The SAO and Annual Disturbances

In Chapter 11 of the book Mathematical GeoEnergy, we model the QBO of equatorial stratospheric winds, but only touch on the related cycle at even higher altitudes, the semi-annual oscillation (SAO). The figure at the top of a recent post geometrically explains the difference between SAO and QBO — the basic idea is that the SAO follows the solar tide and not the lunar tide because of a lower atmospheric density at higher altitudes. Thus, the heat-based solar tide overrides the gravitational lunar+solar tide and the resulting oscillation is primarily a harmonic of the annual cycle.

Figure 1 : The SAO modeled with the GEM software fit to 1 hPa data along the equator
Continue reading

Why couldn’t Lindzen figure out QBO?

Background: see Chapter 11 of the book.

In research articles published ~50 years ago, Richard Lindzen made these assertions:

“For oscillations of tidal periods, the nature of the forcing is clear”

Lindzen, Richard S. “Planetary waves on beta-planes.” Mon. Wea. Rev 95.7 (1967): 441-451.


5. Lunar semidiurnal tide

One rationale for studying tides is that they are motion systems for which we know the periods perfectly, and the forcing almost as well (this is certainly the case for gravitational tides). Thus, it is relatively easy to isolate tidal phenomena in the data, to calculate tidal responses in the atmosphere, and to compare the two. Briefly, conditions for comparing theory and observation are relatively ideal. Moreover, if theory is incapable of explaining observations for such a simple system, we may plausibly be concerned with our ability to explain more complicated systems.

Lunar tides are especially well suited to such studies since it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential.

Lindzen, R.S. and Hong, S.S., 1974. “Effects of mean winds and horizontal temperature gradients on solar and lunar semidiurnal tides in the atmosphere“. Journal of the atmospheric sciences31(5), pp.1421-1446.
Continue reading