In this paper we propose a novel methodology for tracking the maxima of rainfall precipitation fields, whose changes in time may give interesting insights on the evolution of storms. Our approach is based on a topological analysis of rainfall data allowing for the extraction of the most prominent, and hence meaningful, rainfall field maxima. Then, an ad-hoc bottleneck matching is used to track the evolution of maxima along multiple time instances. The potential of our method is exhibited through a set of experiments carried out on a collection of observed punctual rainfall data and radar measurements provided by Genova municipality and Regione Liguria.