Global Radiative Sky Cooling Potential Adjusted for Population Density and Cooling Demand

: Thanks to recent advances in nanophotonics and scalable manufacturing of metamaterials, radiative sky cooling has emerged as a “self-reliant” cooling technology with various potential applications. However, not every region across the globe is well suited for the adoption of radiative cooling technologies, depending on the local climate, population density, cooling demand, air conditioning saturation, economic prosperity, etc. Because the atmospheric downward longwave radiation, especially the portion from the atmospheric window (8–13 µ m), is substantially affected by weather conditions, the performance of a well-designed radiative cooler can be vastly different across regions and seasons. Here, we ﬁrst map the global radiative sky cooling potential in the form of net cooling power density. We then further evaluate it based on the global population density and cooling demand. In terms of the adjusted potential, we show that geographically and demographically “transitional” regions, located between wet and dry climates as well as sparsely and densely populated regions, are better suited for the adoption of radiative cooling technologies because of their temperate climate and moderate population density. Even in densely populated and humid regions, the cumulative impact and other accompanying beneﬁts must not be ignored. layer being the dominant source. Longwave radiation emitted by the surface is mostly trapped by the atmosphere, with only a fraction reaching the deep space mainly through the atmospheric window (8–13 µ m).


Introduction
Radiative sky cooling refers to the process of passively cooling a sky-facing object by maximizing its net emission of longwave thermal radiation and minimizing its absorption of downward shortwave radiation. As illustrated in Figure 1, this process takes advantage of the atmospheric window (8-13 µm) [1] and the extremely low temperature of the universe, i.e., the deep space at~2.7 K [2]. When a horizontally placed surface with high emissivity, preferably in the atmospheric window, emits more radiation than it receives from the sun and the atmosphere, its temperature can drop below the ambient temperature [3]. The Earth itself is the largest radiative cooling object, manifesting its subambient cooling potential through occasional occurrences of dew or frost in some clear-sky mornings [4]. This self-cooling capability of sky-facing surfaces gives the inspiration that a highly solar-reflective and yet highly infrared-emissive object can relentlessly maintain its coolness even during the day.
Significant research progress has been made in recent years to demonstrate daytime sub-ambient radiative sky cooling through materials design [3,[5][6][7][8][9][10][11] and systems engineering [12][13][14][15][16]. Radiative sky cooling can be an attractive complement or even an alternative to traditional cooling technologies such as power-intensive air conditioning [15,[17][18][19][20] and Figure 1. A schematic of radiative heat exchanges between a sky-facing radiative cooling surface and the atmosphere. On the right is the illustration of a complex set of atmospheric profiles, showing the altitude-dependence of various properties such as pressure, temperature, and water vapor. The surface absorbs longwave radiation coming from all altitudes of the atmosphere, with the lowest atmospheric layer being the dominant source. Longwave radiation emitted by the surface is mostly trapped by the atmosphere, with only a fraction reaching the deep space mainly through the atmospheric window (8-13 µm).

Radiative Cooling Model
Creating a global map of radiative cooling potential requires a radiative heat transfer model that is accurate, comprehensive, and yet readily applicable. Although spectral radiative cooling models have been used to estimate the net cooling power of radiative coolers that agrees with specific experimental measurements [3,[48][49][50], there are still misunderstandings and unrealistic practices in the modeling of radiative sky cooling. For example, a common practice is the use of ambient weather conditions such as the surface air temperature and humidity instead of the altitude-dependent atmospheric profiles to eval- Figure 1. A schematic of radiative heat exchanges between a sky-facing radiative cooling surface and the atmosphere. On the right is the illustration of a complex set of atmospheric profiles, showing the altitude-dependence of various properties such as pressure, temperature, and water vapor. The surface absorbs longwave radiation coming from all altitudes of the atmosphere, with the lowest atmospheric layer being the dominant source. Longwave radiation emitted by the surface is mostly trapped by the atmosphere, with only a fraction reaching the deep space mainly through the atmospheric window (8-13 µm).
However, even for a well-designed radiative cooler, how much benefit it eventually brings depends on the local climate. In this regard, studies have been conducted to theoretically and/or experimentally investigate the effect of weather conditions (mainly temperature and humidity) on radiative sky cooling [13,[43][44][45]. A broader understanding of radiative cooling potential is desirable for all prospective regions across the globe to evaluate its feasibility [46,47]. More importantly, the seasonal anomaly of cooling potential, population density, and global cooling demand are important factors that determine the applicability and effectiveness of radiative sky cooling. For example, dry regions tend to have high radiative cooling potential but low population density, diminishing the interest in implementing radiative cooling in these regions. However, humid regions tend to have low radiative cooling potential but high population density, again weakening the interest in radiative cooling if land availability and individual impact become a concern. In this work, we create global maps of radiative sky cooling potential with considerations of weather conditions, seasonal cooling anomaly, global population density, and cooling demand.

