We have used 1 year of multi-GNSS observations at the Onsala Space Observatory on the Swedish west coast to estimate the linear horizontal
gradients in the wet propagation delay. The estimated gradients are compared to the corresponding ones from a microwave radiometer. We have
investigated different temporal resolutions from 5

An accurate modelling of the atmospheric effects on GNSS observations is relevant for both geodetic and meteorological applications, in forecasting as
well as in climate research. In geodetic applications the standard method is to estimate an equivalent zenith propagation delay together with a linear
horizontal gradient. Early results showed an improved repeatability for the estimated coordinates when estimating gradients using GPS data

In meteorological applications the zenith total delay (ZTD) and horizontal gradients may be assimilated directly into the forecasting model; see e.g.

The quality of the estimated gradients has been assessed by comparisons to independent measurements, such as using a microwave radiometer (in the following this instrument is referred to as a water vapour radiometer, WVR), the space geodetic technique of very-long-baseline interferometry (VLBI), and numerical weather models.

Such an assessment was carried out by

The aim of this study is to assess the quality of estimated gradients from multi-GNSS observations with temporal resolutions as high as 5

We have analysed 1 year (1 January–31 December 2019) of ground-based GNSS observations acquired from one station (ONS1) located at the Onsala Space
Observatory, on the west coast of Sweden. For comparison purposes we also used GNSS data from June and July 2019 acquired at the collocated station
ONSA. The data processing was carried out using GipsyX v.1.5
(

The ZTD and linear horizontal delay gradients were estimated every 5

The zenith hydrostatic delay (ZHD) was calculated using ground pressure measurements

The model used for the gradient estimation is presented by

Observations of the sky acquired from ONS1 for 0 to 24

In order to compare to the wet component inferred by the WVR, we subtracted the hydrostatic component computed from the reanalysis product of the
ECMWF, ERA5, from the total gradient to get the GNSS wet gradient. The hydrostatic gradients at
the site are much less variable compared to the wet ones, and especially for timescales of minutes to hours

Number of daily observations for each GNSS constellation acquired by ONS1 applying three different elevation cutoff angles (3, 10, and 15

The data processing was run for three different elevation cutoff angles (3, 10, and 15

An example of the sky coverage of the observations for different GNSS constellations, applying an elevation cutoff angle of 3

Figure

The water vapour radiometer (WVR) and GNSS stations (ONS1 and ONSA) at the Onsala Space Observatory.

One cycle of the WVR observations consists of 52 observations. The cycle is repeated every 5

The WVR, shown in Fig.

Starting in January 2019 the observations were scheduled in 5

A four-parameter model was used to estimate the mean ZWD, a linear trend in the ZWD, and east and north linear horizontal gradients over 5

There are 105 120 possible 5

The time series of the ZWD estimated from the WVR data for each 5

Finally it is noted that the WVR estimates are completely independent of the corresponding estimates from the GNSS data. The study does not need to
assume that the WVR gradients are more accurate compared to the GNSS ones. The main advantage of the WVR gradients is that they are independent, and by
comparing these to the gradients from different GNSS solutions we can assess the different GNSS processing methods. Furthermore, since we want to
study the agreement with as high temporal resolution as possible, we do not apply constraints to the individual 5

The estimated ZWD from the WVR data is shown in Fig.

Before carrying out comparisons of the gradients estimated from different GNSS solutions with the WVR gradients, we investigate the characteristics of
the input data. Table

The mean and standard deviations (SDs) of the east and the north gradients and the gradient amplitude, together with the mean and SD of their 1

As indicated by column 9 in Table

We first carry out comparisons of the gradients estimated from the different GNSS constellations and using the three different elevation cutoff
angles, presented in Table

The WRMS differences and correlations of the east and north gradients, obtained from different satellite constellations, relative to the WVR data.

Table

Correlations between estimated gradients from the GNSS and the WVR data calculated for each month.

For the GPS-only solution, the highest correlation is obtained for the elevation cutoff angle of 3

The WRMS differences and correlations of the east and the north gradients, obtained from different satellite constellations, relative to the WVR data for June and July 2019.

Even though the WVR and the GNSS sample different parts of the sky, it is noted that the agreement becomes worse for all GNSS solutions when the
15

The mean code multipath RMS calculated from ONS1

Correlations and WRMS differences between estimated gradients from the GNSS and the WVR data using different effective temporal resolutions,

In order to study any seasonal variability we compare the estimated gradients from the GNSS and the WVR for each month. The GNSS gradients are
obtained using different constellations and a cutoff angle of 3

The results are summarized in Table

As mentioned in the introduction, GNSS gradients have been compared to other independent estimates over different timescales and temporal
resolutions. We therefore averaged the GNSS and the WVR gradients by applying a Gaussian window with different FWHM from

Correlations between estimated east gradients from the GNSS, given by the GRE solution with a 3

Correlations between estimated north gradients from the GNSS, given by the GRE solution with a 3

The resulting WRMS differences and correlations are shown in Fig.

ZWD (top) and gradient time series from the WVR and the GNSS solution using an elevation cutoff angle of 3

We also study a specific event of short-lived gradients, associated with rapid changes in the ZWD, starting from 00:00 UTC on 23 July (see
Fig.

The changes in WRMS differences and correlations of east and north gradients when a weaker constraint is applied in the GNSS data processing. The changes are the results from the constraint of 1.0

The results from the comparisons using different

Gradient time series from the WVR and from the GNSS (GRE) applying two different constraint values (0.3 and 1.0

All GNSS-derived gradients were so far estimated using a random walk model with a constraint value of 0.3

When a weak constraint is applied with an elevation cutoff angle of 3

More details are seen in Fig.

We have estimated linear horizontal gradients using 1 year of data acquired from the GNSS station ONS1 located on the Swedish west coast. The
GNSS-derived gradients were compared to the ones obtained from a collocated WVR. Overall the multi-GNSS solutions, i.e. combinations of GPS, Glonass,
and Galileo, show small but significant improvements with the WVR gradients compared to the GPS-only solution (Tables

For the GPS-only solution, the best agreement, in terms of the correlation coefficient with the WVR gradients, is obtained when using an elevation
cutoff angle of 3

We investigated different effective temporal resolutions,

Furthermore, weakening the constraint used when estimating the GNSS gradients from 0.3 to 1.0

Possible improvements to study in similar future work would be to include BeiDou observations and use a WVR with better stability. It would also be
of interest to carry out a similar study at low-latitude GNSS stations, where the sky coverage is better, and perhaps also the atmosphere is more
variable. In addition, the role of the geometry of GNSS observations (see Fig.

The input GNSS data, in RINEX format, are available from EUREF (

The two authors (TN and GE) planned the work and the structure of the paper together. TN performed the GNSS data analyses and GE performed the WVR data analyses. Both contributed to the writing of the manuscript and approved it before the submission.

The authors declare that they have no conflict of interest.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank Tobias Nilsson for providing the hydrostatic gradients from the ERA5 data.

This paper was edited by Roeland Van Malderen and reviewed by two anonymous referees.