing the thermal radiation from the cooler to the sky.\u003c/p\u003e \u003cp\u003eThe experiment system also contains a meteorological sub-system, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea. Relative humidity is measured by a portable weather station and wind speed is measured by a three-cup anemometer. Besides, a pyrgeometer is horizontally fixed to monitor the download atmospheric radiative power \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eamb\u003c/em\u003e\u003c/sub\u003e. Details of the pyrgeometer are shown in \u003cb\u003eSupplementary note 4\u003c/b\u003e. The portable weather station and three-cup anemometer are powered by a power supply (MS-305D, MAISHENG) with a voltage of approximately 16 V. All the above data is recorded by a data logger (LR8450, HIOKI).\u003c/p\u003e \u003cp\u003eTwo kinds of radiative coolers, including broadband cooler and selective cooler, are selected for testing in this work. The broadband cooler has high emissivity in the whole mid-infrared wavelength band, while the selective cooler only exhibits high emissivity in the atmospheric window. Notably, the absorbed atmospheric radiative power is the key to radiative cooling prediction and the verification experiments were conducted at night, so spectral property in the solar band is not required in this work. The broadband cooler is a metamaterial \u003csup\u003e7\u003c/sup\u003e that consists of a particle-doped polymer and silver reflective film and the selective cooler is a multilayer photonic cooler that is composed of four layers of aluminum oxide, vanadium dioxide, aluminum oxide, and aluminum. Measured spectral emissivity of broadband and selective cooler are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec, the weighted emissivity of the broadband cooler and selective cooler within the atmospheric window is 0.941 and 0.664, respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Experiment validation under various weather conditions\u003c/h2\u003e \u003cp\u003eTo verify the accuracy of the proposed BG-RC method under different seasons and weather conditions, a considerable amount of experiments were designed and performed on the rooftop at University of Science and Technology of China, Hefei (31\u0026deg;N, 117 E), China. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the validation results of the broadband radiative cooler under different seasons and weather conditions, which include measured maximal cooling power (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eexp\u003c/em\u003e\u003c/sub\u003e), predicted maximal cooling power by the BG-RC simulation method (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim\u003c/em\u003e_\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e), predicted cooling power by the EFFECTIVE SKY EMISSIVITY model-based radiative cooling simulation method (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim\u003c/em\u003e_\u003cem\u003eE\u003c/em\u003e\u003c/sub\u003e) and predicted cooling power by the MODTRAN model-based radiative cooling simulation method (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim\u003c/em\u003e_\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e). Here, we abbreviate the EFFECTIVE SKY EMISSIVITY model-based radiative cooling simulation method as the ESE-RC simulation method, and the MODTRAN model-based radiative cooling simulation method as the MODTRAN-RC simulation method. The details of the ESE-RC simulation method and MODTRAN-RC simulation method are presented in \u003cb\u003eSupplementary notes 5 and 6\u003c/b\u003e .\u003c/p\u003e \u003cp\u003eIn summer clear weather conditions, the predicted cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim\u003c/em\u003e_\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim_M\u003c/em\u003e\u003c/sub\u003e are close to the measured cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eexp\u003c/em\u003e\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea), but the predicted cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim\u003c/em\u003e_\u003cem\u003eE\u003c/em\u003e\u003c/sub\u003e is far away from them and this may be because the selected empirical correlation of the effective sky emissivity is obtained at specific conditions (e.g., locations and weather styles) but such a correlation is not valid at Hefei. In summer cloudy weather conditions, the predicted cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim\u003c/em\u003e_\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e still agrees well with the measured cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eexp\u003c/em\u003e\u003c/sub\u003e, while the predicted cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim\u003c/em\u003e_\u003cem\u003eE\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim_M\u003c/em\u003e\u003c/sub\u003e significantly deviate from the measured power (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). Specifically, in the beginning (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb), the sky was pretty cloudy and the transient sky condition was fluctuant, which can be