###### Abstract

After 30 years since the beginning of the Global Positioning System (GPS), or
more generally Global Navigation Satellite System (GNSS) meteorology, this
technique has proven to be a reliable method for retrieving atmospheric water
vapor; it is low-cost, weather independent, with high temporal resolution and
is highly accurate and precise. GNSS ground-based networks are becoming
denser, and the first stations installed now have quite long time-series that
allows for the study of the temporal features of water vapor and its relevant
role inside the climate system. In this review, the different GNSS
methodologies to retrieve atmospheric water vapor content are examined, such
as tomography, conversion of GNSS tropospheric delay to water vapor estimates,
analyses of errors, and combinations of GNSS with other sources to enhance
water vapor information. Moreover, the use of these data in different kinds of
studies is discussed. For instance, the GNSS technique is commonly a reference
tool for validating other water vapor products (e.g., radiosounding,
radiometers onboard satellite platforms, ground-based instruments).
Additionally, GNSS retrievals are largely used in order to determine the high
spatio-temporal variability and long-term trends of atmospheric water vapor or
in models with the goal of determining its notable influence on the climate
system (e.g., assimilation in numerical prediction, as input to radiative
transfer models, study of circulation patterns, etc.).

###### keywords:

GNSS; GPS; water vapor; ground-based; methodology; validation; spatio-
temporal; time-series; meteorology; climate

1 1 0 Academic Editor: https://dx.doi.org/ Review on the Role of GNSS
Meteorology in Monitoring Water Vapor for Atmospheric Physics Review on the
Role of GNSS Meteorology in Monitoring Water Vapor for Atmospheric Physics
Javier Vaquero-Martinez 1,2,* and Manuel Anton 1,2 Javier Vaquero-Martinez and
Manuel Anton Vaquero-Martinez, J.; Anton, M. Correspondence<EMAIL_ADDRESS>
##  1 Introduction

Water vapor is a trace gas of the Earth’s atmosphere. Despite its relatively
low concentration, it is of paramount importance to the Earth’s climate.
Firstly, water vapor is the major contributor to the natural greenhouse effect
and, therefore, in global warming, presents positive climate feedback (Colman,
2003, 2015). It also has an obvious role in the hydrological cycle, and plays
a key role in energy transport. Water is evaporated at low latitudes, and its
vapor is transported to higher latitudes where, by condensation, it releases
high amounts of heat (Myhre et al., 2013).

Water vapor can be quantified using different methods. One of the most common
is the integrated water vapor (IWV), which is also known by other names in the
literature, such as precipitable water vapor (PWV), precipitable water (PW),
integrated precipitable water vapor (IPWV), and so forth. This quantity
represents the integral of the concentration of water vapor along the vertical
path, and can also be pictured as the height that, in a vessel of a unit
cross-section, the water vapor in a column of the same cross-section would
reach if all of it condensed to liquid water. The density of liquid water
allows the establishment of the equivalence between the superficial
concentration (in $\mathrm{kg~{}m^{-2}}$) and the height in the vessel (in
$\mathrm{mm}$).

Another interesting measurement of water vapor is its distribution with
height. This distribution can be given as a mixing ratio (grams of water per
gram of dry air), as relative humidity, or other measurements of
concentration.

Global Navigation Satellite Systems (GNSS) allow the retrieval of information
about atmospheric water vapor, with different techniques. In this article, we
will focus on the ground-based techniques, since GNSS radio-occultation
techniques have already been discussed elsewhere (Bonafoni et al., 2019; Liu
et al., 2017; Wickert et al., 2009).

Global Positioning System (GPS) meteorology started when Bevis et al. (1992)
suggested this approach to remotely sensing water vapor, in a time when even
GPS, the first GNSS constellation, was not still completed. In that paper, the
methodology to derive IWV from tropospheric delay is thoroughly explained.
Moreover, some possible applications are depicted. One of them is the obvious
use of GNSS-receiver networks to monitor IWV, but also the idea of water vapor
tomography by using dense networks is shown.

The main idea behind remote sensing of the water vapor through GNSS is that
the GNSS signal between satellite and ground-based receiver is delayed by the
troposphere, along with other effects. The GNSS processing for obtaining the
position of the receiver needs to account for this, which is called slant
tropospheric delay (STD). This is usually given in terms of the zenith
tropospheric delay (ZTD), since it is not satellite-dependent and, to convert
STD to ZTD, a mapping function is needed. Once ZTD is obtained, meteorological
data (typically surface atmospheric pressure) are used to compute the non-
dipolar component of this ZTD, known as the zenith hydrostatic delay (ZHD). By
subtracting the ZHD from the ZTD, only the dipolar component remains, which is
exclusively due to the presence of water vapor (because it is the only
atmospheric component with permanent dipolar moment). This component is called
the zenith wet delay (ZWD). It can be converted to IWV using a factor usually
represented by $\Pi$ (sometimes by Q). The $\Pi$ factor has been calculated by
many methods in the literature (see Section 2.1). The most accurate methods
model $\Pi$ as a function of the weighted mean temperature of the atmosphere,
also known as Davis temperature ($T_{m}$).

One simple way to estimate $T_{m}$ is through linear regression with surface
temperature ($T_{s}$). Bevis et al. (1994) performed a linear regression of
$T_{m}$ and surface temperature ($T_{s}$) using radiosonde data in the United
States, which is currently known as the Bevis Formula ($T_{m}=70.2+0.72\cdot
T_{s}$). This work also included a more detailed explanation of the method for
ground-based GNSS water vapor monitoring, providing specific figures for all
the constants involved, and discussing their uncertainty in depth. The
refractivity constants were obtained by statistical treatment of values from
other studies, while the computation of $T_{m}$ values was also carried out
using numerical weather prediction models (NWP), yielding a root mean square
error (RMSE) of $2.4~{}\mathrm{K}$ (as compared to the RMSE of
$4.7~{}\mathrm{K}$ from using the so called “Bevis formula”).

After these studies, the importance of water vapor and the need of improving
its spatial and temporal resolution and coverage was acknowledged in some
studies, such as (Dabberdt and Schlatter, 1996). Moreover, GNSS meteorology
was found to be suitable for this task, as most of the infrastructure was
already there (for navigation and geodetic applications, mainly). Therefore,
it was a unique opportunity to obtain more meteorological information at a
very low cost. However, these efforts would be useless without the information
provided by services like the International GNSS Service IGS (Dow et al.,
2005), operating since 1994 and providing necessary information for the
processing of GNSS data, such as precise and real-time orbits, clock
corrections, tropospheric products, and so on. The IGS counts with a global
network of ground-based receivers and a set of Analysis Centers to process
their data. This global network is depicted in Figure 1.

Figure 1: Current network of 506 stations belonging to IGS. Color and shape
are related to the last data available date. Source:
https://www.igs.org/maps/#station-map (accessed on).

It must be noted that the processing of tropospheric delays must be finely
tuned for meteorological purposes. For navigation techniques, the estimation
of the different delays do not need to be very precise, as long as their
combination adds up to the total delay suffered by the satellite-receiver
signals. However, for meteorological purposes, the other delays need to be
obtained with high precision to avoid that part of the error can be
transferred to the tropospheric delay estimate. For instance, the ocean tide
loading can induce errors of up to $1~{}\mathrm{cm}$ in ZTD if it is not
properly modeled (Dach and Dietrich, 2000).

GFZ-Potsdam started the development of one of the first systematic near real-
time water vapor products based on a German network and in association with
other research centers. This was the so-called GNSS Atmosphere Sounding
Project (GASP). It was partly dedicated to space-based GNSS observations but
also to ground-based measurements (Dick et al., 2001). The STD started to be
assimilated in analysis experiments for dense GNSS networks, developing ways
of estimating the 3D structure of water vapor (MacDonald et al., 2002). The
use of ground-based GNSS networks for tomography of the troposphere, obtaining
4D maps of water vapor, was first discussed by Flores et al. (2000). They
proposed a methodology (software LOTTOS) to retrieve these maps from STD
measurements and concluded that the technique could be used for monitoring the
troposphere.

Later, Morland et al. (2006) presented the STARTWAVE (STudies in Atmospheric
Radiative Transfer and Water Vapour Effects) project, whose objective was to
obtain a database of different water vapor products (including ground-based
GNSS ones) that allowed the study of the role of water vapor in the climate.
At the same time, the idea of using GNSS networks for water vapor tomography
was still in the air, and Bender and Raabe (2007) considered the idea of
different network geometries. They concluded that the spatial resolution would
be given by the mean inter-station distance. It was also reported that the
quality and quantity of measurements depend on the distribution of the
satellite constellation and, therefore, on time, they would improve as more
satellites (including other constellations such as GLONASS or Galileo) became
available. Multi-GNSS processing became operational for near real-time
applications a few years later, when Li et al. (2015) first compared this kind
of measurement with single-GNSS ones. The processing was possible thanks to
the efforts of the IGS Multi-GNSS Experiment MGEX (Montenbruck et al., 2017).

This article reviews different methodologies used to retrieve water vapor
information from GNSS processing in Section 2. The vast applications of these
processing techniques are discussed in the following sections, namely the
inter-comparisons with other techniques (Section 3), the spatio-temporal
analysis of water vapor distribution (Section 4), and the impact of water
vapor variability on meteorology and climate (Section 5). Finally, conclusions
are drawn in Section 6.

##  2 GNSS Methodologies

###  2.1 Conversion of Tropospheric Delays to Water Vapor

The conversion of ZWD to IWV is performed through the factor $\Pi$. Typically,
its value is estimated by the relation described by Equation (1),

$\Pi=\frac{10^{6}}{\rho R_{v}\left[k_{3}/T_{m}+k^{\prime}_{2}\right]},$ (1)

where $\rho$ is the density of liquid water, $R_{v}$ the specific gas constant
for water vapor, $k_{3}$ and $k^{\prime}_{2}$ are refractivity constants and
$T_{m}$ is the weighted mean temperature of the atmosphere, defined as
Equation (2):

$T_{m}=\frac{\int\left(P_{v}/T\right)\mathrm{d}z}{\int\left(P_{v}/T^{2}\right)\mathrm{d}z}.$
(2)

$T_{m}$ is typically obtained by using a linear regression between surface
temperature ($T_{s}$) and $T_{m}$ (obtained from radiosondes). The
relationship $T_{m}-T_{s}$ given by Bevis et al. (1992) was obtained using
radiosondes in the United States. Logically, some efforts have been made to
improve it for application to other locations. Emardson and Derks (2000)
considered two models for $\Pi$ in Europe: (1) series expansion of the
deviation from mean surface temperature, and (2) a combination of the former
with a seasonal variation based on decimal day of year and latitude. Both
models presented RMSE values between $1.0\%$ and $1.2\%$, fitting the
coefficients to all Europe, by regions or by site. Slight increases in RMSE
values were found as the fitting involved wider regions. In more equatorial
regions, such as southern India, $\Pi$ has been reported to be less dependent
on $T_{m}$ variations, allowing to set it to a fixed value without relevant
precision loss (Suresh Raju et al., 2007). Another work addressed the model to
calculate $T_{m}$ in tropical regions, finding that the Bevis formula is shown
to be less adequate with high temperatures and low variability. In fact, the
definition of $T_{m}$ assumes that temperatures are not so high, and Bevis et
al. (1992) indicates a larger dispersion for high $T_{s}$ values. Therefore,
it is suggested that the redefinition of $T_{m}$ should be addressed for
tropical regions.

