*2.2. The v.sun Solar Radiation Model*

The v.sun model is essentially a 3D variant of the r.sun model that can also calculate direct, diffuse, and reflected solar radiation for a given day, latitude and surface, and atmospheric conditions. It is implemented in the GRASS GIS environment and is based on practically the same radiation methodology as the r.sun model. The difference, however, is that the v.sun model uses a new vector-voxel calculation procedure for complex 3D urban surfaces [5].

Buildings and urban areas are represented by 3D vectors in the form of polygons when using the v.sun model in 3D urban models. A typical simple digital representation of buildings is a box model. Although the calculation of the incident solar radiation for each polygon may seem simple, the shading effect of neighboring buildings must also be taken into account. This is why it is important in the v.sun model to take into account the variations in solar incidence and to divide each polygon into smaller segments. By segmenting the polygons in the next step, we are able to determine a more accurate estimate of the solar potential of polygonal areas thanks to voxels [5].

The v.sun model estimates direct, diffuse, and reflected radiation during clear-sky conditions. As solar radiation passes through the atmosphere, airflow and atmospheric cloudiness are taken into account, which can change the nature of the radiation. Similar to r.sun, the calculation works in two modes. The first mode is used to compute solar irradiances (in W/m2) for 3D polygonal data. The second mode aims to use the 3D vector data to determine the daily solar irradiation (in W/m2) over the time span of a particular day within the year. The advantage of these modes is that they can work alone or in combination to estimate the solar radiation impact at different time intervals.

The fundamental difference between the v.sun and r.sun module is in the geometry. While v.sun uses a complete or full 3D model of the city (roofs as well as vertical surfaces, such as facades, are taken into account), r.sun is a 2D (for a given x,y position, only one elevation value is possible). Thus, the r.sun model is more suitable for modeling the distribution of solar radiation for roofs and areas outside buildings.

The preparation of the input data of the v.sun model is quite complicated in terms of structure and topology. The orientation of the polygons (surface normals) must be outwards, and the vertices in all polygons must be ordered in the same manner clockwise or counterclockwise. The accuracy of the calculations depends on the size of the polygons that can be controled by a parameter [5].
