## 3 Results  
### \(T_{\rm L}\) and \(T_{\rm UM}\) Variation: Month-Hour Diagrams for All-Sky Conditions  
[PERSON] et al. [71] first introduced the methodology for the month-hour distribution of a meteorological parameter through its application to daylight levels in Athens. Those researchers listed the advantages of using such an analysis. This methodology is also followed in the present study. Due to the large number of sites considered in this work, it is not possible to show diagrams for all 33 locations; therefore, a pair of representative sites per climatic zone has been chosen (as in Figure 2); these are Irakleio and Kalamata for zone A, Agrinio and Lesvos for zone B, Alexandroupoli and Tripoli for zone C, and Kastoria and Serres for zone D.  
Figure 4 shows the month-hour graphs of \(T_{\rm L}\) under all-sky conditions for the selected sites. A general observation is the relatively high values of \(T_{\rm L}\) during almost all day in January, February, March or even early April. Lower values are observed at midday. The morning and evening peaks (8 a.m. and 5-6 p.m.) may correspond to rush hours as the meteorological data used to calculate \(T_{\rm L}\) comes from HNMS stations mostly situated at airports and/or close to towns. Similar observations to ours have been reported over individual years in Rome and Arcavacata di Rende, Italy [13], various locations in Zimbabwe [16], and over Sfax in Tunisia [18]. In late spring, autumn and winter, \(T_{\rm L}\) decreases in the evening because of its sensitivity to low solar elevation angles (higher air masses).  
Figure 4: _Cont._  
The observations drawn from Figure 4 may have another explanation. According to the definition of the Linke turbidity factor, during the late autumn-winter period, more clean-dry atmospheres are required to produce the observed attenuation of solar radiation because of extended cloudiness and higher humidity in the atmosphere in relation to those in the spring-early autumn period. Another observation from Figure 4 is that the winter \(T_{\rm L}\) values become lower around noon. This occurs for two further reasons: (i) \(T_{\rm L}\) is inversely proportional to the air mass (or solar elevation angle; see Equation (2)), and it therefore decreases at higher \(m^{\prime}\) values, and (ii) cloudiness and/or ambient humidity are reduced at midday. Similar patterns have been found at the other 25 sites (not shown here).  
Figure 5 is equivalent to Figure 4, but it refers to \(T_{\rm UM}\). \(T_{\rm UM}\) also depends on 1/\(m^{\prime}\) as \(T_{\rm L}\), but it has an additional disadvantage that the dust-laden and dust-free atmospheres (see Equation (9)) contain a specified water-vapor content; i.e., the content that exists in the atmosphere at the time of observation (\(u_{w}\) in Equation (14)). This differentiates its behavior slightly in relation to that of \(T_{\rm L}\) as \(T_{\rm L}\) refers to a dry atmosphere only. Nevertheless, the \(T_{\rm L}\) and \(T_{\rm UM}\) patterns for the same site look  
Figure 4: Month-hour diagrams of the \(T_{\rm L}\) values in a Typical Atmospheric Turbidity Year (TATY) under all-sky conditions in climatic zone A: first raw, Irakleio (left), Kalamata (right); climatic zone B: second raw, Agrinio (left), Lesvos (right); climatic zone C: third raw, Alexandroupoli (left), Tripoli (right); climatic zone D: fourth raw: Kastoria (left), Serres (right). The color code refers to the \(T_{\rm L}\) levels, which have been kept in the range \(1\leq T_{\rm L}\leq 10\). The 06.00–20.00 h LST (Local Standard Time = Universal Time + 2h for Greece) interval limitation in the graphs is due to the adopted criterion \(\gamma\geq 5^{\circ}\).  
very similar; one might observe that, if the \(T_{\rm L}\) values are divided by 10, the \(T_{\rm UM}\) values are obtained. [PERSON] et al. [24] have come to a similar conclusion. The other 25 sites present very similar \(T_{\rm UM}\) patterns (not shown here).  
Figure 5: \(Cont.\)