ORIGINAL ARTICLE Robust estimation of spatially varying common‑mode components in GPS time‑series

We present a new method to estimate common-mode components (CMC) in global positioning system (GPS) position timeseries. The method (‘CMC Imaging’) is fully automated, relies entirely on robust statistics, and exploits the recent proliferation of GPS stations by allowing stations with relatively short time-series to be considered as filter stations as well. The spatial extent of the CMC is purposely defined as local as possible and constrained by the proximity of nearby GPS stations. Our approach also avoids the need for subjective assignment of filter stations; every station is considered and those stations that deviate significantly from the local CMC are flagged and excluded as filter stations. We study thousands of GPS position time-series in the intraplate area of western Europe, and we show that CMC Imaging method is superior to other approaches in terms of noise reduction: we obtain an RMS reduction of 50%, 44% and 39% in the residual time-series in vertical, east, and north components, respectively. We show the importance of using filter stations that are as local as possible, because of systematic lateral variations in inter-station correlations and indeed in CMC, particularly in the vertical component. Those spatial variations are largest for continental stations, particularly those around the Baltic Sea, and could be due to atmospheric and nontidal ocean loading. CMC filtering has a large influence on reducing the temporal trend variability and approximately doubles the trend accuracy (by comparing variability in short-term trends with the long-term estimate).