Tidal Harmonic Analysis
Also known as: Tidal Constituents, Harmonic Tidal Prediction
Tidal harmonic analysis is a mathematical method that decomposes observed sea level or current time series into a sum of sinusoidal components with specific frequencies, amplitudes, and phases corresponding to astronomical tidal constituents. Developed by William Thomson (Lord Kelvin) in 1867, harmonic analysis enables prediction of tides and understanding of tidal dynamics in coastal regions.
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When to use it
Harmonic tidal analysis is essential for any coastal application requiring tidal prediction (ship navigation, port operations, tidal energy) or understanding of tidal currents. Use it whenever time series of sea level or current are available. The method is most powerful when data span at least one lunar nodal cycle (18.6 years) to fully capture the variation in tidal amplitudes, though useful results are possible with shorter records.
Strengths & limitations
- Provides accurate tidal predictions at specified locations based on constituent harmonic constants derived from observations
- Physically transparent: constituents correspond to identified astronomical tidal forcing mechanisms
- Requires only short time series (weeks to months) for reasonable accuracy; full nodal variation is optional
- Applicable to both sea level and current time series; enables mapping of tidal currents from observations
- Assumes steady-state tidal response; does not capture changes in tidal amplitudes due to sea level rise or bathymetric changes
- Non-tidal signals (wind-driven surge, freshwater discharge, sea level pressure effects) contaminate observations and must be carefully removed
- Short time series (less than one month) provide biased amplitude estimates for some constituents due to aliasing with non-tidal variability
- Spatial variability of tidal constituents requires dense observational network to map regional tidal fields
Frequently asked
What is the most important tidal constituent and why?
The M2 (semidiurnal lunar) constituent is typically the largest in most locations, representing the twice-daily tidal cycle driven by the Moon's orbit. Its 12.42-hour period creates the characteristic two tides per day observed in most coastal areas. S2 (semidiurnal solar) is usually the second-largest constituent.
How long must observations span to extract tidal constituents accurately?
Useful tidal predictions require minimum 29 days of data to separate semidiurnal (12.42-hour) and solar (24-hour) constituents. For better accuracy, 1 year of data is recommended. Complete nodal cycle resolution requires 18.6 years, but is optional for short-term predictions.
What are overtides and why do they matter?
Overtides are shallow-water tidal constituents created by nonlinear interactions of primary tides in shallow water. Examples include M4 (the second harmonic of M2) and MN4 (combination of M2 and N2). Overtides can be significant in estuaries and become more important as water becomes shallower.
Sources
- Godin, G. (1972). The Analysis of Tides. University of Toronto Press. link ↗
- Pugh, D. T., & Woodworth, P. L. (2014). Sea-Level Science: Understanding Tides, Surges, Tsunamis and Mean Sea-Level Changes. Cambridge University Press. DOI: 10.1017/CBO9781139235778 ↗
How to cite this page
ScholarGate. (2026, June 3). Tidal Harmonic Analysis. ScholarGate. https://scholargate.app/en/oceanography/tidal-harmonic-analysis
Which method?
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