NWP, as with the reanalysis from European Centre for Medium-Range Weather
Forecasts (ECMWF), have been widely used to retrieve surface pressure and
$T_{m}$ since 2009 approximately. Heise et al. (2009) obtained a global
5-minute data-set from the IGS GNSS network using this approach. The ECMWF
reanalysis version used (ERA-Interim) had 6-h resolution, and the estimated
uncertainty due to time interpolation was less than $0.2~{}\mathrm{mm}$.
Later, Wang et al. (2019) compared the GNSS IWV product using the new ECMWF
reanalysis (ERA5) for pressure and $T_{m}$, on the one hand, and using the
legacy version (ERA-Interim), on the other hand, against a reference GNSS IWV
product using data from meteorological stations. The biases and RMSE of both
products were of a few tenths of a millimeter. Against radiosondes, the RMSE
was of about 2–4 $\mathrm{mm}$. ERA5 interpolation data-set was found to be
more stable than ERA-Interim one. Zhang et al. (2019) showed that ERA5 GNSS
IWV improved ERA-Interim GNSS IWV in China, thanks to ERA5’s pressure
enhancement, and with a similar performance on $T_{m}$. The contribution of
ERA5 to the IWV error was estimated to be less than $1~{}\mathrm{mm}$, and
diurnal variations were better caught by ERA5 GNSS IWV than by ERA-Interim
GNSS IWV.

Moreover, there have been some approaches to use NWP data for retrieving
mapping function parameters, pressure and temperature (Böhm et al., 2015;
Landskron and Böhm, 2018). These approaches can be useful when there are not
any meteorological stations available nearby the GNSS station or when access
to NWP data is difficult.

Another possible approach is to use local models of temperature and pressure
to convert ZTD to IWV, using local meteorological stations over a long time
series. Charoenphon and Satirapod (2020) followed this methodology in
Thailand, finding that RMSE was below $3~{}\mathrm{mm}$, therefore it was
considered suitable for weather nowcasting.

All of these different methodologies to convert ZTD to IWV have advantages and
disadvantages. The most precise approach is to use measurements of temperature
and pressure at the station location, but sometimes this is not possible or
not fast enough for some applications. In addition, it is important to apply
the necessary corrections when the meteorological station and the GNSS
receiver are not at the same height. Moreover, the use of models can be very
helpful for some applications or to retrieve data from receivers that are far
away from meteorological stations or to extend the time series of stations
that have a meteorological station nearby in the present but not in the past.

###  2.2 Error Analysis

Since GNSS meteorology is a rather indirect technique, there can be sources of
error in each step of the process. For instance, the presence of patterns of
water vapor gradients can induce errors in GNSS-derived IWV to the point that
methodologies have been developed to correct for this (Iwasaki et al., 2000).
Another important feature when computing ZTD from GNSS measurements is the
satellite Antenna Phase Center (APC) variations. The APC model changed with
the addition of new satellites to the GNSS constellation. Jarlemark et al.
(2010) studied the influence of not applying proper modeling for APC,
obtaining spurious, additional trends in IWV of up
$0.15~{}\mathrm{mm~{}year^{-1}}$. On 6 November 2006, IGS changed their
processing strategy from using relative antenna phase center calibrations to
absolute ones. Ortiz de Galisteo et al. (2010) showed the impact of this
change in GNSS IWV products, using data in four locations in Spain from two
years before and after this change. With relative calibrations, a 2–3
$\mathrm{mm}$ bias of GNSS with respect to other instruments (radiosonde, sun-
photometer) was found. However, GNSS IWV after the change to absolute
calibrations exhibited a practically zero bias. In addition, RMSE reduced to
half and correlations slightly increased.

Satellite positions and clock corrections are fundamental to the retrieval of
tropospheric GNSS products. However, precise data can only be obtained after a
few days, so they cannot be used for near real-time applications. A comparison
of near real-time water vapor product with final products to compare the
effect of rapid/final satellite orbit estimation obtained negligible bias and
RMSE below $1~{}\mathrm{mm}$ (Yadav et al., 2010).

The mapping functions that transform slant delays into zenith delays are also
error-prone. Labib et al. (2019) compared GNSS IWV computed with Global
Mapping Function (GMT) and Vienna Mapping Functions 1 (VMF1) on a global
scale. Both products were compared against radiosonde observations. The
authors concluded that there was not a better option. However, both mapping
functions must be revisited for climate zones other than mid-latitude regions.

Another feature in ZTD processing that can affect IWV measurements is cutoff
in elevation angle. Ning and Elgered (2012) computed IWV trend using data-sets
obtained with 8 different cutoff elevation angles at seven sites in Finland
and Sweden for 14 years (1997–2010). In comparison with radiosonde trends,
best RMSE was found for angles of $10^{\circ}$ and $15^{\circ}$. However, the
best correlation ($0.88$) was found for cutoff angles of $15^{\circ}$.
Therefore, it was shown that GNSS data contained information about trends, but
these were too small to be uniquely detected.

It is important to notice that, specially when dealing with trend estimation,
GNSS-IWV time series data must be retrieved with the same parameters to avoid
inhomogeneities in the series.

###  2.3 Tomography

Although there have been some experiments with single-station retrievals of
the vertical structure of water vapor (Caputo et al., 2000; Iassamen et al.,
2009), profiles are generally obtained from network solutions. Otherwise, a
distribution has to be decided a priori (typically a decreasing exponential
with height). One of the first efforts to water vapor tomography was made by
Bi et al. (2006), who developed a method for obtaining slant water vapor
(water vapor integrated along the slant path) and compared it to water vapor
radiometer (WVR), with RMSE less than $4~{}\mathrm{mm}$.

Voxel approaches, however, discretize the space in cubes (voxels) and try to
obtain the concentration of water vapor in each of these voxels. This way,
they provide a 3D (or 4D, if time is also considered) representation of water
vapor. There are, however, many different approaches to accomplish this and
none of them are trivial. One way to optimize the process was provided by Yao
and Zhao (2017). They proposed the use of a long-term mean radiosonde water
vapor profile in the location of the GNSS network. The horizontal voxel
definition was optimized using a non-uniform symmetrical division, based on
the geometry of the network. Figure 2 shows a representation of the voxel
tomography, with rays crossing the voxels. At a specific time, one voxel can
be crossed by many rays, while other by very few rays. This fact and other
complexities of the tomography problem make it need regularization and
optimization. Haji-Aghajany and Amerian (2018) showed a method to solve some
of these issues, obtaining tomography values of water vapor density with high
spatio-temporal resolution, resulting in RMSE of $0.39~{}\mathrm{g~{}m^{-3}}$.
The method was to use a ray-tracing technique in which rays are allowed to
move in the 3D space with a hybrid regularization method, which mixed direct
and iterative methods. The main idea was to project the large-scale problem
into a small-scale one that can be regularized by a direct method, and then
transform back to large-scale. The technique, apart from being more efficient
computationally, improved the results in some cases with respect to other
methods. A different method by Yang et al. (2019) tried to maximize the number
of rays by considering water vapor density in the upper region outside the
boundaries as four (one per direction) new parameters to obtain. This addition
to the traditional method allowed the use of rays that do not come from the
top boundary of the study region, but from the sides. An experiment in Hong
Kong was carried out to test this method, showing better results than
traditional tomography. Yang et al. (2019) also showed that, to improve
tomography, it is more relevant to increase the number of voxels crossed by
rays than than increasing the number of rays. However, the number of possible
approaches is large and, therefore, Brenot et al. (2019) compared several
variations of approaches to tomographic techniques with radiosonde and ECMWF
reanalysis. This study recommended using stacked data over a 30 min window
(increasing the number of available rays) and pseudo-slant observations in
case studies and nowcasting. Regarding parametrization, another study compared
some methods using the European Cooperation in Science and Technology (COST)
data-set (central Europe) (Adavi et al., 2020). Among them, ray-tracing was
found to be more adequate than straight-line methods. In an effort to increase
the number of observations with respect to the number of unknowns, Zhang et
al. (2020) proposed another method, which consisted on modeling the height
factor for both the isotropic and anisotropic part of slant wet delay (SWD).
This would allow signals that do not cross the tomography top boundary to be
included in the calculations, increasing the number of valid observations.

Figure 2: Voxel-based representation of tomography, with signal rays crossing
the voxels. Source: Dong and Jin (2018).

Voxel-based methodologies, despite being quite popular, have some drawbacks:
(1) the rank deficiency in the coefficient matrix, leading to the need of
applying constraints; (2) the assumption that water vapor is constant in the
space inside each voxel; and (3) the number of unknown parameters is high
compared to the number of observations. In order to avoid these drawbacks,
some methodologies avoiding the use of voxels have been developed. One of then
considered a function-based tomography, as Figure 3 shows. This approach uses
B-spline functions and a distribution of the atmosphere in layers as the base
to build the system of equations. A prior constraint of the 3D structure of
the water vapor needs to be applied in this vector, based on radiosonde data.
A test (Haji-Aghajany et al., 2020) with a 17-station network in California
was carried out, comparing the conventional, voxel-based method, and this new
B-spline function method, both validated against radiosonde observations. RMSE
was reported to reduce by about $0.3~{}\mathrm{g~{}m^{-3}}$. Instead of
B-spline functions, Zhang et al. (2020) proposed another method based on nodes
rather than in voxels, with the aim of reducing the discretization effects.
Also, a piece-wise linear fitting was used, instead of the standard (one-time)
one. In an experiment to compare the standard method and this node-based
method against reference radiosonde profiles, RMSE was found to decrease from
$1.5~{}\mathrm{g~{}m^{-3}}$ to $0.83~{}\mathrm{g~{}m^{-3}}$. The improvement
was stronger in rainy days.

Figure 3: Schematics from Haji-Aghajany et al. (2020) approach. Source: Haji-
Aghajany et al. (2020).

Whatever the tomography method proposed, another way to increase the number of
observations is to include several GNSS (Dong and Jin, 2018). The multi-GNSS
tomography approach was validated using the Continuously Operating Reference
Stations (CORS) network in Wuhan, China, against radiosonde and ERA5,
improving in a $5\%$ GPS-only tomography. The comparison of GPS-only,
GPS+GLONASS (Globalnaya navigatsionnaya sputnikovaya sistema, Russian GNSS)
and GPS+GLONASS+BDS (BeiDou Navigation Satellite System, Chinese GNSS), showed
that BDS did not improve much the tomography. The improvements were associated
to the increase of signals available for tomography ($1.6$ times more for
2-GNSS, and $2.2$ for the three GNSS).

Tomography of water vapor using GNSS networks is an emerging field that,
although it has room for improvement, will provide very useful information
about the 3D water vapor distribution. The use of multi-GNSS approaches and
the densification of station networks will help improving tomography. This
will improve NWP analysis and forecasts, and the general knowledge of
atmospheric water vapor.

