AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-10-2183-2017Inter-technique validation of tropospheric slant total delaysKačmaříkMichalmichal.kacmarik@vsb.czDoušaJanhttps://orcid.org/0000-0002-6668-6207DickGalinaZusFlorianBrenotHugueshttps://orcid.org/0000-0002-5812-0377MöllerGregorhttps://orcid.org/0000-0002-6153-3084PottiauxErichttps://orcid.org/0000-0002-7347-7702KapłonJanhttps://orcid.org/0000-0002-0068-0865HordyniecPawełVáclavovicPavelMorelLaurentInstitute of Geoinformatics, VŠB – Technical University of Ostrava,
Ostrava, Czech RepublicGeodetic Observatory Pecný, Research Institute of Geodesy,
Topography and Cartography, Zdiby, Czech RepublicGFZ German Research Centre for Geosciences, Potsdam, GermanyAtmospheric Composition Department, Royal Belgian Institute for Space Aeronomy, Brussels, BelgiumDepartment of Geodesy and Geoinformation, Vienna University of
Technology, Vienna, AustriaRoyal Observatory of Belgium, Brussels, BelgiumInstitute of Geodesy and Geoinformatics, Wrocław University of
Environmental and Life Sciences, Wrocław, PolandGeF Laboratory, ESGT – CNAM, Le Mans, FranceMichal Kačmařík (michal.kacmarik@vsb.cz)12June2017106218322089November20165January201713April20173May2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/10/2183/2017/amt-10-2183-2017.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/10/2183/2017/amt-10-2183-2017.pdf
An extensive validation of line-of-sight tropospheric slant total
delays (STD) from Global Navigation Satellite Systems (GNSS), ray tracing in
numerical weather prediction model (NWM) fields
and microwave water vapour radiometer (WVR) is presented. Ten GNSS reference
stations, including collocated sites, and almost 2 months of data from 2013,
including severe weather events were used for comparison. Seven institutions
delivered their STDs based on GNSS observations processed using 5 software
programs and 11 strategies enabling to compare rather different solutions and
to assess the impact of several aspects of the processing strategy. STDs from
NWM ray tracing came from three institutions using three different NWMs and
ray-tracing software. Inter-techniques evaluations demonstrated a good mutual
agreement of various GNSS STD solutions compared to NWM and WVR STDs. The
mean bias among GNSS solutions not considering post-fit residuals in STDs was
-0.6 mm for STDs scaled in the zenith direction and the mean standard
deviation was 3.7 mm. Standard deviations of comparisons between GNSS and
NWM ray-tracing solutions were typically 10 mm ± 2 mm (scaled in the
zenith direction), depending on the NWM model and the GNSS station. Comparing
GNSS versus WVR STDs reached standard deviations of 12 mm ± 2 mm also
scaled in the zenith direction. Impacts of raw GNSS post-fit residuals and
cleaned residuals on optimal reconstructing of GNSS STDs were evaluated at
inter-technique comparison and for GNSS at collocated sites. The use of raw
post-fit residuals is not generally recommended as they might contain strong
systematic effects, as demonstrated in the case of station LDB0. Simplified
STDs reconstructed only from estimated GNSS tropospheric parameters, i.e.
without applying post-fit residuals, performed the best in all the
comparisons; however, it obviously missed part of tropospheric signals due to
non-linear temporal and spatial variations in the troposphere. Although the
post-fit residuals cleaned of visible systematic errors generally showed a
slightly worse performance, they contained significant tropospheric signal on
top of the simplified model. They are thus recommended for the reconstruction
of STDs, particularly during high variability in the troposphere. Cleaned
residuals also showed a stable performance during ordinary days while
containing promising information about the troposphere at low-elevation
angles.
Introduction
Tropospheric slant total delay (STD) represents the total delay that
undergoes the GNSS radio signal due to the neutral atmosphere along the path
from a satellite to a ground receiver antenna. This total delay can be
separated into the hydrostatic part, caused by the dry atmospheric
constituents, and the wet part caused specifically by water vapour. By
quantifying the total delay, and by separating the hydrostatic and wet
parts, it is possible to retrieve the amount of water vapour in the
atmosphere along the path followed by the GNSS signal.
During the processing of GNSS observations only the total delay in the
zenith direction (zenith total delay, ZTD) above the GNSS antenna can be
estimated for each epoch or for a time interval. ZTDs from GNSS reference
stations are operationally assimilated into numerical weather prediction models (NWMs)
for almost a decade (Bennitt and Jupp, 2012; Mahfouf et al., 2015). In
Europe, this activity is coordinated mainly in the framework of the EUMETNET
EIG GNSS Water Vapour Programme (E-GVAP, 2005–2017, phases I–III, http://egvap.dmi.dk).
Many recent studies demonstrated a positive impact
of the ZTD or integrated water vapour (IWV) assimilation on precipitation
weather forecasts, especially of the short-time ones (Vedel and Huang, 2004;
Guerova et al., 2006; Shoji et al., 2009; Guerova et al., 2016). In contrast, continuous developments in NWM forecasting and nowcasting tools,
as well as increasing needs for better predictions of severe weather events,
stress the demand of high-quality humidity observations with high spatial
and high temporal resolutions. While ZTDs provide information in zenith
directions above GNSS stations, linear horizontal tropospheric gradients
give information about the first-order spatial asymmetry around the station.
Besides, slant tropospheric delays (STDs) can provide additional details
about the horizontal asymmetry in the troposphere, more specifically in the
directions from a receiver to all observed GNSS satellites. With the
increasing number of GNSS systems and satellites, the atmosphere scanning
will be more complete, hence gaining even more interest. Bauer et al. (2011)
showed a positive impact of STD assimilation into the Mesoscale Model 5
(MM5) and Kawabata et al. (2013) demonstrated a significant advantage of
assimilating STDs into a high-resolution model in the case of forecasting local
heavy rainfall event against the scenario of assimilating ZTDs only. Also,
Shoji et al. (2014) and Brenot et al. (2013) showed promising techniques for
prediction of severe weather events using advanced GNSS tropospheric
products such as horizontal gradients and STDs. The GNSS tomography
technique aiming at the three-dimensional reconstruction of the water vapour
field (Flores et al., 2001) uses STDs as input data as well. Obviously, the
quality of the tomography depends on both the accuracy of the STDs (Bender
et al., 2009) and the observation geometry (Bender et al., 2011).
Validation of GNSS slant delays with independent measurements is not a new
research topic. GNSS slant delays were validated against water
vapour radiometer (WVR) measurements in
Braun et al. (2001, 2002) and Gradinarsky (2002). First
attempts to derive slant delays from NWM fields and to compare them with
GNSS STDs were carried out by De Haan et al. (2002) and Ha et al. (2002).
Additional effort to evaluate GNSS slant delays using WVR and NWM data
was done at GFZ Potsdam over the last few years. Bender et al. (2008) showed an
existing high correlation within the three sources (GPS, WVR, NWM) of slant
wet delays (SWDs) and tried to quantify the effect of removing multipath from GPS
post-fit residuals using a stacking method what was also done by
Kačmařík et al. (2012). Deng et al. (2011) validated
tropospheric slant path delays derived from single- and dual-frequency GPS
receivers with NWM and WVR data. Shangguan et al. (2015) compared GPS
versus WVR slant IWV values (SIWVs) using a 184-day dataset. They also
analysed the influence of the elevation angle setting and the meteorological
parameters (used for the conversion to IWV) on the comparison results. More
recently, a validation of multi-GNSS slant total delays retrieved in
real time from GPS, GLONASS, Galileo and BeiDou was presented
by Li et al. (2015a) using WVR and NWM as independent techniques for the
assessment. Using multiple GNSS constellations brought a visible advantage, in terms of not only the number of
available slants but also their higher
accuracy and robustness.
Nevertheless, most of the studies presented thus far were limited to only a
single strategy for obtaining GNSS STDs and usually restricted to a limited
set of stations and/or a relatively short time period. The main purpose of
this study is an extensive comparison of various solutions from GNSS
processing, NWM ray tracing and WVR measurements using one common dataset as well as a comparison of results from collocated stations. The GNSS solutions
evaluated in this work used 5 different software programs and 11 strategies
and exploited the GNSS4SWEC benchmark dataset (Douša et al., 2016).
Then, the paper studies the impact of various approaches on STD estimates
and aims to find the most suitable strategy for estimating the GNSS-based
STDs.
Section 2 briefly introduces the validation study dataset, and Sect. 3
describes the process of retrieving GNSS STDs including an overview of the
different GNSS solutions. Section 4 provides a description of STDs generated
from NWMs, and Sect. 5 summarizes WVR principals and WVR-based STD
solutions. Section 6 introduces the methodology used in the validation of
STDs, and Sects. 7 and 8 study the results achieved at single GNSS
reference stations and at closely collocated stations, respectively.
Experiment description
The presented work has been carried out in the context of the EU COST Action
ES1206 “Advanced Global Navigation Satellite Systems tropospheric products
for monitoring severe weather events and climate” (GNSS4SWEC; http://www.cost.eu/COST_Actions/essem/ES1206, 2013–2017).
Three mutually cooperating working groups (WG) have been established to
cover the proposed topics: (1) WG1 for Advanced GNSS processing techniques,
(2) WG2 for
GNSS for severe weather monitoring, and (3) WG2 for GNSS for climate
monitoring. Validation of STDs belongs mainly under WG1, which is oriented toward the development of new advanced tropospheric
products, among other topics. The idea of preparing a common benchmark dataset, which could
serve efficiently for most planned activities, was designed in the beginning
of the project; the data were collected, cleaned and documented, and reference
products were generated and assessed (Douša et al., 2016). The selected
geographical area is situated in central Europe (Austria, Germany, the Czech
Republic, Poland) where severe weather events, including extensive floods on
Danube, Moldau and Elbe rivers, occurred between May and June 2013. The
benchmark dataset gathers observations from 430 GNSS reference stations, 610 meteorological
synoptic stations, 21 radiosonde launching sites, 2 WVR, 2 meteorological radars and output fields from
the ALADIN-CZ NWM over a period of 56
days. ZTDs and horizontal tropospheric gradients from the reference GNSS and
NWM-derived tropospheric products were already evaluated, and all resulted
in very good agreement (Douša et al., 2016). All STDs used in this
paper were computed by exploiting the benchmark dataset.
