Paradoxical impact of sprawling intra-Urban Heat Islets: Reducing mean surface temperatures while enhancing local extremes

Cities are at the forefront of climate change impacts and face a growing burden of adaptation to ensuing natural hazards. Extreme heat is a particularly challenging hazard as persistent heatwaves are locally exacerbated by the Urban Heat Island (UHI) effect. As a result, there is an increasing scientific interest in the influence of diverse urban morphologies on UHI. However, as the temperatures within cities are highly spatially heterogeneous, bulk quantification metrics such as UHI Intensity may hamper understanding. Here, we use remotely sensed Land Surface Temperature (LST) data for 78 diverse cities to develop a novel multi-scale framework of quantifying spatial heterogeneity in the Surface UHI. We identify heat clusters emerging within the SUHI using percentile-based thermal thresholds and refer to them collectively as \textit{intra-Urban Heat Islets}. We first develop a Lacunarity based metric ($\Lambda_{score}$) to quantify the spatial organization of heat islets at various degrees of sprawl and densification. Using probabilistic models, we condense the size, spacing, and intensity information about heterogeneous clusters into distributions that can be described using single scaling exponents. This allows for a seamless comparison of the heat islet characteristics across cities at varying spatial scales. From the size distribution analysis, we observe the emergence of two distinct classes wherein the dense cities (positive $\Lambda_{score}$) follow a Pareto size distribution, whereas the sprawling cities (negative $\Lambda_{score}$) show an exponential tempering of Pareto tail. This indicates a significantly reduced probability of encountering large heat islets for sprawling cities. Contrastingly, however, Heat Islet Intensity modeled as exponential distributions reveal that a sprawling configuration is favorable for reducing the mean temperature of a city. However, for the same mean SUHI intensity, it also results in higher local thermal extremes. This poses a paradox for urban designers in adopting expansion versus densification as a growth trajectory to mitigate the UHI.