Theoretical Foundations

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Theoretical Foundations#

PyFES implements the harmonic method for ocean tide prediction, a technique with roots in Lord Kelvin’s work around 1867 and formalised through the contributions of Darwin, Doodson, and Schureman over the following decades. The method rests on the physical insight that the complex, quasi-periodic motion of the tide at any location can be decomposed into a finite sum of sinusoidal components — the tidal constituents — each driven by a distinct astronomical forcing.

This section provides the mathematical foundations underlying the PyFES prediction engines. It complements the practical guidance in Prediction Engines with rigorous derivations of the key equations implemented in the library.

References#

The theoretical development presented here draws primarily from:

  • Doodson, A. T. (1921). The Harmonic Development of the Tide-Generating Potential. Proceedings of the Royal Society of London A, 100(704), 305–329.

  • Cartwright, D. E. & Tayler, R. J. (1971). New Computations of the Tide-generating Potential. Geophysical Journal of the Royal Astronomical Society, 23, 45–74.

  • Cartwright, D. E. & Edden, A. C. (1973). Corrected Tables of Tidal Harmonics. Geophysical Journal of the Royal Astronomical Society, 33, 253–264.

  • Meeus, J. (1998). Astronomical Algorithms, 2nd ed. Willmann-Bell, Inc.

  • Petit, G. & Luzum, B. (2010). IERS Conventions (2010). IERS Technical Note 36.

  • Ray, R. D. (1999). A Global Ocean Tide Model From TOPEX/POSEIDON Altimetry: GOT99.2. NASA Technical Memorandum 209478.

  • Schureman, P. (1940). Manual of Harmonic Analysis and Prediction of Tides. U.S. Coast and Geodetic Survey, Special Publication No. 98.

  • Simon, B. (2013). Marées Océaniques et Côtières (Coll. Synthèses, 943-MOC). Institut Océanographique / SHOM, Paris.

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