PyFES documentation#
This package is the fully revised version of the FES2022 distribution. A full description of the FES2022 tidal solution is given in the handbook and in the paper (Lyard et al. 2024).
The library uses a set of tidal components to predict the ocean tide at any location on the Earth. The source code provides an older version of the FES model (99), because it is significantly smaller than newer versions. Do not use it for scientific purposes. You can download the model from the AVISO website.
Theoretical Background: The Harmonic Method#
The prediction of tides is based on the principle of harmonic analysis, a method developed into a practical application by Sir William Thomson (Lord Kelvin) around 1867. The core idea is that the complex, periodic motion of the tide at any location can be resolved into the sum of a series of simpler, regular wave-like components known as tidal constituents. Each constituent corresponds to a distinct astronomical forcing, such as the gravitational pull of the Moon or Sun, or orbital variations like the evection and variation of the moon.
As detailed in Schureman’s manual [Schureman1940], the height of the tide, h, at any time, t, can be expressed by the fundamental equation of harmonic prediction:
- Where:
\(H_0\) is the mean height of the water level above the chart datum.
Each cosine term represents a single tidal constituent (e.g., the principal lunar semidiurnal tide, \(M_2\); the principal solar semidiurnal tide, \(S_2\); etc.).
Amplitude (\(A\), \(B\), \(C\)…): This is the strength, or half the range, of each constituent. It is a location-specific value determined from the analysis of tidal observations.
Speed (\(a\), \(b\), \(c\)…): This is the angular speed of the constituent, representing how quickly its phase changes. Speeds are constant for each constituent and are derived from universal astronomical data, such as the rotation of the Earth and the orbital periods of the Moon and Sun.
Phase Lag (\(\alpha\), \(\beta\), \(\gamma\)…): Also known as the epoch (\(\kappa\)), this value represents the timing of a constituent’s high water relative to its theoretical astronomical forcing. Like the amplitude, it is a location-specific constant found through observation.
The FES models, such as FES2022, are sophisticated global atlases that provide the location-specific amplitudes (\(H\)) and phase lags (\(\kappa\)) for a large number of tidal constituents. The PyFES library acts as the harmonic prediction engine. When a user requests a tide prediction for a specific location and time, the library:
Retrieves the amplitude and phase for each constituent from the FES model maps at the desired location.
Calculates the astronomical argument (the angle inside the cosine function) for the specified time using the known astronomical speeds of each constituent.
Applies the fundamental prediction equation shown above, summing the contributions of all constituents.
Adds the local mean sea level (\(H_0\)) to produce the final predicted tide height relative to the datum.
References#
Schureman, P. (1940). Manual of Harmonic Analysis and Prediction of Tides. U.S. Coast and Geodetic Survey, Special Publication No. 98.
Bibliography#
Lyard, F., Carrere, L., Fouchet, E., Cancet, M., Greenberg, D., Dibarboure, G., and Picot, N.: FES2022 a step towards a SWOTcompliant tidal correction, Submitted to J. Geophy. Res., in review, 2025
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.
Carrere L., F. Lyard, M. Cancet, A. Guillot, N. Picot: FES 2014, a new tidal model - Validation results and perspectives for improvements, presentation to ESA Living Planet Conference, Prague 2016.
Credits#
When using FES2022, please mention: FES2022 was produced by LEGOS, NOVELTIS
and CLS Ocean and Climate Division; the project was funded by CNES. It is
distributed by AVISO, with support from CNES (http://www.aviso.altimetry.fr/)