How harmonic constituents form a tide curve
Harmonic tide prediction represents water level as a mean datum plus cosine terms whose amplitudes, speeds, and phases come from analysis of observations at a specific station.
This educational calculator combines only M2 and K1 terms. NOAA commonly uses dozens of location-specific constituents plus astronomical adjustments, so this simplified curve is not an operational tide prediction.
How to use the educational tide model
- Set a mean level: Use the same height unit and datum as the constituent amplitudes.
- Enter M2 and K1 constants: Provide educational amplitudes and phase offsets.
- Choose time: Enter 0 to 24 hours after the defined reference epoch.
- Run the model: Inspect the idealized curve and use official station predictions for real decisions.
Formula and variables
The model adds two cosine constituents to a mean water level above the selected datum.
h(t) = H₀ + HM2 cos(2πt/12.4206 + φM2) + HK1 cos(2πt/23.9345 + φK1)- h(t) — Modeled water level
- Height relative to the same datum as H₀
- H₀ — Mean water level
- Model offset above datum
- H — Constituent amplitude
- Half-range contribution of one constituent
- φ — Phase offset
- Constituent phase at the reference epoch (degrees)
Two-constituent demonstration
Combine mean level 3 ft, M2 amplitude 2.5 ft at 0°, and K1 amplitude 1 ft at 45°.
- Time
- 6 h after epoch
- M2 period
- 12.4206 h
- K1 period
- 23.9345 h
- Evaluate each cosine at t = 6 h
- Add both contributions to the mean level
Result: The calculator displays the modeled height and a 24-hour curve.
The curve demonstrates interference between constituents, not a forecast for a real station.
Understanding your results
Amplitude and phase both matter
Constituent peaks reinforce or offset each other as their phases evolve.
- M2 is a principal lunar semidiurnal constituent.
- K1 is a lunisolar diurnal constituent.
- Real stations require locally derived constants.
- Weather-driven water levels are not represented by astronomical harmonic terms alone.
Assumptions
- The two entered constituents and mean datum are internally consistent.
- Periods remain fixed over the illustrated 24-hour interval.
- The model is used only for education.
Limitations
- Includes only two constituents and omits astronomical nodal corrections and equilibrium arguments.
- Does not use a station, date, timezone, tidal datum database, weather, river flow, or real-time observations.
- Must not be used for navigation, flooding, diving, coastal access, or safety decisions.
Common mistakes
- Treating the curve as a local tide forecast.
- Mixing phases referenced to different epochs or timezones.
- Mixing height units or datums.
- Assuming predicted tide equals observed water level during weather events.
Practical use cases
Oceanography education
Explore harmonic addition, phase, and constituent periods.
Model demonstrations
Show why several cosine terms produce a complex water-level curve.
Frequently asked questions
Can I use this for boating?
No. Use official NOAA or the responsible local hydrographic service for the station, datum, date, and timezone.
Why does NOAA use more constituents?
Many astronomical cycles influence local tides; NOAA explains that 37 constituents normally provide the greatest effects in its harmonic framework.
Sources and review
- About Harmonic Constituents — NOAA Tides & Currents. Accessed 2026-07-14.
- NOAA Tide Predictions Help — NOAA Tides & Currents. Accessed 2026-07-14.
Reviewed 2026-07-14.