Mapping Nighttime and All-Day Radiative Cooling Potential in Europe and the Inﬂuence of Solar Reﬂectivity

: Radiative cooling is a natural process to cool down surfaces through the rejection of thermal radiation using the outer space as a cold sink, taking advantage of the transparency of the atmospheric windows (8–14 µ m), which partially matches the infrared radiation band. With the development of new materials that have a high reﬂectivity of solar radiation, daytime radiative cooling can be achieved. This phenomenon depends on the optical properties of the surface and the local weather conditions. In this research, climatological data from 1791 weather stations were used to present detailed nighttime and all-day radiative cooling maps for the potential implementation of radiative cooling-based technologies. The paper offers a parametric study of the variation of the potential as a result of decreasing the solar reﬂectivity. The results show that southern Europe is the region with the highest potential while northern Europe holds more hours of available radiative cooling. After varying the solar reﬂectivity from 1 to 0.5 the average power reduces from 60.18 to 45.32 W/m 2 , and energy from 527.10 to 264.87 kWh/m 2 · year. For solar reﬂectivity lower than 0.5, all-day radiative coolers behave as nighttime radiative coolers, but power and energy values improve signiﬁcantly for high values of solar reﬂectivity. Small variations of solar reﬂectivity have greater impacts on the potential at higher reﬂectivity values than at lower ones.


Introduction
Radiative cooling (RC) is a natural cooling process already used in 400 BC in ancient Iran for ice production [1]. In recent years it has experienced a new awakening. During the 1960s and 1970s the phenomenon began to be studied systematically [2,3]. However, it is in this last decade, driven by the needs for a change in the model of energy production and consumption, when technologies based on RC are positioned as promising solutions for the production of clean and green energies for space cooling purposes.
Radiative cooling is known to be the process by which a surface reduces its temperature through the emission of thermal radiation into the outer space. It benefits from the high transparency of the atmosphere in 8-14 µm wavelength range, named atmospheric window, which partially matches the peak of infrared radiation emitted by terrestrial bodies at ambient temperatures. This cooling process occurs when a net imbalance exists between the emitted and the absorbed heat; solar radiation, atmospheric radiation and parasitic losses (convection and conduction) also accounted for in this net balance. This technique allows for achieving temperatures below ambient [4].
The first selective surfaces (also called emitters), emitting in the 8-14 µm range, were designed to achieve RC during night time [2,5]. In 1975, Catalanotti et al. [3] obtained radiative cooling during daytime, but the performance was poor. Overcoming solar radiation was a great challenge. In 2014, Raman et al. [6] demonstrated a temperature drop-4-5 • C-below ambient under direct sunlight in photonic radiative cooling, which

Methods
The parametric study of the variation of the all-day radiative cooling potential in Europe as a function of the reflectivity in the solar range of the emitter material was conducted based on meteorological data measured in 1791 weather stations. Kriging was the interpolation technique used to obtain radiative cooling maps.

Data Acquisition
The climatological data used was available in the Meteornorm database. Meteonorm is a recognized software in the field of energy simulation of buildings and solar facilities. The downloaded data corresponded to a total of 1791 weather stations distributed in 46 European countries. The distribution of these stations is shown in Figure 1. The data is related to the last volume of measured data available in Metonorm for the year 2005. The resulting dataset included information on weather variables recorded hourly for 365 days of the year. Stored variables included ambient temperature, atmospheric IR radiation and global horizontal solar radiation, relative humidity, clearness index of the sky and atmospheric pressure. Ambient temperature, global horizontal solar radiation, relative humidity, clearness index or atmospheric pressure are data measured at the weather station while atmospheric radiation (L in ) is calculated based on the Aubinet model (1) [27]: 4 (1) where L in is the atmospheric radiation (W/m 2 ); σ is the Stefan-Boltzman constant W m 2 K 4 ; e s is the saturated vapor pressure (hPa); KT d is the clearness index (-) and T a is the ambient temperature ( • C). where is the atmospheric radiation (W/m 2 ); σ is the Stefan-Boltzman constant W ; es is the saturated vapor pressure (hPa); KTd is the clearness index (-) and Ta is the ambient temperature (°C).

