Into and Out of the Icebox

Guest Post by Willis Eschenbach

Inspired by a random comment by Steve McIntyre over at his marvelous blog Climate Audit, I got to thinking about the ice ages. I’ve long heard that the ice ages are caused by the changes in summer insolation in the northern hemisphere. As the story goes, the Milankovitch cycles of variations in the earths orbit make it so that there is a variation in how strong the summer sun is in the northern hemisphere. When the summer sun is weaker, the ice sheets advance, and eventually the buildup of ice reflects enough solar energy to spiral us into the icebox. Then about every hundred thousand years, the sun gets stronger again, and melts away the ice, and within a few thousand years the great ice sheets melt away and we’re out of the icebox.

So of course, once I’ve had that thought, I was doomed, and so I had to take a look. I got the data, and here is the variation in average northern hemisphere insolation for the months of June, July, and August.

Insolation at 40NFigure 1. Average insolation during the summer months (J-J-A) at 40° north latitude. DATA SOURCE: NOAA 

Now, I found that surprising. I hadn’t realized the size of the swings. The cycles are about 21,000 years long and the swings are quite large, up to 100 W/m2 from trough to peak. So IF the temperature is following the forcing as the current hypothesis claims, a swing of 100 W/m2 is certainly large enough to cause a very large swing in temperatures. The current hypothesis is that at equilibrium we should see a swing of ~3°C for each additional 3.7W/m2 of forcing. However, we’re talking annual swings. Transient climate sensitivity is about 70% of equilibrium sensitivity, so I’ll use 50% to give some cushion. So according to the current thinking, a swing of an additional 100 W/m2 which is maintained for a thousand years should result in an increased annual temperature swing of about 40°C (73°F) … and we don’t see anything in the geological records even half that size.

I also didn’t realize that there is an underlying ~400,000 year cycle, which leads to the larger peaks at about 200,000 and 600,000 years before present (BP), and also leads to the very, very small peak at about 400,000 years BP.

But obviously we don’t see such a swing in geological temperatures. In fact, we don’t see anything even near that. So, scratching my head, I went and got the longest temperature record we have. This is the record from the ice cores at the EPICA dome in Antarctica. Figure 2 shows that record:

Epica Ice Core AnomalyFigure 2. Antarctic temperature variations estimated from deuterium data. DATA SOURCE: NOAA 

Here, we can see the ~ 100,000 year cyclical nature of the emergence from the ice ages. The swing is generally on the order of about 12°C, and the usual estimate is that because the poles swing more than the tropics, the global swing is half the Antarctic swing, or about 6°C. We can also see that the current interglacial period, the “Holocene”, has lasted quite a while compared to the other interglacials.

Note also the very large and roughly symmetrical peak at about 400,000 years.

So … how does this relate to the Milankovitch cycles? Figure 3 shows the temperature overlaid over the Milankovitch cycles.

Insolation at 40N and EPICAFigure 3. Antarctic temperature variations estimated from deuterium data, overlaid on the Milankovitch insolation cycles.

I gotta say I’m just not seeing it. The biggest oddity is that around 400,000 years, the very small insolation peak is correlated with a very large temperature peak. In addition, in general there seems to be very little correlation between the swings in insolation and the swings in temperature. Finally, the most interesting thing is the total lack of any 21,000 year cycle in the temperature.

Now, some authorities say that the crucial factor is not the insolation at 40°N, but the insolation at 60°N. So I checked that … but the difference in the pattern is only trivial. It mainly just affects the size of the swings, which are somewhat smaller at 60°N, but the pattern of large and small swings is essentially unchanged.

Now as might be imagined, I’m not the first one to be puzzled by this. It’s widespread enough that there’s a Wikipedia page entitled “The 100,000-year problem”, which points out that:

The 100,000 year problem is a discrepancy between past temperatures and the amount of incoming solar radiation, or insolation. The latter rises and falls according to the strength of radiation given off by the sun, the distance from the earth to the sun, and the tilt of the Earth’s axis of rotation. However, the recent change between glacial and inter-glacial states that occurs on a circa 100,000 year (100 ka) timescale, does not correlate well with these factors.

Due to variations in the Earth’s orbit, the amount of insolation varies with periods of around 21,000, 40,000, 100,000, and 400,000 years. Variations in the amount of incident solar energy drive changes in the climate of the Earth, and are recognised as a key factor in the timing of initiation and termination of glaciations. Isotope analysis shows the dominant periodicity of the climate response to be around 100,000 years, but the orbital forcing at this period is small.

However, my perplexity seems to be for a different reason than the other folks discussing this, which is that the really large insolation swings occur on a 21,000 year cycle, and there’s no trace of that in the EPICA data. I’m not so much interested in the existence of the 100,000-year cycles in the temperatures, as I am by the lack of any temperature response to the ~100 W/m2 swing in the insolation.  Yes, I know that overall for the globe as a whole the swing is small because the hemispheric changes oppose each other, but for each hemisphere the changes are very large. Why do we see no trace of those very large swings?

Anyhow, all comments welcome.

Best wishes to all. It’s one AM, there was a new moon earlier tonight, I’m going outside for some stargazing, and I wish the same level of joy and awe to all of you.

w.

As is my custom, I ask that if you disagree with someone, please QUOTE THE EXACT WORDS YOU DISAGREE WITH so that we can all understand the exact nature of your objection.

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gbaikie
January 23, 2015 1:15 am

–Now, some authorities say that the crucial factor is not the insolation at 40°N, but the insolation at 60°N. So I checked that … but the difference in the pattern is only trivial. It mainly just affects the size of the swings, which are somewhat smaller at 60°N, but the pattern of large and small swings is essentially unchanged.–
I would think max insolation at 30°S would result in most warming.

Lancifer
January 23, 2015 1:23 am

I have also puzzled over the rather blase acceptance of Milankovitch cycles as the cause of ice ages when the data doesn’t seem to correlate particularly well.