From the complete benchmark dataset, we selected a subset of 10 GNSS
reference stations situated at six different locations
(Table 1). The selection was based on the following
requirements: (1) long-term quality of observations and its stability, (2) availability
of another GNSS reference station in the site vicinity, (3) availability of
another instrument capable of STD measurements in the site
vicinity and (4) the location of the station with respect to its altitude and the
weather events which occurred during the evaluation period. The subset also
includes collocated (dual) GNSS stations that played an important role in the
validation. The collocated stations observed GNSS satellites with the same
azimuth and elevation angles, so that they should theoretically deliver the
same or very similar tropospheric parameters – ZTD, linear horizontal
gradients and slant delays. Post-fit residuals of carrier-phase observations
at the collocated stations should represent common effects due to the local
tropospheric anisotropy, while systematic differences could remain due to
instrumentation and environmental effects such as antenna and receiver
characteristics and multipath. Only STDs from the WVR at Potsdam,
collocated with the GNSS stations POTM and POTS, were available for this
study because the second WVR, located at Lindenberg and collocated with the
GNSS stations LDB0 and LDB2, was operated only in the zenith direction
during the period of the study.
The STD cannot be estimated directly from
GNSS data since the total number of unknown parameters in the solution would
be higher than the number of observations. Instead, the total delays in the
zenith direction above the GNSS station (i.e. ZTD) are adjusted together
with, optionally, total tropospheric linear horizontal gradients (G) to
account for the first-order asymmetry of the local troposphere. The
estimates are valid for individual processing epochs whenever using a
stochastic approach or for a given time interval when modelling the
troposphere with a deterministic process, e.g. by a piece-wise constant or
linear model.
In practice, the ZTD is decomposed into an a priori model, usually by
introducing the zenith hydrostatic delay (ZHD; see Saastamoinen, 1972), and
the estimated corrections, representing (mainly) the zenith wet delay (ZWD).
Similarly, the STD is decomposed to the ZHD, ZWD, G and post-fit residuals (RES) as
described in Eq. (1), where ele is the elevation angle and azi is the azimuth
angle in degrees. The STD value is given in metres.
STDele,azi=ZHD⋅mfhele+ZWD⋅mfwele+Gele,azi+RES
The elevation angle dependency of STD is described by the mapping functions,
separately for the hydrostatic (mfh) and the wet (mfw) components.
Nowadays, the Vienna Mapping Function (VMF1; see Böhm et al., 2006a) –
or VMF1-like concept – is commonly used in GNSS data processing. Also, the
empirical mapping function Global Mapping Function (GMF; see Böhm et
al., 2006b) is popular since it is consistent with VMF1 and easier to
implement (independent on external data needing updates). Both the VMF1 and
the GMF are applicable down to 3∘-elevation angles.
The first-order horizontally asymmetric delay G(ele, azi) in Eq. (1)
reflects local changes in temperature and particularly in water vapour.
MacMillan (1995) proposed a model describing the gradient delay as a function
of the elevation and azimuth angles:
Gele,azi=mfg⋅GN⋅cosazi+GE⋅sinazi,
where mfgele=mfhele⋅cotele.
Chen and Herring (1997) replaced the elevation-dependent term mfhele⋅cotele by
the gradient mapping function mfgele=1/(sinele⋅tanele+C), with C=0.0032, nowadays
commonly used in GNSS data processing. Typical range for GN and
GE is below 1–2 mm, but gradients can reach up to 7 mm during
extreme weather events. The gradient of 1 mm corresponds to about 55 mm
slant delay correction when projected to 7∘-elevation angle.
Additionally, post-fit residuals RES may contain un-modelled tropospheric
effects not covered by the estimated tropospheric parameters. Such remaining
effects are supposed to be caused mainly by higher spatial and temporal
variations of the humidity or its significant horizontal asymmetry in the
troposphere. Obviously, residuals contain also other un-modelled effects such
as multipath, errors in antenna-phase centre variations or satellite clocks.
For eliminating such systematic effects, cleaning of post-fit residuals is
applied by generating elevation- and azimuth-dependent correction maps as
described by Shoji et al. (2004). For each solution and each station, we thus
computed mean values of post-fit residuals in 1 × 1∘ bins
using the whole benchmark period. Residuals exceeding ±3 times the
standard deviation were excluded from the computation of the mean. Computed
means were then subtracted from the original post-fit residuals to generate
solutions using cleaned residuals.
For the analysis of GNSS L1 and L2 carrier-phase observations, the
least-squares adjustment or Kalman-filter approach was applied to estimate
the ZWDs and the two horizontal gradient components GN and GE at
each GNSS site (Table 1). Afterwards, Eq. (1) was used to compute STDs for
each satellite in view. Whenever zero-differenced (ZD) post-fit residuals
were available for any solution, three variants of the solution are
presented in the paper: (1) solution without residuals (nonRES), (2) solution
with raw residuals (rawRES) and (3) solution with cleaned residuals
(clnRES). Seven institutions delivered their STD solutions for this
validation study, namely École Supérieure des Géomètres et
Topographes (ESGT CNAM), Geodetic Observatory Pecný (GOP, RIGTC),
Helmholtz Centre Potsdam – German Research Centre for Geosciences (GFZ),
Royal Observatory of Belgium (ROB), VŠB – Technical University of Ostrava (TUO),
Vienna University of Technology (TUW) and Wrocław University of
Environmental and Life Sciences (WUELS). Principal information about
individual solutions is given in Table 2 with a few specific notes
important for the interpretation of the results.
Information about individual GNSS-based STD solutions used
in the validation.
GOP delivered two solutions based on the Precise Point Positioning (PPP)
technique (Zumberge et al., 1997) and using the in-house developed
application Tefnut (Douša and Václavovic, 2014) derived from the
G-Nut core library (Václavovic et al., 2013). Considering all available
GNSS solutions, only GOP used a stochastic modelling approach to estimate
all parameters. Additionally, GOP provided two solutions: (1) GOP_F using
Kalman filter (forward filter only), i.e. capable
of providing ZTD, tropospheric gradients and STDs in real time; and (2) GOP_S
applying the backward smoothing algorithm
(Václavovic and Douša, 2015) on top of the Kalman filter in order to
improve the quality of all estimated parameters during the batch-processing
interval and to avoid effects such as the PPP convergence or
re-convergence.
Some institutions also delivered two STD solutions which differ in a single
processing setting. The aim was to evaluate their impact on STDs: (a) TUO_G
and TUO_R exploit GPS-only and
GPS + GLONASS observations, respectively; (b) TUW_3 and
TUW_7 apply an elevation cut-off angle of 3 and 7∘
respectively; and (c) ROB_G and ROB_V use the
GMF and VMF1 mapping functions, respectively. Additionally, ROB solutions are
the only ones based on the processing of double-difference (DD) observations
and providing ZD carrier-phase post-fit residuals converted from the
original DD residuals using the technique described in Alber et al. (2000).
For other DD solutions, variants without adding residuals were compared
only.
In total, we validated 11 solutions computed with five different GNSS
processing software. Five of the solutions used GPS and GLONASS observations
and six solutions used GPS-only observations; five of them are based on
DD observations and six of them are computed using
zero-difference data in PPP analysis. More information about TUW solutions
can be found in Möller et al. (2016), about GFZ in Bender et al. (2009,
2011) and Deng et al. (2011) and about CNAM in Morel et al. (2014). For ROB,
TUO and WUE solutions we refer the reader to Dach et al. (2015).
Computation of slant total delay from numerical weather prediction
model
Simulating STDs in NWMs consists in integrating the atmospheric
refractivity through the path followed by GNSS signals. STDs have been
simulated using three different NWMs: ALADIN-CZ (4.7 km resolution
limited-area hydrostatic model, operational analysis in 6h interval with
forecasts for 0, 1, 2, 3, 5, 6 h; http://www.umr-cnrm.fr/aladin/), ERA-Interim (1∘ horizontal
resolution, 6 h reanalysis) and NCEP-GFS (1∘ horizontal
resolution, 6 h operational analysis; https://www.ncdc.noaa.gov/data-access/model-data/model-datasets/global-forcast-system-gfs).
None of these NWMs assimilate data from ground GNSS stations. For more
information about the models, see Douša et al. (2016) and specifically
Trojáková (2016) for ALADIN-CZ model and Dee et al. (2011) for
ERA-Interim. First, STD solutions using the ERA-Interim and NCEP-GFS models
were delivered by GFZ Potsdam using the acronym ERA/GFZ and GFS/GFZ,
respectively. Only a short introduction is provided in Sect. 4.1 since the GFZ tool for ray tracing has been
described in the papers cited below. Two STD solutions were then delivered
for the ALADIN-CZ model: (a) the ALA/BIRA, which was generated at the Royal
Belgian Institute for Space Aeronomy (BIRA), described in Sect. 4.2; and (b) the ALA/WUELS, which was provided
by the
Wrocław University of Environmental and Life Sciences, described in Sect. 4.3.
Description of ERA-Interim STD solution (ERA/GFZ) and NCEP-GPS STD solution
(GFS/GFZ)
The ERA-Interim and NCEP-GFS STD solutions by GFZ are based on “assembled”
STDs. At first, for the considered station and epoch, a set of ray-traced
STDs (various elevation and azimuth angles) is computed using technique
described in Zus et al. (2014). Secondly, from this set of ray-traced STDs,
the tropospheric parameters (i.e. zenith delays, mapping function
coefficients, first- and higher-order gradient components) are determined.
Finally, for the required azimuth and elevation angle the STD is “assembled”
using the tropospheric parameters. For a detailed description of the
tropospheric parameter determination the reader is referred to Douša et al. (2016). The
differences between the “assembled” and ray-traced STDs are
sufficiently small in particular for elevation angles above 10∘
(Zus et al., 2016). In essence, the largest uncertainty in the “assembled”
(and ray-traced) STDs remains the uncertainty of the underlying NWM
refractivity field. This uncertainty is estimated to be about 8–10 mm close
to the zenith, increasing to about 8–10 cm at an elevation angle of 5∘
(Zus et al., 2012). Similar uncertainty of around 8 mm for the
zenith direction was also found for ALADIN-CZ model in Douša et al. (2016).
