A contour tree is a topological structure that stores the nesting relationships of contours in a scalar field with the tree nodes being maxima, minima, and saddles points. Given the time varying nature of the hurricane data, we enhance a static contour tree to picture the time-varying topology so that the changes of time-varying contours are captured. The tree nodes are aligned with inner core features, since these features are often associated with minima or maxima of temperature, wind speed, precipitation, etc., and saddles which present the splits and merges of contours are the candidate points where a secondary eyewall may be branched out from a primary eyewall. Quantitative properties, such as volume and time duration of contours, are computed and labelled on the contour tree. As a result, we are able to visualize and track the evolution of the inner core features over time, providing an interesting insight into their development from a topological perspective for the first time.