Reconstruct sea level η(t) by summing the M2, S2, K1 and O1 constituents on top of a mean level H₀. Visualise high/low waters, tidal range and the Courtier form factor.
Reference height above the local datum. Constant in time.
1.762
m-1.499
m3.261
m0.1688
Pure semidiurnal regime
The astronomical tide observed at a harbour can be decomposed as a sum of cosine components with fixed frequencies — the harmonic constituents — derived from the relative motion of the Earth, the Moon and the Sun. Each constituent has an astronomically determined angular speed ωᵢ; the amplitude Aᵢ and the phase φᵢ are local: they depend on bathymetry, coastal geometry, and the resonance of each basin. Direct synthesis uses:
The phase φᵢ enters as a lag (subtracted), following the standard IHO/NOAA convention. Four principal constituents (M2, S2, K1, O1) are enough to reproduce the tide with good fidelity at most harbours in the world.
The classical indicator to classify the tidal regime of a harbour is the dimensionless ratio:
F < 0.25 — Pure semidiurnal
Two highs and two lows per day of similar amplitude (Brest, Buenos Aires).
0.25 ≤ F < 1.50 — Mixed semidiurnal
Two cycles with marked diurnal inequality (San Francisco).
1.50 ≤ F < 3.00 — Mixed diurnal
Usually one dominant cycle with a visible secondary one.
F ≥ 3.00 — Pure diurnal
One high and one low per day (Do Son, Vietnam).
If AM2 + AS2 ≈ 0 the denominator vanishes and F has a singularity: the module flags the configuration as an undefined regime.
The frequency difference between M2 and S2 equals 30.000 − 28.984 = 1.016°/h, producing a beat with period 360° / 1.016°/h ≈ 354.3 h ≈ 14.77 days. When both constituents are in phase (new or full moon) the tidal range is maximum: these are spring tides. When they are in phase opposition the range is minimum: these are neap tides.
M2 = 28.9841042
Twice the mean lunar motion.
S2 = 30.0000000
Twice the mean solar motion (exact 12-hour period).
K1 = 15.0410686
Sum of lunar and solar sidereal motion.
O1 = 13.9430356
Dominant lunar diurnal.