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 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:

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

Gravelle, M., Wöppelmann, G., Gobron, K., Altamimi, Z., Guichard, M., Herring, T., and Rebischung, P.: The ULR-repro3 GPS data reanalysis and its estimates of vertical land motion at tide gauges for sea level science, *Earth System Science Data*, 15, 497–509, https://doi.org/10.5194/essd-15-497-2023, 2023.

**–** **General information** Access the data by clicking on the Download tab

Title: GPS Solution ULR7a

DOI identifier: 10.26166/sonel_ulr7a

Publisher: SONEL Data Assembly Centre

Publication year: 2022

Version: a

Temporal coverage: 2000-01-01 / 2020-12-31

Tile: The ULR-repro3 GPS data reanalysis solution (aka ULR7a)

Language: English

**–** **Authors**

Médéric Gravelle [1], Kevin Gobron [2], Guy Wöppelmann [1]

Affiliation: [1]: UMR 7266 LIENSs, CNRS/LRU, La Rochelle, France. [2]: Royal Observatory of Belgium (ORB), Brussels, Belgium.

**–** **Keywords**

Vertical land motion, sea level, GNSS, tide gauge

**–** **Contributors**

LIENSs, La Rochelle, France

IGN, Saint Mandé, France

CNRS, France

La Rochelle Université, La Rochelle, France

**–** **Data use information**

Citation: *Gravelle, M., Wöppelmann, G., Gobron, K., Altamimi, Z., Guichard, M., Herring, T., and Rebischung, P.: The ULR-repro3 GPS data reanalysis and its estimates of vertical land motion at tide gauges for sea level science, Earth Syst. Sci. Data, 15, 497–509, https://doi.org/10.5194/essd-15-497-2023, 2023.*

Use rights: The ULR7a solution is freely available to anyone. It is asked to all users to acknowledge the SONEL Data Centre in their research papers.

Licence: Creative Commons Attribution 4.0 International (CC BY 4.0)

**–** **Description**

The ULR analysis center has participated in the third reprocessing campaign (repro3) of the International GNSS Service (IGS). Its ULR-repro3 solution (aka ULR7) included 601 stations for which the GNSS data available between 2000.0 and 2021.0 was reprocessed using the models and corrections adopted by the IGS for repro3.

The main steps and features of ULR-repro3 reanalysis are as follows. First, daily GNSS solutions were computed using a free-network weighted least squares adjustment strategy. That is, station positions, Earth Orientation parameters, satellite orbits and zenith tropospheric delays were adjusted simultaneously using GAMIT Software version 10.71. The station networks were regional, but one global. This step yielded a number of daily solutions (subnets) of less than 50 stations each that were expressed in their own (daily) terrestrial frame.

Secondly, the regional and global subnets were combined into daily global solutions (all stations included and expressed in the same but undetermined frame). These daily global solutions were then aligned to the ITRF2014 frame using a time-dependent functional model that included station positions at a reference epoch, velocities, seasonal signals (annual and semi-annual) and transformation parameters (translation, rotation, scale) between the daily undetermined frames and the ITRF2014 for a subset of IGS core stations. Station position offset discontinuities (mostly due to equipment changes or earthquakes), velocity changes and post-seismic displacement signals were added, as appropriate (based on metadata information and visual inspection of the series). This step included manual editing to identify (and remove) outliers as well as additional non-documented position offset discontinuities. It was iterated until convergence (analyst subjective criteria). From this step, daily position time series in the ITRF2014 frame for all (601) stations were retained. A minimum of three continuous years without an offset in the time series was required for the next step to estimate vertical velocities. This selection criteria yielded 546 daily station position time series, among which 457 are nearby a tide gauge (less than 15 km).

The last step was concerned with the estimation of the parameters of interest and their uncertainties, in which both a functional and a stochastic model were adjusted to each of the station position time series from the previous step. To limit biases in the parameter estimation, non-tidal atmospheric loading displacements were subtracted from the position time series prior to this adjustment using the products provided by the Earth System Modelling team of the German research center for geosciences. The stochastic model accounted for a linear combination of white noise and power law process, whose parameters were estimated using the Restricted Maximum Likelihood Estimation method. The functional model included long-term linear trends, position offset discontinuities, and periodic signals (annual, semiannual, and terannual signals, GPS draconitics of 1.04 year up to the 8th harmonics and three fortnightly signals). The parameters of this functional model and their uncertainties were estimated using the weighted least squares estimator and taking the inverse of the estimated observation covariance matrix as weight matrix. Further details in the companion paper submitted to ESSD.

**–** **Related identifiers**

SONEL products: https://www.sonel.org/-Vertical-land-movements-.html

**–** **Acknowlegments**

This solution has been proceeded thanks to the data provided by the Data Providers who collaborate with SONEL.

**–** **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.

Estimated (robust) velocities: | 546 |

CGPS@TG | 461 |

Average of formal errors: | 0.38 mm/yr |

Median of formal errors: | 0.28 mm/yr |