EARTH ROTATION VARIATIONS DUE TO ZONAL TIDES  


Interactive model

UT1, hence the duration of the day D and the Earth's rotation rate w are subject to variations under the effect of zonal tides. We report here below the model of the IERS 96 conventions. It includes 62 periodic components, with periods ranging from 5.6 days to 18.6 years. They are 41 components with period under 35 days (Table A) and 27 above (Table B).

UT1R, ΔR, ωR represent the corrected values of UT1, of the duration of the day D and of the angular velocity of the Earth w. The units are 10-4 s for UT, 10-5 s for D , and 10-14 rad/s for w.

UT1 - UT1R = Σ A i sin ξi
Δ - ΔR = Σ A'i cos ξi
ω - ωR = Σ A"i cos ξi

where ξi is integer linear combination of Delaunay arguments : xi = a1 l + a2 l' + a3 D + a4 F + a5 W

Table A - WITH PERIODS UP TO 35 DAYS
   
              ARGUMENT ( xi)        PERIOD         UT1-UT1R    D - DR     w - wR     
              
         N   l   l'  F   D   W    DAYS             Ai         A'i         A"i   
                                                     
         1   1   0   2   2   2      5.64          -0.024      0.26	 -0.22      
         2   2   0   2   0   1      6.85          -0.040      0.37	 -0.31      
         3   2   0   2   0   2      6.86          -0.099      0.90	 -0.76      
         4   0   0   2   2   1      7.09          -0.051      0.45	 -0.38      
         5   0   0   2   2   2      7.10          -0.123      1.09	 -0.92      
         6   1   0   2   0   0      9.11          -0.039      0.27	 -0.22      
         7   1   0   2   0   1      9.12          -0.411      2.83	 -2.39      
         8   1   0   2   0   2      9.13          -0.993      6.83	 -5.76      
         9   3   0   0   0   0      9.18          -0.018      0.12	 -0.10      
        10  -1   0   2   2   1      9.54          -0.082      0.54	 -0.45      
        11  -1   0   2   2   2      9.56          -0.197      1.30	 -1.10
        12   1   0   0   2   0      9.61          -0.076      0.50	 -0.42
        13   2   0   2  -2   2     12.81           0.022     -0.11	  0.09
        14   0   1   2   0   2     13.17           0.025     -0.12        0.10
        15   0   0   2   0   0     13.61          -0.299      1.38       -1.17
        16   0   0   2   0   1     13.63          -3.208     14.79      -12.48
        17   0   0   2   0   2     13.66          -7.757     35.68      -30.11
        18   2   0   0   0  -1     13.75           0.022     -0.10        0.08
        19   2   0   0   0   0     13.78          -0.338      1.54       -1.30
        20   2   0   0   0   1     13.81           0.018     -0.08	  0.07
        21   0  -1   2   0   2     14.19          -0.024      0.11 	 -0.09
        22   0   0   0   2  -1     14.73           0.047     -0.20	  0.17
        23   0   0   0   2   0     14.77          -0.734      3.12	 -2.64
        24   0   0   0   2   1     14.80          -0.053      0.22	 -0.19
        25   0  -1   0   2   0     15.39          -0.051      0.21	 -0.17      
        26   1   0   2  -2   1     23.86           0.050     -0.13	  0.11      
        27   1   0   2  -2   2     23.94           0.101     -0.26	  0.22      
        28   1   1   0   0   0     25.62           0.039     -0.10	  0.08      
        29  -1   0   2   0   0     26.88           0.047     -0.11	  0.09      
        30  -1   0   2   0   1     26.98           0.177     -0.41	  0.35      
        31  -1   0   2   0   2     27.09           0.435     -1.01	  0.85      
        32   1   0   0   0  -1     27.44           0.534     -1.22	  1.03      
        33   1   0   0   0   0     27.56          -8.261     18.84      -15.90      
        34   1   0   0   0   1     27.67           0.544     -1.24	  1.04      
        35   0   0   0   1   0     29.53           0.047     -0.10	  0.08      
        36   1  -1   0   0   0     29.80          -0.055      0.12	 -0.10      
        37  -1   0   0   2  -1     31.66           0.118     -0.23	  0.20      
        38  -1   0   0   2   0     31.81          -1.824      3.60	 -3.04      
        39  -1   0   0   2   1     31.96           0.132     -0.26	  0.22      
        40   1   0  -2   2  -1     32.61           0.018     -0.03	  0.03      
        41  -1  -1   0   2   0     34.85          -0.086      0.15	 -0.13      
         
Table B- WITH PERIODS LONGER THAN 35 DAYS (Based on Yoder et al.(1981),with K/C = 0.94).

         
              ARGUMENT ( xi)        PERIOD         UT1-UT1R    D - DR  w - wR     
              
         N   l   l'  F   D   W    DAYS             Ai         A'i         A"i   

        42   0   2   2  -2   2     91.31          -0.057      0.04	-0.03      
        43   0   1   2  -2   1    119.61           0.033     -0.02	 0.01      
        44   0   1   2  -2   2    121.75          -1.885      0.97	-0.82      
        45   0   0   2  -2   0    173.31           0.251     -0.09	 0.08      
        46   0   0   2  -2   1    177.84           1.170     -0.41	 0.35      
        47   0   0   2  -2   2    182.62         -48.247     16.60     -14.01      
        48   0   2   0   0   0    182.63          -0.194      0.07	-0.06      
        49   2   0   0  -2  -1    199.84           0.049     -0.02	 0.01      
        50   2   0   0  -2   0    205.89          -0.547      0.17	-0.14      
        51   2   0   0  -2   1    212.32           0.037     -0.01	 0.01      
        52   0  -1   2  -2   1    346.60          -0.045      0.01	-0.01      
        53   0   1   0   0  -1    346.64           0.092     -0.02	 0.01      
        54   0  -1   2  -2   2    365.22           0.828     -0.14	 0.12      
        55   0   1   0   0   0    365.26         -15.359      2.64	-2.23      
        56   0   1   0   0   1    386.00          -0.138      0.02	-0.02      
        57   1   0   0  -1   0    411.78           0.035     -0.01	 0.00      
        58   2   0  -2   0   0   1095.17          -0.137     -0.01	 0.01      
        59  -2   0   2   0   1   1305.47           0.422     -0.02	 0.02      
        60  -1   1   0   1   0   3232.85           0.040      0.00	 0.00      
        61   0   0   0   0   2  -3399.18           7.900      0.15	-0.12      
        62   0   0   0   0   1  -6790.36       -1617.268    -14.95	12.62      
         
Delaunay arguments : following approximate expressions are sufficient for computing zonal tides effects :
         
l    = 134°.96 + 13°.064993(MJD-51544.5)   Mean anomaly of the Moon   
   
l '  = 357°.53 + 0°.985600(MJD-51544.5)	   Mean anomaly of the Sun   
         
F    =  93°.27 + 13°.229350(MJD-51544.5)   L -W  with L : mean longitude of the Moon   
         
D    = 297°.85 + 12°.190749(MJD-51544.5)   Mean elongation of the Moon from the Sun   
         
W    = 125°.04 - 0°.052954(MJD-51544.5)    Mean longitude of the ascending node of the Moon