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TOPEX/POSEIDON tidal solutions on the rise

C. Le Provost (LEGI/IMG, France)

After analysis of just one year of TOPEX/POSEIDON data, the new tide solutions look impressively accurate compared with those by Schwiderski (Sch80, 1980) and Cartwright and Ray (CR91, 1991).

Here is a short review of the new solutions, with preliminary estimates of the gains in accuracy. Seven solutions have been available on CD-ROM since mid-1994.

One solution is independent of altimeter data: the Le Provost et al [LPal94, 1994] hydrodynamic model. This has a computational grid varying from 200 km over deep ocean regions down to 10 km along coastlines. The model covers the whole ocean including the Arctic and the Antarctic in the Weddell Sea, the Ross Sea and the Emery Ice Shelf. We derived nine semi-diurnal components (M2, S2, N2, K2, 2N2, Mu2, Nu2, L2 and T2) and four diurnal (K1, O1, P1 and Q1). The table shows the accuracy for the four main constituents using data from 103 sea truth stations (see next article). Compared to Sch80 and CR91, the LPal94 solutions seem better globally and almost everywhere regionally.
The gain relative to Sch80 is almost 1 cm RMS  for M2 and 0.27 cm for K1. Relative to CR91 it is 0.5 cm for M2. Over the North Atlantic basin the LPal94 solutions are surprisingly good (less than 1.6 cm for M2 and 1.0 cm for S2). However they are less accurate in the Indian Ocean and North Pacific.

Constituent Model Global North Atlan. South Atlan. Indian North Pacif. South Pacif.
O1 Sch80 1.25 0.51 1.19 1.79 1.53 0.77
CR91 1.24 0.95 0.88 1.65 1.56 0.81
LPal94 1.06 0.53 1.10 1.15 1.46 0.68
SR94 1.04 0.54 0.48 1.49 1.39 0.78
EGal94 0.96 0.55 0.52 1.40 1.22 0.68
K1 Sch80 1.50 0.73 0.95 1.91 2.19 0.87
CR91 1.90 1.42 1.89 2.31 2.28 1.28
LPal94 1.23 1.00 0.97 1.08 1.71 1.02
SR94 1.29 1.02 0.69 1.52 1.83 0.74
EGal94 1.25 0.81 0.73 1.92 1.51 0.74
M2 Sch80 3.94 4.17 5.01 3.89 3.04 3.52
CR91 3.55 2.60 2.98 5.37 2.85 3.80
LPal94 2.99 1.57 2.82 3.48 3.68 2.88
SR94 1.96 1.53 1.81 2.56 1.71 2.22
EGal94 2.56 1.54 2.14 3.39 2.38 3.26
S2 Sch80 1.64 1.40 1.40 2.14 1.53 1.77
CR91 2.39 2.37 1.74 3.57 1.81 2.24
LPal94 1.60 0.95 1.39 2.59 1.50 1.26
SR94 1.27 0.88 1.18 1.82 1.11 1.32
EGal94 1.66 1.00 0.92 2.44 1.50 2.17

RMS differences (cm) between Schwiderski [1980], Cartwright and Ray [1991], Le Provost et al. [1994], Schrama and Ray [1994] and Egbert et al. [1994] solutions and the in situ measurements from the ST103 database (see next article). The differences are global (column 3) or regional (columns 4 to 8) according to the geographical limits of the basins defined on next article.


The altimeter tide solutions derived by analyzing one year of TOPEX/ POSEIDON measurements are excellent.
This is mainly because:

  • the TOPEX/POSEIDON tidal aliases are removed from the ocean signals (Parke et al., 1987),
  • the TOPEX/POSEIDON error budget is far better than for previous missions, especially for orbit determination.

The simpler empirical methods using Fourier analysis [Schrama and Ray, SR94, 1994] or admittance [Ma et al., 1994] have been very successful. The table shows that SR94 is more than 1 cm more accurate than LPal94 for M2. The gain is 0.33 cm for S2 but there is none for K1 or O1. Because of the aliasing constraints the data were binned into boxes of several degrees to sample a wider range of phases along the satellite ground tracks. The maps are therefore noisy and do not pick up the sharpest gradients in the cotidal solutions due to regional topographic features.

An application of the Egbert et al. assimilation model [EGal, 1994] using the representer model successfully assimilated most of the crossover data from 38 TOPEX/POSEIDON cycles. The grid is 0.7° by 0.7°. The solutions are computed independently of previous tidal solutions. They are smoother than the empirical solutions presented above. Compared to earlier non-TOPEX/POSEIDON solutions these inverse ones reduce the misfit for the M2 and O1 constituents (see table). For S2 and K1 no improvement is observed. Analyzing the difference relative to pelagic data reveals that the largest discrepancies for S2 are at equatorial latitudes, probably due to the limited one-year data set used. Recall that the TOPEX/ POSEIDON aliased period for K1 is 173 days.

Mazzega et al. [1994] also applied empirical statistical methods based on a generalized least-squares approach to the TOPEX/POSEIDON data, while Pavlis et al. [1994] used semi-empirical methods to fit TOPEX/POSEIDON data to Proudman functions. The solutions are available on the AVISO tide CD-ROM.

This article introduced the new cotidal solutions now available. The test comparing some of the solutions with sea truth from 103 stations gives an idea of the quality of these solutions over the ocean basins. However, the test still has to be done on the full set of tidal solutions. More tests are also needed, as done by Molines et al. [1994] to evaluate the accuracy of the two tide models of the TOPEX/POSEIDON GDR-M.
The new solutions based on TOPEX/POSEIDON data are already greatly improved. With more TOPEX/POSEIDON observations, the signal-to-noise ratio will increase and aliasing problems will be removed. The above figures can be reduced by a factor of 1.4 to 1.5, approaching the limits of the tidal analysis method. The challenge is to predict tidal heights over the world ocean with 2 cm RMS accuracy, but this still has to be proved feasible.


  • Cartwright D.E. and R.D. Ray, 1991, J. Geophys. Res., 96, 16897-16912.
  • Egbert G.D., A.F. Bennett et M.G. Foreman, 1994, J. Geophys. Res. (in press).
  • Le Provost C., M.L. Genco, F. Lyard, P. Vincent and P. Canceill, 1994, J. Geophys. Res. (in press).
  • Ma X.C., C.K. Shum, R.J. Eanes eand B.D. Tapley, 1994, J. Geophys. Res. (in press).
  • Mazzega, P, and M. Bergé, Ocean tides in the Asian Semi-enclosed seas from TOPEX/POSEIDON, 1994, J. Geophys. Res. (in press).
  • Molines J.M., C. Le Provost, F. Lyard, R.D. Ray, C.K. Shum and R.J. Eanes, 1994, J. Geophys. Res. (in press).
  • Pavlis N.K., B.D. Beckley and B.V. Sanchez, 1994, EGS, Grenoble.
  • Parke M.E., R.H. Stewart, D.L. Farless and D.E. Cartwright, 1987, J. Geophys. Res., 92, 11693-11707.
  • Schrama E.J.O. and R. Ray, 1994, J. Geophys. Res. (in press).
  • Schwiderski E.W., 1980, Rev. Geophys. and Space Phys., 18, 243-268.
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