Radiative Cooling Calculation
In the research, the following premises were assumed: the greatest potential of a black-body surface (emittance of the surface (εs) equal to one) (a) could be achieved by minimizing the parasitic losses of conduction and convection, (b) while absorbed solar radiation depended on the reflectivity of the surface. In this study, εs is equal to 1 and parasitic losses are neglected. In RC applications, the emitter surface temperature is close to ambient temperature; in this case it was assumed that (c) the temperature on the surface was equal to ambient temperature. The net balance power per surface unit at each location was calculated (2).
where is the solar reflectivity of the emitter (-) and corresponds to the global horizontal solar radiation (W/m 2 ).
Only positive values of Equation (2), corresponding to observations where radiative cooling occurred, were filtered. The average annual RC potential at each location was calculated according to (3) where is the total number of positive observations: Every value from Equation (2) corresponded to a one-hour observation (t = 1 h). Thus, allowing us to calculate the RC annual energy (6): Finally, a third value was included (5). This value referred to the number of observations where radiative cooling was achieved ( [%]

Radiative Cooling Calculation
In the research, the following premises were assumed: the greatest potential of a black-body surface (emittance of the surface (ε s ) equal to one) (a) could be achieved by minimizing the parasitic losses of conduction and convection, (b) while absorbed solar radiation depended on the reflectivity of the surface. In this study, ε s is equal to 1 and parasitic losses are neglected. In RC applications, the emitter surface temperature is close to ambient temperature; in this case it was assumed that (c) the temperature on the surface was equal to ambient temperature. The net balance power per surface unit at each location was calculated (2).
where ρ is the solar reflectivity of the emitter (-) and S H corresponds to the global horizontal solar radiation (W/m 2 ).
Only positive values of Equation (2), corresponding to observations where radiative cooling occurred, were filtered. The average annual RC potential at each location was calculated according to (3) where n is the total number of positive observations: Every value from Equation (2) corresponded to a one-hour observation (t = 1 h). Thus, allowing us to calculate the RC annual energy (6): Finally, a third value was included (5). This value referred to the number of observations where radiative cooling was achieved (N q net,ideal + ), compared to the total number of observations (8760).

Training and Test Datasets
Data was divided into two subsets: training set and test set. The training set contained information from 80% of the locations and was used in the construction of the interpolation model for each value of ρ. Test set data was used to evaluate the performance of each model.

Interpolation Kriging Model
Kriging is a stochastic interpolation method for values prediction at different points from known reference values. In the study we used the most general version of the methodology, ordinary Kriging, which decomposed the regressor into a stationary part (µ) and a residual (ε ), corresponding to the spatially correlated part (6) [28]: This method worked as a linear regression applied to spatial sample data which was used as regressor, Z(s), in order to predict a dependent variable, Z(s 0 ), at a given location (7). The weight given by the model to each of the points in the sample was determined by a variogram function (8).
where λ 0 is a vector of Kriging weights, n the number of sample points and γ is the semivariance.
The semivariance of the sample was calculated for each pair of points from (9), where Z(s i ) is the value of the target variable at the point s i , Z(s i + h) is the value of the neighbor point at a distance s i + h and E corresponds to the expected value. A theoretical variogram was adjusted to the variogram so that the error of the fitting was minimum.

Assessment Metrics of the Model
Radiative cooling values were predicted using the test set locations in the Kriging model. These predictions were compared with the existing potential values at these locations. In order to evaluate the accuracy of the model, the coefficient of determination (R 2 ) and the root mean square error (RMSE) were calculated (10) and (11): where N is the total number of locations; X i,m is the observed values of the sample; X i,p is the value estimated in the model and X m,avg is the average of the observed values at the weather stations. RMSE has the same units as the variable at interpolation (power, energy and coverage) while R 2 is dimensionless.

