G. Egbert and S. Erofeeva, "Efficient inverse modeling of barotropic ocean tides," Journal of Atmospheric and Oceanic Technology, 19, 183-204, 2002.
Coefficients below were computed by R. Ray, NASA/GSFC.
These spherical harmonic coefficients correspond to the TPXO.6.2 tide model, produced by Gary Egbert at Oregon State University. The tidal solutions are the result of assimilating satellite altimeter data into a hydrodynamic ocean model, using the inverse methods of Egbert et al. (1994).
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 1.364 350.94 1 1 0.530 253.47 0.597 250.06 2 0 10.870 192.04 2 1 0.134 232.04 0.023 261.58 2 2 0.143 175.51 0.018 218.09 3 0 1.107 286.52 3 1 0.341 52.98 0.352 323.23 3 2 0.070 168.94 0.075 144.78 3 3 0.035 275.17 0.033 75.03 4 0 2.949 333.00 4 1 0.067 71.95 0.048 245.71 4 2 0.048 174.95 0.049 189.01 4 3 0.008 110.63 0.005 208.39 4 4 0.007 287.11 0.008 75.64 5 0 3.745 206.29 6 0 1.327 324.86 7 0 4.095 200.89 8 0 0.675 326.27 9 0 2.344 196.21 10 0 0.432 187.48 Mf n m D+ psi+ D- psi- 1 0 2.955 10.54 1 1 1.046 309.42 1.449 292.91 2 0 18.490 197.79 2 1 0.456 251.68 0.263 34.65 2 2 0.360 209.33 0.083 149.08 3 0 2.033 339.24 3 1 0.651 41.97 0.577 326.15 3 2 0.200 173.89 0.173 143.08 3 3 0.059 294.15 0.090 80.58 4 0 6.977 347.48 4 1 0.162 52.67 0.255 258.65 4 2 0.124 151.21 0.101 179.57 4 3 0.016 116.48 0.022 195.82 4 4 0.014 285.00 0.014 76.81 5 0 5.560 217.70 6 0 2.726 351.92 7 0 6.193 207.64 8 0 1.679 20.93 9 0 3.994 200.92 10 0 0.980 160.12 Q1 n m D+ psi+ D- psi- 1 0 2.766 279.05 1 1 0.723 50.52 0.897 335.71 2 0 3.257 319.91 2 1 5.782 136.48 2.876 281.66 2 2 1.057 343.13 0.351 250.88 3 0 1.261 59.26 3 1 3.642 342.90 2.187 102.24 3 2 0.704 293.05 0.172 85.80 3 3 0.444 126.82 0.365 210.34 4 0 7.226 90.88 4 1 3.238 162.19 1.068 114.10 4 2 0.400 286.56 0.059 84.76 4 3 0.122 144.76 0.102 359.55 4 4 0.033 278.16 0.029 71.62 5 1 2.312 333.85 0.915 301.83 6 1 0.658 162.06 0.337 240.69 7 1 0.778 308.38 0.563 299.41 8 1 0.156 332.40 0.210 129.15 9 1 0.107 29.44 0.253 323.75 10 1 0.345 0.87 0.148 239.05 O1 n m D+ psi+ D- psi- 1 0 17.334 275.66 1 1 4.508 63.03 6.169 349.42 2 0 10.083 351.56 2 1 26.279 137.21 11.966 299.66 2 2 5.665 341.09 0.768 233.52 3 0 10.086 36.79 3 1 14.652 6.60 12.041 115.92 3 2 3.893 309.95 1.637 112.23 3 3 2.298 136.82 1.575 233.51 4 0 25.358 96.61 4 1 16.735 172.36 6.078 125.01 4 2 1.764 301.30 0.184 162.64 4 3 0.600 147.93 0.423 24.27 4 4 0.171 291.91 0.169 77.49 5 1 11.110 340.30 3.387 302.17 6 1 3.431 173.45 1.777 244.93 7 1 3.703 318.10 2.389 315.42 8 1 0.531 329.37 0.980 134.00 9 1 0.704 21.53 1.212 354.44 10 1 1.501 4.07 0.171 193.10 P1 n m D+ psi+ D- psi- 1 0 7.178 280.19 1 1 1.557 72.58 3.467 1.01 2 0 1.943 205.38 2 1 9.415 131.48 4.817 313.55 2 2 3.198 351.86 0.476 185.19 3 0 8.281 47.79 3 1 3.616 53.65 5.308 132.60 3 2 1.618 335.78 1.434 143.52 3 3 1.138 152.46 0.654 264.86 4 0 6.836 91.33 4 1 6.764 193.08 2.638 130.19 4 2 0.654 301.67 0.145 290.02 4 3 0.245 157.86 0.115 45.01 4 4 0.084 309.84 0.115 