Using radiant intensity to characterize the anisotropy of satellite-derived city light at night

Abstract

Recent studies have described the anisotropy of ALAN based on statistical analysis of a quadratic model-based relationship between radiances derived from the VIIRS Day/Night Band sensor onboard Suomi-NPP and viewing zenith angle (VZA) (Li et al., 2019). Contrary to conventional wisdom, the satellite-observed radiance of ALAN always decreases at first and then increase with VZA, especially for high building areas. This leads to a so-called ‘cold-spot’ effect (i.e. radiance reaches local minimum in a specific VZA) in the VZA-radiance relationship, one that has not been understood using existing remote sensing methods. In this paper, we propose using radiant intensity – a measure of light power in a specific direction– to characterize the anisotropy of satellite-observed artificial lights at night (ALAN). Accordingly, we propose a new study design based on analysis across fourteen global cities. A linear regression model describing the relationship between VZA and radiant intensity resulted in an averaged regression R2 between 0.26 and 0.73 for the cities, suggesting a decay of radiant intensity with increased VZA. We then introduced a cosine-corrected linear model to describe the VZA-radiance relationship, which is mathematically transformed from the linear VZA-intensity model. Our results suggest that the ‘cold spot’ effect in the VZA-radiance relationship is consistent with the revealed phenomenon that the radiant intensity decays with increased VZA. We also constructed indexes related to urban morphology derived from LiDAR data, including the Blocking Index (BI), the Standard Deviation of Building Height (SDBI) and Average Building Height (ABH). These variables were all moderately or strongly correlated (Pearson correlation coefficient < −0.45) to the Change Index (CI), which describes the anisotropic pattern of ALAN in the VZA-intensity relationship, in the four U.S. cities where LiDAR data is accessible. We conclude that radiant intensity is a suitable physical index to characterize the directional distribution of ALAN that can help understand the anisotropy of ALAN.