###  2.4 Combining with Other Measurements.

Being the atmospheric water vapor highly varying in space and time, the
combination of different data-sets with different characteristics can enhance
the knowledge of its spatial and temporal distribution. For example, Furumoto
et al. (2003) proposed an algorithm to use GNSS-derived water vapor
measurements to improve humidity profiles estimated from middle and upper
atmosphere radar with the radio acoustic sounding technique.

The use of satellite measurements with GNSS data is an interesting idea, since
satellite instruments have opposed characteristics to GNSS: high spatial, but
low temporal resolution. They are also generally not available for all weather
situations, but GNSS data are available for all weather situations without
important quality loss. One example of this approach (Lindenbergh et al.,
2008) used MEdium Resolution Imaging Spectrometer (MERIS) satellite
observations combined with GNSS measurements to estimate IWV by means of a
kriging methodology. Thus, IWV was retrieved at a time and point in space by
means of (1) a kriging combination of GNSS IWV from several locations at that
same time; and (2) MERIS IWV from that point in space at the closest time
available. Another example of combination of satellite and GNSS IWV was
provided by Leontiev and Reuveni (2018). This approach used Meteosat-10 data
to identify cloud features, and then using this information in the GNSS IWV
interpolation (Delaunay triangulation or kriging interpolation) process. Using
this approach in the Israel area, and validating against radiosonde, the
obtained bias and RMSE were $1.77$ and $2.81~{}\mathrm{kg~{}m^{-2}}$ to $0.74$
and $2.04~{}\mathrm{kg~{}m^{-2}}$, respectively.

Other works combine GNSS data with models. An experiment ingested GNSS and
Interferometric synthetic-aperture radar (InSAR) IWV and the Weather Research
and Forcasting (WRF) model to cover areas that are underrepresented by
GNSS/InSAR stations, using a fixed-rank kriging approach (Alshawaf et al.,
2015). The results were compared to MERIS imagery, and uncertainties of less
than $1~{}\mathrm{mm}$ were found. One of the strengths of this technique is
that more data sources can be used, improving further the quality of the
generated IWV maps. Another hybrid data-fusion model has been proposed, using
GPT2 model as base, and correcting it with polynomial fitting and spherical
harmonics functions obtained from GNSS and radiosonde IWV, also considering
correction for height differences associated to each station (Zhao et al.,
2020).

Data fusion approaches allow increasing even more the benefits of the
continuously operating GNSS networks, which have the potential to enhance
weather forecasts and analysis. When applying them, it is important to correct
the IWV for height differences, since IWV decrease with increasing height.

##  3 Inter-Comparisons with Other Techniques

###  3.1 Validations of GNSS Water Vapor with Other Techniques as Reference

Table 3.1 presents a summary of the main findings of the works used to develop
this subsection. One of the first GNSS IWV validations as an emerging system
for water vapor monitoring was performed by Duan et al. (1996). They applied
an approach that incorporated GNSS stations that were far away (long
baselines) to estimate the absolute ZTD, while previous methodologies used WVR
for calibration of the relative ZTD path. This could lead to errors, since WVR
overestimate IWV during rainfall. Then, they compared IWV at a few stations in
Oklahoma and Kansas with nearby WVR stations, obtaining negligible bias and
RMSE in the interval 1.0–1.5 $\mathrm{mm}$. It was proved that GNSS could, by
itself, provide accurate ZTD values without the need of auxiliary instruments,
which was specially important for all-weather IWV retrieval, since WVR
typically fails under intense rainfall. Another work analyzed the usefulness
of GNSS for IWV monitoring, and compared the estimates against NWP. It was
found that, although GNSS IWV showed the potential to become a powerful tool
for improving forecasts, the products still needed to be refined, as biases
were found in the 2–4 $\mathrm{mm}$ and RMSE of $3.8~{}\mathrm{mm}$ (Iwabuchi
et al., 2000). In this work, it must be noted that the meteorological data
used for converting ZTD to IWV was obtained from the NWP itself, and therefore
not as accurate as a meteorological station, specially for near real-time
applications. There were also validations against radiosonde stations, which
are usually a reference for water vapor sensing. For instance, Basili et al.
(2001) studied the comparison of GNSS and WVR against radiosondes during 1999
in non-precipitating conditions, using the Cagliari (Italy) GNSS station and
nearby radiosonde and WVR sites. The bias between GNSS and radiosondes was
$0.4~{}\mathrm{mm}$ and the standard deviation $1.9~{}\mathrm{mm}$, which
already showed better results than Iwabuchi et al. (2000).

It is useful to test the slant-IWV, as it can be used in some applications
(for instance, tomography) and it is also an interesting exercise to evaluate
GNSS observations without the possible errors from mapping functions. Braun et
al. (2003) compared line-of-sight integrals of water vapor from GNSS using WVR
as a reference in Oklahoma. They found very good agreement between both
techniques (correlation $0.99$, RMSE $1.3~{}\mathrm{mm}$). This work concluded
that GNSS data provided an all-weather alternative that is especially useful
under rainfall or sever weather events, situations in which other instruments
(such as WVR itself) fail.

[H] Summary of studies on validation of GNSS measurements. Column Year is the
publication year. N is the number of stations. Instr. is the instruments
(besides ground-based GNSS) used in the study. Start and End mark the period
considered in the study, in year-month format. Bias is the bias in mm, and DEV
is the RMSE or SD also in mm. Corr is the correlation coefficient (R).

Work |  Year |  N |  Instr. |  Start |  End |  Region |  Bias |  DEV |  Corr
---|---|---|---|---|---|---|---|---|---
(Duan et al., 1996) |  1996 |  4 |  WVR |  1993-05 |  1993-05 |  Interior US (US) |  0.05 |  1.28 |  -
(Iwabuchi et al., 2000) |  2000 |  556 |  NWP |  1996-09 |  1996-09 |  Japan |  2–4 |  3.8 |  -
(Basili et al., 2001) |  2001 |  1 |  radiosonde, WVR |  1999-01 |  1999-12 |  Cagliari (Italy) |  0.4 |  1.9 |  -
(Braun et al., 2003) |  2003 |  |  WVR |  2000-05 |  2000-06 |  Oklahoma |  - |  1.3 |  0.99
(Memmo et al., 2005) |  2005 |  5 |  MWR, NWP (MM5), radiosonde |  2002-08 |  2003-09 |  Europe (Italy) |  0.01 |  0.286 |  0.939
(Glowacki et al., 2006) |  2006 |  8 |  NWP(GASP; ECMWF), radiosonde |  2000-01 |  2000-12 |  Australia |  $-$1.4–+1.1 (GASP), $-$1.8–+1.3 (ECMWF) |  3.1–5.3 (GASP), 2.7–3.5 (ECMWF) |  -
(Ha et al., 2010) |  2010 |  3 |  MWR, radiosonde |  2009-08 |  2009-09 |  Ulleungdo (South Korea) |  :3.0 (Radiosonde), 5.0 (MWR) |  12.5 (Radiosonde), 9.3 (MWR) |  -
(Musa et al., 2011) |  |  4 |  radiosonde |  2008-01 |  2008-12 |  Malaysia |  $-$1.5–0.0 |  3.5–4.3 |  0.80–0.88
(Thomas et al., 2011) |  2011 |  12 |  radiosonde, AIRS, MODIS |  2004-01 |  2004-12 |  Antarctic |  $-$0.48 (Radiosonde) |  - |  -
(Vaquero-Martínez et al., 2019) |  2019 |  4 |  radiosonde |  2006-05 |  2018-01 |  global |  $-$0.87–($-$0.49) |  0.61–1.10 |  0.99

2

The potential of GNSS IWV for model verification was assessed by Guerova et
al. (2005). GNSS was starting to be acknowledged as a reliable technique for
validating models and other instruments. Particularly, this work includes some
validation of GNSS IWV against radiosondes and MWR in Switzerland between 2001
and June 2003\. During daytime, GNSS showed a positive bias against radiosonde
($0.9~{}\mathrm{mm}$), while at night, the bias became negative
($-0.4~{}\mathrm{mm}$). However, against MWR, both night and daytime GNSS IWV
showed positive bias ($0.3~{}\mathrm{mm}$). Therefore, in general terms, it
was concluded that GNSS IWV was an accurate technique, and it was used to
evaluate Alpine Model analysis and forecast (Guerova et al., 2005). The model
showed a seasonal dependence with an increased dry bias in summer 2002. The
main conclusion was that GNSS provide information accurate enough for model
verification and assimilation. Another work (Memmo et al., 2005) compared the
Fifth-Generation Penn State/NCAR Mesoscale Model (MM5) forecast IWV against
GNSS, radiosonde and microwave radiometer (MWR), showing that summer had worse
performance (higher errors, smaller correlation) than other seasons. In this
work, summer also had a higher bias (wet in this case) but this is associated
to the fact that IWV values are higher in summer. The diurnal cycle is also
reported to be an aspect to improve, and errors are mainly associated to
errors in the temperature daily cycle by MM5. Therefore, in this work, GNSS
IWV was successfully used as a reference to find deficiencies in models.

However, one of the best tests for GNSS IWV products is to compare them
against radiosonde measurements, a direct method usually considered a
reference despite known bias issues, see (Dirksen et al., 2014). Glowacki et
al. (2006) compared GNSS IWV from eight stations in Australia against
collocated or nearby radiosonde stations, obtaining standard deviations of
$8.8\%$, except for Antarctic stations, which increased to 18–21$\%$. It must
be noticed that GNSS is considered less sensitive to small amounts of water
vapor and, therefore, in regions with small IWV, GNSS technique can perform
worse. This was assessed by a cross-validation including, FTIR, sun-
photometer, multifilter rotating shadowband radiometer (MFRSR), radiosonde,
and GNSS in the Izaña Observatory (Canary Islands, Spain) during years
2005–2009, showed similar biases with respect to GNSS ($-3.58$ to
$+0.42~{}\mathrm{mm}$), and standard deviations (between $0.73$ and
$2.29~{}\mathrm{mm}$), which is consistent with other works. GNSS accuracy was
found to be better than $10\%$ for values over $3.5~{}\mathrm{mm}$. However,
for values under this limit, the accuracy is worse ($\sim$20%) and a
systematic dry bias appears (Schneider et al., 2010).