Results and Discussion
In the first part of this section we present a comparison of the prediction maps for the cases of nighttime and all-day RC of an ideal reflective surface (ρ = 1). In the second part we determine the changes that occur when varying the value of surface reflectivity in all-day RC. In both sections the performance of the interpolation models used has been evaluated.  Figure 2 shows the annual potential maps of radiative cooling for night and ideal all-day cases. The maps were divided into three regions: south, center and north.
It was observed that the regions with the greatest potential were located in the south of Europe (57.36 W/m 2 in nighttime map and 72.33 W/m 2 in all-day), in the Mediterranean basin, especially the cases of Turkey, Spain and Greece. These results were consistent with the findings of Argiriou et al. [24]. The areas of least potential were in the northern countries (41.51 W/m 2 in nighttime map and 53.77 W/m 2 in all-day) where the temperature is lower. The average potential in the central zone was 46.48 (nocturnal) and 58.69 (all-day) and they are values comparable to those in the north but with a wider range of variability (Table 1). In these cases, the performance of the surface is only influenced by the temperature and the atmospheric radiation and the results are coherent with the climatology of Europe where the ambient temperature decreases with the latitude.  Annual energy potential maps are shown in Figure 3. The night map presented homogeneous values with minimal differences between regions. In the all-day predictions there was an average increase of 114% (124% in the south, 116% in the center and 108% in the north) of the available annual energy potential: the average was 245.76 kWh/m 2 ·year in the night case and 527.1 kWh/m 2 ·year in the all-day case. This means that only during daytime can 281.34 kWh/m 2 ·year be produced. In all-day applications, southern countries can radiate, on average, 633.56 kWh/m 2 ·year; center countries, 514.16 kWh/m 2 ·year; and In all-day applications, the potential RC was greater than in night applications. On average in Europe, the change to all-day applications represented an increase of 27.21% (from 47.30 to 60.17 W/m 2 ). The all-day map presented more diversification of the values with respect to the night map (in all-day the range is 43.82-94.01 W/m 2 and in nighttime, 35.14-71.34 W/m 2 ).
It was observed that the regions with the greatest potential were located in the south of Europe (57.36 W/m 2 in nighttime map and 72.33 W/m 2 in all-day), in the Mediterranean basin, especially the cases of Turkey, Spain and Greece. These results were consistent with the findings of Argiriou et al. [24]. The areas of least potential were in the northern countries (41.51 W/m 2 in nighttime map and 53.77 W/m 2 in all-day) where the temperature is lower. The average potential in the central zone was 46.48 (nocturnal) and 58.69 (all-day) and they are values comparable to those in the north but with a wider range of variability (Table 1). In these cases, the performance of the surface is only influenced by the temperature and the atmospheric radiation and the results are coherent with the climatology of Europe where the ambient temperature decreases with the latitude. Annual energy potential maps are shown in Figure 3. The night map presented homogeneous values with minimal differences between regions. In the all-day predictions there was an average increase of 114% (124% in the south, 116% in the center and 108% in the north) of the available annual energy potential: the average was 245.76 kWh/m 2 ·year in the night case and 527.1 kWh/m 2 ·year in the all-day case. This means that only during daytime can 281.34 kWh/m 2 ·year be produced. In all-day applications, southern countries can radiate, on average, 633.56 kWh/m 2 ·year; center countries, 514.16 kWh/m 2 ·year; and  (Table 2). On average, nighttime RC was achieved in 59.6% of the annual observations.  (Table 2). On average, nighttime RC was achieved in 59.6% of the annual observations.   Table 3 lists the values of the performances of the four models. In all cases, R 2 presented high values (between 0.83 and 0.91), which indicates that the models collected more than 83% of the variability of the sample data. In the energy models, the value of RMSE presented values of one order of magnitude greater, in agreement with the values of prediction. The annual RC power potential maps in Europe are displayed in Figure 4 for each value of reflectivity. The reduction of the reflectivity affects the three regions equally (25% reduction) but, in absolute values, the southern regions are especially penalized (average power reduced by 17.28 W/m 2 ). It is observed that the maps tend to homogenize results   Table 3 lists the values of the performances of the four models. In all cases, R 2 presented high values (between 0.83 and 0.91), which indicates that the models collected more than 83% of the variability of the sample data. In the energy models, the value of RMSE presented values of one order of magnitude greater, in agreement with the values of prediction. The annual RC power potential maps in Europe are displayed in Figure 4 for each value of reflectivity. The reduction of the reflectivity affects the three regions equally (25% reduction) but, in absolute values, the southern regions are especially penalized (average power reduced by 17.28 W/m 2 ). It is observed that the maps tend to homogenize results throughout the territory as the reflectivity is reduced: the range of values (minimum to maximum average power potential) diminished from 50. 19 Table 4 shows that the average value of the potential of RC power followed a decreasing trend for solar reflectivity from 1 to 0.8, while between 0.7 and 0.5 the potential increased slightly; 0.8 being the value of solar reflectivity where the average potential was minimum (42.61 W/m 2 ). Between 1 and 0.8 a maximum difference of potentials occurred: reducing the solar reflectivity from 1 to 0.8 caused a decrease of 29% in the potential of RC power. Between 0.8 and 0.5, the potential increased 6.4%.
The explanation behind these results is due to the number of observations with which the annual average is calculated. With the reduction of the reflectivity, the total number of RC observations also decreases (see Section 2.2). To better understand this, Figure 5 is displayed. The figure shows the power calculated in each of the observations for the month of February at the location of Batman. Observations that resulted in high power values when ρ = 1 remained high when ρ = 0.5, while those observations with low power decreased to the point of having negative values (red points) and were discarded in the calculation of the average. As a result, the calculation of the average for solar reflectivity 0.5 and 0.6 had few observations but of higher quality than for solar reflectivity 0.7 and 0.8. This phenomenon is a result of the different heat fluxes occurring during nighttime and daytime RC. During nighttime RC, solar radiation is not present, thus solar reflectivity does not play any role. However, during daytime RC, solar reflectivity has a significant impact on the radiative balance. In Section 3.2.2. we discuss that most of the observations of RC when considering a solar reflectivity of 0.6 and 0.5 are during nighttime, and thus not affected by this parameter.

