J Geod (2005)
DOI 10.1007/s00190-005-0010-z
O R I G I N A L A RT I C L E
K. Snajdrova · J. Boehm · P. Willis · R. Haas
H. Schuh
Multi-technique comparison of tropospheric zenith delays derived
during the CONT02 campaign
Received: 3 May 2005 / Accepted: 17 October 2005
© Springer-Verlag 2005
Abstract In October 2002, 15 continuous days of Very Long
Baseline Interferometry (VLBI) data were observed in the
Continuous VLBI 2002 (CONT02) campaign. All eight radio telescopes involved in CONT02 were co-located with at
least one other space-geodetic technique, and three of them
also with a Water Vapor Radiometer (WVR). The goal of
this paper is to compare the tropospheric zenith delays observed during CONT02 by VLBI, Global Positioning System
(GPS), Doppler Orbitography Radiopositioning Integrated
by Satellite (DORIS) and WVR and to compare them also
with operational pressure level data from the European Centre for Medium-Range Weather Forecasts (ECMWF). We
show that the tropospheric zenith delays from VLBI and GPS
are in good agreement at the 3–7 mm level. However, while
only small biases can be found for most of the stations, at
Kokee Park (Hawaii, USA) and Westford (Massachusetts,
USA) the zenith delays derived by GPS are larger by more
than 5 mm than those from VLBI. At three of the four DORIS
K. Snajdrova · J. Boehm (B) · H. Schuh
Institute of Geodesy and Geophysics, Vienna University of Technology,
Gusshausstrasse 27-29, 1040 Vienna, Austria
E-mail: [email protected]
E-mail: [email protected]
E-mail: [email protected]
Tel.: +43-1-5880112864
Fax: +43-1-5880112896
K. Snajdrova
Institute of Geodesy, Brno University of Technology, Veveri 95,
662 37 Brno, Czech Republic
P. Willis
Institut Géographique National, Direction technique, 2 avenue Pasteur,
BP 68, 94160 Saint-Mande, France
E-mail: [email protected]
P. Willis
Jet Propulsion Laboratory, California Institute of Technology,
MS 238-600, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
R. Haas
Onsala Space Observatory, Department of Radio and Space Science,
Chalmers University of Technology, SE-439 92 Onsala, Sweden
E-mail: [email protected]
stations, there is also a fairly good agreement with GPS and
VLBI (about 10 mm), but at Kokee Park the agreement is
only at about 30 mm standard deviation, probably due to the
much older installation and type of DORIS equipment. This
comparison also allows testing of different DORIS analysis
strategies with respect to their real impact on the precision of
the derived tropospheric parameters. Ground truth information about the zenith delays can also be obtained from the ECMWF numerical weather model and at three sites using WVR
measurements, allowing for comparisons with results from
the space-geodetic techniques. While there is a good agreement (with some problems mentioned above about DORIS)
among the space-geodetic techniques, the comparison with
WVR and ECMWF is at a lower accuracy level. The complete
CONT02 data set is sufficient to derive a good estimate of
the actual precision and accuracy of each geodetic technique
for applications in meteorology.
Keywords Troposphere · Zenith delay · GPS · VLBI ·
DORIS · Water Vapor Radiometer
1 Introduction
Tropospheric parameters play an important role when analyzing microwave space-geodetic measurements. In the standard least-squares fit of these observations, there is a relatively high correlation of about −0.4 between the station
height parameters and the tropospheric zenith delays (Boehm
2004), i.e., errors in the station heights can also be seen in the
zenith delays and vice versa. The agreement between the tropospheric parameters derived from different space-geodetic
techniques at co-located sites is an important indicator for
their accuracy and reliability, since biases in the tropospheric
parameters are mirrored as biases in estimated station heights.
Furthermore, accurate absolute tropospheric estimates are
important for atmospheric studies and — if obtained in near
real-time — even for weather prediction models (Tomassini
et al. 2002). It is also possible to derive atmospheric information from satellite-based measurements by applying the
K. Snajdrova et al.
Table 1 Geodetic instruments co-located at the very long baseline interferometry (VLBI) sites during the continious VLBI 2002 (CONT02)
campaign (October 16–31, 2002)
VLBI Station
IGS acronym
GPS receiver
DORIS acronym
DORIS antenna
Algonquin Park
algo
AOA BENCHMARK ACT
–
–
Gilmore Creek
fair*
ASHTECH UZ-12
faib
Starec
Hartebeesthoek
hrao
ASHTECH Z-XII3
hbkb
Starec
Kokee Park
kokb
ASHTECH UZ-12
koka
Alcatel
Ny-Ålesund
nyal*
AOA BENCHMARK ACT
spib
Starec
Onsala
onsa*
ASHTECH Z-XII3
–
–
Westford
wes2
ROGUE SNR-8000
–
–
Wettzell
wtzr
AOA SNR-8000 ACT
–
–
* The International GNSS Service (IGS) stations at Gilmore Creek, Ny-Ålesund, and Onsala are equipped with radomes
radio-occultation method (Ware et al. 1996; Hajj et al. 2004).