Other comparisons against radiosondes, like the one set in four stations of
the Malaysian Peninsula by Musa et al. (2011) during the year 2008, or the one
with four collocated reference GRUAN radiosonde stations (Vaquero-Martínez et
al., 2019), assessed the high quality of GNSS to monitor water vapor. RMSE
values were in the range 3.5–4.3 $\mathrm{mm}$ in the former, while standard
deviations were 0.61–1.10 $\mathrm{mm}$ in the latter, and correlations were
of 0.80–0.88, reaching $0.99$ in the second work. Both works presented dry
biases, varying between $0.0$ and $-1.5~{}\mathrm{mm}$ in the first cases, and
0.49–0.87 $\mathrm{mm}$ in the second. The different biases are mainly
associated to dry bias in the radiosonde measurements, while the better
results in the second work could be due to the use of GRUAN stations, with
high quality standards, and also to the fact that both radiosondes and GNSS
stations were exactly collocated. These works show that GNSS data are high
quality but, in any case, the presence of redundant measurements help assess
the quality of products. Radiosonde dry bias was also assessed by Bock et al.
(2007). This work inter-compared GNSS, radiosonde, Special Sensor
Microwave/Imager (SSM/I) satellite instrument (in coastal stations only) and
NWP (ERA-40 and National Centers for Environmental Prediction 2, NCEP2) for
stations in Africa. The standard deviations were of $3.0$, $2.1$,$3.6$, and
$5.2~{}\mathrm{mm}$, respectively, while the biases (GNSS - instrument) were
$3.2$, $-0.6$, $0.5$, and $1.6~{}\mathrm{mm}$, respectively. The results
confirmed the high potential of GNSS for water vapor monitoring. Another work
found a cause for dry bias in tropical regions (Zhang et al., 2018): the
Integrated Global Radiosonde Archive (IGRA) product only integrates water
vapor up to a pressure level of $500~{}\mathrm{hPa}$. While this is usually a
fair approximation, in tropical regions it induces a dry bias in the
radiosonde product; in the case of Tahiti, of 9%.

Another interesting region for validation is Antarctica. It is a region with
relatively scarce water vapor observation data; yet its water vapor spatial
distribution and temporal variability influences precipitation patterns and,
therefore, ice accumulation. Hence, a GNSS-derived data set for Antarctica,
with proven accuracy and stability, could be very useful for modeling and
obtaining trends (Thomas et al., 2011). A work used homogeneously reprocessed
GNSS data for the year 2004 in 12 stations (Thomas et al., 2011) in this
region. These data had three important improvements compared to previous GNSS
IWV products: first, it used absolute antenna phase center variations. Second,
it used VMF1 mapping functions. And third, an accurate a priori model for ZHD.
For comparison, radiosonde measurements were used as reference, finding a GNSS
bias of $-0.48~{}\mathrm{mm}$, very adequate even for a region with low IWV
that could affect GNSS sensitivity to water vapor. Atmospheric Infrared
sounder (AIRS) and Moderate Resolution Imaging Spectroradiometer (MODIS) IWV
products were also compared to GNSS in this work, with low bias ($0.58$ and
$0.35~{}\mathrm{mm}$, respectively) and RMSE ($1.24~{}\mathrm{mm}$ and
$1.42~{}\mathrm{mm}$). This concluded that the newly analyzed GNSS IWV product
had enhanced capabilities for assimilation in NWP.

Multi-comparisons can help attribute errors to one or another instrument,
making easier to analyze deeper the possible causes of error. As an example, a
work that compared radiosonde, GNSS, Fourier-transform infrared spectroscopy
(FTIR), MWR, Advanced Microwave Sounding Unit (AMSU-B) satellite based
microwave radiometer, and ERA-Interim NWP in the location of Kiruna (Sweden)
(Buehler et al., 2012) found systematic differences in the range of $\pm
1~{}\mathrm{mm}$, consistent with other mentioned works. Although the overall
comparison shows a good agreement among the different techniques, they aimed
to characterize the slope and offset of the different techniques, combining
their study with others, but no consistent pattern emerged (the only pattern
was that systematic differences were in the 1–2 $\mathrm{mm}$ range). This
work also presented a method to compare values of IWV with different heights
(that is, where the lower limit of the integral starts a different heights),
based on a correction factor linearly dependent with height. The factor was
obtained with radiosonde data. The representativeness error was also
addressed, presenting a method to estimate it and, finding that it can
dominate the differences among techniques, what could make it so that observed
differences do not contain much information about the true precision of the
techniques. This must be taken into account in future works to make
validations more statistically significant. Another interesting inter-
comparison (Van Malderen et al., 2014) involved radiosondes, GNSS, sun-
photometers, a combination of GOME, GOME-2 and SCIAMACHY products, and AIRS
IWV product. The study was carried out in 28 sites in Northern Hemisphere. It
was found that biases were in the $-0.3$ to $+0.5~{}\mathrm{mm}$ interval,
with larger standard deviation (SD) values (0.96–3.96 $\mathrm{mm}$) specially
for satellite instruments. Correlations with GNSS IWV were larger for ground-
based instruments ($R^{2}>0.97$) while slightly smaller for satellite
instruments ($R^{2}>0.88$). Sun-photometers and satellite retrievals were
shown to need low cloud fractions to perform properly, being this more
important than proximity between GNSS station and satellite pixel center or
sun-photometer station. All instruments showed worse performance with respect
to GNSS as cloud fraction increases, which in the case of satellite
instruments can be explained for the so-called screening effect. As cloudy
skies typically have larger IWV, the instruments show stronger dry bias for
high IWV. Radiosonde and AIRS measure both in daytime and nighttime, and both
showed a wet bias during nighttime, being reduced (radiosonde) or changed to
dry bias (AIRS) during daytime. In any case, inter-comparisons are reported to
be site- and instrument-dependent, as Buehler et al. (2012) indicated.

Not only IWV has been tested, but also profiles obtained through tomography.
Ha et al. (2010) validated GNSS water vapor profiles with collocated MWR and
radiosonde observations, using MWR as a reference in Ulleungdo (Korea) for a
few days in July 2009\. It was found that GNSS tomography could even improve
radiosonde’s RMSE values, but in some cases GNSS profiles were degraded, which
was associated with the fact that only two GNSS stations were used in the
tomography. Under severe weather, GNSS showed very good agreement with MWR, in
comparison with radiosonde. This work concluded that another important issue
for improving GNSS tomography was the satellite geometry, which is expected to
improve with multi-GNSS approaches.

The different validations show that GNSS has great potential as a tool for IWV
monitoring. It is important to put an effort into homogenizing the series,
especially when calculating trends and, when performing comparisons, taking
into account possible height differences and other deficiencies in the
instruments considered. These efforts help reduce spurious biases and
variability. The GNSS technique has the advantage of being relatively cheap,
weather-independent and with high temporal resolution, and for these reasons
this technique is preferred to others in many cases.

###  3.2 Validations of NWP with GNSS Water Vapor as Reference.

Table 3.2 presents a summary of the main findings of the works used to develop
this subsection. GNSS ground-based stations have been widely used for testing
NWP. One of the first works of this kind validated High Resolution Limited
Area Model (HIRLAM) against GNSS IWV in Spanish (Madrid Sierra) station
(Cucurull et al., 2000), obtaining a bias of $-0.4~{}\mathrm{mm}$ and RMSE of
$2.0~{}\mathrm{mm}$ during two short periods in December 1996. Another work by
Köpken (2001) compared the Baltic Sea Experiment (BALTEX) model and the Europa
model against 25 GNSS stations in Finland and Sweden. They found relatively
high biases (2.5–3.0 $\mathrm{mm}$), and adequate standard deviations
($2.8~{}\mathrm{mm}$ on average) and correlations ($0.92$ on average), but
with worse results than HIRLAM. Testing against radiosondes yielded smaller
biases, what suggested GNSS could have a slight dry bias in that region. SSM/I
was also analyzed in this work and showed a good correlation with the GNSS
product, assessing the use of both independent instruments for validation and
ingestion in analysis. NCEP reanalysis was deeply validated at a global scale
against GNSS by Vey et al. (2010), for a ten-year period (1994–2004) at daily
resolution. The study considered 11 clusters of stations for regional
analysis. The clusters were based on humidity regimes and geographical
information. Also, homogeneity of time-series from GNSS stations was analyzed
to select only homogeneous time-series or to correct those which had jumps in
the series. The validation of NCEP covered several aspects: correlation, bias,
seasonal signal, anomalies and variability. Correlation was shown to be very
close to the unit, in the range 0.89–0.99, except in some regions of South
America and the Antarctic Peninsula, which are regions that have a small
number of observations available to be assimilated by the model and,
therefore, worse performance is expected. Regarding bias, most stations were
in the $\pm 3.0~{}\mathrm{mm}$ range, and the biases were associated to
differences between the model height and the GNSS station height (which causes
errors due to the assumption of temperature lapse rate). The biases were also
associated with stations with high elevation, where the reduction of pressure
to station level could also be error prone. Biases in stations that did not
fit with these two problems (i.e., large elevation differences or large
elevations) are associated with NCEP problems, such as inconsistencies in
assimilated observations and inability of the model to resolve local changes.
Regarding the seasonal signal, it is found to be strongly underestimated in
Antarctica, while having a good agreement in Europe and most of North America.
The computation of anomalies suggest sub-millimeter accuracy in GNSS,
assessing its suitability for climate studies, providing that the processing
strategy remains unchanged and modifications of hardware or number of GNSS
observations were considered in the analysis. The study also concluded that
the Southern Hemisphere needs more observations for reanalysis assimilation,
suggesting the use of GNSS IWV to accomplish this.

However, not only direct comparisons are performed, but also other aspects,
like the effect of different spatial resolution in NWP, are studied. Yang et
al. (1999) evaluated HIRLAM against GNSS network in Northern Europe, along
with some forecasts. It was found that relatively coarse resolution
($0.4^{\circ}$) runs had a similar performance to finer resolution
($0.21^{\circ}$) ones. Therefore, a finer resolution did not mean better
agreement with observations. It was also found that NWP are useful for
detecting erroneous data in GNSS series.

Other studies have focused on the causes of discrepancies between NWP and
GNSS. The height difference between the orography of the model and the GNSS
station can induce systematic differences, since the integrals are not
measured from the same base level. This issue was studied by Matsuyama et al.
(2020), who compared Japanese 55-year Reanalysis (JRA-55) and GNSS in 26
Japanese stations in the period July 2010 to December 2012. After JRA-55 was
corrected to account for the height difference between the GNSS station and
the JRA-55 integral base level of geopotential, some dry bias in JRA-55 IWV
still remained. This suggested that not all of the discrepancy in IWV could be
attributed to the height difference and, therefore, the hydrological cycle of
this reanalysis needed deeper analysis. Moreover, NWP can provide inaccurate
data when the observations assimilated have erroneous or biased data. For
example, some radiosonde models have a well-known issue that caused a dry
bias. To study this problem, Bock and Nuret (2009) compared radiosondes and
NWP (ECMWF Integrated Forecasting System, and NCEP reanalysis I and II)
against GNSS IWV in western Africa over 2005–2008. In this case, the Vaisala
RS80-A radiosonde had a dry bias leading to errors in NWP through
assimilation, causing a dry bias of NWP with respect to GNSS. Other two
radiosonde models (Vaisala RS92 and MODEM) seemed to cause a wet bias in NWP
models. Another issue is how a pixel from NWP is representative of a point
(i.e., a GNSS station) in the area it covers. Bock and Parracho (2019)
addressed the representativeness error that ERA-Interim can have with respect
to GNSS in stations distributed globally. A “representativeness error
statistic” was developed, showing a correlation of $0.73$ with standard
deviation of IWV differences between ERA-Interim and GNSS. This statistic is
based on the information contained in the ERA-Interim data-set for the four
surrounding pixels for the GNSS station. To reduce the representativeness
error, it was recommended to bilinearly interpolate data to the position of
the GNSS station, as well as time-averaging. Some problematic cases (stations
whose data do not fit as well as the rest) were discussed.

