Atmospheric loading coefficients from homogeneously
reprocessed long-term GPS and VLBI height time series
[email protected]
V. Tesmer1, P. Steigenberger2, B. Meisel1, M. Rothacher2
Geodätisches Forschungsinstitut, Germany, 2GeoForschungsZentrum, Germany
1Deutsches
INTRODUCTION & MOTIVATION
RESULTS
What: Overall scope of the paper is to better understand how the
quality of station position time series improves, if latest high-end
models are used in geodetic data analysis (if possible to judge:
are they more directly interpretable in a geophysical sense?).
Iteration 1:
both series fully reprocessed
VLBI and GPS homogenized
but partially with simple models
(further description see “DATA”)
How: To judge if series improve, the following criteria were
applied to two GPS and VLBI height time series:
WTZR vs. WETTZELL: medians (each 7 days for −+35 days)
dR [cm]
dR [cm]
1997
1998
1999
2000
time [year]
2001
2002
2003
2004
2005
1997
1998
1999
2001
2002
time [year]
2003
2004
2005
2006
1
VLBI
GPS
0
dR [cm]
dR [cm]
2000
NYAL vs. NYALES20: medians (each 7 days for −+35 days)
NYAL vs. NYALES20: medians (each 7 days for −+35 days)
VLBI
GPS
0
−1
−1
1995
1996
1997
1998
1999
2000
time [year]
2001
2002
2003
2004
1996
2005
1998
2000
2002
time [year]
2004
2006
Fig. 2: Examples of median smoothed mean annual behaviour (all data assumed to be in 1 year);
NyAlesund (upper left), Tsukuba (upper right), Fortaleza (lower left), Algonquin (lower right).
−0.2
0.1
0.2
0.3
0.4 0.5 0.6
fraction of year
0.7
0.8
−0.2
0.1
0.6
0.4
0.2
0.3
0.4 0.5 0.6
fraction of year
0.7
0.8
0.1
0.6
0.4
0.2
dR [cm]
VLBI
GPS
0
−0.2
−0.4
VLBI
GPS
0
−0.2
0.2
0.3
0.4 0.5 0.6
fraction of year
0.7
0.8
0.2
0.3
0.4 0.5 0.6
fraction of year
0.7
0.8
0.9
0.1
FORT vs. FORTLEZA: medians (each 7 days for −+35 days)
0.1
0.2
0.3
0.4 0.5 0.6
fraction of year
0.7
0.8
0.2
0.3
0.4 0.5 0.6
fraction of year
0.7
0.8
0.9
ALGO vs. ALGOPARK: medians (each 7 days for −+35 days)
0.6
0.4
0.2
VLBI
GPS
0
−0.2
−0.4
0.9
Similarity of annual harmonics in GPS / VLBI series:
Figure 3 illustrates the harmonic annual signals estimated from the
GPS and VLBI height time series. The WRMS of the differences
in phase and amplitude clearly improves with iteration 2 (iteration
1 / 2: WRMS amplitude 2.2 / 1.7 mm, WRMS phase 44 / 38 deg).
VLBI
GPS
0
−0.2
0.4
0.2
−0.4
0.1
0.2
−0.4
0.9
ALGO vs. ALGOPARK: medians (each 7 days for −+35 days)
0.2
VLBI
GPS
0
−0.2
−0.4
0.9
0.1
0.2
0.3
0.4 0.5 0.6
fraction of year
0.7
0.8
0.9
0.1
0.2
0.3
0.4 0.5 0.6
fraction of year
0.7
0.8
0.9
Similarity of GPS / VLBI estimated atmo-loading coeffients:
As shown in figure 4, the GPS- and VLBI-derived coefficients
(∆height = coefficient * ∆pressure) generally coincide much better
in iteration 2. The WRMS of the GPS-VLBI differences improves
from 0.13 to 0.08 [mm/mbar] from iteration 1 to 2. Additionally,
most of the coefficients of iteration 2 are closer to the values
published by the IERS GGFC (Global Geophysical Fluids Center).
Fig. 3: Annual harmonic signals estimated from the full GPS and VLBI height time series;
the arrows illustrate the estimated amplitudes and phases of all 17 stations considered to
have appropriate data, grey are the corresponding formal errors.
80
80
60
60
40
40
20
φ[deg]
φ[deg]
20
0
VLBI
GPS
−20
−40
0
VLBI
GPS
−20
jan
oct
5 mm
ANNUAL
MAXIMUM
−40
apr
jul
−60
jan
oct
5 mm
ANNUAL
MAXIMUM
apr
jul
−60
−80
−80
−150
−100
−50
0
λ[deg]
50
100
−150
150
−100
−50
0
λ[deg]
50
100
150
Fig. 4: Atmospheric loading coefficients: the estimated values for GPS and VLBI are given
together with the coefficients published by the GGFC (all shown with their formal errors,
the formal errors of the GGFC coefficients are very small).