RC Activity
The maps in Figure 6 show the percentage of hours in a year that the emitter was able to achieve radiative cooling (from now on we refer to this observation of net radiative cooling as "RC activity"). When the reflectivity in the solar range is reduced, the material decreases its behavior as a selective material: when it absorbed more solar radiation the  We did not observe significant differences in performance of the model for each reflectivity value (Table 5). In all six cases, the values of R 2 were greater than 0.80 which means that, in all the cases, the models could explain more than 80% of the variability of the sample values. RMSE values were small, indicating that the models had good accuracy.

RC Activity
The maps in Figure 6 show the percentage of hours in a year that the emitter was able to achieve radiative cooling (from now on we refer to this observation of net radiative cooling as "RC activity"). When the reflectivity in the solar range is reduced, the material decreases its behavior as a selective material: when it absorbed more solar radiation the number of observations in which the surface was unable to do radiative cooling increased. In these daytime observations the device was actually behaving as a solar thermal collector, heating up the surface.
Contrary to what the power maps showed, the percentage of RC activity of the emitter decreased as reflectivity decreased in the six cases (Table 6). For a reflectivity of 0.5, the worst-case scenario, only in 67% of cases was radiative cooling achieved; the remaining 33% were solar collection observations. Northern regions had more observations of radiative cooling, in all the cases, which means more time available to perform radiative cooling, than southern regions. In Section 3.1 it was pointed out that nighttime RC represented 59.6% of the RC activity in Europe, this means that only 7.47% of the activity occurred during daytime when ρ = 0.5; 10.81%, when ρ = 0.6; 16.18%, when ρ = 0.7; 26.98%, when ρ = 0.8; 40.29%, when ρ = 0.9 and 40.4%, when ρ = 1. Atmosphere 2021, 12, x FOR PEER REVIEW 11 of 16

Annual Energy Potential
The maps in Figure 7 show the annual RC energy potential at each point in Europe. It can be seen, again, that the regions of southern Europe are the areas with the highest energy capacity for radiative cooling. For solar reflectivity values between 0.8 and 0.6, northern regions present higher energy potential than central regions. In this range, although the power potential in the north was lower than in the center (Figure 4 and Figure  5), the north had more time available to perform RC ( Figure 6 and Table 6), resulting in higher values of annual energy available. The results of RC activity for ρ = 1 have not been interpolated by Kriging as a variability in the values to be interpolated is required. For this case, all values were equal to 100% and Kriging could not be performed. It was assumed that in unknown locations the RC activity value was 100%.
The model for reflectivity 0.9 showed a low R 2 value and low RMSE. This model could not reproduce much of the variability of the sample but it also gives low errors of prediction. The range of the values of the sample was very small. For reflectivity values below 0.9, the models presented good metrics of R 2 and RMSE (Table 7).