However, in this paper, we concentrate on the estimation of
tropospheric parameters from ground-based techniques.
A large number of studies have been performed to determine the accuracy of tropospheric parameters that were derived from different ground-based techniques (e.g., Cucurull
and Vandenberghe 1999; Haas et al. 1999; Behrend et al.
2000, 2002; Cucurull et al. 2000; Gradinarsky et al. 2000;
Hatanaka et al. 2001; Niell et al. 2001; Schuh and Boehm
2003). Most of these studies were restricted in terms of the
number of co-location space-geodetic sites investigated, and
the length and continuity of the data set. In this paper, we
focus on a particular continuous Very Long Baseline Interferometry (VLBI) observation campaign that involved eight
globally distributed co-location sites during 15 days from
October 16 to 31, 2002, the ContinuousVLBI 2002 (CONT02)
campaign (Thomas and MacMillan 2003). In addition to earlier studies, we include observational results obtained from
the Doppler Orbitography Radiopositioning Integrated by
Satellite (DORIS) system (Tavernier et al. 2003). We also
take this opportunity to test different DORIS analysis strategies in order to investigate their real impact on the precision
of the derived tropospheric products.
The goal of the CONT02 campaign was to observe a long
time-series of the highest quality geodetic data that VLBI
can provide. CONT02 was a follow-on of previous similar
VLBI campaigns (CONT94, CONT95, CONT96) of which
the goals were to acquire the best-possible VLBI data over a
period much longer than the usual 24-h sessions in order to
demonstrate the highest accuracy of VLBI products such as
the Earth orientation parameters (Chao et al. 1996; Gipson
1996) or tropospheric delays (this study). The goal of this
paper is to determine an estimate of the actual precision of
the different zenith delays and to perform a comparison of
all available space-geodetic techniques that were co-located
with CONT02 VLBI radio telescopes and are able to deliver
estimations of the tropospheric parameters.
This section of the paper provides some necessary background and gives a general overview of the different data
types available. It also discusses some general aspects related to modeling zenith delays. Section 2 focuses on details
inherent to each technique, and Sect. 3 presents, compares
and analyzes the results obtained. Table 1 gives an overview of the VLBI stations involved in CONT02 and displays
information on the co-locations with Global Positioning Sys-
WVR
–
–
–
Radiometrix
–
Astrid
–
Radiometrix
tem (GPS) receivers, DORIS beacons and Water Vapor Radiometer (WVR) instruments.
While it is easy to co-locate GPS receivers with all VLBI
sites, it is more challenging in the case of DORIS due to
the technique itself. In particular, even with the new types
of multi-channel DORIS receivers, the number of DORIS
beacons in the same region of the world is still limited.
This is due to possible radio-interferences affecting the receiver on-board the satellite as the Doppler effects from two
DORIS ground stations could still be too close to be distinguished (Tavernier et al. 2002). Furthermore, one of the two
DORIS frequencies (2.4 GHz) is rather close to the VLBI Sband, which could generate interference between the DORIS
ground-transmitted signal and theVLBI ground-recorded signal. This usually justifies a specific type of DORIS installation taking advantage of natural protection by topography
or using pass-driven selection devices to forbid any DORIS
transmission during VLBI observations (Willis et al. 2005a).
Due to these operational limitations and to the distinct geographical distribution of VLBI radio telescopes (mostly in
the Northern Hemisphere), the number of DORIS antennas
co-located with VLBI sites is limited to 11 co-locations.
Table 2 shows the approximate latitude and longitude of
the eight sites participating in the CONT02 campaign, as well
as the ellipsoidal heights of all techniques and the approximate horizontal distances between the VLBI reference point
and reference points of the other co-located techniques. This
information is important to make sure that the same troposphere is seen by all techniques and that a proper correction
can be applied for the differential zenith delay.
At all eight sites used in this study, zenith delays can
be derived from VLBI and GPS measurements and from a
numerical weather model. At four sites, zenith delays can
also be determined from DORIS observations during satellite passes. Furthermore, at three sites, wet tropospheric delays can be derived from the observations with the co-located
WVR instruments. It must be noted that the distances between
the VLBI and DORIS antennas are much larger than between
the VLBI and GPS antennas, because of the technical limitations discussed above.
All space-geodetic techniques (GPS, VLBI, and DORIS)
use microwaves, which are subject to the same tropospheric
refraction. Usually, the tropospheric delays are modeled using
(e.g., Davis et al. 1985)
(1)
L (e) = Lzh · mfh (e) + Lzw · mfw (e) ,
Multi-technique comparison of tropospheric zenith delays derived during the CONT02 campaign
Table 2 Coordinates (ITRF2000) of the geodetic VLBI stations involved in the CONT02 campaign. Additionally, the ellipsoidal heights of the
co-located GPS and Doppler Orbitography Radiopositioning Integrated by Satellite (DORIS) antennas and the horizontal distances with respect
to the VLBI antenna are given
VLBI Station
Country
Algonquin Park
Gilmore Creek
Hartebeesthoek
Kokee Park
Ny-Ålesund
Onsala
Westford
Wettzell
Canada
USA
S. Africa
USA
Norway
Sweden
USA
Germany
Latitude Longitude VLBI height GPS height DORIS height VLBI–DORIS VLBI–GPS VLBI–WVR
(deg.)
