Temporally and spatially correlated noise has long been reported in Global Navigation Satellite System (GNSS) station position time series. Accounting for the temporal correlations of the noise is crucial to obtain realistic uncertainties for deterministic parameters, e.g., station velocities, while accounting for its spatial correlations is beneficial to various applications such as offset detection, velocity estimation and detection of local geophysical signals. The origins of the spatio-temporally correlated noise in GNSS series are however still unclear, and a realistic spatio-temporal noise model also remains to be elaborated. In this study, we therefore analysed GNSS residual time series from the International GNSS Service (IGS) third reprocessing (repro3), corrected from loading deformation models, with the purpose of characterizing and modeling their spatio-temporal correlations in detail.
We first estimated spectral correlation coefficients as a function of both the distance between GNSS stations and the temporal frequency. Different spatial correlation regimes could thus be evidenced for different frequency bands. Spatial correlations are in particular higher, and range longer distances, at the frequencies of the periodic (e.g., draconitic, fortnightly) errors in GNSS time series. Broadband spatial correlations are consequently reduced when these periodic errors are filtered out from the series.
To investigate possible spatial non-stationarities of the noise, we then estimated its spatial covariance, as a function of the distance between stations, over different regions. While the estimated spatial covariance is similar to the global average in Europe, Eastern US and Australia, it is consistently higher in Eastern South America, New Zealand and Western US. This may point to a partially geophysical origin of the spatially correlated noise in the latter regions, possibly attributable to unmodeled hydrological loading and tectonic deformation, respectively.
We finally converted the globally averaged spatial covariance of the residual repro3 series into a spatial power spectrum, i.e., power as a function of the spherical harmonic degree. It thus turns out that the average spatial covariance is well described by a spatial power-law model attenuated at the lowest degrees.