Guest Post by Willis Eschenbach
There’s been a recent paper claiming a long-term correlation between CO2 and sea level, discussed here at WUWT. The paper implies that CO2 controls temperature and thus indirectly sea level. I thought I might follow up the comments on that thread by looking at what the ice core records actually tell us about variations in CO2. There is plenty of dispute about the ice core records, but I don’t want to touch on that here, that’s a separate discussion. Instead, let me take the ice core records as given and see where that leads us. Figure 1 shows the Vostok ice core CO2 and temperature variations.
Figure 1. Temperature and CO2 variations as per the cited data sources. Temperature variations have been divided by 2, as discussed in the text. Graph ends at 1950, most recent CO2 data is from about 2,300 years ago. Maximum temperature during the previous interglacial was about a degree and a half warmer than 1950. Photograph shows that Photo Source http://dxing.at-communication.com/en/ri1anc_vostok-base_antarctica/
These two data traces, unfortunately, are from two different records. The temperature record contains almost ten times the number of data points as the CO2 record (~ 3,100 vs ~360). Accordingly, I have smoothed the temperature data (17-point Gaussian) and then interpolated it to match the dates of the CO2 data points.
In addition, the temperature record is (presumably) a proxy for the temperature of Southern Ocean and environs. This, like all areas near the Poles, tends to experience larger temperature swings than the world as a whole. As a result, I’ve followed the common practice of making a rough estimate of global average temperature changes by dividing the Vostok changes in half.
So what can we learn from these graphs? Well, first off, we can see that this is the coldest interglacial we’ve enjoyed in the last hundreds of thousands of years. I note that humans, and indeed the majority of all species, survived the previous warmer interglacials without thermal meltdown. Next, we can tell from this data whether CO2 is causing the temperature variations, or vice versa.
Let me introduce and discuss five pieces of evidence that all show that the likely direction of the causation is that the temperature is causing the CO2 change, and not the other way around. These are 1) the linearity of the relationship, 2) the agreement with known physics, 3) the lag in the CO2 with respect to temperature, 4) the Granger causality of the relationship, and 5) the disagreement with the IPCC values for climate sensitivity.
The weakest piece of evidence is the linearity of the relationship. The outgassing of the ocean is a linear function of temperature. Looked at the other way, the temperature of the world is said to relate, not linearly to CO2, but to the logarithm of CO2 to the base 2. In the data above, the R^2 (a measure of correlation) between the temperature and the CO2 is 0.68 … but the R^2 between the temperature and the logarithm of CO2, rather than being better as we’d expect if CO2 were actually driving temperature, is marginally worse for the logarithmic relationship (0.67) than the linear. Weak evidence, as noted, but you’d expect the correlation with log CO2 to be better than linear, if not a lot better, if the relationship were actually logarithmic.
Second, the agreement with known physics. Given the data above, I calculate that for every 1°C of temperature increase, CO2 goes up by about 15 ppmv. According to this source, for every 1°C of temperature increase, CO2 goes up by about 12.5 ppmv … so the number I calculate from the data is in rough agreement with known physics.
Third, the lag. Direct correlation of the two datasets is 0.83 (with 1.0 indicating total agreement). The correlation between the two datasets is better (0.86) with a one-point lag, with the change in CO2 lagging the change in temperature. That is to say, first the temperature changes, and then the CO2 changes at some later date. Additionally, correlation is worse (0.79) with the opposite lag (CO2 leading temperature). Again, this is in general agreement with other findings that the changes in CO2 lag the changes in temperature.
Fourth, the Granger causality. You can’t establish a cause statistically, but you can say whether something “Granger-causes” something else. A Granger test establishes whether you have a better chance of predicting variable A if you know variable B. If you do, if knowing B gives you a better handle on A (beyond random chance), we say that B “Granger-causes” A.
