The Effect of Signal-to-Noise Ratio on the Study of Sea Level Trends

Extracting secular sea level trends from the background ocean variability is limited by how well one can correct for the time-varying and oscillating signals in the record. Many geophysical processes contribute time-dependent signals to the data, making the sea level trend difficult to detect. In this paper, cyclostationary empirical orthogonal functions (CSEOFs) are used to quantify and improve the signal-to-noise ratio (SNR) between the secular trend and the background variability, obscuring this trend in the altimetric sea level record by identifying and removing signals that are physically interpretable. Over the 16-yr altimetric record the SNR arising from the traditional least squares method for estimating trends can be improved from 4.0\% of the ocean having an SNR greater than one to 9.9\% when using a more sophisticated statistical method based on CSEOFs. From a standpoint of signal detection, this implies that the secular trend in a greater portion of the ocean can be estimated with a higher degree of confidence. Furthermore, the CSEOF method improves the standard error on the least squares estimates of the secular trend in 97\% of the ocean. The convergence of the SNR as the record length is increased is used to estimate the SNR of sea level trends in the near future as more measurements become available from near-global altimetric sampling.