89.83 5 1 4.401 347.94 1.960 296.47 6 1 0.910 191.70 1.145 245.76 7 1 1.474 323.81 1.099 328.08 8 1 0.351 317.86 0.053 125.80 9 1 0.437 11.80 0.619 9.13 10 1 0.676 19.13 0.216 173.80 K1 n m D+ psi+ D- psi- 1 0 25.124 285.30 1 1 5.761 81.81 11.503 3.41 2 0 5.880 197.00 2 1 29.485 132.48 15.258 315.78 2 2 10.185 353.86 1.499 185.67 3 0 26.185 46.72 3 1 10.286 55.16 16.926 137.31 3 2 5.024 339.55 4.610 147.73 3 3 3.589 154.97 2.066 267.73 4 0 22.818 72.97 4 1 21.346 195.76 8.014 133.25 4 2 2.065 300.65 0.583 289.84 4 3 0.728 160.32 0.390 51.61 4 4 0.264 311.88 0.378 92.38 5 1 14.045 345.64 6.650 295.23 6 1 2.911 190.28 4.016 252.20 7 1 5.069 319.50 3.617 320.22 8 1 0.856 303.34 0.196 210.97 9 1 1.302 11.25 1.722 4.93 10 1 1.959 22.17 0.972 192.67 N2 n m D+ psi+ D- psi- 1 0 0.720 82.18 1 1 1.108 262.42 0.423 349.23 2 0 5.107 227.03 2 1 2.883 166.13 1.929 187.38 2 2 6.955 120.64 1.118 6.56 3 0 13.746 278.03 3 1 2.505 106.44 5.722 39.20 3 2 0.999 278.91 0.307 124.02 3 3 1.016 32.93 0.942 355.15 4 0 16.835 172.15 4 1 3.104 40.86 2.524 87.30 4 2 2.351 308.09 1.227 56.27 4 3 0.371 252.86 0.479 153.04 4 4 0.178 140.73 0.085 178.61 5 2 0.739 89.43 1.702 173.35 6 2 0.650 93.42 0.365 282.16 7 2 0.329 208.17 0.539 309.37 8 2 0.283 228.03 0.148 254.42 9 2 0.092 212.05 0.075 113.01 10 2 0.039 141.91 0.084 280.00 M2 n m D+ psi+ D- psi- 1 0 11.451 48.53 1 1 6.808 305.04 3.301 17.97 2 0 28.292 266.50 2 1 13.748 199.09 3.641 156.65 2 2 32.185 129.75 6.197 28.57 3 0 39.330 298.51 3 1 14.273 105.77 32.810 52.48 3 2 2.942 280.40 2.192 138.72 3 3 4.453 53.91 4.535 8.90 4 0 50.305 151.82 4 1 22.710 59.65 17.085 108.98 4 2 10.535 320.94 4.155 89.83 4 3 2.225 270.71 2.254 170.91 4 4 0.791 147.64 0.431 222.38 5 2 2.869 80.70 6.998 193.02 6 2 4.089 117.80 1.197 326.05 7 2 1.210 248.12 2.353 335.84 8 2 1.292 238.67 0.653 299.91 9 2 0.368 318.92 0.592 85.75 10 2 0.252 103.14 0.414 1.05 S2 n m D+ psi+ D- psi- 1 0 3.322 48.31 1 1 2.895 35.67 1.251 20.91 2 0 13.324 308.69 2 1 6.356 263.06 3.657 116.84 2 2 11.038 136.00 2.635 75.72 3 0 20.436 295.76 3 1 4.840 135.01 10.519 103.83 3 2 2.850 243.40 0.963 250.04 3 3 0.835 123.82 1.723 39.42 4 0 27.912 172.75 4 1 11.603 105.75 4.007 92.81 4 2 3.689 344.67 0.620 32.34 4 3 0.947 334.64 0.649 196.71 4 4 0.326 154.75 0.187 288.50 5 2 1.545 70.26 2.171 202.34 6 2 1.732 163.82 0.368 310.72 7 2 0.421 296.92 0.700 10.03 8 2 0.480 266.01 0.426 348.52 9 2 0.263 22.59 0.195 109.03 10 2 0.157 131.37 0.181 53.21 K2 n m D+ psi+ D- psi- 1 0 0.623 25.28 1 1 0.660 21.60 0.344 2.27 2 0 4.755 300.52 2 1 1.764 263.12 0.973 118.04 2 2 3.124 132.68 0.681 75.93 3 0 6.998 288.06 3 1 1.398 126.25 2.773 99.17 3 2 0.834 241.21 0.333 252.64 3 3 0.208 132.02 0.475 34.89 4 0 6.717 169.84 4 1 3.093 106.08 1.046 89.51 4 2 1.041 337.62 0.196 21.68 4 3 0.264 332.54 0.171 188.89 4 4 0.092 148.47 0.051 285.17 5 2 0.405 66.48 0.647 198.53 6 2 0.480 160.22 0.126 306.27 7 2 0.141 288.95 0.193 1.62 8 2 0.137 257.82 0.120 337.06 9 2 0.070 12.82 0.038 106.20 10 2 0.038 153.92 0.042 33.38