(deg.)
(m)
(m)
(m)
distance (m)
distance (m) distance (m)
46
65
−26
22
79
57
43
49
282
213
28
200
12
12
289
13
224.0
332.1
1415.7
1177.6
87.3
59.3
86.8
669.1
200.9
319.0
1414.2
1167.4
78.5
45.6
85.0
666.0
–
339.6
1559.4
1165.7
52.6
–
–
–
–
1166
2244
389
1475
–
–
–
111
93
165
46
112
78
58
139
–
–
–
* ∼50
–
78
–
* ∼30
*Unfortunately, the exact location of the Water Vapour Radiometer (WVR) at Wettzell and Kokee Park was not available
Table 3 Ellipsoidal height differences between VLBI and GPS/DORIS antennas and the corresponding tropospheric offsets for the total zenith
delays derived from European Centre of Medium-Range weather Forecasts (ECMWF) pressure level data for CONT02
VLBI station
VLBI–GPS height
difference (m)
GPS tropospheric
offset (mm) w.r.t. VLBI
VLBI–DORIS
height difference (m)
23.1
13.1
1.5
10.2
8.8
13.7
1.8
3.1
7.07
3.86
0.41
3.19
2.71
4.29
0.56
0.93
–
−7.5
−143.7
11.9
34.7
–
–
–
Algonquin Park
Gilmore Creek
Hartebeesthoek
Kokee Park
Ny-Ålesund
Onsala
Westford
Wettzell
where the total tropospheric delay in the zenith direction Lz
is defined as the integral over the total refractivity N between
the station height H and the highest part of the neutral atmosphere.
∞
z
z
z
−6
N (z) · dz
(2)
L = Lh + Lw = 10
H
The total delay L(e) at an elevation angle e is the sum
of a hydrostatic and a wet part Lh and Lw . Each of them
is the product of the delay in the zenith direction and the corresponding mapping function mfh,w , which maps the zenith
delay to a certain elevation angle e. Whereas the hydrostatic
zenith delay is assumed to be known from locally observed
pressure values recorded at each VLBI site (accuracy below
1 mm if pressure values are better than 0.5 hPa) or from a standard atmosphere model (accuracy at the cm level), the wet
zenith delays are estimated with the classical least-squares
method (Gauss Markov model) or filter analysis, using the
wet mapping function mfw as a partial derivative. Details
about the particular estimation strategies applied by each
technique are discussed in Sect. 2.
Since the antennas of the different techniques are located
at different altitudes (see Table 2), the additional zenith delays
for antennas at lower heights have to be accounted for in order
to be able to directly compare the tropospheric delays estimated from the different techniques.
Table 3 summarizes the height differences betweenVLBI,
GPS, and DORIS and the differential total zenith delays as derived from the European Centre for Medium-Range Weather
DORIS tropospheric offset
(mm) w.r.t. VLBI
–
−2.21
−39.66
3.72
10.69
–
–
–
Forecasts (ECMWF) pressure level data by numerical integration using Eq. (2). A height difference of 10 m approximately corresponds to a differential total delay of 3 mm. This
can also be derived from the assumption that the refractivity
N (Eq. 2) is ∼300. For stations at higher altitudes, a value
smaller than ∼3 mm per 10 m is obtained. To get the differential delay between the stations at different altitudes with
an accuracy better than 1 mm, the height difference has to be
known within 3 m.
2 Techniques
The tropospheric parameters used in this investigation are
provided from various institutions that apply different software packages and estimate the tropospheric parameters with
different temporal resolution and using different analysis strategies. Furthermore, some of the data are a combination of
individual solutions. A summary of the data is shown in
Table 4.
2.1 GPS
Since 1997, the IGS (International GNSS (Global Navigation Satellite System) Service) regularly generates a combined tropospheric product in the form of weekly files containing the total zenith delays in 2-h time intervals for the
IGS tracking stations. During the CONT02 campaign, the
IGS tropospheric product was a combination of individual
K. Snajdrova et al.
Table 4 Summary of the data used for the comparisons
Data
Institution
Combination
Software
Estimation interval
total/wet zenith delay
VLBI
GPS
DORIS
a
IVS
b
IGS
c
IGN/JPL
Yes
Yes
No
CALC/SOLVE, OCCAM, QUASAR
Bernese, GIPSY/OASIS II, GAMIT
GIPSY/OASIS II
TZD, WZD
TZD
TZD
WVR (Wettzell, Kokee Park)
WVR (Onsala)
ECMWF
d
No
No
No
RadGrad
RadGrad
1h
2h
per satellite pass
per measurement
30 min
15 min
6h
BKG
OSO
ECMWF
e
WZD
WZD
TZD, WZD
a
International VLBI Service for Geodesy and Astrometry
International GNSS Service
c
Institut Géographique National/Jet Propulsion Laboratory
d
Bundesamt für Geodäsie und Kartographie
e
Onsala Space Observatory
b
solutions submitted by seven IGS Analysis Centers (ACs)
(Beutler et al. 1999). Estimates with formal errors exceeding a limit of 30 mm were not used for the combination.
