Modelagem espaço temporal de variáveis altimétricas e climatológicas em estações maregráficas do litoral brasileiro: uma abordagem estatística e computacional

Abstract

This thesis aims to model and analyze the temporal and pointwise dynamics of mean sea level (MSL) and other altimetric and climatological variables (precipitation and air temperature) from tide gauge stations along the Brazilian coast from 2002 to 2023, seeking to identify and quantify the influence of non-oceanic forces that may mask true marine variations. The research began with a comprehensive bibliometric analysis of 35 scientific articles between 2009-2021, which revealed France, the United States, and China as the most influential countries in the theme. Subsequently, an innovative statistical and computational approach based on robust methods for non-stationary time series was employed. Time series from seven tide gauge stations of the Permanent Tide Gauge Network for Geodesy (RMPG) managed by IBGE (Santana/AP, Bel´em/PA, Fortaleza/CE, Salvador/BA, Arraial do Cabo/RJ, Imbituba/SC, and Maca´e/RJdiscontinued in 2015) were analyzed. The methodology included the application of Detrended Fluctuation Analysis (DFA) to assess long-term persistence, Detrended Cross-Correlation Analysis (ρDCCA) and Detrended Multiple Cross-Correlation (DMC) coefficients to quantify bivariate and multivariate correlations, respectively, and entropy (FastApEn) to measure the degree of predictability of the time series. The main results revealed persistent behavior (α > 0.5) at most stations, indicating long-range memory in MSL time series. The correlation with GNSS altimetry, used in the estimation of the Earth’s vertical motions, internationally known as Vertical Land Motion (VLM), proved to be the strongest and most stable, especially in Salvador and Santana, suggesting a direct relationship with vertical crustal movements. In contrast, precipitation showed weaker and more fluctuating correlations, while air temperature exhibited persistent patterns of positive correlation, consistent with the thermal expansion effect. Entropy analysis identified that Fortaleza and Arraial do Cabo stations have more regular and predictable series, while Maca´e and Imbituba exhibited more chaotic behavior. The sliding windows approach allowed for the dynamic detection of annual seasonality patterns and the influence of large-scale climate phenomena such as El Ni˜no and La Ni˜na. It is concluded that non-oceanic factors exert a significant and regionally differentiated influence on MSL variations along the Brazilian coast, demonstrating the effectiveness of the proposed methodology for integrated sea level modeling, providing vital support for coastal planning, the management of risks associated with climate change, and the updating of altimetric references, aligning with the Sustainable Development Goals, particularly SDG 13 (Climate Action).