[H] Summary of studies on validation of NWP data. Column Year is the
publication year. N is the number of stations. Instr. is the instruments
(besides ground-based GNSS) used in the study. Start and End mark the period
considered in the study, in year-month format. Bias is the bias in mm, and DEV
is the RMSE or SD also in mm. Corr is the correlation coefficient (R).

Work |  Year |  N |  Instr. |  Start |  End |  Region |  Bias |  DEV |  Corr
---|---|---|---|---|---|---|---|---|---
(Yang et al., 1999) |  1999 |  25 |  HIRLAM |  1995-08 |  1995-11 |  Northern Europe (Finland, Sweden) |  $-$0.1 |  2.3 |  0.94
(Cucurull et al., 2000) |  2000 |  5 |  HIRLAM, radiosonde |  1996-12 |  1996-12 |  Madrid Sierra (Spain) |  $-$0.4 |  2.0 |  -
(Köpken, 2001) |  2001 |  25 |  BALTEX; European, SSM/I, WVR |  1995-08 |  1995-10 |  Finland, Sweden |  2.5–3.0 |  2.8 |  0.92
(Bengtsson, 2004) |  2004 |  160 |  ERA-40; NOSAT |  2000-07 |  2001-01 |  global |  $-$31.26–10.75 % |  - |  -
(Guerova et al., 2005) |  2005 |  20 |  MWR, Alpine Model, radiosonde |  2001-01 |  2003-06 |  Switzerland |  $-$2.8 (forecast), $-$1.5 (analysis) |  - |  -
(Bock and Nuret, 2009) |  2009 |  11 |  ECMWF, NCEP, radiosonde |  2005-01 |  2008-12 |  Africa |  - |  - |  -
(Parracho et al., 2018) |  2018 |  104 |  |  |  2010-12 |  global |  - |  - |  -
(Bock and Parracho, 2019) |  2019 |  120 |  ERA-Interim |  1995-01 |  2010-12 |  global |  $-$1–1 |  <2 |  -
(Matsuyama et al., 2020) |  2020 |  26 |  JRA-55 |  2010-07 |  2012-12 |  Japan |  - |  - |  -

2

Nevertheless, not only is IWV tested in NWP, but also its trends. Trends of
IWV are very important for discussing how climate is evolving over the years.
For this reason, Bengtsson (2004) discussed whether reanalysis data can
provide valid trends for IWV and other variables. Particularly, IWV and its
trends, computed with the ERA40 and NOSAT experiment (reanalysis without
satellite data assimilation to mimic the pre-satellite era), were compared
globally against GNSS data. ERA40 trends were corrected to avoid spurious
trends due to changes in the observation system. In any case, the trends could
not be properly reproduced when compared to GNSS data. Later, Parracho et al.
(2018) studied trends from ERA-Interim and Modern-Era Retrospective analysis
for Research and Applications, Version 2 (MERRA-2) IWV data-sets for the
period 1980–2016, as well as for 104 GNSS sites globally from 1995 to 2010. It
was found that ERA-Interim was generally consistent with GNSS trends, while
MERRA-2 tended globally to more moistening trends. Inconsistent trends between
both reanalyses were found in Antarctica and most of the Southern Hemisphere,
as well as central and Northern Africa. These regions have a high uncertainty
in both reanalysis, due to the low number of in-situ observations, and the
dispersion between one model and the other is generally high. Arid regions are
found to have an important dependence of water vapor on circulation patterns,
and therefore, in those regions the Clausius-Clapeyron scaling ratio is not a
good proxy to infer IWV inter-annual variability and decadal trends.

GNSS IWV products have proven to be a reliable source of data for testing NWP
performance. However, some issues must be addressed, like the homogenization
of time-series (specially when dealing with trend estimation) and possible
height differences between GNSS station and pixel in the orography of the NWP.

###  3.3 Validation of Satellite Measurements with GNSS as Reference.

Table 3.3 presents a summary of the main findings of the works used to develop
this subsection. GNSS IWV data have been widely used as a reference to
validate satellite IWV products. Satellite radiometers use different regions
of the electromagnetic spectrum in which water vapor have absorption bands.
One of the most common is the infra-red (IR) or near infra-red (NIR), in which
water vapor is the main absorbent when compared to the rest of atmospheric
species. However, liquid water masses, like clouds, can disrupt the signal.
This is the so-called screening effect: water vapor below the cloud remains
“hidden” to the satellite radiometer, resulting in a dry bias. This is not
always reflected in the comparisons, probably due to corrections in the
retrieval algorithms. [H] Summary of studies on validation of satellite
measurements. Column Year is the publication year. N is the number of
stations. Instr. is the instruments (besides ground-based GNSS) used in the
study. Start and End mark the period considered in the study, in year-month
format. Bias is the bias in mm, and DEV is the RMSE or SD also in mm. Corr is
the correlation coefficient (R). Work Year N Instr. Start End Region Bias DEV
Corr (Raja et al., 2008) 2008 375 AIRS 2004-04 2004-10 US 0.5–1.2 3.0–4.5
0.91–0.98 (Bennouna et al., 2013) 2013 18 MODIS 2002-01 2008-12 Iberian P.
(Spain) 0.1–0.4 4.4–5.7 0.83–0.88 (Van Malderen et al., 2014) 2014 28
radiosonde, AIRS, GOME, GOME-2, SCIAMACHY, sunphotometer 1995-01 2011-04
Northern Hemisphere - - - (Román et al., 2015) 2015 21 GOME2 2007-01 2012-12
Iberian P. (Spain) 0.7 4.4 0.84 (Nelson et al., 2016) - MWR, radiosonde,
OCO-2, sunphotometer 2014-09 2016-02 global <0.5 1.3 0.994 (Ningombam et al.,
2016) 1 MODIS-NIR 2012-12 Trans-Himalayan $-$0.18 1.37 0.9848858 (Wang et al.,
2016) 2016 250 OMI, SSMIS, sunphotometer 2005-01 global - - - (Vaquero-
Martínez et al., 2017a) 9 OMI 2009-12 Iberian P. (Spain) $-$0.3 5.1(IQR) 0.79
(Vaquero-Martínez et al., 2017b) 2017 21 MODIS Iberian P. (Spain) 0.9% 39.36%
(IQR) 0.78 (Vaquero-Martínez et al., 2018) 2018 9 AIRS, GOME-2, MODIS, OMI,
SCIAMACHY, SEVIRI 2007-01 2012-12 Iberian P. (Spain) $-$5.2–16.7% - 0.75–0.91
(Gong et al., 2019) 1 FengYun-3A-MERSI, MODIS, sunphotometer 2013-07 Tibetian
Plateau $-$1.14–0.64 1.87–2.75 - (He and Liu, 2019) 370 ENVISAT-MERIS,
FengYun-3A-MERSI, Terra-MODIS 2010-01 2010-12 US $-$5.9–5.6 2.5–12.4 0.73–0.94
(Wang et al., 2019) 2019 303 OMI, SSMIS 2006-01 2006-12 global $-$3–4 3–10 -
(Carbajal Henken et al., 2020) 300 IASI, MIRS, MODIS, MODIS-FUB 2012-05
2014-06 Europe (Germany) $-$1.7–1.4 2.52–3.77 0.88–0.96 (Vaquero-Martínez et
al., 2020) 2020 1 AIRS, GOME2, MODIS, OMI, POLDER, SCIAMACHY 2010-01 2017-12
European Arctic $-$2.67–5.87 2.36–7.32 0.47–0.85 2 Another common region for
water vapor sensing is the visible, typically red or blue bands. In this case,
we have the same problem as with infra-red: clouds are opaque to visible
light. In addition, water vapor bands are not so strong in this region, and
therefore the sensitivity will not be as high as in the IR case. However, this
can be an advantage in some situations. When there is a high amount of IWV,
the infra-red absorption can saturate and therefore we would not be able to
sense water vapor over a certain threshold. Nevertheless, in that case, the
visible bands would not saturate.

The microwave, which GNSS also use, is another common region for extracting
information about water vapor. This region has the advantage of being more
independent of clouds. However, passive systems (that is to say, radiometers
that just receive the electromagnetic radiation reflected by the Earth’s
surface and atmosphere) receive very small amounts of microwave energy. This
makes it difficult to properly sense water vapor with this kind of instrument.

As we show in the following lines, different works provide very different
values depending mostly on three parameters: the region studied, the specific
satellite product and the quality control applied. Other sources of
differences can be the use of averaged data (daily or monthly means, for
example) and the period involved.

One of the first validations of satellite IWV products using GNSS as a
reference was carried out by Raja et al. (2008). They compared AIRS IWV
retrieval against GNSS data from a network in the United States (375 stations)
during April–October 2004. Bias (AIRS-GNSS) were in the range 0.5–1.2
$\mathrm{mm}$, while RMSE values were between $3.0$ and $4.5~{}\mathrm{mm}$.
Correlations (0.91–0.98) were calculated monthly. The biases were found to
have a seasonal behavior (from negative in April, to peak positive in July and
then decreasing). It was concluded that GNSS data are an excellent tool for
satellite validation, because they allow all-weather verification, with a high
number of pairs thanks to their high temporal resolution (30 min in this
work), and their accuracy. The quality of AIRS retrievals was assessed.

The Iberian Peninsula has been widely tested, in part because of two main
reasons: first, it is a region that gives home to different climate regimes in
a relatively small area and, second, it is a region with a relatively dense
network of GNSS stations and collocated (or nearby) meteorological stations.
Bennouna et al. (2013) studied the performance of MODIS-IR and NIR IWV annual
cycle against ground-based techniques, mainly GNSS, in 18 locations in the
Iberian Peninsula. The comparison is very detailed by zones of this region and
by season, finding high differences in MODIS performance between coastal and
interior stations. Representativeness error is also studied, finding that
using only time-coincident data for monthly means improves the agreement
between MODIS and GNSS. RMSE were found to be between $4.4$ and
$5.7~{}\mathrm{mm}$, biases of 0.1–0.4 $\mathrm{mm}$, and correlations of
0.83–0.88. Global Ozone Monitoring Experiment 2 (GOME-2) satellite instrument
was later evaluated by Román et al. (2015) in this region, using 21 stations
during the years 2007–2012. Bias was found to be $0.7~{}\mathrm{mm}$ on
average, and standard deviation $4.4~{}\mathrm{mm}$. They also analyzed some
factors that can influence GOME-2 retrieval performance. It was found that
increasing solar zenith angle also increases both bias and standard deviation,
that cloud presence increases bias but does not have an effect on standard
deviation, and that, under cloudless conditions, GOME-2 errors are within its
nominal error. Other studies followed in the Iberian Peninsula, like those by
Vaquero-Martinez et al. Vaquero-Martínez et al. (2017a, b); Vaquero-Martínez
et al. (2018), who compared Ozone Monitoring Instrument (OMI), MODIS and a set
of satellite instruments, respectively, against reference GNSS data. We will
focus on the last article, as it includes OMI and MODIS (both NIR and IR
products), and also other products like GOME-2, SCanning Imaging Absorption
SpectroMeter for Atmospheric CHartographY (SCIAMACHY), AIRS, and Spinning
Enhanced Visible and Infrared Imager (SEVIRI). They studied the pseudomedian
(rather than mean bias) and the inter-quartile range (rather than standard
deviation) of relative differences between satellite products and reference
GNSS product in nine stations the interior Iberian Peninsula during the period
2007-2013. It was found that all satellite products tended to smooth IWV
values (low IWV values tended to be overestimated, while high IWV ones tended
to be underestimated). $R^{2}$ was in the range
$0.56~{}(\text{AIRS})-0.83~{}(\text{GOME-2})$, pseudomedians between $-5.2\pm
0.1\%~{}(\text{SEVIRI})$ and $16.7\pm 0.8\%~{}(\text{GOME-2})$, and inter-
quartile ranges between $32.58\%~{}(\text{GOME-2})$ and
$47.84\%~{}(\text{AIRS})$. Dependencies on some variables were also studied,
namely, solar zenith angle, IWV, season and cloudiness, which highlighted the
differences among the different satellite remote sensing approaches.

