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A brief descripton of the available ocean tide models

Last updated: 2 November 2022

For a broad overview, status of 2014, see Stammer et al. (2014).

The Schwiderski model is the oldest (1980) model in this collection and is included because it has been the standard for so many years. It is a hydrodynamic model, given on a 1 by 1 degree grid and uses an interpolation scheme to fit the tide gauges.

NAO.99b is based on the same hydrodynamics as the Schwiderski model but has TOPEX/Poseidon data assimilated into it and is given on a 0.5 by 0.5 degree grid.

FES94.1 is a pure hydrodynamic tide model tuned to fit tide gauges globally. It has been calculated on a finite element grid with very fine resolution near the coast but the version used here is given on a 0.5 by 0.5 degree grid. In FES95.2 the tides in the Arctic were improved and TOPEX/Poseidon data has been used to adjust the long wavelength behaviour of FES94.1. FES98 is again a pure hydrodynamic model that has assimilated a set of roughly 700 carefully selected tide gauges into it. Another improvement is the fact that is has been computed on a global grid instead of computing the ocean tides in a few ocean basins separately and then glueing the solutions together. FES99 is an update of FES98 and has TOPEX/Poseidon data assimilated into it. Both FES98 and FES99 are given on a 0.25 by 0.25 degree grid.

FES2004 is a further development in the FES series. Letellier is shown in our reference list as responsible for both; the thesis (in French) produced FES2004 and discusses FES99. FES2004 has a 0.125 degree resolution. It assimilates TOPEX/POSEIDON altimetry into a hydrodynamic  tide model. The thesis also presents higher-harmonic waves (M3, M4, M6) which so far have not been adapted to the loading provider site.

FES2014b has a still higher resolution (1/161/16 degree). In the tradition of its predecessors (including FES2012) it emphasizes ocean hydrodynamics and especially keeps impact from assimilation of altimetry low, thus avoiding a fallacy of biased consistency in these missions. FES2014 has gained endorsement from a.o. IERS.    

CSR3.0 and CSR4.0 are long wavelength adjustments of FES94.1 using TOPEX/Poseidon data and are given on a 0.5 by 0.5 degree grid. Unfortunately, these two models have spurious gridcells over land that have been removed using the grid of GOT00.2 as a mask. At the same time GOT00.2 has been used to add extra tidal values in the Weddell and Ross Sea in the Antarctic. For the other tidal values below and above the 66S and 66N latitude (the limits of the TOPEX/Poseidon satellite), these models become equal to FES94.1.

GOT99.2b and GOT00.2 is again long wavelength adjustments of FES94.1 using TOPEX/Poseidon data and are given on a 0.5 by 0.5 degree grid. GOT99.2b also becomes equal to FES94.1 outside the 66 degree latitudes. GOT00.2 is different from FES94.1 in the polar region because ERS1/2 data is used in the assimilation process. Follow-up models GOT4.7  and GOT4.8 are based primarily on evolving satellite altimetry missions with refined adjustments for global tidal mass and mass-centre, and atmospheric corrections. GOT4.10 is the latest version of Richard Ray's tide models and is solely based on Jason1&2 altimetry. GOT4.8 has become one of the standard tide models, besides FES2004, that is used for Satellite Altimetry corrections and  for GNSS software and data products from JPL.

HAMTIDE is based on the generalized inverse methods for tides developed at the University of Hamburg. DGFI altimeter data bank obtained from 15 years time series observed by TOPEX and Jason-1 was used in the assimilation process. It is hoped that more information can be found in the future publication of Taguchi et al.

TPXO.5 through TPXO.7.1 have been computed using inverse theory using tide gauge and TOPEX/Poseidon data. It finds the optimum balance between observations and hydrodynamics. TPXO.5 is given on a 0.5 by 0.5 degree grid while TPXO.6.2 and successors are given on a 0.25 by 0.25 degree grid. TPXO.7.0 and TPXO.7.1 differ only in the constituents P1 and S2. The latest version TPXO.7.2 also includes GRACE data. The TPXO_Atlas version is a combination of the global solution TPXO.7.2, patched with local tide models.

EOT08a and EOT11a are based on harmonic analysis of multi-mission altimetry (TOPEX, Jason-1, ERS1, ERS2, ENVISAT, GFO) which implies a 13 year time base. The tides are represented on a 0.125 degree grid.

AG06a is an adjustment of the FES94.1 model to multi-mission altimetry ((TOPEX, Jason-1, ERS1, ERS2, ENVISAT, GFO). The tides are represented on a 0.5 degree grid.  This model has been superseded by DTU10 which is an adjustment of FES2004.

OSU12 is a pure empirical tide model based on satellite altimetry data from TOPEX, Jason-1/-2, Envisat, and GFO that have been interpolated using least-squares collocation onto a 0.25x0.25 degree grid. The covariance matrix used in this procedure varies from place to place and depends on the depth of the ocean. Only diurnal and semi-diurnal harmonics are provided.

Not all models come with long-period tides. In order to cover the whole spectral range, recognising that long-period tide loading effects are generally at the millimetre level, the models have been supplemented as shown in Table 1.

Next, one must be aware that some ocean tide models miss certain shallow water areas. This could lead to erroneous ocean loading values if your station is close to a sea that your chosen ocean tide model is lacking. These areas are given in Figure 1. Each coloured area is associated with the names in the same colour. For example, the Mediterranean Sea is missing in Schwiderski (SCHW) and FES94.1.

The ocean tides are small in the Mediterranean Sea and very small in the Baltic and Black Sea. Omision of these particular areas in the models is therefore not a big problem.
Figure 1: Water areas that are missing in the ocean tide models

Missing Seas
Table 1: Long period tides supplemented

Andersen 2006
Mf Mm Ssa FES99
Mf Mm Ssa FES2004
Mf Mm Ssa FES2004
Mf Mm EOT11a | Ssa FES2004
Mf Mm Ssa FES99
Mf Mm Ssa FES99
Mf Mm Ssa FES99
Mf Mm Ssa FES99
Mf Mm Ssa FES2004
Mf Mm Ssa FES99
Mf Mm Ssa FES99
Mf Mm Ssa FES98
Mf Mm Ssa FES99
Mf Mm Ssa FES99
Mf Mm Ssa FES99
Mf Mm Ssa NAO.99b
Mf Mm SsaFES2012
Mf Mm TPXO.5 | Ssa FES99
Mf Mm TPXO.5 | Ssa FES99
Mf MmTPXO.7.0 | Ssa FES99
Mf MmTPXO.7.1 |Ssa FES99
Mf MmTPXO.7.2 |Ssa FES99
Mf MmTPXO_Atlas |Ssa FES99
Mf Mm Schwiderski,
Ssa equilibrium