The combination itself is a two-step procedure that is applied
independently on a site-by-site basis (Gendt 2004).
It has to be mentioned that the IGS ACs use different
cut-off elevation angles from 3◦ to 15◦ , different mapping
functions and different time intervals for the estimation of
the tropospheric delays (temporal resolution from 5 min to
2 h). Additionally, some ACs down-weight the low-elevation
observations, which effectively increase the cut-off elevation
angle. Most of the ACs apply the hydrostatic or wet new mapping function (NMF) (Niell 1996) for the estimation of the
total or wet zenith delay, or they use the mapping function by
Saastamoinen (1973). The precision is at the level of 2 mm
for the weekly biases as well as for the standard deviation at
the two-hourly epochs (Gendt 2004).
2.2 VLBI
The International VLBI Service for Geodesy and Astrometry
(IVS, Schlueter et al. 2002) provides total and wet zenith delays of all IVS-R1 and IVS-R4 sessions since January 2002
(Schuh and Boehm 2003). Additionally, there was a combination of all tropospheric zenith delays determined by seven
ACs specifically performed for the CONT02 campaign. The
combined estimates comprise the total and wet zenith delays at 1-h time intervals and the corresponding meteorological values (total pressure, temperature and relative humidity)
measured at the VLBI stations. Only those hourly combined
estimates were accepted for the final output that fulfilled the
requirement that the difference between the total zenith delays and the wet plus the hydrostatic zenith delays determined
from the pressure values differed by <3 mm.
We would like to point out that the seven ACs used different software packages (Table 4), a different treatment of the
terrestrial reference frame (fixed station coordinates or free
network solutions) and different mapping functions. Six ACs
applied the NMF (Niell 1996) while one AC applied the Vienna Mapping Function (VMF) (Boehm and Schuh 2004).
All ACs used the hydrostatic zenith delays determined from
the pressure values at the stations as a-priori information, and
they estimated the remaining wet zenith delays as continuous
piecewise linear functions.
It has been shown that the standard deviations of the
weekly biases between the estimates of the ACs compared
to their weekly mean value, as well as the standard deviation
of the hourly values of the ACs after removing the weekly
biases, are approximately 2 mm (Schuh and Boehm 2003).
The precision of the tropospheric zenith delays determined
with VLBI is at the 2–4 mm level.
2.3 DORIS
DORIS activities are now performed within the International
DORIS Service (IDS) (Tavernier et al. 2005), even if until
very recently the Institut Géographique National /Jet Propulsion Laboratory (IGN/JPL) Analysis Group was the only
AC to deliver geodetic products on a regular basis, i.e., timeseries of weekly station coordinates after a delay of 3–6 weeks
(Willis et al. 2005b) using the preprocessed DORIS data from
Centre National d’Etudes Spatiales (CNES), France.
For the CONT02 campaign, several estimation strategies
were conducted at the IGN/JPL AC with the Gipsy/Oasis II
software (Webb and Zumberge 1995; Willis et al. 2005a). The
goal was to assess the relative performance of four selected
analysis strategies for deriving tropospheric estimates. In particular, the DORIS wet tropospheric delay was estimated either per satellite pass (typically lasting for 10–20 min) or per
measurement (typically every 10 s), applying constraints or
otherwise (colored noise or random walk process), or even
determining horizontal tropospheric gradients (Bar-Sever et
al. 1998).
In all cases, the Lanyi (1984) mapping function was used
and station coordinates were fixed to ITRF2000 (Altamimi
et al. 2002). The dry tropospheric component was held fixed,
computed from the station altitude only without using information from ground pressure measurements provided in the
DORIS data files. In this study, we will focus on the newly
developed strategies mimicking the current JPL/IGS processing for GPS, where the troposphere parameter is reset at every
Multi-technique comparison of tropospheric zenith delays derived during the CONT02 campaign
Table 5 Different estimation strategies applied for DORIS data processing for the CONT02 campaign
Strategy Random walk
Horizontal gradient
Comment
constraint (over 1 day) (mm) constraint (over 1 day) (mm/day)
A
B
C
D
15
50
15
50
–
–
50
50
Total zenith
tropospheric delay precision (mm)
Current JPL / DORIS strategy
Current JPL / GPS strategy
11.7
8.4
12.4
9.5
Table 6 Offsets (mean values) and standard deviations between DORIS (strategies A, B, C, and D) and VLBI. An outlier rejection of 2.5 times
the standard deviation is used
GILC
HART
KOKE
NYAL
VLBI–DORIS(A) (mm)
VLBI–DORIS(B) (mm)
VLBI–DORIS(C) (mm)
VLBI–DORIS(D) (mm)
−2.7 ± 6.5
+2.5 ± 12.8
−9.3 ± 27.8
+0.3 ± 5.8
−2.4 ± 8.3
+2.7 ± 14.0
−7.2 ± 32.1
+1.5 ± 7.9
−1.8 ± 6.4
+3.8 ± 12.8
−7.2 ± 28.5
+0.6 ± 6.4
−1.5 ± 8.3
+4.0 ± 14.4
−7.1 ± 31.7
+1.8 ± 8.7
epoch by a random walk approach with or without horizontal
gradient estimation. Table 5 describes the different processing strategies that are analyzed here.
