A Cyclone Identification Algorithm with Persistent Homology and Merge-Tree

Abstract

This paper addresses a cyclone identification algorithm with the superlevel set filtration of the persistent homology together with the merge-tree reconstruction of data. Based on the information of peaks and saddles of the scaler field, the newly developed algorithm divides the analysis area into several homology classes, each of which satisfies the peak-to-saddle difference larger than a criterion that should be set in advance. Applied to the 850-hPa relative vorticity in the western North Pacific at 1200 UTC on 2 March 2013, 3 homology classes were found with the criterion of 100 × 10⁻⁶ s⁻¹ and 17 homology classes were found with the criterion of 50 × 10⁻⁶ s⁻¹. The merge-tree restructuring clarified the neighbour relation among homology classes. The result suggests that the weak criterion detected too much homology classes, some of which are small peaks inside of a single cyclone. The climatology feature density provides the Pacific storm track with the strict criterion. Finally, a possible way to extend toward cyclone tracking with the persistent homology is discussed.