A similar multi-comparison including AIRS, GOME-2, MODIS (NIR and IR), OMI,
POLarization and Directionality of the Earth’s Reflectances (POLDER) and
SCIAMCHY against GNSS data in the Ny-Alesund station (European Arctic) during
the period 2010–2017 was performed in another work (Vaquero-Martínez et al.,
2020). It was found that NIR had a very low performance in this region, and
that some external source for filtering out cloudy scenes is needed. OMI
version 4.0 product showed high bias and variability as compared with the
other products. The biases were in the range $-2.7$–5.9 $\mathrm{mm}$, RMSE
2.4–5.2 $\mathrm{mm}$ and $R^{2}$ between $0.22$ and $0.73$.

OMI IWV product has also been validated in successive versions of its
algorithm retrieval (Wang et al., 2016, 2019). We will only discuss the latest
version (4.0) of the algorithm, which was tested against GNSS IWV globally
distributed network for land and SSMI/S over the oceans. The influence of
cloud scenes is studied, recommending filtering data with cloud fraction less
than 0.05–0.25 and cloud top pressure more than $750~{}\mathrm{mm}$, apart
from quality flag. In the comparison, cloud fraction limit is set to $0.05$,
with bias of $0.32~{}\mathrm{mm}$, standard deviation of $5.2~{}\mathrm{mm}$
and correlation $0.87$ with respect to GNSS. They also demonstrate the
usefulness of OMI data for assimilation with WRF. However, on a more local
scale, Vaquero-Martínez et al. (2020) showed that, in the Arctic, OMI-GNSS
bias can be very high. Therefore, although OMI product has a good performance
globally, it is important to study local performance when using it for
specific regions.

Ningombam et al. (2016) validated MODIS-NIR IWV against a GNSS station in the
Trans-Himalayan region. Bias was $-0.18~{}\mathrm{mm}$ and RMSE
$1.37~{}\mathrm{mm}$, while correlation was $0.95$ for daily data. The
comparison was also performed in a monthly/seasonal basis, finding that summer
values were worse than in other seasons, which is expected because IWV
increases in summer. These values were better than others reported in the
literature for this product, probably because of the use of daily data.

Orbiting Carbon Observatory-2 IWV was compared against the SuomiNet global
network and other instruments (IGRA’s radiosondes and AERONET sun-photometers)
as references (Nelson et al., 2016). RMSE value reported against SuomiNet is
$1.3~{}\mathrm{mm}$ and correlation of $0.994$.

Gong et al. (2019) analyzed the Fengyun-3A Medium resolution spectral imager
(FY-3A/MERSI) IWV product against GNSS and sun-photometer measurements in the
Tibetan Plateau in 2009-2013. RMSE was in the range 1.87–2.75 $\mathrm{mm}$
and bias $-1.14$–0.64 $\mathrm{mm}$. He and Liu (2019) compared FY-3A/MERSI,
Terra/MODIS and Envisat/MERIS (all NIR satellite instruments) against GNSS in
US. It was found that NIR instruments tend to underestimate IWV under cloudy
conditions, as NIR cannot penetrate clouds. RMSE was of $8.644~{}\mathrm{mm}$,
$5.480~{}\mathrm{mm}$ and $3.708~{}\mathrm{mm}$. RMSE was found to increase
under moist conditions. Under clear-sky conditions, $R^{2}$ was of $0.93$ and
$0.95$ for MERIS and MODIS, and $0.80$ for MERSI.

Carbajal Henken et al. (2020) validated the satellite instruments, Infrared
Atmospheric Sounding Interferometer (IASI), MIRS, MODIS, and MODIS-FUB,
against the GNSS network in Germany. The biases were $1.77$, $1.36$, $1.11$,
and $-0.31~{}\mathrm{mm}$, respectively, while RMSE were in the range
2.11–3.77 $\mathrm{mm}$ and correlations 0.88–0.96. Monthly means showed
similar differences, and no impact was found on time-averaging or low temporal
sampling from satellite instruments. Therefore, sampling of IWV seemed to
affect the mean values only marginally, but it could have an effect on
frequency distribution. Nevertheless, in more challenging regions, satellite
estimates of water vapor can improve greatly when averaged in time, as shown
by Alraddawi et al. (2018). In this work, monthly IWV products from GOME-2,
MODIS and SCIAMACHY were compared against GNSS in three Arctic stations (in
the period 2001–2014). The Arctic is known to be a challenging region for
satellite retrieval, as high solar zenith angle, high frequency of cloudy
skies and presence of snow are problematic conditions for retrieval and remote
sensing algorithms. Generally, seasonal biases were less than
$1~{}\mathrm{mm}$ for AIRS, $2.5~{}\mathrm{mm}$ for SCIAMACHY, and
$3.5~{}\mathrm{mm}$ for MODIS. Moreover, the increase in cloud fraction was
related to increasing dry bias. Therefore, authors suggested that more robust
information about clouds must be included in the retrievals to reduce the
aforementioned biases.

The wide variety of satellite products using different instruments and
algorithms, together with different quality criteria and the use of different
regions for testing, makes it very difficult to extract common conclusions to
different works. Even the most used statistical parameters can largely change
with different methodological approaches, especially different quality
controls. For that reason, we conclude that the scientific community should
establish a series of common practices to perform validations in order to make
different works comparable. Moreover, it can be concluded that satellite
measurements can have very good quality if the right conditions are met. There
is a general agreement that cloudy and/or high moisture situations tend to
cause worse values of accuracy and precision metrics (i.e., MBE or SD).

##  4 Spatio-Temporal Analysis

Table 4.1 summarizes some of the findings of each paper from this section.

###  4.1 Asia

China. Jin et al. (2008) investigated the spatial, seasonal and diurnal
distribution of water vapor for three years (2004–2007). The region with the
highest IWV was the South-East, with a strong annual cycle (amplitude of
$\sim$$15~{}\mathrm{mm}$), while the lowest IWV was found in the North-West
region, with a smaller annual cycle (amplitude of $\sim$$4~{}\mathrm{mm}$).
Mean diurnal cycle amplitude was found to be $0.7~{}\mathrm{mm}$. The spatial
distribution was dependent on latitude, topography, season and monsoon. Wu et
al. (2020) studied midsummer diurnal variations over 18 stations around the
Poyang Lake during three year period (2015–2018). Diurnal IWV typically peaks
at 1200–2000 Local Solar Time (LST). Air temperature diurnal cycle was
reported to be likely behind the IWV diurnal cycle. The semi-diurnal cycle was
found to account for about $50\%$ of variance contribution. Tibetan Plateau is
a region of high interest in China, specially because of its role in the
summer monsoon. Takagi et al. (2000) studied the premonsoon and monsoon
diurnal variability at the station of Lhasa in this region. Premonsoon minima
and maxima occurred at 1800 and 0400 LST, respectively, while, in the monsoon
period, these were displaced to 1500 and 2300 LST. This result shows that
water vapor is affected by local circulation. It also indicates the usefulness
of GNSS for studying the IWV daily cycle and recommends the addition of more
stations to the Plateau in order to study moisture transport in the region.

Japan. Iwasaki and Miki (2001) studied the diurnal variability in 5 GNSS
stations and the other three radiosonde stations. The maximum was found around
1800–2000 LST, some hours later than in China. Li et al. (2008) also analyzed
the diurnal variations in central Japan during August 2000, which found the
maximum at the same hours. The moisture transport was found to cause the
differences in phase of the diurnal cycle of IWV among different locations.

Sumatra. Wu et al. (2003) presented the diurnal variation in the island of
Sumatra, and found a distinct diurnal cycle. Torri et al. (2019) used data
from the Sumatran GNSS array to study the diurnal cycle of water vapor. The
Madden–Julian oscillation (MJO) was found to impact on the diurnal cycle,
appearing smaller in both the daily mean and the amplitude of the diurnal
cycle during the suppressed phase relative to the developing/active MJO phase.
The evening/nighttime peaks of IWV offshore appeared later during the
suppressed phase of the MJO compared to its active phase (from 1900 LST in the
active phase to 2200 LST in the suppressed phase).

South Korea. Sohn and Cho (2010) estimated the trend over 5 stations of South
Korea (2000–2009) as $0.11~{}\mathrm{mm}$ year-1. They also calculated
seasonal trends for summer ($0.16~{}\mathrm{mm}$ year-1), winter
($0.04~{}\mathrm{mm}$ year-1), spring ($0.05~{}\mathrm{mm}$ year-1), and
autumn ($-0.14~{}\mathrm{mm}$ year-1).

[H] Summary of spatio-temporal studies. Unless indicated otherwise, times are
given in local solar time and trends in $\mathrm{mm~{}{year}^{-1}}$. Work Year
N Start End Region Type Value (Iwasaki and Miki, 2001) 2001 5 1999-07 1999-08
Japan Diurnal max: 1900 (Dai et al., 2002) 54 1996-01 North America (US)
Diurnal max: 1000–1400 (winter) and midafternoon-midnight (summer)
(Gradinarsky et al., 2002) 2002 17 1993-08 2000-12 Scandinavia (Sweden) Trends
0.15 (Combrink et al., 2007) 2007 2 1998-01 2006-12 Africa (South Africa)
Trends non-significant (Li et al., 2008) 2008 6 2000-08 2000-08 Japan Diurnal
max: 1900, min: noon (Jakobson et al., 2009) 32 1996-01 Baltic (Finland,
Latvia, Sweden) Diurnal - Seasonal (Suparta et al., 2009) 2009 9 2003-01
2005-12 Antarctic Diurnal max: 0600–0900 UTC, min: 1800–2100 UT (Sohn and Cho,
2010) 2010 5 2000-01 2009-12 SouthKorea Trends 0.11 (Ortiz de Galisteo et al.,
2011) 2011 10 2002-01 2011-12 Iberian P. (Spain) Diurnal min: 0430–0530 UTC,
Afternoon Seasonal (Sharifi and Souri, 2015) 2015 4 2009-01 2012-12 Europe
Diurnal - (Alshawaf et al., 2017) 113 1996-01 2015-12 Europe (Germany) Trends
$-$0.15–0.23 Northeast India (India) Seasonal max: summer, min: winter (Barman
et al., 2017) 2017 5 2004-01 2012-12 Northeast India (India) Diurnal max:
1000–1300 UTC Central France (France) Diurnal - (Hadad et al., 2018) 2018 2
2006-01 2018-01 Central France (France) Trends non-significant (Torri et al.,
2019) 24 2005-01 2008-12 Sumatra Diurnal max: 1900 (land); 1300 and 0100
(offshore) Seasonal (Zhao et al., 2019) 2019 192 2004-01 2017-12 Global Trends
- (Bernet et al., 2020) 35 2000-01 2018-12 Europe (Switzerland) Trends
0.001–0.109 (Bousquet et al., 2020) 8 2018-06 2020-03 SW Indian Ocean Diurnal
- Seasonal max: austral summer (Lees et al., 2020) 12 2009-01 2019-12 Indian
Ocean Diurnal max: late afternoon/evening (land); night (ocean); early morning
(coastal), min: morning (land); mid-day (ocean); late afternoon (coastal)
Seasonal max: mid-May–end-October (Trakolkul and Satirapod, 2020) 11 2007-01
2015-12 Thailand Trends - (Wu et al., 2020) 2020 18 2015-01 2018-12 Poyang
Lake (China) Diurnal max: 1600 2

