With the availability of smart devices and affordable data plans, social media platforms have become the primary source of information dissemination across geographically dispersed users/locations. It has shown great potential across different application domains including event detection, opinion analysis, recommendation, and prediction. However, the process of extracting useful information from the collected voluminous social media data during natural hazards is a standing problem that needs significant attention from the research community. The fine-grained knowledge detailing users’ participation in information spreading could be advantageous in developing a reliable social network for the adverse events (Natural Hazards, Man-made attacks etc.). However, there has been no such findings related to identification of leader and their leadership characteristics associated with natural hazards in previous studies. We have collected 20.6 million tweets which were posted by 5.3 million users, during distinct devastating hazards namely - Floods, Hurricane, Earthquake and Typhoons. To achieve the goal, we divided our work in to three parts. Firstly, classify the collected crises data into four domains i.e resource, causality, news, and sympathy by employing deeper recurrent neural network model. Secondly, we used statistical physics of complex network to recognize local as well as global prominent leaders. At last, we curate leadership characteristics in terms of their big five personality traits and emotional traits. Our experimental, results find evidence that local leadership behaviour characteristics are significantly different from global potentials. Where as we also finds that some behaviour traits were certain to classified domains (resource, causality, news, and sympathy) and some were certain to hazard divisions, though emotional characteristics remained consistent. Later, we conclude that local potentials leaders have comparatively higher emotional strength. Furthermore, when the complete local network structure is unavailable, we find that the dynamic rank is reliable indexing proxy for local potentials. The current study, provide useful insight to understand how leadership characteristics are influenced to hazards, domains and centrality of users.