directly reflected by the measured download atmospheric radiative power and measured radiative cooling power. After 2:00 AM, the sky changed to be clear with a relatively stable download atmospheric radiative power. Under such a dynamic atmosphere, the predicted cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim\u003c/em\u003e_\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e always closely matches the measured cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eexp\u003c/em\u003e\u003c/sub\u003e, demonstrating good robustness. As for the \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim_M\u003c/em\u003e\u003c/sub\u003e, the prediction accuracy is relatively poor due to that the transient sky condition cannot be captured by the MODTRAN atmospheric radiation model. To further demonstrate the applicability of the proposed BG-RC simulation method for different seasons, we conducted experiments validation in the winter season, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec \u003cb\u003eand d\u003c/b\u003e. It is obvious that the temperature and humidity in winter are lower than those in summer, which accounts for the relatively low atmospheric radiative power. Under winter conditions, the predicted cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim\u003c/em\u003e_\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e also agrees well with the measured cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eexp\u003c/em\u003e\u003c/sub\u003e regardless of weather conditions, but the accuracy of the predicted cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim_M\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim_E\u003c/em\u003e\u003c/sub\u003e is poor even in clear sky conditions. The above results are based on the broadband cooler, Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee \u003cb\u003eand f\u003c/b\u003e demonstrate the validation results of the selective cooler under different weather conditions, which also confirms that the proposed BG-RC simulation method can accurately predict the radiative cooling power and the prediction accuracy is better than other two traditional models. Importantly, the consideration of spectral properties in the proposed BG-RC simulation method is more targeted towards selective coolers, as selective coolers have a high emissivity only within the atmospheric window bands.\u003c/p\u003e \u003cp\u003eTo quantitatively represent the deviation between predicted cooling power and measured cooling power, mean biased error (MBE) is implemented to assess the accuracy of two models:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$${\\text{MBE=}}\\frac{1}{K}\\sum\\limits_{{k=1}}^{K} {\\left( {\\frac{{\\left| {{P_{sim}} - {P_{exp}}} \\right|}}{{{P_{exp}}}}} \\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, \u003cem\u003eK\u003c/em\u003e represents the total available data points. Figures\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eg,h \u003cb\u003eand i\u003c/b\u003e show the MBE of three methods under different conditions for broadband and selective cooler, respectively. We can find that the MBE of the proposed BG-RC simulation method among all weather conditions is always low (\u0026lt;\u0026thinsp;0.1), while the MBE of the other two traditional methods is very high in most of the tested conditions, demonstrating the proposed BG-RC simulation method can reflect the effect of the transient condition of a local location on radiative cooling and has potential to behaves as a universal radiative cooling prediction method that can be used for long-term radiative cooling performance simulation at city scales.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Experiment validation under different cities\u003c/h2\u003e \u003cp\u003eThe experiment validation in Section 2.3 was conducted in Hefei, China, we also performed outdoor experiment verifications in Haikou, China, and Lhasa, China to demonstrate the applicability of the proposed BG-RC simulation method under different cities with various climate styles. The detailed information and climate types of Hefei, Haikou, and Lasa are shown in \u003cb\u003eSupplementary note 7\u003c/b\u003e. Based on the given data, it is observed that Hefei and Lhasa have similar latitudes but differ significantly in terms of climate and average humidity. Consequently, the performance of a specific radiative cooling system may vary considerably between these two cities. Herein, we have selected Lhasa as an experimental site to validate the proposed BG-RC simulation method that aims to improve the accuracy of radiative cooling performance analysis across diverse regions. To further verify its accuracy, we have also selected Haikou, which belongs to the tropical zone, for experimental validation.