Improving estimates of built-up area from night time light across globally distributed cities through hierarchical modeling

Built-up area has become an important indicator for studying urban environments, but mapping built-up area at the regional/global scale remains challenging due to the complexity of impervious surface features. Nighttime light data (NTL) is one of the major remote sensing data sources for regional/global built-up or impervious surface mapping. A single regression relationship between fractional built-up/impervious area and NTL or various indices derived based on NTL and vegetation index (e.g., NDVI) data had been established in many previous studies. However, due to the varying geographical, climatic, and socio-economic characteristics of cities, the same regression relationship may vary significantly across cities. In this study, we examined the regression relationship between percentage of built-up area (pBUA) and vegetation adjusted nighttime light urban index (VANUI) for 120 randomly selected cities around the world with a hierarchical hockey-stick regression model. We found that there is a substantial variability in the slope (0.658 ± 0.318), the threshold VANUI (−1.92 ± 0.769, log scale) after which the linear relationship holds, and the coefficient of determination R² (0.71 ± 0.14) among globally distributed cities. A small proportion of this substantial variability can be attributed to socio-economic status (e.g., total population, GDP per capita) and landscape structures (e.g., compactness and fragmentation). Due to these variations, our hierarchical model or no-pooling model (i.e., fit each city individually) can significantly improve model prediction accuracy (17% in terms of root mean squared error) over a complete-pooling model. We, however, recommend hierarchical models as they can provide meaningful priors for future modeling under a Bayesian framework, and achieve higher prediction accuracy than no-pooling models when sample size is small.