Radiative cooling resource maps for the contiguous United States

Cooling loads for the built environment, including roads, commercial and residential buildings, factories, power plants, and data centers, accounts for a significant portion of the global energy consumption. Commercial buildings consume 40% of total energy in the European Union, with space cooling accounting for nearly half of the total power load.¹ In the United States, about 39% of the total energy consumed was spent on the residential and commercial sectors in 2017, with nearly 15% of the energy consumed for air conditioning purposes.^2,3 Overloaded transformer and transmission line failures due to peak loads during the daytime are often caused by air conditioning demands.⁴ Currently, most buildings use reversible heat pumps or powered air conditioning systems with associated high electricity loads for space cooling.¹ A promising technology for reducing the air conditioning load on the grid, especially for locations where the majority the heat load is from solar radiation, is the use of passive radiative cooling devices and paints. These engineered materials are optically selective for reflecting (shortwave) solar radiance while emitting strongly on the (longwave) infrared portion of the electromagnetic spectrum. Passive radiative cooling requires little to no electricity input,⁵ and can be deployed in a sustainable way due to modern photonic design of microstructured plastics and selective paints.⁶ 

The Earth's atmosphere has low absorptivity for electromagnetic waves within the atmospheric window band (longwave, approximately 8–13 μm). Thus, terrestrial objects with high emissivity within the atmospheric window band can be cooled by radiating longwave energy to outer space when directly exposed to the sky. This form of passive cooling is often referred to as “radiative cooling” and has been suggested for nighttime applications.^7–10 In the daytime, even a small value of solar absorptivity will offset the longwave emitting power of the surface, effectively heating the surface. To offset the large cooling demand during the daytime, particularly under direct sunlight, nanophotonic and polymeric photonic devices have been optically designed recently to exhibit near-zero solar absorptivity while retaining the highly emissive properties in the atmospheric window band.^3,6,^11–13 

In addition to the physical constraints for spectral optical properties of surfaces, the heat rejection from passive cooling devices is also limited by local meteorological conditions. The presence of water vapor and clouds increases the emissivity (and the absorptivity) of the atmosphere, with complementary reduction of the transmissivity through the atmospheric window, thus reducing the ability of surfaces to radiate to outer space.^4,14–16 The previous literature on modern radiative cooling devices reports cooling power efficiencies only at one or two testing sites during specific (and short) periods of time. For example, Zhai et al.⁶ report cooling rate ranges from 100 to 145 W m⁻² during two clear days in Cave Creek, Arizona, which could only be achieved under cloudless skies with dry atmospheric conditions, based on the analysis performed by Li and Coimbra.¹⁶ For mostly humid and/or frequently cloudy climates, the heat rejection capacity of passive devices is necessarily much lower. Hence, there is a need for radiative cooling resource potential maps in order to proper assess the effectiveness of these passive technologies. As recently pointed out by Vall and Castell,¹ very little research has been directed at evaluating the radiative cooling potential for diverse climates and regions. A summary of studies related to location-specific radiative cooling resources is presented in Table I (including this work for comparison). The literature found on this topic is limited, and none of the previous studies have used extensive and up-to-date meteorological measurements over continental regions.

The main goal of this work is to present radiative cooling resource maps for the contiguous United States (CONUS) and to examine diurnal and seasonal variability in order to propose optimal locations for deployment of passive radiative cooling technologies. Section II presents the theoretical foundations for calculating radiative cooling potentials. Section III presents the methodology for processing the meteorological data used in this work. The passive cooling resource maps are presented in Sec. IV, and conclusions follow in Sec. V.

