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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The Indian Ocean Dipole

In the book, we modeled the ENSO and QBO climate behaviors. Based on the approach described therein we have since extended this to the PDO, AMO, and NAO indices, with the IOD the focus of this post.

In Chapter 11, we concentrated on the Pacific ocean dipole referred to as ENSO (El Nino/Southern Oscillation).  A dipole that shares some of the characteristics of ENSO is the neighboring Indian Ocean Dipole and its gradient measure the Dipole Mode Index.

The IOD is important because it is correlated with India subcontinent monsoons. It also shows a correlation to ENSO, which is quite apparent by comparing specific peak positions, with a correlation coefficient of 0.2.  This post will describe the differences found via perturbing the ENSO model …

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North Atlantic Oscillation

In Chapter 11 of the book, we derived an ENSO standing wave model based on an analytical Laplace’s Tidal Equation formulation. The results of this were so promising that they were also applied successfully to two other similar oceanic dipoles, the Atlantic Multidecadal Oscillation (AMO) and the Pacific Decadal Oscillation (PDO), which were reported at last year’s American Geophysical Union (AGU) conference. For that presentation, an initial attempt was made to model the North Atlantic Oscillation (NAO), which is a more rapid cycle, consisting of up to two periods per year, in contrast to the El Nino peaks of the ENSO time-series which occur every 2 to 7 years. Those results were somewhat inconclusive, so are revisited in the following post:

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Commenting at PubPeer

For our Mathematical GeoEnergy book, there is an entry at PubPeer.com for comments (one can also comment at Amazon.com, but you need to be a verified purchaser of the book to be able to comment there)

PubPeer provides a good way to debunk poorly researched work as shown in the recent comments pertaining to the Zharkova paper published in Nature’s Scientific Reports journal.

An issue with the comment policy at Amazon is that one can easily evaluate the contents of a book via the “Look Inside” feature or through the Table of Contents. Often there is enough evidence to provide a critical book review just through this feature — in a sense, a statistical sampling of the contents — yet Amazon requires a full purchase before a review is possible. Even if one can check the book out at a university library this is not allowable. Therefore it favors profiting by the potential fraudster because they will get royalties in spite of damaging reviews by critics that are willing to sink money into a purchase.

In the good old days at Amazon, one could actually warn people about pseudo-scientific research. This is exemplified by Curry’s Bose-Einstein statistics debacle, where unfortunately political cronies and acolytes of Curry’s have since purchased her book and have used the comments to do damage control. No further negative comments are possible since smart people have not bought her book and therefore can no longer comment.

PubPeer does away with this Catch-22 situation.

SSAO and MSAO

In Chapter 12 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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Peak Oil Barrel

The first part of our book Mathematical GeoEnergy deals with the mathematics behind the depletion of fossil fuels, and specifically crude oil. One of the co-authors, Dennis, helps maintain and moderate the Peak Oil Barrel blog. Recently, Dennis posted a blog entry on Oil Shock model scenarios, which is based partly on the mathematics described in Chapter 5 (and elsewhere in the book, as the shock model is a fundamental aspect of modeling oil depletion).

There’s lots of commentary on the POB blog, including climate science topics on the Non-Petroleum comment threads, so worthwhile to have it bookmarked.

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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Characterizing spatial standing waves of ENSO

In Chapter 11 of the book, we did not delve into the details of the spatial aspects of the LTE-based ENSO standing wave model to any great degree. We did include a concise derivation of the steps involved in creating separable equations, corresponding to solutions for the temporal and spatial parts of the standing wave dipole. However, only passing mention was made of the unique nature of the spatio-temporal coordination which emerges from the model — and which should be observed in the empirically observed behavior. We can do that now with the abundance of comprehensive data available.

Figure 1: The challenge is to capture the spatial profile of the ENSO standing wave dipole — the El Nino to La Nina oscillation, with the dipole node location indicated by the yellow bar (site)
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