Precision of continuous GPS velocities from statistical analysis of synthetic time series

Abstract

Abstract. We use statistical analyses of synthetic position time series to estimate the potential precision of GPS (Global Positioning System) velocities. The synthetic series represent the standard range of noise, seasonal, and position offset characteristics, leaving aside extreme values. This analysis is combined with a new simple method for automatic offset detection that allows an automatic treatment of the massive dataset. Colored noise and the presence of offsets are the primary contributor to velocity variability. However, regression tree analyses show that the main factors controlling the velocity precision are first the duration of the series, second the presence of offsets, and third the noise level (dispersion and spectral index). Our analysis allows us to propose guidelines, which can be applied to actual GPS data, that constrain velocity precisions, characterized as a 95 % confidence limit of the velocity biases, based on simple parameters: (1) series durations over 8.0 years result in low-velocity biases in the horizontal (0.2 mm yr−1) and vertical (0.5 mm yr−1) components; (2) series durations of less than 4.5 years are not suitable for studies that require precisions lower than mm yr−1; (3) series of intermediate durations (4.5–8.0 years) are associated with an intermediate horizontal bias (0.6 mm yr−1) and a high vertical one (1.3 mm yr−1), unless they comprise no offset. Our results suggest that very long series durations (over 15–20 years) do not ensure a significantly lower bias compared to series of 8–10 years, due to the noise amplitude following a power-law dependency on the frequency. Thus, better characterizations of long-period GPS noise and pluri-annual environmental loads are critical to further improve GPS velocity precisions.

Extracting small deformation beyond individual station precision from dense GNSS networks in France and Western Europe

“…vertical) velocity biases are smaller than 0.2 mm yr -1 (resp. 0.5 mm yr -1 ) at 95% 15 confidence levels for series longer than 8 years (Masson et al, 2019).…”

“…In agreement with other recent studies (Santamaria-Gomez et al, 2011;Nguyen et al, 2016), we observe that the spectral indices vary from -0.8 to -0.4, indicating a combination of white and flicker noise. Using synthetic time series analyses, Masson et al (2019) show that the simple "least-square spectrum" approach yields estimations of velocity standard errors that are reasonable for series with a spectral index smaller than -0.6 but that are underestimated for series with a spectral index greater than -0.4. The latter corresponds to only 18% of our data, 25 allowing us to have confidence in the calculated velocity standard errors.…”

“…Because only a small percentage of stations is associated with reliable equipment logs that could provide position offset dates, the dates of potential offsets are automatically detected according to the method described in Masson et al (2019).…”

“…There is no standard method for estimating campaign velocity uncertainty, but most of them rely scaling based on the nearby continuous GNSS sites (Tarayoun et al, 2018;Beavan et al, 2016;Reilinger et al, 2006). In this study, we use synthetic time series constructed from permanent-station parameters (Masson et al, 2019) to 30 generate synthetic campaign time series with the Alps and Pyrenees campaign characteristics (dates and number of surveys).…”

“…1), with all parameters based on our GPS data characteristics (cf. Masson et al, 2019 for details). Thus, this dataset corresponds to null velocity and strain rate fields with additional noise representative of our actual GPS data.…”