\u003c/p\u003e \u003cp\u003eAs indicated in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cb\u003eSupplementary note 8\u003c/b\u003e, we conducted field experiments by using the selective (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) and broadband cooler (\u003cb\u003eSupplementary note 8\u003c/b\u003e) in Lhasa and Haikou under different weather conditions, which reveals several important pieces of information. First, the predicted cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esim\u003c/em\u003e_\u003cem\u003enew\u003c/em\u003e\u003c/sub\u003e always agrees well with the measured cooling power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eexp\u003c/em\u003e\u003c/sub\u003e regardless of cities and weather conditions, but the MODTRAN-RC simulation method and ESE-RC simulation method can not achieve this point. Second, although Lhasa and Hefei have similar latitudes, the sky condition is different for radiative cooling since the level of measured cooling power is different in Lhasa and Hefei, indicating the currently popular solution that uses mid-latitude winter/summer conditions in MODTRAN to evaluate the atmospheric transmittance for the regions with similar latitudes can not fully reflect the real conditions. Third, the advantage of the proposed BG-RC simulation method is more prominent when there are transient changes in the weather, such as dynamic changes in cloud cover, which can also be demonstrated by the MBE value (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed and \u003cb\u003eFigure S4d\u003c/b\u003e). Next, radiative cooling performance is sensitive to climate styles because the measured cooling power of the same cooler in dry Lhasa and humid Haikou are quite different, revealing that long-term radiative cooling potential evaluation at a large scale can contribute to objective recommendations for carbon-neutral policy development.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3 Long-term atmospheric spectral energy database","content":"\u003cp\u003eIn the solar energy field, the normalized solar radiation spectrum is regarded as a stable spectrum, so solar radiation data is summarized as a database for references, such as solar radiation data included in typical meteorological year database, which provides many benefits when quantifying the effects of solar irradiance at long-term scale. However, in the field of radiative cooling, there is currently no similar database available for reference since the normalized atmospheric radiation spectrum differs dramatically, especially within the atmospheric window. So, we intend to develop a long-term atmospheric spectral energy database based on the BG atmospheric radiation model and locally measured atmospheric radiation power to promote the performance prediction of radiative cooling.\u003c/p\u003e \u003cp\u003eHerein, the atmosphere wavelength region is first divided into three band regions, including Region I (3\u0026ndash;8 \u0026micro;m), Region II (8\u0026ndash;13 \u0026micro;m), and Region III (\u0026gt;\u0026thinsp;13 \u0026micro;m). According to the BG assumption, the atmosphere is a blackbody within bands of Regions I and III and the atmospheric radiative power can be calculated based on the transient local ambient temperature. Then, the atmospheric radiative power within Region II is determined by subtracting the above-calculated power from the measured atmospheric radiative power. So, the absorbed atmospheric radiative power can be expressed by\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$${P_{atm}}={\\alpha _{Region\\;I}} \\times {E_{Region\\;I}}+{\\alpha _{Region\\;II}} \\times {E_{Region\\;II}}+{\\alpha _{Region\\;III}} \\times {E_{Region\\;III}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eRegion I\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eRegion II\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eRegion III\u003c/em\u003e\u003c/sub\u003e are atmospheric radiative power within the band of Region I, Region II, and Region III, which can be introduced to the long-term atmospheric spectral energy database. \u003cem\u003eα\u003c/em\u003e\u003csub\u003e\u003cem\u003eRegion I\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eα\u003c/em\u003e\u003csub\u003e\u003cem\u003eRegion II\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eα\u003c/em\u003e\u003csub\u003e\u003cem\u003eRegion III\u003c/em\u003e\u003c/sub\u003e denote the effective absorptivity of the radiative cooler within the corresponding bands.\u003c/p\u003e \u003cp\u003eTo preliminary demonstrate such an idea, we conducted a demo based on Hefei meteorological data (Fig.\u0026nbsp;5a). We obtained the long-wave atmospheric radiative power data and universal meteorological data (e.g., ambient temperature and solar radiation power) based on field measurement (From March 2023 to September 2023). As shown in \u003cb\u003eFig.\u0026nbsp;5a\u003c/b\u003e, the variation in atmospheric radiative power is relatively small in the bands of Region I and Region III, and it changes consistently with changes in ambient air temperature. However, the atmospheric radiative power within the atmospheric window shows significant fluctuations, which is closely influenced by local meteorological conditions, such as dynamic humidity and cloud cover. Finally, the long-term maximum radiative cooling power of the broadband cooler is evaluated and presented in \u003cb\u003eFig.