Are the Strongest Lunar Perigean Spring Tides Commensurate with the Transit Cycle of Venus?

The following graph inspired my 2014 paper entitled:

Wilson, I.R.G. Are the Strongest Lunar Perigean Spring Tides Commensurate with the Transit Cycle of Venus?,  Pattern Recogn. Phys., 2, 75-93

Received: 25/Jul/2014 - Revised: 10/Sep/2014 - Accepted: 18/Sep/2014 - Published: 28/Nov/2014

It was accepted for publication in the second volume of the Journal Pattern Recognition in Physics (PRP) on the 18th of November 2014. The publishers of the PRP, Copernicus Publications, decided to close the journal in 2014, despite having accepted my paper for publication. It temporarily appeared on-line (i.e. was published) and then removed. In protest, I refused to pay the publication fee until they put my paper back up on-line. They never did.  I didn't realize that a publisher could accept a paper for publication, publish it and then remove it from publication, without giving any rational reason for their actions.

This graph shows the remarkable alignment between the dates for the transits of Venus over a 700-year period between 1600 and 2300 A.D. and the repetition pattern for the most extreme Perigean Spring tides that are closest to the nominal date of the Perihelion of the Earth's orbit. 

Abstract: 

This study identifies the strongest perigean spring tides that reoccur at roughly the same time in the seasonal calendar and shows how their repetition pattern, with respect to the tropical year, is closely synchronized with the 243-year transit cycle of Venus. It finds that whenever the pentagonal pattern for the inferior conjunctions of Venus and the Earth drifts through one of the nodes of Venus’ orbit, the 31/62 year perigean spring tidal cycle simultaneously drifts through almost exactly the same days of the Gregorian year, over a period from 1 to 3000 A.D. Indeed, the drift of the 31/62 year tidal cycle with respect to the Gregorian calendar almost perfectly matches the expected long-term drift between the Gregorian calendar and the tropical year. If the mean drift of the 31/62 perigean spring tidal cycle is corrected for the expected long-term drift between the Gregorian calendar and the tropical year, then the long-term residual drift between: 

a) the 243-year drift-cycle of the pentagonal pattern for the inferior conjunctions of Venus and the Earth with respect to the nodes of Venus’s orbit and 

b) the 243-year drift-cycle of the strongest seasonal peak tides on the Earth (i.e. the 31/62 perigean spring tidal cycle) with respect to the tropical year,

is approximately equal to -7 ± 11 hours, over the 3000-year period. The large relative error of the final value for the residual drift means that this study cannot rule out the possibility that there is no long-term residual drift between the two cycles i.e. the two cycles are in perfect synchronization over the 3000 year period. However, the most likely result is a long-term residual drift of -7 hours, over the time frame considered.

Keywords: Solar System — Planetary Orbits — Lunar Tides 

The Easterly Trade Winds Over the Equatorial Pacific Ocean Have Disappeared Over the Last 5 Days or So!

UPDATED 22/09/2019 09:25 AEST
FURTHER UPDATED 28/09/2019 14:20 AEST

If you want to find out why go to the following post:

https://astroclimateconnection.blogspot.com/2019/09/tropical-storms-in-equatorial-pacific.html

UPDATE 22/09/2019

On the 21 September 00:00 UTC, the equatorial trade winds in the Western Pacific are still dead, as far east as 165W!

Shown below are the Sea-Surface Temperature Anomalies (SSTA) for the 6th of September 00:00 UTC (on the right) and the 21st September 00:00UTC (on the left).

Note that warm surface water in the Western Pacific has moved eastward by ~ 3,300 km in 15 days.

The battle in between the warmer waters in the Western Pacific and the cooler waters in the Eastern Pacific Oceans.

Update 28/09/2019

Tropical Storms in the Equatorial Pacific Ocean are being triggered by the passage of Kelvin Waves

 N.B. If our claim is correct that Equatorial Kelvin Waves (EKWs) are being generated by the interaction between maxima in the lunar atmospheric/oceanic tides with minima in the diurnal sea-level pressure variations in the tropics (please read): 

https://astroclimateconnection.blogspot.com/2019/09/a-lunar-tidal-mechanism-for-generating.html 

then this post implies that the lunar tides must play a crucial role in initiating the Westerly Wind Bursts (WWBs) in the western equatorial Pacific ocean that are directly responsible for weakening the easterly equatorial trade winds that help trigger El Nino events.

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If you visit Kyle MacRitchie's excellent blog site on Tropical waves at:

https://www.kylemacritchie.com/learn-about-tropical-waves/

he states that convectively decoupled Equatorial Kelvin Waves (EKWs) can have outflows from their convection zones that cause Equatorial Rossby Wave (ERWs) trains to develop in their wake. 

