Recently, an abrupt structural phase transition for two interconnected random networks has been analyzed by Radicchi and Arenas (see [F. Radicchi and A. Arenas, Nature Physics (2013)]). They mainly investigated the sudden changes of the second smallest eigenvalue of the Laplacian matrix, λ₂, and its eigenvector. This provides a good method for measuring how two networks are coupled. We use a similar method to study the coupling strength between two climate networks and its variation. Our results on the coupled air temperature networks on the Pacific reveal that during El Niño events, the inter-connectivity links will be reduced. However, the real system will become relatively better coupled.