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We construct climate networks based on surface air temperature data toidentify distinct signatures of diverse climatic events, here El Nino, LaNina and tropical cyclones. The climate network, which functions as apercolating network, shows discontinuous phase transition in the size ofthe normalised largest cluster and the susceptibility during these events.The correlation matrix of the network shows a structure that has distinctcharacteristics for each climatic event, e.g. El Nino events, La Ninaevents, and normal conditions of the Pacific oceans well as in extremeevents like tropical cyclones. These signatures can be seen in heat maps,percolation measures, network quantifiers like the betweenness centrality,and the node degrees and the critical values of the correlations. Thedistribution of teleconnections of distinct strengths, the betweennesscentrality distributions, and the geographic location of nodes of highdegree and high betweenness centrality yields important insights into thestructure of the network and the transfer of information between differentparts. We further discuss the predictive power of these quantities, aswell as their connections with phenomena like the North AtlanticOscillation, and the paths of cyclones.