Mean sea level (MSL) behavior is a relevant indicator for monitoring climate change and coastal processes. Historically, its fluctuation has been studied based on tide gauge and altimetric observations. However, local and regional variations, such as land subsidence, rainfall patterns, and air temperature, can significantly influence the interpretation of these measurements. In this context, the main objective of this research is to measure the correlation between the MSL time series (dependent variable) and three independent variables (GNSS altimetry, precipitation, and air temperature) along the Brazilian coast, using the ₃₂₂₀ (Detrended Cross-Correlation Analysis) and the DMC²ₓ (Detrended Multiple Cross-Correlation Coefficient) coefficients. ₃₂₂₀ was applied to measure the level of cross-correlation between pairs of time series, while the DMC²ₓ assessed the joint influence of the independent variables on MSL (Multiple Correlation). Our findings identified that GNSS altimetry showed stronger and more stable correlations with MSL, especially in Salvador (EMSAL) and Santana (EMSAN), suggesting concordance with vertical crustal movements. In contrast, correlations with precipitation were weaker and showed greater fluctuations over time, possibly influenced by local hydrological factors. Air temperature showed more persistent patterns of positive correlation, particularly in Arraial do Cabo (EMARC) and Belém (EMBEL), consistent with the effect of ocean thermal expansion. In general, the multiple cross-correlation (DMC²ₓ), with the exception of EMIMB, showed higher values for larger scales (n>100). Sliding window analysis allowed the identification of dynamic regional patterns and seasonal extreme events, as observed in Fortaleza (EMFOR) in 2021. These findings reinforce the complexity of the factors controlling the MSL and demonstrate the effectiveness of the methods used in identifying multivariate patterns, offering important insights for coastal planning and the assessment of risks related to climate change.
Junior et al. (2026) studied this question.