Radiative Cooling Model
Creating a global map of radiative cooling potential requires a radiative heat transfer model that is accurate, comprehensive, and yet readily applicable. Although spectral radiative cooling models have been used to estimate the net cooling power of radiative coolers that agrees with specific experimental measurements [3,[48][49][50], there are still misunderstandings and unrealistic practices in the modeling of radiative sky cooling. For example, a common practice is the use of ambient weather conditions such as the surface air temperature and humidity instead of the altitude-dependent atmospheric profiles to evaluate the atmospheric downward longwave radiation. This practice of treating the atmosphere as a solid surface appears counter-intuitive because, as illustrated in Figure 1, the downward longwave radiation comes from various altitudes of the atmosphere with different tem- peratures, pressures, and water vapor contents. Since the ambient temperature represents the maximum temperature of the lowest and densest layer of the atmosphere, we can easily conclude that using only the ambient temperature (as opposed to the atmospheric temperature profile) leads to an overestimated atmospheric downward radiation. The temperature plays two roles here: a direct role in Planck's blackbody emission to determine the atmospheric downward radiation, and an indirect role in limiting the atmospheric precipitable water (PW) [13,51,52]. Here, precipitable water is defined as the thickness of the atmospheric water vapor when condensed into liquid water. Precipitable water in the atmosphere dynamically changes throughout a day depending on the temperature and relative humidity, thus affecting the atmospheric transmittance or its effective emissivity, especially in the atmospheric window of 8-13 µm [3]. The atmospheric effective emissivity may be better defined as (1-Transmittance) because the atmosphere is not a solid surface and does not have uniform density, composition, and temperature across its thickness. Therefore, the accuracy of temperature and precipitable water in the model used eventually affects the validity of the atmosphere spectral emissivity and thus the downward longwave radiation. We briefly discuss below why and when using only surface air temperature and relative humidity is acceptable.
Under clear-sky conditions, downward longwave monochromatic radiation received at a given altitude z in the sky and a zenith angle θ can be calculated by integrating radiation from all altitudes above this altitude z [51]. Considering the attenuation of radiation as it travels through the atmosphere, it is expressed as where ρ(ξ) and T(ξ) are respectively the altitude-dependent atmospheric density and temperature profiles, k λ is the wavelength-dependent absorption coefficient of atmospheric species, and E λ (T) is the blackbody spectral radiance. The above equation satisfies the boundary condition that at the top of the atmosphere downward longwave radiation is zero; that is, P λ,θ,z=∞ = 0. The atmospheric radiation absorbed by a radiative cooling surface on the Earth's surface (z = 0) under clear-sky conditions can be then obtained by integrating over all altitudes, directions, and wavelengths as where ε s (λ, θ) is the spectral and angular emissivity or absorptivity of the radiative cooling surface. Although the above equations accurately describe the total atmospheric downward radiation absorbed by a radiative cooling surface under clear-sky conditions, it requires well-defined atmospheric profiles for temperature, species densities (HO 2 , O 2 , CO 2 , O 3 , N 2 O, CH 4 , etc.), spectral absorption coefficients of species, etc., at each geographical location [51,52]. Among these parameters, the temperature and precipitable water vapor are the most dynamic, whereas other parameters such as O 2 and CO 2 densities are relatively stable over short periods. Complex atmospheric profiles can be defined, and atmospheric downward longwave radiation can be solved with specialized tools such as MODTRAN [52,53].
In recent studies, as an approximation by treating the atmosphere as a solid surface, the ambient temperature (T amb ), rather than the altitude-dependent temperature profile, has often been used. In this simplified case, where the effective atmospheric spectral emissivity ε atm can be evaluated from the transmittance of the atmosphere as a function of various compositions, especially PW. In case PW is not directly known, it may be estimated from the ambient temperature (T amb ) and the specific humidity (SH) or relative humidity (RH). Even though PW is technically an integrated water vapor over the altitude, both T amb and RH are specific to the near-surface ambient [13,54]. That is, where SH is the surface air specific humidity (g/kg), p amb is the near-surface ambient pressure (Pa), the surface air ambient temperature T amb has the unit of • C, PW has the unit of mm, and a and b are constants. Here, the value of coefficient a mostly varies within 2~2.5 depending on the altitude and sky clarity based on our regression analyses of the US weather data. Meanwhile, the value of b is of less significance compared to the value of generally observed precipitable water. Upward radiation from the radiative cooling surface working at the ambient temperature, P sur f ace (T amb ), can be readily calculated using its spectral emissivity [13]. Solar absorption by the surface, P solar = α solar P sun , should be taken into consideration for daytime radiative cooling. The net cooling power is then expressed as P net,rad = P sur f ace (T amb ) − P atm,z=0 − P solar .
The above model is applicable under clear-sky conditions. However, clouds can have substantial effects on the net cooling power of a cooler, especially under humid tropical and subtropical climates. The downward radiation from clouds varies significantly depending on the cloud base height, base temperature, thickness, and properties [55]. As only the global cloud cover fraction data is available in this work, we consider the cloud cover effect on the global radiative cooling potential by following the evaluated approaches from Ref. [56]. By parameterizing the atmospheric downward longwave radiation received at the Earth surface into clear-sky and cloudy-sky two components, P atm,z=0 is written as P atm,z=0 = (1 − f )P atm,Z=0,clear + f P atm,Z=0,cloudy , where f is the cloud cover fraction. P atm,Z=0,cloudy is evaluated using the method described below.
Regarding the downward radiation from clods, two major uncertain factors are cloud temperature and cloud emissivity. Martin et al. [57]. argued that the cloud factor (different from the cloud cover fraction) is expected to be small for high (cold) clouds and to be near unity for low (warm) clouds, and that it is exponentially proportional to the cloud base temperature or cloud base height. Since we have only cloud cover fraction data on the global scale, we argue in a similar manner next. (i) If the sky is completely covered by clouds ( f = 1), the cloud base is near the Earth's surface and acts as a black body (T cloud ≈ T amb and ε cloud = 1). (ii) If the sky is partially covered by clouds ( f < 1), the cloud base tends to be higher and colder, and the cloud cover fraction is exponentially proportional to the cloud base temperature, where ∆T o is a reference temperature difference. We still assume the cloud emissivity is unity since the main component of clouds is water crystals that can have an emissivity of 1 even in the atmospheric window of 8-13 µm [58]. Targeting the least overall error across the globe, we assume ∆T o = 10 • C (see Section 3.1). Therefore, the cloud base temperature may be evaluated from the cloud cover fraction as Atmosphere 2021, 12, 1379 5 of 20 The net cooling power with the cloud effect is then Above, when the cloud cover fraction approaches 0, the cloud temperature is allowed to be very low since f σT 4 cloud also approaches zero. When the cloud cover fraction is 1, the cloud temperature is the same as the ambient temperature.
Further uncertainties in the net cooling power may be introduced by insufficient temporal resolutions of the ambient temperature, precipitable water, and cloud cover fraction datasets. The uncertainties in the net cooling power associated with model simplification, temporal resolution, and data inaccuracies are discussed in Section 3.1.

