Could social media data aid in disaster response and damage assessment? Countries face both an increasing frequency and an increasing intensity of natural disasters resulting from climate change. During such events, citizens turn to social media platforms for disaster-related communication and information. Social media improves situational awareness, facilitates dissemination of emergency information, enables early warning systems, and helps coordinate relief efforts. In addition, the spatiotemporal distribution of disaster-related messages helps with the real-time monitoring and assessment of the disaster itself. We present a multiscale analysis of Twitter activity before, during, and after Hurricane Sandy. We examine the online response of 50 metropolitan areas of the United States and find a strong relationship between proximity to Sandy's path and hurricane-related social media activity. We show that real and perceived threats, together with physical disaster effects, are directly observable through the intensity and composition of Twitter's message stream. We demonstrate that per-capita Twitter activity strongly correlates with the per-capita economic damage inflicted by the hurricane. We verify our findings for a wide range of disasters and suggest that massive online social networks can be used for rapid assessment of damage caused by a large-scale disaster.