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.

and

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.
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Characterizing Wavetrains

In Chapter 11 and Chapter 12 of the book we characterize deterministic and stochastic variability in waves. While reviewing the presentations at last week’s EGU meeting, one study covered some of the same ground [1] and was worth a more detailed look. The distribution of stratospheric wind wave energy collected by Nastrom [2] (shown below) that we model in Chapter 11 is apparently still not completely understood.

From Mathematical Geoenergy, Chap 11
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Stratospheric Sudden Warming

Chapter 11 of the book describes a model for the QBO of stratospheric equatorial winds. The stratified layers of the atmosphere reveal different dependencies on the external forcing depending on the altitude, see Fig 1.

Figure 1 : At high altitudes, only the sun’s annual cycle impacts the stratospheric as a semi-annual oscillation (SAO). Below that the addition of the lunar nodal cycle forces the QBO. The earth itself shows a clear wobble with the lunar cycle interacting with the annual.

Well above these layers are the mesosphere, thermosphere, and ionosphere. These are studied mainly in terms of space physics instead of climate but they do show tidal interactions with behaviors such as the equatorial electrojet [1].

The behaviors known as stratospheric sudden warmings (SSW) are perhaps a link between the lower atmospheric behaviors of equatorial QBO and/or polar vortex and the much higher atmospheric behavior comprising the electrojet. Papers such as [1,2] indicate that lunar tidal effects are showing up in the SSW and that is enhancing characteristics of the electrojet. See Fig 2.

Figure 2 : During SSW events, a strong modulation of period ~14.5 days emerges, close to the lunar fortnightly period as seen in these spectrograms. Taken from ref [2] and see quote below for more info.

“Wavelet spectra of foEs during two SSW events exhibit noticeable enhanced 14.5‐day modulation, which resembles the lunar semimonthly period. In addition, simultaneous wind measurements by meteor radar also show enhancement of 14.5‐day periodic oscillation after SSW onset.”

Tang et al [2]

So the SSW plays an important role in ionospheric variations, and the lunar tidal effects emerge as the higher atmospheric density of a SSW upwelling becomes more sensitive to lunar tidal forcing. That may be related to how the QBO also shows a dependence on lunar tidal forcing due to its higher density.

References

  1. Siddiqui, T. A. Relationship between lunar tidal enhancements in the equatorial electrojet and stratospheric wind anomalies during stratospheric sudden warmings. (2020). Originally presented at AGU 2018 Fall Meeting
  2. Tang, Q., Zhou, C., Liu, Y. & Chen, G. Response of Sporadic E Layer to Sudden Stratospheric Warming Events Observed at Low and Middle Latitude. Journal of Geophysical Research: Space Physics e2019JA027283 (2020).

Chandler Wobble according to Na

In Chapter 13 of the book, we have a description of the mechanism forcing the Chandler Wobble in the Earth’s rotation. As a counter to a recent GeoenergyMath post suggesting there is little consensus behind this mechanism, a recent paper by Na et al provides a foundation to understand how the lunar forcing works. 

Chandler wobble and free core nutation are two major modes of perturbation in the Earth rotation. Earth rotation status needs to be known for the coordinate conversion between celestial reference frame and terrestrial reference frame. Due mainly to the tidal torque exerted by the moon and the sun on the Earth’s equatorial bulge, the Earth undergoes precession and nutation.

Na, S.-H. et al. Chandler Wobble and Free Core Nutation: Theory and Features. Journal of Astronomy and Space Sciences 36, 11–20 (2019).
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AO, PNA, & SAM Models

In Chapter 11, we developed a general formulation based on Laplace’s Tidal Equations (LTE) to aid in the analysis of standing wave climate models, focusing on the ENSO and QBO behaviors in the book.  As a means of cross-validating this formulation, it makes sense to test the LTE model against other climate indices. So far we have extended this to PDO, AMO, NAO, and IOD, and to complete the set, in this post we will evaluate the northern latitude indices comprised of the Arctic Oscillation/Northern Annular Mode (AO/NAM) and the Pacific North America (PNA) pattern, and the southern latitude index referred to as the Southern Annular Mode (SAM). We will first evaluate AO and PNA in comparison to its close relative NAO and then SAM …

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SSAO and MSAO

In Chapter 11 of the book, we concentrated on the mechanism behind the QBO of stratospheric equatorial winds. In a related topic (but only briefly touched on in the book), there is interesting data from a presentation on the equatorial-only Semi-Annual Oscillation (SAO) of the upper stratosphere and lower mesosphere wind pattern [1]. The distinction between QBO and the SAO is that the QBO has a longer periodic cycle and exists at altitudes lower in the stratosphere than the SAO.

[1] T. Hirooka, T. Ohata, and N. Eguchi, “Modulation of the Semiannual Oscillation Induced by Sudden Stratospheric Warming Events,” in ISWA2016, Tokyo, Japan, 2016, p. 16.

— presentation slides from International Symposium on the Whole Atmosphere

What’s interesting at the core fundamental level is that the SAO is understood by consensus to be forced by a semi-annual cycle (a resonant condition happening to match 1/2 year is just too coincidental) whereas there is no consensus behind the mechanism behind the QBO period (the tidal connection is only available from Chapter 12). To make the mathematical connection, the following shows how the SAO draws from the QBO tidal model.