Effective Atmospheric Emissivity
The clear-sky effective atmospheric spectral emissivity was modeled using a complete set of atmospheric profiles. Among the atmospheric compositions, CO 2 , O 2 , O 3 , N 2 O, CH 4, and many other gases including refrigerants are relatively constant, whereas PW changes over the range of 2.5~60 mm [59,60]. Default profiles of temperature and water vapor column density provided within MODTRAN are shown in Figure 2a,b, respectively, for the mid-latitude summer atmosphere model. By taking advantage of the relatively constant lapse rate at a given latitude and across a layer of the atmosphere, various temperature profiles were generated by shifting the default temperature profiles, e.g., as in Figure 2a. Specifically, atmospheric profiles at various latitudes and temperatures were generated by modifying 5 default atmospheric models in MODTRAN (tropical, mid-latitude summer, mid-latitude winter, sub-arctic summer, and sub-arctic winter). Default atmospheric models were extracted as text files, which were then edited with new precipitable water values and new shifted temperature profiles. The modified atmospheric profiles were then put back into MODTRAN to carry out the computations of necessary data such as atmospheric spectral transmittance and downward longwave radiation. We modeled the effects of temperature, precipitable water, and zenith angle on the effective atmospheric spectral emissivity by using altitude-dependent atmospheric profiles with MODTRAN [52,53]. As shown in Figure 3a, the atmospheric temperature profile (represented by the ambient temperature) does not have a substantial effect on the effective atmospheric emissivity. However, as shown in Figure 3b, precipitable water (PW) significantly affects the effective atmospheric emissivity, especially in the atmospheric window (8-13 µm). Since the atmospheric window is essential for the upward radiation from a radiative cooling surface into the deep space, an atmosphere with high precipitable water content essentially traps this upward radiation from the surface and amplifies the greenhouse effect [61,62]. Figure 3c shows that the effective atmospheric spectral emissiv- Precipitable water is directly defined by specifying values in MODTRAN, which is then scaled back to H 2 O column density profiles as in Figure 2b. In case the relative humidity exceeds 100% in an atmospheric layer, MODTARN places the excess water vapor in other layers of the atmosphere. Under actual atmospheric conditions, the atmospheric temperature and precipitable water can be closely related [14,43]. For instance, cold weather in winter tends to have low precipitable water content, and hot weather in summer tends to have high precipitable water content. Hot and humid weather, of course, has a very high precipitable water content [59]. A relation between precipitable water, ambient temperature, and relative humidity can be obtained based on experimental observations and thermodynamic formulations [13,54]. Based on Equation (4) and assuming a = 2.15 (for 1600 m elevation in Boulder, CO) [13], Figure 2c shows that precipitable water increases with rising ambient temperature or relative humidity.
In modeling, other atmospheric profiles such as pressure and chemical compositions except for PW were based on standard profiles as they remain relatively constant over time and so are their effects on the atmospheric emissivity. Indeed, those profiles can also be modified to define a specific atmosphere, which is beyond the scope of our work.
We modeled the effects of temperature, precipitable water, and zenith angle on the effective atmospheric spectral emissivity by using altitude-dependent atmospheric profiles with MODTRAN [52,53]. As shown in Figure 3a, the atmospheric temperature profile (represented by the ambient temperature) does not have a substantial effect on the effective atmospheric emissivity. However, as shown in Figure 3b, precipitable water (PW) significantly affects the effective atmospheric emissivity, especially in the atmospheric window (8-13 µm). Since the atmospheric window is essential for the upward radiation from a radiative cooling surface into the deep space, an atmosphere with high precipitable water content essentially traps this upward radiation from the surface and amplifies the greenhouse effect [61,62]. Figure 3c shows that the effective atmospheric spectral emissivity increases as the air mass increase with the zenith angle, which is also much more significant in the atmospheric window.

