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The resilience of internet service is crucial for ensuring consistent communication, situational awareness, facilitating emergency response in our digitally-dependent society. However, due to empirical data constraints, there has been limited research on internet service disruptions during extreme weather events. To bridge this gap, this study utilizes observational datasets on internet performance to quantitatively assess the extent of internet disruption during two recent extreme weather events. Taking Harris County in the United States as the study region, we jointly analyzed the hazard severity and the associated internet disruptions in the context of two extreme weather events. The results show that the hazard events significantly impacted regional internet connectivity. There exists a pronounced temporal synchronicity between the magnitude of disruption and hazard severity: as the severity of hazards intensifies, internet disruptions correspondingly escalate, and eventually return to baseline levels post-event. The spatial analyses show that internet service disruptions can happen even in areas that are not directly impacted by hazards, demonstrating that the repercussions of hazards extend beyond the immediate area of impact. This interplay of temporal synchronization and spatial variance underscores the complex relationships between hazard severity and Internet disruption. Furthermore, the socio-demographic analysis suggests that vulnerable communities, already grappling with myriad challenges, face exacerbated service disruptions during these hazard events, emphasizing the need for prioritized disaster mitigation strategies and interventions for improving the resilience of internet services. To the best of our knowledge, this research is among the first studies to examine the Internet disruptions during hazardous events using a quantitative observational dataset. The insights obtained hold significant implications for city administrators, guiding them towards more resilient and equitable infrastructure planning. [ABSTRACT FROM AUTHOR]