How much may one « cheat » the non-rigid Earth nutation theory to make it match VLBI results?

1. How much may one « cheat » the non-rigid Earth nutation theoryto make it match VLBI results? M. Feissel (1, 3), M. Yseboodt (2), V. Dehant (2), O. de Viron (2), C. Bizouard (1) (1) Observatoire de Paris (2) Royal Observatory of Belgium (3) Institut Géographique National - MHB2000 methodology and environment - Excitation of nutations by the atmosphere - Stability of the VLBI celestial reference frame - Discrepancies between observation and theory - How much can one change a part of the parameters in the model and still match the observed values of others? Feissel et al. - JSR2001

2. MHB2000 methodology and environment • Adopt • a rigid Earth nutation model (astronomical) • oceanic tidal excitations • mean values for atmospheric and non-tidal oceanic excitations • Construct atheoretical transfer function of the non-rigid Earth based on realistic physical properties • Adjust (least squares) parameters in the theory to fit theoretical predictions to VLBI-derived amplitudes • Adjusted parameters concern: • Dynamical ellipticities of mantle and fluid core • Magnetic couplings at Mantle-Core and Core-Inner Core boundaries • Free nutations amplitudes (FCN, FICN) • ... Feissel et al. - JSR2001

3. Atmospheric excitation of nutation(AER, pressure term)Wavelet transform of the Prograde component

4. Atmospheric excitation of nutation(AER, pressure term)Wavelet transform of the Retrograde component

5. Origin: diurnal waves (solar heating) AAM series (1958 =>) corrected for non-IB at diurnal frequencies Results for the Retrograde Annual nutation Maximum excitationfrequencychanges in time Amplitude is variable The atmospheric excitation of nutation Feissel et al. - JSR2001

6. Stability of the extragalactic reference frameSource position time series at 0.5-year intervals, 1984-1999(from Eubanks, 1999)

7. Stability of the extragalactic reference frame Feissel et al. - JSR2001

8. Analysis of VLBI time series • - VLBI data (available at the IERS/EOP Product Center): • time series of celestial pole offsets <= 24-hour sessions • ------------------------------------------------------------ • Institute Data span No of StError Stdev (mas) No of • Series points (mas) /MHB2000 sources • ------------------------------------------------------------- • BKG 01 R 01 1984.0-2001.0 2273 0.19 0.22 578 • GSFC 01 R 01 1980.0-2000.9 2696 0.27 0.23 552 • IAA 01 R 01 1980.0-2001.2 2155 0.17 0.25 667 • SHA 01 R 01 1980.0-2001.2 2735 0.24 0.23 675 • USNO 99 R 03 1980.0-2001.0 2489 0.30 0.25 652 • ------------------------------------------------------------- • - Form differences of the five VLBI series with the MHB2000 model • - Estimate linear (precession, obliquity rate) + 18.6 year terms • on the total data span • - Estimate 1025d + 430d + annual + semi-annual nutations • on 6-year data spans • - « VLBI result »: weighted mean of the five solutions

9. Estimation of the linear and 18.6-year nutation terms based on 13- through 21-year time series of the celestial pole offsets obtained by GSFC (o) and IAA(star)

10. Precession correction and obliquity rate: MHB2000 and VLBI values ----------------------------------------------------------------Data Precession corr. Obliquity rate ----------------------------------------------------------------MHB2000 -2.997 -0.255 VLBI-MHB +0.024 +-.002 +0.015 +-.002DCRF +0.010 +-.002 -0.008 +-.001 ---------------------------------------------------------------- Feissel et al. - JSR2001

11. Corrections to the MHB2000 18.6 years nutation term • - VLBI : obtained from the analysis of the VLBI series • -  +CRF : corrected for the celestial pole motion effect • - +Atmo: corrected for the atmospheric excitation (+Atmo) Unit: 0.001'' Feissel et al. - JSR2001

12. Prograde and retrograde components of the annual nutation derived from VLBI observations. Unit: 0.001'' • Celestial frame unstability effect < 10 mas Feissel et al. - JSR2001

13. Sensitivity of the theoretical FCN and FICN periods to perturbation of the MHB2000 transfer function • Perturb the MHB2000 transfer function by introducing plausible changes : • in the retrograde annual term • in the prograde & retrograde 18.6-year term • Evaluate departure of the FCN and FICN periods that are allowed by the size of actual discrepancies (VLBI + atmospheric) Feissel et al. - JSR2001

14. 988.2 1008.0 1017.9 1028.1 FICN period (days) 1038.5 13.6 days prograde 13.6 days retrograde 1 year retrograde 18.6 years prograde 18.6 years retrograde 1049.1 1059.9 1071.0 431.8 428.6 428.1 429.1 429.7 430.2 430.7 431.3 432.4 FCN period (days)

15. VLBI-derived amplitudes at the FCN and FICN frequencies • Origin of phases: J2000.0 • Celestial frame unstability effect < 10 mas Feissel et al. - JSR2001

16. Frequency of atmospheric excitation and VLBI-derived amplitudes of FCN and annual term • Period of maximum atmospheric excitation and observed amplitudes of the FCN and Retrograde Annual term

17. Summary – 1. Metrology • VLBI-MHB2000 (precision ~10 mas) • long term: 10-50 mas • medium term: observed variations <50 mas • Atmospheric excitation via diurnal waves has varying dominant period • Celestial reference frame unstability: • long term: 10-30 mas • medium term: < 10 mas Feissel et al. - JSR2001

18. Summary – 2. Physics • Atmospheric excitation of annual nutation is observable • The atmosphere may have excited the retrograde FCN (430d)in the 1980 ’s (250 mas) • The prograde FICN (1025d) may have been excited around 1984 (100 mas) Feissel et al. - JSR2001

19. Future work • In order to understand still unmodelled nutation signals at the level 10-50 mas: • Validate atmospheric data from various meteorological centres • Monitor atmospheric excitation • Monitor long-term and medium-term stability of the VLBI celestial reference frame Feissel et al. - JSR2001