1. Modelling and prediction of the FCN Maciej Kalarus 1 Brian Luzum 2 Sébastien Lambert 2 Wiesław Kosek 1 Maciej Kalarus 1 Brian Luzum 2 Sébastien Lambert 2 Wiesław Kosek 1 Journées 2005 Systèmes de Référence Spatio-Temporels Warsaw, 19-21 September 2005 1 Space Research Centre, Polish Academy of Sciences 2 United States Naval Observatory

2. Input data Modelling and prediction of the FCN Atmospheric Angular Momentum NCEP/NCAR (1984 - August 2005) four-times daily data reanalyses Nutation residuals IERS C04(1984 - August 2005) daily data IAU 2000 Gravity field C 20 Cox & Chao(1984 - December 2002) variable 2/9

3. Wavelet analysis Complex Morlet Wavelet f b – bandwidth parameter f c – wavelet centre frequency T - dilation parameter (scale) t i - translation parameter (space) Complex Wavelet Transform Coefficients Modelling and prediction of the FCN 3/9

4. Wavelet analysis of the nutation residuals amplitude high low Wavelet transform modulus Period [days] Gradient of the phase Period [days] ++ -- 0 ++ -- 0 + _ 0 Modelling and prediction of the FCN 4/9

5. FCN - model Level of the residuals epoch A n [  as] sin cos 01-Jan-1985 01-Jan-1986 01-Jan-1987 01-Jan-1988 01-Jan-1989 01-Jan-1990 01-Jan-1991 01-Jan-1992 01-Jan-1993 01-Jan-1994 01-Jan-1995 01-Jan-1996 01-Jan-1997 01-Jan-1998 01-Jan-1999 01-Jan-2000 01-Jan-2001 01-Jan-2002 01-Jan-2003 01-Jan-2004 01-Jan-2005 -166.370 -208.422 -219.178 -100.623 -215.352 - 15.716 3.591 72.035 91.281 69.309 58.881 38.750 123.360 107.109 59.529 38.284 - 75.214 - 77.095 -133.172 - 95.037 -165.210 87.276 21.833 56.794 208.980 167.002 168.486 159.484 115.488 75.739 112.588 8.222 60.086 25.473 12.903 4.079 102.449 125.502 203.734 61.128 24.683 42.205 T FCN =442.3days dX MHB2000 dY MHB2000 Modelling and prediction of the FCN 5/9

6. Prediction of the FCN model Modelling and prediction of the FCN 6/9 dX dY Distribution of the prediction errors for 180 days in the future RMS prediction error error computed in 1986 – 2004

7. Possible excitation of the FCN FCN period Gravity field C 20 nino4 El Niño event 1997/98 Modelling and prediction of the FCN 7/9 AAM annual oscillation AAM annual oscillation FCN annual AAM p Wavelet transform modulus Wavelet transform modulus

8. Conclusions Characteristic of the FCN model - variable amplitude and period (phase) - apparent relationship to geophysical phenomena - mean prediction error - 70-80  as for 180 days in the future - earthquakes (T. Shirai, T. Fukushima) - anomalous fluctuations in the core (C. M. Cox, B. F. Chao) Other possible sources of excitation - subpolar glacial melting (J. O. Dickey, S. L. Marcus, O. de Viron, I. Fukumori) Modelling and prediction of the FCN 8/9 Possible excitation of the FCN Impulse excitation - global mass redistribution - perturbations of the annual atmospheric and oceanic circulation - land hydrology

9. Thank you for your attention Acknowledgements: This research has been partially supported by the Descartes-Nutation project.

10. Bibliography J. O. Dickey, S. L. Marcus, O. de Viron, I. Fukumori Recent Earth Oblateness Variations: Unraveling Climate and Postglacial Rebound Effects Science, vol 298 C. M. Cox, B. F. Chao Detection of a Large-Scale Mass Redistribution in the Terrestrial System Since 1998 Science, vol 297 S. Lambert Empirical modelling of the free core nutation Earth Orientation Department, USNO C. Bizouard, A. Brzeziński, S. Petrov Durial atmospheric forcing and temporal variations of the nutation amplitudes Journal of Geodesy, 1998, 72: 561-577 A. Brzeziński, W. Kosek Free core nutation: Stochastic modelling versus predictability Proc Journées Systèmes de Référence Spatio-Temporels 2003, St. Petersburg R. Holme, O. de Viron Geomagnetic jerks and a high-resolution length-of-day profile for core studies Geophysical Journal International, 2005, 160,435-439 Z. Malkin A New Free Core Nutation Model with Variable Amplitude and Period IVS 2004 General Meeting Proceedings R. S. Gross Atmosphere and Oceanic Excitation of Subdialy Earth Orientation Variations FGS Workshop 2004, „Ringlaser Gyroscopes and Earth Rotation”