Description of ALADIN-CZ STD solution from BIRA (ALA/BIRA)
To compute STDs from ALADIN-CZ, a simplified strategy has been used to model
the curve path followed by GNSS signals through the neutral atmosphere, as
suggested by Saastamoinen (1972). The delays simulated with this strategy
show small differences in comparison to straight-line simulations
(differences of about 4, 5 and 10 mm, respectively, at 15,
10 and 5∘ elevation). Simulations have computed STDs
down to 3∘ elevation; however, under an elevation of
15∘ a proper ray-tracing strategy, as mentioned in Sect. 4.1,
should be applied.
For each latitude–longitude grid point and each level of ALADIN-CZ model,
the NWM outputs considered to compute STDs are geopotential height
(geopotH in m), pressure (P in Pa), temperature (T in K), partial pressure of water
vapour (e in Pa) and mixing ratio of liquid and solid water (in kg kg-1). The
ground pressure of each column is also retrieved. The geopotential height is
converted to the altitude above the geoid:
hgeoid=(g0⋅Re⋅geopotH)/(gcR˙e-g0⋅geopotH),
where g0 is a standard gravity acceleration (mean value of
9.80665 m s-2 from the
World Meteorological Organization, WMO); Re= 6378137/(1.006803 - 0.006706 × sin2 (lat)) is the
radius of the ellipsoid in metres for the latitude (lat in degrees); g is
the gravity acceleration (in m s-2) of the considered location given
as
g=9.7803267714⋅(1.+0.00193185138639⋅sin2(lat))/1.-0.00669437999013⋅sin2(lat).
Then, the height above the geoid is converted to height above the WGS84
ellipsoid (in m) with the use of the EGM96 (Earth Gravitational Model;
Lemoine et al., 1998) undulation. Note that for the region of the benchmark
campaign the difference between geoid and WGS84 altitude is about 47 m.
Using the hypsometric equation, the ground pressure and the pressure of each
level are considered to estimate the altitude for the different levels. In
total ALADIN-CZ outputs provide 87 levels up to an altitude of about 55 km.
However, to assess STDs from ALADIN-CZ, the integration was stopped at 15 km
since the contribution of water vapour above this altitude is negligible. An
adaptive step is considered (100, 200, 250, 500, 1000 m,
respectively, for vertical altitudes between 0 and 1, 1 and 3, 3 and 5, 5 and 10, and
10 and 15 km). Bi-linear interpolations of ALADIN-CZ parameters at the altitude
of the GNSS station and for each step of the integration were proceeded.
Note that there is no station selected for the validation located below the
first layer of ALADIN-CZ.
The expression of simulated STDs from ALADIN-CZ is the summation of these
four contributions:
STD=SHDint+SWDint+SHMDint+STDext,
where SHDint, SWDint and SHMDint are, respectively, the inside-model
integration contribution of the hydrostatic, wet and hydrometeor delays, and
STDext is the external model contribution (over 15 km).
SHDint=10-6∑k=1k=ktopk1PiTviΔsi,SWDint=10-6∑k=1k=ktopk′2eiTi+k3eiTi2Δsi,
with k2′=k2-k1⋅Rd/Rw, where k1 (in
K Pa-1), k2 (in K Pa-1) and k3 (in K2 Pa-1) are the empirical refractivity
coefficients of Bevis et al. (1994); Rd and Rw the gas
constants,
respectively, for dry air and water vapour (in J kmol-1 K-1); and Tv is the
virtual temperature (in K). For the estimation of the hydrometeor
contribution inside the model, as presented in Eq. (8), (Nlw,Mlw) and
(Nice,Mice) are atmospheric refractivity and mass content per unit of
air volume of the liquid and ice water, respectively.
SHMDint=10-6∑k=1k=ktopNlw+NiceΔsi=∑k=1k=ktopαlwMlw+αiceMiceΔsi
The estimation of coefficients αlw∼1.45 and αice∼0.69 is presented in Brenot (2006). The ALADIN-CZ model provides mixing
ratios of cloud water (liquid components) and pristine ice (solid water
components). The mass content per unit of air volume is obtained using the
associated mixing ratio, pressure, water vapour partial pressure and
temperature.
STDext is obtained with the hydrostatic formulation (Saastamoinen, 1972)
mapped with mfh (see Eq. 1) and using the elevation, latitude and
pressure of the last step of the integration (i.e. at 15 km). Note that the
wet contribution over 15 km is neglected since it is practically zero. The
estimation of STDext (about 0.21 m) provides sufficiently accurate
modelling for the hydrostatic contribution over 15 km (as shown by the
sensitivity test from Brenot, 2006).
Description of ALADIN-CZ solution from WUELS (ALA/WUELS)
The ray-traced tropospheric delays for WUELS' solution are based on
piece-wise bent-2-D model propagation. Thus, it prevents us from knowing the exact
trajectory in advance, in contrast to straight-line models, and must be
solved iteratively based on the preceding ray refractive index. Similar examples
are given by Böhm and Schuh (2003) and Hobiger et al. (2008). We assume
the ray path does not leave the plane of constant azimuth for a given
elevation angle to a satellite. The out-of-plane contribution to the delay
is thus neglected, making the propagation two-dimensional (hence 2-D). The real
ray path is then approximated by a finite number of linear ray pieces in
WGS84 coordinates using Euler's formula for the Earth radius:
R=(cos2A/M+sin2A/N)-1,
where A is the azimuth angle between a satellite and a receiver, and M and N are
radii of curvature along meridian and prime vertical, respectively. We
follow height-dependent increments as presented in Rocken et al. (2001): 10, 20,
50, 100 and 500 m, respectively, for geometric altitudes between 0 and 2, 2 and 6, 6 and
16, and
16 and 36 km and above 36 km, which require meteorological
parameters to be vertically interpolated in order to obtain finer
resolution. Both P and e are interpolated exponentially from the two nearest
layers, while the temperature change is considered linear. Horizontally, we
find the four nearest nodes for each ray to perform weighted mean
interpolation, where the weighting function equals the inverse squared
distance. The reference hybrid level of the ALADIN-CZ model is determined by
surface geopotential, which is converted to geopotential metres by dividing
the geopotential values by g0. Meteorological parameters are expressed
on pressure levels which represent standard vertical coordinates. The
hypsometric equation is used to calculate geometric thickness between
consecutive isobaric surfaces:
dz=Rd⋅Tm/g0⋅ln(P1/P2),
where Rd= 287.058 JK-1 kg-1 is the gas constant for dry air, and Tm is the
mean virtual temperature of the layer between P1 and P2 pressure
levels in Kelvin. The conversion from ALADIN-CZ vertical coordinate system
to geometric altitudes is then consistent with the BIRA approach described
in Sect. 4.2. In WUELS' solution, the signal
tracking is performed exploiting a full model vertical resolution up to the
uppermost ALADIN-CZ layer at 55 km. Above the top layer, we adopt the US
Standard Atmosphere (1976) to provide supplementary meteorological data up
to 86 km. For each ray-path coordinate, the refractive index is calculated
as a function of P (in hPa), e (in hPa) and T (in K) with empirically derived “best available”
coefficients k given by Rueger (2002).
N=(n-1)×106=k1⋅(P-e)/T+k2⋅e/T+k3⋅e/T2
The contribution of water droplets and ice crystals in the atmosphere is
neglected in the total delay. All tropospheric delays are traced with
respect to vacuum elevation angles. The electromagnetic delay is calculated
for a given chord length (s) using the mean refractive index n between two
consecutive rays, yielding the total delay in metres:
STD=∑si(ni-1)×106,
which can be separated on hydrostatic and wet part using respective
refractive indices. Additionally to the radio path length, the accumulated
bending effect (bend) along the ray path is added to the hydrostatic mapping
function which, together with the wet mapping function, can be calculated as
follows:
bend=∑(si-cos(elei-elek)si),mfh=(SHD+bend)/ZHD,mfw=SWD/ZWD,
where elei is the elevation angle for a given model layer and elek is
the outgoing elevation angle at uppermost altitude.
Assessment of the hydrostatic, wet and hydrometeor contributions to the
slant delays
ALADIN-CZ NWM has been used to estimate the hydrostatic, wet and hydrometeor
contributions to slant delays. During the whole period of the benchmark
campaign, the maximum contribution of hydrometeors reached 17 mm at the
zenith during the extreme weather events on 20–23 June (Douša et al.,
2016). The 2-D fields of ZTD, ZHD, ZWD and ZHMD (zenith hydrometeor delays)
are presented in Fig. 1. They illustrate the
large-scale convection with the presence of hydrometeors along the
convergence line associated with a strong contrast of dry and wet air
masses. The contribution of hydrometeors to ZTD reached up to 7 mm (as
scaled in the zenith direction) for the stations POTS and POTM at 15:00 UTC
on 23 June 2013 (see Fig. 1d). According to
satellite trajectories at this time for the station POTS, a maximum SHMD of
25.6 mm is observed for a satellite at 22∘-elevation angle.
Simulation of ZTD, ZHD, ZWD and ZHMD at 15:00 UTC on 23 June 2013.
Each black dot represents a GNSS station included in the benchmark dataset.
For stations included in this STD validation study their names are given.
Figure 2 shows simulated differential STDs for a
cone with a 10∘-elevation angle during the severe weather
condition of the 23 June 2013 and mapped in the zenith direction
(at 90∘) using the mapping functions of Eq. (1): mfh for SHD
and mfw for SWD and SHMD. For this 10∘ cone, the minimum
present values of total, hydrostatic, wet and hydrometeors delays simulated
at 15:00 UTC on 23 June are given as STDmin, SHDmin, SWDmin and SHMDmin in
Fig. 2. The respective differences of STD, SHD,
SWD and SHMD and corresponding minimum values simulated at 15:00 UTC are
presented in Fig. 2. The anisotropic variation of
total, hydrostatic, wet and hydrometeor delays can be visualized on a
skyplot. As a confirmation of Figs. 1b and 1d,
2 shows weak hydrostatic anisotropy. This
anisotropy (up to 5.8 mm) is almost the same as the hydrometeors one (up to
6 mm). The area within the red curve is larger than the purple area
(hydrostatic anisotropy), meaning that the total effect of the hydrometeor
anisotropy is slightly larger than the one from the hydrostatic component.
Note that Fig. 2 shows the anisotropies simulated
at 10∘ and mapped at 90∘ (giving an idea of the
variations in the zenith direction). The largest anisotropy is clearly
induced by water vapour (values up to 20 mm in the south-east direction of
POTS, also shown in Fig. 1c). With mean
hydrostatic and hydrometeor anisotropies oriented in the opposite direction
of the wet one, Fig. 2 presents a total
anisotropy with weaker values (up to 12 mm) than the wet anisotropy.
