Ground-based GNSS (Global Navigation Satellite System) has efficiently been
used since the 1990s as a meteorological observing system. Recently
scientists have used GNSS time series of precipitable water vapor (PWV) for
climate research. In this work, we compare the temporal trends estimated from
GNSS time series with those estimated from European Center for Medium-Range
Weather Forecasts (ECMWF) reanalysis (ERA-Interim) data and meteorological
measurements. We aim to evaluate climate evolution in Germany by monitoring
different atmospheric variables such as temperature and PWV. PWV time series
were obtained by three methods: (1) estimated from ground-based GNSS
observations using the method of precise point positioning, (2) inferred from
ERA-Interim reanalysis data, and (3) determined based on daily in situ
measurements of temperature and relative humidity. The other relevant
atmospheric parameters are available from surface measurements of
meteorological stations or derived from ERA-Interim. The trends are estimated
using two methods: the first applies least squares to deseasonalized time
series and the second uses the Theil–Sen estimator. The trends estimated at
113 GNSS sites, with 10 to 19 years temporal coverage, vary between

Water vapor is considered the most active greenhouse gas that permanently
affects the Earth's climate. Due to its high temporal and spatial variations,
the precipitable water vapor (PWV) content in the atmosphere has to be
regularly and accurately determined for meteorological and climatological
purposes. PWV is the amount of water (in millimeters) that would result from
condensing a column of water vapor that extends from the measurement point to
altitudes of about 12 km. Water vapor mainly resides in the lowest 3 km of
the atmosphere and its content generally increases with air temperature.
While other observation systems such as radiosondes and microwave radiometers
provide PWV measurements that are limited in the temporal and (or) spatial
resolutions, ground-based GNSSs provide time series of accurate PWV estimates
with 15 min (for this work) sampling at dense GNSS networks, without
significant additional costs. Since

Typically, climate scientists consider a period of 30 years as an appropriate
time necessary to average variations in weather and evaluate climatic effects
for a particular site, as described by the World Meteorological Organization

In this paper, we want to show that GNSSs are, and will remain, a promising data source for climate research, particularly in the future when the time series are adequately long. We first extract PWV time series by processing GPS data and evaluate their quality using ERA-Interim as a reference. These PWV time series are then used to estimate the water vapor trends using both least squares and Theil–Sen estimator. The same procedure is applied to the ERA-Interim data over the same time period, for validation. Since the GNSS sites are independently mounted, the length of the PWV time series at the network sites is variable. For a reasonable trend estimation, we used time series with lengths of 10 to 19 years. Since the length of time series is variable and it is still below the normal (30 years), suggested by climatologists, we extended the research using other data sets (e.g., ERA-Interim and synoptic data). First, it is more reasonable to give a mean value of the change per decade (trend) using longer time series; second, using time series of the same length at all sites in the research region enables us to observe specific spatial features of the trend, as presented later in the paper. We also calculate the change in PWV per degree Celsius rise in temperature to check if it is consistent with the Clausius–Clapeyron relation.

This paper is organized as follows. In Sect.

We used GPS data collected in central Europe, mainly in Germany as shown in
Fig.

Based on the method of precise point positioning

The location of the GNSS and meteorological sites within the research region; 119 GNSS sites of 351 have time series of 10 to 19 years long.

PWV estimated at three GNSS sites (site 0269 in Wertach, Germany, at altitude of 907 m a.m.s.l.; site 0522 in Pirmasens, Germany, at altitude of 399 m a.m.s.l.; and site 0285 in Garmisch, Germany, at altitude of 1779 m a.m.s.l.) and the corresponding PWV from ERA-Interim. The bottom sub-figures show (left) the mean of PWV difference (ERA-Interim–GNSS) and (right) the standard deviation at all sites.

We compared the PWV obtained from GNSS with ERA-Interim data.
Figure

For accurate determination of the PWV from GNSS measurements, it is required
to have measurements of mainly air pressure and temperature at the GNSS sites
or within a short spatial range. In the absence of meteorological
measurements, would the interpolation of pressure and temperature from
reanalysis data be a good replacement? To answer this question, we compared
the PWV time series extracted from the ZTD by using both measurements at the
meteorological stations and ERA-Interim data. To calculate the ZHD, the in
situ measured pressure and temperature are horizontally interpolated to the
GNSS site and then vertically interpolated to the GNSS antenna phase center.
For GNSS sites below the lowest ERA-Interim level, the pressure and
temperature are extrapolated at the site altitude as described in

Mean atmospheric temperature,

Besides station pressure, an important factor for an accurate determination
of PWV is the conversion factor

Econometricians have developed reasonably simple models that are capable of
interpreting, testing hypotheses, and forecasting economic data. The method
was to decompose the time series into a trend, a seasonal, a cyclic, and an
irregular component

The seasonal adjustment is applied as an iterative procedure as follows. To
best estimate the seasonal component, the linear trend has first to be
estimated and removed from the time series. There are different methods to
estimate the trend such as using moving average or parametric trend
estimation. Here, we used the method of moving average with a window length
of 1 year that is able to smooth out seasonal and irregular signals. We
employ time series of PWV and temperature with daily values (the GNSS-based
estimates of PWV have a temporal resolution of 15 min, but we average
them to get mean daily values for climatological studies). The trend is
estimated as follows:

Trend, seasonal, and irregular components of PWV time series estimated from GNSS observations (2001–2016) at the site 0896 (Berlin, Germany; 68.37 m a.m.s.l.).

