F. Lyard, F. Lefevre, T. Letellier, O. Francis, "Modelling the global ocean tides: insights from FES2004," Ocean Dynamics, 56, 394-415, 2006.
Coefficients below were computed by R. Ray, NASA/GSFC.
These spherical harmonic coefficients correspond to the FES2004 tide model, produced by Christian Le Provost's group at CNES. The tidal solutions are the result of assimilating satellite altimeter data into a hydrodynamic ocean model, using the inverse methods of Egbert et al. Several of the constituents, however, are purely numerical solutions, not based on altimetry; these include the long-period tides, the semidiurnal 2N2, and the quarter-diurnal M4.
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.
Mm n m D+ psi+ D- psi- 1 0 1.496 355.78 1 1 0.481 259.20 0.537 252.58 2 0 10.945 189.99 2 1 0.180 223.28 0.033 28.40 2 2 0.128 182.63 0.009 162.20 3 0 0.683 288.16 3 1 0.360 46.46 0.372 323.60 3 2 0.073 171.02 0.071 142.08 3 3 0.033 272.30 0.034 78.15 4 0 2.732 341.46 4 1 0.083 61.67 0.053 271.54 4 2 0.054 170.41 0.053 184.20 4 3 0.008 113.69 0.006 201.29 4 4 0.007 286.49 0.007 77.12 5 0 3.578 200.90 6 0 1.102 341.95 7 0 4.064 195.30 8 0 0.502 341.85 9 0 2.354 188.09 10 0 0.482 173.51 Mf n m D+ psi+ D- psi- 1 0 2.737 8.21 1 1 1.164 314.10 1.431 284.99 2 0 18.881 196.39 2 1 0.445 259.97 0.290 46.16 2 2 0.367 188.81 0.055 116.81 3 0 2.087 327.51 3 1 0.558 53.97 0.667 327.05 3 2 0.184 176.75 0.178 137.50 3 3 0.070 278.46 0.080 82.74 4 0 6.470 341.60 4 1 0.227 55.35 0.196 249.57 4 2 0.111 157.50 0.116 184.89 4 3 0.017 121.88 0.021 199.55 4 4 0.015 288.56 0.015 79.18 5 0 5.609 215.48 6 0 2.436 348.55 7 0 6.762 206.59 8 0 1.243 1.42 9 0 4.311 198.78 10 0 0.865 168.47 Mt n m D+ psi+ D- psi- 1 0 0.482 22.16 1 1 0.238 348.01 0.335 314.03 2 0 3.319 199.63 2 1 0.112 312.98 0.074 66.65 2 2 0.086 206.28 0.016 126.97 3 0 0.482 353.07 3 1 0.074 32.56 0.111 332.04 3 2 0.042 178.03 0.044 142.87 3 3 0.016 281.38 0.018 91.27 4 0 1.368 344.38 5 0 0.883 226.39 6 0 0.562 355.23 7 0 1.204 213.13 8 0 0.265 29.70 9 0 0.783 206.88 10 0 0.244 167.75 Q1 n m D+ psi+ D- psi- 1 0 2.476 262.94 1 1 0.843 46.80 0.922 328.65 2 0 3.760 319.93 2 1 5.528 133.54 2.719 283.68 2 2 1.118 342.91 0.299 234.90 3 0 1.489 43.88 3 1 3.631 344.78 2.419 98.73 3 2 0.686 296.73 0.242 103.22 3 3 0.442 126.34 0.358 208.98 4 0 6.854 94.20 4 1 3.246 162.39 1.015 109.94 4 2 0.410 283.79 0.064 34.70 4 3 0.119 145.99 0.112 356.22 4 4 0.034 275.65 0.030 73.93 5 1 2.317 334.43 0.887 310.98 6 1 0.567 159.45 