Alan the Brit
Reply to  Lancifer
January 23, 2015 4:15 am

Actually I think you’ll find it took a while for the theory to be accepted, so I wouldn’t say it was blasé at all!

Viewer from Afar
Reply to  Alan the Brit
January 23, 2015 6:30 am

Even back in the late 1800s, people were musing on the Earth’s orbit as a cause of ice ages: “The Cause of an Ice Age”, 1891, by Sir Robert Ball, Royal Astronomer of Ireland.

latecommer2014
Reply to  Lancifer
January 23, 2015 7:53 am

My belief is that the ice core records are the problem….with all the possible corruptions of migration of gases, contamination in processing and unknown climate factors, the ice core record is an unreliable source for much of anything, except perhaps snowcones

Mandobob
Reply to  latecommer2014
January 23, 2015 8:11 am

Because the resolution on ice core analysis is likely tens to 100’s of decades cross contamination, which does exist, is somewhat homogenized. Leading to an “error” determination with each measurement. These “errors” are most commonly shown as error bars which are, at least for true scientific data presentation, necessary for correct data evaluations. Just because the data has some issues with resolution does not automatically make the data set unreliable. I just means that care and caution is necessary when using those data sets for conclusions.

Reply to  latecommer2014
January 23, 2015 11:28 am

latecommer, the temperature record in ice cores is not from the gas bubbles, but from the D/H ratio and 18O/16O ratio in the water molecules of the ice itself: the heavy isotopes relative increase with increasing ocean temperatures, which make it possible to estimate the ocean temperatures at the time of deposit. The resolution depends of the snow deposit and its ice equivalent over time, from yearly for coastal ice cores (which catch areas are the nearby oceans) to decades for inland ice cores where deposit is only a few mm ice equivalent per year but the catch area is the whole SH oceans. The yearly ice layers get thinner with depth and ice flow.
Gas migration in the Antarctic ice cores is very small for the relative “warm” coastal cores and immeasurable for the much colder inland ice cores.

george e. smith
Reply to  latecommer2014
January 23, 2015 1:14 pm

So what happened to the idea that atoms and molecules were pretty stable things, when left to themselves.
So if I’m a water molecule, I could be a HH16O, or a HH18O, or HD16O, or a HD18O, or a DD16O, or a DD18O, and maybe once in a while have a T in there; who knows.
So what is it about the Temperature of the ocean that changes a D to an H or verse vicea, or switches an 18O for a 16O atom ??
I suppose each of those species has its own unique boiling / evaporating / subliming Temperature ??
But what about their relative abundance in the ocean water itself, as a function of say water depth.
Would the DD18O molecules sink deeper than the HH16O molecules; or just how “well mixed are all the water species around the world ? Is the South Atlantic the same as the South Pacific or the South Indian Ocean as regards abundance of the various water species, because they slosh back and forth around the Horn, and around Africa twice a day, in all kinds of weather.
So I guess there is a computer teramodel of Antarctic Plateau snow versus southern ocean weather somewhere that says what ocean temperature goes along with what snow species ??
How do you do an experiment to connect Plateau snow with a specific measure ocean Temperature that supposedly sourced that snow ??

Reply to  latecommer2014
January 23, 2015 2:02 pm

Latecommer, In addition to Ferdinands remark, the isotopes in the Antarctic ice cores are matched closely by the foraminifera isotopes in oceanic cores. ie the LR04 benthic stack http://www.lorraine-lisiecki.com/stack.html which is assumed (but not by me) to represent ice volume. Obiously the more ice with “light” isotopes on the continents, the more “heavier” the water that stays behind in de oceans (reservoir effect).
There is a world of discussions behind this.

Reply to  latecommer2014
January 23, 2015 2:53 pm

George,
The idea behind the isotopes used as temperature “proxy” is that the evaporation speed is different: at a certain temperature the lighter molecules escape faster from the liquid than the heavier one’s in moister undersaturated air. That is measured in laboratories and in the field, not only for water but for isotopes from all kinds of molecules at evaporation, condensation, sublimation and freezing.
That makes that water vapor is “lighter” in composition than water itself. The difference gets smaller at higher temperatures. The same where vapor freezes directly into snow/ice crystals. I don’t remember which way that goes, but anyway there is an isotope shift too. Thus by measuring the ratio between the isotopes in the ice one can have an idea of the temperature at evaporation.
Similar things happen with CO2 when it escapes from the oceans and goes back into the oceans (pure a matter of physical differences, not biological as in plants).
It seems that the isotopic composition of seawater in general is rather uniform on “short” periods of hundreds of years, but changes with the formation of ice sheets, as ice sheets water is “lighter” and leave the oceans with more heavier isotopes. There are some tricks from which they estimate the volume growth and melt of the ice sheets, out of the 18O/16O ratio in N2O.
There was some discussion in the scientific world about the translation into “temperature” from the double isotope fractionation (evaporation/freezing), but that seems rather quiet these days…
http://onlinelibrary.wiley.com/enhanced/doi/10.1029/2002JD002677/
http://onlinelibrary.wiley.com/doi/10.1029/2009JD012054/pdf
http://onlinelibrary.wiley.com/doi/10.1029/90JD02232/abstract

4TimesAYear
Reply to  latecommer2014
January 23, 2015 10:33 pm

“Like” I’m not fond of proxies of any kind.

