Modelling and predictionof the FCN

Maciej Kalarus 1

Brian Luzum 2

Sébastien Lambert 2

Wiesław Kosek 1

Journées 2005Systèmes de Référence Spatio-Temporels

Warsaw, 19-21 September 2005

1 Space Research Centre, Polish Academy of Sciences2 United States Naval Observatory

Input data

Modelling and prediction of the FCN

Atmospheric Angular MomentumNCEP/NCAR (1984 - August 2005) four-times daily datareanalyses

Nutation residualsIERS C04 (1984 - August 2005) daily dataIAU 2000

Gravity field C20

Cox & Chao (1984 - December 2002) variable

2/9

Wavelet analysis

Complex Morlet Wavelet

-1 .0

-0 .5

0.0

0.5

1.0 Re ()Im ()

t

bc

b fttfi

ft

2

exp 2exp1Ψ

fb – bandwidth parameterfc – wavelet centre frequency

T - dilation parameter (scale) ti - translation parameter (space)

dttzTtt

TtT ii ˆ 1),(ˆ

W

Complex Wavelet Transform Coefficients

Modelling and prediction of the FCN 3/9

Wavelet analysis of the nutation residuals

1986 1988 1990 1992 1994 1996 1998 2000 2002-600-550-500-450-400-350-300

tTtT ,ˆmod, WA am

plitudehigh

low

Wavelet transform modulusP

erio

d [d

ays]

TttT

dtdtT 2,ˆarg, WGGradient of the phase

Per

iod

[day

s] +

-

0

1986 1988 1990 1992 1994 1996 1998 2000 2002-600-550-500-450-400-350-300 +

-

0

1986 1988 1990 1992 1994 1996 1998 2000 2002-600-550-500-450-400-350-300 +

_

0

1986 1988 1990 1992 1994 1996 1998 2000 2002-600-550-500-450-400-350-300

442.3

Modelling and prediction of the FCN 4/9

FCN - model

aMJDbfiAFCN FCNnMJD 2exp

200004 IAUCoriginalstd

residualsstd 0.87dX 0.91dY

Level of the residuals

epoch An[as]sin cos

01-Jan-198501-Jan-198601-Jan-198701-Jan-198801-Jan-198901-Jan-199001-Jan-199101-Jan-199201-Jan-199301-Jan-199401-Jan-199501-Jan-199601-Jan-199701-Jan-199801-Jan-199901-Jan-200001-Jan-200101-Jan-200201-Jan-200301-Jan-200401-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

TFCN=442.3days

1984 1988 1992 1996 2000 2004

-1000

0

1000

1984 1988 1992 1996 2000 2004

-1000

0

1000

[as]

[as]

dXMHB2000

dYMHB2000

Modelling and prediction of the FCN 5/9

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

0 50 100 150 2000

5

10

[%]

[as]

90%0 50 100 150 200

0

5

10

[%]

[as]

90%

RMS prediction error

0 20 40 60 80 100 120 140 160 1800

20406080

[as]

[days]

dXdY

error computed in 1986 – 2004error computed in 1986 – 2004

Possible excitation of the FCN

FCN period

Gravity field C20

nino4El Niño event 1997/98

-1-0.5

00.5

1

-480-440-400

[years]1986 1990 1994 1998 2002

-2

0

2

r=0.84

r=0.46[days][C 0] *10 -10

Modelling and prediction of the FCN 7/9

AAM annualoscillation

1986 1990 1994 1998 2002350

360

370

380[days]

[years]

velocitypressure

FCNannual AAMpWavelet

transformmodulus

[years]1986 1990 1994 1998 2002

r=-0.87

high

low

ConclusionsCharacteristic of the FCN model

- variable amplitude and period (phase)

- apparent relationship to geophysical phenomena

- mean prediction error - 70-80as 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

Thank you for your attention

Acknowledgements:This research has been partially supported by the Descartes-Nutation project.