M4

M4 is the first overtide of the principal lunar constituent M2, a shallow-water harmonic at exactly twice the M2 frequency, period 6.2103 hours and speed 57.9682 degrees per hour. It is generated by nonlinear distortion of the M2 wave as it enters shallow estuaries and crosses banks, where friction and the advective terms steepen the tidal curve. The amplitude and phase of M4 relative to M2 set the tidal asymmetry between flood and ebb, which controls the direction of net sediment transport in many estuaries. M4 is the dominant member of the shallow-water constituent set that must be added to the astronomical constituents for accurate near-shore tide prediction.