george e. smith
Reply to  Lancifer
January 23, 2015 11:29 am

There’s that old joke about the idiot scheduled for the guillotine; who has elected to meet his maker in the “eyes up” position, instead of the chicken “nose to the ground” pose.
When the blade fails to drop twice in a row; our hero says to the executioner:
Hang on a minute; I think I can see the glitch that is jamming the works up there !
So I think I see the glitch; not in Willis report, but in the concept itself.
Willis will correct me, if I’m wrong (often am) but I believe that the Milankovitch cyclic graph that willis posts (the red amplitude modulated carrier) in Fig. 1 is simply calculated from orbital dynamics parameters, relating to the polar precession, and the orbit eccentricity, and other fairly Newtonian (or Einsteinian) gravitational theory.
That’s why it is such a pretty graph compared to the blue ice core graph.
So since when did Newtonian Orbital dynamics know anything at all about CLOUDS !! ??
Mother Gaia, pays no attention to Newton or Einstein when she sets the Temperature on earth.
She looks up at the clouds, holds her finger (not the middle one) up to test the wind, collapses her Brolly to check for rain, and a whole bunch of other stuff going on everywhere that has nothing to do with why tops spin.
So more Milankovitchinsolation, more evaporation; more CLOUDS, less SURFACEINSOLATION; lessevaporationmoreprecipitation; less CLOUDS, and more surfaceinsolation.
So nyet on Milankovitchinsolation driving ice ages; but not to deny some effect on their occurrences.
Mother Gaia decides when to have ice ages.
G

Mike M.
Reply to  george e. smith
January 23, 2015 12:02 pm

The climate modellers have long recognized that the Milankovitch cycles can not produce ice ages without strong feedbacks. I think that is actually what first led to the idea of positive climate feedbacks, long before global warming became a concern.

DD More
Reply to  george e. smith
January 23, 2015 2:53 pm

Can someone also answer the question of how stable the wobble and tilt is. If a small piece of bubble gum stuck to the side of a child’s toy top, can make it wobble out of control. What would giga tonnes of ice do to a spinning globe? The vast ice sheets unevenly arranged around the globe during the glacial times has no effect on the size of the wobble?

Reply to  george e. smith
January 23, 2015 10:18 pm

Mike M,
strong positive feedbacks quickly lead to nonlinearities. Non linearities in dynamical systems lead to unpredictable, but certain bifurcations to new attractors. The system is not calculable, but given the money the modellers try anyway.

RoHa
Reply to  Lancifer
January 23, 2015 11:08 pm

Ice ages happen when the frost giants get too powerful. If Thor does not slap them down in time, they can cause real trouble. Of course, if Loki decides to lead them, we will face Fimbulvinter, and then Ragnarök.
We really will be doomed.

Stephen Richards
January 23, 2015 1:23 am

I have to say that I have never been sold on the MCs. It doesn’t make sense. Also, I remember reading that the ice age cycle changed from 40.000 to 100.000 a million or two years ago. How coud that happen if the ice ages were down to MCs.
However, this is good work WE. Thanks.

mpainter
Reply to  Stephen Richards
January 23, 2015 4:10 am

Nor was I, as I have commented on previous posts. Willis shows well enough that claims concerning the M-cycle do not hold up under close inspection. It is just more of that cosmic arm-waving that some people love to do in regards to climate.

January 23, 2015 1:25 am

I got a better answer, using a composite signal given by all members astronomical, place an article of Solar Activity in which I explain the whole thing.
is in Italian but the graphics and all.
greetings Luigi
http://www.attivitasolare.com/la-fine-del-mondo-lavori-corso/

Drake
Reply to  ferdberple
January 23, 2015 8:51 am

Nicely done! I am surprised that no one has commented on your paper. The simple mindedness of the AGW crowd and their inability/refusal to incorporate ALL known variations of FORCINGS is ridiculous. The acceptance of their limited climate models by the consensus is mind boggling. To them, purely from a political/ideological perspective, current temperature changes are all due to changes in carbon-dioxide levels. The reality of earth climate is incredibly complicated.
Someday governments may fund truly comprehensive research to create a “Unified Theory” of climate forcings that can explain the actual historical record and predict future conditions. That would be of benefit to mankind. The current funding of the climate science community is a complete waste.

Luis Anastasía
Reply to  Luigi Lucato
January 23, 2015 4:40 pm

Stimato Luigi:
Molto apprezza il vostro articolo. Molto interessante.
Saluti da Uruguay

Reply to  Luigi Lucato
January 23, 2015 4:54 pm

Great work Luigi, excellently visible. I just got an idea from looking to your graphs. Periods of cooling earth were represented with increasing dust content. I have read that around 30% of dust collection in household is of extraterrestrial origin. What if dust is not result but reason? Simply space dust obscuring sun and decreasing insolation. This could be nicely tied to orbital mechanics where apsidal precession together with orbit inclination can put outer planets to more dense region of space. And send stream of dust towards center of solar system. This would also nicely explain 4000 years shift between insolation and its effect on Earth. 4000y should represent actual time for dust to reach Earth. Actually period of apsidal precession for Mars is 79606 years, which rings a bell with 41k glacial period and period for Jupiter is 197862 years which rings a bell with 100k year period. Jupiter and Mars are shepherding main asteroid belt what could cause regular dust mass sending towards inner solar system affecting Earth. Such dust can be trapped in Earth L1 obscuring solar flow to Earth mainly during perihelion.

Ian W
Reply to  Peter
January 24, 2015 5:18 am

Nir Shaviv has a paper on this very subject:
Is the Solar System’s Galactic Motion Imprinted in the Phanerozoic Climate?
A new δ18O Phanerozoic database, based on 24,000 low-Mg calcitic fossil shells, yields a prominent 32 Ma oscillation with a secondary 175 Ma frequency modulation. The periodicities and phases of these oscillations are consistent with parameters postulated for the vertical motion of the solar system across the galactic plane, modulated by the radial epicyclic motion. We propose therefore that the galactic motion left an imprint on the terrestrial climate record. Based on its vertical motion, the effective average galactic density encountered by the solar system is . This suggests the presence of a disk dark matter component.

January 23, 2015 1:29 am

current hypothesis is that we should see a swing of ~3°C for each additional 3.7W/m2.
I don;t think this is correct. A 1% swing gives 0.5C swing in temperature.

Evan Jones
Editor
Reply to  Willis Eschenbach
January 23, 2015 3:32 am

Not sure I understand this, Doc. A 1% variation would be ~17 wpm^2, right?

rooter
Reply to  Willis Eschenbach
January 23, 2015 3:51 am

3.7w/m2 is the global change globally at TOA. That is not the same as change of insolation on the surface.

