Tidal Spherical Harmonic Coefficients


Citation for these data:

R D Ray, A global ocean tide model from Topex/Poseidon altimetry: GOT99.2, NASA Tech. Memo. 209478, Goddard Space Flight Center, 58 pp., 1999.


These spherical harmonic coefficients correspond to the GOT99.2 tide model of Ray (1999). (Note: GOT = Goddard/Grenoble Ocean Tide.) The data are primarily based on the tidal analyses of 6 years of Topex/Poseidon altimeter data, supplemented with several hydrodynamic models in shallow and polar seas. See Ray (1999) for details on model development, as well as for comparisons of the model with tide gauge measurements.

These coefficients follow a consistent convention. Coefficients are given for prograde and retrograde waves. (In this context, "prograde" means in the direction of the tide-raising body, i.e. westward; this use follows standard tidal terminology, but it is opposite to that used for polar motion.)
Amplitude units are mm; phase lags are in degrees.


Q1

  n  m       D+     psi+       D-     psi-

  1  0     3.048  283.72
  1  1      .736   56.92      .894  325.10
  2  0     3.382  313.82
  2  1     5.771  136.62     2.888  284.04
  2  2      .977  344.01      .341  252.46
  3  0     1.273   15.53
  3  1     3.750  341.58     2.356   98.53
  3  2      .695  289.31      .200   88.53
  3  3      .441  126.46      .361  209.79
  4  0     7.091   87.20
  4  1     3.213  162.63     1.115  104.99
  4  2      .395  289.76      .054   63.32
  4  3      .128  145.66      .104  358.11
  4  4      .032  278.60      .029   72.60
  5  1     2.301  336.87      .848  304.89
  6  1      .686  169.80      .209  259.83
  7  1      .710  316.50      .496  307.69
  8  1      .123  322.60      .276  114.33

O1

  n  m       D+     psi+       D-     psi-

  1  0    15.403  276.91
  1  1     3.324   63.87     5.443  340.63
  2  0     9.646  330.70
  2  1    25.871  136.04    11.755  300.32
  2  2     5.773  339.75      .650  246.89
  3  0     9.371   45.49
  3  1    13.965    6.71    11.987  115.49
  3  2     3.892  310.63     1.692  112.88
  3  3     2.325  136.41     1.566  235.19
  4  0    22.029  101.02
  4  1    15.599  171.50     6.063  122.10
  4  2     1.682  300.88      .134  173.45
  4  3      .596  148.79      .421   24.27
  4  4      .170  291.60      .171   76.33
  5  1    10.218  337.87     3.423  301.51
  6  1     2.566  168.13     1.486  249.42
  7  1     3.284  308.96     2.428  316.84
  8  1     1.213  350.24     1.079  114.96

P1

  n  m       D+     psi+       D-     psi-

  1  0     8.241  284.65
  1  1     1.690   84.63     3.249    2.61
  2  0     1.940  219.56
  2  1     9.897  131.79     4.935  314.41
  2  2     3.348  353.07      .496  179.51
  3  0     7.691   41.53
  3  1     3.477   48.89     5.666  134.79
  3  2     1.639  338.18     1.457  147.65
  3  3     1.169  152.94      .697  265.56
  4  0     6.490   73.73
  4  1     6.966  193.83     2.778  132.40
  4  2      .691  299.83      .199  289.08
  4  3      .246  160.19      .134   49.14
  4  4      .085  309.55      .122   91.12
  5  1     4.642  345.44     2.095  293.68
  6  1      .915  186.85     1.204  247.60
  7  1     1.630  321.06     1.076  322.15
  8  1      .278  323.67      .207  131.19

K1

  n  m       D+     psi+       D-     psi-

  1  0    25.184  285.19
  1  1     5.168   86.12    10.042    3.92
  2  0     6.809  210.94
  2  1    29.396  131.36    14.829  315.66
  2  2    10.297  353.91     1.593  177.06
  3  0    24.060   41.35
  3  1    10.237   54.86    17.229  136.28
  3  2     4.966  340.54     4.603  149.02
  3  3     3.564  154.15     2.125  267.98
  4  0    19.010   70.27
  4  1    21.125  195.65     8.396  133.24
  4  2     2.064  299.73      .656  290.27
  4  3      .737  161.22      .395   52.05
  4  4      .259  310.87      .380   91.87
  5  1    14.011  346.06     6.459  293.21
  6  1     2.715  188.83     3.762  247.52
  7  1     4.960  321.97     3.240  322.61
  8  1      .787  319.18      .559  134.71
  9  1     1.490   17.50     1.518   17.38
 10  1     2.221   18.80     1.048  160.67