Skyplot of differential slant delays simulated at 10∘
and mapped at 90∘, for a 360∘ azimuthal range (at 15:00 UTC
on 23 June 2013). For total, hydrostatic, wet and hydrometeors delays, a
differential slant delay is the difference between a slant delay simulated
and the respective minimum value (obtained considering slant delays
simulated at 10∘ elevation along all the azimuthal directions).
To complement the snapshot of Fig. 2 the
time evolutions of SHD, SWD, SHMD and STD in the direction of all observed
GNSS satellites for the station POTS are presented in
Fig. 3. Slant delays have been simulated in the
direction of observed satellites (hydrostatic, wet, hydrometeor and total
contributions) and, to avoid the effect of the elevation and to look at the
same order of magnitude of delays, corresponding delays in the zenith
direction have been computed and mapped using mapping functions presented in
Eq. (1) (mfh for SHD and mfw for SWD and SHMD). These values
(STDmin= 2310.6 mm, SHDmin= 2240.8 mm, SWDmin= 43.1 mm
and SHMDmin= 0 mm), obtained during the whole period of the
benchmark campaign, have been subtracted from their corresponding values
simulated in direction of satellites. Then, the differences have been mapped
back at 90∘. For day of year (DOY) 174 (i.e. 23 June 2013), we can see
a contribution of hydrometeors up to 10 mm. Looking at the
whole period of the benchmark campaign, the variation ranges of STD, SHD and
SWD (mapped at 90∘) are 275, 80 and 230 mm, respectively.
Figure 3 illustrates the use of GNSS delay
observations in meteorology (detection of variation of water vapour
represented by the wet delay, as well as detection of heterogeneities from
hydrostatic delays and occasionally from hydrometeors in specific severe
weather cases). Note that there are no data available for POTS station
between DOY 121 and 125 and DOY 160 and 163. For this reason, we have not
simulated the slant delays for this period, as shown by the gaps in
Fig. 3. The simplified strategy used to simulate
curve slant paths gives some inaccurate simulations of slant delays for
elevations between 3 and 5∘, shown by isolated values
in Fig. 3. Such inaccuracies could be avoided by
using a ray-tracing algorithm. For a comprehensive overview on ray-tracing
algorithms and comparisons the reader is referred to Nafisi et al. (2012).
Time series of slant delays (STD, SHD, SWD and SHMD) differences
(in direction of all GNSS visible satellites, then mapped in the zenith
direction) during the whole period of the benchmark campaign for the station
POTS.
Water vapour radiometer measurements
During the benchmark period, the WVR located at GFZ Potsdam operated in a
mode that scanned the atmosphere at selected elevation and azimuth angles. The
instrument is situated on the same roof as the GNSS reference stations POTM
and POTS. All three devices are within 10 m from each other. The
HATPRO WVR from Radiometer Physics was set up to scan the atmosphere to
extract profiles of atmospheric temperature, water vapour and liquid water
using frequencies between 22.24 and 27.84 GHz and a window channel at 31.4 GHz.
The WVR switches between “zenith mode” when it measures
IWV and “slant mode” when it tracks GPS
satellites using an in-built GPS receiver. In the latter case, SIWV values are delivered for the direction of
satellites. Since the instrument can track only one satellite at one moment
the number of observations is quite limited compared to slants from GNSS
that are simultaneously observed from several GNSS satellites.
Our study focuses on the comparison of STDs, not SIWV. It was thus necessary
to convert the WVR SIWV into STDs. Firstly, WVR observations with rain flag
and atmospheric liquid water (ALW) values exceeding 1 kg m-2 were
rejected. Both rain and high values of ALW can significantly distort the
quality of WVR measurements. Secondly, SIWV values were converted into SWDs
using the Askne and Nordius (1987) formula and the refractivity constants
from Bevis et al. (1994). ZHD values were computed with the precise model
given by Saastamoinen (1972). For the described conversions, we used values
of the atmospheric pressure and temperature measured in situ of the GNSS
reference station POTS. A hydrostatic correction for the altitude difference
between the meteorological station and the WVR position was applied to the
atmospheric pressure values. ZHD values were mapped to elevation angles of
the WVR using the hydrostatic mapping function derived from the NCEP-GFS
(Douša et al., 2016). In order to convert accurately SIWV to STDs, we
took into account the influence of the hydrostatic horizontal gradients (see
e.g. Li et al., 2015b). We used the hydrostatic horizontal gradients derived
from the NCEP-GFS for that purpose. Finally, SHD and SWD values were summed
up to deliver STDs. The described conversion of WVR SIWV to STDs aimed to
minimally distort the accuracy of original WVR observations.
Methodology of STD comparisons
We provide the specificities of each type of technique comparisons in this
section. Since NWM outputs are restricted to the time resolution of their
predictions (typically 1, 3 or 6 h) and, since WVR is able to
track only one satellite at one moment, all three sources provide different
numbers of STDs per day. Therefore, three different comparisons are
presented: (1) results for GNSS versus GNSS comparisons, (2) results for GNSS
versus NWM comparisons and (3) results for GNSS versus WVR comparisons.
Section 7 presents the validation at individual
stations and Sect. 8 intercompares results
obtained at GNSS dual stations. All the given results are obtained over the
whole benchmark period. No outlier detection and removal procedure was
applied during the statistics computation within the study.
Two variants of the comparisons are presented: “ZENITH” and “SLANT”.
“ZENITH” stands for original STDs mapped back to zenith direction using
1/sin(e) formula. Such mapping aimed to normalize STD differences for their
evaluation in a single unit. The “SLANT” type of comparison denotes an
evaluation of STDs at their actual elevation angles. To be more specific,
slant delays were grouped into individual elevation bins of 5∘; i.e.
for example all slants with an elevation angle between 10 and 15∘
were evaluated as a single unit. There was one exception regarding the size
of a bin since the lowest one contained slants from elevation angles of 7 to
10∘, 7∘ being the lowest elevation angle
common to all GNSS STD solutions. This cut-off angle was thus used in all
GNSS versus GNSS and GNSS versus NWM comparisons.
Presented values of biases and standard deviations were computed directly
from all STDs within the processed benchmark campaign period, and therefore they
are not based on any kind of daily or other averaging. In some tables, only
median values of bias and standard deviation over all GNSS STD solutions
(Tables 5, 7 and 8) or over all processed stations (Tables 3 and 4) are
given to consolidate the presentation of validation results. Median was used
as a parameter minimally affected by outliers.
Statistics from comparisons of individual GNSS STDs
(projected in the zenith direction) while using none, raw and clean
residuals; median values of biases and standard deviations (SD) calculated
over all stations with an exception of LDB0 station are given.
Impact of selected strategy modifications assessed via
comparing individual STDs solution variants. Median values of biases and
standard deviations (SD) calculated over all stations with an exception of
LDB0 station using the estimated model only (without residuals) are given.
Compared solutionsRemarks on solution differences Bias (mm)SD (mm)TUW_3 – TUW_7Elevation angle cut-off:3∘ versus 7∘+0.46±0.690.98 ± 0.45ROB_G – ROB_VMapping function:GMF versus VMF1+0.94±0.281.90 ± 0.27TUO_G – TUO_RGNSS observations:GPS versus GPS + GLO+0.18±0.321.95 ± 0.37ROB_V – TUO_RZTD/gradient resolution:15 min/1 h versus 1 h/3 h+0.28±0.183.24 ± 0.30GOP_F – GOP_SProcessing strategy:Kalman filter versus backward smoothing-0.60 ± 0.554.81 ± 0.79
Medians of bias and standard deviation values of
differences between all GNSS solutions and a particular NWM-based solution
at each reference station, expressed in the zenith direction.
StationBias (mm) Standard deviation (mm) ALA/BIRAERA/GFZGFS/GFZALA/WUELSALA/BIRAERA/GFZGFS/GFZALA/WUELSGOPE0.33.38.611.58.310.37.122.4KIBG-19.34.99.622.511.617.811.026.7LDB0-2.00.75.510.69.910.38.526.2LDB2-1.60.96.115.19.110.18.625.4POTM3.46.312.518.98.010.69.426.2POTS-1.71.47.612.57.710.39.225.8SAAL-19.47.811.724.312.717.911.822.9WTZR-4.8-1.54.910.211.011.88.523.1WTZS-3.5-0.94.210.811.412.38.723.7WTZZ-2.10.96.011.611.312.08.923.7GNSS versus GNSS comparisons
In the case of individual inter-GNSS solutions validation, the situation was
straightforward and no interpolation nor specific hypothesis was necessary:
the comparisons were done on a direct point-to-point basis of observations
coming from identical azimuth and elevation directions.
GNSS versus WVR comparisons
To find pairs of STDs observations between WVR and GNSS, the following rules
were used: (1) the time difference between both observations had to be
shorter than 120 s and (2) the difference between both azimuth and elevation
angles had to be smaller than 2.5 and 0.25∘,
respectively. From these criteria, the maximum difference in elevation angle
has the largest impact on the number of observation pairs found. Hence the
smaller values for these settings, the smaller number of pairs found and the
smaller standard deviations resulted between GNSS and WVR STDs. As an
illustration, a change from 0.35 to 0.25∘ led to the
decrease of the number of STD pairs between the GNSS GFZ solution and the
WVR at station POTS from 63 703 to 48 583 pairs; the standard deviation of
the projected STD differences in the zenith direction then decreased from
14.6 to 11.7 mm too. Since the bias practically remained unchanged (-6.1 mm
versus -5.9 mm), the applied selection procedure mainly influenced the
stability of the comparison between WVR and other sources of slant delays.
When comparing GNSS versus WVR STDs, a cut-off elevation angle was set to 15∘
to exclude low-elevation angle observations from WVR as their
quality could be further degraded by a ground radiation or other local
environment conditions.
GNSS versus NWM comparisons
Given the very small distances between collocated antennas and the coarse
resolution of the global NWM models, STDs from NWM ray tracing using the
ERA-Interim and the NCEP GFS models were derived only for one of the
collocated stations. The same set of NWM-derived STDs was then used for the
validation of the results at the collocated receivers.
Results at individual stationsGNSS versus GNSS
The total of STD pairs available for this part of the validation is roughly 1.7
million and varies from 140 987 to 206 320 according to the station.