He indicates that these ERWs aren't as strong as those created by MJOs since EKWs generally move from west-to-east along the Earth' equator at 3 to 4 times rate of Madden Julian Oscillations (MJOs).  

In addition, MacRitchie states that Kelvin waves provide favorable conditions for the development of Tropical Cyclones i.e. intense convection, low-level vorticity (in the form of trailing ERWs), vertical shear, and mid-level moisture.

****************

I light of this, we present a report on the passage of a convectively-decoupled Kelvin Wave across the Equatorial Pacific Ocean, over the last several days, that has set off a series of weak tropical storms and possibly one Hurricane.

The following plot shows the location of MJOs in the equatorial regions of the Indo-Pacific (as represented by the MJO phase - vertical axis) for times between May 15th and September 15th, 2019 (horizontal axis).

This plot showed that the most recent MJO event:

a) started off the east coast of equatorial Africa (MJO Phase 1) around the 17th of August, 

b) reached the region on the Equator between the Philippines and New Guinea (MJO phase 5), around about the 4th -- 5th of September, where it started producing Westerly Wind Bursts (WWBs) to the north of Papua New Guinea.

c) generated a convectively decoupled Kelvin wave, most likely around September 8th, that began moving out across the equatorial Pacific Ocean at a speed of roughly 1350 km/day, reaching the coast of South America roughly 9 -- 10 days later.  

The following weather map shows that the passage of the convectively decoupled Kelvin wave (between September 8th to 17th) generated at least 5 weak topical tropical storms and possibly one hurricane, straddling the Earth's equator at roughly 15 degrees north latitude.

Ref: (https://earth.nullschool.net/)

The following plots show that:

1) the MJO event produces WWBs in the western equatorial Pacific ocean between the 8th and 11th of September.

2) the convectively de-coupled EKW that emerges from the MJO event (sometime after September 8th) starts to move across the equatorial Pacific ocean leaving a series of weak tropical storms in its wake (starting on September 13th), straddling the Earth's equator at roughly 15 degrees North latitude.

3) the cumulative westerly wind flows that are produced on the southern sides of this string of tropical storms effectively eliminates the easterly equatorial trade winds as far east as the mid-Pacific ocean, at 160 degrees West longitude (N.B. the red vertical line on the Equator marks the most easterly longitude of the stalled trade winds for that date).

 All it would take is a series of vigorous EKWs like this one to trigger a major El Nino event, showing that the lunar atmospheric/oceanic tides must play a role in initiating these significant climate events.  

8th Sept

9th Sept

10th Sept

11th Sept

12th Sept

13th Sept

14th Sept

15th Sept

16th Sept

17th Sept

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:

Hypothesis: 

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

[Rhetorical Question] Do you think that the Moon might have something to do with it?

SUMMARY

Given the link to the 8.85/9.1 year lunar tidal cycles, what the Brandt et al. (2011) paper is telling us is that:

a) The Moon is continuously producing semi-monthly pulses of (easterly moving) Equatorial Kelvin waves and (westerly moving) Equatorial Rossby waves that are rushing across the equatorial Atlantic Ocean.

b) These produce the high baroclinic [Atlantic] basin [oscillation] modes. This can be thought of as a slow resonant sloshing motion of the surface waters of the equatorial Atlantic that is constrained by the coasts of eastern South America (at the Mouth of the Amazon) and eastern Equatorial Africa (at Equatorial Guinea).

c) These, in turn, are driving the 4.5-year cycle seen in the upwelling of energy from the depths of the equatorial Atlantic Ocean.

Reference:

Brandt, P., Funk, A., Hormann, V., Dengler, M., Greatbatch, R.J., and Toole, J.M., 2001, Interannual atmospheric variability forced by the deep equatorial Atlantic Ocean, Nature volume473, pages497–500

Main Conclusion: 

"We propose that the variability in the equatorial zonal surface flow is not due to wind forcing with the same period but rather is a mode internal to the ocean, with its origin in the abyss (perhaps as deep as several thousand metres). If this is indeed the case, then the observed atmospheric variability in the 4–5-yr period band in the equatorial Atlantic can be interpreted as a consequence of internal ocean dynamics."


Brandt et al. (2011) contends that the Tropical Atlantic (meteorological) variability has two dominant modes:

1) The meridional mode that peaks in the boreal spring and is characterized by a latitudinal (N-S) sea-surface temperature (SST) gradient that drives cross-equatorial wind velocities anomalies from the colder to the warmer hemisphere.

2) The zonal mode that is most pronounced during the boreal summer and is characterized by a longitudinal (E-W) SST gradient along the Equator that is associated with marked zonal wind anomalies. The boreal summer months also correspond to a time when there is a seasonal maximum in equatorial upwelling deep-ocean water that leads to the development of the eastern Atlantic SST cold tongue.