India. Barman et al. (2017) analyzed GNSS IWV from five stations in India
during the period 2004–2012. They found that high altitude sites had weaker
annual variability than low altitude ones. However, seasonal variability was
similar in the five sites. Seasonal IWV was strongly linked to the monsoon,
with maximum in summer and minimum in winter. The diurnal cycle was marked in
high altitude sites, while weak in low altitude ones. Bousquet et al. (2020)
presented a new GNSS network in the Southwest Indian Ocean in the frame of the
Indian Ocean GNSS Application for Meteorology Project, which is being deployed
since November 2017. They analyzed the period from 2018 to 2020 and found that
minimum seasonal values decrease away from the equator. Diurnal cycle was
found to differ at both sides of Madagascar. This study was extended by Lees
et al. (2020), where the seasonal time-scale was studied. The annual amplitude
of IWV was reported to vary in the interval 10–15 $\mathrm{mm}$ near the
equator and in the interval 20–30 $\mathrm{mm}$ in the subtropics. The
strongest daily IWV amplitudes were found in the mountainous islands. The
reanalysis ERA5 was found to reproduce the main features of IWV time series.

Thailand. Trakolkul and Satirapod (2020) studied GNSS IWV series of 11 CORS
stations in Thailand to analyze seasonal features and trends. The annual
variation amplitude was reported to be in the range 6–19 $\mathrm{mm}$.

###  4.2 Europe

General. Sharifi and Souri (2015) used a hybrid approach to time series
modeling of GNSS IWV series over four sites in Europe (years 2009–2012, 5-min
sampling), combining least squares harmonic estimation (for modeling harmonic
characteristics) with least squares support vector machine optimized by cross-
validation strategy (for modeling non-harmonic features). Inter-seasonal
variability was found to be greater than inter-annual variability. Diurnal
cycles were strong in summer with maxima between 1200 and 1800 LST. The peaks
were related to solar flux and the phase to other features, such as location
or wind/temperature patterns.

Northern Europe. Gradinarsky et al. (2002) studied trends of water vapor in
the region of Scandinavia during the years 1993 and 2000. They found that the
GNSS station radome can affect measurements to an extent between $0.0$ and
$1.8~{}\mathrm{mm}$. Trends were positive, 0.1–0.2 $\mathrm{mm~{}year^{-1}}$.
These GNSS-calculated trends were found to be consistent with other
measurements (i.e., radiosondes and MWR), assessing the potential of GNSS IWV
in climate monitoring. Jakobson et al. (2009) analyzed the diurnal variability
of water vapor in 32 sites in the Baltic region, during 1996–2005. Peak to
peak difference was of 0.5–0.6 $\mathrm{mm}$ in spring/summer, while winter
and autumn lacked a clear pattern. The high variability (mainly with synoptic
situation, or substitution of air masses) makes that the diurnal cycle can
only be observed when averaging over many years.

France. Hadad et al. (2018) combined different types of water vapor
measurements to study two sites in France. The work presented a non-
significant trend at the site of Cézeaux of $0.42\pm
0.45~{}\mathrm{mm~{}decade^{-1}}$. Both stations presented almost no diurnal
cycle and the authors concluded that variability of surface water vapor was
influenced by sporadic circulation patterns rather than by regular diurnal
variations.

Switzerland. Bernet et al. (2020) studied trends of water vapor over
Switzerland using different instruments, including 31 GNSS sites in the period
1995 to 2018. Jumps caused by instrumentation changes were corrected. IWV was
found to increase with a rate of $2-5\%~{}\mathrm{decade^{-1}}$. From the
comparison among different instruments, it was concluded that GNSS data are
reliable for the detection of trends, but a few stations need quality control
and harmonization.

Spain. Ortiz de Galisteo et al. (2011) analyzed the diurnal cycle of IWV in 10
GNSS Spanish stations for the years 2002-2011, finding that it explained 3%–7%
of sub-daily annual variability. IWV was found to peak at 0430–0530 UTC, and
the diurnal cycle was found to be more important in the Mediterranean sites
than in the inland or Atlantic ones. The summer diurnal cycle is also more
variable among sites. The first two harmonics (diurnal and semidiurnal cycles)
explained $97\%$ of the variance. Another work analyzed the annual cycle in
the same period and stations (Ortiz de Galisteo et al., 2014), finding that
the 12-month harmonic explained $96\%$ of variance, with a maximum in summer
and minimum in the winter months. Southwestern sites, however, showed a local
minimum in July, which can be explained by the presence of dry air masses. The
Mediterranean sites had larger amplitudes than inland sites. The July local
minimum had been already reported by Torres et al. (2010), who characterized
the IWV in the Gulf of Cadiz region, in southern Iberian Peninsula using GNSS,
radiosondes and a sun-photometer.

Germany. Alshawaf et al. (2017) studied the IWV time series over 113 GNSS
stations in Germany, with 10–19 years of temporal coverage, together with
meteorological data from automatic stations and ERA-Interim reanalysis. GNSS
IWV trend ranged between $-1.5$ and $2.3~{}\mathrm{mm~{}decade^{-1}}$.
However, longer time-series from ERA-Interim ($\sim$$26~{}\mathrm{year}$)
revealed positive trends in all sites, which also had a gradient from
southwest to northeast. Trends obtained from dew-point temperature were
comparable with the other estimates, and therefore can be used when
observations are not available.

###  4.3 Africa

Combrink et al. (2007) studied times-series of GNSS-derived IWV in South
Africa, with the aim of detecting trends in the period. They used the
autoregressive–moving-average (ARMA)(1,1) model, concluding that this model
represents better the real trend, provided that more than five years of data
are used. They also concluded that none of the two stations used had
statistically significant trends.

###  4.4 America

Dai et al. (2002) studied GNSS IWV from 54 stations over North America.
Diurnal variations were significant, explaining over the $50\%$ of the
subdaily variance, specially in summer, with weaker diurnal cycles in the rest
of the seasons. Peaks are found around 1000–1400 LST in winter, and from
midafternoon to to midnight in summer. The semidiurnal cycle is rather weak.

Yu et al. (2017) proposed a model to spatially interpolate GNSS ZTD and used
interpolated values from meteorological stations for pressure and $T_{m}$ in
California. The interpolation method is iterative and tries to decouple
turbulent- and elevation-dependent ZTD components. Validation with MODIS as a
reference yielded RMSE of $1.70~{}\mathrm{mm}$.

Bordi et al. (2014) studied temporal series of six GNSS stations in Eastern
US, where it was found that the variability of IWV is dominated by the annual
cycle, with a missing daily cycle, while RH from weather stations is more
characterized by the daily cycle, without an annual cycle.

###  4.5 Antarctic Region

Suparta et al. (2009) studied the GNSS IWV over 9 sites in Antarctic during
two years (2003–2005). The diurnal variation was remarkable in summer, but not
in winter. IWV was higher in summer than in winter. Moreover, it was found
that the presence of strong winds can cause a decrease in monthly IWV.

###  4.6 Global

Shuanggen Jin and Luo (2009) analyzed 13 years (1995–2007) of data from 155
GNSS stations globally and distributed and studied the seasonal variation of
IWV. Globally, seasonal maxima were found in summer and minima in winter.
Annual cycle amplitude was $10\textendash 20\pm 0.5~{}\mathrm{mm}$ in mid-
latitudes and $5\pm 0.5~{}\mathrm{mm}$ in high latitudes and equatorial areas.
Semiannual variation amplitudes were less important, at about $0.5\pm
0.2~{}\mathrm{mm}$. The diurnal cycle was also studied and it was found to
have an amplitude of $0.2\textendash 1.2\pm 0.1~{}\mathrm{mm}$, and the
maximum and minimum occurred around noon and midnight, respectively. The
semidiurnal cycle was reported to have a weaker amplitude below
$0.3~{}\mathrm{mm}$. Zhao et al. (2019) agreed with this, finding that annual
variability was the more important component in IWV variation. This last work
used 192 IGS stations distributed globally to interpolate and analyze IWV at a
global scale during the period 2004–2017. Despite the different periods with
very few years in common, both works show similar results.

Regarding trends, Chen and Liu (2016) presented a global analysis of the
trends of IWV using different products, including reanalysis ERA-Interim and
NCEP, SSM/I microwave satellite, radiosondes and GNSS. Particularly, 100 GNSS
stations were used in the study, with a time-span of 15 years. The other
products had longer time-series, reaching 36 years of reanalysis and
radiosondes. Therefore, the trends were calculated at different timescales to
allow comparisons. The 15 year period 2000–2014 was concluded to have stronger
upward trends than longer periods. The trends were not homogeneous, being
negative in Asia, the United States or North Africa, while large positive
trends were found in the North and West Pacific, Europe, the eastern Indian
Ocean, and southern Asia. The polar region is the one with a larger increase
in IWV. Another interesting issue discussed in this work is the relationship
between surface temperature and IWV. According to Clausius-Clapeyron equation,
the increase rate of water vapor should be 6%–13%$\mathrm{K^{-1}}$. However,
some regions depart greatly from this range, reaching negative values in this
rate. Such large departures were associated to regional moisture
divergence/convergence. At a global scale, the Clausius-Clapeyron estimate
remains valid. This issue was also studied by Wang et al. (2016), who found
that using night surface temperature had better correlation with IWV, and
therefore it was suggested to use it for studies on water vapor feedback.