Radiative Cooling Potential
We modeled the clear-sky atmospheric downward radiation, P atm,z=0,clear , and the net cooling power of an "ideal black" radiative cooler by using both ambient-temperaturebased and temperature-profile-based approaches. The "ideal black" radiative cooler here refers to a solid surface with 95% solar reflectivity in the range of 0.3-2.5 µm and 100% infrared emissivity at all other wavelengths, whereas an "ideal selective" radiative cooler has 100% emissivity in the atmospheric window and zero emissivity at all other wavelengths. The reason for choosing the "ideal black" radiative cooler is that it has better cooling performance when the surface temperature is higher than or the same as the ambient temperature [3,63]. In the simplified ambient-temperature-based approach, the atmosphere is treated as a solid surface with a given temperature and spectral emissivity. Based on our trials, assuming the cooler surface temperature is the same as the ambient, the simplified approach gives the least error when we use T amb , which is the highest in the densest atmospheric layer, and the zenith-0 • atmospheric emissivity, which is the lowest over the hemisphere.
For the ambient temperature range of 0-40 • C and the precipitable range of 2.5-60 mm, we compare in Figure 4 the results from the ambient-temperature-based and temperatureprofile-based approaches. The direct observation from the contour lines in Figure 4a is that net cooling power goes up with increasing T amb and decreasing PW in the atmosphere, although the rate depends on the specific T amb and PW. It can be easily inferred that hot but dry regions can benefit the most from radiative cooling, although humid and hot regions can still see benefits to a much lesser extent. No solar absorption is included in Figure 4a as it can be simply subtracted.  Absolute and relative errors associated with the net cooling power are given in Figure 4b,c, respectively. Negative and positive signs are retained to highlight overestimation and underestimation. The absolute error in the net cooling power is mostly within ±5 W/m 2 , with occasional overestimation of 10 W/m 2 or more. The corresponding relative error is mostly within ±10%, rarely with 20% underestimation. Reviewing Figure  2c, exceptionally high precipitable water (e.g., PW > 40 mm) only occurs at high ambient temperatures and very high humidity levels (e.g., T amb > 40 • C and RH > 70%,). Therefore, for frequently observed weather conditions, calculating radiative cooling power using the simplified ambient-temperature-based approach is expected to result in less than 5% relative error for clear-sky conditions. A lookup table (Table 1) of the baseline net cooling power was also created for the "ideal black" radiative cooler as a function of T amb and PW when the cooler surface temperature is the same as the ambient temperature. In this table, the intervals of T amb and PW are 2.0 • C and 2.5 mm, respectively. Solar absorption is not included in the table as it can be easily extracted from the baseline net cooling power if necessary. If 5% solar absorption is also included, the modeled cooling power values in Figure 4a and Table 1 agree reasonably well with previously reported experimental data [13,64].

Global Datasets of Weather, Population Density, and Cooling Degree Days
To create global radiative cooling potential maps, we collected global monthly weather datasets of the most recent five years (2015-2019), global population density, as well as global cooling degree days from climate observation and data publishing sources (see Table 2 for the data information). The datasets of air temperature at 2 m above the surface and the datasets of horizontal downward solar irradiance were obtained from the European Commission's Copernicus Climate Change Service [65]. In addition, the datasets of observed downward longwave radiation from the atmosphere were also obtained from Ref. [65]. to evaluate errors in the modeled cooling potential. The atmospheric precipitable water datasets and cloud cover fraction datasets were obtained from the NASA Earth Observatory [66]. 2015 global population density data were obtained from the NASA Socioeconomic Data and Applications Center [67]. The datasets of global monthly cooling degree days were obtained from PANGAEA-Data Publisher for Earth & Environmental Science [68,69]. The datasets were interpolated, if necessary, to have a spatial resolution of 2.5 min, approximately equivalent to 4.6 km at the Equator.

