GPS foundamentals

1. Analysis of SeasonalAnalysis of Seasonal
Signals in GPS PositionSignals in GPS Position
Time SeriesTime Series
Peng FangPeng Fang
Scripps Institution of OceanographyScripps Institution of Oceanography
University of California, San Diego, USAUniversity of California, San Diego, USA
Toulouse Workshop, Sept. 2002
CGPS@TG Working Group

2. CreditCredit
Anatomy of apparent seasonal variations
from GPS-derived site position time series,
JGR Vol. 107, No. B4, ETG 9-1, 2002
D. Dong, JPL, California Inst. of Technology, Pasadena, USA
P. Fang, IGPP, SIO, Univ. of Calif. San Diego, La Jolla, USA
Y. Bock, IGPP, SIO, Univ. of Calif. San Diego, La Jolla, USA
M. K. Cheng, CSR, Univ. of Texas Austin, Austin, USA
S. Miyazaki, Earthquake Res. Inst., Univ. of Tokyo, Tokyo, Japan

3. OUTLINEOUTLINE
 Signal CategorizationSignal Categorization
 DataData
 ProcessingProcessing
 AnalysisAnalysis
 VerificationVerification
 Discussion and SummaryDiscussion and Summary

4. I. Gravitational excitationI. Gravitational excitation
 Rotational displacements due toRotational displacements due to
seasonal polar motionseasonal polar motion
 Universal time corrected for polarUniversal time corrected for polar
motion (UT1) variationmotion (UT1) variation
 Loading induced displacement due toLoading induced displacement due to
solid Earth tides, ocean tides, andsolid Earth tides, ocean tides, and
atmospheric tidesatmospheric tides
 Pole tidePole tide

5. II. Thermal origin coupled withII. Thermal origin coupled with
hydrodynamicshydrodynamics
 Atmospheric pressure, non-tidal seaAtmospheric pressure, non-tidal sea
surface fluctuations, and groundsurface fluctuations, and ground
water (liquid and solid)water (liquid and solid)
 Thermal expansion of bedrock, andThermal expansion of bedrock, and
wind shearwind shear

6. III. Various errorsIII. Various errors
 Satellite orbital models, atmosphericSatellite orbital models, atmospheric
models, water vapor distributionmodels, water vapor distribution
models, phase center variationmodels, phase center variation
models, thermal noise of themodels, thermal noise of the
antenna, local multi-path, and snowantenna, local multi-path, and snow
cover on the antennacover on the antenna

7. DataData
 Long observation history (>4.5 yearLong observation history (>4.5 year
time span starting from 1996)time span starting from 1996)
 Good geographical distributionGood geographical distribution
128 (out of 429 total) high quality sites
are selected for the final analysis

8. ProcessingProcessing
 Orbit/EOP tightly constrainedOrbit/EOP tightly constrained
 ITRF reference frame usedITRF reference frame used
 Distributed mode (subnetworks)Distributed mode (subnetworks)
 Tropospheric delay estimatedTropospheric delay estimated
 Antenna phase center correctedAntenna phase center corrected
 Solid Earth tide removedSolid Earth tide removed
 GAMIT/Globk softwareGAMIT/Globk software

9. AnalysisAnalysis
 Parameters for each componentParameters for each component
at each site with tat each site with t00 = 1996.0:= 1996.0:
• BiasBias
• VelocityVelocity
• AAannualannualsin(sin(ωω(t-t(t-t00) +) + φφannualannual))
• AAsemiannualsemiannualsin(sin(ωω(t-t(t-t00) +) + φφsemiannualsemiannual))
Offsets due to earthquake or instrument
setup change are treated separately

10. Resulting Time SeriesResulting Time Series
 Vertical:Vertical: 4-10mm4-10mm formal errorformal error
1mm1mm
 Horizontal:Horizontal: 1-3mm1-3mm formal errorformal error
0.5mm0.5mm

Annual phase (Vertical):Annual phase (Vertical): 5-105-10οο

Annual phase (Horizontal):Annual phase (Horizontal): 7-157-15οο
These are typical signal range