For a body with temperature T_s facing the open sky (see Fig. 1), the broadband cooling power of the body is

where ν₁ = 2500 cm⁻¹ is the wavenumber cutoff between solar shortwave and atmospheric longwave irradiance; ε_s,lw is the monochromatic longwave emittance/absorptance of the body; I_b(ν, T_s) (W m⁻²sr⁻¹cm) is the monochromatic blackbody emissive intensity of the body, following Planck's law; J_sky (ν, T_a) (W m⁻²cm) is the monochromatic sky radiosity at ambient temperature T_a (detailed in Sec. II B); α_s,sw is the monochromatic solar shortwave absorptance of the body; q_sun (ν) (W m⁻²cm) is the spectral solar irradiance on the body, and h_c (W m⁻² K⁻¹) is the heat transfer coefficient considering both convective and conductive heat losses.

Figure 2 plots the spectral sky radiosity and solar irradiance for a cloudless atmosphere using previously developed radiative models.^25,26 In the longwave spectrum from 8 to 13 μm, the cloudless atmosphere has a smaller radiosity than the blackbody emissive power of terrestrial objects, making the first term in Eq. (1) positive. Therefore, radiative cooling is mostly via this spectral band, the so-called atmospheric window.

When using spectrally averaged properties, the cooling power is

where σ = 5.67 × 10⁻⁸ W m K⁻⁴ is the Stefan-Boltzmann constant and ε_sky is the effective emissivity of the sky, which depends on local atmospheric conditions.

To achieve radiative cooling power during both the daytime and the nighttime, radiative coolers need to be highly reflective in the shortwave solar spectrum while highly emissive in the longwave spectrum. For example, Zhai et al.⁶ developed a material that has a spectrally averaged solar absorptance of 0.04 and a longwave emittance of 0.93. For maximum radiative cooling power, the radiative cooler should have reflectance approaching unity (absorptance approaching zero) in the solar spectrum and emittance approaching unity in the longwave spectrum. In addition, convection and conduction heat loss should be suppressed by means of insulation and/or engineered honeycomb to suppress the onset of fluid motion.²⁷ Ideally, the maximum cooling power (cooling potential) is

When the passive cooling surface is kept at temperature T_s = T_a (to further minimize convective and conductive losses), the cooling power flux at the surface is

with cooling power increasing with decreasing values of sky emissivity. The high water vapor content and the presence of clouds tend to increase the sky emissivity (detailed in the Sec. II B), thus decreasing the cooling potential.¹⁶ 

A spectrally resolved two-flux radiative model was developed to compute spectral longwave radiative transfer (wavelength greater than 4 μm) for the earth-atmosphere system under clear skies with different water vapor contents.²⁵ As shown in Fig. 2, the clear sky has a transparent window from 8 to 13 μm, through which radiative cooling is possible. As discussed above, the transparency of this window decreases with the increasing water vapor content¹⁶ and with the presence of clouds. The model allows us to quantify these effects on the passive cooling potential for ideal surfaces.

Water clouds are modeled using similar methods as used for aerosols. Each water droplet is assumed to have a spherical shape, and thus, the absorption and scattering efficiencies of droplets are calculated using Mie theory results,²⁵ with the refraction index of water retrieved from the study by Hale and Querry.²⁸ The absorption and scattering coefficients as well as the asymmetry factors of clouds are further calculated by integrating the efficiencies over a model droplet size distribution.²⁹ The size distribution of droplets in clouds is assumed to follow a Gamma distribution^30–33 

where r_e and σ_e are the mean effective radius and variance, respectively. Here, we assume the mean effective radius of r_e = 10.0 μm and σ_e = 0.1, as suggested in the studies by Barker et al. and Walther et al. and used in several geoestationary satellite products.^32,33 Miles et al. suggested that an effective radius of 5.4 μm may better represent continental clouds. We use the smaller effective radius distribution to assess the uncertainty of the modeled cooling potential (see Fig. 5). The spectral dispersion k often used to represent the spread of the droplet size (instead of σ_e) is defined as $k = ( 1 / σ e − 2 ) − 1 / 2$⁠. When σ_e = 0.1, k = 0.354, which is a typical value for both marine and continental clouds.³¹ The size distribution of water droplets is shown in Fig. 3(a).

