Geometrical Assessment of Sunlit and Shaded Area of Urban Trees Based on Aligned Orthographic Views

Abstract

To quantify the ecosystem services of trees in urban environments, it is necessary to assess received direct solar radiation of each tree. While the Sky View Factor (SVF) is suitable for assessing the total incoming short- and longwave radiation fluxes, its information is limited to specific points in space. For a spatial analysis, it is necessary to sample the area for SVF. A new geometrical method, Area View Factor (AVF), for the calculation of sunlit areas is proposed. AVF is the ratio of the unhidden, projected surface of an object to the whole projected surface of an object in a complex environment. Hereby, a virtual, orthographic camera is oriented in accordance to the sun’s position in the 3D model domain. The method is implemented in the microscale model SkyHelios, utilizing efficient rendering techniques to assess AVF of all urban trees in parallel. The method was applied to Rieselfeld in Freiburg, Germany. The assessed sunlit area is compared to the SVF at the top of each tree and solar altitude angle, revealing a strong relationship between sunlit areas to solar altitude angles. This study shows that AVF is an efficient methodology to assess received direct radiation of urban trees. Based on AVF, it is possible to identify urban areas with shaded and sunlit trees, but it can also be applied to other objects in complex environments. Therefore, AVF is applicable for urban architecture or energetic research questions.