Wednesday, February 6, 2019

The Lunar Tidal Model - Part 2

Please read:
The Lunar Tidal Model - Part 1


Lian et al. 2014 [1] and Chen et al. 2015 [2] show that for every major El Nino event since 1964, the drop off in easterly trade wind strength at the start of these events has been preceded by a marked increase in westerly wind bursts (WWBs) in the western equatorial Pacific Ocean. These authors contend that the WWBs generate easterly moving equatorial surface currents which transport warm water from the warm pool region into the central Pacific. In addition, the WWBs create downwelling oceanic Kelvin waves in the western Pacific that propagate towards the eastern Pacific where they produce intense localized warming (McPhaden 1999 [3]). It is this warming that plays a crucial in the onset of El Nino events through its weakening of the westerly trade winds associated with the Walker circulation.

The WWBs are predominantly produced by twin low-pressure cells that straddle the Earth's equator in the western Pacific Ocean. Most of these low-pressure cell pairs are generated by westerly moving equatorial Rossby waves that are formed in the trailing edges of the active phase of the Madden Julian Oscillation (MJO).

Madden-Julian Oscillations (MJO)

Madden Julian Oscillations (MJOs) are the dominant form of intra-seasonal (30 to 90 days) atmospheric variability in the Earth’s equatorial regions ([4]). They are characterized by the eastward progression of a large region of enhanced convection and rainfall that is centered upon the Equator. 

This region of enhanced precipitation is followed by an equally large region of suppressed convection and rainfall. The precipitation pattern takes about 30 – 60 days to complete one cycle when seen from a given point along the equator ([5], [6]).

At the start of the enhanced convection phase of an MJO, a large region of greater than normal rainfall forms in the far western Indian Ocean and then propagates in an easterly direction along the equator. This region of enhanced rainfall travels at a speed of ~ 5 m/sec across the Indian Ocean, the Indonesian Archipelago (i.e. the Maritime Continent) and on into the western Pacific Ocean. However, once it reaches the central Pacific Ocean, it speeds up to ~ 15 m/sec and weakens as it moves out over the cooler ocean waters of the eastern Pacific.

An MJO consists of a large-scale coupling between the atmospheric circulation and atmospheric deep convection. When an MJO is at its strongest, between the western Indian and western Pacific Oceans, it exhibits characteristics that approximate those of a hybrid cross between a convectively-coupled Equatorial Kelvin Wave (EKW) and an Equatorial Rossby Wave (ERW, [7], [8], [9]).

MJOs are larger scale structures than either EKWs or ERWs. Figure 1 shows the hybrid structure of an MJO  that resembles a cross between a convectively-coupled EKW and an ERW.

Figure 1.

As with the EKWs, MJO's can spawn twin cyclones straddling the equator that can spin off and become tropical depressions. However, since MJO's are slower moving than EKWs, they tend to produce stronger and longer lasting WWBs than those produced by EKWs alone.

"There is strong year-to-year (interannual) variability in Madden–Julian oscillation activity, with long periods of strong activity followed by periods in which the oscillation is weak or absent."[10]

"This interannual variability of the MJO is partly linked to the El Niño-Southern Oscillation (ENSO) cycle. In the Pacific, strong MJO activity is often observed 6 – 12 months prior to the onset of an El Niño episode but is virtually absent during the maxima of some El Niño episodes,.."[10]

Possible Implications

In an earlier post:

observational evidence was presented to show that El Ninos events must be initiated by a physical phenomenon that occurs at times when Perigean New/Full moons are either crossing the Earth's equator or reaching a lunar standstill. 

The one factor that occurs when New/Full moons either cross the Earth's equator or reach a lunar standstill is that the lunar-induced acceleration of the Earth's rotation changes sign. When this happens there is an ebb in the lunar-induced atmospheric/oceanic tides at the Earth's equator, at each  tidal minimum (when the Moon is furthest from the Equator i.e at a lunar standstill) or tidal maximum (when the Moon is crossing the Earth's equator i.e. at a lunar equatorial crossing), provide measurements are taken at the same point in the 24.8-hour lunar tidal day [N.B. this effectively removes the diurnal variation of the lunar tides so that the long-term variations caused by the north-south movement of the Moon are evident over the tropical month].

Figure 2 shows a schematic diagram of the relative (lunar-induced) tidal height on the Earth's equator when measurements are taken at a fixed point in the 24.8-hour lunar tidal day. [Note that this is only a rough schematic diagram that is designed to give an idealistic view of how the tides would vary over a lunar tropical month. No attempt is made to allow for the varying distance of the Moon from the Earth and the actual values shown in the graph are only intended to create a qualitative impression.]

Figure 2 starts out with the sub-lunar point at its northernmost latitude and it shows that there are four times during a tropical month where there is an ebb in the equatorial tidal height [when measured at a fixed point in the lunar day]. Each one corresponds to a lunar equatorial crossing or a lunar standstill.

Figure 2

This leads us to ask the question: Are the equatorial Rossby waves that are seen trailing the active phase of an MJO being generated at the times where there is an ebb in the lunar-induced atmospheric/oceanic tides at the Earth's equator, either at a tidal minimum (i.e. at a lunar standstill) or at a tidal maximum (i.e. at a lunar equatorial crossing)?

This question will be further investigated in part 3.


1. Lian, T., Chen D., Tang Y., and Wu Q. 2014, Effects of westerly wind bursts on El Niño:
A new perspective
, Geophys. Res. Lett., 41, 3522–3527, doi:10.1002/2014GL059989.

2. Chen D., Lian T., Fu C., Cane M.A., Tang Y., Murtugudde R., Song X., Wu Q., and Zhou L., 2015, Strong influence of westerly wind bursts on El Niño diversity, Nature Geoscience, Vol. 8 No 5, pp. 339 – 345, doi: 10.1038/NGEO2

3. McPhaden, M. J. (1999), Genesis and Evolution of the 1997-98 El Nino, Science, Vol 283, pp. 950 – 954.

4. Zhang, C. (2005), Madden-Julian Oscillation, Rev. Geophys., 43.

5. Madden R. and P. Julian, 1971: Detection of a 40-50 day oscillation in the zonal wind in the tropical Pacific, J. Atmos. Sci., 28, 702-708.

6. Madden R. and P. Julian, 1972: Description of global-scale circulation cells in the tropics with a 40-50 day period. J. Atmos. Sci., 29, 1109-1123.

7. Masunaga, H. Seasonality and Regionality of the Madden-Julian Oscillation, Kelvin Wave, and Equatorial Rossby Wave. J. Atmos. Sci., Vol. 64, pp. 4400-4416, 2007

8. Kang, In-Sik; Liu, Fei; Ahn, Min-Seop; Yang, Young-Min; Wang, Bin., 2013, The Role of SST Structure in Convectively Coupled Kelvin-Rossby Waves and Its Implications for MJO Formation, Journal of Climate, vol. 26, issue 16, pp. 5915-5930.


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