Evaluation of all GNSS solutions versus the reference GNSS
solution
Individual GNSS solutions were first compared to the GFZ solution in the
zenith direction (ZENITH). We chose the “GFZ” solution as the reference
because GFZ Potsdam has long-term experience in producing GPS slant delays
and because the GFZ near-real-time solution for German GNSS reference
stations is already being operationally delivered to the Deutscher
Wetterdienst (German Meteorological Service) for NWM assimilation
testing purposes (Bender et al., 2016). Figure 4
shows all the solutions using STDs calculated from the estimated ZTD and
horizontal gradient parameters, i.e. without adding post-fit residuals.
Adding raw or clean residuals, applied consistently to both compared and
reference solutions, provided very similar graphs (not displayed). Colours
in Fig. 4 indicate the processing software used
in individual solutions. Medians of all solutions (dotted lines in each bin)
are displayed for each station in order to highlight differences among the
stations. These were observed mainly as biases ranging from -3.6 to 0.6 mm.
The better agreement between GOP and GFZ solutions could be attributed
to a similar strategy of both solutions compared to others. It is
particularly visible for LDB0 and POTM stations where median values over all
solutions differ by -2.3 and -3.6 mm, respectively. The reason for the
divergent behaviour at the two stations has not been identified although
site metadata were cross-checked carefully. A significant difference can
also be noticed for TUW_3 and TUW_7 at the
station KIBG where these solutions used individual antenna calibration files
while all others solution used type mean calibration (Schmid et al., 2016).
However, plots with standard deviations show agreements within 3–5 mm
among all the stations and all solutions. The only exception is the
GOP_F solution representing a simulated real-time analysis
applying only a Kalman filter (not backward smoothing) and providing results
by a factor of 2 worse compared to the others in terms of precision.
Comparison of individual GNSS STD solutions against GFZ solution,
all without using residuals (nonRES) and projected in the zenith direction:
bias (a) and standard deviation (b). The median value of all
solutions at each station is represented by the dotted blue line in each
bin.
Impact of post-fit residuals
All individual GNSS STD solutions were compared independently using none
(nonRES), raw (rawRES) and clean (clnRES) residuals. The comparison aimed to
assess the impact of different strategies for reconstructing GNSS STDs.
Figure 5 displays biases and standard deviations
for all solutions when comparing STDs with and without raw residuals.
Similarly, Fig. 6 shows results for STDs with and
without clean residuals. Both comparisons demonstrate biases at a
sub-millimetre level over all stations and solutions. Smaller biases are,
however, observed in the latter case (clnRES), which demonstrates the presence
of station-specific systematic errors in raw residuals (over all days of the
benchmark campaign) projected into zenith directions. Although the decrease of biases
is visible for all solutions, several solutions (GFZ, GOP, WUE) resulted in almost zero values over all the stations. It could be attributed to
easier removal of systematic effects in PPP as absolute residuals are
accessible directly. This is in contrast to the DD solutions
by ROB with ZD residuals reconstructed using relative information in
original values. Interestingly, the TUW PPP solutions seem to perform
similarly to the ROB DD solution in this case.
Comparison of individual GNSS STD solutions without residuals
(nonRES) and with raw residuals (rawRES); statistics are projected in the
zenith direction: bias (a) and standard deviation (b).
Comparing standard deviations in both figures demonstrates that the impact
of cleaning residuals led to the standard deviations reduced by the factor
of 1.2–1.5 over all stations and solutions, namely reaching 2.5–4.5 mm for
clean residuals compared to 3.0–6.5 mm resulting from raw residuals. The
station-specific behaviour is more obvious for the latter rather than for
the former and, generally, the relative performance over all stations is in
a good agreement among different solutions applying clean residuals (see
Fig. 6). In particular, LDB0 and LDB2 stations
show high discrepancies for raw residuals (see
Fig. 5), while their standard deviations were
significantly reduced after cleaning the residuals becoming more homogeneous
with other stations. In this context it should be noted that the station
LDB0 is missing in both ROB solutions since it has been excluded from the
network solution during the pre-processing phase due to a lower quality of
observations. Besides the GOP_F demonstrating simulated
real-time solution, showing about 25 % worse standard deviations compared
to other solutions in Fig. 6, we can also observe
by a 12 % worse performance of the GOP_S solution using
forward filtering and backward smoother. Both can be attributed to the
stochastic model applied in the GOP software with epoch-wise parameter
estimation and partly also to remaining deficiencies in implementations of
all applied models – the only in-house software has been developed from
scratch recently and, in contrast to others, could not have been extensively
used in a variety of applications. Finally, there are rather small
differences observed due to the applied strategy, namely forward versus
backward filtering, GPS versus GPS + GLO and the cut-off 3 versus
7∘ for elevation angles (statistically compared for STDs above the elevation
cut-off angle of 7∘).
Comparison of individual GNSS STD solutions without residuals
(nonRES) and with clean residuals (clnRES); statistics are projected in the
zenith direction: bias (a) and standard deviation (b).
Table 3 summarizes statistics related to the
figures providing medians and standard deviations over all stations.
Notably, biases of STDs (over all stations) expressed in the zenith
direction are negligible in all solutions, i.e. not affected by adding raw
or clean residuals. The impact of adding raw residuals to the estimated
model can be characterized by the median
standard deviation of 3.9 mm (first two data
columns), which may vary for different stations, e.g. as evident for stations
LDB0 and LDB2 in Figs. 5 and 6. Adding cleaned residuals shows an overall
impact of 2.8 mm (middle data columns) corresponding to the reduction of 29 %
compared to raw residuals and up to 50 % for problematic stations
such as LDB0 and LDB2. The comparison is understood as the impact of
removing systematic errors from the residuals – in other words, as a
degradation of STD quality when applying uncleaned residuals due to the
contamination by systematic errors. From this reason, we would not recommend
adding uncleaned (raw) residuals, but cleaned only, when providing STDs from
GNSS. However, this comparison does not suggest any preference for
using the estimated model without residuals or for adding clean
residuals to reconstruct STDs. Both approaches still comprise of various
errors due to approximations, local environmental effects, instrumentation
effects or applied models. Additionally, the impact of cleaning the post-fit
residuals for the reconstruction of STDs can be characterized by a median
standard deviation of 2.6 mm when projected into the zenith direction,
roughly 25 mm at the elevation of 6∘, which is estimated from
differences between STDs using raw and clean residuals over all solutions
and stations (last data columns).
Evaluation of ZTD processing settings
Individual GNSS solutions also provided variants using the same software and
strategy but with modified settings. This allows us to assess its impact on
the estimated parameters; see Table 4.
Consequently, we evaluated STDs calculated without residuals expecting the
impact (mainly) on estimated ZTDs and horizontal gradients. Biases reached a
sub-millimetre level and were almost insignificant, with the exception of
using GMF versus VMF1 mapping function resulting in a positive bias of
+0.94 ± 0.28 mm over all days and stations. Studied effects were
sorted by the magnitude of standard deviations. The impact of the elevation
angle cut-off (3∘ versus 7∘) resulted in a median of
standard deviation below 1 mm; see TUW_3 and
TUW_7. In this regard, it is necessary to mention that the
difference between those two solutions comes mainly from estimated
horizontal tropospheric gradients since no STDs below 7∘ entered
the STD validation. The impact of cut-off angle is also dependent on number
and quality of observations below 7∘ used in TUW_3
solution. The use of mapping functions based on climatology (GMF) or
meteorological (VMF1) data resulted in a slightly larger impact, at the
level of 2 mm, which is similar as the impact found for using single (GPS)
or dual (GPS + GLO) GNSS constellations. The use of different temporal
resolutions of ZTDs and gradients could not be avoided among various
contributions due to limited capabilities of handling a high number of
parameters. An assessment of the temporal resolution is also influenced by
applying relative constrains in deterministic approach or setting a noise
level in stochastic process. We compared two solutions
(ROB_V and TUO_R) using the Bernese software
and DD method with the same settings but different temporal resolutions of
ZTDs and gradients. The results show discrepancies at a level of 3 mm which
could be partly explained by different sampling, but we also assume
contributions from specific differences in strategies such as data
pre-processing. Last but not least, the impact of using a Kalman filter for
simulating real-time solutions compared to the back-smoother
(offline)
solution resulted in the discrepancies represented by a standard deviation of
4.8 mm.
Evaluation in the slant direction
Figure 7 provides an evaluation of the STDs at
their original elevation angles for the station POTS. Four individual panels
show bias (top left), normalized bias (NBIAS, top right), standard deviation
(bottom left) and normalized standard deviation (NSD, bottom right).
Normalized bias and normalized standard deviation were computed to see the
dependence of relative errors in STDs at different elevations. For its
computation, absolute differences of STDs from two solutions were divided by
the STD values from the reference solution. For example, when the solution
from GFZ (taken here as the reference) was compared against TUO, the
standard deviation was computed from all valid absolute differences given as
diff_absolute=STDGFZi-STDTUOi
and normalized standard deviation from all valid relative differences given
as
diff_relative=(STDGFZi-STDTUOi)/STDGFZi.
Since STDs are reconstructed mainly from ZTDs and horizontal gradients, any
small differences between the two solutions in the zenith direction should
become much larger after mapping down to lower elevations. Therefore, higher
values of bias and standard deviation are expected with the decreasing of
elevation angle. Indeed, we found that the agreement among individual
solutions compared to the GFZ STDs is rather stable above the elevation
angle of 30∘. Corresponding biases of individual elevation bins are
within ±4 mm and standard deviations are slowly increasing up to 10 mm
at 30∘. With elevation angles decreasing below 30∘ the
biases slightly increase for some solutions.
Comparison of individual GNSS STD solutions against GFZ STD
solution at station POTS, in slant directions.
In terms of standard deviation, the presumption about the dependency of
statistics on the elevation angle is clearly visible in the increasing
errors with the decreasing elevation angles (Fig. 7) while following an
exponential decay up to 45 mm at 7∘.
Normalized standard deviation remains almost constant over all elevation
angles, indicating a very consistent relative performance of STDs among all
the solutions. A similar behaviour is present at all stations although the
absolute values can be higher for some stations or solutions, namely
GOP_F for LDB0 and WTZZ with standard deviations reaching up
to 72 mm.