All tropospheric estimations from the DORIS data were
done using the same models. The GGM01C GRACE-derived
gravity field (Tapley et al. 2004) was taken for the satellite
orbit determination to improve the geodetic results (Willis
and Heflin 2004). It must also be noted that data from all
DORIS satellites were used during the CONT02 campaign,
except the DORIS/Jason due to an abnormal behavior of the
DORIS oscillator over the South Atlantic Anomaly (Willis et
al. 2004), leaving us in total five available DORIS satellites
for geodetic purposes.
Recent studies show that the DORIS precision of the wet
tropospheric delay is between 5 and 10 mm depending on the
number of available DORIS satellites (Willis et al. 2005a). In
order to test the precision of the DORIS-derived tropospheric
delay during the CONT02 campaign, we derived for each
strategy an estimator that was obtained as follows: all DORIS
data were processed on a daily basis using 30-h arcs (from
21:00 the day before until 03:00 the day after). For all overlapping periods (from 21:00 to 03:00 every day), we compared
the total zenith tropospheric delay derived separately from
the 2 consecutive days for all stations on a pass-per-pass or
on a measurement-per-measurement basis, depending on the
estimation strategy used. This consistency value (column 5 of
Table 5) provides some information on the internal precision
of the DORIS tropospheric results. It does not correspond
to the accuracy of this parameter, but at least it represents a
lower bound on the DORIS accuracy for these products.
Table 5 summarizes the four different strategies that were
applied to determine total zenith delays from DORIS for
CONT02. Two of them (C and D) involve the estimation of
horizontal gradients (Bar-Sever et al. 1998), whereas A and
B do not account for azimuthal asymmetries. Furthermore,
different constraints for the random walk parameters were
also tested, but are not discussed here because the differences were only marginal. Table 6 shows the offsets (mean
values) and the standard deviations between the total zenith
delays estimated from VLBI and those estimated from each
of the four DORIS strategies.
Table 6 shows that the individual DORIS solutions yield
results with rather small offsets compared to VLBI. The current IGN/JPL DORIS strategy B (cf. Table 5) will be used
for further comparisons in Sect. 3. It is surprising to see that
strategies B and D, which allow more variability, provide
a better internal agreement for DORIS (Table 5), but show
larger discrepancies with the VLBI results because of larger
offsets and larger standard deviations. This shows that strategies B and D, by giving more freedom for the estimated
parameters, provide results that are more consistent within
each DORIS solution. However, this does not allow us to get
rid of possible systematic errors which do not get absorbed
in the estimated parameters and that become visible when
compared to VLBI results.
For all four strategies, the station Kokee Park (Hawaii,
USA) shows larger discrepancies (standard deviation of about
3 cm) with VLBI, while at the other three stations the results
from DORIS and VLBI agree at the 1 cm level (Table 6). Figure 1 displays the total zenith delays at Kokee Park estimated
over the whole period of CONT02 with all techniques. The
DORIS results are much worse than those from the other techniques. Even if a few bad points (equivalent to the DORIS
measurement from a whole satellite pass) were eliminated as
outliers, DORIS still shows a much larger dispersion than the
other techniques.
The DORIS equipment at Kokee Park is one of the oldest
in the DORIS tracking network. The log file indicates that it
was installed on September 26, 1990, and equipped with a
generation 1.0 transmitter (KOKA). More recently, the IGN
started a major renovation project concerning the DORIS
network (Willis et al. 2005a). On November 17, 2002 the
old KOKA beacon was replaced by a generation 3.0 beacon
(KOLB), located on a 50 cm metal tower standing on a 7.4 m
reinforced concrete tower with 30 cm thick walls (Fagard
2002), replacing the initial 3 m high guyed tower. Figure 2
displays the improvement in the JPL/IGN DORIS weekly
solutions for the station Kokee Park after this equipment
change. It shows the ellipsoidal heights for Kokee Park from
weekly solutions expressed in ITRF2000: neither drift nor
bias were removed and the connection between the KOKA
and KOLB time-series was realized by directly using the
K. Snajdrova et al.
2300
VLBI
GPS
ECMWF
DORIS
Total Zenith Delay in mm
2250
2200
2150
2100
2050
2000
17
19
21
23
25
Day in October 2002
27
29
31
Fig. 1 Total zenith delays at Kokee Park (KOKA) during CONT02 from Very Long Baseline Interferometry (VLBI, solid line), Global Positioning System (GPS, dotted line), European Centre for Medium-Range Weather Forecasts (ECMWF, dashed line), and Doppler Orbitography
Radiopositioning Integrated by Satellite (DORIS, crosses for epochs)
ered obsolete, and is gradually being upgraded for the whole
DORIS network (Willis et al. 2005a). The completion of this
whole renovation project is expected for the end of 2005.