Global Radiative Cooling Potential
Using the monthly mean weather datasets, the radiative cooling potential of the globe was computed for the "ideal black" radiative cooler with 5% solar absorptivity and working temperature the same as the ambient temperature. Figure 6 shows global maps of the annual mean upward longwave radiation from the cooler, downward longwave radiation from the atmosphere, and the net cooling power. Here, the upward and downward longwave radiations are integrated over the wavelength range of 2.5-100 µm. The downward longwave radiation from the atmosphere also includes cloud cover effects. The net cooling power density includes the upward and downward longwave radiations, as well as the absorbed solar irradiance.
The upward radiation map in Figure 6a resonates well with the temperature map, showing the "ideal black" cooler emits as much as 500 W/m 2 into the sky in hot regions. Note that the upward radiation at a given location differs if the cooler works at a temper- Precipitable water refers to the thickness of the atmospheric water vapor when condensed into liquid water. Only data for land surfaces are presented.

Global Radiative Cooling Potential
Using the monthly mean weather datasets, the radiative cooling potential of the globe was computed for the "ideal black" radiative cooler with 5% solar absorptivity and working temperature the same as the ambient temperature. Figure 6 shows global maps of the annual mean upward longwave radiation from the cooler, downward longwave radiation from the atmosphere, and the net cooling power. Here, the upward and downward longwave radiations are integrated over the wavelength range of 2.5-100 µm. The downward longwave radiation from the atmosphere also includes cloud cover effects. The net cooling power density includes the upward and downward longwave radiations, as well as the absorbed solar irradiance.
The upward radiation map in Figure 6a resonates well with the temperature map, showing the "ideal black" cooler emits as much as 500 W/m 2 into the sky in hot regions. Note that the upward radiation at a given location differs if the cooler works at a tempera-Atmosphere 2021, 12, 1379 11 of 20 ture different from the ambient temperature, or if the cooler is not "ideal black". However, the atmospheric downward radiation map in Figure 6b is the result of combined effects from the ambient temperature, precipitable water, and cloud cover, meaning hot and humid regions are subject to the most downward radiation of more than 400 W/m 2 from the atmosphere. Here, all atmospheric downward radiation is absorbed by the "ideal black" radiative cooler. The atmospheric downward radiation map agrees well with previous reports [71][72][73].  As shown in the annual mean net radiative cooling potential map (Figure 6c), hot and dry regions are the ideal places for the application of radiative cooling as the cooling potential is in the higher range of 80-110 W/m 2 . By comparison, hot and humid regions have substantially lower radiative cooling potential in the range of only 10-40 W/m 2 . Based on the varying degrees of radiative cooling potential across different regions, hot and humid regions may require a much larger radiative cooling area than hot and dry regions to generate the same amount of cold. Consequently, the cost-effectiveness of radiative cooling varies significantly across the globe. If other aspects, such as population density, cooling demand, air conditioning adoption, air pollution, city skylines, etc., are considered, the radiative cooling potential and its cost-effectiveness across the globe can be even more vastly different. Note that the radiative cooling potential map in Figure 6c is an update to the clear-sky cooling potential map in Ref. [47] by including the cloud cover effects.
The cloud cover effects are included in the above results, even though the downward longwave radiation from clouds is subject to significant uncertainties. Precipitable water and cloud cover are closely correlated [66], although clouds tend to be discreetly distributed with a thickness unlike the altitude-dependent continuous distribution of precipitable water. Large uncertainties remain in the estimation of cloud impact on the atmospheric radiation as it is strongly affected by the cloud type, height, thickness, and temperature [55], which is beyond the scope of this work. In addition to errors associated with clouds, the low temporal resolution of temperature and precipitable water datasets may also introduce substantial errors to the atmospheric downward radiation and thus to the net cooling power as they are not linearly related to temperature and precipitable water. Note that for the upward longwave radiation from the "near black" cooler surface, a simple analysis shows that the insufficient temporal resolution does not introduce significant error within a generally observed temperature range in a month (e.g., σ T 4 − (σT 4 ) ≈ 1.1 W/m 2 for T = 10, 11, . . . , 29, 30°C, where~means average).
Using the observed global downward longwave radiation from the atmosphere [65], we re-evaluated the global annual mean radiative cooling potential and compared it against the modeled cases with and without the cloud effects (only the net cooling power with cloud cover effects is given in Figure 6c). Figure 7 shows the histogram of errors across the globe, where the counts are weighted by the cosine of the corresponding latitudes because the datasets are uniformly distributed on the geographic coordinate system. In the case without cloud cover, the annual mean cooling potential is mostly overestimated with a large spread, with most overestimations being in tropical and sub-tropical climates. In the case with cloud cover, the annual mean cooling potential is only overestimated or underestimated with a narrow spread, with overestimations being in humid and hot coastal regions and underestimations being in dry and cold regions. We attribute the reductions in errors across the globe to the inclusion of clove cover and scaling of the cloud temperature with cloud cover. The remaining errors are mainly due to the insufficient temporal resolution of the temperature and PW datasets, uncertainties in the cloud temperature and emissivity, and uncertainties in the modeled clear-sky atmospheric emissivity.