##  5 Impact of Water Vapor Variability on Meteorology and Climate

###  5.1 Assimilation

NWP models need to ingest real data in the process known as assimilation to be
able to perform predictions. Therefore, GNSS data can be an interesting source
for NWP assimilation, especially in regions where other sources of atmospheric
water vapor information are missing. Gutman and Benjamin (2001) showed that
GNSS data improved forecasts from NWP models. Particularly they used the Rapid
Update Cycle in the US, and assimilated data from 18 and 55 stations. They
found improvements in relative humidity (RH) of up to $4.5\%$ for the
55-station experiment and up to $1.0\%$ for the 18-station experiment. Despite
being a modest improvement, it must be taken into account that the US had
already good knowledge of the moisture from other kinds of measurements
already assimilated by the model. Therefore, in other regions this could be
enhanced, and even in the US, the improvement was evident, especially in the
3-h forecast. They also developed techniques to retrieve GNSS IWV measurements
every 30 min to be available for forecasters and modelers, improving IGS
service in latency. Other works from the 2000s found moderated improvements in
models as well: Guerova et al. (2004), who assimilated GNSS IWV from COST
Action 716 into the MeteoSwiss NWP model; Yuan et al. (2005), who assimilated
IWV data from 11 GNSS stations in China into the MM5 model; Gendt et al.
(2004), who presented a near real-time GNSS IWV product in the context of the
project GASP and assimilated it into the local model from German Weather
Service; and Zhang et al. (2006), who tested the GNSS assimilation in a severe
weather event in Beijing.

All these works considered the assimilation of the IWV GNSS data. However, it
is possible to use more direct data, such as SWD. Ha et al. (2003) compared
the assimilation of SWD and IWV from the GNSS network and found SWD to be more
appropriate for correctly retrieving temperature and moisture profiles. They
used a hypothetical GNSS network of 64 stations in the US, using the MM5
4-dimensional variational data assimilation system. Liu and Xue (2006) used a
similar approach, but assimilated slant water vapor (SWV) into the
3D-variational (3DVAR). The tests included hypothetical GNSS stations as well
and sensitivity analysis, concluding that GNSS SWV assimilation is positive
even with the inclusion of typical errors in measurements.

The introduction of multi-GNSS processing can improve near real-time
measurements in several ways. First, it can provide more accurate data by
increasing the number of frequencies used, as new GNSS satellites introduce a
third frequency (better combinations of signals). Second, having more
satellites available makes possible to increase temporal resolution (below 30
min) and spatial resolution through networks and tomography techniques.
Karabatić et al. (2011) performed an experiment in Austria with the use of
multi-GNSS (GNSS and GLONASS) network, finding the assimilation of multi-GNSS
data very positive and concluding that Galileo constellation inclusion could
improve analysis even more.

In addition to this, it must be noted that regions lacking dense networks of
ground-based GNSS stations can also benefit from GNSS data assimilation. Kumar
et al. (2017) showed that assimilating GNSS data from a single station was
enough to locally improve ($\sim$$10\%$) the short-term forecasts in an
experiment over southern India during the monsoon. Of course, it will be
better if there is moisture information from more GNSS stations, but regions
lacking moisture information from other sources can benefit from GNSS data
even with a single station in the region of interest. If two-frequency
stations are not available, it may be possible to use single-frequency
receivers for assimilation. This issue is still under study and more research
could be useful, as the use of single-frequency receivers can provide very
dense networks as compared to dual-frequency ones. One experiment was
performed using the Regional Atmospheric Modeling System (RAMS) 3D variational
data assimilation system to assimilate GNSS-ZTD from single-frequency
receivers. It was concluded that, although results are preliminary and some
issues must be addressed, the assimilation was very positive for both ZTD and
IWV fields (Mascitelli et al., 2019).

###  5.2 Circulation

As pointed out in Section 3, water vapor is greatly affected by circulation
patterns, which can transport moisture or dry air to different regions. For
this reason, GNSS can provide information about these circulation patterns in
certain regions. Graham et al. (2012) used GNSS IWV data to show that
important differences in IWV can occur between the Swiss plains and nearby
Alps during some thunderstorms events, attributable to regional airflow
convergence. They presented a method to acquire information about the amount
and change of total IWV over time for the mesoscale in the Bernese Oberland
area using the GNSS IWV data. An anti-correlation pattern was found between
Payerne and Saanen, which suggested a mountain-plain circulation pattern.
Moreover, Kingsmill et al. (2013) and Neiman et al. (2013) used GNSS IWV
products among other remote-sensing information about the state of the
atmosphere to study the northern California Valley, which has sierra barrier
jets and land-falling atmospheric rivers (ARs), modulators of the rainfall in
this region. The study links these two phenomena with the orographic
configuration of the Valley, and the concurrence of both phenomena at the same
time, or just one of them, affects the spatio-temporal rainfall pattern.

GNSS has been used to study water vapor during El Niño events in the coast of
the South China Sea (Suparta, 2018). During these events, IWV drops, reaching
a minimum about 10 weeks later, while the opposite happens during La Niña
events. Therefore, GNSS IWV is suggested to be a useful instrument for
studying ENSO activity.

###  5.3 Radiative Transfer Studies

There has been recent interest in the role of water vapor in radiative
balance, enhanced by the increase in water vapor data availability, with
higher spatial and temporal resolution. Vaquero-Martínez et al. (2018) studied
the short-wave effects of water vapor using 20 GNSS stations in the Iberian
Peninsula as input to Santa Barbara’s dissort radiative transfer model
(SBDART). They found that the effect for cloudless skies followed an empirical
power relation of the short-wave effect with IWV and the cosine of the solar
zenith angle. An extended study (Vaquero-Martínez et al., 2020), including
short- and long-wave in seven selected stations, found that positive trends
for long-wave (and total) water vapor effects could partially explain the
well-known increase of surface air temperatures in the Iberian Peninsula,
while the negative trend in the short-wave effect represented about a quarter
of the contribution of aerosols to the so-called brightening effect.

In a more practical fashion, GNSS data are also used for the modeling of
atmospheric transmission. The PWV_KPNO python package (Perrefort et al., 2019)
uses GNSS IWV data from the SuomiNet network for modeling atmospheric
transmission function due to water vapor. The package interpolates IWV data
from the GNSS stations to the desired position and then applies the MODTRAN
model to obtain the atmospheric transmission.

##  6 Conclusions

GNSS sensing of atmospheric water vapor is already a well established
technique that allows for the monitoring of this trace gas with wide (yet
land-only) coverage, with high temporal resolution and without weather
restrictions. These features make this technique very suitable for testing
other techniques, especially when weather is adverse. In comparison with other
products, GNSS water vapor data are high quality, being considered a reference
for the validation of other ground-based and satellite-based water vapor
measurements and model estimates. However, we consider that special care must
be taken with some issues. First, IWV is dependent on height and therefore
when comparing data related to different heights (i.e., ground-based stations
and different heights, satellite or NWP pixels at a mean height of the area,
different from the real height of the GNSS station) it is important to apply
the corresponding correction to account for this height difference. Second,
the homogeneity of the series must be checked (especially if there are changes
in antenna or processing strategy). Third, it is considered a rule of thumb
that GNSS retrieve water vapor information of about $100~{}\mathrm{km}$
radius, which can be used to set a condition on distance to GNSS station when
performing validations.

Nowadays, time-series of GNSS data products are starting to be long enough to
study water vapor in long term studies, such as its trends and variability
across different time scales. Additionally, the increasing amplitude of the
ground-based GNSS networks allows for a detailed analysis of its spatial
distribution. It is observed that, despite the average behavior based mainly
on temperature (according to the Clausius-Clapeyron equation), local
circulation is more important. Although there are clear cycles in daily and
annual regimes, situations with relevant local circulation can disrupt these.
Therefore, it is fundamental to use long-term data to study daily and annual
cycles, especially in regions where strong circulation patterns can modify air
moisture.

GNSS water vapor has been widely used for several meteorological and climate
applications such as assimilation, circulation of the atmosphere and radiative
effects. It is shown that assimilation can be improved with GNSS data,
especially in regions where there may be a lack of moisture information. It
must be noted that GNSS are relatively cheap and easy to maintain, and provide
continuous measurements for all-weather conditions. This means they can be
used in regions with fewer resources or those where human access is difficult.

Despite being a well established technique, it must be noted that many other
GNSS-based techniques, such as tomography or data fusion approaches, can make
the best out of the information that GNSS meteorology has to offer. The use of
multi-GNSS techniques, especially, have the potential to improve the quality
of these approaches. The use of low-cost devices (i.e., single frequency
receivers) can be interesting in terms of retrieving moisture information
cost-effectively.

In summary, the GNSS technique allows the retrieval of accurate atmospheric
water vapor data. This method exhibits great potential to be extraordinarily
useful in the monitoring of the weather and climate.

Conceptualization, M.A.; Data curation, J.V.-M.; writing—original draft
preparation, J.V.-M.; writing—review and editing, M.A.; supervision, M.A. All
authors have read and agreed to the published version of the manuscript.

This work was partly supported by the Ministerio de Economia y Competitividad
of the Spanish Government (CGL2017-87917-P), and by Junta de Extremadura and
European Regional Development Fund (IB18092). Javier Vaquero-Martinez was
supported by a predoctoral fellowship (PD18029) from Junta de Extremadura and
European Social Fund.

note

note

note

The authors declare no conflict of interest.

AbbreviationsThe following abbreviations are used in this manuscript:
AIRS Atmospheric Infrared sounder AMSU-B Advanced Microwave Sounding Unit APC
Antenna Phase Center AR atmospheric river BALTEX Baltic Sea Experiment BDS
BeiDou Navigation Satellite System (Chinese GNSS) CORS Continuously Operating
Reference Stations COST Cooperation in Science and Technology ECMWF European
Centre for Medium-Range Weather Forecasts FTIR Fourier-transform infrared
spectroscopy FY-3A/MERSI Fengyun-3A Medium resolution spectral imager GASP
Atmosphere Sounding Project GLONASS Globalnaya navigatsionnaya sputnikovaya
sistema (Russian GNSS) GNSS Global Navigation Satellite Systems GOME-2 Global
Ozone Monitoring Experiment 2 GPS Global Positioning System GPT Global
Pressure and Temperature HIRLAM High Resolution Limited Area Model IGS
International GNSS Service InSAR Interferometric synthetic-aperture radar IPWV
Integrated precipitable water vapor ITU-R International Telecommunication
Union - Radiocommunications IWV Integrated water vapor JRA-55 Japanese 55-year
Reanalysis MERIS MEdium Resolution Imaging Spectrometer MERRA-2 Modern-Era
Retrospective analysis for Research and Applications Version 2 MFRSR
Multifilter rotating shadowband radiometer MGEX Multi-GNSS Experiment MJO
Madden–Julian oscillation MM5 Fifth-Generation Penn State/NCAR Mesoscale Model
NWP Numerical weather models OMI Ozone Monitoring Instrument POLDER
POLarization and Directionality of the Earth’s Reflectances PW Precipitable
water PWV Precipitable water vapor RAMS Regional Atmospheric Modeling System
RH Relative humidity RMSE Root mean square error SBDART Santa Barbara’s
dissort radiative transfer model SCIAMACHY SCanning Imaging Absorption
SpectroMeter for Atmospheric CHartographY SD Standard deviation SEVIRI
Spinning Enhanced Visible and Infrared Imager SSM/I Special Sensor
Microwave/Imager SSMI/S Special Sensor Microwave Imager / Sounder STD Slant
tropospheric delay SWD Slant wet delay Tm Weighted mean temperature of the
atmosphere Ts Surface temperature VMF1 Vienna Mapping Functions 1 WVR Water
vapor radiometer ZHD Zenith hydrostatic delay ZTD Zenith tropospheric delay
ZWD Zenith wet delay References

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