## 4 Conclusions and Discussion

Table 3: Number of (daytime) hourly SSD values at each site within the year indicated for the various \(\mathrm{k_{d}}\) conditions; percentages of the individual cases to the total are given in parentheses. showed that the \(\rm k_{dl}\) and \(\rm k_{du}\) values ranged between 0.24 and 0.26, and between 0.73 and 0.80, respectively, as average values over the selected sites. The value of the presented methodology lies not only in the accurate determination of the \(\rm k_{du}\) and \(\rm k_{dl}\) values at any site, but also contributes to the solar radiation climatology of a site, and the derivation of its SSD values, if they are not available. The estimation of the SSD values is not, of course, that accurate because of the great dispersion of the SSD-\(\rm k_{d}\) pairs (Figures 11-17). Nevertheless, the methodology gives a qualitative indication; this is something than nothing. It must be mentioned here that various attempts to estimate \(\rm k_{d}\) in the past were based on modelling than measurements as in the present study. The use of models may result in reduced accuracy because the intrinsic error in the estimation of \(\rm k_{d}\) increases in comparison with a measurements-based methodology. For instance, [PERSON] and [PERSON] (2018) used 8 models for the estimation of \(\rm k_{d}\) as function of \(\rm k_{t}\); all of them gave high MBD (mean bias difference, in %) and RMSD (root mean square difference, in %) values. Last but not least, the present study provided a methodology to compute the two \(\rm k_{d}\) limits from which one may categorise the sky at his/her site in the three main statuses: clear, intermediate, and overcast. This was done for the first-time worldwide. The developed mathematical formulation, therefore, clearly determines the upper and lower diffuse-fraction limits, and seems to work quite efficiently over the globe. Therefore, it may have a universal character. However, the method should be tested for applicability at sites in Russia, central and south Asia, Japan, Australia, and Oceania in order to fully manifest its universality. Conceptualisation, methodology, data download, data curation, software application, writing--original draft preparation, H.D.K. ; data curation, visualisation, writing--review and editing, S.I.K. ; writing--review and editing, D.K. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Data Availability Statement: Data from the PV-GIS platform were downloaded from [[https://ec.europa.eu/jrc/pvgis](https://ec.europa.eu/jrc/pvgis)]([https://ec.europa.eu/jrc/pvgis](https://ec.europa.eu/jrc/pvgis)), and BSRN data from [[https://bsrn.awi.de](https://bsrn.awi.de)]([https://bsrn.awi.de](https://bsrn.awi.de)). Both web sources provide their data free-of-charge for scientific purposes and were accessed on 1 July 2021. The authors are especially grateful to the following scientists: (i) [PERSON] (LIN) and [PERSON] (KIS) for providing formulated data from their BSRN stations for years 2018 and 2020, respectively; (ii) [PERSON] (World Radiation Monitoring Centre) for providing access to the PANGAEA website ([[https://bsrn.awi.de/data-retrieval-via-pangaea](https://bsrn.awi.de/data-retrieval-via-pangaea)]([https://bsrn.awi.de/data-retrieval-via-pangaea](https://bsrn.awi.de/data-retrieval-via-pangaea)), accessed on 1 July 2021) and downloading data for 11 BSRN stations. Data from the ATH station have been possessed by the first author as member of the Institute where the station belongs to. Also acknowledged are the following scientists who are/were responsible for their BSRN stations used in this study: [PERSON] for BOU; [PERSON] for CAR; [PERSON] for DAA; [PERSON] for GAN; [PERSON] for ILO; [PERSON] for LER; [PERSON] for OHY; [PERSON] for PAY; [PERSON]. Halliwell for REG; [PERSON] for SON; and, [PERSON] for SOV. [PERSON] and [PERSON] are acknowledged for the maintenance of the ATH solar radiation station. The authors declare no conflict of interest.