Global Radiative Cooling Potential Anomaly
Considering most cooling demands occur during the summer, it is important to understand how radiative cooling potential is affected by the summer weather across the globe. We mapped in Figure 8 the global seasonal cooling potentials and their anomaly for summer and winter, respectively. Here, the summer refers to June, July, and August, and the winter refers to January, February, and December. The radiative cooling potential anomaly is defined as the deviation of the seasonal mean cooling potential from the annual mean. A positive anomaly means an increase in the cooling potential and a negative anomaly means a reduction. As Figure 8a,b shows, hot and dry regions can still yield cooling potential as high as 80-110 W/m 2 . However, regions with subtropical or tropical climates, such as the Indian subcontinent and Southeast Asia, see the most deterioration in the radiative cooling potential during the summer, falling to as low as 10-30 W/m 2 , because of a substantial increase in precipitable water in their atmosphere. African regions that transition from tropical savanna climates to semi-arid climates see modest declines in the radiative cooling potential to 20-40 W/m 2 . Other subtropical regions such as the southern US and eastern China also see a slight drop to 20-40 W/m 2 . The cooling potential of regions with tropical rainforest climates in Africa and South America remains low in the summer because of year-round high precipitable water vapor in their atmosphere. In winter, the opposite of the above changes is mostly true, as shown by Figure 8c,d. The hottest regions with low cooling potential in the summer are also the most densely populated, implying a mismatch between the cooling demand and the radiative cooling potential, which is discussed in Section 3.2.
Atmosphere 2021, 12, x FOR PEER REVIEW 13 of 20 Figure 7. A histogram of errors in the modeled global net cooling power with and without the cloud effect. These two modeled cases are compared against the net cooling power based on the observed downward longwave radiation obtained from Ref. [65]. The counts are weighted by the cosine of the corresponding latitudes because the datasets are uniformly distributed on the geographic coordinate system.

Global Radiative Cooling Potential Anomaly
Considering most cooling demands occur during the summer, it is important to understand how radiative cooling potential is affected by the summer weather across the globe. We mapped in Figure 8 the global seasonal cooling potentials and their anomaly for summer and winter, respectively. Here, the summer refers to June, July, and August, and the winter refers to January, February, and December. The radiative cooling potential anomaly is defined as the deviation of the seasonal mean cooling potential from the annual mean. A positive anomaly means an increase in the cooling potential and a negative anomaly means a reduction. As Figure 8a,b shows, hot and dry regions can still yield cooling potential as high as 80-110 W/m 2 . However, regions with subtropical or tropical climates, such as the Indian subcontinent and Southeast Asia, see the most deterioration in the radiative cooling potential during the summer, falling to as low as 10-30 W/m 2 , because of a substantial increase in precipitable water in their atmosphere. African regions that transition from tropical savanna climates to semi-arid climates see modest declines in the radiative cooling potential to 20-40 W/m 2 . Other subtropical regions such as the southern US and eastern China also see a slight drop to 20-40 W/m 2 . The cooling potential of regions with tropical rainforest climates in Africa and South America remains low in the summer because of year-round high precipitable water vapor in their atmosphere. In winter, the opposite of the above changes is mostly true, as shown by Figure 8c,d. The hottest regions with low cooling potential in the summer are also the most densely populated, implying a mismatch between the cooling demand and the radiative cooling potential, which is discussed in Section 3.2.
The mean radiative cooling potential tells how radiative cooling overall performs across the globe. This is especially useful in passive applications such as radiative cooling paints, rooftops, pavements, outdoor clothing, etc., as well as in active cooling systems. The cooling anomaly, however, can also be useful for evaluating if and how large cold storage is needed for active systems such as large-scale cold-water generators [14]. Cold can be better generated during cool seasons or hours, stored, and then used during hot seasons or hours. Regions with a large seasonal cooling potential anomaly may require massive cold storage, if feasible. If the cooling potential anomaly occurs only at a daily or hourly scale, small cold storage can satisfy the need. Underground cold-water reservoirs The winter mean cooling potential and its anomaly, respectively. The cooling potential anomaly is defined as the deviation of seasonal mean cooling potential from the annual mean. A positive anomaly means an increase in the cooling potential and a negative anomaly means a reduction.

Global Radiative Cooling Potential Adjusted for Population Density and Cooling Demand
In addition to the radiative cooling potential and its anomaly, the cooling potential The winter mean cooling potential and its anomaly, respectively. The cooling potential anomaly is defined as the deviation of seasonal mean cooling potential from the annual mean. A positive anomaly means an increase in the cooling potential and a negative anomaly means a reduction.
The mean radiative cooling potential tells how radiative cooling overall performs across the globe. This is especially useful in passive applications such as radiative cooling paints, rooftops, pavements, outdoor clothing, etc., as well as in active cooling systems. The cooling anomaly, however, can also be useful for evaluating if and how large cold storage is needed for active systems such as large-scale cold-water generators [14]. Cold can be better generated during cool seasons or hours, stored, and then used during hot seasons or hours. Regions with a large seasonal cooling potential anomaly may require massive cold storage, if feasible. If the cooling potential anomaly occurs only at a daily or hourly scale, small cold storage can satisfy the need. Underground cold-water reservoirs could sever this purpose for district cooling [74], and insulated water storage tanks for individual home cooling [14].

