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Lunar influence on equatorial atmospheric angular momentum and consequences for nutation
Christian BIZOUARD, Leonid ZOTOV, & Nikolay SIDORENKOV Observatoire de Paris, Moscow University & Hydrometeorological Centre of Russia


Introduction - 1
· Lunar influence on atmosphere: on old subject · Global diagnostic: equatorial atmospheric angular momentum function - a strong retrograde diurnal component (~10 mas) as large as the seasonal one, squeezed in a band from 20 to 30 hours. · By demodulation (removing diurnal carrier) : + =

Celestial Intermediate pole

True equator c'X q X x cx ( - ) cy c'Y y

Y

-( + )
referred to Gxyz (ITRF)





: Equatorial Angular Momentum Function EAMF : Celestial Equatorial Angular Momentum Function EAMF = + : Earth's rotation angle

it spreads over the frequency band of the precession-nutation from 2 days


Introduction ­ 2
· Most prominent terms are thermal waves caused by sun heating: +365 d (S1, 24 h), +182 d (P1, 24.07h), (K1, 23.93h), -365 d (y1, 23.87h) and it mostly perturbs annual nutation at the level of 100 mas
· Below 100 d, sharp peaks at 13.66 d (O1, 25.8h) and 13.63 d · Broad band peak around 7 d (28 h)

· Is it related to the lunar tide O1?


"Lunar band" 2-30 days - First striking feature
Pressure term and wind term w are almost proportional by contrast to seasonal band (S1); wind term variations are ~2-5 times larger than the ones of the pressure term (NCEP).

High band pass Filter periods < 30 days N.B.: 1 mas = 5 10-9 rad


Interpretation ­ local torques are negligible with regard to the bulge torque
· At a given frequency proportionality / explained theoretically from atmospheric angular momentum balance, as far as
- -


·

This is not the case for seasonal band in a non-rotating frame (Marcus et al, 2004).


· Expected ratio:

=

-

=

~13 around 13.6 d ~6 around 7 d


"Lunar band" 2-30 days - Second striking feature
By contrast to S1 band (of thermal origin), almost equal contributions of northern (NH) and southern hemispheres (HS) to the wind term. This hints a global simultaneous cause, like gravitational tides.


Tidal peak at 13.6 days ­ estimates and model
Tidal waves O1 (13.66 d, tidal argument f1) and side lobe (13.63 d, argument f2) estimated over the period 1949 - 2013

() (



[] = (0.05 - 0.02 ) (1 + ) [] = (0.17 - 0.06 ) (1 = 0. 73 - 0.04 (1

/2) +

+





+ (0.02 - 0.00 ) (2 + /2) /2) + (0.06 - 0.01 ) (2 + /2) /2) + (0.23 - 0.01 ) (2 + /2)

Pressure NIB term fits a simple equilibrium tidal model:

()

~14

;

~ 13





, Earth inertia moments, 0 mean atmospheric density, =2.64 m2/s2 Doodson constant for the Moon, = 23,5° (obliquity)

4 8 0 =- 0 sin 15 -

(1 + /2)


Broad band peak round 7 days
· More powerful than 13.6 d harmonics 1 · 1 atmospheric resonance excited by lunar tides Q1 (6.86 d), s1 (7.05 d) ?

/

= ( + )

1

Least square fit over 6 year sliding window

Gabor transform

Expected ratio of





()

=

-

~6 around 7 d i


Synthesis
· NIB pressure term O1 explained by tidal equilibrium model: clearly a lunar effect

· At 13.6 d expected ratio works for IB (over continents) pressure term ; at 7 d expected ratio works for NIB (full) pressure term · Proportionality wind / pressure term is consistent with 2 facts Lunar tesseral tidal pressure do not cause topographic torque Tidal wind only blows in the upper layer of the atmosphere and do not cause any friction torque Local atmospheric torque much smaller than the bulge torque, leading to proportionality of the pressure and wind term at a given period


Conclusion
Below 30 days Celestial Equatorial Atmospheric angular momentum is only significant for prograde band and is characterized by: · a 13.6 day wave, resulting from the fortnightly lunar tide · a broad band weekly oscillation, possibly resulting from lunar tidal
1 effect amplified by the 1 atmospheric resonance.

· Proportionality wind/pressure term at a given period & equal contributions of northern and southern hemispheres strongly supports the fact that the whole band is caused by the lunar tide
· Effect on nutation (Liouville equation in Celestial Frame, Brzezinski 1994): ~5 mas at 13.6 days (not observable), up to 30 mas at 7 days (densification needed)