\u0026nbsp;5b\u003c/b\u003e, which provides a convenient way for performance evaluation of radiative cooling and will contribute to the development of passive radiative cooling. \u003c/p\u003e "},{"header":"4 Summary and conclusion","content":"\u003cp\u003eIn summary, this work propose an accurate long-term radiative cooling simulation method by developing a black-gray (B-G) body atmospheric radiation model based on the atmospheric spectral properties and the locally measured transient atmospheric radiative power. Validation experiments were carried out in various cities (Heife, Lhasa, and Haikou, China) under different weather conditions (clear and cloudy sky) and seasons (winter and summer) using spectral broadband and selective coolers. The results confirm that on a spatial scale the BG-RC simulation method exhibits city-level accuracy and is scalable for global applications; On a temporal scale, it allows for precise tracking at the minute level, thereby enhancing the accuracy of long-term simulation forecasts of radiative cooling. To further apply the proposed method and facilitate accurate long-term radiative cooling simulation analysis we introduce the concept of atmospheric spectral energy databases for the first time and provide a demo case study in Hefei, China. This approach allows for the rapid and straightforward assessment of the accurate long-term radiative cooling power potential, thereby fostering the widespread application of radiative cooling technology.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThis work was supported by the National Natural Science Foundation of China (NSFC 52106276 and 52130601), USTC Research Funds of the Double First-Class Initiative (YD2090002014), Young Elite Scientists Sponsorship Program by CAST (2023QNRC001), the research center for multi-energy complementation and conversion of USTC, and the USTC Center for Micro and Nanoscale Research and Fabrication.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003e\u0026lt;https://www.iea.org/\u0026gt; (\u003c/li\u003e\n\u003cli\u003eAo, X.\u003cem\u003e et al.\u003c/em\u003e Self-adaptive integration of photothermal and radiative cooling for continuous energy harvesting from the sun and outer space. \u003cem\u003eProc Natl Acad Sci U S A\u003c/em\u003e \u003cstrong\u003e119\u003c/strong\u003e, e2120557119, doi:10.1073/pnas.2120557119 (2022).\u003c/li\u003e\n\u003cli\u003eChen, Z., Zhu, L., Raman, A. \u0026amp; Fan, S. 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Unlike the mature methods for annual performance evaluation of solar energy harvesting, appropriate long-term radiative cooling performance simulation methods that can be used across different cities in the world are still missing. The main reason is that the spectral distribution of atmospheric radiation varies sensitively with sky status (e.g., cloudy, humid, etc.), while the normalized solar radiation spectrum is relatively stable regardless of weather conditions. Currently reported atmospheric radiation models in radiative cooling field, including the effective sky emissivity model and Modtran model, cannot simultaneously meet the spectral, spatial, and temporal requirements. Herein, we propose an accurate long-term radiative cooling simulation method by developing a novel black-gray (BG) body atmospheric radiation model based on the atmospheric spectral properties and the measured atmospheric radiative power. Experimental validation has been performed in cities with different climate styles and results show superior accuracy than reported methods. The proposed radiative cooling simulation method is well-suited for diverse environmental conditions, encompassing different weather conditions, climate styles, and seasons. It is also applicable for both spectral broadband and selective coolers, particularly for recently proposed selective coolers. To further apply the proposed method, we propose a concept of atmospheric spectral energy databases for the first time and provide a demo case study in Hefei, China, which aims to guide the accurate long-term radiative cooling simulation analysis.\u003c/p\u003e","manuscriptTitle":"A novel black-gray body atmospheric radiation model for accurate long-term radiative cooling performance simulation and analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-26 20:36:34","doi":"10.21203/rs.3.rs-4019641/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"6b131a36-dc0a-4f30-b933-933f4561bf30","owner":[],"postedDate":"March 26th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":29204154,"name":"Physical sciences/Energy science and technology/Renewable energy"},{"id":29204155,"name":"Physical sciences/Energy science and technology/Energy harvesting"},{"id":29204156,"name":"Earth and environmental sciences/Climate sciences/Atmospheric science"}],"tags":[],"updatedAt":"2025-02-25T10:10:10+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-26 20:36:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4019641","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4019641","identity":"rs-4019641","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}