GNSS versus NWM
STDs from four individual NWM ray-tracing solutions delivered by three
different institutions entered the validation (see Sects. 4.1–4.3 for
more information). Even though the time resolution of NWM is not continuous (only
NWM-based results given at 00:00, 06:00, 12:00 and 18:00 UTC were used), the comparison
with GNSS STDs measurements can be used to estimate the quality of the
weather prediction. However, when the meteorological situation is
well simulated by NWM, it is relevant for this study to compare the model with
GNSS observations. To ensure the consistency of the comparison, only epochs
for which STD values were available in all GNSS solutions were considered;
i.e. if a single STD value was missing in any GNSS solution, then the STD
values at the same epoch were also removed from all other GNSS solutions.
This selection of observations and the low time resolution of the NWM models
(6 h) led to a restricted set of STDs available for the validation
consisting of 9866 observations in total.
Evaluation of all GNSS solutions without residuals in the zenith
direction
Figure 8 presents the comparison of individual NWM
STDs and GNSS STDs (without residuals) expressed in the zenith direction.
From top to bottom, plots show biases (left) and standard deviations (right)
for ALA/BIRA, ERA/GFZ, GFS/GFZ and ALA/WUELS. For most stations, the bias
varies between -5 and +3 mm for the ALA/BIRA solution, with all GNSS
solutions performing similarly. Slightly higher biases and more variability
between GNSS solutions are observed at the station POTM. This behaviour is
accounted for by the GNSS solutions since POTM and POTS are collocated and the
ALA/BIRA provides the same STDs for the validation at both stations. If we
exclude both GOP solutions and the GFZ solution, the range of biases at
station POTM is very similar to the range at station POTS. The difference in
height of those two stations is 0.5 m. The station POTS is equipped with a
choke ring antenna while the station POTM is not, which indicates large
multipath effects (see Fig. 12) causing higher
range of biases for individual solutions at station POTM. Significant biases
of approximately -20 mm are present at two Austrian stations, KIBG and SAAL,
and are similar for all GNSS solutions. Both stations are situated in the
mountainous area south-west of Salzburg. Since the same biases
occur at neither GNSS versus ERA/GFZ nor GNSS versus GFS/GFZ comparisons, they are
most likely due to a deficiency of the ALADIN-CZ orography representation.
Note that ALA/BIRA and ALA/WUELS STDs show an unexpected opposite behaviour
for KIBG and SAAL stations (Fig. 8), which is
related to the difference in the strategy used. This is possibly due to the
estimation of the altitude of parameters, their interpolations and the
difference in the step of integration. Except at those two stations, similar
biases as for ALA/BIRA can be also found for the GNSS versus ERA/GFZ
comparison, ranging from -3 to +7 mm (+11 mm at POTM). Although the
bias characteristics for GFS/GFZ are practically identical to those obtained
for ERA/GFZ, the results for the NCEP GFS model are shifted by approximately
+5 mm, resulting in biases ranging from +3 to +12 mm (+17 mm at
POTM). The origin of this systematic deviation was identified in ZWD values
estimated from the GFS model (Douša et al., 2016) and understood as the
effect of the lower vertical resolution of NCEP GFS model compared to other
NWMs, leading to larger errors in vertical interpolations.
Comparison of individual GNSS STD solutions without residuals
(nonRES) against NWM solutions ALA/BIRA, ERA/GFZ, GFS/GFZ and ALA/WUELS (from
top to bottom), projected in the zenith direction: bias (a, c, e, g) and standard
deviation (b, d, f, h).
Comparison of NWM-based solutions (ALA/BIRA, ERA/GFZ and GFS/GFZ)
against GNSS GFZ solution at station POTS, in the slant direction.
Standard deviations between GNSS STDs and ALA/BIRA, ERA/GFZ and GFS/GFZ
solutions are usually around 10 mm when projected into the zenith.
Generally, they are higher than the comparison of individual GNSS solutions
presented in Sect. 7.1 and they are also more
station dependent. Degradations can be observed at mountainous stations KIBG
and SAAL for the ERA/GFZ, GFS/GFZ and ALA/BIRA STDs, reaching standard
deviations up to 18 mm in the case of the ERA-Interim NWM.
The solution of ALA/WUELS performed differently compared to all other NWM
solutions. It is biased against GNSS solutions, with biases ranging from
+9 to +25 mm and highest values observed at stations KIBG and SAAL.
Standard deviation values are also much higher by about a factor of 2.5
worse compared to values obtained from the GNSS versus GFS/GFZ comparison.
The probable reason for this is that signal tracking was performed for
vacuum elevation angles. As we discuss in the following subsection this
impact is especially visible at low-elevation ray paths at which the signal
has to travel through the troposphere for a longer time, enhancing the
negative effect of underestimated delays.
Finally, comparisons between the three versions of GNSS solutions (nonRES,
clnRES, rawRES) and the ALA/BIRA, ERA/GFZ and GFS/GFZ NWM solutions were
done to test the influence of post-fit residuals on GNSS STDs. The ALA/WUELS
solution was excluded from this comparison because of the lower quality of
its STDs. All GNSS solutions without post-fit residuals reached slightly
lower standard deviation values than the solutions which included either raw
or cleaned post-fit residuals, while differences in biases were negligible
(not displayed). An average increase of standard deviation was 4.5 % for
clean residuals and 8.3 % for raw residuals. Indeed, because of their low
horizontal and time resolution, the used NWMs can barely capture the
very fine-scale tropospheric structures which are supposed to be included in
the GNSS residuals. As a consequence, this comparison does not allow us to
draw a clear conclusion about the potential benefits of post-fit residuals in the
reconstruction of the GNSS STDs.
Evaluation in the slant direction
Statistics from the comparison of ALA/BIRA, ERA/GFZ and GFS/GFZ against all
three versions of GNSS GFZ solution expressed at original elevation angles
of slant delays are presented for the station POTS in
Fig. 9. Significantly higher biases can be found
at the lowest-elevation bin in all three solutions and at all stations (not
displayed). At some stations, sudden increases of bias at individual
elevation bins were observed. They happened at any elevation angle
(different for each NWM STD solution) and were particularly visible in terms
of normalized bias. These sudden increases of the bias might be either
because the model sometimes cannot render the tropospheric
structures at their exact locations (unexpected location of high/low values
of water vapour partial pressure) or because models running at these
resolutions have a tendency to smooth out such tropospheric heterogeneities.
Comparing with a model running at convective-permitting scale (e.g. 1 to 4 km)
would help to sort out if the origin of such behaviours is
the NWM STD or the GNSS STD.
For all stations, standard deviations present the shape with significantly
higher values at elevations below 30∘ followed by more gentle
decrease towards the zenith direction. An exception was found at stations
WTZR, WTZS and WTZZ where a rather smooth shape of the curve is disrupted
with sudden changes of standard deviation at particular bins over all
elevation angles. This is true mainly for GNSS versus ALA/BIRA
solution,
while results for GNSS versus ERA/GFZ and GNSS versus GFS/GFZ results show such changes less
frequently and with lower magnitude by a factor of 2 or 3. Normalized
standard deviations vary at all elevation angles for all validated stations
without distinct common characteristics. Values range between 0.2 and
0.9 % with the highest values occurring usually at lower-elevation
angles.
Results from the GNSS versus ALA/WUELS solutions (not displayed) show an
enormous increase of both absolute and normalized bias and standard
deviations at low-elevation angles below 25∘ at all stations. They
reached biases up to 350 mm and standard deviations up to 300 mm at some
stations. Statistical parameters became more stable above 25∘, with
occasional disturbances similar to those observed in other NWM-based
solutions.
Summary of results for GNSS versus NWM
A summary of the GNSS versus NWM validation is presented in
Table 5. For each reference station a median of
bias and a median of standard deviation in the zenith direction between all
GNSS solutions and a particular NWM-based solution are given. If we consider
ALA/BIRA and ERA/GFZ only, without the two mountainous stations KIBG and
SAAL, absolute biases between NWM and GNSS solutions stay mostly below 3 mm,
which represents a very good agreement between these independent sources
used for retrieving slant delays. Standard deviations generally range from 8
to 12 mm in the zenith projection, with the exception of ALA/WUELS,
which shows lower precision by a factor of 2.5. Statistics stem from the
complete benchmark period, and it should be noted that the daily variation
of GNSS STDs was much lower than of NWM ray-traced STDs. Significantly
higher values of biases and standard deviations were observed at particular
days for NWM solutions. A detail evaluation of daily statistics with
respect to the extreme weather conditions is one of the topics that we will
study in future.
GNSS versus WVR
Figure 10 compares GNSS and WVR solutions at
stations POTM and POTS, in the zenith direction. The number of slant
observations which entered the comparison was 32 794 at station POTM and
36 070 at station POTS. Two remarks can be made on the evaluation of biases.
Firstly, an overall bias of about 4 mm between the stations POTM and POTS,
visible for all GNSS solutions already in Fig. 8,
indicates a common issue with the GNSS data processing at the station POTM.
It was particularly increased for GOP_F, GOP_S
and GFZ PPP solutions. Secondly, a bias of about 5.5 mm in the zenith
direction can be found between WVR and GNSS solutions even at station POTS.
This bias roughly corresponds to 1 kg m-2 of IWV, which can be considered the achievable accuracy of either of the two techniques;
however, WVR accuracy is more dependent on a proper instrument calibration.
Comparison of individual GNSS STD solutions for stations POTM and
POTS versus WVR measurements, expressed in the zenith direction,
bias (a) and standard deviation (b). The median value of all solutions at each
station is represented by the dotted blue line in each bin.
Values of standard deviation, resulting mostly in 12 mm, are higher than
those observed in GNSS versus GNSS comparisons (Sect. 7.1) and slightly
higher than from GNSS versus NWM comparisons (Sect. 7.2). A cut-off elevation
angle of 15∘ was used for the comparison with WVR STDs instead of
7∘ used in other validations. Additionally, it has to be noted
that the results can be partly influenced with the settings applied for
finding pairs between GNSS and WVR STDs (Sect. 6). STDs from WVR can thus originate from slightly
different azimuth/elevation angles and times than the GNSS ones. All GNSS
solutions perform similarly against WVR, with the exception of
GOP_F due to the application of a real-time capable strategy.