Clouds are considered as layers with a predefined Cloud Optical Depth (COD) at 497.5 nm defined as COD = κ_e,cld ΔH_c, where κ_e,cld (cm⁻¹) is the extinction coefficient of clouds and ΔH_c (cm) is the thickness of clouds. The spectral optical depth, single albedo, and asymmetry factors of clouds are shown in Fig. 3(b) for COD = 1.0.

The extinction coefficient, single albedo, and asymmetry factor of each atmospheric layer containing clouds are

where the asymmetry factor e_g is the weighted sum for the mixture of aerosols and clouds using scattering coefficients as the weights. The scattering is then treated as isotropic using the δ-M scaling method,³⁴ and the monochromatic fluxes are solved using the procedures outlined in the study by Li et al.²⁵ 

For partly cloudy skies, the spectral downwelling longwave irradiance (sky radiosity) calculated from the model is expressed as

where ν is the wavenumber (cm⁻¹), T_a (K) is the ambient air temperature at the screening level (10 m above the surface), CF is the cloud fraction, and the subscripts “c” and “oc” represent the clear skies and overcast skies, respectively. Then, the spectral cooling power of an ideal cooler at ambient temperature is calculated from Eqs. (1) to (4). Figure 4 shows the spectral longwave cooling power for T_s = T_a = 294.2 K and ϕ = 70%. Clearly, the cooling power decreases when more clouds are present in the atmosphere because clouds also “block” the atmospheric window. Figure 5 shows the broadband cooling potential with respect to both COD and cloud base temperature (CBT) when CF = 1.0. The ambient is at 294.2 K and ϕ = 70%. The cooling power for clear skies at the nominal conditions described above is 71.9 W m⁻² for the Air Force Geophysics Laboratory (AFGL) midlatitude summer temperature profile, and it decreases with increasing COD and CBT. Different temperature profiles (corrected to match the ambient conditions) introduce less than 5 W m⁻² deviations to the cooling power potential. When the effective radius of clouds is assumed to be 5.4 μm, the cooling power is increased by less than 10 W m⁻² when compared to the cooling power calculated with r_e = 10 μm.

If detailed atmosphere temperature, pressure, and concentration vertical profiles are specified, the sky radiosity can be calculated precisely using the radiative transfer model. If only ambient temperature and relative humidity are given, empirical expressions of effective sky emissivity can be used. The empirical all-sky effective emissivity of the sky for the contiguous United States has been recently determined to be³⁵ 

where ε_sky,c is the effective sky emissivity under clear skies, ϕ is the ambient relative humidity, and P_w (Pa) is the ambient water vapor partial pressure. From local measurements of ambient temperature, relative humidity (or dew point), and cloud fraction, the effective sky emissivity and radiative cooling potentials can be calculated. The mean bias error found by using Eq. (8) to estimate the Downwelling Longwave Flux (DLW) is −4.94 W m⁻² (Ref. 35), which implies that the uncertainty in estimating seasonally and annually averaged cooling potentials is of the order of 5 W m⁻².

Local meteorological measurements were retrieved from the National Oceanic and Atmospheric Administration (NOAA) Automated Surface Observing System (ASOS) network via direct File Transfer Protocol (FTP) access.³⁶ A total of 1681 stations across the contiguous United States were used to collect data for the year 2017 (see Fig. 6 for the spatial distribution of the stations). Most stations considered in this work reported a full year worth of data, with some reporting incomplete or low quality data periods, and those periods were removed from consideration.

Each station records intra-hour measurements of meteorological variables, including air temperature (T_a), dew point (T_d), and cloud fraction (CF). Only measurements designated as having passed all quality control checks (based on QC codes provided by ASOS) were used. ASOS data have multiple entries of cloud fraction values based on cloud types, and the CF values used in this work are the average of all entries.

