Modelling Multi-angle Nighttime Light Observations to Investigate the Impact of Urban Structure on Angular Effect

Nighttime light (NTL) data, a remote-sensing record of surface brightness, offer unique observations of cities. With the advantage of high spatiotemporal coverage, NTL data have been widely used to extract urban extents, monitor human activities, quantify socio-economic resources, and estimate energy consumption. Recent products with a higher spatiotemporal resolution have further expanded applications, enabling daily 500-m-resolution monitoring of festivals, wars, and fishing vessels. Most existing studies, however, use only the radiance or spatial extent of NTL and ignore the angular information, which limits their application in observing the internal spatial structure of cities.

Beyond brightness features, the angular information of NTL data characterizes the urban spatial structure. As the viewing zenith angle (VZA) of daily satellites varies, recorded radiance differs because buildings increasingly mask the light, creating an angular effect. Existing studies have modelled angular effects with linear, quadratic, or polynomial models, revealing divergent angular signatures between urban centres and suburbs. However, two gaps persist. First, no unified angular-effect model exists. Although linear and quadratic regressions can depict positive, negative, or U-shaped angular effects, the angular effects they quantify are not directly comparable. Second, explanatory insight into the drivers of the angular effects remains unclear. Although correlations with building height and density have been reported, interpretability is lacking. These knowledge gaps hinder the translation of angular effect research from theory into practice.

Here, we quantify and explain the angular effects across five U.S. cities—Baltimore, Boston, Dallas, Washington D.C., and New York—from 2013 to 2024. We first construct a novel model that captures the relationship between VZA and NTL intensity, introducing a new metric for quantifying angular effects. The model performs well overall, with R² > 0.6 for more than 70% of pixels. We then develop a series of indicators and apply an interpretable machine-learning framework. We found that pixels with high angular-effect values are characterized by high building-light blockage, high building density and significant variation in building height. All ten indicators collectively explain the angular effect. This study bridges the gap between the angular effects and urban structure, enabling large-scale and high-frequency monitoring of urban structure in data-deficient regions (such as Africa) in the future.