Multichannel Singular Spectrum Analysis in the Estimates of Common Environmental Effects Affecting GPS Observations

Abstract

We described a spatio-temporal analysis of environmental loading models: atmospheric, continental hydrology, and non-tidal ocean changes, based on multichannel singular spectrum analysis (MSSA). We extracted the common annual signal for 16 different sections related to climate zones: equatorial, arid, warm, snow, polar and continents. We used the loading models estimated for a set of 229 ITRF2014 (International Terrestrial Reference Frame) International GNSS Service (IGS) stations and discussed the amount of variance explained by individual modes, proving that the common annual signal accounts for 16, 24 and 68% of the total variance of non-tidal ocean, atmospheric and hydrological loading models, respectively. Having removed the common environmental MSSA seasonal curve from the corresponding GPS position time series, we found that the residual station-specific annual curve modelled with the least-squares estimation has the amplitude of maximum 2 mm. This means that the environmental loading models underestimate the seasonalities observed by the GPS system. The remaining signal present in the seasonal frequency band arises from the systematic errors which are not of common environmental or geophysical origin. Using common mode error (CME) estimates, we showed that the direct removal of environmental loading models from the GPS series causes an artificial loss in the CME power spectra between 10 and 80 cycles per year. When environmental effect is removed from GPS series with MSSA curves, no influence on the character of spectra of CME estimates was noticed.

A Filtering of Incomplete GNSS Position Time Series with Probabilistic Principal Component Analysis

“…A change in CME variances arises from the fact that the environmental loading models remove much of CME variance (Fig. 10), especially with a frequency band between 9 and 12 cpy (cycles per year) mainly affected, which was also noticed before by Gruszczynska et al (2018). The above described results are consistent with the assertion that GNSS residuals are highly affected by environmental mass loading influences, mostly in the vertical direction.…”

What Causes the Common‐Mode Error in Array GPS Displacement Fields: Case Study for Taiwan in Relation to Atmospheric Mass Loading

“…This estimate agrees with the ~60% of AML contributions evident from the GPS vertical position measurements (for 19 global stations) estimated by van Dam et al (1994). Our results agree with the recent study of Gruszczynska et al (2019) for the overall reduction of 68% for 229 global stations when compared to the environmental mass loading models.…”

“…Some studies (e.g., Dong et al, 2006; Yuan et al, 2008) found these crustal deformations to contribute to the spatially correlated “errors” in the GPS data. Recent studies (Gruszczynska et al, 2019; Gruszczynski et al, 2019; Zhu, Zhou, & Liu, 2017) have further explored the relation of CME with the environmental sources. Zhu, Zhou, Deng, et al (2017) examined the effects of environmental loading and thermal expansion on the estimated CME for a large network of the Crustal Movement Observation Network of China.…”

Modeling Seasonal Variations in Vertical GPS Coordinate Time Series Using Independent Component Analysis and Varying Coefficient Regression

“…All the methods above are aimed at the GPS time series at a single GPS site, and are not conducive to the overall analysis of regional GPS observations. Actually, the seasonal signals at regional GPS sites have similar features [ 29 , 30 ]. Gruszczynska et al [ 30 ] used multichannel singular spectrum analysis (MSSA) to model the common seasonal signals in GPS observations in different regions around the world and without influencing the high frequency part of the spectra.…”

“…Actually, the seasonal signals at regional GPS sites have similar features [ 29 , 30 ]. Gruszczynska et al [ 30 ] used multichannel singular spectrum analysis (MSSA) to model the common seasonal signals in GPS observations in different regions around the world and without influencing the high frequency part of the spectra. Some other data-driven mathematical methods have been proposed to be used in modeling the geophysical signals from regional geodetic time series, e.g., principle component analysis (PCA) and independent component analysis (ICA), which have been widely used in smoothing and modeling GPS time series [ 15 , 23 , 31 , 32 , 33 , 34 , 35 , 36 , 37 ].…”