Solar radiation has a crucial role in photosynthesis, evapotranspiration and other biogeochemical processes. The amount of solar radiation reaching the Earth's surface is a function of astronomical geometry and atmospheric optics. While the first is deterministic, the latter has a random behaviour caused by highly variable atmospheric components such as water and aerosols. In this study, we use daily radiation data (1978-2014) from 37 FLUXNET sites distributed across the globe to inspect for climatic traits in the shape of the probability density function (PDF) of the clear-day (c) and the clearness (k) indices. The analysis was made for shortwave radiation (SW) at all sites and for photosynthetically active radiation (PAR) at 28 sites. We identified three types of PDF, unimodal with low dispersion (ULD), unimodal with high dispersion (UHD) and bimodal (B), with no difference in the PDF type between c and k at each site. Looking for regional patterns in the PDF type, we found that latitude, global climate zone and Köppen climate type have a weak relation and the Holdridge life a stronger relation with c and k PDF types. The existence and relevance of a second mode in the PDF can be explained by the frequency and meteorological mechanisms of rainy days. These results are a frame to develop solar radiation stochastic models for biogeochemical and ecohydrological modelling.