A Satellite-Based Sky Luminance Model for the Tropics

This paper presents a sky luminance model for the tropics. The model is mathematically expressed as a multiplication of two functions. These are phi, which is a function of the zenith angle of a sky element and solar zenith angle, and f, which is a function of the angle between the sky element and the sun. To obtain the analytical forms of these functions, the sky luminance data collected at Nakhon Pathom (13.82 degrees N, 100.04 degrees E), Thailand, during a four-year period were analyzed. Additionally, satellite-derived cloud index at the position of the sky luminance measurements during the same period was estimated. Based on values of the cloud index, the skies were classified into 10 types, from clear to overcast skies. By using appropriate grouping and mathematical operation of the sky luminance data, the values of the two functions were obtained and then fitted with empirical equations. The multiplication of these equations gives the final form of the sky luminance model. To validate the model, it was used to calculate the relative sky luminance at other three sites in the tropics. It was found that values of relative sky luminance calculated from the model and those obtained from the measurements were in reasonable agreement.