2.4 WVR
Fig. 2 Weekly DORIS determination of the ellipsoidal height of Kokee
Park (KOKA from January 1, 1993 to November 14, 2002; KOLB from
November 17, 2002 to February 28, 2005)
geodetic local tie information from ITRF2000 (http://itrf.
ensg.ign.fr/ITRF solutions/2000/doc/itrf2000.tie). It can be
seen in Fig. 2 that the geodetic results for station KOKA are
almost three times worse than for the new KOLB station. Due
to this dramatic improvement in precision, an annual signal
is now clearly visible in the Kokee Park heights. Such an
annual signal could have a true geophysical interpretation as
demonstrated by Mangiarotti et al. (2001).
Unfortunately, this equipment change occurred after the
end of the CONT02 campaign. Thus, the DORIS results presented here still suffer from the old equipment (KOKA) and
from the physical instabilities of a 3 m guyed tower located
on a one-story concrete building. This generation 1.0 equipment and installation on a 3 m metallic tower are now consid-
The WVRs used at three sites during the CONT02 campaign
(Table 1) performed continuous and repeating sky scanning
observations at different elevation and azimuth angles. For
theAstrid radiometer operated at Onsala, a complete sky-scan
takes about 12–15 min. During this sky-scan the sky emission at the two frequencies 21.0 and 31.4 GHz is measured
for the tip curve observations. This sky emission is caused
by the amount of water vapor, liquid water and oxygen in
the atmosphere. The radiometer is calibrated using the tip
curve measurements, resulting in an absolute calibration of
the measured sky emission (Elgered 1993).
The retrieval algorithm for the wet delay results is based
on the millimeter propagation model by Liebe (1992). Details
of the retrieval algorithm are described in Elgered (1993),
Jarlemark (1994) and Elgered and Jarlemark (1998). A leastsquares-based post-processing software (RadGrad) is used
to determine the zenith wet delay and gradient parameters
with a temporal resolution of 15 min at Onsala and 30 min at
Wettzell and Kokee Park. (Radiometrix WVRs are operated
at Wettzell and Kokee Park.) RadGrad is an unpublished inhouse software of the Onsala Space Observatory and applies
the gradient model described by Davis et al. (1993).
2.5 ECMWF
For the investigations presented here, the operational analysis pressure level data set of the ECMWF is used. It provides
heights, temperature and humidity values at 21 pressure levels (from 1,000 up to 1 hPa), at 6-h time intervals and with an
Multi-technique comparison of tropospheric zenith delays derived during the CONT02 campaign
Table 7 Number of common epochs of GPS, DORIS, WVR, and ECMWF with VLBI
Algonquin Park
Gilmore Creek
Hartebeesthoek
Kokee Park
Ny-Ålesund
Onsala
Westford
Wettzell
GPS
DORIS
WVR
ECMWF
162
177
173
172
177
172
162
165
–
170
61
64
218
–
–
–
–
–
–
210
–
267
–
267
35
57
52
56
54
54
46
48
internal computational resolution of ∼ 0.3◦ . After increasing
the vertical resolution from 21 levels to about 1,000 levels up
to 140 km (Rocken et al. 2001), the total and wet zenith delays
were derived by numerical integration through the refractivity N, which can be separated into a hydrostatic part Nh and
a wet part Nw (Davis et al. 1985).
N = Nh + Nw
R
pw −1
pw
Zw + k3 2 Zw−1 .
Nh + Nw = k1 ρ + k2
md
T
T
(3)
In Eq. (3), k1 , k2 and k3 are empirically determined values
(Bevis et al. 1994), R is the universal gas constant, md is the
molar mass of dry air, and Zw is the compressibility factor
of wet air (Owens 1967). The temperature T is in Kelvin and
the water vapor pressure pw is in hPa, and the total atmospheric density ρ can be determined from the meteorological
parameters pw , T, and the total pressure p.
3 Data analysis
The zenith delays from VLBI, GPS, and ECMWF are available at integer hours in 1, 2, and 6-h intervals, respectively.
The results of the Astrid WVR at Onsala are given with a
temporal resolution of 15 min and the estimates from the
two Radiometrix WVRs with a resolution of 30 min. On the
other hand, the estimates from DORIS correspond to distinct epochs of actual measurements during the DORIS satellite passes. Therefore, in a first step, the zenith delays from
DORIS are linearly interpolated to adjacent integer hours.
This interpolation is only performed for those integer hours
when the time difference between the last observation before and the first observation after the integer hour is less
than 1 h, or in other words, there is at least one observation
within 30 min of the interpolated epoch. The numbers of common epochs between the different techniques can be found in
Table 7. Then, the offsets and standard deviations between
each pair of techniques were determined.
The sign of the offsets always refers to the order of: VLBI,
GPS, ECMWF, DORIS, WVR, e.g. VLBI minus GPS. All
estimates that either have a formal error larger than 8.5 mm
for VLBI, GPS, DORIS or which deviate from the mean
value at a common epoch by more than three times the standard deviation were rejected as outliers. After this, the offsets (mean values) and standard deviations were determined
again. While there are approximately 170 common epochs after outlier rejection for VLBI with GPS (2-h time intervals),
and 50 for ECMWF with VLBI or GPS (6-h time intervals),
the number of common epochs for DORIS and WVR differ
for the different CONT02 stations.