Historically, the variability of the eastern equatorial Atlantic SSTs has been best represented by the ATL3 index. This index measures the average SST anomaly inside a box with a latitude range of 3^O S – 3^O N, and a longitude range of 0^O E – 20^O W. The ATL3 index is used as a proxy to monitor the effects of the zonal and meridional modes upon the gradients in SST in the Tropical Atlantic.

Brandt et al. (2001) show that, during the last couple of decades, the ALT3 index shows significant variability on interannual timescales with a dominant periodicity between about 4 – 5 years. They find that the variance of the different ocean parameters is maximized by adopting a harmonic period of 1,670 days (= 4.5723 tropical years). The associated amplitude of these fluctuations is 0.29 +/- 0.08 C, when averaged over the ATL3 region, with the largest amplitudes (~ 0.4 C) occurring in the eastern equatorial Atlantic Ocean.

In addition, Brandt et al. (2011) find that:

1) the oceanic surface zonal geostrophic velocity anomaly, measured along the Equator between longitudes 15^O W – 35^O W, and

2)  the zonal velocity measured at 1000-m depth, as observed by the Argo floats, between 1^O S – 1^O N and 15^O W – 35^O W.

both exhibit inter-annual variations that is best described by a harmonic period of 1,670 days.

Confirmation of these results is provided by the curves displayed in figure 1b (shown below - Brandt et al. 2011). 

The top part of figure 1b shows the ATL3 SST anomaly index (red dashed line) and the HADISST anomaly (red thin solid line- presumably covering the same zone as the ATL3 index), with its 1,670-day harmonic fit (red thick solid line). In contrast, the bottom part of figure 1b shows the oceanic surface zonal geostrophic velocity anomaly (black thin solid line), with its 1,670-day harmonic fit (black thick solid line), and the zonal velocity at a depth of 1000-m (black dots with standard error bars), with its 1,670-day harmonic fit. 

Figure 1

Analysis of the zonal velocities at 1,000-m depth reveals a periodic behavior that is similar to the SST and surface geostrophic zonal velocity anomalies (Fig. 1b), with the dominant period of the Argo float drift data being 4.4 years [over the period from 1998 to 2010]. The data shows a series of jets, alternating with depth, with a vertical wavelength of 300 to 700 metres.  Interestingly, linear internal wave theory indicates that the downward phase velocity of the equatorial deep jets (~100 metres per year) corresponds to an upward energy propagation that reaches the surface and affects sea-surface conditions.

Finally, Brandt et al. point out that the observations in the equatorial Atlantic reveal a similar periodic behavior for the deep-jet oscillations over varying time intervals and depths. They suggest that a consistent behavior of this nature could arise from the development of high baroclinic [Atlantic] basin [oscillation] modes established by the eastward propagation of Kelvin and Rossby waves.

The Connection to the Lunar Tidal Cycles

Interestingly, the 1670-day periodicity associated with the upward propagation of energy from the ocean depths in the equatorial Atlantic Ocean is half 9.145 tropical years or if you believe the 4.4-year periodicity associated with Argo float data (for the zonal velocities at 1000-m depth), half of 8.8 tropical years.  

What is fascinating is that each of these periods is close to well-known long-term cycles associated with the lunar tides.

The 9.145 tropical year periodicity is close to the observed 9.1-year cycle in the world mean temperature. Half of this 9.1-year variation (i.e. 4.55 tropical years = 1662 days) is often associated with the harmonic mean of half the 18.6-year Lunar Nodical Cycle (i.e. LNC/2 = 9.3 years) and the 8.85-year Lunar Anomalistic Cycle (LAC). Similarly, the twice the 4.4.-year period that is associated with the Argo float data (i.e. 8.8 years) is reasonably close to the 8.85-year LAC.

Figure 2 below shows that 1670-day harmonic-period that is representative of the upwelling of energy from the depths of the equatorial Atlantic Ocean, compared to the rate of change of the angle between the lunar line-of-apse and the Earth-Sun line, as measured at the time of Perihelion [units - degree per year].

Figure 2

The very close phase alignment between these two phenomena raises the possibility that the lunar tides are responsible for the eastwardly propagating Kelvin and Rossby waves that are believed to produce the high baroclinic [Atlantic] basin [oscillation] modes. It is believed that these, in turn, are driving the upwelling of energy from the depths of the equatorial Atlantic Ocean.

Support for this hypothesis is given by the lunar tidal model developed by the author in February 2019, details of which can found at:

http://astroclimateconnection.blogspot.com/2019/02/the-lunar-tidal-model-part-4.html

N.B. Unfortunately, the short time periods covered by the equatorial SST data [17 years for the Brandt et al (2011) data and 12 years for the Argo float data], means that there has been insufficient time to distinguish whether a periodicity of 8.85 years or 9.1 years best fits the SST data.