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
"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 3O S – 3O N, and a longitude range of 0O E – 20O 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 15O W – 35O W, and
2) the zonal velocity measured at 1000-m depth, as observed by the Argo floats, between 1O S – 1O N and 15O W – 35O 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.
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].
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:
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.