[note, I believe the term cyclomania was invented by Willis, so I want to make sure he gets credit. Rud got it from me.~cr]

Guest post by Rud Istvan

WUWT reader DS (you know who you are) sent a tip to Charles concerning the retraction of a recent Nature publication on solar cycles, predicting a ‘modern Maunder Minimum’ before 2050—thus debunking anthropogenic global warming (AGW, aka climate change).

Previous investigative forays of this solar cyclomania sort have not ended well, so Charles asked me to investigate this one.

I did, and at first was not certain the simple obvious answer was worthy of a guest post. Charles differed. Having reconsidered most of today while hunting and pecking at additional factoid tidbits, I now agree with him. Here is the sorry saga plus some maybe neat sciency stuff: gravitational ideas like barycenters for those that want to learn more themselves.

The retracted paper is Zharkova et.al. 2019 . This is already interesting, because Valentina Zharkova is a well-known ‘mini ice age coming’ ‘skeptic’. She got published, and then retracted. A Skeptical set up? Nope.

Her saga is reported in three parts: what she did, why Nature retracted over her objection, and why she should never have been published by Nature in the first place because of fundamental background math and physics issues.

**What she did**

Her team took satellite measurements of the solar whole disk magnetic fields from solar cycles 21-23, so about 33 years. They used this independent variable to model the crucial dependent insolation variable. Note the unproven assumption that insolation is a function of solar magnetic flux. (Sunspot theorists do, but their observational substantiation is at best sketchy.) Their model used principle components analysis (PCA, of Mann hockey stick fame) to find TWO magnetic flux components (so much for THE principle component) collectively explaining only 67% of their insolation data.

That seems an overt admission of poor fit statistics, which should have been flagged by peer reviewers. Then they used a theoretical causal model of varying solar magnetic fields to ‘backgenerate’ 3000 years of solar magnetic flux, finding a max/min/max cycle of roughly 350 years full wave form (peak to peak). So the paper concluded that in the last 3000 years, we have seen about 9 insolation minima caused by solar magnetic flux, including (conveniently, except observationally wrong decadal timing wise) the Maunder. And so the next ‘grand minimum’ will be before 2050!!!

An admonition to potential persnickety WUWT critics, like DS. The above is not exactly precise, but captures faithfully the essence of the matter. There is no poetic license. And her paper Figure 2 makes her ‘scientific’ situation MUCH worse than represented here. I am being kind to her in what follows.

**Why Nature retracted 9 months later in 2020**

Post publication, a number of astrophysicists pointed out that a key calculation assumption—Earth/Sol barycenter fluctuations are random—was just wrong. Nature editors therefore had no choice but to retract the faulty paper when this was easily verified. (See the linked retraction notice footnotes.)

Insolation depends on the barycenter between Earth and Sol. Zharkova assumed that this barycentric variation was random (it matters for insolation, since as you get closer to a hot object you get hotter—something about an inverse square law of radiation physics). For Earth-Sol, the barycenter is always somewhere within the Sun since the Sun has so much more mass than Earth. But Earth does wiggle a bit closer and farther, affecting incoming insolation energy. Random washes out statistically. A very convenient but since proven false assumption.

But for Jupiter, the barycenter is actually always OUTSIDE the Sun, because Jupiter has so much more mass than Earth compared to the Sun. As a result, the Earth-Sol barycenter actually is closely linked to the 12 year Jupiter orbit that much more strongly influences the Sun’s solar system barycentric wobbles. Jupiter on the ‘Earth side’ of its orbit pulls the Sun closer to Earth, and on the ‘far side’ of its orbit pulls the Sun away from Earth. So the paper’s assumptional math was just wrong. Showing yet again that ‘climate scientists’ need to be generalist polymaths, while most (as shown by this paper) are not.

My personal issue with this retraction specific is not that it happened, rather it is that NASA has had the Earth/Jupiter barycenter explanations on an easily accessible website for several years, so the paper’s ‘random’ assumption is inexcusable intellectual laziness by the authors and then by Nature’s peer reviewers. Heck, Newton sorta figured these gravitational basics out long ago. We have been measuring it precisely for decades.

Side comment. The solar cycle is supposedly ~11 years, Jupiter’s orbit ~12 years. So the barycentric ‘drift’ per solar cycle is ~11/12, or about 8% per Jupiter orbital cycle. So a max to min Jupiter kiltered Earth/Sol barycenter would be about 13 Jupiter orbits, and back another 13, so about 26 for a full insolation wave form. So about 312 years in total for a full peak to peak barycentric Jupiter cycle. And her beyond sketchy PCA found about 350. Huummm???

**What is REALLY wrong**

What I found beyond incredible is that none of the authors, Nature’s editors, or the peer reviewers spotted a much more fundamentally fatal mathematical problem in this paper’s analysis.

Recall what the paper did. Used about 33 years (three solar sunspot cycles) of satellite observations of solar magnetic flux to reconstruct a solar magnetic flux amplitude wave form of about 350 years peak to peak frequency, supposing that then related to equivalent relative insolation energy.

There is an analog/digital conversion mathematical thingy called the Nyquist sampling theorem. It says a band limited (excluding any higher frequencies) continuous time signal comprising multiple wave frequency amplitudes (analog) can be digitally sampled and perfectly reconstructed from discrete (digital) samples of the simple net analog amplitude waveform at a sampling rate >= 2x its highest frequency component.

We experience the Nyquist sampling theorem every day in CDs (now also all digitally streamed music). The sampling rate was set originally by Sony at 44.1kHz (44,100 digitally sampled net amplitude of recorded analog audio sound samples/second). That will faithfully reproduce any sound wave (pitch, frequency) below about 22kHz. Average humans can hear from about 20Hz to 20kHz. The best younger ears can hear 12 Hz to 28KHz. Most older adults experience a drop in hearing acuity above 15kHz, used to design hearing aids centered on about 3kHz.

Sony set a practical Nyquist analog/digital audio music sampling standard, which analog groovy record audiofiles continue to deny to this day to their utterly foolish great analog equipment expense. They believe one thing; Nyquist proved otherwise. Climate analogies abound.

The fundamental physics/math problem with this now retracted on other grounds paper is that they used 33 years of satellite data to very poorly reconstruct via discredited and ill fitted PCA a ~350 year frequency full solar magnetic field strength wave form, when Nyquist says you need at least 700 years to reliably do that. And 700 years of solar magnetic field strength amplitude variation data DOES NOT EXIST.

Any generally knowledgeable peer reviewer should have rejected this paper on first principles of high school math and physics: CD basic digital music stuff. And that is why I reconsidered, now think Charles original opinion was correct, and then wrote up this ‘trivial’ guest post for him in thanks.