0.278 240.97 7 1 0.711 314.74 0.536 308.90 8 1 0.141 338.40 0.222 112.27 9 1 0.136 48.84 0.277 342.42 10 1 0.363 359.73 0.085 244.53 O1 n m D+ psi+ D- psi- 1 0 15.790 272.89 1 1 3.581 57.42 5.715 342.85 2 0 10.288 336.74 2 1 26.412 137.13 11.825 299.89 2 2 5.917 339.71 0.578 251.37 3 0 9.284 45.52 3 1 14.726 7.13 11.818 113.64 3 2 3.882 310.62 1.711 114.50 3 3 2.334 136.61 1.582 236.32 4 0 23.497 101.20 4 1 16.409 172.56 6.182 124.77 4 2 1.732 302.48 0.106 175.65 4 3 0.592 149.23 0.416 25.20 4 4 0.174 291.31 0.170 77.51 5 1 10.690 340.44 3.556 303.82 6 1 3.059 173.69 1.642 245.96 7 1 3.473 317.20 2.478 319.20 8 1 0.926 335.11 1.020 133.73 9 1 0.420 38.78 1.425 353.81 10 1 1.660 358.65 0.103 152.88 P1 n m D+ psi+ D- psi- 1 0 8.125 283.43 1 1 1.586 87.98 3.173 0.93 2 0 2.456 208.46 2 1 9.733 132.83 4.927 317.18 2 2 3.294 354.60 0.520 173.62 3 0 7.658 44.46 3 1 3.202 55.80 5.647 136.41 3 2 1.668 339.42 1.522 147.24 3 3 1.184 154.60 0.701 267.73 4 0 5.922 74.66 4 1 7.105 196.53 2.864 131.84 4 2 0.650 300.57 0.192 288.07 4 3 0.241 161.18 0.127 50.88 4 4 0.086 310.64 0.125 92.31 5 1 4.525 345.82 2.055 294.48 6 1 0.888 193.93 1.125 244.05 7 1 1.601 318.00 1.053 326.38 8 1 0.410 322.18 0.199 126.34 9 1 0.351 5.56 0.612 16.67 10 1 0.766 15.68 0.348 164.45 K1 n m D+ psi+ D- psi- 1 0 24.473 283.84 1 1 4.788 89.54 9.678 0.17 2 0 7.645 207.22 2 1 29.389 132.95 14.913 317.16 2 2 9.991 354.62 1.657 172.74 3 0 23.341 44.62 3 1 9.627 55.19 17.138 136.33 3 2 5.018 339.35 4.633 147.70 3 3 3.583 154.64 2.109 268.22 4 0 18.405 73.91 4 1 21.437 197.12 8.697 131.54 4 2 1.948 299.74 0.603 288.23 4 3 0.725 160.99 0.385 50.79 4 4 0.261 310.97 0.376 92.46 5 1 13.776 345.47 6.264 294.23 6 1 2.710 195.77 3.474 245.21 7 1 4.825 317.58 3.255 325.34 8 1 1.234 319.69 0.542 129.39 9 1 1.097 8.09 1.789 16.03 10 1 2.344 16.80 1.066 169.46 2N2 n m D+ psi+ D- psi- 1 0 0.405 26.81 1 1 0.266 336.53 0.128 329.62 2 0 0.770 352.93 2 1 0.333 138.03 0.329 168.55 2 2 0.913 108.16 0.138 355.68 3 0 2.218 258.06 3 1 0.275 89.91 0.849 33.57 3 2 0.138 236.74 0.034 73.58 3 3 0.163 20.29 0.136 338.35 4 0 2.947 152.63 4 1 0.324 18.36 0.332 55.88 4 2 0.360 292.35 0.206 15.74 4 3 0.044 239.12 0.066 131.99 4 4 0.025 122.98 0.011 131.45 5 2 0.144 71.54 0.227 141.08 6 2 0.064 56.92 0.048 261.99 7 2 0.052 161.07 0.082 289.38 8 2 0.034 236.12 0.010 269.83 N2 n m D+ psi+ D- psi- 1 0 2.193 44.85 1 1 1.299 281.80 1.049 11.34 2 0 2.100 272.65 2 1 2.418 165.70 1.615 179.99 2 2 7.210 121.08 1.062 3.91 3 0 12.476 