Abstract

Networks are highly effective tools for analyzing the dynamics of Earth’s climate system. In this approach, nodes represent geographical locations and edges represent correlations or causal relationships with respect to climate fields, such as air and sea surface temperatures. We extend this technique by integrating it with topological data analysis (TDA), which shifts the focus from pairwise relationships—typical of conventional network methods—to higher-order interactions among geographic locations. Through techniques such as persistent homology and simplicial distributions, we investigate how the global climate dynamics—summarized by this representation—have evolved over the last 75 years. Additionally, we evaluate changes in oceanic connectivity with the Arctic using directed metrics and simulations to better understand the effects of global warming on circulation patterns. Our results indicate that the global climate has undergone significant alterations in its topology, characterized by both short-term fluctuations and long-term shifts. At the same time, preliminary evidence suggests that the directed topology of the Arctic circulation has exhibited notable trends and short-term variability, as well as large-scale shifts in external modes of influence. Our findings underscore the pivotal role that such changes can play in triggering tipping points, with profound implications for Earth’s climate stability.

Publication Date

5-2026

Document Type

Thesis

Student Type

Graduate

Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

Mathematical Sciences, School of

College

College of Science

Advisor

Nishant Malik

Advisor/Committee Member

Matthew Hoffman

Advisor/Committee Member

James J Benedict

Campus

RIT – Main Campus

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