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Prediction of the Chandler wobble
Leonid Zotov1,2,3, Christian Bizouard
1

2

Sternberg Astronomical Institute of Moscow State University 2Paris Observatory, SYRTE, France 3Higher School of Economics, Moscow, Russia

Journees Pulkovo Observatory (GAO) 22-24 September 2014


Motion of the Earth's pole
EOP CO1

2D trajectory
m(t ) x iy

1846-2010 step 0.05 yr
L.V.Zotov, C. M. Bizouard


Complex Singular Spectrum Analysis (CSSA) of the Polar Motion
0.2

SSA-decomposition of X-coordinate of the pole Chandler component annual component t re n d

0.1

ar c s e c

0

-0.1

-0.2 1860 1880 1900 1920 1940 1960 1980 2000

yea rs

X-component (Y ­ similar, with /2 phase shift).
L.V.Zotov, C. M. Bizouard


Dynamical model of the rotating Earth
()

+() = ()

= 1 + 2

= +



1 fc 4 33
L.V.Zotov, C. M. Bizouard

days-

1

Q 175

Munk W.H., MacDonald G.J.F., The rotation of the Earth, 1960


Filters' transfer functions and PM spectrum

L.V.Zotov, C. M. Bizouard


What is Chandler wobble?
Complex Fourier spectrum represents the signal by the set of constant harmonics, but it incorporates information about changes of instantaneous amplitude and phase

Filtering in time domain ­ convolution

Filtering in frequency domain ­ spectra multiplication

L.V.Zotov, C. M. Bizouard


Filtered Chandler wobble
X-component (Y ­ similar, with /2 phase shift).

L.V.Zotov, C. M. Bizouard


Chandler wobble and its excitation
X-component (Y ­ similar, with /2 phase shift).

L.V.Zotov, C. M. Bizouard


Chandler wobble and its excitation
X-component (Y ­ similar, with /2 phase shift).

L.V.Zotov, C. M. Bizouard


Envelope can be transferred through the dynamical model
()

+() = ()
()=
()

() =

( )


=





-()

=

days
-1

( +

()

()) + 1 -
fc 1 4 33

()
Q 175

= 2

L.V.Zotov, C. M. Bizouard


40-year PM changes will give 20-year oscillations in the excitation envelope
A(t)=sin() E(t) ~|cos |

L.V.Zotov, C. M. Bizouard


Envelope calculation
() ()

()

E()

L.V.Zotov, C. M. Bizouard


Envelope calculation
() ()

()

E()

L.V.Zotov, C. M. Bizouard


Amplitude model and forecast

3-layer Neural Network with (7, 7, 1) neurons

L.V.Zotov, C. M. Bizouard


Phase model and forecast

3-layer Neural Network with (7, 7, 1) neurons

L.V.Zotov, C. M. Bizouard


Phase and amplitude models
~Chandler wobble amplitude NLSM fit Period, years ~80-year omponent 83.44 Amplitude 42.6 mas Phase (1880) 40.8o

~40-year component
mean

42.0

54.6 mas
134.8 mas

-101.5

o

~Chandler wobble phase NLSM fit Period, years ~100-year omponent 117.8 ~50-year component 1-order trend 50.9 Amplitude 59 dg 34 dg 2dg /year Phase (1880) -118o 95
o


Excitation forecast

L.V.Zotov, C. M. Bizouard


Chandler wobble and its excitation depending on the filter width

L.V.Zotov, C. M. Bizouard


Chandler wobble and its excitation

L.V.Zotov, C. M. Bizouard

X-component (Y ­ similar, with /2 phase shift)


Chandler wobble and its excitation

Along the abscissa 18.6-year wave of the Moon orbit inclination
L.V.Zotov, C. M. Bizouard


18.6 year period of orbital nodes regression
max 28o
ecliptic 23o -5o Moon orbit max 18o equator equator ecliptic 23o +5o

Moon orbit is between ecliptic and equator, It does not have large inclinations

Moon orbit is above the ecliptic, Its inclinations can be high

L.V.Zotov, C. M. Bizouard

1997, 2015

1988, 2007


20-year changes in SL rate, LOD, Temperature and Chandler excitation

SAI MSU L.V.Zotov, C. M. Bizouard


60-year changes in SL, LOD, MD, Temperature and Chandler excitation

L.V.Zotov, C. M. Bizouard


Conclusions
· CSSA or Panteleev's filtering allows to extract Chandler wobble component of PM, its amplitude has ~80 and ~40 year modulations · From the envelope of the Chandler wobble the excitation envelope can be calculated using Euler-Liouville equation · If It 's true, that Chandler wobble has 40-year modulations, then excitation has 20-year amplitude changes · Prediction of the Chandler wobble and its excitation can be made, based on the envelope forecast. Now the Chandler wobble has decreased, its phase can jump, our epoch is crucial for understanding · Reconstructed Chandler excitation has modulations very similar with the ~20 and ~60-year components of temperature and sea level rate changes · The 20-year variations in the Chandler excitation and climate characteristics can be caused by the changes of atmospheric and oceanic circulation under the influence of 18.6-year cycle of the Moon orbital nodes regression L.V. Zotov, C. M. Bizouard


Thank you

Milky Way above Atacama Salt Lagoon ,Alex Tudorica