Now, there’s an oddity about Granger causation. There are four possibilities for Granger causation with two variables, viz:
1) Variable A doesn’t Granger-cause variable B, and B doesn’t Granger-cause A
2) Variable A Granger-causes variable B, and B doesn’t Granger-cause A
3) Variable A doesn’t Granger-cause variable B, and B Granger-causes A
4) Variable A Granger-causes variable B, and B also Granger-causes A
It is this last one that is an oddity … for example, this last one is true about the CO2 variation versus temperature on a monthly basis. This makes sense, because of the seasonally varying drawdown of CO2 by plant life and the seasonal temperature variations. CO2 levels affect plant life, and plant life also affects CO2 levels, and all of that is in a complex dance with the seasonal temperature changes. So the dual causality is not surprising.
In the current example, however, the results of the Granger test in the case of the Vostok data is that temperature variations Granger-cause changes in CO2, but not the other way around—CO2 doesn’t Granger-cause the temperature.
Finally, the disagreement with the IPCC values for “climate sensitivity”. If we use the data above, and we assume that the temperature actually is a function of the CO2 level, we can calculate the climate sensitivity. This is a notional value for the change in temperature due to a doubling of CO2. When we calculate this from the Vostok data given above, we find that to work, the climate sensitivity would have to be 23°C 7°C per doubling of CO2 (corrected, thanks to commenters) … and not even the most rabid alarmist would believe that.
So those are my five reasons. The correspondence with log(CO2) is slightly worse than that with CO2. The CO2 change is about what we’d expect from oceanic degassing. CO2 lags temperature in the record. Temperature Granger-causes CO2, not the other way round. And (proof by contradiction) IF the CO2 were controlling temperature the climate sensitivity would be seven degrees per doubling, for which there is no evidence.
Now, the standard response from AGW supporters is that the CO2, when it comes along, is some kind of positive feedback that makes the temperature rise more than it would be otherwise. Is this possible? I would say sure, it’s possible … but that we have no evidence that that is the case. In fact, the changes in CO2 at the end of the last ice age argue that there is no such feedback. You can see in Figure 1 that the temperatures rise and then stabilize, while the CO2 keeps on rising. The same is shown in more detail in the Greenland ice core data, where it is clear that the temperature fell slightly while the CO2 continued to rise.
As I said, this does not negate the possibility that CO2 played a small part. Further inquiry into that angle is not encouraging, however. If we assume that the CO2 is giving 3° per doubling of warming per the IPCC hypothesis, then the problem is that raises the rate of thermal outgassing up to 17 ppmv per degree of warming instead of 15 ppmv. This is in the wrong direction, given that the cited value in the literature is lower at 12.5 ppmv
Finally, this is all somewhat sensitive to the assumption that I made early on, which is that the global temperature variation is about half of the variation shown in the Vostok data. However, this is only a question of degree. It does not negate any of the five points listed above.
w.
PS—One final thought. IF we assume that the change in CO2 is due to the temperature change, as my five arguments support, this would indicate that the degassing from temperature changes is far from sufficient to cause the recent rise in CO2. I hold that the recent rise in CO2 is anthropogenic, but others have claimed that it is not from the burning of fossil fuels, that it is (at least in significant part) due to the temperature change.
But my calculations, as well as those in the reference I cited, show that CO2 only goes up by ten or fifteen ppmv for a one-degree temperature rise. As such, this is way too small to explain the rise in atmospheric CO2, which has been on the order of 75 ppmv since 1959.
SOURCES
D Böehm says:
January 4, 2013 at 6:42 am
Richard Telford, wise up. There is no empirical evidence supporting the IPCC’s wild-eyed estimate. They simply picked a scary number and ran with it.
You assert:
“Your Granger causality analysis is erroneous as it assumes that Vostock temperatures are in phase with global temperatures.”
That is wrong. Both Greenland ice cores and Antarctic ice cores show high correlation. In other words, they are in phase.
————————–
You might not like the empirical evidence of climate sensitivity, but it is foolish to say there is none.
Sure d18Oatm is in phase between Greenland and Antarctica. That is not in the least surprising as the 18O has a long life span in the atmosphere and is well mixed. But the Vostock dD record is not in phase with the GISP2 d18O record. Sure they are not in antiphase, I never argued that they were, but as the figure you link to makes clear, Antarctica temperature leads Greenland temperature at the last termination.