11. Phases are counted counterclockwise from east
Ellipses represent 95% confidence level

12. Seasonal TermsSeasonal Terms
 Pole TidePole Tide
McCarthy, 1996McCarthy, 1996
ddλ = 9.0λ = 9.0 coscos θ (θ (xp sinxp sin λ +λ + yp cosyp cos λ)λ)
ddθ = −9.0θ = −9.0 coscos 2θ (2θ (xp cosxp cos λ −λ − yp sinyp sin λ)λ)
drdr = −32.0= −32.0 sinsin 2θ (2θ (xp cosxp cos λ −λ − ypyp
sinsin λ)λ)
Be very careful with the sign
of ddθθ,, positive forpositive for SOUTHSOUTH
θθ is colatitude

13. Seasonal Terms (Cont.)Seasonal Terms (Cont.)
 Ocean tideOcean tide
Scherneck, 1991Scherneck, 1991
Coefficients ofCoefficients of 11 tides (amp. &11 tides (amp. &
phases):phases):
M2, S2, N2, K2, K1, O1, P1, Q1, MF,M2, S2, N2, K2, K1, O1, P1, Q1, MF,
MM, SSAMM, SSA
Mostly vertical, typically in mm range

14. After pole tide and ocean tide terms corrected

15. Seasonal Terms (Cont.)Seasonal Terms (Cont.)
 Atmospheric mass loadingAtmospheric mass loading
Farrell, 1972, vanDam and Wahr, 1987Farrell, 1972, vanDam and Wahr, 1987
Green function approachGreen function approach
Re-analysis of surface pressure byRe-analysis of surface pressure by
National Center for EnvironmentNational Center for Environment
Prediction (NCEP), 6 hour samplingPrediction (NCEP), 6 hour sampling
Inverted barometer (IB) modelInverted barometer (IB) model
ECMWF land-ocean mask modelECMWF land-ocean mask model
Horizontal < 0.5mm Vertical < 1.0 mm typical
Eurasian, Arabian Peninsula ~ 4.0 mm

16. Seasonal Terms (Cont.)Seasonal Terms (Cont.)
 Non-tidal ocean mass loadingNon-tidal ocean mass loading
Interaction of surface wind, atmosphericInteraction of surface wind, atmospheric
pressure, heat and moisture exchange,pressure, heat and moisture exchange,
hydrodynamicshydrodynamics
Time-varying ocean topography fromTime-varying ocean topography from
TOPEX/Poseidon altimeter, 1x1TOPEX/Poseidon altimeter, 1x1oo
10 days,10 days,
Tapley, 1994Tapley, 1994
Correction term: seasonal steric variation due to salinityCorrection term: seasonal steric variation due to salinity
and temperature variations above thermocline (noand temperature variations above thermocline (no
contribution to mass variation). Dynamic Height <-contribution to mass variation). Dynamic Height <-
Specific volume anomaly (Gill, 1982) <- WOA-94 modelSpecific volume anomaly (Gill, 1982) <- WOA-94 model
(Levitus and Boyer, 1994) with 19 depths.(Levitus and Boyer, 1994) with 19 depths.
Vertical: Typical 1mm, low latitude islands/coasts 2-3mm

17. Seasonal Terms (Cont.)Seasonal Terms (Cont.)
 Snow/soil moisture mass loadingSnow/soil moisture mass loading
Snow cover/soil moisture modelSnow cover/soil moisture model
NCEP/DOE reanalysis (Kanamitsu et al,NCEP/DOE reanalysis (Kanamitsu et al,
1999, Roads et al, 1999) <- Climate1999, Roads et al, 1999) <- Climate
Data Assimilation System-1 reanalysisData Assimilation System-1 reanalysis
NCEP/NCAR + adjusted soil moistureNCEP/NCAR + adjusted soil moisture
from Climate Prediction Center Mergedfrom Climate Prediction Center Merged
Analysis of Precipitation (CMAP)Analysis of Precipitation (CMAP)
Ice/snow capped reg. treated separatelyIce/snow capped reg. treated separately
Vertical: BRAZ 7mm, most 2-3mm, island sites
submm (underestimated due to model problem)

