## 1 Introduction  
Ultraviolet radiation is the region of the solar spectrum with wavelengths between 100 and 400 nm. It is usually divided into three spectral bands: UV-C (100-280 nm), completely absorbed in the Earth's atmosphere; UV-B (280-315 nm), partially absorbed by the stratospheric ozone; and UV-A (315-400 nm), weakly absorbed by ozone and therefore transmitted to the Earth's surface [1]. UV radiation varies greatly on the ground, depending mainly on latitude, solar elevation, temperature, cloud characteristics, total ozone, aerosol pollution, and surface albedo [2, 3]. Ultraviolet radiation can induce serious adverse health effects and may be responsible for premature skin aging, proliferation of skin cancer [4, 5, 6], immune deficiencies and cataracts, as well as damage to ecosystems, crops [7, 8], and the biosphere [9]. However, ultraviolet radiation in moderate doses has health benefits, can reduce blood pressure, has been linked to improvements in mental health, and promotes the synthesis of vitamin D, among other advantages [10]. As not all ground meteorological stations have sensors to measure ultraviolet irradiance [11], mathematical models are therefore usually developed to generate ultraviolet values based on experimental measurements of other meteorological data that are more frequently recorded at ground meteorological stations, such as horizontal global irradiance [12]. In many works, the ratio between the ultraviolet component and the horizontal global irradiance, \((\mathrm{I_{UV}}/\mathrm{I_{GH}})\), has been studied, obtaining values of between 2.5% and 6% [13]. A complete review of this relation can be found in [14]. The ratio between both magnitudes is location dependent and is influenced by the clearness index, \(\mathrm{k_{K}}\); when cloudiness increases, the ratio of \(\mathrm{I_{UV}}\) to \(\mathrm{I_{GH}}\) increases [15], i.e., the presence of clouds reduces the global horizontal irradiance to a greater extent than the UV component [16, 17, 18]. The dependence of solar UV irradiance on solar elevation has also been studied, observing that when solar elevation increases, the levels of I\({}_{\rm UV}\) reaching the surface also increase. It can be concluded that solar elevation is one determining factor when modeling solar UV radiation under all sky conditions [18]. It has been found that the dependence of I\({}_{\rm UV}\) upon I\({}_{\rm GH}\) and the relative optical air mass can be parameterized with the brightness index on a daily basis [19; 20], revealing a strong inverse linear dependence on the logarithm in relation to the optical air mass. Several works have developed different mathematical models for obtaining UV values as a function of certain atmospheric parameters such as relative optical air mass, cloud modification factors [3; 21; 22], aerosols, different tilt angles and ozone as well as local surface characteristics (albedo) [23], cosine of the solar zenith angle [2], precipitable water content, total ozone column, aerosol optical depth, temperature, humidity and dew point temperature under all sky conditions [13]. Many other works observed that I\({}_{\rm UV}\) and I\({}_{\rm GH}\) are mainly affected by solar zenith angle [24]. Besides the variation in solar zenith angle, cloud cover is an important factor in UV levels [25]; however, under clear skies, the most important factor in the attenuation of solar radiation are aerosols [26]. The model is therefore often programmed to perform a preliminary classification of the atmospheric conditions, based on sky types, using the clearness index as a classifier with different time intervals [2; 3; 27]. The UV component has been modeled in China, using two input parameters: the effect of the comprehensive attenuation factors for assumed cloud-free conditions and the effect of the clouds; this has obtained good results at a different location from the one at which model was developed [28].