Application of Topological Data Analysis to Multi-Resolution Matching of Aerosol Optical Depth Maps

Dorcas Ofori-Boateng,Yulia R Gel,Krzysztof M Gorski,Huikyo Lee,Michael J Garay

doi:10.3389/fenvs.2021.684716

Abstract

Topological data analysis (TDA) combines concepts from algebraic topology, machine learning, statistics, and data science which allow us to study data in terms of their latent shape properties. Despite the use of TDA in a broad range of applications, from neuroscience to power systems to finance, the utility of TDA in Earth science applications is yet untapped. The current study aims to offer a new approach for analyzing multi-resolution Earth science datasets using the concept of data shape and associated intrinsic topological data characteristics. In particular, we develop a new topological approach to quantitatively compare two maps of geophysical variables at different spatial resolutions. We illustrate the proposed methodology by applying TDA to 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 different observational and model datasets without regridding the datasets into common grids.

Highlights

While systematic, multi-model experimentation and evaluation have been undertaken for years (e.g., the Coupled Model Intercomparison Project—CMIP—Taylor et al (2012); Eyring et al (2016)), the development and application of methodologies for comparing spatial patterns in key climate variables from observational and model datasets with different spatial resolutions are less mature
There is no community standard for regridding datasets onto common grids, datasets at higher resolutions are Topological data analysis (TDA) of aerosol optical depth (AOD) Maps usually upscaled onto low-resolution grids for the quantitative comparison with lower resolution datasets
The first thing that is apparent is that all four metrics have similar overall behavior, which means that Wasserstein distances are consistent with biases and RMSEs

Summary

Introduction

Multi-model experimentation and evaluation have been undertaken for years (e.g., the Coupled Model Intercomparison Project—CMIP—Taylor et al (2012); Eyring et al (2016)), the development and application of methodologies for comparing spatial patterns in key climate variables from observational and model datasets with different spatial resolutions are less mature. The Taylor diagram (Taylor, 2001) is popular among climate modelers since it displays both RMSE and a pattern correlation coefficient simultaneously In this way, Taylor diagrams provide a concise summary of the similarity in spatial patterns useful for quantitative comparison of different datasets. There is no community standard for regridding datasets onto common grids, datasets at higher resolutions are TDA of AOD Maps usually upscaled onto low-resolution grids for the quantitative comparison with lower resolution datasets. In this way, the regridding averages out fine-scale features contained in the high-resolution datasets without elucidating the information lost due to the upscaling

Methods

Results

Conclusion