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The paper presents the results of research related to the application of GNSS solutions in short observational periods in geodynamical investigations. Authors used the 3-hour solution appointed from hour-long interval of about 30 chosen stations on mountainous terrains from over 100 which were worked out. The main aim was to check the correctness of such solutions by the comparison with the daily ones. Some outliers in East component could testify, that tropospheric or ionospheric models used in the data adjustment are not sufficient for so short-time solutions. The second principal problem, which was considered in the present work is the ability to detect diurnal and sub-diurnal oscillations in changes of permanent stations' coordinates. Results show unambiguously, that such oscillations appear in all analysed stations. In the paper there are examples of stations with dominant oscillations in different frequencies. The clear homogeneous in the frequencies was not found among any group of stations. It is therefore difficult to affirm, if their origin comes purely from the geodynamical phenomena. surface provided by gravity satellite missions. It shows that a variety of sensor systems, mission characteristics, and tracking systems have to be combined with utmost precision (Plag and Pearlman, 2009). The interconnections between mass transport processes, and the relations between observable parameters of gravity and geometry and the different processes are sketched in Figure 2.
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Acta Geodyn. Geomater., Vol. 7, No. 3 (159), 295–302, 2010
APPLICATION OF SHORT-TIME GNSS SOLUTIONS
TO GEODYNAMICAL STUDIES
Andrzej ARASZKIEWICZ *, Janusz BOGUSZ, Mariusz FIGURSKI
and Karolina SZAFRANEK
Centre of Applied Geomatics, Military University of Technology, Gen. S. Kaliskiego 2, 00-908 Warsaw,
p
hone: (+48) 22-70-77
*Corresponding author‘s e-mail: aaraszkiewicz@wat.edu.pl
(Received January 2010, accepted May 2010)
ABSTRACT
The paper presents the results of research related to the application of GNSS solutions in short observational periods i
n
geodynamical investigations. Authors used the 3-hour solution appointed from hour-long interval of about 30 chosen stations
on mountainous terrains from over 100 which were worked out. The main aim was to check the correctness of such solutions
by the comparison with the daily ones. Some outliers in East component could testify, that tropospheric or ionospheric models
used in the data adjustment are not sufficient for so short-time solutions. The second principal problem, which was considere
d
in the present work is the ability to detect diurnal and sub-diurnal oscillations in changes of permanent stations’ coordinates.
Results show unambiguously, that such oscillations appear in all analysed stations. In the paper there are examples of stations
with dominant oscillations in different frequencies. The clear homogeneous in the frequencies was not found among any
group of stations. It is therefore difficult to affirm, if their origin comes purely from the geodynamical phenomena.
KEYWORDS: ASG-EUPOS, short-time solutions, frequency analysis, periodic signals
surface provided by gravity satellite missions. I
t
shows that a variety of sensor systems, mission
characteristics, and tracking systems have to be
combined with utmost precision (Plag and Pearlman,
2009). The interconnections between mass transport
p
rocesses, and the relations between observable
p
arameters of gravity and geometry and the differen
t
processes are sketched in Figure 2.
MOTIVATION
Most of the phenomena pointed out in Figure 2
could be detected through the satellite observations
(navigational, altimetric and gravimetric as well). Bu
t
in the time resolution diurnal, sub-diurnal and
instantaneous effects are very difficult to be monitored
from space. In case of GNSS observations the
problem lies in the time Windows which is used
for precise ambiguity determination. Usually it is
24 hours which yields daily solutions. In order to
evaluate shorter time resolution and research the
short-time phenomena the length of the window has to
be reduced as much as possible. Additionally the
overlapping has to be applied even though it could
implement many correlations into the results.
DATA ADJUSTMENT
In order to determine the stations’ positions the
data from ASG-EUPOS (Polish Active Geodetic
N
etwork) was used. ASG-EUPOS multifunctional
precise satellite positioning system established by the
INTRODUCTION
N
owadays geodetic space techniques have
reached a level of precision that make them an
important tool for Earth system sciences. Importan
t
added-value and new areas of application will resul
from a combination of the fundamental three types o
f
geodetic parameters: surface geometry, Earth rotation
and gravity. This is what GGOS (Global Geodetic
Observing System) intends to provide. Examples o
f
this modern development are detection an
d
monitoring of tectonic, ice and ocean motion, the
determination of mass anomalies and implicitly
density anomalies, observation and quantification o
f
mass transport processes in the hydrosphere and in the
oceans, estimation of global and regional mass
changes in the Earth components, separation of the
thermal and mass components of sea level change,
ionospheric and tropospheric sounding (Plag an
d
Pearlman, 2009).
The quantities to be delivered from the
combination of the three fundamental pillars
geometry, gravity/geoid, Earth rotation are small and
therefore difficult to determine. In order to be useful
for global change studies they have to be derived free
of bias and consistently in space and time. In general
they are derived from the combination o
f
complementary sensor and observation systems. Fo
r
example, dynamic ocean topography is to be derived
from the accurate measurement of the ocean surface
by radar altimetry in combination with a geoid
A. Araszkiewicz et al.
296
Fig. 1 Interconnections between processes and research themes related to mass
transport and mass distribution (Plag and Pearlman, 2009).
