## 3 Results
### Sunshine Duration and Atmospheric Scattering  
This section is focused on these two parameters, as indicated by the title of the article. As far as the sunshine duration is concerned, this coincides with the DCS events, as shown in the previous sections. Therefore, no further discussion is needed to be made. This gives some space for the second parameter. [PERSON] [23] has presented an interpretation of \(\mathrm{k_{d}}\) as an ASI and used it as such. The count of the hourly \(\mathrm{k_{d}}\) values within the posed limits mentioned in step 5, Section 2.2, actually corresponds to the DCS, DIS, and DOS events (i.e., hours) at all sites in their respective TMYs, as already explained previously. In this context, by using the notion of \(\mathrm{k_{d}}\) as ASI, one could interpret the results presented so far as atmospheric scattering (AS) under clear-, intermediate-, and overcast-sky conditions. Having this in mind, the distribution of the three types of AS over Greece on annual basis is 33% for AS\({}_{\mathrm{CS}}\) (subscript CS for clear skies), 40% for AS\({}_{\mathrm{IS}}\) (subscript IS for intermediate skies), and 27% for AS\({}_{\mathrm{OS}}\) (subscript OS for overcast skies). It is seen that greater AS is caused by intermediate-sky conditions followed by clear and overcast skies. This may look fallacious at first glance, as one would expect that AS should increase with the presence of more clouds (i.e., DOS cases). In fact, the scattering mechanism depends on the type of clouds and the cloud cover of the sky, as well as their altitude. [PERSON] [37] claims that:  
* Thick clouds (nimbostratus, cumulonimbus) reflect 80-90% of the incident solar light (in the 300-3000 nm spectrum) back to space, while they absorb just 10-20% of it;
* Fair weather cumulus clouds reflect and absorb 68-85% and 4-9%, respectively; they scatter to the surface the remaining solar flux, accounting for 15-32%;
* Thin stratus clouds reflect and absorb 45-72% and 1-6%, respectively, of the solar flux, while they scatter 28-55% to the surface;
* For alto-stratus clouds, these figures are 57-77% and 8-15%, respectively, while the scattering to the surface of the Earth constitutes 23-43%;
* The absorption mechanism is triggered in the near-infrared band of the solar spectrum, i.e., for wavelengths longer than 700 nm. The above conclusions have not taken into account the scattering mechanism by air molecules and atmospheric aerosols, which contribute to the mechanism [38]. If both factors (clouds and aerosols) are considered, then one can justify the results of the occurrence of AS\({}_{\mathrm{CS}}\), AS\({}_{\mathrm{IS}}\), and AS\({}_{\mathrm{OS}}\) shown above as follows:  
* In clear-sky conditions, scattering of solar light is only due to atmospheric aerosols (natural or anthropogenic) and in certain fair-weather cases to cumulus clouds; this occurs for 33% of the time in a year over Greece;
* In intermediate-sky conditions, when a variety of clouds (cumulus, stratus, cirrus) may be present in the sky at different instances in a year, aided by the presence of atmospheric aerosols, the scattering of solar light occupies more time in a year (40%);
* In overcast-sky conditions, scattering to the surface of the Earth is least as the major part of the incident solar flux is reflected to space; this gives a figure of 27% of the time in a year over Greece. In order to investigate AS further, an additional subdivision of the \(\mathrm{k_{d}}\) limits for intermediate skies is employed here for the first time worldwide. Three new ranges are defined: (i) intermediate-1-sky conditions for \(0.26<\mathrm{k_{d}}\leq 0.43\) (i.e., presence of cirrus cloudswith a clear-sky look), (ii) intermediate-2-sky conditions for \(0.43<\mathrm{k_{d}}\leq 0.60\) (i.e., mix of clear skies with broken or fast-moving clouds [39; 40]), and (iii) intermediate-3-sky conditions for \(0.60<\mathrm{k_{d}}\leq 0.78\) (i.e., prevailing broken clouds with a more permanent character).