What are tidal harmonic constituents?

A tide is the sum of many sinusoidal components, each driven by a specific astronomical motion. M2 is the principal lunar semidiurnal, S2 the principal solar semidiurnal, K1 and O1 the main diurnal terms. Their amplitudes and phases are published per station.

How accurate is a four-constituent estimate?

M2, S2, K1, and O1 capture the bulk of the tidal signal at most ports, so the shape and timing are usually close. Full predictions use dozens of constituents, so treat this as an approximation, not a replacement for an official tide table.

What speeds does the tool use for each constituent?

It uses the standard angular speeds in degrees per hour: M2 = 28.984, S2 = 30.000, K1 = 15.041, O1 = 13.943. These are fixed astronomical rates, so you only supply amplitude and phase.

What is the phase lag g?

The phase lag, in degrees, is how far each constituent is delayed relative to its astronomical forcing at a reference meridian. It is published alongside the amplitude in a station's harmonic constants and sets when each component peaks.

Why might my predicted high water be off by an hour?

This simplified model treats the start of the day as the common phase reference and omits nodal corrections and minor constituents. Errors of tens of minutes in timing are normal. Always defer to official predictions for navigation.

Tidal Height Harmonic Estimator

When official tide predictions are out of reach, you can still reconstruct a useful tide curve from a station’s published harmonic constants. This estimator sums the four dominant constituents — M2, S2, K1, and O1 — using their fixed astronomical speeds and your supplied amplitudes and phases.

How it works

Each constituent contributes a cosine wave, and the total height at hour t is the datum plus the sum of those waves:

h(t) = Z0 + Σ Hᵢ × cos( ωᵢ × t − gᵢ )

ω(M2) = 28.984°/h   ω(S2) = 30.000°/h
ω(K1) = 15.041°/h   ω(O1) = 13.943°/h

Hᵢ is the amplitude in metres, gᵢ the phase lag in degrees, and ωᵢ × t is the constituent’s astronomical argument advanced from the start of the day. Degrees are converted to radians internally before the cosine is taken.

Example and notes

A semidiurnal port with M2 amplitude 1.8 m at phase 200 degrees, S2 0.6 m at 240, K1 0.15 m at 60, and O1 0.10 m at 30, on a 0.0 m datum, produces two highs and two lows per day with a spring-tide character driven by M2 plus S2. Because this model omits nodal factor corrections and the many minor constituents that a full tidal analysis includes, expect height errors of a few tens of centimetres and timing errors of tens of minutes. Use it for planning intuition, never for navigation where an official prediction exists.