## 1 Introduction  
The notion of sunshine duration (SSD) or bright sunshine hours have been introduced by the World Meteorological Organisation (WMO) in order to indicate the time duration at a site with visible Sun. The SSD parameter is recorded as long as the direct-normal solar irradiance exceeds the value of 120 W\(\cdot\)m\({}^{-2}\). The sunshine duration is a parameter of secondary significance in the determination of the climatology at a site, while its prime parameters are temperature, humidity, wind, precipitation, and solar radiation. Nevertheless, sunshine duration nowadays plays a significant role in estimating the solar radiation intensity at a location via modelling [1, 2]. In addition to the above, sunlight has many other applications. [PERSON] et al. [3] have developed a digital tool for predicting the necessary sunshine for plants. [PERSON] et al. [4] have provided a methodology for reconstructing aerosol-optical-depth (AOD) series from sunshine records. [PERSON] et al. [5] have derived a satellite-based SSD climate data record for Europe. [PERSON] and [PERSON] [6] and [PERSON] et al. [7] have reported the variations in cloudiness/sunshine and sunshine over Greece, respectively. [PERSON] et al. [8] have studied the relationship between SSD and air-temperature trends across Europe, while [PERSON] et al. [9] have investigated the relationships between cloudiness, AOD, and SSD over Poland. Solar radiation on a horizontal plane (H\({}_{\text{g}}\)) is the sum of the diffuse (scattered) radiation (H\({}_{\text{d}}\)) coming from all parts of the sky vault at a site and the direct one (H\({}_{\text{b}}\)) coming from the Sun exclusively. As H\({}_{\text{b}}\) can be estimated accurately, it is the other solar component (i.e., H\({}_{\text{d}}\)) that needs attention, because its estimation is not straightforward due to multiple scattering of the incoming solar radiation in the Earth's atmosphere by atmospheric molecules, atmospheric aerosols, and clouds. To overcome the difficulty in estimating H\({}_{\text{d}}\), many researchers have used the notion of the clearness index (k\({}_{\text{t}}\)) or of the diffuse fraction (k\({}_{\text{d}}\)). The first is defined as the ratio of H\({}_{\text{g}}\) to the extraterrestrial solar radiation (H\({}_{0}\)), while k\({}_{\text{d}}\) is defined as the ratio of H\({}_{\text{d}}\) to H\({}_{\text{g}}\). Use of the k\({}_{\text{d}}\) has been made in several works [10; 11; 12; 13]. Nevertheless, almost all of them relate k\({}_{\text{d}}\) as a function of k\({}_{\text{t}}\)[14; 15; 16; 17]. [PERSON] [18] has given results from a relevant study about high-temporal resolution estimates of k\({}_{\text{d}}\) for south-eastern Australia. A similar study for India has been performed by [19]. [PERSON] et al. [12] evaluated the diffuse fraction and diffuse coefficient from statistical analysis over two sites in Algeria. An interesting work [20] has presented a new methodology to derive typical meteorological years (TMYs) from hourly diffuse-fraction values. [PERSON] et al. [21] have developed a model to estimate the diffuse fraction of solar radiation on a horizontal surface. Nevertheless, none of the above studies or others from the international literature not mentioned here have used k\({}_{\text{d}}\) to characterise the sky conditions over a site. [PERSON] et al. [22] have developed a methodology with which the sky is categorised as clear, intermediate, or overcast by only determining the upper and lower limits of the diffuse fraction (k\({}_{\text{du}}\) and k\({}_{\text{d}}\), respectively). Their methodology has been applied to 14 sites around the world and verified. The authors concluded that the k\({}_{\text{du}}\) and the k\({}_{\text{d}}\) boundaries may take the universal values of 0.78 and 0.26, respectively. Moreover, [PERSON] [23] has used the notion of the diffuse fraction in defining the solar radiation climatology of Greece and has shown that k\({}_{\text{d}}\) can also be used as an atmospheric scattering parameter.