Fig. 2 Mass transport phenomena and mass distribution characteristics.
APPLICATION OF SHORT-TIME GNSS SOLUTIONS TO GEODYNAMICAL STUDIES
.
297
Fig. 3 Adjusted GPS network (www.asgeupos.pl).
Table 1 Data processing strategy and applied models.
Orbit: IGS precise final orbit
Troposhere: Saastamoinen – based dry component
Wet-Niell mapping function
Ionoshere: CODE global iono models
ionoshere-free linear combination
Ambiguity: QIF strategy
L3/L5 – for baselines shorter than 100km
L1/L2 – for baselines shorter than 20km
Planetary ephemeris: DE40
Solid Earth tides: IERS2003
Ocean tides: OT_CSRC
Earth geopotential model: JGM3
Nutation model: IERS2000
Ocean loading model: FES2004
Head Office of Geodesy and Cartography in 2008. I
t
consists of:
84 Polish sites with GPS module;
14 Polish sites with GPS/GLONASS module;
20 foreign sites.
The adjusted network consisted of over 100
stations (Fig. 3), the period covered observations
collected from 10.01.2009 to 25.03.2009.
The Bernese software v. 5.0 was used (Dach
et. al., 2007) with elevation angle cutoff - 3 degrees
and elevation dependent weighting using cos(z).
The same strategy as in EPN (EUREF Permanen
t
GNSS Network)
p
rocessing was applie
d
(www.epncb.oma.be). The particular models are
presented in Table 1.
Only GPS observations (RINEX format) were
used with carrier phase as a basic observable (double-
differences, ionosphere-free linear combination) with
reference (datum) to several EPN stations (BOR1,
WTZR, METS, POTS, ONSA).
A. Araszkiewicz et al.
298
Fig. 4 Stations considered in this elaboration.
Fig. 5 Comparison of daily (black) and hourly
(gray) solutions (GANP station).
VALIDATION OF THE RESULTS
Short-term solutions are less reliable than diurnal
ones
b
ecause of the problems with ambiguity
determination. The examination of the correctness
depended on comparison between diurnal and hourly
solutions for the same period. Figure 5
p
resents such
a comparison for all three components for GANP
(Poprad Ganovce, Slovakia) station.
In order to obtain short-time solutions the 3-hou
r
window with 1-hour shift was applied. From over 100
stations for further analyses the mountainous sites
were chose, because there the biggest geodynamical
effects were expected. They were (Fig. 4):
7 Czech;
6 Slovak;
20 Polish.
APPLICATION OF SHORT-TIME GNSS SOLUTIONS TO GEODYNAMICAL STUDIES
.
299
Table 2 Standard deviations of the chosen stations’ coordinates from 3-hour solution.
Site σB [mm] σL [mm] σH [mm]
CBRU 2.4 4.5 5.6
CLIB 4.5 6.9 9.1
CSUM 2.4 3.5 7.3
WLBR 3.9 5.1 8.4
SKSK 5.1 7.2 12.8
SKSL 4.7 4.5 10.2
JLGR 2.8 3.3 6.9
used. Because of the obtained results the adjuste
d
stations were divided into several groups:
sites with almost no oscillations,
sites with strong long-period changes,
sites with no dominant oscillation,
sites with dominant diurnal oscillation,
sites with dominant sub-diurnal oscillations,
12-hours,
8-hours,
6-hours,
noisy sites,
sites with strange frequency behaviour.
Examples of the oscillations mentioned above
are presented in Figures 6-12.
The same construction of the network as well as
input parameters were used in both solutions. Only in
several sites the significant discrepancies were
discovered, but mostly due to the short time o
f
observations. For most of the stations correlations on
the level of 90 % were obtained. Several outliers in
East component were noticed, probably because of the
short time of particular solutions (3 hours). We
suppose that better ionospheric (scintillations,
fluctuations of TEC, moving ionosphere perturbations
TID) and tropospheric (4D model of water vapou
r
distribution) models should be implemented.
Relatively high consistency of the analysed time
series was obtained (Table 2).
DIURNAL AND SUB-DIURNAL OSCILLATIONS
In order to obtain oscillations in the coordinates’
time-series FFT procedure and Matlab®software were
Fig. 6 Spectra of the coordinates of LIE1 (Liesek,
Slovakia) station (North, East and Up [mm] fro
m
upper left) with dominant long-period oscillations.
A. Araszkiewicz et al.
300
Fig. 7 Spectra of the coordinates of LEGN (Legnica, Poland) station (North, East and Up [mm] fro
m
upper left) with dominant diurnal oscillations.
Fig. 8 Spectra of the coordinates of KUZA (Zilina, Slovakia) station (North, East and Up [mm] fro
m
upper left) – noisy station.
2. Even 4-hour oscillations are clearly seen, so the
3-hour window used in the processing seems to
b
e correct. But the interpretation should be made
very carefully because of the 6-hour Nyquis
t
frequency clearly seen in our spectra.