Global Radiative Cooling Potential Adjusted for Population Density and Cooling Demand
In addition to the radiative cooling potential and its anomaly, the cooling potential available per capita and a unit amount of cooling demand in a region is an even more practical factor to determine the viability of implementing radiative sky cooling for a particular region. Figure 9 shows annual mean and accumulative cooling potentials adjusted for the global population density and further for the global annual cooling demand (cooling degrees days). Since different regions may have different cooling potentials and yet require different amounts of cooling during the same month, we presented the adjusted cooling potentials based on the annual mean cooling power to ensure consistency across the globe. Assuming 0.1% of a 1 km 2 unit land area is available for radiative cooling applications, cooling potential per capita (Watts per person, W pP) was obtained by dividing the total annual mean cooling power of this land area by its population density, as shown in Figure 9a. Any unpopulated unit area (less than 1 person per km 2 ) [67] was omitted in the evaluation. As a result, most regions that are previously shown to have the highest cooling potential in Figure 6c now appear as regions with no potential because their harsh desert or semi-desert climates are not suitable for habitation, if at all. The cooling potential of regions with a high population density and a wet climate is further diminished. Still, these densely populated regions can see a cooling potential of 10~10 3 W pP, implying highly uneven distribution. Other hot but moderately populated regions possess even higher radiative cooling potential in the range of 10 3~1 0 5 W pP. We do admit that the available cooling potential can change depending on future land availability and population density. In active cold generation applications, building a large radiative cooling system for a whole district, instead of building an individual cooling system for each household, may result in higher cooling potential when the cooling system is built on the outskirts where land is more likely available at lower costs.
We further adjusted the cooling potential for both population density and cooling demand in Figure 9b. Here, the cooling demand is represented by the annual cooling degree days, which is defined as the annual sum of the positive difference between the daily mean temperature and a baseline temperature of 18 • C [75]. The annual accumulative cooling potential (in kWh) is used instead of the annual mean cooling potential in Watts. The range of available cooling potential per person and cooling degree day is much wider, 10 −2~1 0 6 kWh pP pCDD, indicating extremely uneven distribution across the globe. The map further highlights the fact that densely populated and humid regions may not be suitable for radiative cooling applications solely based on the individual impacts. The cumulative impact, however, can still be immense. It is the regions with moderate population densities and temperate climates that are better suited for radiative cooling applications in terms of the adjusted benefits. These regions are generally "transitional" regions located between dry and humid climates, and sparsely and densely populated areas.
10 ~10 kWh pP pCDD, indicating extremely uneven distribution across the globe. The map further highlights the fact that densely populated and humid regions may not be suitable for radiative cooling applications solely based on the individual impacts. The cumulative impact, however, can still be immense. It is the regions with moderate population densities and temperate climates that are better suited for radiative cooling applications in terms of the adjusted benefits. These regions are generally "transitional" regions located between dry and humid climates, and sparsely and densely populated areas.

Discussion and Conclusions
Daytime radiative sky cooling has added excitement to the development of sustainable cooling technologies thanks to its several potential advantages. A well-designed radiative cooling surface or device can passively send more energy back to the deep space than it absorbs from the sun and the ambient. It is however of great importance to understand how much expectation it can live up to, in terms of not only its net cooling power but also its availability to the total population and cooling demand in a region. We thus mapped the global radiative cooling potential based on global historic weather datasets and evaluated it in terms of the global population density and cooling degree days.
Based on the net cooling power alone, hot and dry regions are ideal places for the adoption of radiative sky cooling technologies with their annual mean potential of 80-110