0.2
0.2
0
−0.2
mm per mbar
0
−0.2
−0.4
−0.6
VLBI
GPS
GGFC
−0.8
−0.4
−0.6
VLBI
GPS
GGFC
−0.8
R
B
TSK
WES
2
WTZ
AO
1
AGU Fall Meeting, San Francisco, December 10-14, 2007
SH
AL
SA
PIE
ON
I
B
NLI
MED
NY
TE
O1
MA
MD
B2
KB
AO
HO
KO
IR
RT
FA
FO
HR
O
ALG
2
WES
WTZ
R
1
B
AO
TSK
SH
AL
SA
PIE
NY
ON
I
B
NLI
TE
O1
MED
MD
B2
KB
MA
AO
HO
HR
KO
FA
IR
−1
RT
−1
Similarity of the mean GPS / VLBI annual behaviour:
Figure 2: to uncover annually repeating patterns (not necessarily
harmonic), all data of one station was assumed to be in one year.
For 8 out of the 17 sites under investigation, like NyAlesund (upper
left) and Tsukuba (upper right), the advanced modelling of iteration
2 significantly improves the similarity of the GPS and VLBI signal.
Especially the VLBI series is stabilized.
The GPS-VLBI-similarity for some of the sites (5 out of 17), like
Fortaleza (lower left) does not change much.
For few sites (4 out of 17) like Algonquin (lower right), the similarity slightly degrades with iteration 2.
0.4
−0.4
0.9
TSKB vs. TSUKUB32: medians (each 7 days for −+35 days)
0.6
VLBI
GPS
0
−0.4
FORT vs. FORTLEZA: medians (each 7 days for −+35 days)
NYAL vs. NYALES20: medians (each 7 days for −+35 days)
0.2
dR [cm]
VLBI
GPS
0
−0.4
dR [cm]
0.6
0.4
0.2
dR [cm]
dR [cm]
−0.2
0.6
TSKB vs. TSUKUB32: medians (each 7 days for −+35 days)
0.4
VLBI
GPS
0
dR [cm]
0.6
0.2
dR [cm]
NYAL vs. NYALES20: medians (each 7 days for −+35 days)
0.4
dR [cm]
0.6
FO
∆height [mm] = coefficient [mm/mbar] * ∆pressure [mbar]
VLBI
GPS
0
−1
1
mm per mbar
Pressure data: In order to estimate the atmospheric loading
coefficients, pressure time series at each site were derived from
the ECMWF (thanks to J. Boehm!) for both techniques:
1
VLBI
GPS
0
−1
DATA
Geodetic data: We used GPS and VLBI height time series with
daily resolution (data from 94-07):
Iteration 1: Both series are fully reprocessed and the a priori
models were homogenized in both softwares used (GPS:
Bernese 5.1 @ GFZ, VLBI: OCCAM 6.1 @ DGFI); Nevertheless not all models were state of the art (e.g. NMF, constant a
priori ZD ...).
Iteration 2: Besides the efforts in iteration 1, all models were
updated according to the latest state of knowledge (e.g. VMF1,
apriori ZD from ECMWF, thermal deformation for VLBI, the
VLBI ZD was estimated in full UTC hours as for GPS ...).
Similarity of GPS / VLBI series concerning episodic patterns:
The upper panel of figure 1 (Wettzell) illustrates the maximum
similarity possible if the modelling is carefully adapted.
If besides, the models are state of the art (iteration 2), episodic
height changes become clear in both techniques for many
stations (e.g. NyAlesund, lower panel).
WTZR vs. WETTZELL: medians (each 7 days for −+35 days)
1
O
The critical points of this investigation are:
to find objective criteria for VLBI & GPS similarity and
to find out if a possible improvement of VLBI & GPD
similarity could directly be translated to a better “geophysical
interpretability”.
Iteration 2:
same as iteration 1, but with
enhanced modelling (further
description see “DATA”)
Fig. 1: Median smoothed GPS and VLBI height time series; the given examples are series
of the stations Wettzell (upper panel) and NyAlesund (lower panel).
ALG
similarity of the two techniques’ series concerning episodic patterns
(figure 1),
similarity of the mean GPS and VLBI annual behaviour, so that all
data is assumed to be in one year (figure 2),
similarity of annual harmonics estimated from the GPS and VLBI
height series (figure 3),
similarity of atmospheric loading coefficients estimated independently from both techniques, using homogeneous ECMWF
pressure time series (figure 4).
DISCUSSION
CONCLUSIONS
The enhanced similarity of the annual patterns in GPS and VLBI
height series suggests that iteration 2 allows “better” modelling.
However, this could still be induced by shortcomings of the new,
homogeneously implemented correction models.
Nevertheless, the complex pressure signal found in GPS and VLBI
in iteration 2 was also more similar, which indicate the latest
software updates to be steps towards an improved interpretability
of geodetic station height time series.