Glossary#

Admittance#: The complex ratio between a minor tidal constituent and a major constituent, used to infer amplitudes and phases of constituents not explicitly provided in a tidal atlas. Both prediction engines support admittance inference but use different algorithms. See also Inference.
Astronomical Argument#: The angle \(V_k(t) = n_1\tau + n_2 s + n_3 h + n_4 p + n_5 N' + n_6 p_1\) that determines the phase of a tidal constituent at time t. It is computed from the six fundamental variables using integer coefficients encoded in the constituent’s Doodson number. See Harmonic Development and the Doodson Classification for the full derivation.
AVISO#: Archiving, Validation and Interpretation of Satellite Oceanographic data.
CLS#: Collecte Localisation Satellites, a subsidiary of CNES, is a company that provides satellite-based services for environmental monitoring, maritime surveillance, and sustainable resource management.
CNES#: The Centre National d’Études Spatiales is the French space agency.
Compound Wave#: A tidal constituent whose frequency is an integer linear combination of two or more astronomical constituent frequencies, arising from non-linear hydrodynamic interactions in shallow water. For example, the quarter-diurnal constituent \(M_4\) has twice the frequency of \(M_2\). See Compound and Shallow-Water Waves.
Darwin Notation#: A harmonic constituent notation system developed by Sir George Darwin and refined by Paul Schureman. Each constituent is expressed in terms of fundamental astronomical arguments (s, h, p, N, p₁) with time-varying nodal corrections. The FES/Darwin prediction engine uses this notation system for tidal constituents. See FES/Darwin Engine for details.
Doodson Number#: A systematic numerical classification of tidal constituents developed by Arthur Doodson in 1921. Each constituent is assigned a six-digit number (format: \(D_1D_2D_3.D_4D_5D_6\)) encoding the coefficients of fundamental astronomical arguments. For example, the M₂ tide is represented as 255.555. The PERTH/Doodson prediction engine uses this notation system. See PERTH/Doodson Engine for details and Harmonic Development and the Doodson Classification for the mathematical derivation.
Equilibrium Tide#: The hypothetical ocean surface shape that would exist if the ocean were in static gravitational equilibrium with the tide-generating potential. For long-period tidal constituents, the ocean response closely approximates this equilibrium state. PyFES uses the Cartwright-Tayler-Edden spectral tables to compute the equilibrium long-period tide.
FES#: Finite Element Solution, a series of global ocean tide atlases.
Fundamental Variables#: The six time-varying astronomical angles that define all tidal constituent frequencies: \(\tau\) (local mean lunar time), \(s\) (mean longitude of the Moon), \(h\) (mean longitude of the Sun), \(p\) (longitude of lunar perigee), \(N'\) (negative longitude of the Moon’s ascending node), and \(p_1\) (longitude of solar perihelion). Every tidal frequency is a linear combination of the rates of change of these six variables. See Harmonic Development and the Doodson Classification.
Group Modulation#: A nodal correction technique where related constituents are modulated together as groups, rather than applying individual corrections to each constituent. This approach provides computational efficiency while maintaining accuracy. Enabled via with_group_modulations(True) in the runtime settings.
Inference#: The process of estimating minor tidal constituents from major constituents using admittance relationships. PyFES offers four generic inference types usable with any engine: ZERO (no inference), LINEAR (linear interpolation, recommended for GOT atlases), SPLINE (spline-based interpolation, recommended for FES atlases), and FOURIER (Fourier-based interpolation). See also Admittance and Inference Modes.
Laplace Species#: The three classes of tidal oscillation resulting from the spherical harmonic decomposition of the second-degree tide-generating potential: long-period (zonal, \(m=0\)), diurnal (tesseral, \(m=1\)), and semidiurnal (sectoral, \(m=2\)). The species number corresponds to the number of tidal cycles per day. See The Tide-Generating Potential.
Legendre Polynomial#: Mathematical functions \(P_n(\cos z)\) used in the expansion of the gravitational potential in spherical harmonics. The \(n=2\) term dominates the tide-generating potential and gives rise to the three Laplace species.
LEGOS#: Laboratoire d’Etudes en Géophysique et Océanographie Spatiales, a research laboratory involved in the development of FES.
Lunar Node#: The point where the Moon’s orbital plane crosses the ecliptic. The retrograde precession of this node, with a period of 18.61 years, produces the dominant long-term modulation of tidal amplitudes and phases, accounted for by nodal corrections.
Nodal Correction#: Time-dependent factors \(f\) (amplitude) and \(u\) (phase) that account for the 18.61-year modulation of tidal constituents due to the precession of the lunar node. In the prediction equation, the observed amplitude is \(f \cdot H\) and the phase is adjusted by \(u\). See Nodal Corrections: Amplitude and Phase Modulations.
Nodal Factor#: The amplitude modulation factor \(f\) in the harmonic prediction equation. It varies slowly over the 18.61-year nodal cycle. For example, \(f(M_2) = \cos^4(I/2) / 0.9154\) where \(I\) is the obliquity of the lunar orbit. See Nodal Corrections: Amplitude and Phase Modulations for all formulae.
NOVELTIS#: A French company specializing in environmental sciences and sustainable development, involved in the development of FES.
Phase Lag#: The angular delay \(G\) (or \(\kappa\)) of a constituent’s high water relative to the passage of the corresponding tide-generating potential maximum. It is a location-specific value determined from tidal observations or numerical models, and forms one of the two harmonic constants (together with the amplitude) characterising a constituent at a given site.
Rayleigh Criterion#: The minimum observation duration \(T\) required to resolve two tidal constituents of frequencies \(f_1\) and \(f_2\): \(T > 1/(f_1 - f_2)\). This criterion determines the number of independent constituents recoverable from harmonic analysis of a given record length. See Harmonic Analysis: From Observations to Constituents.
Tidal Constituent#: A single harmonic component of the tide. Each constituent represents a specific astronomical cycle that influences the Earth’s tides and is characterised by a unique frequency derived from the fundamental variables, an amplitude, and a phase lag.
Tidal Species#: Classification of tidal constituents by their approximate frequency band: long-period (species 0), diurnal (species 1), semidiurnal (species 2), terdiurnal (species 3), quarter-diurnal (species 4), and so on. The species number equals the coefficient \(n_1\) of the local mean lunar time \(\tau\) in the Doodson number.
Tide-Generating Potential#: The gravitational potential arising from the differential attraction of the Moon and Sun between a point on the Earth’s surface and the Earth’s centre. It is the fundamental physical driver of ocean tides and can be expanded in Legendre polynomials and decomposed into Laplace species. See The Tide-Generating Potential.
XDO Notation#: Extended Doodson Ordering, an alphabetical encoding of Doodson numbers. Each integer coefficient is mapped to a letter via the sequence R, S, T, U, V, W, X, Y, Z, A, B, C, D, E, F, G, H, I, J, … where Z corresponds to coefficient 0. For example, \(M_2\) with coefficients (2, 0, 0, 0, 0, 0, 0) is encoded as BZZZZZ. See Harmonic Development and the Doodson Classification.