3. Many outliers in East component were obtained.
Better ionospheric (scintillations, fluctuations o
f
TEC, moving ionosphere perturbations TID) and
tropospheric (4D model of water vapou
r
distribution) models should be implemented.
SUMMARY
1. This research confirmed that using this method o
f
GNSS data processing we are able to obtain
reliable information for many further short-time
analyses. It was proved by the consistency with
daily solutions, but also relatively high
consistency of analysed time series was also
obtained. The variety of received results excludes
systematic errors, which could be introduced by
the applied method.
APPLICATION OF SHORT-TIME GNSS SOLUTIONS TO GEODYNAMICAL STUDIES
.
301
Fig. 9 Spectra of the coordinates of JLGR (Jelenia Góra, Poland) station (North, East and Up [mm]
from upper left) with almost no oscillations.
Fig. 10 Spectra of the coordinates of KRAW (Kraków, Poland) station (North, East and Up [mm] fro
m
upper left) with dominant 12-hour oscillation.
REFERENCES
Dach, R., Hugentobler, U., Fridez, P. and Meindl, M.
(Eds.): 2007, Bernese GPS Software Version 5.0”.
Astronomical Institute, University of Bern.
Hefty, J. and Igonfova. M.: 2008, Diurnal and semi-diurnal
site coordinates variation resulting from processing
with BV42 and BV50”. 6th LACs Workshop,
Frankfurt am Main, Germany, October 2008.
Hefty, J., Kartikova, H. and Igondova, M.: 2002, Time
series analysis of GPS station coordinates with daily
4. Almost no stations with the same frequency
behaviour in all three coordinates were found
lack of visible regularities. It is necessary to
distinguish between pure dynamic effects and
others (e.g. thermal effects) for prope
r
interpretation.
5. According to these results the verification of the
existing models (e.g. IERS tidal model used in the
GPS data processing) could be possible.
A. Araszkiewicz et al.
302
Fig. 11 Spectra of the coordinates of PROS (Proszowice, Poland) station (North, East and Up [mm]
from upper left) with dominant 8-hour oscillation.
Fig. 12 Spectra of the coordinates of KROS (Krosno, Poland) station (North, East and Up [mm] fro
m
upper left) with no dominant oscillation.
Plag, H.P. and Pearlman, M. (Eds.): 2009, Global Geodetic
Observing System: Meeting the requirements o
f
a global society on a changing planet in 2020”. XLIV.
and subdaily resolution. EGS XXVII General
Assembly, Nice, 21-26 April 2002
King, M., Colemar, R. and Nguyen, L.N.: 2003, Spurious
periodic horizontal signals in sub-daily GPS position
estimates. Journal of Geodesy, 77, N 1-2, 15–21.
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 Periodic horizontal signals have been identified in sub-daily estimates of position obtained from GPS data using batch least-squares solutions. The estimation of sub-daily position is commonly used for ocean loading and ice movement studies, for example. These spurious motions are artefacts of the processing methodology due to the presence of unmodelled, tidally-induced vertical signals in the GPS data. The periodic horizontal signals have magnitudes of about 40–50% of the amplitude of the vertical periodic signal. The shape of the periodic horizontal signals is related to the first derivative and the square of the vertical signal. The artefacts are mostly evident in the east–west component and can be removed by fixing the carrier phase ambiguities to integer values. We introduce a sensitivity analysis to study in detail the effects of ambiguity resolution and latitudinal variation of the artefacts. The overall conclusions are that for high precision batch processing of time series of geodetic positions, using sub-daily data spans, care needs to be taken to avoid aliasing of horizontal coordinates due to the vertical motion of the site.
Diurnal and semi-diurnal site coordinates variation resulting from processing with BV42 and BV50 " . 6 th LACs Workshop, Frankfurt am Main
  • J Hefty
  • M Igonfova
Hefty, J. and Igonfova. M.: 2008, Diurnal and semi-diurnal site coordinates variation resulting from processing with BV42 and BV50 ". 6 th LACs Workshop, Frankfurt am Main, Germany, October 2008.
Diurnal and semi-diurnal site coordinates variation resulting from processing with BV42 and BV50". 6 th LACs Workshop
  • J Hefty
  • Igonfova
Hefty, J. and Igonfova. M.: 2008, Diurnal and semi-diurnal site coordinates variation resulting from processing with BV42 and BV50". 6 th LACs Workshop, Frankfurt am Main, Germany, October 2008.
Time series analysis of GPS station coordinates with daily 4. Almost no stations with the same frequency behaviour in all three coordinates were foundlack of visible regularities
  • J Hefty
  • H Kartikova
  • M Igondova
Hefty, J., Kartikova, H. and Igondova, M.: 2002, Time series analysis of GPS station coordinates with daily 4. Almost no stations with the same frequency behaviour in all three coordinates were foundlack of visible regularities. It is necessary to distinguish between pure dynamic effects and others (e.g. thermal effects) for proper interpretation.