An Adaptive Method for Nonlinear Sea Level Trend Estimation by Combining EMD and SSA

Adaptive and accurate trend estimation of the sea level record is critically important for characterizing its nonlinear variations and its study as a consequence of anthropogenic climate change. Sea level change is a nonstationary or nonlinear process. The present modeling methods, such as least squares fitting, are unable to accommodate nonlinear changes, including the choice of a priori information to help constrain the modeling. All these problems affect the accuracy and adaptability of nonlinear trend estimation. Here, we propose a method called EMD-SSA, that effectively combines adaptive empirical mode decomposition (EMD) and singular spectrum analysis (SSA). First, the sea level change time series is decomposed by EMD to estimate the intrinsic mode functions. Second, the periodic or quasiperiodic signals in the intrinsic mode functions can be determined using Lomb-Scargle spectral analysis. Third, the numbers of the identified periodicities/quasiperiodicities are used as embedding dimensions of SSA to identify possible nonlinear trends. Then, the optimal nonlinear trend with the largest absolute Mann-Kendall rank is selected as the final trend for the sea level change. Based on a comprehensive experiment using simulated sea level change time series, we concluded that the EMD-SSA method can adaptively provide better estimate of the nonlinear trend in a realistic sea level change time series with consistency or high accuracy. We suggest that EMD-SSA can be used not only to robustly extract nonlinear trends in sea level data, but also for trends in other geodetic or climatic records, including gravity, GNSS observed displacements, and altimetry observations.