The GNSS versus WVR validation at the station POTS using original elevation
angles is displayed in Fig. 11. Although some
differences between GNSS solutions are visible, all of them performed in a
very similar manner. The decrease of values of four statistical parameters
strongly follows the increase of elevation angle and, generally, it is
steeper than statistics dependency of GNSS versus NWM. It indicates that
slant delays from WVR below 40∘ become generally unreliable,
which is particularly clear from normalized biases and standard deviations
at lower-elevation angles. A sudden increase of the values is observed at
elevations of 55–60∘, most likely originating from WVR observations
which are not yet understood.
Comparison of WVR against individual GNSS STD solutions at
station POTS, in the slant direction.
Generally, standard deviations for all solutions using cleaned residuals
(raw residuals) are on average 1.7 % (3.8 %) higher than
for the solutions without residuals. Differences between solutions variants
are smaller due to an overall higher uncertainty of WVR observations,
but the results are in a good agreement with those obtained for GNSS
versus NWM comparisons presented in Sect. 7.1.
Validation of results at collocated stations
Two erroneous techniques for STD retrievals have been compared in
previous sections (GNSS vs. NWM, GNSS vs. WVR) without knowing the true
reference. The errors stem from the observation noise on one hand and from
the processing models including the model for adjusted parameters on the
other hand. From this perspective, the higher standard deviations for GNSS
STD solutions applying clean residuals compared to those using adjusted GNSS
parameters only (without residuals) do not necessarily mean the lower
quality of the former. GNSS and NWM models with limited temporal and spatial
approximations are not able to represent true signal tropospheric delays
between a receiver and all visible satellites. The simplifications certainly
result in better agreement of STDs without residuals in Eq. (1), but they
hardly represent the true tropospheric path delays, deviating particularly
during the events with high spatiotemporal variations in the troposphere.
For this reason, we assessed all GNSS solutions at the collocated (dual)
stations because for such constellation we are able to provide troposphere-free
differences of STDs to evaluate noise of GNSS STD retrievals. We
particularly focused on days with a high variability in the troposphere
selected from the benchmark period. Dual stations were available in the
benchmark campaign at three different locations in Germany. The first two
sites collocate twin GNSS reference stations (LDB0 + LDB2 and
POTM + POTS) and
the third location collocates three individual reference stations
(WTZR + WTZS + WTZZ). Nevertheless, in the case of Wettzell, only results
for WTZR+WTZS are presented due to their similarity with the two other
combinations at the same place. Characteristics of the stations are
summarized in Table 6.
Comparison of GNSS STDs from the elevation angles ranging
from 7 to 15∘ at three dual stations; results for days with high
daily variability of cleaned post-fit residuals (top) and results for days with low
daily variability of post-fit residuals (bottom). Median values of
biases and standard deviations (SD) calculated over all GNSS STD solutions
are given; statistics are expressed in the zenith direction.
nonRES clnRES rawRES Bias (mm)SD (mm)Bias (mm)SD (mm)Bias (mm)SD (mm)Days with high variability of post-fit residuals LDB0 + LDB2-1.564.63-1.445.51-1.525.89POTM + POTS-5.241.89-5.163.47-5.914.24WTZR + WTZS-0.242.31-0.063.25-0.033.77Days with low variability of post-fit residuals LDB0 + LDB2-0.523.06-0.524.23-0.595.05POTM + POTS-4.971.87-5.033.00-5.793.87WTZR + WTZS-0.011.87-0.053.22-0.093.82
Comparison of GNSS STDs from the elevation angles ranging
from 15 to 90∘ at three dual stations; results for days with high
daily variability of cleaned post-fit residuals (top) and results for days with low
daily variability of post-fit residuals (bottom). Median values of
biases and standard deviations (SD) calculated over all GNSS STD solutions
are given; statistics are expressed in the zenith direction.
nonRES clnRES rawRES Bias (mm)SD (mm)Bias (mm)SD (mm)Bias (mm)SD (mm)Days with high variability of post-fit residuals LDB0 + LDB2-0.924.19-0.886.13-0.888.87POTM + POTS-5.281.68-5.303.39-5.304.64WTZR + WTZS-0.532.29-0.564.12-0.495.21Days with low variability of post-fit residuals LDB0 + LDB2-0.072.59-0.074.930.047.83POTM + POTS-4.961.82-4.923.30-4.934.65WTZR + WTZS-0.011.74-0.053.770.025.07Slant residuals and slant delay differences
STD validations in this paper were done for 2 months of the benchmark period
during which heavy rain events occurred for some days, particularly 31 May–3 June,
9–11 and 21–26 June, all causing severe flooding in central
Europe. During normal weather conditions, the tropospheric variation is
reasonably smooth, meaning it can be well represented by GNSS STDs
reconstructed from ZTDs and horizontal gradients. However, during high
temporal or spatial variabilities in the troposphere, post-fit residuals
certainly contain tropospheric signals which were not modelled. If they
surpass the observation noise and other residual errors from GNSS models,
cleaned residuals should be considered in the GNSS STD model as described in
Eq. (1).
In order to initially address optimal STD modelling under different weather
conditions within the benchmark period, we tried to identify days with a high
variability in the troposphere. Daily standard deviations of cleaned
post-fit residuals were computed individually for each day of the benchmark period,
for every station and GNSS solution for 1∘-elevation-angle bins. We
studied their daily variations considering the GNSS model applied. If
cleaned post-fit residuals consist of the noise of observations only, the
variation in time should be negligible. However, the days showing
significantly higher values, correlated at all collocated stations, indicate
highly variable tropospheric conditions.
Three such days were identified at LDB0, LDB2, POTM and POTS stations
(31 May, 20 June, 23 June) and 2 days at WTZR and WTZS stations (19 and
20 June). They all very well correspond to the days initiating heavy
precipitations in the domain (Douša et al., 2016). Typical differences
between raw and clean residuals are displayed in Fig. 12 for all elevations
during the normal day (19 June, DOY 170) and the day with high variability in
the troposphere (DOY 171, 20 June) for LDB0, LDB2, POTM and POTS stations
using GFZ solution. Obviously, the variability of clean residuals (black
dots) and their 2σ envelopes are higher by a factor of 2 for the day
of year 171 compared to 170. The variability is clearly visible over all
elevations, but the increase is slightly higher at low elevations. The plots
for these four stations clearly demonstrate the different quality of GNSS
observations, particularly related to a multipath effect displayed by
2σ envelope (green curves). A low multipath is common to the stations
using choke ring antennas, in our case POTS and LDB2, but LDB2 still suffers
from unknown systematic effects at 35–55∘ elevations. A very high
multipath effect was observed at LDB0 station over all elevations.
Variability of 2σ envelopes of clean residuals (red curves) indicates
a higher sensitivity of clean residuals to the weather conditions compared to
station selection and observation quality, thus suggesting a significant
contribution from the troposphere to the cleaned residuals. In the same
context, raw residuals show much higher sensitivity to the observation
quality compared to different weather conditions, which is particularly true
in the case of LDB0 and LDB2 stations.
Elevation-dependent variability of clean residuals (black dots)
and their 2σ envelopes (red curves) are showed for 19 June (DOY 171) and
20 June (DOY 170) and four stations: POTS, POTM, LDB0 and LDB2.
Additionally, plots display 2σ envelopes for raw residuals (blue
curves) and multipath (green curves).
Elevation-dependent differences of STDs using clean residuals (black dots)
are displayed in Fig. 13 for the same days as in
Fig. 12, selecting GFZ solution and station pairs
WTZS–WTZR and LDB0–LDB2. Additionally, 2σ envelopes are plotted for
differences without residuals (red curves), clean residuals (green curves)
and raw residuals (blue curves).
Firstly, we note that STD differences are more or less similar for
both days, i.e. not significantly different between days with normal and high
variations in the troposphere, which is also found for other days of the
benchmark period. It suggests that increased residuals in
Fig. 12 for DOY 171 contain strong contributions
from the tropospheric effect that could not have been assimilated into ZTDs
and tropospheric horizontal gradients. An alternative explanation suggests a
possible contribution of satellite-specific errors common to both
receivers, thus easily eliminated in STD differences at the dual stations.
However, systematic errors at satellites are well absorbed by initial phase
ambiguities in PPP and short-term or random errors, e.g. due to
satellite clocks, are in this study eliminated by the use of final products,
i.e. stable enough to avoid observed day-to-day variability in cleaned
residuals. The DOY 171 thus shows the situation when cleaned residuals
contain a tropospheric signal that should be added to the STD retrievals. In
the case of GFZ, the contribution from residuals is particularly important
due to local troposphere variation in time when using model of piece-wise
constant function with 15 min time resolution for ZTD and 60 min for
horizontal gradients. It is not so obvious in the case of a stochastic process
used for epoch-wise estimates of all tropospheric parameters. However, the
uncertainty of estimated parameters is then higher compared to the
deterministic model, which makes it more difficult to separate errors in estimated
parameter and errors due to insufficiency of the linearized tropospheric
model in time.
Secondly, we can see that envelopes of differences using raw residuals are
always the largest ones. Raw residuals vary more with the elevation angle,
which is particularly visible for differences between LDB0 and LDB2. Obviously, it is
due to the large systematic errors at LDB0 station and additional
contribution from LDB2 errors observed at 35–55∘ elevations. The
2σ envelopes of STD differences with clean residuals smoothly follows
the 2σ envelope of STDs differences without residuals, keeping the
difference within ±15 mm over all elevations. This indicates a stable
and reliable usage of clean residuals under any conditions. In contrast, applying raw residuals at problematic sites may seriously degrade STDs
as observed at LDB0 station.
Finally, we can consider error contribution from both stations to STD
differences at dual stations equal, i.e.
δSTD_dif2=2δSTD_res2,
with δSTD_dif2 variance calculated from cleaned
STD differences at specific elevations when using the same processing
strategy at both dual stations and with δSTD_res2
characterizing the variance over errors in GNSS STD retrievals
corresponding to the observation elevation angle and the applied strategy.
Although we can note some differences in δSTD_dif2
in collocations, partly due to differences in contributions from
both stations, the relative performance of differences from STDs with clean
residuals (green curves) and without residuals (red curves) for different
days remains similar. Uncertainties of the simplified STDs at low elevations
surpass additional uncertainties due to applying clean residuals (green
curves vs. red curves). According to the magnitude of clean residuals at
these elevations (Fig. 12), the small
uncertainties from calculated differences indicate the presence of
tropospheric signals in the residuals at low elevations, roughly below 30∘.