RACookPE1978
Editor
Reply to  Willis Eschenbach
January 23, 2015 4:12 am

rooter
3.7w/m2 is the global change globally at TOA. That is not the same as change of insolation on the surface.

??? Is a watt somehow different now? The entire CAGW religion is based on a calculated average net on a mythical flat earth forcing due to increased CO2 absorption and re-radiation for a 3.7 watts increase at the surface based on a assumed LW and short wave IR radiation balance.

Alan McIntire
Reply to  Willis Eschenbach
January 23, 2015 5:27 am

in reply to evanjones
see
http://www-paoc.mit.edu/labweb/notes/Lecture_4.pdf or
http://jennifermarohasy.com/2009/03/radical-new-hypothesis-on-the-effect-of-greenhouse-gases/
and plug in a few numbers to get numerical values. A blocking of 3.7 watts will result in a surface increase of 3.7 watts.

kim
Reply to  Willis Eschenbach
January 23, 2015 8:04 am

3.7 Watts/meter squared on the Petri Dish; on the Earth’s surface, Gaia only knows.
===========

Mike M.
Reply to  Willis Eschenbach
January 23, 2015 11:59 am

Willis wrote: “the IPCC says that for each additional 3.7 W/m2 of forcing the temperature should increase by 3°C”.
I think that should be 14.8 W/m2 to be in the same units as Figures 1 and 3. The 3.7 value is per square meter of the Earth’s total surface area. But it says in the readme file associated with the data http://www1.ncdc.noaa.gov/pub/data/paleo/climate_forcing/orbital_variations/berger_insolation/readme_insolation.txt
that the solar constant is 1360 W/m2, which is per square meter perpendicular to the beam. With the first units the area of the earth is pi*R^2, with the second it is 4*pi*R^2.

Reply to  Willis Eschenbach
January 23, 2015 7:45 pm

Just simply estimating from the table at http://climatewiki.org/wiki/Category:Essential_Physics#Stefan-Boltzmann_law of power versus temperature between our mean orbital gray body temperature of about 279K corresponding to about 343 W%m^2 adding about 100 W%m^2 gets us up to about 297K , a difference of about 18K , not 80 . Changes in our spectrum due to additional CO2 are going to be inconsequential compared to that .

RWturner
Reply to  Leif Svalgaard
January 23, 2015 9:16 am

Dr. Svalgaard, you once linked a paper that concluded that Earth may be in the midst of a natural super-interglacial because of low eccentricity. I can’t find it now. You still remember the title to that paper?

January 23, 2015 1:43 am

Willis writes “I gotta say I’m just not seeing it.”
Its the typical “we got nuthin else” explanation that science uses…and then over time the shaky theory (based on comparisons to the actual data as you’ve done) takes on life of its own and becomes embedded in the psyche.
Pretty much everyone thinks that milankovich cycles are responsible for ice ages and there’s little room for scepticism because well see point one…”we got nothin else”

Evan Jones
Editor
Reply to  TimTheToolMan
January 23, 2015 3:35 am

Note that the big upward and downward swings have a lot of minor jig-jags that “appear to” coincide roughly with Precession.

Jeff Alberts
Reply to  TimTheToolMan
January 23, 2015 12:03 pm

“Its the typical “we got nuthin else” explanation that science uses”
Exactly, like the “global temperature” nonsense.

January 23, 2015 1:52 am

I recommend this series of posts at SoD:
http://scienceofdoom.com/roadmap/ghosts-of-climates-past/

MikeB
Reply to  Willis Eschenbach
January 23, 2015 2:52 am

I like Science of Doom also. He summarises the effect of Milankovitch cycles as below :-

In previous articles we have discussed the Milankovitch hypothesis – classically paraphrased as:
Solar insolation at 65ºN in summer determines the start and end of ice ages – with minimum summer insolation preventing snow melt at high latitudes which allows perennial snow cover, positive feedback from reflected solar radiation and the consequent growth of ice sheets.
Conversely maximum solar insolation at high latitudes causes ice sheets to melt and (with the same positive feedback effect) ends the ice age.

http://scienceofdoom.com/2014/01/07/ghosts-of-climates-past-pop-quiz-end-of-an-ice-age/

JJM Gommers
January 23, 2015 1:54 am

One interesting result is that the natural variabillity is substantial, appr. 12 oK at 90o, 6 oK appr. global and my assumption in the tropics no more than 1 oK. How do we know where we are now? Are we in longterm downtrend naturally?

Hoser
Reply to  JJM Gommers
January 23, 2015 4:07 am

Oh that was painful. First of all, Kelvins are a unit. There are no degree symbols used, just K. If you want to write a degree symbol as in °C or °F, on Windows use alt-248. OK?

Twobob
Reply to  Hoser
January 23, 2015 4:35 am

Err! Stubid eer, What is alt-248.please?

CodeTech
Reply to  Hoser
January 23, 2015 6:49 am

Hold down the Alt key, type 248 (or Alt 0176) on the numeric keypad, and you get the degree symbol. Unfortunately many of us using laptops from time to time don’t have a numeric keypad. The generally accepted way is ampersand deg semicolon, or ° to get °

Don K
January 23, 2015 1:55 am

a swing of 100 W/m2 which is maintained for a thousand years should result in a temperature swing of about 80°C (146°C) …

Maybe (146°F?)
Other than that. I share your doubts. Maybe Milankovitch cycles plus something else? What else? I have no idea.
Subjective observation: I live near 45N — well within the glaciated zone during the last ice age. But by March 21st when the midday sun is 45 degrees above the horizon, snow and ice melt pretty quickly. It’s only around December 21st when the maximum sun is down around 22 degrees that ice and snow hang around for long periods of time. So what sort of climate could allow ice to accumulate here and not melt in Summer? Cloudy, wet and quite cold, I imagine. But it’s hard to envision.

