Teleconnection vs Common-Mode

/ Paul Pukite (@whut)

A climate teleconnection is understood as one behavior impacting another — for example NINOx => AMO, meaning the Pacific ocean ENSO impacting the Atlantic ocean AMO via a remote (i.e. tele) connectiion. On the other hand, a common-mode behavior is a result of a shared underlying cause impacting a response in a uniquely parameterized fashion — for example NINOx = g(F(t), {n1, n2, n3, ...}) and AMO = g(F(t), {a1, a2, a3, ...}), where the n's are a set of constant parameters for NINOx and the a's are for AMO.

In this formulation F(t) is a forcing and g() is a transformation. Perhaps the best example of a common-mode response to a forcing is in the regional tidal response in local sea-level height (SLH). Obviously, the lunisolar forcing is a common mode in different regions and subtle variations in the parametric responses is required to model SLH uniquely. Once the parameters are known, one can make practical predictions (subject to recalibration as necessary).

The solution to Laplace’s Tidal Equations (LTE) can theoretically provide one with a formulation that can describe g() and the accompanying parameters. We do that for a proposed simplified solution to LTE in Chapter 12 of Mathematical Geoenergy, where F(t) is defined as the tidal forcing.

Below are LTE fits to AMO and NINO4, with the common-mode tidal forcing shown in the middle panel. Very similar in shape — not identical, but with correlation coefficient of 0.98. The amplitudes of the tidal coefficients are shown to the right. Only a few of the weaker coefficients differ significantly as highlighted in yellow. The bottom two panels show the LTE modulations for the NINO4 and AMO models, which show a distinct difference in modulation frequency.

The fundamental LTE modulation is 9.57 for NINO4 and 9.9 for AMO, which although roughly similar in scale, is significant for causing the two climate indices to not remain coherent over the multidecadal range.

NINO4 

     Frequency         Amplitude           Phase      
  -0.95765299105,    7.24988316572,    0.05205471280 1
 -13.40714187474,    0.19562646948,    2.52292810939 14
  -9.57652991053,    0.45109757666,   -1.13540609153 10
 -12.44948888369,    0.20483997005,   -0.10458020125 13
  -1.91530598211,    1.26411927021,    3.08927241597 2
-125.45254182794,    0.16172438056,    1.58415779282 131

AMO

  -0.99111332693,    4.29087202901,    0.29768854238 1
  -9.91113326930,    1.41201845026,   -0.94193545109 10
  -8.92001994237,    1.99311825197,   -2.59682571836 9
 -31.71562646177,    0.44693951998,    1.48952165013 32
 -39.64453307721,    0.40193935698,   -2.09283560249 40

For PDO the common-mode forcing is even more closely aligned with that for NINO4. The correlation coefficient is 0.996. According to the LTE power spectrum, the fundamental modulation frequency aligns with NINO4 as well but is broader in width.

 PDO

  -0.92231593392,    1.08520943714,   -0.83600050007 1
 -12.91242307482,    0.55375908448,    2.45652487829 14
  -9.22315933915,    0.49010470703,   -1.16296125655 10
 -11.06779120699,    0.37834117468,   -0.84698123914 12
 -29.51410988530,    0.50214469753,   -1.49892571238 32
 -22.13558241397,    0.35874973853,    0.30694975985 24
-115.28949173943,    0.23228623001,    0.33279807159 125

For the IOD (Indian Ocean Dipole), the common-mode forcing is also closely aligned with that for NINO4. The correlation coefficient is 0.994. According to the LTE power spectrum, the fundamental modulation frequency also aligns with NINO4 but, like the PDO, is broader in width. It also shows a strong cross-validation in the test region 1995-2000

IOD

  -0.98972560536,    0.23896494973,    0.37237174278 1
  -7.91780484288,    0.09125273122,   -2.62976141532 8
  -9.89725605361,    0.15005387072,   -1.75954183585 10
 -40.57874981978,    0.08644702198,    1.08735782521 41
 -49.48628026803,    0.05887676849,    0.63172937771 50
 -93.03420690389,    0.06150982039,   -0.40639075917 94

Summary » Substantiation

The primary ocean indices show a significant common-mode forcing F(t) according to a causal model as follows:

  1. NINO4 = g(F(t), {n1, n2, n3, ...})
  2. AMO = g(F(t), {a1, a2, a3, ...})
  3. PDO = g(F(t), {p1, p2, p3, ...})
  4. IOD-E = g(F(t), {i1, i2, i3, ...})

The fact that the forcing only varies slightly, thus showing domain cross-validation, while also showing a temporal cross-validation via a non-trained test interval, provides substantiating evidence of the validity of an LTE modulation-based model. On the contrary, a stochastic data set would fail such a cross-validation. While the idea of teleconnection as a synchronization is not ruled out, it lacks a well-grounded physical mechanism.

