Modeling seasonal oscillations in GNSS time series with Complementary Ensemble Empirical Mode Decomposition

We present the modeling of annual and semiannual signals in position time series of GNSS stations. The employed method is the Complementary Ensemble Empirical Mode Decomposition (CEEMD), dedicated to analyzing nonstationary and nonlinear signals. The input data were daily time series of position residuals for 25 stations of the EUREF Permanent Network (EPN) collected over 16 years. The CEEMD method was applied to decompose the GNSS time series into nine intrinsic mode functions (IMF1–IMF9). The set of the IMFs was divided into high- and low-frequency sets with mutual information entropy (MIE). IMF5 turned out to be the threshold for high- and low-frequency IMFs in most cases. Hence, IMF1 to IMF4 are considered functions of the high-frequency part of the signal, while IMF5 to IMF9 cover the low-frequency band. The spectral analysis demonstrated that IMF5 and IMF6 represent annual and semiannual signals, respectively, with time-dependent amplitudes. Therefore, IMF5 and IMF6 were used as seasonal oscillation models and juxtaposed with seasonal models from fitting periodic functions using the least-squares (LS) method as well as with the seasonal models obtained using singular spectrum analysis (SSA) decomposition. This way, the suitability of the CEEMD method for modeling seasonal signals in GNSS time series was verified. The calculated spectral index for the GNSS time series after subtracting seasonal models varies from − 1 to 0, which corresponds to the fractional Gaussian noise. The analyses provided new insight into GNSS time series by defining their time-dependent seasonal models as well as demonstrated the suitability of the CEEMD method for this purpose.