John A
January 23, 2015 2:04 am

Willis
As Socrates would say: “Examine your assumptions”
On that scale of time, Antarctica has not remained fixed and has not been a separate continent for most of that time.
When the Drake Passage opened some 21 million years ago, the circumpolar current thermally isolated Antarctica until it froze over with the huge ice cap we see today.

Hugh
Reply to  John A
January 23, 2015 6:23 am

Willis talks about the last 800 000 years, not 80 000 000 years.

steveta_uk
Reply to  John A
January 23, 2015 7:48 am

John A – I think you’re missing the timescales involved by an order of magnitude.

Paul Mackey
January 23, 2015 2:15 am

What is the thermal time constant of the earth? What sort of order of magnitude is it?

scot
January 23, 2015 2:18 am

The thing I notice is that higher temperatures seem to weakly correlate with the largest swings while the coldest temperatures seem to correlate with periods that have smaller swings.
Perhaps there’s a threshold of insolation that must be crossed to begin the process of ice sheet recession.
The periods of smaller swings also correspond to periods of lower eccentricity. Again, if there’s some threshold that must be crossed to push back the ice sheets, then orbits with the greatest eccentricity have perihelions most likely to provide an insolation great enough to cross some threshold.
There’s one more thing that’s bothered me a bit concerning insolation calculations involving eccentricity. Perhaps it doesn’t matter much, but most calculations assume a simple square relation between distance and insolation and treat the earth simply as a disk. This isn’t quite right, though.
The sun being so much larger than the earth and the earth being a sphere actually provides the earth with slightly more energy as the earth comes nearer the sun than would be expected by applying the square law.
This can be observed by imagining the earth very near the surface of the sun and observing that more than half the earth’s surface receives the sun’s rays.
Whether this makes much of a difference I can’t say. It probably doesn’t. Still I’d like to see things worked out in more detail.

Reply to  scot
January 23, 2015 4:40 am

Of course the inverse square law is for a point source. For a line source it is inverse linear and for a large area source it is no change with distance. To the extent that the sun is a little area source, the law is less than inverse square but more than inverse linear.

george e. smith
Reply to  jim karlock
January 24, 2015 4:33 pm

Well not so fast; a finite sized isotropic source produces an irradiance that differs by about half of one percent, from a point source at a distance that is ten times the diameter of the finite source, and beyond that the difference from 1 /r^2 is negligible.
For a Lambertian disk source, the same result occurs, but the irradiance on a plane surface falls as cos^4 of the off axis angle.
So the sun produces a 1/r^2 irradiance the same as a point source within a half percent beyond 8.64 million miles.
So at our distance the error in irradiance would be unmeasurable.

scot
Reply to  scot
January 23, 2015 6:10 am

At present there is about 6.8% more incoming solar radiation at perihelion than aphelion.
When Earth’s orbit is most elliptical, the difference is 23%!

Curt
January 23, 2015 2:19 am

A couple of quick points, as I’m on the road. The total insolation averaged over a year changes virtually not at all. When summer is stronger, winter is weaker.
About a decade ago, Roe of UW got much better correlations by matching the rate of change in climatic indicators to summer insolation.

William Astley
January 23, 2015 2:21 am

The glacial/interglacial cycle is not caused by insolation changes at 65N. There are at least a dozen different observations and logical pillars to support that assertion. (Typically one or two paradoxes would kill a theory, a dozen is sufficient to not only kill the incorrect theory but to solve the problem, there is only one mechanism that can explain all of the anomalies and paradoxes.) The following are a couple of the paradoxes: Insolation at 65N is currently the same as the coldest part of the last glacial period (paradox we are still in the interglacial phase), the Southern hemisphere also cools when the Northern Hemisphere cools which does not make sense if insolation was the forcing function as the Southern hemisphere summer insolation is maximum when the Northern hemisphere is summer insolation is minimum and vice versa, actual cooling and warming is abrupt (start and end of the interglacial periods is abrupt, the true forcing agent is capable of causing Younger Dryas type abrupt climate change both poles), and finally abrupt climate change events occur prior or after the maximum/minimum of insolation at 65N, and so on.
I will provide a couple of comments to provide a Coles notes summary of the mechanisms, as it appears the start of Dansgaard-Oeschger cooling is imminent. The Dansgaard-Oechger cycle is at 1500 years with beats of 400 years. The Dansgaard-Oeschger cycle occurs at high latitude regions at both poles. There has the recent firing of a senior Nature editor for attempting to publish unequivocal ice core evidence (from the Antarctic peninsula which is outside of the polar vortex and hence reflects south sea temperature rather than Antarctic ice sheet temperature.) that shows there has been 250 warming and cooling cycles in the last 250,000 year in the Southern hemisphere. The Antarctic peninsula ice core data is very important as it means the Northern and Southern hemisphere repeatedly warm and cool, exactly in fact as we have just observed. Note Antarctic sea ice is suddenly the highest in recorded history which supports the assertion the cooling has started.
http://wattsupwiththat.com/2012/09/05/is-the-current-global-warming-a-natural-cycle/

“Does the current global warming signal reflect a natural cycle”
…We found 342 natural warming events (NWEs) corresponding to this definition, distributed over the past 250,000 years …. …. The 342 NWEs contained in the Vostok ice core record are divided into low-rate warming events (LRWEs; < 0.74oC/century) and high rate warming events (HRWEs; ≥ 0.74oC /century) (Figure). … ….The current global warming signal is therefore the slowest and among the smallest in comparison with all HRWEs in the Vostok record, although the current warming signal could in the coming decades yet reach the level of past HRWEs for some parameters. The figure shows the most recent 16 HRWEs in the Vostok ice core data during the Holocene, interspersed with a number of LRWEs. …. ….We were delighted to see the paper published in Nature magazine online (August 22, 2012 issue) reporting past climate warming events in the Antarctic similar in amplitude and warming rate to the present global warming signal. The paper, entitled "Recent Antarctic Peninsula warming relative to Holocene climate and ice – shelf history" and authored by Robert Mulvaney and colleagues of the British Antarctic Survey ( Nature, 2012,doi:10.1038/nature11391), reports two recent natural warming cycles, one around 1500 AD and another around 400 AD, measured from isotope (deuterium) concentrations in ice cores bored adjacent to recent breaks in the ice shelf in northeast Antarctica. ….

