# Ice: Five Million Years

A new paper by Willeit et al. reports on the first successful model simulation of global climate over the last three million years. That’s a lot of years. You can find out more, from the lead author himself, at the RealClimate blog.

One of the real-world data sets they use, for comparison to their model results, covers an even longer time span: the LR04 stack, a stacked estimate of d18O (delta-oxygen-18) in sediment cores from around the world going back 5.3 million years. It’s a very good proxy for global ice volume; higher numbers mean more ice, lower numbers less ice.

Here’s the data along with a thick red line showing the long-term trend, and I inverted the y-axis (as did Willeit et al.) because global ice volume is itself a proxy for global temperature; colder means more ice, hotter means less (physics doesn’t get any more basic), so “hot” is at the top and “cold” at the bottom:

When I call the red line a long-term trend, I mean long; the smoothing time scale is about half a million years. It tells a story of long slow decline into icier and icier conditions, although we may have levelled off over the last million years.

But there’s more to the data than the very-long-term trend. There’s all that wiggling around up and down, which it turns out isn’t just random. It shows structure, in fact it shows cyclic behavior, and although its cycles look fast on the 5-million-year time scale of the graph, they’re only “fast” by comparison; these cycles have periods of tens of thousands of years.

I went looking for periodic/pseudoperiodic behavior with a wavelet transform. In the graph below, the x-axis is time (in thousands of years) to show how periodic behavior may have changed over time. The y-axis is frequency, the number of cycles per thousand years. The color indicates how active that frequency is at that time.

I’ve also put in some dashed lines to mark frequencies that are of special interest because we find them in another set of data: the changing parameters of earth’s orbit. I’ve even labelled them, “Obliquity” for the cycle of how tilted earth’s axis is, “Precession” for the cycle of how that axis itself spins around the sky, and “Eccentricity” for (one of) the cycle(s) of how flattened earth’s orbit is.

The most consistent strong response is at frequency of 0.0244 cycles per thousand years, or 1 cycle per 41,000 years. In fact, for much of the time span this is the only active cycle in the data; the ebb and flow of ice growth and decay was ruled by the cycle of earth’s obliquity. Some have even referred to most (but not all!) of this time period as the “41-ky world” (dominated by the 41,000-year cycle)

But in the last million years or so, another cycle has become dominant. This is easiest to see if we compare two different segments. First is the time span from 2.5 to 1.7 million years ago, which shows the 41,000-year cycle prominently; then is the time span from 0.8 million years ago until now, which just as prominently matches a 100,000-year cycle far better. Here they are, with thin black lines showing the data and thick red lines the matching cycles:

We can also see this with plain old Fourier analysis applied to the two separate segments. The earlier one shows the 41,000-year cycle (frequency 0.024 cycles per thousand years), while the later one shows that cycle but also includes another which now dominates, at 0.01 cycles per thousand years (100,000-year cycle, like eccentricity):

I’ll note that for the most recent segment, there is also some activity (not strong, but there) around frequencies from 0.042 to 0.044 cycles per thousand years (roughly 23,000-year cycles, like precession).

We have oscillations at three primary frequencies, but all of them seem to change throughout time. I estimated their time evolution using windowed Fourier analysis, and found that they have strengthened and weakened thus:

The waxing and waning of these cycles mark the progress of geologic epochs over the past five million years. About 2.6 million years ago, the 41 kY cycle (obliquity) got stronger, and has remained so since (despite continuing to fluctuate in strength). This is the end of the pliocene epoch and the beginning of the pleistocene, which continued until a “mere” 12,000 years ago when the holocene epoch began.

The 41 kY cycle dominated until about a million years ago, when the 100 kY cycle became its rival in strength. After about 600,000 years ago the 100 kY cycle has dominated. The transition is referred to as the “mid-pleistocene transition“.

And that is one of the things the new paper has found. Their model successfully explains why the mid-pleistocene transition happened. For the best explanation of that, I refer you to the article at the RealClimate blog, or to the paper itself.

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### 11 responses to “Ice: Five Million Years”

1. Very fine! I particularly like the wavelet transform result.

2. Ig

Sorry Tamino, this is not directly related to the paper you’re discussing here but the topic is somewhat related. It’s a paper that studies the relationship between CO2 levels and temperature in the very distant past. A denier has directed me to it in CO2Science (I know, rubbish fossil fuel funded blog) which leaves me a bit confused because it’s been published in what sounds like a credible journal _ Climate.

Title of the article in CO2 Science is “500 Million Years of Unrelatedness between Atmospheric CO2 and Temperature”.

Davis, W.J. 2017. The relationship between atmospheric carbon dioxide concentration and global temperature for the last 425 million years. Climate 5: 76; doi: 10.3390/cli5040076.