The estimated trend component is subtracted from the original time series and
the detrended signal is averaged to estimate the seasonal component

The Theil–Sen estimator presented by

We also analyze the change in PWV in relation to the change in temperature.
As temperature rises, the air capacity to hold moisture increases at the
Clausius–Clapeyron rate. The water vapor pressure

The estimated PWV trend at 351 GNSS sites and the corresponding uncertainty in the estimated trend using Theil–Sen estimator. The size of the marker indicates the length of the PWV time series; i.e., the larger the marker, the longer time series.

Comparison between the estimated trends (mm decade

Validation of the PWV trend estimated from GNSS and ERA-Interim data using time series of at least 10-year-long length.

The estimated PWV trend using (2 m) ERA-Interim data by applying
least squares regression to the seasonally adjusted time series

In this section, we show the estimated trends using three data sets, GNSS,
ERA-Interim, and synoptic data of PWV and temperature. First, we estimated
the trends of PWV at 351 GNSS sites with time series of 4 to 19 years long
and the corresponding standard deviations of the estimated slope as shown in
Fig.

Since the trend is estimated from GNSS time series of different length, it is
reasonable to provide a mean value for the whole region or observe spatial
features of the trends. Therefore, and in order to get more insight and more
reasonable conclusions about the long-term temporal variations of PWV, it is
necessary to analyze time series spanning one predefined period for all
stations. Since the last climate normal extends from 1991 to 2020, we
analyzed time series of 26 years (January 1991–June 2016) from ERA-Interim
and synoptic data. We investigated time series at 227 meteorological stations
where the ERA-Interim is horizontally interpolated at the synoptic station
using bilinear interpolation. Figure

In order to validate these results, it is necessary to have a long data set,
which is not available for this research. However, DWD provides surface
measurements of atmospheric parameters that are accurate and homogenous so
that they are proper for climate studies. It is not possible to accurately
determine the total column water vapor using surface meteorological
observations alone. However, it was shown in the 1960s that it is possible to
approximate the atmospheric PWV based on dew point temperature measurements,
which is considered an indicator of the amount of moisture in the air

Estimated trends using dew-point-based PWV and the corresponding standard error of the estimated slope.

In this work, we estimated the coefficients

We used measurements of surface dew point temperature to obtain the daily PWV
and time series for the whole network are evaluated using the ERA-Interim
data. The PWV value at the meteorological station is computed by applying
bilinear interpolation to the ERA-Interim PWV at four grid points around that
station. The altitude difference was not accounted for.
Figure

The increase in atmospheric water vapor pressure and PWV per 1

Estimated temperature trends using surface measurements of

Next, we estimated the trends using the time series of dew-point-based PWV
after removing local environment effects, which are presented in
Fig.

The same procedure is applied to estimate the trends from temperature and dew
point temperature time series. The estimated temperature trends from surface
measurements at 227 stations shown in Fig.

Also, the estimated trend in PWV is correlated with that from the dew point
temperature, which is exhibited in Fig.

In this paper, we aimed at estimating climatic trends from GNSS-based
precipitable water vapor time series and surface measurements of air
temperature in Germany. First, we compared PWV time series obtained from GNSS
and ERA-Interim, which show strong correlation with an average bias of

By comparing the GNSS-based PWV with those from ERA-Interim, the results show small bias values in flat terrain, while the bias increases in mountainous regions. This is mostly caused by the coarse spatial resolution of the ERA-Interim data and hence the inability to properly represent the topography.

To evaluate the temporal evolution of PWV and temperature, we modeled the
time series with an additive model that contains trend, seasonal, and
stochastic irregular components. The time series are seasonally adjusted to
remove the periodic signal, and the trend component is then analyzed after
filtering out the irregular component caused mainly by weather variations.
The comparison of this method with the Theil–Sen estimator shows
insignificant differences in the estimated trends. The GNSS-based estimated
PWV trends change between

The increment in PWV varies between 4.5 and 6.5 % per degree Celsius rise in temperature, which is comparable to the theoretical rate of the Clausius–Clapeyron equation. The magnitude of the PWV trend slightly differs from that of the dew point temperature. Hence, we can consider the trends estimated from the dew point temperature as a measure for the PWV trends in case of lack of observations.

It would be illuminating to validate the results of this research using a data set that has a higher spatial resolution than the ERA-Interim.

In this paper, we used (1) ERA-Interim data, which can be
downloaded from the ECMWF servers
(

The authors declare that they have no conflict of interest.

The authors would like to thank the ECMWF for making publicly available the ERA-Interim data. Thanks also go to the German Meteorological Service (DWD) for providing us with hourly meteorological measurements. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: Ralf Sussmann Reviewed by: two anonymous referees