Topological Data Analaysis for Rossby Wave Estimation

Multiscale methods are a widespread topic of interest in statistical research. One particularly valuable aspect of these methods is to identify meaningful features in data across different scales, which allows practitioners to interact with their data in an interpretable manner. We present a multiscale method related to the growing topic of topological data analysis (TDA) which we call a sequential filtration. This method provides a multiscale application of TDA principles, which serves as a powerful tool in estimation of a response surface. We apply these methods to atmospheric data, specifically geopotential heights in the northern hemisphere. After describing a variety of applications of sequential filtrations, we show the performance of each in estimating the number of Rossby waves on a daily basis, leading to a discussion of the utility of multiscale persistence generally.