18. After all mass loading terms corrected

19. Terms not counted forTerms not counted for
 Atmospheric modelingAtmospheric modeling
• Imperfect, separate studiesImperfect, separate studies
 Bedrock thermal expansionBedrock thermal expansion
• Appendix B, 0.5mm, 45Appendix B, 0.5mm, 45οο
behindbehind
 Phase center & environmental factorPhase center & environmental factor
• HOLP example,HOLP example, Hatanaka, 2001Hatanaka, 2001
 Glacier surge & internal ice flowGlacier surge & internal ice flow
• Alaska region,Alaska region, Sauber et al, 2000Sauber et al, 2000
• AntarcticaAntarctica, Cazenave et al, 2000, Cazenave et al, 2000
Note: Signal may not be sinusoidal

20. VerificationVerification
 JPL solution (GIPSY)JPL solution (GIPSY)
 GEONET solution (Bernese)GEONET solution (Bernese)
Different data
processing methods

21. JPL solution with all mass loading terms corrected

22. Annual vertical term at USUD relative to TSKB
Solution Amplitude (mm) Phase (degree)
GEONET 8.5 237.5
JPL 8.7 225.1
SOPAC 10.9 229.7
The amplitude A and phase f are defined as
Asin[ω(t-t0
)+φ], where t0
is 1996.0, ω is the
annual angular frequency.
*GEONET solution is the average of three local
Usuda sites relative to three local Tsukuba
sites.

23. Mean annual vertical amplitude and power explained
SOPAC * JPL *
Mean amplitude without
pole tide correction
5.47 (5.49) mm
Mean amplitude after
pole tide correction
4.19 (4.19) mm 3.49 (3.44) mm
Mean amplitude after mass
loading correction
3.19 (3.08) mm 2.89 (2.74) mm
Ratio of site numbers & 90/128 (90/123) 81/121 (79/116)
Power explained (pole tide
and mass loading together)+
66% (67%)
Power explained (mass
loading only)+
42% (46%) 31% (37%)
*
The values in parentheses represent the results without 5 abnormal sites (FAIR,
STJO, TSKB, MDVO, XIAN for SOPAC, and FAIR, STJO, TSKB, ZWEN, KIT3 for
JPL)
+
Power explained is defined as 1 – (A2
/A1
)2
, where A1
is the mean amplitude
before correction, A2
is the mean amplitude after correction.
&
The numerator is the site number with reduced annual amplitudes after mass
loading correction. The denominator is the total site number.

24. SummarySummary
 The modeled loading and nonloadingThe modeled loading and nonloading
terms can explain 66% (if pole tide isterms can explain 66% (if pole tide is
included) or 42% (pole tideincluded) or 42% (pole tide
excluded) the observed power (meanexcluded) the observed power (mean
amplitude squared).amplitude squared).
 Some candidate terms for theSome candidate terms for the
residual signal are proposed.residual signal are proposed.
 Impact on other related geodetic andImpact on other related geodetic and
geophysical problems are discussed.geophysical problems are discussed.

25. Contributions of geophysical sources and model errors to
the observed annual vertical variations in site positions
Sources Range of effects
Pole tide ~4 mm
Ocean tide ~0.1 mm
Atmospheric mass ~4 mm
Non-tidal ocean mass 2-3 mm
Snow mass 3-5 mm
Soil moisture 2-7 mm
Bedrock thermal expansion ~0.5 mm
Errors in orbit, phase
center and troposphere
models
No quantitative
results yet
Error in network
adjustment*
~0.7 mm
Differences from different
software
~2-3 mm, at
some sites 5-7 mm
*The value is network-dependent.

26. Atmosphere (purple arrow), non-tidal ocean (red arrow), snow
(green arrow) and soil wetness (blue arrow) caused vertical
annual variations of site coordinates.