From air temperature T_a and dew point T_d, the water vapor partial pressure P_w and relative humidity ϕ are calculated using Magus-like expressions³⁷ 

where P₀ = 610.94 Pa, c_T = 17.625, and T₀ = 243.04 °C. Note that in the above two equations, temperatures T_a and T_d have units of degrees Celsius.

The radiative cooling potential is then calculated from T_a, P_w, ϕ, and CF using Eqs. (4) and (8) for each entry. Data are separated into the four seasons according to the timestamps of the entries. Timestamps are also used to calculate the solar zenith angles of the entries to separate them into daytime or nighttime periods. Clear sky periods are determined when the cloud fraction equals zero. With this, the overall annual, annual daytime, and nighttime and seasonal averages of radiative cooling potential across CONUS are computed and interpolated for mapping.

An inverse distance weighting (IDW) spatial interpolation methodology is used to derive variables (air temperature, water vapor partial pressure, and ratio of clear sky period and cooling potential) in order to form a uniform latitude-longitude grid. The variable values for nonstation locations are interpolated using values from all stations³⁸ 

where N is the number of stations; d_i is the geographic distance between a station i and the current location; Z_i is the variable value at a station i, and w(d_i) are weighting functions that inversely depend on d

where p is a positive power factor set to unity in this work.

After the IDW interpolation, 2-dimensional gradients at each grid point are calculated according to latitude and longitude values to determine the degree of similarity to adjacent points. Extreme (top 2%) gradients are interpreted as resulting from potentially faulty data. These outliers are replaced with averages for adjacent points.

Table II presents the spatial range and mean of annually and seasonally averaged ambient temperature T_a, water vapor partial pressure P_w, and ratio of clear sky periods R_c and radiative cooling potential q_cool,ideal over the contiguous United States (CONUS). The average radiative cooling potential for the entire CONUS area is 50.5 W m⁻².

The total area of CONUS can be divided into four census regions: the West, Midwest, South, and Northeast.³⁹ The following discussion uses this common geographic division when referring to specific regions.

Figure 7 shows a map of annually averaged T_a, P_w, R_c, and q_cool,ideal. Temperature decreases with the increasing latitude. The West is the driest as indicated by P_w, while the South is more humid. The Southwest has over 50% clear sky periods throughout the year, while the Southeast has less than 30%. Since radiative cooling is most effective in dry and cloudless conditions, the Southwest has an annual average radiative cooling potential of over 70 W m⁻². The other regions have lower than 50 W m⁻² cooling potential, with the South having the lowest. Note that the cooling potential is the maximum possible cooling rate under given meteorological conditions. Absorption of solar irradiance and convective and conductive heat loss all reduce the cooling rate of radiative coolers as they operate.

Figures 8 and 9 show the maps of annually averaged variables during the daytime and nighttime, respectively. The water vapor partial pressure and ratio of clear sky periods show little diurnal variation, while ambient temperature is around 6 °C higher during the day. Therefore, the cooling potential is around 5 W m⁻² higher during the day than the night, which matches the cooling demands for most residential and commercial buildings. According to the longwave irradiance distribution within the atmosphere,¹⁶ ambient air is primarily heated by the Earth's surface, which itself is heated by absorbing solar irradiance during the day. If the ground is covered by passive coolers (objects highly reflective in the solar spectrum), the ambient air is heated to a lesser degree, reducing the ambient temperature during the day. With this, the deployment of passive coolers decreases diurnal variations in temperature.

