Gravitational effect of ocean and atmospheric tides

Here we provide ocean and atmospheric tide models for easy consideration in precise satellite orbit determination. The gravitational effect of tides including loading effects at a given time can be represented as corrections to the Stokes coefficients of a spherical harmonics expansion. This requires not only an atlas of selected major tidal consitutents but also a calculation rule to complement all frequency lines. This can be done by interpolation using an admittance matrix. For this purpose, a file format and an algorithm are defined here. All required information can be found in the README. We provide also reference implementations in MATLAB, Python and Fortran.

The following models are currently available (We currently recommend the use of MIXED2025 or GOT5.6 for ocean tides and TiME22 for atmospheric tides, as these models show the smallest residuals in our GRACE-FO processing):

MIXED2025 (based on GOT5.6, extended by consituents of FES2022 and TiME22)
GOT5.6 (Schrama and Ray 1994, Ray 1999, Ray 2013)
FES2022, updated 2025-03-09 (Lyard et al. 2022)
FES2014b (Lyard et al. 2021)
TPXO10 (Egbert et al. 2002)
EOT20 (Hart-Davis et al. 2021)
EOT11a (Savcenko et al. 2012)
DTU23 (Andersen 2023)
TiME22, updated 2025-03-09 (Sulzbach et al. 2022)
TiME22 atmospheric tides, updated 2025-03-09 (Balidakis et al. 2022)
... more models will be published in the future.

Please cite the models accordingly and respect their license.

Download

README.pdf: format description and evaluation algorithm
FTP-Server: directory with README, all models, and software

Conversion of other tide models from gridded data

If you want to convert your own ocean tide model from NETCDF data you can use our GROOPS software (https://github.com/groops-devs/groops). A example script with description is provided at our FTP-Server.

References

For FES2022, please cite: The FES2022 Tide product was funded by CNES, produced by LEGOS, NOVELTIS and CLS and made freely available by AVISO. CNES, 2024. FES2022 (Finite Element Solution) Tidal model (Version 2024) [Data set]. CNES. https://doi.org/10.24400/527896/A01-2024.004

For FES2014, please cite: "FES2014 was produced by Noveltis, Legos and CLS and distributed by Aviso+, with support from Cnes (https://www.aviso.altimetry.fr/)".

Andersen, Ole Baltazar (2023). DTU23 Global Ocean Tide model (DTU23_OceanTide). Technical University of Denmark. Dataset. https://doi.org/10.11583/DTU.23828874.v1

Balidakis, K., Sulzbach, R., Shihora, L., Dahle, C., Dill, R., & Dobslaw, H. (2022). Atmospheric contributions to global ocean tides for satellite gravimetry. Journal of Advances in Modeling Earth Systems, 14, e2022MS003193. https://doi.org/10.1029/2022MS003193

Egbert, G. D., and S. Y. Erofeeva, 2002: Efficient Inverse Modeling of Barotropic Ocean Tides. J. Atmos. Oceanic Technol., 19, 183–204, https://doi.org/10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2.

Hart-Davis Michael, Piccioni Gaia, Dettmering Denise, Schwatke Christian, Passaro Marcello, Seitz Florian (2021). EOT20 - A global Empirical Ocean Tide model from multi-mission satellite altimetry. SEANOE. https://doi.org/10.17882/79489

Hart-Davis Michael G., Piccioni Gaia, Dettmering Denise, Schwatke Christian, Passaro Marcello, Seitz Florian (2021). EOT20: a global ocean tide model from multi-mission satellite altimetry. Earth System Science Data, 13 (8), 3869-3884. https://doi.org/10.5194/essd-13-3869-2021

Lyard, F. H., Allain, D. J., Cancet, M., Carrère, L., and Picot, N.: FES2014 global ocean tide atlas: design and performance, Ocean Sci., 17, 615–649, https://doi.org/10.5194/os-17-615-2021, 2021

Ray, <text></text>R. D., A global ocean tide model from Topex/Poseidon altimetry: GOT99.2, NASA Tech Memo 209478, 58 pages, Sept. 1999.

Ray, R. D. (2013), Precise comparisons of bottom-pressure and altimetric ocean tides, J. Geophys. Res. Oceans, 118, 4570–4584, https://doi.org/10.1002/jgrc.20336.

Savcenko, Roman; Bosch, Wolfgang; Dettmering, Denise; Seitz, Florian (2012): EOT11a - Global Empirical Ocean Tide model from multi-mission satellite altimetry, with links to model results. PANGAEA, https://doi.org/10.1594/PANGAEA.834232

Savcenko, Roman; Bosch, Wolfgang (2012): EOT11a - Empirical Ocean Tide Model from Multi-Mission Satellite Altimetry. Deutsches Geodätisches Forschungsinstitut (DGFI), München, 89, 49 pp, hdl:10013/epic.43894.d001

Schrama, E. J. O., and R. D. Ray (1994), A preliminary tidal analysis of TOPEX/POSEIDON altimetry, J. Geophys. Res., 99(C12), 24799–24808, https://doi.org/10.1029/94JC01432.

Sulzbach, Roman; Balidakis, Kyriakos; Dobslaw, Henryk; Thomas, Maik (2022): TiME22: Periodic Disturbances of the Terrestrial Gravity Potential Induced by Oceanic and Atmospheric Tides. GFZ Data Services. https://doi.org/10.5880/GFZ.1.3.2022.006

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Contact

Torsten Mayer-Gürr
Steyrergasse 30/III
8010 Graz
Austria
Tel: +43 316 873-6359
Fax: +43 316 873-6845
mayer-guerr@tugraz.at

Felix Öhlinger
Steyrergasse 30/III
8010 Graz
Austria
Tel: +43/316/873- 6333
Fax: +43/316/873-6845
felix.oehlingernoSpam@tugraz.at