Singular Spectrum Analysis of Nonstationary Tidal Currents Applied to ADCP Data from the Northeast Brazilian Shelf

Abstract

The development of new tools for the analysis of nonstationary currents, including tidal currents, has been the subject of recent research. In this work a method for studies of nonstationary barotropic or baroclinic currents based on empirical orthogonal function (EOF) and singular spectrum analysis (SSA) is proposed. It represents a new alternative to other methods of analysis of tidal currents in strong interaction with nontidal forcing, for example, the continuous wavelet transform. The advantage of the SSA method resides in the fact that it is fast, easy to implement, efficient for short-time records, and is based on the covariance structure of the data. If significant tidal constituents occur in the measurements, these are determined by the method itself even with short-time-series records. This is in contrast to the harmonic analysis (HA), where a large table of tidal constituents stated a priori are fitted to the data, even if the presence of some of these are spurious and not justified physically. The method is first demonstrated in the analysis of a synthetic current time series and then applied to an hourly current ADCP profile dataset of 410 days from the northeast Brazilian shelf. In both cases the SSA results were compared to the classical HA and the neoclassical short-term HA (STHA). The description of the shelf area where the ADCP was placed, the deployment and data acquisition operations, and the quality control data analysis are included for completeness. Analysis of the full ADCP quality-controlled data was done after a separation of the subtidal from the tidal high-frequency bands, although this traditional separation is not strictly necessary and was only made to better compare with HA and STHA. Analysis of the tidal band obtained from the ADCP data showed that the extracted tidal ellipse constituents present coherent oscillations dominated by the annual and 57-day periods, and changes in the sense of rotation of the current vector from anticyclonic to cyclonic in the ellipses. The subtidal band variability is shown to be also dominated by an annual and a 57-day period component, both polarized along the isobaths, which is suggestive of a nonlinear interaction of the subtidal and the tidal variability.