Figures 10–13 show maps of seasonally averaged variables in the spring (March-April-May), summer (June-July-August), fall (September-October-November), and winter (December-January-February). Duringthe spring, Arizona and New Mexico experience dry and generally cloudless weather, yielding a high cooling potential of around 80 W m⁻². California, Nevada, Utah, and Colorado have potentials around 60–70 W m⁻². The ambient temperature for the above-mentioned states is around 10–15 °C such that radiative cooling is expected to fulfill most of the cooling demands from residential sectors. In contrast, the South has an ambient temperature of around 20 °C and a cooling potential of around 40–50 W m⁻² such that additional methods of cooling are necessary. During the summer, the West is dry and mostly clear, yielding a cooling potential above 70 W m⁻². Nevada and Utah have the highest potential of around 80 W m⁻². The South experiences generally humid and cloudy summers, with a low cooling potential of around 30 W m⁻². Therefore, radiative cooling during the summer is most promising in the West. During the fall, the spatial distribution of radiative cooling potential is similar to that in the spring, with radiative cooling being effective primarily in the Southwest. During the winter, the water vapor content in the atmosphere (represented by P_w) is low due to lower air temperature. Consequently, the Southwest has a cooling potential of around 60 W m⁻², while other regions have potentials of around 40–50 W m⁻². To prevent unnecessary cooling and/or the coolers from icing over during the winter, they should be covered.

Radiative coolers are optically designed to reject heat to outer space through the longwave atmospheric window spectral band (8–13 μm). The cooling rates of radiative coolers are found to be dependent not only on their optical properties but also on local meteorological conditions. The presence of water vapor and clouds reduces the “transparency” of the atmospheric window, thus reducing the cooling potential (capability) of the coolers. This work presents radiative cooling resource (potential) maps for the contiguous United States to assist in the design and deployment of such cooling devices. The cooling potential of a cooler is defined to be its maximum possible cooling rate, assuming its optical properties are ideal and neglecting convective/conductive heat losses. For real (nonideal) surfaces, the cooling power is smaller than the estimates in this work due to nonzero solar absorption, nonblackbody longwave emissive power, and nonzero convective heating. Therefore, the estimates in this work represent upper bounds for passive cooling rates. It is also relevant to note that the radiative cooling resource maps for the contiguous United States presented here are generated using extensive meteorological data collected from 1681 weather stations over the entire year of 2017. Diurnal and seasonal variations of cooling potentials are also analyzed below.

Annually, the Southwestern United States is dry and mostly clear, resulting in an average radiative cooling potential of over 70 W m⁻² and making it the region where radiative cooling is most effective. In contrast, the South has the lowest cooling potential of around 30 W m⁻² due to local humid and cloudy meteorological conditions. Convective/conductive heat loss and/or as little as 5% solar irradiance absorption lead to ineffective radiative cooling in the South. Additionally, the water vapor content in the atmosphere and clearness of the sky are weaker functions of time of day, as opposed to ambient air temperature, which is always higher during the day. Therefore, cooling potentials are around 5 W m⁻² higher during the daytime than during the nighttime.

For the spring (March-April-May) and fall (September-October-November), Arizona and New Mexico exhibit cooling potentials around 80 W m⁻², due to dry and cloudless conditions. Surrounding states such as California, Nevada, Utah, and Colorado have potential ranging from 60 to 70 W m⁻². Other states exhibit cooling potentials about 10 W m⁻² lower. During the summer, the entire West reaches cooling potential values over 70 W m⁻², again due to high ambient temperatures, low humidities, and clear skies. The South, in contrast, has a cooling potential lower than 40 W m⁻² due to humid and cloudy summer climate. Most regions of CONUS during the winter are generally dry and clear, with cooling potentials of around 50 W m⁻². To prevent over-cooling and/or icing during colder weather, cooling devices must be properly stored or covered, which also diminishes their range of practical applications.

In summary, passive radiative cooling has much potential in the western region of CONUS, due to the prevalent hot and dry weather in the region. Just as with swamp or evaporative coolers, but due to different physical mechanisms, the effectiveness of passive radiative cooling devices is greatly reduced for hot and humid conditions. Unfortunately, those are the conditions that often demand very high power loads for air conditioning.

The authors gratefully acknowledge partial support of the U.S. Department of Energy's Office of Energy Efficiency and Renewable Energy (EERE) under Solar Energy Technologies Office (SETO) Agreement No. EE0008216.