Friday, September 6, 2019

A lunar tidal mechanism for generating Equatorial Kelvin waves

To find out more details about the lunar tidal mechanism that could generate Equatorial Kelvin waves, please read the following post.

 Please click on the diagram below to activate the GIF animation

If you were to observe the Moon from a fixed point on the Equator at the same time each day, you would notice that the sub-lunar point on the Earth's surface appears to move at a speed of 15 — 20 m/sec from west-to-east. This results from the fact that the west-to-east speed of the Moon along the Ecliptic (as seen from the Earth’s center) varies between 15.2 — 19.8 m/sec. 

Interestingly, the west-to-east group (and phase) velocity for the convectively-decoupled Equatorial Kelvin wave (EKW) is 15 — 20 m/sec, as well. This remarkable "coincidence" raises the question:

Could it be that easterly moving convectively-decoupled EKW are produced by the interaction between the day-to-day movement of the lunar-induced atmospheric/oceanic tides with a meteorological phenomenon that routinely occurs at roughly the same time each (24 hr) solar day?

One meteorological phenomenon that fits this bill is the atmospheric surface pressure variations measured at any given fixed location in the tropics. At many points near the equator, the atmospheric surface pressure spends much of its time sinusoidally oscillating about its long-term mean with an amplitude of 1 to 2 hPa (or millibars). Generally, this regular daily oscillation is only disrupted by the passage of a tropical low-pressure cell (e.g. tropical lows, tropical storms, and Hurricanes, Typhoons, and Cyclones).

For example, figure 1 shows the diurnal surface pressure variations in the Carribean as measured by Haurwitz (1947). What this figure indicates is that, like many points near the Earth's equator, the atmospheric surface pressure reaches a minimum near 4:00 -- 4:30 a.m. and 4:00 -- 4:30 p.m.

Figure 1

Source; Figure 1 of Haurwitz B., 1947, Harmonic Analysis of the Diurnal Variations of Pressure and Temperature Aloft in the Eastern Caribbean, Bulletin of the American Meteorological Society, Vol. 28, pp. 319-323.  
This leads us to propose the hypothesis that:


EKWs are generated when the peak in the lunar-induced tides passes through the local meridian at roughly 4:00 a.m. and 4:00 p.m. local time, when the diurnal surface pressure is a minimum. This type of lunar tidal event takes place once every half synodic month = 14.77 days.

Some important points to note:

* The lunar-induced tidal peak in the atmosphere and oceans passes through the local meridian (during its daily passage from west-to-east) both when the Moon is passing through the meridian, and when the Moon is passing through the anti-meridian. This is due to the semi-diurnal nature of the tides.

** If you select times when the Moon passes through the local meridian at a fixed time (e.g. 4:00 p.m. or 4:00 a.m.), you are in fact selecting times when the Moon is at a specific phase (or a fixed point in the Synodic month). Hence, when the Moon is passing through the meridian at 4:00 p.m., the Moon has a Waxing Crescent phase (~33.3 %), and when the Moon is passing through the local anti-meridian at 4:00 p.m. it has a Waning Gibbous phase (~33.3 %).

The following diagram shows a view of the Earth (fawn-colored circle) as seen from above the North Pole, in a frame-of-reference that is fixed with respect to the Sun. In this frame-of-reference, the Earth rotates and the Moon revolves in a clockwise direction. Included in this diagram is a light blue elliptical annulus that represents the sea-level atmospheric pressure at the Earth's equator. This ellipse highlights the fact that the sea-level atmospheric pressure is typically a minimum at 4 a.m. and 4 p.m., and a maximum at 10 a.m. and 10 p.m. In addition, there is a dark blue elliptical annulus that represents the lunar-induced tides in the Earth's atmosphere and oceans. 

If you click on the gif animation you will see the lunar-induced tidal peak at 4.00 a.m. (4.00 p.m.) move to 4.00 p.m. (4.00 a.m.) over a 14.77 day period, where it induces an atmospheric Kelvin wave that travels along the Earth's equator from west-to-east at a speed of 15 -- 20 m/sec. Then you will see the whole process repeat itself when the lunar-induced tidal peak at 4.00 p.m. (4.00 a.m.) moves to 4.00 a.m. (4.00 p.m.) over the remaining 14.77 days of the lunar Synodic cycle.       

Please click on the diagram below to activate the GIF animation


  1. Thank you sir! I had not considered this as a driver for weather and am quite interested! In process engineering, it is all in the details; defining the process of weather needs to include this set of variables.

  2. Thank you for your comment. It would be good if someone with more skills than I have could monitor the movement of convection de-coupled equatorial Kelvin waves to see if my hypothesis is true.