Abstract

We investigate higher-order interactions in climate networks using topological data analysis (TDA) and analyze their evolution since 1948. Using the correlation between surface air temperature (SAT) anomalies, we define relationships between spatial locations and examine the patterns that emerge over time. We extend the framework of temporal climate networks and apply TDA methods, including persistent homology, curvature analysis, and the Euler characteristic, to identify dynamic structural features. Persistent homology tracks the births and deaths of topological features such as connected components and loops. Curvature quantifies a node’s participation in higher- order structures (cliques), while the Euler characteristic captures global trends in clique organization over time. Our results indicate that patterns in the Betti numbers and Euler characteristics are associated with evolving climate regimes, as well as short-term impacts of major volcanic eruptions, and the El-Niño-Southern Oscillation (ENSO). We also perform temporal trend and diffusion analyses on directed networks constructed using the same steps. We find significant exchange of information between the eastern tropical Pacific and the Atlantic Ocean, and a structure overlaying the Atlantic Meridional Overturning Circulation (AMOC) that participates in high final flows. This work demonstrates that topological analysis can reveal meaningful structural signals in complex real-world systems such as the climate.

Library of Congress Subject Headings

Climatic changes--Mathematics; Topology

Publication Date

5-7-2026

Document Type

Thesis

Student Type

Graduate

Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

Mathematics and Statistics, School of

College

College of Science

Advisor

Nishant Malik

Advisor/Committee Member

Matthew Hoffman

Advisor/Committee Member

Carolyn Branecky Begeman

Campus

RIT – Main Campus

Plan Codes

ACMTH-MS

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