QBO Aliased Harmonics

In Chapter 12, we described the model of QBO generated by modulating the draconic (or nodal) lunar forcing with a hemispherical annual impulse that reinforces that effect. This generates the following predicted frequency response peaks:

From section 11.1.1 Harmonics

The 2nd, 3rd, and 4th peaks listed (at 2.423, 1.423, and 0.423) are readily observed in the power spectra of the QBO time-series. When the spectra are averaged over each of the time series, the precisely matched peaks emerge more cleanly above the red noise envelope — see the bottom panel in the figure below (click to expand).

Power spectra of QBO time-series — the average is calculated by normalizing the peaks at 0.423/year.
Each set of peaks is separated by a 1/year interval.

The inset shows what these harmonics provide — essentially the jagged stairstep structure of the semi-annual impulse lag integrated against the draconic modulation.

It is important to note that these harmonics are not the traditional harmonics of a high-Q resonance behavior, where the higher orders are integral multiples of the fundamental frequency — in this case at 0.423 cycles/year. Instead, these are clear substantiation of a forcing response that maintains the frequency spectrum of an input stimulus, thus excluding the possibility that the QBO behavior is a natural resonance phenomena. At best, there may be a 2nd-order response that may selectively amplify parts of the frequency spectrum.

See my latest submission to the ESD Ideas issue : ESDD – ESD Ideas: Long-period tidal forcing in geophysics – application to ENSO, QBO, and Chandler wobble (copernicus.org)

2 thoughts on “QBO Aliased Harmonics

  1. https://acp.copernicus.org/preprints/acp-2021-190/#discussion

    The semiannual oscillation (SAO) in the tropical middle atmosphere and its gravity wave driving in reanalyses and satellite observations
    Manfred Ern et al.

    final response to my comments (no further rebuttal)

    Thank you very much for your comment and your interest in our work!

    The gravity waves that contribute to the driving of the QBO and the SAO are more or less continuously generated in the troposphere and lower stratosphere by several different source processes, such as flow over orography, spontaneous emission of gravity waves by out-of-balance wind jets, and, most prominent in the tropics, deep convection.

    The long-period tidal forcings that you are mentioning are not directly involved in these processes of gravity wave excitation.


    For the QBO, there are several model studies showing that the period of the QBO is strongly related to the source strength of gravity waves.

    See, for example, Sect. 6 in Giorgetta et al. (2006).

    Giorgetta, M., Manzini, E., Roeckner, E., Esch, M. , and Bengtsson, L.:

    Climatology and Forcing of the Quasi-Biennial Oscillation in the MAECHAM5 Model,

    J. Atmos. Sci., 19, 3882-3901, 2006.

    Still, there are indications that the 11-year solar cycle has some minor effect on the period length of the QBO. See, for example, Salby and Callaghan (2000). However, to my knowledge, this effect is not related to long-period tidal forcings.

    Salby, M. L., and Callaghan, P.:

    Connection between the Solar Cycle and the QBO: The Missing Link,

    J. Climate, 13, 2652-2662, 2000.


    Different from the QBO, the SAO is more strongly linked to the general global seasonality on Earth:

    In addition to the effect of upward propagating gravity waves as described in our study, also horizontal advection and meridional momentum transport of extratropical planetary waves from the respective winter hemisphere contributes significantly to the SAO westward phase and its timing.

    (e.g., Delisi and Dunkerton, 1988; Hamilton and Mahlmann, 1988; Ern et al., 2015).

    Delisi, D. P. and Dunkerton, T. J.:

    Seasonal variation of the semiannual oscillation,

    J. Atmos. Sci., 45, 2772-2787, 1988.

    Hamilton, K. and Mahlmann, J. D.:

    General Circulation Model simulation of the semiannual oscillation of the tropical middle atmosphere,

    J. Atmos. Sci., 45, 3212-3235, 1988.

    Ern, M., Preusse, P., and Riese, M.:

    Driving of the SAO by gravity waves as observed from satellite,

    Ann. Geophys., 33, 483-504, doi:10.5194/angeo-33-483-2015, 2015.

    Citation: https://doi.org/10.5194/acp-2021-190-AC3

    Amazing that they deflect the lunar tidal forcing possibility with a sunspot cycle forcing (!).

    Liked by 1 person

  2. Pingback: Controlled Experiments | GeoEnergy Math

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