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Diurnal and semidiurnal polar motion induced by the ocean tides
OCEAN-TIDAL DIURNAL AND SEMIDIURNAL POLAR MOTION - IERS 1996 MODEL


Oceanic tides cause diurnal and semidiurnal components in the polar motion. Table here below report the model of the IERS 96 conventions. It includes 8 periodic components (4 diurnal terms, 4 semidiurnal terms) under the form:

Δx = Σi Fi sin ξi + Gi cos ξi
Δy = Σi Hi sin ξi + Ki cos ξi

where ξi is integer linear combination of Delaunay arguments, GMST + π and constant phase : ξi = a1 l + a2 l' + a3 D + a4 F + a5 Ω + a6 (GMST +π) + Φ0. Unit for Fi, Gi, Hi, Ki is microarsecond. 


                  
       l  l' F  D  Ω GMST+π  Φ0   PERIOD      Fi       Gi          Hi       Ki   
                           (deg.) (hours)                       
Q1    -1  0 -2  0 -2  1     -90°  26.868   - 0.026    0.006    - 0.006  - 0.026
O1     0  0 -2  0 -2  1     -90°  25.819   - 0.133    0.049    - 0.049  - 0.133
P1     0  0 -2  2 -2  1     -90°  24.066   - 0.050    0.025    - 0.025  - 0.050
K1     0  0  0  0  0  1      90°  23.935   - 0.152    0.078    - 0.078  - 0.152
N2    -1  0 -2  0 -2  2           12.658   - 0.057   - 0.013     0.011    0.033
M2     0  0 -2  0 -2  2           12.421   - 0.330   - 0.028     0.037    0.196
S2     0  0 -2  2 -2  2           12.000   - 0.145     0.064     0.059    0.087
K2     0  0  0  0  0  2           11.967   - 0.036     0.017     0.018    0.022 
  
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 ) 15.0d0 + 648000.0

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