Analysis of Seasonal Analysis of Seasonal Signals in GPS Position Signals in GPS Position

Time SeriesTime SeriesPeng FangPeng Fang

Scripps Institution of OceanographyScripps Institution of OceanographyUniversity of California, San Diego, USAUniversity of California, San Diego, USA

Toulouse Workshop, Sept. 2002CGPS@TG Working Group

CreditCreditAnatomy 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

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

I. Gravitational excitationI. Gravitational excitation Rotational displacements due to Rotational displacements due to

seasonal polar motionseasonal polar motion Universal time corrected for polar Universal time corrected for polar

motion (UT1) variationmotion (UT1) variation Loading induced displacement due to Loading induced displacement due to

solid Earth tides, ocean tides, and solid Earth tides, ocean tides, and atmospheric tidesatmospheric tides

Pole tidePole tide

II. Thermal origin coupled with II. Thermal origin coupled with hydrodynamicshydrodynamics

Atmospheric pressure, non-tidal sea Atmospheric pressure, non-tidal sea surface fluctuations, and ground surface fluctuations, and ground water (liquid and solid)water (liquid and solid)

Thermal expansion of bedrock, and Thermal expansion of bedrock, and wind shearwind shear

III. Various errorsIII. Various errors Satellite orbital models, atmospheric Satellite orbital models, atmospheric

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

DataData Long observation history (>4.5 year Long 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

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

AnalysisAnalysis Parameters for each component Parameters for each component

at each site with tat each site with t00 = 1996.0: = 1996.0:• BiasBias• VelocityVelocity• AAannualannualsin(sin((t-t(t-t00) + ) + annualannual))• AAsemiannualsemiannualsin(sin((t-t(t-t00) + ) + semiannualsemiannual))

Offsets due to earthquake or instrument setup change are treated separately

Resulting Time SeriesResulting Time Series Vertical: Vertical: 4-10mm4-10mm formal error formal error

1mm 1mm Horizontal: Horizontal: 1-3mm1-3mm formal error formal error

0.5mm0.5mm Annual phase (Vertical): Annual phase (Vertical): 5-105-10

Annual phase (Horizontal): Annual phase (Horizontal): 7-157-15

These are typical signal range

Phases are counted counterclockwise from eastEllipses represent 95% confidence level

Seasonal TermsSeasonal Terms Pole TidePole TideMcCarthy, 1996McCarthy, 1996ddcoscosxp sinxp sinyp cosyp cosddcoscosxp cosxp cosyp yp

sinsindrdrsinsinxp cosxp cosyp yp

sinsinBe very careful with the sign of ddpositive for positive for SOUTHSOUTH

is colatitude

Seasonal Terms (Cont.)Seasonal Terms (Cont.) Ocean tideOcean tideScherneck, 1991Scherneck, 1991Coefficients ofCoefficients of 11 tides (amp. & 11 tides (amp. &

phases):phases):M2, S2, N2, K2, K1, O1, P1, Q1, M2, S2, N2, K2, K1, O1, P1, Q1,

MF, MM, SSAMF, MM, SSA

Mostly vertical, typically in mm range

After pole tide and ocean tide terms corrected

Seasonal Terms (Cont.)Seasonal Terms (Cont.) Atmospheric mass loadingAtmospheric mass loadingFarrell, 1972, vanDam and Wahr, 1987Farrell, 1972, vanDam and Wahr, 1987Green function approachGreen function approachRe-analysis of surface pressure by Re-analysis of surface pressure by

National Center for Environment National Center for Environment Prediction (NCEP), 6 hour samplingPrediction (NCEP), 6 hour sampling

Inverted barometer (IB) modelInverted barometer (IB) modelECMWF land-ocean mask modelECMWF land-ocean mask model

Horizontal < 0.5mm Vertical < 1.0 mm typicalEurasian, Arabian Peninsula ~ 4.0 mm

Seasonal Terms (Cont.)Seasonal Terms (Cont.) Non-tidal ocean mass loadingNon-tidal ocean mass loadingInteraction of surface wind, atmospheric Interaction of surface wind, atmospheric

pressure, heat and moisture exchange, pressure, heat and moisture exchange, hydrodynamicshydrodynamics

Time-varying ocean topography from Time-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 salinity Correction term: seasonal steric variation due to salinity and temperature variations above thermocline (no and temperature variations above thermocline (no contribution to mass variation). Dynamic Height <-contribution to mass variation). Dynamic Height <-Specific volume anomaly (Gill, 1982) <- WOA-94 model Specific 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

Seasonal Terms (Cont.)Seasonal Terms (Cont.) Snow/soil moisture mass loadingSnow/soil moisture mass loadingSnow cover/soil moisture model Snow cover/soil moisture model

NCEP/DOE reanalysis (Kanamitsu et al, NCEP/DOE reanalysis (Kanamitsu et al, 1999, Roads et al, 1999) <- Climate 1999, Roads et al, 1999) <- Climate Data Assimilation System-1 reanalysis Data Assimilation System-1 reanalysis NCEP/NCAR + adjusted soil moisture NCEP/NCAR + adjusted soil moisture from Climate Prediction Center Merged from 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)

After all mass loading terms corrected

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, 45 behind behind 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

VerificationVerification JPL solution (GIPSY)JPL solution (GIPSY) GEONET solution (Bernese)GEONET solution (Bernese)

Different data processing methods

JPL solution with all mass loading terms corrected

Annual vertical term at USUD relative to TSKB

Solution Amplitude (mm) Phase (degree)

GEONET 8.5 237.5JPL 8.7 225.1SOPAC 10.9 229.7

The amplitude A and phase f are defined as Asin[(t-t0)+], where t0 is 1996.0, is the annual angular frequency.*GEONET solution is the average of three local Usuda sites relative to three local Tsukuba sites.

Mean annual vertical amplitude and power explainedSOPAC * 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.

SummarySummary The modeled loading and nonloading The modeled loading and nonloading

terms can explain 66% (if pole tide is terms can explain 66% (if pole tide is included) or 42% (pole tide excluded) included) or 42% (pole tide excluded) the observed power (mean amplitude the observed power (mean amplitude squared).squared).

Some candidate terms for the Some candidate terms for the residual signal are proposed.residual signal are proposed.

Impact on other related geodetic and Impact on other related geodetic and geophysical problems are discussed.geophysical problems are discussed.

Contributions of geophysical sources and model errors to the observed annual vertical variations in site positionsSources Range of effectsPole tide ~4 mmOcean tide ~0.1 mmAtmospheric mass ~4 mmNon-tidal ocean mass 2-3 mmSnow mass 3-5 mmSoil moisture 2-7 mmBedrock thermal expansion ~0.5 mmErrors 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.

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