NUTATIONS INDUCED BY OCEAN TIDAL VARIATIONS


Tidal fluctuations in water heigh and currents induce retrograde diurnal variation of equatorial oceanic angular momentum (OAM), hence small perturbation on nutation at the level of 1 mas. Most important contribution comes from water height variations.

Model MHB 2000 (Mathews, Herring, Buffett, "Modeling of nutation and precession : new nutation series for non-rigid Earth and insights into the Earth's interior", J.G.R., vol. 107, NO B4 (2002), Table 5).

This model is based upon the Oceanic Tidal Angular Momentum model of Chao et al. (1996) [Diurnal/semidiurnal polar motion excited by oceanic tidal angular momentum variations, JGR, 101, 20151-20163]. Effects on nutation in longitude Δψ and nutation in obliquity Δε refered to ecliptic of date are modelled as a sum a circular terms, prograde and retrograde :

Δψ sin ε0+ i Δε = Σj (ainj + i aopj) ei (θj - π/2) where θj is integer linear combination of Delaunay arguments:

θj = a1 l + a2 l' + a3 D + a4 F + a5 Ω.

Total effect and separate contributions of matter term and current term are presented in the table here-below: 
                  
l  l' F  D  Ω    PERIOD      Matter term      Current term            Total 
                 (days)      
a1 a2 a3 a4 a5                ain     aop        ain      aop      ain     aop 
0  0  0  0  1   -6798.38    -0.920   0.986    0.005  -0.020    -0.915   0.966      
0  0  0  0 -1    6798.38     0.117  -0.126   -0.001   0.003     0.116  -0.123
0 -1  0  0  0    -365.26     0.174  -0.216    0.000  -0.001     0.174  -0.217 
0  1  0  0  0     365.26    -0.021   0.023    0.000  -0.001    -0.021   0.022
0  0 -2  2 -2    -182.62     0.061  -0.069    0.001  -0.002     0.062  -0.071
0  0  2 -2  2     182.62     0.574  -0.615   -0.014   0.005     0.560  -0.610
0  0 -2  0 -2     -13.66     0.006  -0.009    0.000  -0.005     0.006  -0.014  
0  0  2  0  2      13.66     0.021  -0.019   -0.056   0.104    -0.035   0.085
 
Delaunay arguments 
(IERS Conventions 2000, from Simon et al., 1994, A&A 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.