Topological Data Analysis of Urban Heat Islands Using Persistent Homology: Case Study of Holy Karbala

Abstract The UHI (Urban Heat Island) problem in Karbala, Iraq is complicated and extends beyond normal city maps. To better understand this problem, the researchers utilized QRS (Quantitative Remote Sensing) along with TDA (Topological Data Analysis), treating the thermal field(s) like a Topological Manifold. The researchers used Vietoris-Rips filtering on Landsat-8 imagery to make "Thermal Shape Fingerprints" of the UHI (Urban Heat Island); at a global average temperature of 48.7°C (but many structured thermal features were found), Persistent Homology was calculated, and it became evident that a transition was located at a thermal level of 42°C, giving rise to 7 main thermal loops (beta1 generation elements) encircling the centre. The researchers also found that the stable H1 cycle situated at the shrines proved that the architectural elements of these structures acted as a "topological void." This effect produces (~14°C (Delta QA)) in cooling from the surrounding ambient temperature. This effect was also supported by the calculation of Wasserstein Stability of 3.1, confirming that the structures themselves are fixed and presented the requirement for "Topological Urban Design" to separate the 18 stable thermal clusters. Keywords: Urban Heat Island (UHI), Topological Data Analysis (TDA), Persistent Homology, Vietoris-Rips Filtration, Betti Numbers; Thermal Manifold, Holy Karbala, Remote Sensing Physics