As a definitively conclusive cross-validation of the model, consider the time-series for the North Pacific Gyre Oscillation (NPGO). This index occupies the same Pacific region as the PDO but is orthogonal to it in terms of a spatio-temporal standing-wave arrangement, indicated by both SST and sea-surface height (SSH) measurements.

The co-location + orthogonality properties imply that a different LTE modulation should be invoked for precisely the same tidal forcing. Thus, the variation in LTE modulation, which is by definition orthogonal (any two sinusoids of different frequencies are orthogonal1), should be enough to fit the NPGO based on the reference PDO forcing. Testing this over the shorter time interval for NPGO :

The fit is remarkable in terms of showing a strong primary modulation that is nearly linear — note the long-period variations being in sync as indicated by the up-arrows in the chart below left (and the linear slope reference line below right). And consider also a distinct sinusoidal LTE modulation that is 20% faster than that of PDO, thus demonstrating orthogonality.

This incredible piece of cross-validation does not happen by accident. In fact, only through many stages of supporting cross-validation2 and a novel geophysical fluid dynamics model model will it be revealed, much like a decoding algorithm works in practice — with the intermediate forcing acting as a decryption key. It is perhaps fitting that this last piece of cross-validation operated on a sea-surface height measurement, a domain that we earlier defined to be a prime example of common-mode forcing via lunisolar gravitational cycles.

Footnotes

  1. Provable as a fundamental property of Fourier analysis, covered in many textbooks on signal processing and mathematical methods for engineers. A classic reference is: Signals and Systems, Oppenheim, A. V., Willsky, A. S., & Nawab, S. H. (1997), Prentice Hall. The orthogonality of sinusoids is discussed in the context of Fourier series and transforms, and it is a key concept in understanding the decomposition of signals into their frequency components. ↩︎
  2. All of the model fitting results reported on this post are based on artifacts stored at https://gist.github.com/pukpr/87223b66cdeaf9e5bff150d1d79663c6. Also contains additional results for the El Nino Modoki Index (EMI) and the Atlantic Nino time series. ↩︎

3 thoughts on “Teleconnection vs Common-Mode”

  1. https://www.nature.com/articles/s41598-024-62089-w.pdf

    The South Atlantic Dipole via multichannel singular spectrum analysis

    We perform the M-SSA analysis of the ERA5 datasets40 frst for the SST and SLP felds separately, and then a joint SST and SLP analysis (hereinafer referred to as coupled). For each of these analyses, we obtain the principal components (PCs) that correspond to each mode. Oscillatory modes come in pairs, as described in the “Methods and data” section. In all three cases, we obtain a trend mode (PC 1) followed by two oscillatory modes with
    fundamental frequencies of 12.8 years (PCs 2–3) and 5.3 years (PCs 5–6 for SLP and 4–5 for SST and coupled).

    Reply

  2. “Mitigation needed to avoid unprecedented multi-decadal North Atlantic Oscillation magnitude” https://www.nature.com/articles/s41558-025-02277-2

    First, model simulations of the NAO are highly chaotic, such that tiny changes that would be impossible to measure can lead to opposite trends12. If this is true for the real world, the future NAO will be highly uncertain due to irreducible internal variability13. However, there is mounting evidence that the real-world NAO is much more predictable than models suggest14,15,16,17,18,19,20,21. This model error has been called the ‘signal-to-noise paradox’ (SNP) because a climate model can predict the real world better than one of its own ensemble members despite perfectly representing itself22. This arises when the ratio of the predictable signal to unpredictable noise is too small in models. Consequently, the magnitude of the modelled ensemble mean is too small and must be inflated to obtain realistic and reliable predictions

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