The DORIS stations in Gilmore Creek (Fairbanks,Alaska,
USA) and in Ny-Ålesund (Spitsbergen, Norway) provide
more data as their latitudes are closer to the inclination of the
TOPEX satellite (Morel and Willis 2002). Figure 3 displays
the total zenith delays from VLBI, GPS, DORIS, and ECMWF at station Ny-Ålesund for CONT02. It can be seen that
the DORIS results are relatively more consistent (Table 9)
with results from the other techniques than those presented
above for Kokee Park (cf. Fig. 1). For example, four histograms for Ny-Ålesund are given in Fig. 4. (WVR data from
Ny-Ålesund were not available.)
Table 8 shows the mean offsets and standard deviations
for the total zenith delays for all stations. In the case of the
WVRs, the total zenith delays have been determined from the
observed wet zenith delays plus the hydrostatic zenith delays
from VLBI. It has to be mentioned here that the offsets would
differ by up to 5 mm if median values were used instead of
mean values. This is particularly valid for offsets with relatively high standard deviations indicating that there might
still be outliers in the data.
In Table 8, the offsets between the total zenith delays
from VLBI and GPS are negative for most of the CONT02
stations. This supports previous findings reported by Behrend
et al. (2000, 2002) for a restricted number of space-geodetic
stations in Europe equipped with co-located techniques, by
Niell et al. (2001) for a co-located station in North America, and by Schuh and Boehm (2003) for globally distributed sites. It can be partly explained by the fact that, for the
IGS combination, the absolute phase center models for the
GPS satellites (Schmid and Rothacher 2003) were not used.
Further deviations might be due to radomes for some GPS
antennas (Hatanaka et al. 2001; Rothacher, personal communication).
The comparison between ECMWF total zenith delays
and the VLBI and GPS techniques reveals systematic biases up to 16 mm, with varying signs (Table 8). No preferred
sign for the biases can be detected; however, the signs of
the biases appear to be station-dependent. Previous studies
with the HIRLAM (Källén 1996) and MM5 (Dudhia et al.
2001) high-resolution numerical weather prediction (NWP)
models for a restricted number of European stations showed
K. Snajdrova et al.
2400
VLBI
GPS
ECMWF
DORIS
2380
Total Zenith Delay in mm
2360
2340
2320
2300
2280
2260
288
290
292
294
296
298
Day in 2002
300
302
304
306
Fig. 3 Total zenith delays at Ny-Ålesund during CONT02 from VLBI (solid line), GPS (dotted line), ECMWF (dashed line), and DORIS (crosses
for epochs)
VLBI – ECMWF
Number of common epochs
Number of common epochs
VLBI – DORIS
60
Total number of common epochs: 218
40
20
0
–30
–20
–10
0
10
20
30
25
Total number of common epochs: 54
20
15
10
5
0
–30
–20
Total number of common epochs: 177
100
50
0
–30
–20
–10
0
10
Differences in mm
0
10
20
30
GPS – DORIS
150
Number of common epochs
Number of common epochs
VLBI – GPS
–10
20
30
30
Total number of common epochs: 109
20
10
0
–30
–20
–10
0
10
Differences in mm
20
30
Fig. 4 Histograms for differences of total zenith delays at Ny-Ålesund during CONT02 between VLBI and the other techniques (in mm)
systematically negative biases between space-geodesy and
NWP (Behrend et al. 2000, 2002). It was not possible to calculate offsets and standard deviations between ECMWF and
DORIS at Kokee Park (KOKA) and Hartebeesthoek because
the number of common epochs was too small (<10) to provide
any conclusive results.
In order to be able to compare GPS and DORIS, which
yield only total zenith delays with WVR providing only wet
zenith delays, we added the hydrostatic part derived from
VLBI to the wet zenith delays from WVR. The comparison
of VLBI and GPS results with the WVR results (Table 8)
always shows negative biases for all three stations. The comparison of DORIS to WVR results also reveals negative biases. This might indicate that WVR measures systematically
larger wet delays than the space-geodetic techniques. However, this contradicts to some extent earlier findings reported
by Behrend et al. (2000, 2002) and Niell et al. (2001).