Just because the correlation is high, does not mean the records are perfectly in phase.
Thanks, Willis. Excellent post.
This article now has 4 more links for my climatology pages.
@crosspatch
See: http://www.appinsys.com/GLobalWarming/SixtyYearCycle_files/image002.jpg
That shows we had very similar variation in tides then, too. Tides change depth of surface mixing, so cooling from the water. I’m now wondering if that can also change CO2 levels…
The warm and cold cycles of history match rather well with tide forces based on lunar cycles of motion.
http://www.pnas.org/content/97/8/3814/F1.large.jpg
More detail here:
http://chiefio.wordpress.com/2013/01/04/lunar-cycles-more-than-one/
There is also a variation in the Gulf Stream and where it cools / descends that causes it to sporadically ‘back up’ and cause cold ‘far north / EU’ and a warmer Florida. This would mean that differential heat levels would be made even higher. For Florida, that means more rain washing the carbonation into the soil to erode the Karst soils. I wonder if there are any ‘rate of erosion’ data that could show CO2 / acidity changes… Having a much colder polar water with faster rain washing in the tropics sounds to me like a formula for CO2 stripping…
In general, I notice that everyone talks about CO2 dissolving into the ocean surface, but that ignores the rain falling through the air (rather like a counter current stripper). I think gig-tons of snow and cold water falling through the air will tend to remove a lot of CO2 into water puddles, rivers, and into the ocean.
Also, we’re at the top of a warming cycle and the deep ocean is still near max cold. There just isn’t going to be a lot of thermal degassing of the deep layers until they become surface layers. We’re limited by ocean overturn speeds.
That means changes in THCirculation speed of the ocean can change rate of CO2 both in and out.
Rain also is likely why glacials end faster than they form. A warm rain melts snow and glaciers fast. But a cold snow can only deliver its own mass of snow… Mass flow limited ice growth and in times of decreasing precipitation. For glacial loss, increasing precipitation and warmer melting ice.
Maybe we need a mantra… “Don’t forget the precipitation”…
Mosher – I can visualize Mosher standing in the center of his eclectic San Fransisco flat doing a pirouette with his damp finger in the air.
Chiefio
You made the interesting comment above;
“In general, I notice that everyone talks about CO2 dissolving into the ocean surface, but that ignores the rain falling through the air (rather like a counter current stripper). I think gig-tons of snow and cold water falling through the air will tend to remove a lot of CO2 into water puddles, rivers, and into the ocean.”
Surely clouds- or more correctly the water vapour they consist of-must also be full of co2? Has anyone ever specifically measured the co2 content of a cloud as opposed to ‘the general atmosphere’ at ground level such as at Mauna Loa
How many tons of co2 is that directly delivering into the oceans/land each year?
Does that mean that clouds are strongly negative because they remove co2 fromn the atmosphere? (irrrespective of their cooling effect by shielding the sun)
tonyb
Powerful argument. I am new to Granger causality. Is there a fifth outcome in which the Granger test would suggest that both temperature and CO2 respond to an entirely different driver? In comparing the two curves, that seems to be a legitimate third possibility beyond one driving the other.
Being the world biggest dummy,I should not be writing here. When I started to school it was in a two
room school bldg. grades 1-5. When in thr 3rd grade there was a hugh world map hanging at the front.Each day I would stare at it and wonder.One day I said to my self,Africa and S.A. were once
conected.One day I said to the teacher I think Africa and S.A. were at one time conected.Her reply was”you are the worlds biggest dummy.” I learned my lesson, I never asked another question the
whole time I was in school. Many years later waiting in a doctor’s office I picked a mag.and read
the contenants were once conected,I said I always knew that !
Now my question,when guys are looking 1000ky,what does the earth look like in your mind.Is it
like it looks now? Was the ocean larger than now? Was there more “dirt”then? Would any of this
make a difference?
his name “was Pegleg;because in his days the earth was divided” I Chron.1:19
A
E.M.Smith says:
January 4, 2013 at 8:05 am
Having a much colder polar water with faster rain washing in the tropics sounds to me like a formula for CO2 stripping
When water evaporates from the sea surface, CO2 is released too. That increases the CO2 levels near the sea surface (but that is readlily dispersed by convection, as good as the water vapour).
