Sunspots/NotSunspots

[pukpr]

It's long been clear that climate variability is not about matching to sunspots or measures related to sunspot variability

From a discussion at RC https://www.realclimate.org/index.php/archives/2023/10/unforced-variations-oct-2023/

The sunspot believer coward closed his GitHub commenting here bobf34/GlobalWarming#2

[pukpr]

R.D. Ray of NASA, a tide expert has very recently been providing published critiques of papers that ascribe the natural climate variation of ENSO to a combination of sunspot and tidal cycles. The two critiques are on papers that I already have created PubPeer entries for:

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"Comment on 'Linkage of El Niño-Southern Oscillation to astronomic forcing'"
https://iopscience.iop.org/article/10.1088/1748-9326/add1f2 -- Environment Research Letters

PubPeer: https://pubpeer.com/publications/8070CC6B7AFEF1DAB3F6826710FA37

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"There is no six-year periodicity in tidal forcing"
https://www.nature.com/articles/s41598-025-97361-0 -- Scientific Reports

PubPeer: https://pubpeer.com/publications/C57095317935FE75B92183A3EB1C6F

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He has a good point in both cases and provides good evidence that the authors claims don't hold water.

My position on the situation is orthogonal. I definitely don't agree with the rather naive take that one can map ENSO variation directly via the primary tidal cycles (and harmonics or sub-harmonics) and especially not via sunspot cycles. I also don't agree with the strategy Ray and his co-authors take in debunking based primarily on the direct mapping. As I described in the 1st PubPeer comment

It's become clear that the frequencies in a ENSO time-series come about from the interaction of an annual impulse with another signal. Sub-band satellite peaks in the frequency spectrum arise from the modulation of a signal with an impulse train due to the periodic nature of the impulse train itself. How it works:

An impulse train is a periodic sequence of delta functions, mathematically represented as: x(t)=∑δ(t−nT) where T is the period of the impulse train, and δ(t) is the Dirac delta function. The Fourier transform of an impulse train is another impulse train in the frequency domain. Specifically: X(f)=1/T ∑δ(f−k/T)

This means the impulse train has spectral components at multiples of the fundamental frequency f0=1/T.

When a signal s(t)s is modulated by the impulse train, the resulting signal in the time domain is: y(t)=s(t)⋅x(t) This multiplication in the time domain corresponds to a convolution in the frequency domain. The Fourier transform of the modulated signal Y(f) is given by the convolution of the Fourier transform of the signal S(f) with the Fourier transform of the impulse train X(f): Y(f)=S(f)∗X(f)

Since X(f) consists of impulses at multiples of f0, this convolution results in copies of the original signal's spectrum S(f) centered at each harmonic of f0​.

Explaining Sub-band Satellite Peaks: These copies of the original signal's spectrum at multiples of f0​ create what are called "satellite peaks" in the frequency spectrum. These peaks are essentially shifted versions of the original signal spectrum and appear as distinct sub-bands around each harmonic of the impulse train’s fundamental frequency. The key here is that any sub-bands can be observed by flipping the measured Fourier amplitude spectrum about the Nyquist frequency and looking for mirror symmetry.

If one does that for the NINO34 time-series, the symmetry is clear, but busy.

The point is that none of the known lunar or solar periodicities will emerge as conventional Fourier series peaks. Instead, the spectrum is composed of satellite peaks at frequencies that are not directly related to the reciprocal of any single period of the original signal. This creates a more complex spectral structure that differs from what would be seen in a Fourier series of a purely periodic function.

That's only a start. Another factors to consider is that ENSO is likely a dynamic response to tides operating on the ocean's thermocline. The solution to this is described in Chapters 12 and 13 of Mathematical GeoEnergy, Pukite et al (Wiley, 2019). That should be cited, as it demonstrates how well a model can be fit to the observations using the correct interpretation of modulation of an annual impulse, followed by a canonical solution of the ocean's fluid dynamics.

Here are the positions

1. Naive tidal or SS harmonic mapping (wrong)
2. Not tidal or SS harmonic mapping (Ray's debunking)
3. Do some extra signal processing (my position)

The last is orthogonal because it both debunks the naive position yet keeps the options open for tidal forcing. The hope is that Ray will comment on my PubPeer entries.