<div><br></div><div>Extreme heat is one of the deadliest health hazards that is projected to increase in intensity and persistence in the near future. Temperatures are further exacerbated in the urban areas due to the Urban Heat Island (UHI) effect resulting in increased heat-related mortality and morbidity. However, the spatial distribution of urban temperatures is highly heterogeneous. As a result, metrics such as UHI Intensity that quantify the difference between the average urban and non-urban air temperatures, often fail to characterize this spatial and temporal heterogeneity. My objective in this thesis is to understand and characterize the spatio-temporal dynamics of UHI for cities across the world. This has several applications, such as targeted heat mitigation, energy load estimation, and neighborhood-level vulnerability estimation.</div><div><br></div><div>Towards this end, I have developed a novel multi-scale framework of identifying emerging heat clusters at various percentile-based thermal thresholds T_thr and refer to them collectively as <i>intra-Urban Heat Islets</i>. Using the Land Surface Temperatures from Landsat for 78 cities representative of the global diversity, I have showed that the heat islets have a fractal spatial structure. They display properties analogous to that of a percolating system as T_thr varies. At the percolation threshold, the size distribution of these islets in all cities follows a power-law, with a scaling exponent = 1.88 and an aggregated Area-Perimeter Fractal Dimension =1.33. 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. In addition, analogous to the UHI Intensity, the mean islet intensity, i.e., the difference between mean islet temperature and thermal threshold, is estimated for each islet, and their distribution follows an exponential curve. This allows for a single metric (exponential rate parameter) to serve as a comprehensive measure of thermal heterogeneity and improve upon the traditional UHI Intensity as a bulk metric.</div><div><br></div><div><br></div><div>To study the impact of urban form on the heat islet characteristics, I have introduced a novel lacunarity-based metric, which quantifies the degree of compactness of the heat islets. I have shown that while the UHIs have similar fractal structure at their respective percolation threshold, differences across cities emerge when we shift the focus to the hottest islets (T_thr = 90^th percentile). Analysis of heat islets' size distribution demonstrates the emergence of two classes where the dense cities maintain a power law, whereas the sprawling cities show an exponential deviation at higher thresholds. This indicates a significantly reduced probability of encountering large heat islets for sprawling cities. In contrast, analysis of heat islet intensity distributions indicates that while a sprawling configuration is favorable for reducing the mean Surface UHI Intensity of a city, for the same mean, it also results in higher local thermal extremes. </div><div><br></div><div>Lastly, I have examined the impact of external forcings such as heatwaves (HW) on the heat islet characteristics. As a case study, the European heatwave of 2018 is simulated using the Weather Research Forecast model with a focus on Paris. My results indicate that the UHI Intensity under this HW reduces during night time by 1^oC on average. A surface energy budget analysis reveals that this is due to drier and hotter rural background temperatures during the HW period.</div><div>To analyze the response of heat islets at every spatial scale, power spectral density analysis is done. The results show that large contiguous heat islets (city-scale) persist throughout the day during a HW, whereas the smaller islets (neighborhood-scale) display a diurnal variability that is the same as non-HW conditions. </div><div><br></div><div>In conclusion, I have presented a new viewpoint of the UHI as an archipelago of intra-urban heat islets. Along the way, I have introduced several properties that enable a seamless comparison of thermal heterogeneity across diverse cities as well as under diverse climatic conditions. This thesis is a step towards a comprehensive characterization of heat from the spatial scales of an urban block to a megalopolis.</div><div><br></div>