Understanding how midlatitude weather may change due to global warming is one of the central challenges in climate science. This MRC will explore the use of topological data analysis (TDA) as a novel tool for addressing this question, with a broader goal of fostering new collaborations between TDA, climate science and dynamical systems theory.
From a dynamical systems perspective, predicting weather and climate amounts to determining future trajectories of the atmosphere on its attractor, with the main difficulties arising from the extremely high dimensionality of the climate system. Techniques from TDA, such as persistent homology, are particularly well suited to address this, as they allow one to study coarse invariants of the data that do not depend on embedding dimension or scale. Topological features of the attractor, such as loops and holes, place strong constraints on future trajectories that can then be studied and linked to important weather phenomena, such as the midlatitude jetstreams.
The MRC will consider practical questions, such as improving algorithms and software, and theoretical questions, such as analyzing dynamical properties of topological features. The use of TDA in climate and weather is in its infancy and there are many exciting potential avenues. We welcome applicants from academia or industry with a wide range of backgrounds, including TDA, climate science and dynamical systems. Tutorials on TDA, climate science, and dynamical systems will take place before the research week to cover the basic background.
Applications will be accepted on MathPrograms.org through Thursday, February 15, 2024 (11:59 p.m. EST).