Analysis of Seasonal Signals in GPS Position Time Series

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Analysis of Seasonal Signals in GPS Position Time
Series

• Peng Fang
• Scripps Institution of Oceanography
• University of California, San Diego, USA

Toulouse Workshop, Sept. 2002 CGPS_at_TG Working
Group
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Credit
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
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OUTLINE

• Signal Categorization
• Data
• Processing
• Analysis
• Verification
• Discussion and Summary

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I. Gravitational excitation

• Rotational displacements due to seasonal polar
  motion
• Universal time corrected for polar motion (UT1)
  variation
• Loading induced displacement due to solid Earth
  tides, ocean tides, and atmospheric tides
• Pole tide

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II. Thermal origin coupled with hydrodynamics

• Atmospheric pressure, non-tidal sea surface
  fluctuations, and ground water (liquid and solid)
• Thermal expansion of bedrock, and wind shear

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III. Various errors

• Satellite orbital models, atmospheric models,
  water vapor distribution models, phase center
  variation models, thermal noise of the antenna,
  local multi-path, and snow cover on the antenna

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Data

• Long observation history (gt4.5 year time span
  starting from 1996)
• Good geographical distribution

128 (out of 429 total) high quality sites are
selected for the final analysis
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Processing

• Orbit/EOP tightly constrained
• ITRF reference frame used
• Distributed mode (subnetworks)
• Tropospheric delay estimated
• Antenna phase center corrected
• Solid Earth tide removed
• GAMIT/Globk software

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Analysis

• Parameters for each component at each site with
  t0 1996.0
• Bias
• Velocity
• Aannualsin(w(t-t0) fannual)
• Asemiannualsin(w(t-t0) fsemiannual)

Offsets due to earthquake or instrument setup
change are treated separately
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Resulting Time Series

• Vertical 4-10mm formal error 1mm
• Horizontal 1-3mm formal error 0.5mm
• Annual phase (Vertical) 5-10o
• Annual phase (Horizontal) 7-15o

These are typical signal range
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Phases are counted counterclockwise from
east Ellipses represent 95 confidence level
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Seasonal Terms

• Pole Tide
• McCarthy, 1996
• dl 9.0 cos q (xp sin l yp cos l)
• dq -9.0 cos 2q (xp cos l - yp sin l)
• dr -32.0 sin 2q (xp cos l - yp sin l)

q is colatitude
Be very careful with the sign of dq, positive for
SOUTH
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Seasonal Terms (Cont.)

• Ocean tide
• Scherneck, 1991
• Coefficients of 11 tides (amp. phases)
• M2, S2, N2, K2, K1, O1, P1, Q1, MF, MM, SSA

Mostly vertical, typically in mm range
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After pole tide and ocean tide terms corrected
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Seasonal Terms (Cont.)

• Atmospheric mass loading
• Farrell, 1972, vanDam and Wahr, 1987
• Green function approach
• Re-analysis of surface pressure by National
  Center for Environment Prediction (NCEP), 6 hour
  sampling
• Inverted barometer (IB) model
• ECMWF land-ocean mask model

Horizontal lt 0.5mm Vertical lt 1.0 mm
typical Eurasian, Arabian Peninsula 4.0 mm
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Seasonal Terms (Cont.)

• Non-tidal ocean mass loading
• Interaction of surface wind, atmospheric
  pressure, heat and moisture exchange,
  hydrodynamics
• Time-varying ocean topography from TOPEX/Poseidon
  altimeter, 1x1o 10 days, Tapley, 1994
• Correction term seasonal steric variation due to
  salinity and temperature variations above
  thermocline (no contribution to mass variation).
  Dynamic Height lt-Specific volume anomaly (Gill,
  1982) lt- WOA-94 model (Levitus and Boyer, 1994)
  with 19 depths.

Vertical Typical 1mm, low latitude
islands/coasts 2-3mm
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Seasonal Terms (Cont.)

• Snow/soil moisture mass loading
• Snow cover/soil moisture model NCEP/DOE
  reanalysis (Kanamitsu et al, 1999, Roads et al,
  1999) lt- Climate Data Assimilation System-1
  reanalysis NCEP/NCAR adjusted soil moisture
  from Climate Prediction Center Merged Analysis of
  Precipitation (CMAP)
• Ice/snow capped reg. treated separately

Vertical BRAZ 7mm, most 2-3mm, island sites
submm (underestimated due to model problem)
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After all mass loading terms corrected
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Terms not counted for

• Atmospheric modeling
• Imperfect, separate studies
• Bedrock thermal expansion
• Appendix B, 0.5mm, 45o behind
• Phase center environmental factor
• HOLP example, Hatanaka, 2001
• Glacier surge internal ice flow
• Alaska region, Sauber et al, 2000
• Antarctica, Cazenave et al, 2000

Note Signal may not be sinusoidal
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Verification

• JPL solution (GIPSY)
• GEONET solution (Bernese)

Different data processing methods
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JPL solution with all mass loading terms corrected
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Annual vertical term at USUD relative to TSKB Annual vertical term at USUD relative to TSKB 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 Asinw(t-t0)f, where t0 is 1996.0, w is the annual angular frequency. GEONET solution is the average of three local Usuda sites relative to three local Tsukuba sites. The amplitude A and phase f are defined as Asinw(t-t0)f, where t0 is 1996.0, w is the annual angular frequency. GEONET solution is the average of three local Usuda sites relative to three local Tsukuba sites. The amplitude A and phase f are defined as Asinw(t-t0)f, where t0 is 1996.0, w is the annual angular frequency. GEONET solution is the average of three local Usuda sites relative to three local Tsukuba sites.
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Mean annual vertical amplitude and power explained Mean annual vertical amplitude and power explained 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. 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. 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.
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Summary

• The modeled loading and nonloading terms can
  explain 66 (if pole tide is included) or 42
  (pole tide excluded) the observed power (mean
  amplitude squared).
• Some candidate terms for the residual signal are
  proposed.
• Impact on other related geodetic and geophysical
  problems are discussed.

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Contributions of geophysical sources and model errors to the observed annual vertical variations in site positions 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. The value is network-dependent.
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Atmosphere (purple arrow), non-tidal ocean (red
arrow), snow (green arrow) and soil wetness (blue
arrow) caused vertical annual variations of site
coordinates.