N2

  n  m       D+     psi+       D-     psi-

  1  0     2.272   33.46
  1  1     1.293  281.35      .659    2.12
  2  0     2.244  257.89
  2  1     2.534  161.35     1.394  178.71
  2  2     6.978  120.43     1.132   10.86
  3  0    13.083  292.65
  3  1     2.173   95.30     6.415   40.12
  3  2     1.026  282.13      .314  112.30
  3  3     1.019   33.39      .973  355.36
  4  0    15.089  162.58
  4  1     3.643   37.95     3.262   74.36
  4  2     2.360  309.30     1.307   54.22
  4  3      .365  252.50      .481  152.05
  4  4      .178  140.36      .085  179.67
  5  2      .772   84.71     1.651  170.81
  6  2      .661   93.14      .347  294.19
  7  2      .251  211.65      .556  317.82
  8  2      .238  229.03      .087  282.94

M2

  n  m       D+     psi+       D-     psi-

  1  0    10.715   52.15
  1  1     6.981  308.57     3.135   10.98
  2  0    28.753  265.91
  2  1    13.687  201.63     3.719  154.95
  2  2    32.300  129.97     6.129   28.90
  3  0    38.633  298.08
  3  1    14.004  103.17    33.022   52.82
  3  2     2.933  280.39     2.193  139.25
  3  3     4.514   54.39     4.555    8.92
  4  0    51.573  155.18
  4  1    22.274   59.76    17.052  107.75
  4  2    10.507  320.60     4.146   89.68
  4  3     2.239  271.00     2.276  170.66
  4  4      .794  148.21      .430  222.85
  5  2     2.837   81.40     7.032  192.92
  6  2     4.067  119.16     1.175  324.56
  7  2     1.210  244.52     2.359  336.61
  8  2     1.334  238.19      .638  295.80
  9  2      .354  317.18      .617   90.66
 10  2      .229  110.90      .375  357.31


S2

  n  m       D+     psi+       D-     psi-

  1  0     3.911   69.61
  1  1     2.613    7.21     1.225   61.36
  2  0    11.724  312.89
  2  1     5.613  261.29     3.730  121.19
  2  2    11.911  130.12     2.767   82.14
  3  0    19.630  297.25
  3  1     5.168  131.42    10.870  103.69
  3  2     3.023  246.71     1.087  249.23
  3  3      .789  127.54     1.753   39.13
  4  0    29.084  171.30
  4  1    11.491  104.88     4.562   97.31
  4  2     3.650  343.94      .556   29.48
  4  3      .958  334.74      .647  195.99
  4  4      .320  155.66      .185  286.33
  5  2     1.485   69.39     2.206  201.21
  6  2     1.786  164.53      .346  304.08
  7  2      .440  290.82      .652   11.76
  8  2      .472  259.69      .382  345.93


K2

  n  m       D+     psi+       D-     psi-

  1  0     1.249   66.08
  1  1      .679  340.24      .177  293.97
  2  0     3.460  300.54
  2  1     1.805  255.83     1.101  113.76
  2  2     3.107  133.48      .787   78.44
  3  0     5.436  277.65
  3  1     1.487  114.98     2.990  100.38
  3  2      .877  242.59      .295  243.23
  3  3      .230  123.04      .491   34.11
  4  0     7.457  161.64
  4  1     3.394  104.23     1.295   98.48
  4  2     1.030  337.54      .207   20.54
  4  3      .265  333.78      .171  188.66
  4  4      .096  148.64      .054  287.08
  5  2      .422   67.20      .656  196.29
  6  2      .479  158.98      .112  311.10
  7  2      .129  279.00      .169    5.24
  8  2      .127  249.69      .092  350.18