I don’t have the knowledge to be able to evaluate whether it’s nonsense or not so I’d like to know if you or anyone here knows about it and what your opinion of it is. Thanks

3. Davis, W.J. Who he?
Claims to be “Division of Physical and Biological Sciences, University of California, Santa Cruz”. Is this the same W. Jackson Davis who has posted at Whatsupwithdat with Peter Taylor, “Emeritus Professor of Biology, University of California at Santa Cruz”? The Santa Cruz website lists a William Jackson Davis Emeritus of ecology and evolutionary biology. Is this the same W. Jackson Davis calling Taylor’s book on Amazon a “must read”? and is that the same W. Jackson Davis with a couple of books on Amazon whose biography on Alibris reads:

“W. JACKSON DAVIS is professor of ecology and evolution at the University of California at Santa Cruz (UCSC), where he teaches exercise physiology. He is a certified health and fitness instructor of the American College of Sports Medicine and serves as strength and conditioning coach in the UCSC athletic department, where he has trained athletes for their individual sports. He has published more than 150 scientific papers, books, reviews, op-ed pieces, and articles.”

At Whatsup he is listed as “founding director” and “President and Chief Executive Officer” of a couple of institutes that Google doesn’t seem to have any information about.

A sceptic might think that Davis, W.J. has no expertise in global warming and could perhaps be guilty of bigging up his qualifications.

The journal “Climate” accepts papers “paid by authors or their institutions”. It claims that manuscripts are peer reviewed, stating “potential reviewers suggested by the authors may also be considered”.

A sceptic might wonder about that too.

4. As to the science of the paper, Skepticalscience.com has a good article.

“Do high levels of CO2 in the past contradict the warming effect of CO2?”

Basically the sun was weaker that far back in geological history, so relatively high levels of CO2 might not have been enough to prevent a glacial period- and a cold earth. Temperature apparently correlates well with CO2 *and* solar output.

At least according to climate scientists rather than a sports scientist.

5. First time I’ve heard of “a professor of ecology and evolution” who “teaches exercise physiology” and “serves as strength and conditioning coach.”

Must be quite a lot of research literature he has to keep up on… ;-)

6. I’m a little concerned that the irrational thinking gambit is beginning to affect environmental progressives more than one might expect given a base rate of irrational thinking. It might be affecting some climate scientists, too.

First, sure, climate scientists are people and, often, as Dr Neil deGrasse Tyson observes, many famous scientists have big egos. They like to demonstrate they have a deeper knowledge than a peer, at least some of the time. So, in general, Professor Michael Mann is less concerned about pace of change than Professor James Hansen seems to be. I’ve recently seen this in an old review Mann did of the precursor to the book Uninhabitable Earth by David Wallace-Wells which appeared (I believe) in New York Magazine. Mann claimed Wallace-Wells cherry-picked scientific papers on the exaggeration side and was claiming things were worse than they are. Mann even made comparisons of Wallace-Wells with Guy McPherson, who clearly is out there (“I can’t imagine there will be a human being alive in 2030”) .

I’ve read the article, and am reading Wallace-Wells’ book. And, while I disagree with Wallace-Wells in places, and agree with him and, as he’s stated on interviews, Uninhabitable Earth is a bit much for a title, I think Mann was unfair to claim this of Wallace-Wells.

But, curiously, another thing Mann cited in that verbal review was that “Carbon emissions had plateaued” and, while this wasn’t sufficient, he said, he indicated it was progress. What Mann was doing is fundamentally bad science and statistics: He was extrapolating a curve. That extrapolation has now been falsified, so Mann was cherry-picking as well, on the optimistic side.

The trouble is, the public isn’t this disciplined, and when I look at the supposed evidence backing up, for example, plastic bag bans, it is appalling. Yet everyone there thinks it is okay to argue that way.

WHOI is studying microplastics and the key people feel that it is way too soon to claim huge harms. For one thing the mass balance of plastics in oceans doesn’t work out, so something is happening to it, something we don’t know. So to claim all the plastic we’ve put there is still there is premature.

It’s a nit, but, also, plastic bags in oceans are the least of the plastic problems.

• Philippe Chantreau

Non medical single use disposable plastic products in general should be banned. They are an aberration. That includes single use plastic bags. Full life cycle analysis show that re-useable tote bags made of recycled materials are the best solution to replace them.

• @Philippe Chatreau,

Full life cycle analysis show that re-useable tote bags made of recycled materials are the best solution to replace them.

Agreed, but without penalties on use, such as fees, the public moves to using paper bags, which are arguably worse than plastic ones.

7. Tony McLeod

Speaking of ice Javier is giving you a mention as “desperate scaremongers like Tamino” over at WTF.

• Tamino is hardly “desperate”. If that’s the depiction, as I say to people who doubt the gravity of things (ha, ha), just wait a couple of years. No need for wasted breath.

https://www.pnas.org/content/early/2019/04/16/1904242116

Don’t pay attention to the absolute amounts of resulting SLR. Look at the rate. No reason to believe, given where we’ve come, this is going to slow down.

• KiwiGriff.

Projection .
The desperation is the Watties as the world is waking up to the fact they represent flat earth level of idiocy that is risking humanity’s future.
The last year has seen a change towards reality in how climate change is treated by media and online.

There is every reason to think sea level rise is going to continue accelerate .