What’s wrong with Perry and Hsu, “…a solar-output model for climate change”

Proceedings of the National Academy of Sciences, vol. 97 no. 23, Charles A. Perry and Kenneth J. Hsu,  1243312438; Proc. Natl. Acad. Sci. USA, 10.1073/pnas.230423297.  “Geophysical, archaeological, and historical evidence support a solar-output model for climate change”

So, what’s wrong with Perry and Hsu’s paper?

This is not a complete list, nor am I really an expert on this topic.  But here are a few of the more obvious problems.

The missing physics of the paper.

And, finally, the thing that Perry and Hsu didn’t say is that their effect is way too small to make a difference.  Basic physics gives us a pretty good idea of how much the Earth would heat up if the Sun became 0.4% brighter.  And 0.4% is about the size of the swing that they claim between “full glacial” and the warm Medieval Maximum.

Unfortunately, physics tells us that 0.4% change in solar energy would heat the Earth by about 0.28 degrees Celsius, whereas the actual temperature shift between glacial and warm periods is 4.5 degrees Celsius.  They needed to find an effect that was about 20x larger; even ignoring other problems with this paper, their nice plots explains only tiny fraction of the warming we’ve seen.

Where does the rest come from?    CO2 and the greenhouse effect.  [Where else?]

The flawed logic of the paper.

It’s pretty clear (to all but emotionally committed climate deniers) that that last few decades have been very warm.  Nearly every year since 2000 has been a record-setting year [1], with the top five being 2005, 2010, 2013, 2014, 2015 (and now 2016).  Glaciers are disappearing.

Now, is that warming being driven by the sun (as Perry and Hsu would presumably argue)?   Well, there isn’t a solar spike visible on any of Figures 1, 2, or 3 around the year 2000.   So, they didn’t predict it. [Which is a problem in itself.]

But if we believe Perry and Hsu, the Sun should be the big, important effect.  And if the Sun isn’t causing the recent warming, then what is?  [Carbon dioxide and the greenhouse effect, I suppose…]

Problems in the “Solar-Output Model” section.

First of all, what exactly did they do here?  As near as I can tell, they computed a weighted sum of sine and cosine waves with periods of 11 years, 22, years, 44 years, 88 years, 176 years, …., 45056 years.   Maybe.  Except that they mention a 90,000-year cycle, which doesn’t quite fit in with the rest of the description.  Thirteen cycles, each twice as long as the previous (from that 2N comment above) gives 45000 years for the longest one, not 90,000.

Oh well, it’s probably just a mistake.

And then they do this somewhat mysterious shift from a 12-year cycle before 9000bp to a 10-year cycle.  This shift is really just speculation; if you read the reference (Friis-Christensen & Lassen), you find that it’s an extrapolation from 130 years of modern data extrapolated 9,000 years backwards in time.

But an interesting mathematical thing about the shift is that it allows — it forces — Perry and Hsu to make their model twice as complex.  Their model is a weighted sum of sine and cosine waves, and changing the period means that they have different sine and cosines on the two sides of 9000bp.   So, they essentially have different models on each side of the dividing line. [The twos sides are coupled only in that they agree on the value, and maybe on the slope of the curve at 9000bp.]

Cynically speaking, that’s very convenient, because the model looks quite different on the two sides of the dividing line, and it’s much easier to make the model behave differently if it is really two models that are barely connected.

Anyway, in their model, the authors have either 50 or 54 coefficients that they can adjust to match the data.  24 or 26 on either side of the 9000bp line, and two that are shared by both parts of the model.  With that many adjustable parameters, it’s no surprise that the authors can match their data fairly well.   By and large, such a sum can be expected to precisely match any data set with fewer than about, oooh, a dozen wiggles.   And, their data set has about 9 major wiggles, so mathematically speaking, it’s no surprise at all that their model can match the data it was trained on.  The interesting question is whether or not it can predict data that wasn’t used in the training process.

Perry and Hsu (as far as anyone can tell from reading the paper) train their model on all the available data, so they don’t leave any data for testing the model.  See, a better written paper would have trained the model up to, maybe, 5000bp, and left the remaining data available for testing.  Then, they would have predicted forward from 5000bp to now and compare that prediction against their unused data.  But they didn’t.  [Oh well, we can’t tell how good their model is for prediction.  Should we assume it’s really good, or really bad?]

Now, in the last paragraph or two we’ve been mentioning “data”.  If you look carefully, you will not see any actual data related to solar cycle length or the Sun’s brightness.  That’s another indicator that the paper is junk.  [What the heck did they base the model on?  Does their data agree with anyone else’s?   There is kind of a reference, but it doesn’t seem to exist on the web.]

Problems in the “Comparison of Modeled Solar Output and Archaeological and Historical Evidence” section

Various things are dubious, for one thing, it’s not clear that the “Medieval Warm Period” was world-wide, or just related to the North Atlantic (e.g. 1, 2).

But, more than that, they present this as evidence: “Did the people of Easter Island eventually fall into cannibalism by the late 1600s as a result of environmental degradation by overpopulation, or was it a major change in global climate caused by a decrease in solar output that converted their home from a wet tropical island into a desert island during the Little Ice Age?”

Well, did they?  That’s speculation, badly abused, in an attempt to look like evidence.  I look at the literature, and it seems that the experts are not very sure (e.g. 1, 2).  [So, yes, it’s fine that Perry and Hsu ask the question, but they should ask it over a beer and not in the middle of a paper where they are supposed to be presenting evidence.]  It’s not evidence.

The flawed plots of the paper.

Those of you who know about sines and cosines know that they are incredibly smooth functions without corners.  Smooth, like gentle waves on a pond.  But a close look at Figures 1, 2, 3 shows corners everywhere!

Really, that’s just incompetence.  It happens when you don’t understand that a sine wave with an 11-year period has a wiggle every 11 years.   So, if you draw your plots with points spaced about a century apart, you’ll end up sometimes drawing lines from the top of one wiggle to the bottom of the next, and you’ll get corners.

But, really, do you want to trust your future to people who don’t know how to plot sine waves?

There’s one more oddity in the plots that I’ll mention.   Early in the paper, Perry and Hsu mention one of the very few details of their model.  They say that the 11-year cycle has an amplitude of 0.08%.  That’s actually pretty big on the scale of the plot.  From peak-to-peak that’s twice as big, about what they call the difference between “glacial” and “cool interglacial”.  But it doesn’t show on the plots at all.  [Oops, that’s because they sampled the data only once a century…   Just another mistake.]

A problem in the Introduction:

The introduction is poorly done, because of what it doesn’t mention.  A good scientific theory should match all of the available evidence, and one of the interesting facts about the Sun is that it’s a perfectly ordinary type-G main-sequence star.

Now, astronomers know quite a bit about Sun-like stars; a  Google Scholar search for “variability of G stars” yields 667,000 results.  I’ll bet that at least one or two are relevant.  [I’d have referenced one or two.]