The correct primary forcing mechanism explains all of the observations such as the polar see-saw and the abrupt commencement and termination of interglacial cycle.
Comment: The polar see-saw is incorrectly named. The phenomena is the Antarctic ice sheet cools slightly when the Greenland ice sheet warms during a Dansgaard-Oeschger cycle and vice versa. It is only the two ice sheets that are affected, not the entire pole. High latitude southern regions warm when high latitude northern latitudes warm during the Dansgaard-Oeschger cycle which is exactly what we have just observed in the last 150 years.
See Svensmark’s paper for description and explanation of the polar see-saw.
http://arxiv.org/abs/physics/0612145v1

The Antarctic climate anomaly and galactic cosmic rays
Borehole temperatures in the ice sheets spanning the past 6000 years show Antarctica repeatedly warming when Greenland cooled, and vice versa (Fig. 1) [13, 14]. North-south oscillations of greater amplitude associated with Dansgaard-Oeschger events are evident in oxygenisotope data from the Wurm-Wisconsin glaciation[15]. The phenomenon has been called the polar see-saw[15, 16], but that implies a north-south symmetry that is absent. Greenland is better coupled to global temperatures than Antarctica is, and the fulcrum of the temperature swings is near the Antarctic Circle. A more apt term for the effect is the Antarctic climate anomaly.
Attempts to account for it have included the hypothesis of a south-flowing warm ocean current crossing the Equator[17] with a built-in time lag supposedly intended to match paleoclimatic data. That there is no significant delay in the Antarctic climate anomaly is already apparent at the high-frequency end of Fig. (1). While mechanisms involving ocean currents might help to intensify or reverse the effects of climate changes, they are too slow to explain the almost instantaneous operation of the Antarctic climate anomaly.

AnonyMoose
January 23, 2015 2:29 am

I also looked at the explanations for ice ages and Milankovitch cycles doesn’t make sense to me either. The main reason for their being accepted seems to be that something “known” has to be assigned as the reason because climate alarmists don’t want to admit that they don’t know. It is important to climate alarmists that the present climate be presented as being stable (before human interference), so solar and other influences have to be stable and carbon dioxide is the only thing which is changing.

Kasuha
January 23, 2015 2:30 am

Judging just from the graph and with no ambitions to resolve the problem, each of glacial->interglacial swings closely follows ascending edge of one of 21k swings. Most importantly, not starting when the swing is at the maximum but while it is still at low levels (i.e. the insolation is still low but Earth is already recovering). All of them except the one that starts 400k years ago where the recovery took two periods.
That suggests the Milanchovitch swing is just some kind of kickoff impulse or “primary pulling force” but the Earth is already prepared for the change and there is some kind of positive feedback potential collected over the past that’s needed for that.
Why? I doubt there’s lack of hypotheses, rather lack of ways to verify them. Just one of many – during ice ages, water vapor levels in atmosphere are very low and precipitation is small. Dust may keep collecting in upper levels of snow cover until it becomes dark enough that increased insolation pulls the Earth out of ice age in just one swing.

rogue
January 23, 2015 2:42 am

It might be worth taking a look at a paper by Gerard Roe that looks at the correlation between the rate of change of ice volume and high latitude insolation.
http://onlinelibrary.wiley.com/doi/10.1029/2006GL027817/abstract

TRM
Reply to  rogue
January 23, 2015 10:30 am

You beat me to it. They are up front about the limitations and have no idea how the deglaciations occur but their conclusion is pretty straight forward:
” focusing on the rate of change of ice volume, as opposed to the ice volume itself. The available evidence supports the essence of the original idea of Köppen, Wegner, and Milankovitch as expressed in their classic papers [Milankovitch, 1941; Köppen and Wegener , 1924], and its consequence: 1) the strong expectation on physical grounds that summertime insolation is the key player in the mass balance of great Northern Hemisphere continental ice sheets of the ice ages; and 2) the rate of change of global ice
volume is in antiphase with variations in summertime insolation in the northern high latitudes that, in turn, are due to the changing orbit of the Earth”

Reply to  rogue
January 23, 2015 4:19 pm

Beat me to it as well! Willis, Dick Lindzen pointed me towards this paper some five years ago ;-). The reference is the paper Roe published in 2006 (he was a former student of Lindzen’s), highlighting a compelling relationship between the _rate_ of ice accumulation versus insulation changes at 60 N. Partly based on my writings, Lubos Motl then did a nice piece on the subject here: http://motls.blogspot.com/2010/07/in-defense-of-milankovitch-by-gerard.html

January 23, 2015 2:51 am

I believe the effect is a bit more complex, because the two hemispheres are connected. This means the Sourhern hemisphere experiences its own changes in exposure to sunlight. This gets even more complicated because Antarctica is covered with ice, it is surrounded by sea ice formed in winter, and the Southern Hemisphere has more ocean surface, which has changing albedo as clouds are formed.
I’m also starting to suspect there’s interaction between the elevation of the Labrador and Scandinavia regions and the amount of snow they get. Evidently as the ice forms it depresses the continents, which in turn lowers the elevation. This puts the glaciers at a disadvantage once the melting starts. But once the glaciers melt the continent rebounds, gains elevation, and this allows easier formation of the next glacier which kicks off the ice age.
This can get so complicated I can’t visualize the scientific community ever having it all pinned down.

