- M2 – The largest lunar constituent – is related to the direct gravitational effect of the Moon on the tides. The Earth rotates on its axis every 24-hours, but the Moon is orbiting in the same direction as the Earth’s rotation. It takes a location on the Earth an additional 50 minutes to “catch up” to the Moon. This results in a tidal signal (M2) which has 2 peaks every 24-hours and 50 minutes.
- S2 – The largest solar constituent – is related to the direct gravitational effect of the Sun on the tides. The Earth rotates on its axis every 24-hours. This results in a tidal signal (M2) which has 2 peaks every 24-hours.
- SA – Solar Annual constituent – is related to the changing positions of the Earth and Sun on an annual basis, every 365.25 days.

(PDF) Special Publication No. 98: Manual of Harmonic Analysis and Prediction of Tides

h = height of tide at any time t.

Ho = mean height of water level above datum used for prediction.

H = mean amplitude of any constituent A.

ƒ = factor for reducing mean amplitude H to year of prediction.

a = speed of constituent A.

t = time reckoned from some initial epoch such as beginning of year of predictions. (Vo+u) = value of equilibrium argument of constituent A when t = 0.

K = epoch of constituent A.

Ho = mean height of water level above datum used for prediction.

H = mean amplitude of any constituent A.

ƒ = factor for reducing mean amplitude H to year of prediction.

a = speed of constituent A.

t = time reckoned from some initial epoch such as beginning of year of predictions. (Vo+u) = value of equilibrium argument of constituent A when t = 0.

K = epoch of constituent A.

- The harmonic constants values provided for a station are H and K from this formula.
- The units used for H and Ho (feet or metric) will determine the type of units of the resulting tidal heights.
- The units for K (Local Standard Time or GMT) will determine the timezone of the times of the tide predictions generated.
- Speeds of individual harmonic constants are published in a number of publications and online services.
- (PDF) NOAA Special Publication NOS CO-OPS 3 - Tidal Analysis and Predictions
- (PDF) Special Publication No. 98: Manual of Harmonic Analysis and Prediction of Tides
- Equilibrium argument (Vo+u) are published in several publications, provided in online services, or may be calculated through mathematical formulas.
- (PDF) Special Publication No. 98: Manual of Harmonic Analysis and Prediction of Tides
- (PDF) Special Publication No. 98 Supplement: Computer Application to Tides in the National Ocean Survey