The Lunar Tidal Model - Part 1
The Lunar Tidal Model - Part 2
The Lunar Tidal Model - Part 3
An MJO is a complex atmospheric wave that moves from west-to-east along the equator. It is most evident when it couples with atmospheric convection/precipitation between East Africa and the equatorial Western Pacific Ocean. It consists of an active region of enhanced precipitation/uplift followed by a region of suppressed precipitation. The precipitation pattern takes about 30 – 60 days to complete one cycle when seen from a given point along the equator.
The slow-moving MJO wave can be thought of as a combination of an easterly moving Kelvin-wave and a westerly moving equatorial Rossby wave. The compound MJO wave moves with a group velocity of about 5 m/sec from west-to-east. Within the large MJO wave train, Kelvin waves move from west-to-east with a phase velocity of 15 to 20 m/sec, and the equatorial Rossby Waves travel from east-to-west with a phase velocity of 5 m/sec.
Equatorial Rossby Waves (ERW)
In parts 1, 2, and 3, it was shown that the westward-moving ERWs trailing the active phase of the MJO are being generated at the times when there is an ebb in the lunar-induced atmospheric/oceanic tides at the Earth's equator [when measured at the same time in the 24.8-hour lunar tidal day], i.e. either at a tidal minimum (at a lunar standstill) or at a tidal maximum at the Earth's equator (at a lunar equatorial crossing).
Figure 2 reminds us that these ebbs in the lunar-induced atmospheric/oceanic tides at the Earth's equator occur roughly every 6-7 days, either when the peak of the Moon's tidal bulge crosses the Earth's equator (tidal maximum) or when it reaches its maximum distance from the Earth's equator i.e. lunar standstill (tidal minimum).
Equatorial Kelvin Waves (EKW)
The MJO can be thought of as a combination of an easterly moving EKW and a westerly moving ERW with the compound MJO wave moving with a group velocity of about 5 m/sec from west-to-east. Within the larger MJO wave train, Kelvin waves move from west-to-east traveling through MJO with a phase velocity of 12 to 20 m/sec. Specifically, the phase velocity of an EKW is typically 15 — 20 m/sec (west-to-east) over the western Pacific Ocean and 12 — 15 m/sec (west-to-east) over the Indian Ocean. In addition, EKWs are non-dispersive waves, so their phase velocity is equal to their group velocity. Hence, their slower speed over the Indian Ocean is attributed to the fact that, in these regions, EKWs are coupled with the atmospheric convection and precipitation.
See Dr. Kyle MacRitchie's excellent blog site for further details:
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 is the result of 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 EKW in the western Pacific Ocean is 15 — 20 m/sec, as well. This remarkable "coincidence" leads to a very intriguing hypothesis (N.B. the following assumes that the observer is at a fixed location on the Earth's equator).
THE FIRST POSSIBILITY
The first meteorological phenomenon that comes to mind is the observation that in the tropics the peak in convective thunderstorm activity routinely takes place at roughly 3.00 p.m. each afternoon.
Some important notes:
* The lunar-induced tidal peak can pass through the local meridian (during its daily passage) both when the Moon is passing through the meridian and when the Moon is passing through the anti-meridian due to the semi-diurnal nature of the peak tides.
** If you select times when the Moon passes through the local meridian at a fixed time (e.g. 3:00 p.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 3:00 p.m. for someone located in the equatorial Indian and western Pacific Oceans, the Moon's phase is at ~15 % (Waxing Crescent), and when the Moon is passing through the local anti-meridian it's at ~85 % (Waning Gibbous).
***There are four times where the Moon either crosses the equator or reaches a standstill in one Tropical month.
The main prediction of this hypothesis is that WWBs should be enhanced near the active phase of an MJO every time an ebb in the lunar-induced equatorial tides coincides with the time when the peaks in the semi-diurnal tides pass through the local meridian at 3:00 p.m.
One way to test this prediction is to look at a Hovmoller diagram of Westerly Wind Burst anomalies (WWBanom). This should show that whenever there is a temporal alignment between the two generating mechanisms, there should be an increase in the WWBanom.