CAL
January 23, 2015 2:55 am

Some years ago there was a chart in WUWT showing temperature changes over 4 million years. From memory this was from sea sediments but I may be wrong. This plot showed that at that time the dominant cycle was 41K and was correlated with the MC. This clear signal became fuzzy at the same time as the Isthmus of Panama closed preventing the warm Pacific waters flowing into the Atlantic. From about 1million years ago the cycle switched to the 100k periodicity we see now.
My take on this is that the 100K cycle is a resonant frequency characteristic of the earth’s climate system. This is analogous to a musical instrument where the vibration is triggered by an external force ( the bow of the blow ) but the sound is amplified by the resonance.
For this to happen there has to be an energy store and in the case of the global system this has to be the sea since it is the only one large enough to store sufficient energy to eventually melt the ice which forms during the ice age itself. It is easy to postulate mechanisms ( like albedo change ) for amplifying the cooling period but we know that many of the ice ages ended abruptly with huge swings in temperature occurring over decades rather than millennia. It is this chaotic period that needs explanation.
My view is heretical
I believe that the earth warms during the ice age!!
By this I mean that the radiation balance is positive during the period where the ice covers the North Atlantic. This is because the warm water that flows north during normal times and radiates strongly into space is trapped under the ice which radiates very weakly. At the same time the cloud cover in the tropics would have been low due to the proximity of the ice front reducing relative humidity. Thus there would have been a strong sun at the surface but the overall surface radiation back into space would have been low. A strongly positive radiation balance!
In this way the temperature of water under the ice would have increased and indeed there has been research showing warm water in the Baltic indeed increased under the ice during the last ice age.
http://onlinelibrary.wiley.com/doi/10.1029/2008GL036563/abstract;jsessionid=C78C1C0C4B107A2FC698A51F23CC90CB.f01t03
At the same time the warm water would have been melting the sea ice from below. this would have produced huge ice shelves too thin to survive. At some point these would have calved into the warm seas creating huge ice bergs. This sudden exposure to the warm sea would have led to sudden increases in temperature followed by increased radiation to space and sudden drops in temperature. Hence the oscillatory nature of the end of the ice age.
If this scenario is any thing like correct it has great implications for the narrative relating to the evolution of man. The reason is that what I have been describing at sea is not mirrored by what was happening on land. During the onset of the ice age the sea level would have dropped and the deserts would have grown sqeezing all species into a narrow area around the current Mediterranean. The competition would have been tough and innovation would have been crucial as would the development of the social skills to support cooperation. It should therefore be no surprise that the evolution of man began to accelerate just at the time these dramatic climate swings began to appear. Then the latter period of the ice age would have seen the land south of the arctic basking in sun and fed with rivers of melting ice. A land of milk and honey!
As the ice receded there would have been space and food for all the survivors to proliferate and exploit their new found skills. This cycle of climate pressure and benevolent aftermath is analogous to the rapid innovation and evolutionary development we see in countries and companies during and after wars or other global shocks.
It might therefore follow that the idea that Homo Sapiens suddenly appeared “out of Africa” 80,000 years ago is a mistake. I think it is highly likely that these migrants appeared every 100,000 years and they interbred and with all the other global tribes that were forced to coexist in the declining habitable land space around rivers – sharing their cultures and their expertise. The groups that eventually dispersed as the climate became more temperate would thus have become more homogenous thus explaining the lack of really large genetic variation within the human species.

Reply to  CAL
January 24, 2015 6:50 am

Homo sapiens definitely emigrated out of Africa long ago, such as Neanderthal in Europe and many sub-species of homo erectus in Asia. But homo sapiens sapiens, modern man, did not develop until about 60-80k in Africa, and it is this sub-species that moved out into Europe and Asia shortly thereafter, and eventually colonized the whole globe. There was some interbreeding with Neanderthals and Devonians, but over time all rival sub-species were wiped out.
No one know for sure why this happens, but some sort of mutations appeared in the African population that proved immensely advantageous. Probably a combination of some sort of intelligence multiplier, since this is the first time that rapid advances were made in tools, culture, and especially, burial rituals, indicating the beginnings of religion and belief in an afterlife. Another factor was likely the development of a more advanced voice-box capable of complex speech – not evident in other human sub-species.
Climate probably played a huge role in this. The eruption of Tambora created terrible climate effects around the globe, leading to our human ancestors in Africa being reduced to less than 2,000 total population, and possibly as low as a few hundred. That probably severely weakened other human sub-species elsewhere as well. These severe environmental stresses likely contributed to rapid mutation as a survival mechanism, producing modern man as a result.

David Hall
January 23, 2015 3:12 am

I have to say more convincing is the theory of Svensmark, supported by the late Nigel Calder which claims that cloud nuclei from cosmic rays generated by nearby supernovae account for cooling and lack thereof promotes warming.
https://calderup.wordpress.com/2012/04/24/a-stellar-revision-of-the-story-of-life/
Here are the main results:
The long-term diversity of life in the sea depends on the sea-level set by plate tectonics and the local supernova rate set by the astrophysics, and on virtually nothing else.
The long-term primary productivity of life in the sea – the net growth of photosynthetic microbes – depends on the supernova rate, and on virtually nothing else.
Exceptionally close supernovae account for short-lived falls in sea-level during the past 500 million years, long-known to geophysicists but never convincingly explained..
As the geological and astronomical records converge, the match between climate and supernova rates gets better and better, with high rates bringing icy times.

Reply to  David Hall
January 23, 2015 3:32 am

David Hall–Very interesting–will have to read this (I just read Calder’s page on it). Per my note below, more clouds = more precip = feeding mechanism for growth of ice sheets. I’m looking forward to the day when ‘Climate Scientist’ includes (requires) the study of the astro-climate and geology, not just modeling CO2 levels and sea level. Between supernovae, variations in interstellar dust, cyclical comet strikes, and other factors, there is so much we don’t know. Unfortunately, intellectual humility is not something found today in the current AGW crowd or its mouthpieces (Mooney, Borenstein, etc.).

