## 1 Introduction  
Daylighting is a design concept of buildings used over the years with varying degrees of success. It has been proven that buildings with good daylighting have positive effects on the well-being and health of occupants, reducing stress levels, and improving mood and photobiological effects [1; 2; 3; 4; 5]. The International Energy Agency (IEA) promoted the use of daylight as a means of reducing electricity consumption on lighting [6], and increasing the energy efficiency of buildings [7; 8]. International Net Zero Energy Building (NZEB) standards and regulations recommend the incorporation of natural lighting strategies in their design and define minimum standards [9; 10]. A fundamental step towards building design that illuminates interiors with daylight is the compilation of information on daylight availability outside the building. Illuminance on vertically oriented surfaces is, therefore, important for modeling the daylight availability, especially for high-rise buildings with substantial areas of glazed surfaces [11]. Solar radiation data on vertical surfaces can also be used to evaluate the performance of Building Integrated Photovoltaics (BIPV), because the vertical facades of modern cities occupy larger areas than roof surfaces and usually present better maintenance conditions for photovoltaic panels [12]. However, the basic outdoor solar irradiance and illuminance data for the surfaces of interest are not usually available in many parts of the world [13]. The Vertical Sky Component (VSC) is defined as the ratio of the vertical diffuse illuminance (0) over the unobstructed horizontal diffuse illuminance 0 simultaneously measured at the same point [14]. City planners and developers use the VSC to assess the impact of newly built constructions on the access to daylighting. Its potential in early stage design decisions is widely recognized [15]. The VSC is an important daylight parameter, which has been also used for different applications: Sky classification [16; 17], unobstructed sky irradiance and illuminance determinations [18], and calculations of indoor illuminance [19]. Global and diffuse outdoor illuminance on a horizontal surface and vertical global illuminance on the four (north, east, south, and west) cardinal orientations have been used to compute the VSC. However, as experimental data of \(\mathrm{L_{dv}}\) and \(\mathrm{L_{dh}}\) are scarce, different alternatives are used to calculate VSC [11; 17; 20]. With a well-defined luminance distribution, the daylight illuminance on various inclined surfaces, such as vertical planes facing towards different directions, can be estimated by integrating the luminance distribution of the sky dome over each surface [21]. The usual instrument for measuring sky luminance distribution is by means of a sky scanner [8]. On the other hand, empirical models of homogeneous skies represent a low-cost approach to obtain sky luminance distribution. Generally, sky conditions can be subdivided into overcast, partly cloudy, and clear skies. In 2003, CIE [22] and the International Organization for Standardization (ISO) [23] adopted 15 Standard Sky Luminance Distributions (SSLD) as the most versatile definition of skylight in various localities and daylight climate regions, making it possible to simulate annual daylight profiles in absolute units based on typical luminance sky patterns. Despite the high interest in those measurements, very few studies at only a handful of European [24; 25; 26; 27; 28; 29] and Asian [15; 30; 31] locations have been conducted to characterize the sky under the CIE standard, mainly due to scarce sky luminance data obtained from sky scanner devices. Different alternatives to the use of sky scanners have been proposed for classifying the skies [32] including the use of different climatic parameters [33; 34; 35; 36], vertical [12; 20] and horizontal illuminance [37; 38], and satellite data [39].