292.42 3 1 2.273 98.17 6.541 38.88 3 2 1.005 283.01 0.422 110.08 3 3 1.007 30.82 0.981 355.25 4 0 14.683 163.84 4 1 3.600 39.73 3.140 75.97 4 2 2.386 310.05 1.302 53.28 4 3 0.367 252.62 0.480 150.57 4 4 0.178 139.10 0.088 181.15 5 2 0.752 86.28 1.643 170.81 6 2 0.653 90.13 0.334 293.86 7 2 0.298 206.60 0.544 316.24 8 2 0.227 232.03 0.086 290.33 9 2 0.043 247.40 0.120 83.88 10 2 0.051 75.13 0.067 317.47 M2 n m D+ psi+ D- psi- 1 0 10.152 49.06 1 1 6.767 308.66 3.143 16.90 2 0 28.685 269.62 2 1 13.610 199.55 3.746 152.59 2 2 32.340 130.07 5.817 29.09 3 0 38.272 297.84 3 1 13.560 104.48 33.183 53.26 3 2 2.905 278.05 2.176 138.27 3 3 4.522 53.51 4.575 8.80 4 0 50.873 154.46 4 1 22.225 59.59 17.226 108.00 4 2 10.581 321.08 4.125 90.53 4 3 2.248 271.46 2.265 171.28 4 4 0.793 147.36 0.427 222.57 5 2 2.858 80.18 7.104 192.97 6 2 4.023 118.93 1.175 325.81 7 2 1.235 243.87 2.345 336.43 8 2 1.310 238.56 0.598 295.18 9 2 0.382 314.15 0.574 92.74 10 2 0.252 96.07 0.394 0.27 S2 n m D+ psi+ D- psi- 1 0 3.133 75.49 1 1 2.310 23.71 0.944 51.10 2 0 11.696 308.55 2 1 5.695 262.11 4.014 124.81 2 2 11.770 134.80 2.726 84.20 3 0 18.319 296.13 3 1 4.799 133.62 10.756 102.38 3 2 2.980 244.75 1.176 249.42 3 3 0.807 121.95 1.772 37.01 4 0 28.409 171.84 4 1 11.628 105.28 4.380 100.98 4 2 3.684 343.59 0.616 28.77 4 3 0.966 334.56 0.647 194.36 4 4 0.328 154.87 0.194 284.25 5 2 1.551 68.54 2.225 201.55 6 2 1.761 164.61 0.343 298.79 7 2 0.419 291.97 0.623 7.90 8 2 0.476 261.48 0.400 344.80 9 2 0.247 19.12 0.201 123.10 10 2 0.163 137.50 0.168 57.65 K2 n m D+ psi+ D- psi- 1 0 1.031 53.29 1 1 0.626 6.65 0.035 187.03 2 0 3.606 298.17 2 1 1.298 259.00 1.139 114.94 2 2 2.919 128.91 0.618 72.32 3 0 5.126 287.86 3 1 1.398 116.68 2.916 95.82 3 2 0.803 239.24 0.335 250.53 3 3 0.207 120.21 0.473 33.85 4 0 7.669 162.05 4 1 2.970 102.59 1.382 97.83 4 2 0.995 338.06 0.209 2.79 4 3 0.242 328.19 0.156 178.74 4 4 0.087 145.38 0.050 281.02 5 2 0.400 67.95 0.593 192.23 6 2 0.455 160.80 0.095 312.01 7 2 0.110 286.63 0.156 0.17 8 2 0.115 251.93 0.108 343.58 9 2 0.065 27.95 0.050 113.30 10 2 0.035 124.61 0.036 66.26 M4 n m D+ psi+ D- psi- 1 0 0.011 273.42 1 1 0.021 77.33 0.015 200.89 2 0 0.142 315.84 2 1 0.033 281.33 0.017 22.72 2 2 0.006 287.81 0.007 219.74 3 0 0.197 154.11 3 1 0.006 260.16 0.036 129.43 3 2 0.010 175.95 0.005 113.66 3 3 0.006 155.08 0.003 191.66 4 0 0.069 74.47 4 1 0.068 105.81 0.052 227.74 4 2 0.005 52.88 0.011 241.36 4 3 0.003 336.31 0.001 325.57 4 4 0.000 341.93 0.001 312.80