Discussion and Conclusions
Daytime radiative sky cooling has added excitement to the development of sustainable cooling technologies thanks to its several potential advantages. A well-designed radiative cooling surface or device can passively send more energy back to the deep space than it absorbs from the sun and the ambient. It is however of great importance to understand how much expectation it can live up to, in terms of not only its net cooling power but also its availability to the total population and cooling demand in a region. We thus mapped the global radiative cooling potential based on global historic weather datasets and evaluated it in terms of the global population density and cooling degree days.
Based on the net cooling power alone, hot and dry regions are ideal places for the adoption of radiative sky cooling technologies with their annual mean potential of 80-110 W/m 2 . In comparison, hot and humid regions tend to have a much lower potential of only 10-40 W/m 2 . Further analyses of seasonal radiative cooling potential maps show that hot and dry regions can achieve 80-110 W/m 2 net cooling power during the summer months (June, July, and August), whereas hot but humid regions only see 10-30 W/m 2 net cooling power because of a substantial increase in precipitable water in their atmosphere. Different regions are subject to varying degrees of cooling performance anomaly during the summer. While the cooling potential can be useful to determine the size of a radiative cooling system for a given cooling demand, the cooling potential anomaly can be useful to determine the size of cold storage for active radiative cooling systems.
Net cooling power alone does not tell the whole picture regarding the viability of radiative cooling. Human civilizations have been built centering around regions with sufficient water resources and precipitation. And many, if not most, such regions happen to be humid and hot, whereas dry regions tend to be sparsely populated. We thus mapped the global radiative cooling potential adjusted for the 2015 population density, assuming only 0.1% of a unit area (1 km 2 ) is available for radiative cooling applications. When any unpopulated areas are omitted in the evaluation, the regions with the highest cooling power now appear as regions with no potential because their desert or semi-desert climates may not be suitable for human habitation at all. However, regions with large population densities and wet climates see further reductions in their cooling potential. These regions possess cooling potential in the order of 10~10 3 Watts per capita (WpP), implying a highly uneven yet valuable distribution. Hot and dry, but less populated regions have an even higher potential in the range of 10 3~1 0 5 WpP.
Because climate affects not only radiative cooling power and population distribution but also cooling demand, we further mapped global radiative cooling potential adjusted for both population density and annual cooling degree days. This adjusted global cooling potential demonstrates highly uneven distribution in the range of 10 −2~1 0 6 kWh pP pCDD. In terms of individual benefits, this adjusted cooling potential again highlights the fact that densely populated and humid regions are not well suitable for radiative cooling applications. However, regions with moderate population densities and temperate climates are better suited for the adoption of radiative cooling technologies. These regions tend to be geographically and demographically "transitional", being located between dry and wet climates as well as desolate and populous regions.
In addition to the individual and cooling-demand-related impacts, widespread adoption of radiative cooling technologies across the globe, even in humid regions, will have other potential benefits. If used as cool roofs on large scales in urban areas, in addition to bringing energy saving in buildings [18,76], radiative sky cooling can drastically reduce solar irradiance into the urban environment and decrease its temperature [41,77]. When radiative cooling technologies improve building energy efficiency, it can lead to other climate and health benefits such as reductions in carbon emissions and PM2.5 emissions [78][79][80]. If used in thermal power plants as primary or supplemental cooling systems, radiative sky cooling can save water and maintain plant efficiency [21,25]. A direct global-scale impact may arise from the enhancement of surface albedo with the adoption of radiative cooling technologies, even in unpopulated desert climates. Increased surface albedo has the potential to offset radiative forcing caused by carbon emissions [81,82], although the impact depends on the location. In tropical and subtropical regions, the Earth's land surface contribution to the planetary albedo is low because of the strong attenuation of surface albedo by the atmosphere [83]. However, in dry regions, the land surface contribution to the planetary albedo seems much higher. Nevertheless, widescale adoption of radiative cooling could reduce air temperature near the surface, if not the whole atmosphere, even in humid regions.
Other unexplored considerations, such as the effects of air conditioning saturation and economic prosperity, could further complicate the prospect of widespread adoption of radiative cooling. For example, regions with more economic power could easily afford to integrate radiative cooling materials and systems into existing buildings and future developments. However, the same regions have much higher air conditioning saturation rates than less developed regions [70] and thus are possibly more resistant to the adoption of radiative cooling. Given the fact that inexpensive radiative cooling materials can now be mass-manufactured in the form of thin films, paints, and even woods [6,7,9], less developed regions with low air conditioning adoption rates may be better suited for radiative cooling applications.
The global maps of radiative cooling potential presented in this work offer both exciting and cautious outlooks. If implemented at the right locations with a moderate population density and a temperature climate, radiative cooling can potentially meet individual cool-ing demands. If implemented worldwide, its cumulative cooling impact can be enormous, even in humid and densely populated regions. Even though economic incentives may vary among different regions, one cannot deny the fact that the widespread implementation of radiative sky cooling could yield far-reaching benefits: reducing the reliance on electricity for cooling in buildings and thermal power plants, curtailing greenhouse gas emissions, decreasing water consumptions in wet cooling processes, containing thermal pollution of water resources, mitigating urban heat island effect, and even regulating the Earth's energy budget.  Data Availability Statement: The 2 m temperature datasets and the global horizontal downward solar irradiance datasets were obtained from the European Commission's Copernicus Climate Change Service [65]: available at cds.climate.copernicus.eu (accessed on 1 September 2021); The atmospheric precipitable water data were obtained from the Nasa Earth Observatory [66]: available at neo.sci.gsfc.nasa.gov (accessed on 1 September 2021); 2015 global population density data were obtained from the NASA Socioeconomic Data and Applications Center [67]: available at sedac.ciesin.columbia.edu (accessed on 1 September 2021); And the global monthly cooling degree days data were obtained from PANGAEA-Data Publisher for Earth & Environmental Science [68,69]: available at doi.pangaea.de (accessed on 1 September 2021). Other datasets generated in this work are available upon request.

Conflicts of Interest:
The authors declare no conflict of interest.