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Teleconnections vs Common-mode mechanisms

The term teleconnection has long been defined as interactions between behaviors separated by geographical distances. Using Google Scholar, the first consistent use in a climate context was by De Geer in the 1920’s [1]. He astutely contrasted the term teleconnection with telecorrelation, with the implication being that the latter describes a situation where two behaviors are simply correlated through some common-mode mechanism — in the case that De Geer describes, the self-registration of the annual solar signal with respect to two geographically displaced sedimentation features.

As an alternate analogy, the hibernation of groundhogs and black bears isn’t due to some teleconnection between the two species but simply a correlation due to the onset of winter. The timing of cold weather is the common-mode mechanism that connects the two behaviors. This may seem obvious enough that the annual cycle should and often does serve as the null hypothesis for ascertaining correlations of climate data against behavioral models.

Yet, this distinction seems to have been lost over the years, as one will often find papers hypothesizing that one climate behavior is influencing another geographically distant behavior via a physical teleconnection (see e.g. [2]). This has become an increasingly trendy viewpoint since the GWPF advisor A.A. Tsonis added the term network to indicate that behaviors may contain linkages between multiple nodes, and that the seeming complexity of individual behavior is only discovered by decoding the individual teleconnections [3].

That’s acceptable as a theory, but in practice, it’s still important to consider the possible common-mode mechanisms that may be involved. In this post we will look at a possible common-mode mechanisms between the atmospheric behavior of QBO (see Chapter 11 in the book) and the oceanic behavior of ENSO (see Chapter 12). As reference [3] suggests, this may be a physical teleconnection, but the following analysis shows how a common-mode forcing may be much more likely.

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Detailed Forcing of QBO

In Chapter 11 of the book, we present the geophysical recipe for the forcing of the QBO of equatorial stratospheric winds. As explained, the fundamental forcing is supplied by the lunar draconic cycle and impulse modulated by a semi-annual (equatorial) nodal crossing of the sun. It’s clear that the QBO cycle has asymptotically approached a value of 2.368 years, which is explained by its near perfect equivalence to the physically aliased draconic period. Moreover, there is also strong evidence that the modulation/fluctuation of the QBO period from cycle to cycle is due to the regular variation in the lunar inclination, thus impacting the precise timing and shape of the draconic sinusoid. That modulation is described in this post.

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Applying Wavelet Scalograms

Dennis suggested:

“I was thinking about ENSO model and the impulse function used to drive it.  Could it be the wind shift from the QBO that is related to that impulse function.

My recollection was that it was a biennial pulse, which timing wise might fit with QBO. “

5/19/2019

They are somehow related but more than likely through a common-mode mechanism. Consider that QBO has elements of a semi-annual impulse, as the sun crosses the equator twice per year.  The ENSO model has an impulse of once per year, with more recent evidence that it may not have to be biennial (i.e. alternating sign in consecutive years) as we described it in the book.

I had an evaluation Mathematica license for a few weeks so ran several wavelet scalograms on the data and models. Figure 1 below is a comparison of ENSO to the model

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Asymptotic QBO Period

The modeled QBO cycle is directly related to the nodal (draconian) lunar cycle physically aliased against the annual cycle.  The empirical cycle period is best estimated by tracking the peak acceleration of the QBO velocity time-series, as this acceleration (1st derivative of the velocity) shows a sharp peak. This value should asymptotically approach a 2.368 year period over the long term.  Since the recent data from the main QBO repository provides an additional acceleration peak from the past month, now is as good a time as any to analyze the cumulative data.



The new data-point provides a longer period which compensated for some recent shorter periods, such that the cumulative mean lies right on the asymptotic line. The jitter observed is explainable in terms of the model, as acceleration peaks are more prone to align close to an annual impulse. But the accumulated mean period is still aligned to the draconic aliasing with this annual impulse. As more data points come in over the coming decades, the mean should vary less and less from the asymptotic value.

The fit to QBO using all the data save for the last available data point is shown below.  Extrapolating beyond the green arrow, we should see an uptick according to the red waveform.



Adding the recent data-point and the blue waveform does follow the model.



There was a flurry of recent discussion on the QBO anomaly of 2016 (shown as a split peak above), which implied that perhaps the QBO would be permanently disrupted from it’s long-standing pattern. Instead, it may be a more plausible explanation that the QBO pattern was not simply wandering from it’s assumed perfectly cyclic path but instead is following a predictable but jittery track that is a combination of the (physically-aliased) annual impulse-synchronized Draconic cycle together with a sensitivity to variations in the draconic cycle itself. The latter calibration is shown below, based on NASA ephermeris.



This is the QBO spectral decomposition, showing signal strength centered on the fundamental aliased Draconic value, both for the data and the set by the model.


The main scientist, Prof. Richard Lindzen, behind the consensus QBO model has been recently introduced here as being “considered the most distinguished living climate scientist on the planet”.  In his presentation criticizing AGW science [1], Lindzen claimed that the climate oscillates due to a steady uniform force, much like a violin oscillates when the steady force of a bow is drawn across its strings.  An analogy perhaps better suited to reality is that the violin is being played like a drum. Resonance is more of a decoration to the beat itself.
Keith 🌛 ?

[1] Professor Richard Lindzen slammed conventional global warming thinking warming as ‘nonsense’ in a lecture for the Global Warming Policy Foundation on Monday. ‘An implausible conjecture backed by false evidence and repeated incessantly … is used to promote the overturn of industrial civilization,’ he said in London. — GWPF