The aim of this study is to calculate and analyse the effect of aerosols and water vapour on solar irradiance at ground level in the Mediterranean basin. For that purpose, the methodology recently developed by Obregón et al. [

23] has been used in this study. This methodology, which was successfully validated at nine stations representative for different regions in the world [

23], is here applied to a wide area such as the Mediterranean basin using satellite data. According to it, aerosols are characterized by the aerosol optical thickness (AOT) and water vapour by the integrated water vapour (PWV). AOT is representative for the aerosol load in the atmospheric column. Specifically, AOT at 550 nm has been used since it is a reference wavelength extensively used (e.g., [

28,

29]), therefore convenient for comparison purposes. PWV is the column integrated amount of water vapour. AOT and PWV data used in this study have been obtained from satellite-based instruments, offering an unprecedented opportunity since they provide data with a global coverage. In this framework, CERES (Clouds and the Earth’s Radiant Energy System) provides long-term global estimates of the radiative fluxes within the Earth’s atmosphere and consistent cloud and aerosol estimates. Specifically, CERES SYN 1deg [

30,

31,

32] daily AOT at 550 nm and PWV products, version Ed4A, have been used to calculate aerosol and water vapour effects. The “1deg” stands for 1-degree spatial resolution. The temporal resolution used is daily. The SYN1deg product combines Terra and Aqua CERES and MODIS observations, and 3-hourly geostationary (GEO) data. In particular, aerosol data comes from the NASA/GSFC MODIS MOD04_L2/MYD04_L2 products [

33] as assimilated by MATCH Aerosol Transport Model constituents [

34]. These MODIS retrievals consist of two readings (1030 and 1330 local time on Terra and Aqua, respectively) at 1-degree resolution. The dataset used was composed of 6880 daily CERES values of AOT and PWV, corresponding to the available period from March 1, 2000 to December 31, 2018. It should be mentioned that the stable anticyclonic weather conditions in the Mediterranean region facilitate the availability of long periods with continuous measurements, especially in summer. The uncertainty on AOT is ±0.03±0.05*AOT over ocean and ±0.05±0.15*AOT over land [

33]. The uncertainty on PWV ranges between 5% and 10% [

35]. MODIS retrievals of AOT have been thoroughly validated by comparison to AERONET (Aerosol Robotic Network) data worldwide. For instance, Sayer et al. [

36] compare Deep Blue Collection 6 AOT at 550 nm from MODIS Aqua against AERONET data from 60 sites worldwide, obtaining a good correlation between the two datasets, with R = 0.92. Chu et al. [

37] made an extensive validation of MODIS and AERONET data encompassing 315 co-located AOT from more than 30 AERONET sites, finding retrieval errors of ΔAOT = ±0.05 ±0.2 AOT. Moreover, Remer et al. [

33] made an extensive validation effort with over 8000 MODIS retrievals collocated with AERONET measurements of AOT. They concluded that, globally, MODIS products are accurate to within prelaunch expectations, namely, ±0.05 ± 0.15 AOT over land and ±0.03 ±0.05 AOT over ocean. Regarding our area of study, Mishra et al. [

38] compared AOT from MODIS and AERONET at 15 sites around the Mediterranean basin and obtained a strong spatial agreement and relatively low biases of model AOT against MODIS observations, with moderate to high correlations (R > 0.5) around each site up to ~200–500 km radius. With regard to PWV, Prasad et al. [

39] found that MODIS NIR clear column (R

^{2}= 0.97, RMSE = 5.44 mm) and IR (R

^{2}= 0.81, RMSE = 7.17 mm) water vapour show similar performance on comparison with AERONET data.

Obregón et al. [

23] estimated the effect of AOT and PWV on solar radiation at the surface as a function of the AOT and PWV values. Following that methodology, downwelling shortwave (SW) irradiances under cloud-free conditions were simulated using the libRadtran (Version 1.7) radiative transfer model for each of 100 combinations consisting of pairs of selected values for AOT (between 0 and 1.5) and for PWV (between 0 and 60 mm). Thus, the individual effect of AOT or PWV was estimated as the variation in SW irradiance caused by a change in one variable (AOT or PWV) while the other one remains fixed. This variation is quantified by the relative difference (Rel.Dif), expressed as percentages, and calculated with respect to an atmosphere with AOT = 0 or PWV = 0. The expression used to calculate the individual effect of AOT is [

23]:

where I is the simulated SW irradiance for each AOT value, and I

_{ref} is the simulated SW irradiance for AOT equal to 0, while PWV value remains fixed. This calculation is done for every AOT value, obtaining at look-up table of Rel. Dif. for the individual effect of AOT (

Table 1).

Similarly, the expression for the PWV effect is:

where I is the simulated SW irradiance for each PWV value, and I

_{ref} is the simulated SW irradiance for PWV equal to 0, while now it is AOT which remains fixed. This calculation is done for every PWV value, obtaining the look-up table of Rel. Dif. for the individual effect of PWV (

Table 2).

The calculation of the combined effect of AOT and PWV follows the same methodology, but now both variables (AOT and PWV) can vary:

where I is the simulated SW irradiance for any combination of AOT and PWV, and I

_{ref} is the simulated SW irradiance for AOT and PWV equal to 0. The look-up table of Rel. Dif. for the combined effect of AOT and PWV calculated by Equation (3) is shown in

Table 3.

Once the three look-up-tables have been computed, they are applied to AOT and PWV values provided by CERES product in order to obtain the effect on the SW irradiance of AOT and PWV individually, and combined. Thus, the daily relative differences (Rel.Dif(AOT), Rel.Dif(PWV) and Rel.Dif(AOT-PWV)) for each pixel of the Mediterranean basin were calculated. The bilinear interpolation method was used to obtain the intermediate value between the existing values in the look-up-tables. Subsequently, the spatial and temporal variability of these effects has been analysed. Temporal analysis was performed using a trend analysis to determine if AOT, PWV, AOT effects, PWV effects or AOT-PWV effects over time are increasing, decreasing or remaining the same. For this purpose, the Mann–Kendall Trend Test was used. This non-parametric test has the advantage of assuming no specific statistical distribution of the data. The application of the Mann–Kendall Trend test allows estimating the statistical significance of the trend. To determine the magnitude of the trend, Sen’s method was used [

40]. Before applying this test, the data has been deseasonalized in order to remove the large influence of the annual cycle, obtaining time series of AOT, PWV, AOT effects, PWV effects or AOT-PWV effects for each grid cell. The monthly anomaly is defined as the difference between the value for a certain month and the mean over the whole period of study for that month.

Obregón et al., 2018 [

23] validated the methodology based on irradiance measurements in nine stations. The results obtained showed differences lower than 3% in 84% of the cases. The sensitivity of the model to different input variables of the model, as the aerosol and atmospheric vertical profiles and the surface albedo, was also calculated by Obregón et al. [

23]. Rel.Dif values for different aerosol vertical profiles defined by the season and the aerosol type were calculated, obtaining maximum relative differences lower than 0.15%. When the aerosol type is considered, these relative differences are higher, but they do not exceed the value of 4.5%. This maximum relative difference was obtained due to the difference between urban and maritime aerosol types. A maximum relative difference of 0.24% was obtained when the sensitivity of Rel.Dif to the atmospheric profile was calculated. A maximum relative difference of 8.31% was obtained due to the variation of surface albedo between 0.05 and 0.8. These values guarantee the possibility of keeping the values of these variables fixed since they have no influence on the effect of aerosols and water vapour on radiation. These effects are modulated by the solar zenith angle.