Temperatura da superfície dos oceanos sob a perspectiva da teoria das matrizes aleatórias

Abstract

The temporal series of ocean surface temperature data have been collected since 1970. These observations make it possible to study the variability of some oceanographic phenomena in time and space scales. The surface layer of the oceans has uniform properties, where the processes of interaction of the ocean with the atmosphere occur, able to regulate the climate of the planet, interfere with the dynamics of the atmosphere and influence the climate. Because sea surface temperature (SST) data play an important role in the global climate system, in this paper we use random matrices theory to correctly describe the behavior of spectral statistical properties based on the randomness of each chaotic quantum system. SST matrices obtained from NOAA, representative of the north, central, south and pole regions of the Pacific, Atlantic and Indian Oceans, were delimited in the temporal space of 35 years. The first results show that the matrices of the geographic areas: north, central and south of the three oceans obtained a good fit for the universal class GOE, described by the Brody distribution, with the southern regions presenting the best adjustments, indicating more chaotic dynamic systems. However, the regions delimited in the Antarctic pole exhibited the distribution of the spacings adjusted by the Poisson model, indicating a cohesive and deterministic system. In more detailed analyzes, the parameter (β), which quantifies the correlation between the eigenvalue spacings of the temperature matrices, was calculated per year accumulated for all regions. The results of the central region were modified from the year 2006, for the three oceans. The TSM data set from the TropFlux database was then used for comparisons, resulting in the same behavior change in 2001. The investigations pointed to the inclusion of new measurement instruments. From these years, NOAA's included microwave sensors, and those of TropFlux TPR matrices, which consider data obtained in situ. A constructed numerical model was also able to identify this loss of autocorrelation between two simulated data sets that suffer from artificial interference. Finally, some directions for further investigations and continuity of this work were pointed out.