Emergent self-similarity and scaling properties of fractal intra-Urban Heat Islets for diverse global cities

Urban areas experience elevated temperatures due to the Urban Heat Island (UHI) effect. However, temperatures within cities vary considerably and their spatial heterogeneity is not well characterized. Here, we use Land Surface Temperature (LST) of 78 global cities to show that the Surface UHI (SUHI) is fractal. We use percentile-based thermal thresholds to identify heat clusters emerging within SUHI and refer to them collectively as intra-urban heat \textit{islets}. The islets display properties analogous to that of a percolating system as we vary the thermal thresholds. At percolation threshold, the size distribution of these islets in all cities follows a power-law, with a scaling exponent ($\beta$) of 1.88 ($\pm 0.23, 95\% CI$) and an aggregated Perimeter Fractal Dimension ($D$) of 1.33 ($\pm 0.064, 95\% CI$). This commonality indicates that despite the diversity in urban form and function across the world, the urban temperature patterns are different realizations with the same aggregated statistical properties. Furthermore, we observe the convergence of these scaling exponents as the city sizes increase. Therefore, while the effect of diverse urban morphologies is evident in smaller cities, in the mean, the larger cities are alike. Lastly, we calculate the mean islet intensities, i.e. the difference between mean islet temperature and thermal threshold, and show that it follows an exponential distribution, with rate parameter, $\lambda$, for all cities. $\lambda$ varied widely across the cities and can be used to quantify the spatial heterogeneity within SUHIs. In conclusion, we present a basis for a unified characterization of urban heat from the spatial scales of an urban block to a megalopolis.