## 5 Conclusions
Linear fits of ASI (i.e., of k\({}_{\rm d}\)) to the \(\varphi\) of the sites were derived for the DCS, DIS-1, DIS-2, DIS-3, and DOS cases; in the first four groups, no actual trend was shown, while in the DOS case, a slight negative trend was found. The developed methodology of using k\({}_{\rm d}\) for characterising the sky conditions was evaluated against real SSD records from 4 sites out of the 43 and 1 site outside Greece. The SSD hourly values were compared with the DCS ones for the same sites and large differences were found. In order to investigate these differences further, a new formulation was created as far as the estimation of the sunshine duration from the 43 TMYs was concerned, i.e., SSD\({}_{\rm m}\) = DCS + DIS-1 + 0.8 \(\times\) DIS-2 + 0.5 \(\times\) DIS-3. Comparison of the results from this formula with the mentioned SSD records gave much smaller differences. This formula is promising, but it must be evaluated further with more data. The rationale behind the derivation of the expression for SSD\({}_{\rm m}\) was the following. The number of the k\({}_{\rm d}\) events belonging to the three ranges (clear, intermediate, overcast skies) can be attributed to durations of sunshine under the above three types of skies, i.e., DCS, DIS, and DOS. Though k\({}_{\rm d}\) has certain limits for characterising the sky, this does not mean that these limits are clear-cuts, at least at hourly scale. Within one hour, the sky may turn from clear to intermediate with light cloudiness. This means that even though the k\({}_{\rm d}\) value is accommodated in the intermediate range, it still carries intrinsic characteristics of a clear sky. Let us suppose that there are available 5 min solar radiation data; then, twelve 5 min k\({}_{\rm d}\) values can be calculated in the hour. If for seven 5 min intervals the sky was clear with rather high turbulence (high H\({}_{\rm d}\)) and during the other five 5 min intervals the sky had a light cloudiness (still high H\({}_{\rm d}\)), the hourly value of the k\({}_{\rm d}\) will be accommodated as a DIS event very close to the k\({}_{\rm dl}\) = 0.26 limit. In this way, any k\({}_{\rm d}\) points close to the k\({}_{\rm dl}\) limit at either side (clear or intermediate) have an ambiguity as far as their clear representation of the sky conditions they belong to is concerned. This ambiguity becomes less and less as the k\({}_{\rm d}\) point moves away from the limit. Therefore, one might talk about an \"intrusion\" of some k\({}_{\rm d}\) points from the intermediate range with clear-sky characteristics into the clear range and vice versa; this intrusion that becomes weaker with the distance of the k\({}_{\rm d}\) point from the k\({}_{\rm dl}\) limit was expressed by the division of the DIS range into three sub-ranges; use of weights for each sub-range was made to form the proposed model that estimates the SSD values at a site. Three-dimensional maps of the annual mean DCS, DIS, and DOS values were created for Greece. The distribution of the clear-sky conditions showed a clear division of Greece in two halves, northern and southern, the diving line being at \(\varphi=39^{\circ}\). The pattern for the overcast skies was found to be just the opposite that for clear skies, i.e., greater number of sunshine hours in the northern part of Greece in comparison with that in the southern half. The pattern for intermediate-sky conditions was shown to be between those for clear and overcast conditions. In order to investigate the efficiency of the proposed model in estimating SSDs from DCS, DIS-1, DIS-2, and DIS-3 events, a 3D map of the annual mean SSD values was prepared for Greece. Its pattern very much resembled that for SSD\({}_{\rm CS}\) events, thus verifying its validity. In interpreting k\({}_{\rm d}\) as ASI, a 3D map for Greece was derived for the clear-sky cases. Its pattern was found to be very similar to that of T\({}_{\rm L}\) from another study about the atmospheric turbulence over Greece; this justified the results received in the present work.