The effects of sky diffuse light on indoor illuminance through radiosity models: a case study in Burgos

Diffuse radiation can play a critical role in the design of sustainable urban environments, in so far as it can transmit natural light to areas that direct sunlight cannot reach because of buildings and other structures. This characteristic of sky luminance is crucial for radiosity-based methods where luminance is used to determine energy transfer between surfaces. Consequently, the accuracy of a radiosity-based model will depend upon how well it can capture the subtle variations of sky luminance. In this study, both the accuracy and the performance of three luminance models are evaluated: the All-Weather model, the All-Sky model, and the CIE Standard General Sky model, focusing on their capability to replicate luminance at any point in the sky and at any given time. The results showed that while the CIE Standard Sky model offered the highest accuracy, it required more complex input data. The All-Weather and the All-Sky models rely on radiometric measurements. Both produced reliable results, with the All-Weather model standing out, because of its efficiency and minimal data requirements. Despite those strong points, all the models demonstrated higher error rates near the horizon, due to the challenges of accurately modeling luminance in this region. In this study, two radiosity methods were compared for calculating indoor illuminance: the Simplified Radiosity Algorithm (SRA), which considers spatial luminance variations across the openings, and the DeLight method, which assumes a uniform luminance distribution throughout the window view. The analysis of the results showed that the error rates produced in the luminance pattern estimations were reflected in the Radiosity model. Taking that effect into account, the combination of the All-Sky model with the SRA algorithm demonstrated a strong balance between accuracy and resource efficiency, offering a practical approach for sustainable urban lighting design.