January 23, 2015 3:13 am

Willis–It’s never sat right with me either, and in my mind it’s the greatest puzzle in climate. While there are many papers examining the insolation-temperature relationship (a la Milankovitch/other cycles), I have yet to see anything that clearly and logically explains the localized precipitation-to-ice accumulation mechanisms that fed the Laurentide ice sheet and show likely rates of ice accumulation. It would be interesting if the science eventually ‘stood on its head’ and revisited some ‘sibling’ model of the Ewing Donn theory–a warm, open Arctic ocean feeding a growing ice mass on/around Baffin, along the lines of the growth of subtropical glaciers like those in NZ. It’s amazing to think about snow falling on Baffin and feeding a conveyor belt of ice eventually sculpted the hills of southeastern Wisconsin. Must it necessarily have been cold EVERYWHERE, or could it, like at the base of NZ’s glaciers, have been warmer than currently supposed? Cheers~
PS–Love your writing!

tty
January 23, 2015 3:20 am

Actually there is very little doubt that up to about 1 million years ago climate (including relatively small amplitude ice-ages) was very closely tied to the 41,000 years Milankovich obliquity cycle. The cycle-length matches perfectly and so do the position of peaks, as far as they can be reasonably well dated. However during the “Mid Pleistocene Shift” climate gradually changed over to approximately 100,000 years long glacial cycles with a very much larger amplitude. The previously largely sinusoidal cycles also became much more complicated with usually several smaller sub-peaks (“stadials” and “interstadials”). So far we have been through eight full “100 KA”‘ cycles, and they have all been somewhat different, both in length, amplitude and number and timing of sub-peaks.
As for what caused the change from the “41,000 year World” to the “100,000 year World” it is, as they say, “not well understood” . There are a number of different hypotheses but none of them is very convincing.
There is an approximately 100,000 year eccentricity Milankovich cycle, but it only has slight effect on insolation. There is evidence from older geological periods that the longer 404,000 year eccentricity cycle has climatic effects, but very little evidence for any 100 KA cyclicity.

Evan Jones
Editor
Reply to  tty
January 23, 2015 3:39 am

The theory is that with more regular orbits, the winters are warmer, but the summers are cooler and the ice never gets a good chance to melt. That leads to a positive feedback (both coming and going) from albedo.

Reply to  Evan Jones
January 23, 2015 3:51 am

And the orbital regulatity cycle (ie. circular vs ellipticL) is the 100k year cycle ??

tty
Reply to  Evan Jones
January 23, 2015 5:23 am

The problem is that the effect is minute. If this very slight change drives ice-ages, why don’t others much larger changes (e. g. the 41 KA obliquity cycle) do too?

Rob
January 23, 2015 3:21 am

I`ve never been convinced that we know the cause of the Ice Ages. Nice work.

aGrimm
January 23, 2015 3:21 am

Clearly the solar insolation and temperature anomaly are cyclic. By definition, solar insolation is the deposition of energy, but it does not indicate how that energy is distributed. Energy is gained and lost in almost innumerable ways in our Earth’s system. It can also be stored in all sorts of ways, being released slowly or quickly depending on circumstances. The temperature anomaly gives an indication of energy being lost or gained, but not the mechanisms for how it happens. In order to connect the dots between the two graphs, if there is a connection, we need to determine all the mechanisms by which our system distributes gains and losses, and stored/released energy from the sun. So many questions still be answered and there are just way too many angles at this time for us to connect the dots.
Here is an example of another angle. How much does tectonics play a role? From the Utah Geological Survey http://geology.utah.gov/surveynotes/gladasked/gladice_ages.htm
“Do ice ages come and go slowly or rapidly? Records show that ice ages typically develop slowly, whereas they end more abruptly. Glacials and interglacials within an ice age display this same trend.
On a shorter time scale, global temperatures fluctuate often and rapidly. Various records reveal numerous large, widespread, abrupt climate changes over the past 100,000 years. One of the more recent intriguing findings is the remarkable speed of these changes. Within the incredibly short time span (by geologic standards) of only a few decades or even a few years, global temperatures have fluctuated by as much as 15°F (8°C) or more.
For example, as Earth was emerging out of the last glacial cycle, the warming trend was interrupted 12,800 years ago when temperatures dropped dramatically in only several decades. A mere 1,300 years later, temperatures locally spiked as much as 20°F (11°C) within just several years. Sudden changes like this occurred at least 24 times during the past 100,000 years. In a relative sense, we are in a time of unusually stable temperatures today—how long will it last?”
The graph shown with this article correlates well with the temperature anomaly graph that Willis has shown and adds notations for the glacial/interglacial periods which helped me visualize what is going on a little better. I doubt that tectonics somehow contributes to the cyclic nature of the temperature anomalies. However, I would bet tectonics plays a role in how fast or slow a change can occur – and tectonics is just one variable.
On a humorous note: do you suppose if the insolation graph was put into a sound synthesizer that it would be the song “Sunshine On My Shoulders”? It does appear to have a beat.

Evan Jones
Editor
Reply to  aGrimm
January 23, 2015 3:42 am

Records show that ice ages typically develop slowly, whereas they end more abruptly.
That could be the knock-on effect of CO2 variation (~100 ppm). Faster onset of interglacials and slower descent into ice ages.

Evan Jones
Editor
January 23, 2015 3:25 am

I also didn’t realize that there is an underlying ~400,000 year cycle, which leads to the larger peaks at about 200,000 and 600,000 years before present (BP), and also leads to the very, very small peak at about 400,000 years BP.
Oh, yeah, the Milliecycles themselves are irregular, especially Eccentricity. There’s also a (proposed) “fourth cycle”, Inclination, involving a ~100k variation in the orbital plane, taking the earth through greater or lesser “space dust” conditions.
Note that the 20k variations roughly coincide with Precession, the “lesser” of the three cycles, the theory being that if the NH is tilted toward the sun during aphelion, there will be less warmth absorbed because there is less land surface in the NH.

Reply to  Evan Jones
January 23, 2015 8:16 am

“…because there is less land surface in the NH.” ??

mpainter
Reply to  opluso
January 24, 2015 8:22 am

Ditto

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