Annual Energy Potential
The maps in Figure 7 show the annual RC energy potential at each point in Europe. It can be seen, again, that the regions of southern Europe are the areas with the highest energy capacity for radiative cooling. For solar reflectivity values between 0.8 and 0.6, northern regions present higher energy potential than central regions. In this range, although the power potential in the north was lower than in the center (Figures 4 and 5), the north had more time available to perform RC ( Figure 6 and Table 6), resulting in higher values of annual energy available.
The available energy was reduced by lowering solar reflectivity (Table 8). At low reflectivities, maps presented a homogenization pattern. When solar reflectivity is equal to 0.5 it behaves as a nighttime surface (when ρ = 0.5 it was able to provide, on average, 264.87 kWh/m 2 ·year, while a nighttime surface was able to provide 245.76 kWh/m 2 ·year). The largest differences in the average annual RC energy were observed between ρ = 1 and ρ = 0.8. In this range, the difference between average values in Europe was equal to 204.67 kWh/m 2 ·year, and it was equal to 272.58 kWh/m 2 ·year in southern Europe. In the range of 0.8-0.5, the existing difference in the average was equal to 57.56 kWh/m 2 ·year in Europe. Between ρ = 1 and ρ = 0.8, the average annual RC energy reduction for Europe was 38.83%, while between ρ = 0.8 and ρ = 0.5 it was 17.85%. Small variations in reflectivity have a greater impact on the energy potential at high reflectivity values than at low ones. Atmosphere 2021, 12, x FOR PEER REVIEW 13 of 16 Southern countries were more affected by the reduction of than northern and central countries: differences in the average RC energy available between = 1 and = 0.5 were 333.63 kWh/m 2 ·year in southern regions, 259.42 kWh/m 2 ·year in central regions and 217.49 kWh/m 2 ·year in northern regions. The model presented a good performance in the six cases (Table 9). Southern countries were more affected by the reduction of ρ than northern and central countries: differences in the average RC energy available between ρ = 1 and ρ = 0.5 were 333.63 kWh/m 2 ·year in southern regions, 259.42 kWh/m 2 ·year in central regions and 217.49 kWh/m 2 ·year in northern regions. The model presented a good performance in the six cases (Table 9).

Conclusions
In this article we presented the potential of implementing nighttime and all-day radiative cooling technologies in Europe for different solar reflectivity values of the RC emitting surface. Based on climatological data from weather stations and using Kriging interpolation techniques, maps of annual potential for RC power, RC energy and RC activity were displayed. The following conclusions can be drawn from the study:

•
Kriging is a good methodology to predict radiative cooling values from known climatological data. The areas with the greatest potential of implementation are the regions of southern Europe. These regions present high values of power and energy potential. • Compared to the other regions, the north holds more hours of available radiative cooling.

•
The best performance, in all the three regions defined, is achieved when solar reflectivity is equal to one. In order to minimize the solar radiation absorbed by the surface, the reflectivity values in the solar range must be close to 1.

•
For solar reflectivity values below 0.5, the behavior of the surface can be assimilated to a nighttime radiative cooler. • Annual energy and RC activity decreases with reflectivity, while average power potential presents higher values in the 0.6-0.5 range for reflectivity, rather than in the 0.8-0.7 range. This is a result of calculating the average powers using only the observations where RC is achieved, and not for all the observations; for low solar reflectivity values, RC observations correspond mainly to nighttime values where high-power values are obtained. On the contrary, for solar reflectivity values between 0.8 and 0.7, the same nocturnal RC values are achieved, as well as a higher number of low-power daytime observations, thus reducing the average power. Finally, when the solar reflectivity is equal to 0.9, diurnal observations present higher powers, thus increasing the average power.

•
For low values of solar reflectivity, maps tend to show homogeneous patterns. • Small variations in solar reflectivity have greater impacts on the potential at higher reflectivity values than lower ones: in the range of 1-0.8, the reduction of average power potential is 29.19% and the annual energy is 38.83%.