# ULR7A

The ULR7a GPS solution is a preliminary version of the reanalysis of 21 years of GPS data from 2000 to 2020 that has been undertaken within the framework of the 3rd data reprocessing campaign of the International GNSS Service (IGS). Its associated vertical velocity field is expressed in ITRF2014.

Double-differenced ionosphere-free GPS carrier phase observations from daily regional (plus one global) networks of 546 stations were reanalyzed using through a free-network strategy (station positions, Earth Orientation parameters, satellite orbits and zenith tropospheric delays adjusted simultaneously using GAMIT software. The daily subnetworks were then combined into daily global network of stations using GLOBK software. The data analysis strategy (models, corrections...) was compliant with the specifications adopted by the IGS for this reanalysis (more information here).

Position time series expressed in ITRF2014 were then computed using CATREF software using a time-dependent functional model that includes station positions at reference epoch, velocities, semi-annual and annual seasonal signals and transformation parameters (translation, rotation, scale, and their velocities) between the daily undetermined frames and the ITRF2014 for a subset of IGS core stations. Where appropriate, station position offsets (mostly due to equipment changes or earthquakes), velocity changes and post-seismic displacement signals were added.

After the substraction of non-tidal atmospheric loading displacements in the time series (provided by the Earth System Modelling team of the German research center for geosciences at Potsdam), both a functional and a stochastic model were adjusted including long-term linear trends, position offset discontinuities, and periodic signals, following the equation:

\begin{align} x(t) = & x_{ref}+ v_{x}(t-t_{ref}) & \textit{reference position and velocity}\\ & + \sum_{i=1}^{N_{O}} a_{i}H(t-t_{i}) & \textit{position offsets}\\ & + \sum_{j=1}^3 s_{j}\sin(\frac{2\pi}{\tau_{j}}t)) + c_{j}\cos(\frac{2\pi}{\tau_{j}}t)) & \textit{seasonnal signals} \\ & + \sum_{d=1}^8 s_{d}\sin(\frac{2\pi}{\tau_{d}}t)) + c_{d}\cos(\frac{2\pi}{\tau_{d}}t)) & \textit{draconitic signals}\\ & + \sum_{f=1}^3 s_{f}\sin(\frac{2\pi}{\tau_{f}}t)) + c_{f}\cos(\frac{2\pi}{\tau_{f}}t)) & \textit{fortnightly signals} \\ & + \sum_{k=1}^{N_{PSD}}PSD_{k}(t) & \textit{post-seismic deformation signals} \end{align}

where:

\begin{align} x_{ref} & \text{ is the position at the reference epoch} t_{ref} \\ v_{x} & \text{ is the linear velocity} \\ H(t-t_{i}) = & \begin{cases} 0 & \text{if } t \lt t_{i}\\ \\ \frac{1}{2} & \text{ if } t = t_{i}\\ \\ 1 & \text{if } t \gt t_{i} \end{cases} \\ \tau_{j} = & \frac{1}{j} \text{ years} \\ \tau_{d} = & \frac{P_{D}}{365.25} \text{ years}, P_{D} \text{ being the period in days of the draconitics} \\ \tau_{f} = & \frac{P_{F}}{365.25} \text{ years}, P_{F} \text{ being the period in days of the fortnightly signals}\\ PSD_{k}(t) = & \begin{cases} a_{k} \log(1+ \frac{t-t_{k}}{\tau_{k}}) \text{ if PSD model is log} \\ \\ a_{k}(1- \exp(-\frac{t-t_{k}}{\tau_{k}})) \text{ if PSD model is exp} \\ \\ a_{1k} \log(1+ \frac{t-t_{k}}{\tau_{1k}}) + a_{2k}(1- \exp(-\frac{t-t_{k}}{\tau_{2k}})) \text{ if PSD model is log+exp} \\ \\ a_{1k} \log(1+ \frac{t-t_{k}}{\tau_{1k}}) + a_{2k} \log(1+ \frac{t-t_{k}}{\tau_{2k}}) \text{ if PSD model is log+log} \\ \\ a_{1k}(1- \exp(-\frac{t-t_{k}}{\tau_{1k}})) + a_{2k}(1- \exp(-\frac{t-t_{k}}{\tau_{2k}})) \text{ if PSD model is exp+exp} \end{cases} \end{align}

## Citation

Gravelle, M., K. Gobron, G. Wöppelmann, et al. (in prep.). The ULR-repro3 GPS data reanalysis and its estimates of vertical land motion at tide gauges for sea level science. In preparation.

## DOI ULR-repro3 solution

Vertical velocities table

The ULR7a_Vertical-Velocities_Table provides the vertical GPS velocities and uncertainties for the 546 stations fulfilling the criteria of 3 years of minimum length without discontinuities and with data gaps not exceeding 30%.

The velocities come from the adjustment of both a functionnal and stochastic model, the latter accounting for a linear combination of white noise and power law process, whose parameters were estimated using the Restricted Maximum Likelihood Estimation method.

Daily time series

The ULR7A_neu.zip file contains individual station data files of daily position time series in ITRF2014 with respect to the position at the reference epoch. These positions are expressed in meters in the local frame (North, East, and Up). The reference position and the 3D velocity in the local coordinate system (East, North, Up) are provided in the header of each file. .

The ULR7A_neu_model.zip file contains individual station data files of daily position time series predictions (i.e. modelled) in ITRF2014 with respect to the position at the reference epoch. These predictions are expressed in meters in the local frame (North, East, and Up). The reference position and the 3D velocity in the local coordinate system (East, North, Up) are provided in the header of each file. More information about the model used can be found in the About tab.

Position discontinuities

The ULR7a_discontinuities_Table.txt file provides the position offsets that were estimated.

## Statistics

### Vertical velocity field

 Estimated (robust) velocities: 546 CGPS@TG 461 Average of formal errors: 0.38 mm/yr Median of formal errors: 0.28 mm/yr