1. 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@TG Working Group

2. 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

3. OUTLINE Signal Categorization Signal Categorization Data Data Processing Processing Analysis Analysis Verification Verification Discussion and Summary Discussion and Summary

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

5. II. Thermal origin coupled with hydrodynamics Atmospheric pressure, non-tidal sea surface fluctuations, and ground water (liquid and solid) Atmospheric pressure, non-tidal sea surface fluctuations, and ground water (liquid and solid) Thermal expansion of bedrock, and wind shear Thermal expansion of bedrock, and wind shear

6. 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 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

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

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

9. Analysis Parameters for each component at each site with t 0 = 1996.0: Parameters for each component at each site with t 0 = 1996.0: BiasBias VelocityVelocity A annual sin((t-t 0 ) +  annual )A annual sin((t-t 0 ) +  annual ) A semiannual sin((t-t 0 ) +  semiannual )A semiannual sin((t-t 0 ) +  semiannual ) Offsets due to earthquake or instrument setup change are treated separately

10. Resulting Time Series Vertical: 4-10mm formal error 1mm Vertical: 4-10mm formal error 1mm Horizontal: 1-3mm formal error 0.5mm Horizontal: 1-3mm formal error 0.5mm Annual phase (Vertical): 5-10  Annual phase (Vertical): 5-10  Annual phase (Horizontal): 7-15  Annual phase (Horizontal): 7-15  These are typical signal range

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

12. Seasonal Terms Pole Tide Pole Tide McCarthy, 1996 dcosxp sinyp cos dcosxp cosyp sin drsinxp cosyp sin d positive for SOUTH Be very careful with the sign of d positive for SOUTH   is colatitude

13. Seasonal Terms (Cont.) Ocean tide 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

14. After pole tide and ocean tide terms corrected

15. Seasonal Terms (Cont.) Atmospheric mass loading 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 < 0.5mm Vertical < 1.0 mm typical Eurasian, Arabian Peninsula ~ 4.0 mm

16. Seasonal Terms (Cont.) Non-tidal ocean mass loading Non-tidal ocean mass loading Interaction of surface wind, atmospheric pressure, heat and moisture exchange, hydrodynamics Time-varying ocean topography from TOPEX/Poseidon altimeter, 1x1 o 10 days, Tapley, 1994 Correction term: seasonal steric variation due to salinity and temperature variations above thermocline (no contribution to mass variation). Dynamic Height <- Specific volume anomaly (Gill, 1982) <- WOA-94 model (Levitus and Boyer, 1994) with 19 depths. Vertical: Typical 1mm, low latitude islands/coasts 2-3mm

17. Seasonal Terms (Cont.) Snow/soil moisture mass loading Snow/soil moisture mass loading Snow cover/soil moisture model NCEP/DOE reanalysis (Kanamitsu et al, 1999, Roads et al, 1999) <- 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)

18. After all mass loading terms corrected

19. Terms not counted for Atmospheric modeling Atmospheric modeling Imperfect, separate studiesImperfect, separate studies Bedrock thermal expansion Bedrock thermal expansion Appendix B, 0.5mm, 45  behindAppendix B, 0.5mm, 45  behind Phase center & environmental factor Phase center & environmental factor HOLP example, Hatanaka, 2001HOLP example, Hatanaka, 2001 Glacier surge & internal ice flow Glacier surge & internal ice flow Alaska region, Sauber et al, 2000Alaska region, Sauber et al, 2000 Antarctica, Cazenave et al, 2000Antarctica, Cazenave et al, 2000 Note: Signal may not be sinusoidal

20. Verification 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 SolutionAmplitude (mm)Phase (degree) GEONET8.5237.5 JPL8.7225.1 SOPAC10.9229.7 The amplitude A and phase f are defined as Asin[(t-t 0 )+], where t 0 is 1996.0,  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) mm3.49 (3.44) mm Mean amplitude after mass loading correction 3.19 (3.08) mm2.89 (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 – (A 2 /A 1 ) 2, where A 1 is the mean amplitude before correction, A 2 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. 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). 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. Some candidate terms for the residual signal are proposed. Impact on other related geodetic and geophysical problems are discussed. Impact on other related geodetic and geophysical problems are discussed.

25. Contributions of geophysical sources and model errors to the observed annual vertical variations in site positions SourcesRange of effects Pole tide~4 mm Ocean tide~0.1 mm Atmospheric mass~4 mm Non-tidal ocean mass2-3 mm Snow mass3-5 mm Soil moisture2-7 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.