Application of topological data analysis to comparing aerosol optical depth map

Topological data analysis (TDA) combines concepts from algebraic topology, machine learning, statistics, and data science that allows us to study data in terms of their latent shape properties. Despite the of TDA in a broad range of applications, from neuroscience to power systems to finance, the utility of TDA in the Earth Science applications is yet untapped. The current study aims to offer a new direction to analysis of multi-resolution Earth science data using the concept of data shape and the associated intrinsic topological data characteristics. In particular, we develop a new topological approach for multi-resolution data matching and evaluation of the associated impact of spatial scale on the derived conclusions. We illustrate the proposed new methodology in application to the aerosol optical depth (AOD) datasets from the Goddard Earth Observing System, Version 5 (GEOS-5) model over the Middle East. Our results show that contrary to the existing approaches, TDA allows for systematic and reliable comparison of spatial patterns from various observational and model datasets without regridding the datasets into common grids.