Monday, December 10, 2018

Are MJOs affected by the lunar-induced (bi-monthly) acceleration and deceleration of the Earth's rotation?

N.B. The following discussion about Madden Julian Oscillations (MJOs) is based upon the information that is posted by Atmospheric and Data Scientist Kyle Macritchie's at his blog site: [1]

The reader is strongly encouraged to visit this excellent blog site to get a much more detailed description of this phenomenon.

In order to answer the proposed question, we must first have an understanding of the main characteristics of Equatorial Kelvin Waves (EKWs), Equatorial Rossby Waves (ERWs) and Madden-Julian Oscillations (MJOs).

Madden Julian Oscillations (MJOs)

Equatorial Kelvin Waves

An Equatorial Kelvin Wave (EKW) is a coupled area of atmospheric divergence and convergence (i.e. high and low pressure) that travels along the Earth's equator from west to east (see figure 1). 

Figure 1  

The Earth's Coriolis force turns the equator into a waveguide that rapidly suppresses any meridional (north-south) wind components of the EKW. Hence, the dominant wind components of the EKW are almost exclusively zonal (west-to-east) in nature. 

The active or convergence (low pressure) part of an EKW is associated with convection/clouds and precipitation. It is preceded by a region of easterly zonal winds and followed by a region of westerly zonal winds.

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. [N.B. EKWs are non-dispersive waves, so their phase velocity is equal to their group velocity]. The slower speed of an EKW over the Indian Ocean is attributed to the fact that the wave is coupled with the atmospheric convection and precipitation. 

N.B. The west-to-east velocity of the Moon along the Ecliptic (as seen from the Earth's centre) varies between 15.2 -- 19.8 m/sec. This is very close to the west-to-east group (and phase) velocity of 15 -- 20 m/sec of the convectively-decoupled EKW.

Speculation: 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 would appear to move at a speed of 15 to 20 m/sec from west-to-east. This suggests that lunar tides are emphasizing or reinforcing a weather phenomenon that routinely occurs at roughly the same time each day. One such phenomenon could be the peak in convective thunderstorm activity that routinely takes place at roughly the same time each afternoon along the equator.    

The zone of westerly winds at the back of the active phase of an EKW is associated with Westerly Wind Bursts (WWBs). These wind bursts are thought to be involved in the triggering of El Nino events.

EKWs travel through the more slowly moving MJO, with nearly every MJO having an EKW at some point in its life.

The active (i.e. convective) phase of an EKW can cause weak Rossby waves trains to develop. 

EKW can provide favorable conditions for the development of tropical cyclones.

Equatorial Rossby Wave

These are twin cyclone/anti-cyclone pairs that produce convective zones that are displaced either side of the Earth's equator. Equatorial Rossby Waves (ERWs) come in a number of forms. Figure 2 shows the structure of an n=1 ERW.

Figure 2.

Twin cyclones and twin convective zones displaced either side of the equator are often associated with this type wave. The whole wave structure moves from east-to-west at roughly 5 m/sec.

Outflows from the zones of convection can cause Rossby wave trains to develop. 

As with the EKWs, WWBs will form along the equator between the two low-pressure cells.

ERWs travel through MJOs just like EKW's

Twin cyclones can spin off and become tropical depressions.

Madden-Julian Oscillations (MJO)

The Madden Julian Oscillation (MJO) is the dominant form of intra-seasonal (30 to 90 days) atmospheric variability in the Earth’s equatorial regions ([2]). It is characterized by the eastward progression of a large region of enhanced convection and rainfall that is centred 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 ([3], [4]).

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.

A 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 Kelvin wave and an Equatorial Rossby wave ([5], [6], [1]

MJOs are larger scale structures than either EKWs or ERWs. Figure 3 shows the hybrid structure of an MJO  that resembles a cross between a convectively-coupled EKW and an ERW.

Ref:  [1]

As with the EKWs, MJO's can spawn twin cyclones that can spin off and become tropical depressions.

Since MJO's are slower moving that EKWs, they tend to produce stronger and longer lasting WWBs than those produced by EKWs.

Final Comments on the role of MJOs in spawning WWBs that trigger El Nino events.

"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."[7]

"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,.."[7]

"..changes in the structure of the MJO with the seasonal cycle and ENSO might facilitate more substantial impacts of the MJO on ENSO. For example, the surface westerly winds associated with active MJO convection are stronger during advancement toward El Niño and the surface easterly winds associated with the suppressed convective phase are stronger during advancement toward La Nina."[7], [8]


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

3. 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.

4. 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.

5. 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

6. 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.


8. Roundy, P.E.; Kravitz, J.R. (2009). "The Association of the Evolution of Intraseasonal Oscillations to ENSO Phase". J. Climate. 22: 381–395. 

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