It seems to be almost independent from the weather conditions and
is supposed to represent mainly unmodelled horizontal asymmetry in the
troposphere. However, further study on detail impact of residuals on GNSS
STDs modelling during severe weather conditions requires longer datasets,
which will be subject of our upcoming study.
Figure 14 displays results for comparisons of
individual dual stations in slant directions calculated from all days of the
benchmark period. The same statistics and plots (not displayed) were prepared also
for days identified with “severe” weather conditions, but only minor
differences were observed. Strong variations are observed mainly in
normalized biases over all elevation angles for the solutions using raw
post-fit residuals (rawRES) regardless weather conditions. These are clearly
related to local effects such as multipath or modelling instrument-related
effects (phase centre offsets and variations) and disappear after using the
cleaned residuals (clnRES). The standard deviations and normalized standard
deviations at all stations are clearly the lowest for variants without using
post-fit residuals (nonRES), slightly higher using cleaned residuals and
significantly higher when using raw residuals, i.e. corresponding to above-performed inter-technique validations.
Elevation-dependent variability in STD differences of clean
residuals (black dots) and their 2σ envelopes (green curves) are showed
for 19 June (DOY 171) and 20 June (DOY 170) and two dual-stations:
WTZS–WTZR and LDB0–LDB2. Plots also display 2σ envelopes for
differences of raw residuals (blue curves) and without residuals (red
curves).
Differences in zenith direction
Tables 7 and 8 show the statistics expressed in the zenith direction for observations
ranging in elevation angles from 7 to 15 and from 15 to 90∘,
respectively. Median values computed over all GNSS solutions for which
residuals were available are presented. Results for the identified days with
high daily tropospheric variation are given in the upper part of the table
– days are stated in the previous section. In the bottom part results for
selected days with low daily variation of post-fit residuals are presented.
These days were the same for all collocated stations: 25 May, 30 May and 6 June
(DOY 145, 150, 157). Biases remain stable regardless of the severe weather
occurrence and whether post-fit residuals are used. The lowest standard
deviations for all dual stations are always related to the solutions without
using post-fit residuals. Interestingly, when comparing the statistics for STDs
evaluated separately for ranges of 7–15 and 15–90 elevation degrees,
standard deviations are smaller in high compared to low elevations for
variants without using residuals and vice versa for variants using either
cleaned or raw residuals. This can be interpreted as the standard GNSS
tropospheric model (ZTD and horizontal gradients) representing well
observations at elevations above 15∘ but suffering under the modelling
deficiencies mainly at low elevations. These statistics also support the
above statement that cleaned residuals are valuable particularly for
reconstructing low-elevation STDs regardless of the weather conditions as they
certainly contain non-negligible tropospheric signals from high-order
horizontal asymmetry. During the days with high variation of residuals, the
standard deviations are usually a little bit higher than during the days
with low variation, but there is no difference between these two
regarding the above-mentioned behaviour.
Conclusions
We presented results of validating tropospheric slant total delays obtained
from GNSS data processing with those obtained from NWM ray tracing, WVR
measurements and collocated GNSS stations, in search of the optimal method
for estimating GNSS STDs. Ten GNSS reference stations were selected,
exploiting data from the 56-day COST ES1206 benchmark campaign. Eleven GNSS
solutions, four NWM-based solutions and one WVR-based dataset entered this
validation study. Eight out of 11 GNSS solutions delivered STDs in three
variants: (1) without post-fit residuals, (2) with raw post-fit residuals and
(3) with cleaned post-fit residuals. The comparisons were carried out into
two scenarios, firstly for STDs at their true elevation angles and
secondly for STD differences mapped into the zenith direction using a
simple mapping function.
Comparison of GNSS STDs at dual stations computed over whole
benchmark period from individual GNSS solutions in the slant direction for
dual stations from left to right: LDB0-LDB2, POTM-POTS and WTZR-WTZS.
Statistical parameters from top to bottom: bias, normalized bias, standard
deviation and normalized standard deviation.
Comparisons of STD solutions without residuals, with raw or with cleaned
residuals were used to study the impact of different strategies for
optimally retrieving STDs from GNSS. The impact of cleaning residuals led to
the standard deviations reduced by a factor of 1.2–1.5 over all stations
and solutions, namely reaching 2.5–4.5 mm in the zenith direction for clean
residuals compared to 3.0–6.5 mm for raw residuals, the latter
also being highly dependent on the station. The impact of adding raw or cleaned
residuals was practically negligible in terms of biases, which always remained within ±0.1 mm.
Biases and standard deviations between GNSS and NWM solutions depended on
applied ray-tracing method, NWM source and station location. Worse results,
by a factor of 2.5 in terms of standard deviation, were observed for the
ALA/WUELS solution originating from the deficiency of the applied ray-tracing
method. Generally, biases in the zenith direction were below ±3 mm
for other solutions with the exception of a positive bias of 5 mm observed
for GFS NWM model. Standard deviations for all GNSS versus NWM STD
comparisons were at the level of 10 mm, excluding the ALA/WUELS solution.
Contrary to the GNSS versus GNSS comparisons, normalized standard deviations
showed pronounced variability with the elevation angle.
Using the simulation of delays from ALADIN-CZ weather model, we illustrated
the impact of the hydrostatic, wet and hydrometeors contributions to zenith
and slant delays. These showed strong horizontal variations that allowed
relevant characterization of mesoscale meteorological situations.
Visualizing the slant anisotropic variation of total, hydrostatic, wet and
hydrometeor delays in a common skyplot illustrated a weak hydrostatic
anisotropy (up to 5.8 mm) that was almost the same as that of the hydrometeor
(up to 6 mm). The largest anisotropy was induced by water vapour (up to 20 mm),
but the total anisotropy was much weaker (12 mm) due to the
compensation of mean hydrostatic and hydrometeor anisotropies oriented in
the opposite direction.
GNSS STDs from stations POTM and POTS were validated against collocated WVR
observations pointed to GNSS satellites. A positive bias of about 5.5 and
10 mm was observed for POTS and POTM station, respectively. Standard
deviations from comparisons of GNSS versus WVR STDs reached 12 mm in the
zenith direction, thus higher compare to NWM solutions. Normalized standard
deviations revealed a strong elevation dependency, indicating the WVR
observations lack this quality at low elevations, particularly below 40∘.
Collocated GNSS stations at three different locations were used to evaluate
the quality of GNSS STD retrievals applying statistics over troposphere-free
STD differences from theoretical point of view. We could observe strong
systematic errors in raw residuals at any elevation angles, particularly at
stations without the choke ring antenna, such as LDB0 and POTM. We found a
strong elevation dependency of bias when using raw residuals which almost
vanished when cleaning the residuals from visible systematic errors. This
suggests that the use of raw residuals should not be recommended, at least not without any
information about possible systematic errors. Although the simplified STDs
reconstructed from the estimated GNSS tropospheric parameters performed the
best in all the comparisons, it obviously missed part of tropospheric
signals due to non-linear temporal and spatial variations in the
troposphere. By identifying low and high variability in the troposphere during
all days in the benchmark period, we showed that residuals contain significant
tropospheric signals in addition to the simplified model, particularly
during high variability in the troposphere. Additionally, we also identified
tropospheric signals at low elevations due to a non-linear horizontal
asymmetry in cleaned residuals regardless of the station selection and the
quality of its observations. From such findings, we recommend the use of
cleaned residuals for an optimal STD retrievals from GNSS, at least for low-elevation angles and during high variability in the troposphere. We also
have not seen any obvious degradation of STD retrievals in other conditions.
The better inter-solution and inter-technique agreements of STDs without
residuals compared to those using clean residuals are attributed to the too-simple tropospheric model resulting in smooth and robust STDs and,
consequently, not containing all interesting signals from the troposphere.
The majority of evaluated GNSS solutions used deterministic models with
rather long validity of estimated tropospheric parameters for which the
residuals are important to overcome modelling deficiencies of low-resolution
parameter estimates in time. Our future study will focus on the evaluation
of GNSS STDs estimated using a stochastic process easily applicable in
real time and on a long-term evaluation of azimuthal dependency of post-fit
residuals under severe weather conditions.
GNSS data from the EUREF Permanent Network (EPN) stations
are freely available through the anonymous FTP, e.g. from the EPN historical
data centre at ftp://epncb.oma.be/pub/obs/ maintained by the Royal
Observatory of Belgium. Other GNSS and WVR data were primarily collected for
the purpose of the COST Action ES1206 (GNSS4SWEC project; see Dousa et al.
2016) and cannot be distributed. Numerical weather model data fields from
ALADIN-CZ were provided by the Czech Hydrometeorological Institute only for
the purpose of the GNSS4SWEC project. Data were available only to the project
members until the end of 2017 through the licence signed by the Research
Institute of Geodesy, Topography and Cartography (RIGTC). The ERA-Interim
data from the European Centre for Medium-Range Weather Forecasts (ECMWF,
http://www.ecmwf.int/) were provided to GFZ by the German Weather
Service. The Global Forecast System data were provided by the National
Centers for Environmental Prediction
(http://nomads.ncdc.noaa.gov/data/gfsanl). All the validation results
in the form of figures and tables for all types of presented comparisons and
stations can be provided by request to michal.kacmarik@vsb.cz.
The authors declare that they have no conflict of interest.
Acknowledgements
This study has been organized within the EU COST action ES1206 (GNSS4SWEC).
The authors thank all the institutions that provided data for the benchmark
campaign on which the validation was based on. Namely we want to thank
S. Heise (GFZ) for providing the WVR data. The GFS data were provided by the
National Centers for Environmental Prediction (www.ncep.noaa.gov). The
ERA-Interim data were provided by the European Centre for Medium-Range
Weather Forecasts (http://www.ecmwf.int/en/forecasts/datasets).
M. Kačmařík, J. Douša and P. Václavovic acknowledge the
support from the Czech Ministry of Education, Youth and Sports (project
nos. LD14102 and LM2015079). E. Pottiaux (ROB) and
H. Brenot (BIRA) acknowledge the support from the Solar-Terrestrial Centre of
Excellence (STCE). J. Kapłon and P. Hordyniec (WUELS) acknowledge the
support of Polish National Science Centre (project
no. UMO-2013/11/D/ST10/03473) for financial support and
Wrocław Center of Networking and
Supercomputing (http://www.wcss.wroc.pl) for computational grant using
MATLAB software license no. 101979. Edited by:
J. Jones Reviewed by: two anonymous referees
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