Global correlation matrix spectra of the surfacetemperature of the Oceans from Random MatrixTheory to Poisson fluctuations

TL;DR

This study applies random matrix theory to analyze sea surface temperature data from NOAA, revealing distinct spectral properties and a transition from RMT to Poisson fluctuations in Antarctic regions, aiding ocean classification.

Contribution

It introduces a novel application of RMT to ocean surface temperature data, identifying correlation behaviors and spectral transitions across different ocean regions.

Findings

Ocean systems exhibit specific β values for classification.

Nearest-neighbors spacing aligns with RMT in most regions.

Antarctic regions show a transition to Poisson fluctuations.

Abstract

In this work we use the random matrix theory (RMT) to correctly describethe behavior of spectral statistical properties of the sea surface temperatureof oceans. This oceanographic variable plays an important role in theglobalclimate system. The data were obtained from National Oceanic and Atmo-spheric Administration (NOAA) and delimited for the period 1982 to 2016.The results show that oceanographic systems presented specific $\beta$ values thatcan be used to classify each ocean according to its correlation behavior. Thenearest-neighbors spacing of correlation matrix for north, central and south ofthe three oceans get close to a RMT distribution. However, the regions delim-ited in the Antarctic pole exhibited the distribution of the nearest-neighborsspacing well described by the Poisson model, which shows astatistical changeof RMT to Poisson fluctuations.