The offsets between the DORIS solutions and VLBI are
rather small compared to the standard deviations between the
techniques at the co-located sites (Table 8). Furthermore, the
Multi-technique comparison of tropospheric zenith delays derived during the CONT02 campaign
Table 8 Mean offsets and standard deviations of the total zenith delays in mm between VLBI, GPS, ECMWF, DORIS, and WVR. The hydrostatic
zenith delays from VLBI were added to the wet zenith delays to obtain the total zenith delays for WVR
VLBI–GPS
VLBI–ECMWF
VLBI–DORIS
VLBI–WVR
GPS–ECMWF
GPS–DORIS
GPS–WVR
ECMWF–DORIS
ECMWF–WVR
DORIS–WVR
nyal
koke
gilc
hart
algo
onsa
west
wett
+0.1±3.3
+7.1±4.7
+1.5±7.9
−5.7±6.6
−8.8±21.0
−7.2±32.1
−17.9±12.4
−1.9±17.4
+2.7±34.7
−11.9±11.6
−0.3±3.5
−8.4±12.6
−2.4±8.3
−3.4±5.8
−4.8±19.4
+2.7±14.0
0.0±3.8
−11.8±3.4
+0.7±4.1
+8.1±5.7
−6.5±3.5
−16.2±5.9
−2.1±4.5
+13.2±8.8
−8.3±11.8
−1.5±8.7
−0.3±18.6
+5.5±14.5
−9.8±2.1
−2.8±6.7
+7.6±5.5
−9.1±7.1
−17.2±9.0
+15.1±7.8
+6.6±3.5
+1.2±8.1
−6.8±8.5
−7.7±23.6
−10.0±34.4
+8.3±12.6
−3.7±5.4
−14.7±8.1
−11.7±10.2
−26.2±7.5
Table 9 Correlation coefficients between the total zenith delays derived from the different techniques. In brackets are the coefficients without the
DORIS station at Kokee Park
VLBI–
GPS
0.99
VLBI–
ECMWF
0.93
VLBI–
DORIS
0.90 (0.94)
VLBI–
WVR
0.94
GPS–
ECMWF
0.94
GPS–
DORIS
0.89 (0.94)
GPS–
WVR
0.95
ECMWF–
DORIS
0.91 (0.91)
ECMWF–
WVR
0.84
DORIS–
WVR
0.39 (−)
standard deviations at KOKA are worse than at the other stations (also see Table 6) due to the old type of DORIS beacon
and improper installation as discussed in Sect. 2.3.
Correlation coefficients were also determined between
the results obtained from the different techniques (Table 9).
A very high correlation of 0.99 is observed between the tropospheric zenith delays from VLBI and GPS. The correlation
between GPS and VLBI with DORIS (neglecting KOKA),
ECMWF and WVR is between 0.93 and 0.95. When the
DORIS results at KOKA are included in the comparisons, the
correlation coefficients with respect to VLBI and GPS reduce
to 0.90 and 0.89. The correlation coefficient between results
from DORIS and WVR is much lower and only reaches 0.39.
However, one has to keep in mind that only the station
KOKA had the co-located DORIS and WVR equipment, so
this result is based entirely on the DORIS observations at
KOKA, which are unfortunately of low quality as shown before. If the correlation coefficient between DORIS and WVR
is not considered, the coefficient between ECMWF and WVR
is the lowest (0.84), which might be due to the fact that the
highly variable wet part in the atmosphere cannot be modeled
perfectly with a numerical weather model of a certain spatial
resolution.
range of 3–7 mm. The worst agreements in terms of standard
deviations are at Kokee Park (KOKA) and Hartebeesthoek,
which also hold true for the comparisons with and between
the other techniques. There are high temperature and humidity changes at both of these stations, probably causing larger
differences than at other sites. Comparisons of zenith delays
derived from ECMWF with space-geodetic techniques also
show a rather good agreement, except at the two stations
mentioned above and at Gilmore Creek, where the standard
deviation is not as high as at Kokee Park and Hartebeesthoek,
but is still in the level of about 1 cm.
The DORIS results are at an accuracy level worse by a
factor of 2–3 for most of the stations due to the relatively poor
satellite constellation. Nevertheless, it can provide valuable
information about the troposphere, in particular for regions
where no other space-geodetic measurements are available.
The comparison with other space-geodetic techniques also allowed testing of different DORIS analysis strategies. The biases between VLBI and DORIS determined for the CONT02
campaign are very small. This is an indication that DORIS
provides unbiased results that could be interesting for climate
studies due to the long-term stability of the DORIS network.
In the case of Kokee Park, it is expected that future results,
based on the new KOLB station, should be considerably improved.
4 Discussion and conclusions
Acknowledgements The DORIS solutions were carried out at the JPL,
California Institute of Technology, under a contract with the National
Aeronautics and Space Administration. We would also like to thank the
Zentralanstalt für Meteorologie und Geodynamik in Austria for providing us access to the ECMWF data and the Austrian Science Fund
(FWF) (project P16992-N10) for supporting this work. All the various
institutions that contributed to the CONT02 campaign within the IVS
for Geodesy and Astrometry or which provided additional Water Vapor
Radiometer data (Bundesamt für Kartographie und Geodäsie and Onsala Space Observatory) are greatly acknowledged. We are also grateful to the IGS and the IDS for providing their data. Finally, we like to
thank Mattia Crespi and an anonymous reviewer for their very useful
comments.
It should be pointed out that the study presented here was
the first worldwide comparison of three space-geodetic techniques, WVR measurements and data from the ECMWF for
a continuous time period of 15 consecutive days. While there
is a good agreement between the space-geodetic techniques
(with some problems with DORIS), the comparison with
ground WVR and ECMWF is at a lower accuracy level.
The comparison between GPS and VLBI, as the two obviously most precise techniques, yields height accuracies in the
K. Snajdrova et al.
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