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 . 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. ). 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 .
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  suggests, this may be a physical teleconnection, but the following analysis shows how a common-mode forcing may be much more likely.
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.
“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. “
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
In Chapter 12 of the book, we describe in detail the solution to Laplace’s Tidal Equations (LTE), which were introduced in Chapter 11. Like the solution to the linear wave equation, where there are even (cosine) and odd (sine) natural responses, there are also even and odd responses for nonlinear wave equations such as the Mathieu equation, where the natural response solutions are identified as MathieuC and MathieuS. So we find that in general the mix of even and odd solutions for any modeled problem is governed by the initial conditions of the behavior along with any continuing forcing. We will describe how that applies to the LTE system next:
In Chapter 12 of the book, we describe the forcing mechanism behind the El Nino / Southern Oscillation (ENSO) behavior and here we continue to evaluate the rich dynamic behavior of the Southern Oscillation Index (SOI) — the pressure dipole measure of ENSO. In the following, we explore how the low-fidelity version of the SOI can reveal the high-frequency content via the solution to Laplace’s Tidal Equations.
In Chapter 12 of the book, we have a description of the mechanism forcing the El Nino / Southern Oscillation (ENSO) behavior. ENSO shows a rich dynamic behavior, yet for the pressure dipole measure of ENSO, the Southern Oscillation Index (SOI), we find even greater richness in terms of it’s higher frequency components. Typically, SOI is presented with at least a 30-day moving average applied to the time-series to remove the higher-frequencies, but a daily time-series is also available for analysis dating back to 1991. The high-resolution analysis was not included in the book but we did present the topic at last December’s AGU meeting. What follows is an updated analysis …
In Chapter 12 of the book, we provide a short introduction to ocean tidal analysis. This has an important connection to our model of ENSO (in the same chapter), as the same lunisolar gravitational forcing factors generate the driving stimulus to both tidal and ENSO behaviors. Noting that a recent paper  analyzing the so-called long-period tides (i.e. annual, monthly, fortnightly, weekly) in the Drake Passage provides a quantitative spectral decomposition of the tidal factors, it is interesting to revisit our ENSO analysis in the conventional ocean tidal context …
In Chapter 12 of the book, we have a description of the mechanism forcing the El Nino / Southern Oscillation (ENSO) behavior. An important ingredient to the modeled forcing is an annual impulse (with a likely biennial asymmetry) that modulates the hypothesized lunar tidal forcing. We will show next how to confirm that the annual impulse exists simply by analyzing the ENSO power spectrum …