The El Niño Southern Oscillation (ENSO) is a set of coupled ocean-atmosphere phenomena characterised by an irregular cycle of warming (El Niño) and cooling (La Niña) in the eastern tropical Pacific together with a corresponding variation in sea level pressure. ENSO significantly impacts global weather patterns and it is one of the main phenomena of atmospheric variability studied and modelled by climate scientists. A better understanding of the ENSO dynamics is crucial in the modelling of the climate’s response to continued anthropogenic emissions.

In the light of its many successful results, this work has the purpose of establishing a baseline for the study of ENSO using Persistent Homology (PH), through simulations of quasi-periodic signals. We are using the deterministic version of a delayed oscillator (DO) model used to describe the thermocline depth anomaly in Central and Eastern Tropical Pacific region[1]. At first we use sublevel set filtrations, which was then used to conducted PH analysis and then split into two different studies: one for k-means clustering and the other for CROCKER plots [2]. The former was applied to the synthetic and simulated data. The latter was only used for simulations of the deterministic DO for 282 values of κ — the ocean-atmosphere coupling parameter. CROCKER plots are a method recently introduced in TDA to qualitatively identify bifurcations in dynamical systems. In all methods described, while they still need more statistical validation, results suggest that TDA and PH potentially provide new insights to and can help to analyze the dynamics of climatic systems.

This internship was funded through a PEPR Maths Vives grant, and took place at the Laboratoire de Mathématiques d’Orsay.

References:

[1] Hannah Christensen, Judith Berner, Danielle Coleman, Tim Palmer, Stochastic Parameterization and El Niño–Southern Oscillation, Journal of Climate, 2017

[2] İsmail Güzel, Elizabeth Munch, Firas A. Khasawneh; Detecting bifurcations in dynamical systems with CROCKER plots. Chaos 1 September 2022; 32 (9): 093111. https://doi.org/10.1063/5.0102421