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Diurnal and semi-diurnal polar motion due to atmosphere
ATMOSPHERIC DIURNAL AND SEMIDIURNAL POLAR MOTION

updated : September, 2015

Atmospheric tides (both thermal and tidal) cause diurnal and semidiurnal components in the polar motion. Most important contributions have been computed by Brzezinski, Bizouard and Petrov (2002) ["Influence of the atmosphere on Earth Rotation : what new can be learned from the recent atmospheric angular momentum estimates?", Surveys in Geophysics, 23, 33-69, 2002] from NCEP/NCAR Angular Atmospheric Momentum data spanning the period from 1958 to 1997.7. Corresponding model includes 6 periodic circular components (4 prograde diurnal terms, 2 semidiurnal terms) under the form :

Δx - i Δy = Σj i (ainj + i aopj) ei ξj
or :
Δx = Σj -aopj cos ξj - ainj sin ξj
Δy = -Σj ( ainj cos ξj - aopj sin ξj)
where ξi is integer linear combination of Delaunay arguments and GMST + π :
ξi = a1 l + a2 l' + a3 D + a4 F + a5 Ω + a6 (GMST +π)

The reported values are quite indicative and cannot be trusted : indeed other AAM series (analysis Centers JMA, UKMO, ECWF) give contradictory results, presenting disagreement both in phase and in amplitude, sometimes as large as the effect under consideration (~10 mas). More recent estimates can be found in Brzezinski, Ponte et Ali (2004), Nontidal oceanic excitation of nutation and diurnal/semidiurnal polar motion revisited, JGR, vol. 109, B11407. 
                  
       l   l'  F   D   Ω GMST + π      PERIOD     ainj     aopj         
                                      (hours)   µas)    µas)                  
P1+    0   0  -2   2  -2   1           24.066     0.6    -1.2   
S1+    0  -1   0   0   0   1           24.000    -5.2     4.9
K1+    0   0   0   0   0   1           23.935     1.4     0.7  
ψ1+    0   1   0   0   0   1           23.870    -0.5     0.5    
S2+    0   0  -2   2  -2   2           12.000    -2.8     0.6 
S2-    0   0   2  -2   2  -2          -12.000     2.8    -0.6 

  
Delaunay arguments 
(IERS Conventions 2000, from Simon et al., 1994, Astron. Astrophys. 282, 663-683):
     
 Mean anomaly of the Moon :
   l = 134°.963 402 51 + 1 717 915 923.2178" t + 31".879 2 t2 + 0".051 635 t3 - 0".000 244 70 t4
 
 Mean anomaly of the Sun  : 
   l'= 357°.529 109 18 +   129 596 581.0481" t - 0".553 2 t2 -  0".000 136 t3 - 0".000 011 49 t4
 
 F = L -Ω  with L mean longitude of the Moon  
   F =  93°.272 090 62 + 1 739 527 262.8478" t - 12".751 2 t2 - 0".001 037 t3 + 0".000 004 17 t4
 
 Mean elongation of the Moon from the Sun :
   D = 297°.850 195 47 + 1 602 961 601.2090" t -  6".370 6 t2 + 0".006 593 t3 - 0".000 031 69 t4

 Mean longitude of the ascending node of the Moon :
   Ω = 125°.044 555 01  - 6 962 890.543 1" t + 7".472 2 t2 + 0".007 702 t3 - 0".000 059 39 t4

where t is measured un Julian Centuries of 36525 days of 86400 seconds of Dynamical Time since J2000.0.          

Rotation angle in arcseconds : Greenwich Mean Sidereal Time + 180°

   GMST + π = (67310.54841 + (876600 * 3600 + 8640184.812866) t 
             + 0.093104 t2 - 6.2 10-6 t3 ) 15 + 648000.0


where t is measured un Julian Centuries of 36525 days of 86400 seconds of Dynamical Time since J2000.0.