Figure 3 below shows the Hovmeller diagram of the WWBanom (between +/- 15 degrees latitude) versus geographic longitude between January 1st, 2002 and December 31st, 2003. The starting and ending dates were chosen to cover the 2002/2003 El Nino event, which spans the period from May 2002 and February 2003.
Ref: Australian Bureau of Meteorology (BOM) - last accessed 12/02/2019.
The thick black horizontal lines that are superimposed on this plot show the 45 degrees East and 180 degrees East meridians. The former marks the western-most part of the Indian Ocean off the coast of East Africa and the later marks the location of the International Date-Line.
Large crosses are superimposed on figure 3, using:
a) the dates on which the peaks in the semi-diurnal tides pass through the local meridian at 3:00 p.m (which are assumed to be responsible for the EKWs), at the same time as there is an ebb in the lunar-induced equatorial tides (which are assumed to be responsible for the ERWs).
b) the longitude of the MJO phase for that date.
[Note: the following table is used to convert between MJO phase and longitude: Phase 1 = 60 deg. E; Phase 2 = 75 deg. E; Phase 3 = 90 deg. E; Phase 4 = 105 deg. E; Phase 5 = 120 deg. E; Phase 6 = 150 deg. E; Phase 7 = 170 deg. E; Phase 8 arbitrarily set to 120 deg. W.]
All of the points are plotted that have a difference between, the time when the peaks in the semi-diurnal tides pass through the local meridian at 3:00 p.m., and the time when there is an ebb in the lunar-induced equatorial tides, that is either -1, 0, or +1 days.
1. The passage of MJO events across the Indian and Western Pacific oceans in figure 3 are traced out by positive (purple) WWB anomalies. Hence, simply plotting a point in figure 3, using its MJO phase and its date, will automatically place that point along one of the purple paths traced out by the MJO event. Hence, what we are looking for in figure 3 is not whether the alignment points lie along the paths traced out by the MJO but whether or not these points are near noticeably enhanced periods of WWB anomalies in a given MJO event.
2. The points that have alignments of 0 or 1 days appear to lie in MJO phase regions 5, 6 or 8, at least over the one and half year period that is centered on the 2002/2003 El Nino event.
[Note: information from a much longer time series extending from January 1996 to January 2019 shows that points that are not aligned (i.e. not 0 or 1 days) are not preferentially clustered in MJO phase regions 5 and 6.]
3. The points that have alignments of 0 or 1 days and which are located in the MJO phase regions 5 and 6, appear to immediately precede noticeably enhanced periods of WWB anomalies by a couple of days. This appears to confirm the main prediction of our hypothesis.
4. There appear to be noticeably enhanced periods of WWB anomalies in MJO phase regions 5 and 6 that lie halfway in between the points that have alignments of 0 or 1 day.
Note 4. strongly suggests that our orginal hypothesis needs to be modified to allow for the possibility that the easterly moving EKW that are embedded within the MJO wave complex is produced by the interaction between the day-to-day movement of the lunar-induced atmospheric/oceanic tides with a meteorological phenomenon that not only occurs at around 3:00 p.m. local time but also 12 hours earlier around 3:00 a.m. local time.
A MORE LIKELY POSSIBILITY
One meteorological phenomenon that fits this bill is the atmospheric surface pressure variations measured at a given 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.
Figure 4 shows the diurnal surface pressure variations in the Carribean as measured by Haurwitz (1947). What this shows is that like many points near the Earth's equator, the atmospheric surface pressure in the Carribean reaches a minimum near 4:00 -- 4:30 a.m. and 4:00 -- 4:30 p.m.
This leads us to modify our original hypothesis so that it reads:
EKWs are generated when the peak in the lunar-induced tides passes through the local meridian at either 4:00 a.m. or 4:00 p.m. local time when the diurnal surface pressure is a minimum (this takes place roughly once every quarter of a synodic month = 7.38 days). In addition, if the generation of an EKW occurs at roughly the same time as the generation of an ERW (which takes place roughly once every quarter of a Tropical month = 6.83 days), the combined atmospheric waves reinforce the Westerly Wind Bursts (WWBs) that are produced by ERWs.
Further research is being carried out to test this modified hypothesis.
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