MARITIME – TIDE & TIDAL TREAM CALCULATOR
Harmonic Prediction
A precise tool.
What is the Harmonic Prediction & How does it work?
Harmonic tidal prediction decomposes the sea‑level signal into a sum of sinusoidal constituents, each representing a celestial forcing such as the lunar semi‑diurnal M2 or the solar semi‑diurnal S2. By knowing the amplitude and phase of each constituent at a reference location, the water level at any future time can be reconstructed. The semi‑diurnal constituents dominate most coastal stations. M2 has a period of about 12.42 h, while S2 repeats every 12.00 h. Their interaction creates the characteristic high‑low‑high‑low pattern observed twice each day. Because the tidal response is linear, the total height is simply the algebraic sum of the individual sinusoidal terms. This simple harmonic model is sufficient for short‑term forecasts and for educational purposes.
h(t) = A_{M2}cosleft(omega_{M2} t + phi_{M2}right) + A_{S2}cosleft(omega_{S2} t + phi_{S2}right)
A_{M2} = amplitude of M2 (m); phi_{M2} = phase of M2 (rad); omega_{M2} = angular frequency of M2 (rad·h⁻¹); A_{S2} = amplitude of S2 (m); phi_{S2} = phase of S2 (rad); omega_{S2} = angular frequency of S2 (rad·h⁻¹); t = time since epoch (h).
Parameters
Result
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Frequently Asked Questions
What is harmonic tidal prediction?
It’s a method that breaks down sea-level changes into simple sine waves to predict future water levels.
How many hours does the M2 constituent take to complete one cycle?
The M2 constituent has a period of about 12.42 hours.
What is the period of the S2 constituent?
The S2 constituent repeats every 12.00 hours.
Why are semi-diurnal constituents important in tidal prediction?
They dominate most coastal stations due to their significant impact on water levels.
How does the interaction of M2 and S2 create characteristic tides?
Their overlapping cycles cause predictable patterns in sea-level changes.
Can harmonic prediction be used for any location?
It works best at coastal stations where these tidal constituents are significant.
What information is needed to use this calculator?
You need the amplitude and phase of each constituent at a reference location.
Results are for informational purposes only and do not constitute professional advice.