CO2 solubility in fresh water is very limited compared to seawater and mainly occuring at the CO2 pressure where the drops are formed. When these fall down, the CO2 pressure increases with the air pressure, but at the other side, temperature increases, thus decreasing CO2 solubility. And a part of the raindrops may evaporate at the surface, thus again releasing CO2…
Thus in balance, at most there will be some more CO2 near the surface than higher in the atmosphere. Hardly relevant (and hardly measured)…
That means changes in THCirculation speed of the ocean can change rate of CO2 both in and out.
Not important: even if the speed of the THC doubles, that doubles the CO2 releases at the upwelling side and CO2 uptake at the downwelling side. Net result: faster turnover, zero change in CO2 levels of the atmosphere. Only temperature (and human emissions) is important in changing the atmospheric CO2 pressure/levels…
Steven Mosher says:
January 3, 2013 at 9:26 pm
since hansen predicted the lag of versus temperature in 1990, folks might want to watch this
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“Crock of the Week” is an appropriate name for Peter Sinclair’s propaganda efforts. The target audience are persons of average intellect and scientifically illiterate. He offers comfort to the faithful at a time of evolving crisis, far different than that for which they had hoped.
richard telford says:
January 4, 2013 at 6:02 am
You are correct, I used the regular log rather than log to the base 2. However, the answer is still absurd, at 7°/doubling.
Thanks,
w.
Interestingly enough the same lag between temperature and CO2 is readily apparent in modern satellite data. http://www.woodfortrees.org/plot/esrl-co2/isolate:60/mean:12/scale:0.2/plot/hadcrut3vgl/isolate:60/mean:12/from:1958
Richard Telford still argues that there is not correlation between the hemispheres. How many examples does it take to correct his confusion?
Of course, if Telford admits there is a high correlation between the hemispheres, he loses the argument he has been trying to make. Telford’s “perfectly in phase” comment is just a failed attempt to get some wiggle room. The fact is that the hemispheres’ temperatures are in phase, as the three links I posted convincingly demonstrate.
W,
Regarding the sensitivity of CO2 to temperature, you’re comparing apples and oranges. There’s no reason that the sensitivity on time scales of tens of thousands of years (Vostok record) should be the same as the sensitivity on time scales of decades (modern record).
I have not yet seen the source of CO2 proposed if the CO2 really did rise before the ocean temp. Volcanoes? “Dry ice”, i.e. solid CO2, meteors? Massive methane releases from methane hydrate w/ the ocean at it’s lowest temp? Magic? C’mon!!!
The only explanation, based on the evidence, is the oceans started warming for some reason not related to a greenhouse effect then the oceans degassed CO2 at ~9 – 16 ppmv/°C w/ the CO2 conc. lagging temp by 800±200 yrs….but in spite of the lack of any evidence it still could be due to CO2 driving the temperature. (that last part required to keep faculty cocktail invitations and grant monies flowing in)
The steady state level of atmospheric CO2, in geological time, is dependent on the input rate and the efflux rate.
The input rate is the rate at which CO2 is released by vulcanos and mantle vents.
The efflux rate, or true sink rate, is the rate of mineralization or inorganic and organic, biotic, carbon; mostly due aquatic organisms.
If dust levels increase, then sun light is blocked, Earth cools, ice age starts. Dust is full of trace transition metals and fertilizes the oceanic deserts.
Total biotic productivity increases, deposition rate of organic matter to sea floor increases and [CO2] goes down.
Could you provide a CO2 vs Temperature graph, colour-coding the data by time?
The colour-coding will reveal non-CO2 causitive factors at play by showing a circularity in the temp-CO2 data points around some other central trend. If you don’t colour-code the time aspect, you get a spread of data that looks like normal variance or error bars.
I’d do it, but I am computer challenged and don’t have a 12-year-old with me.
See my article on the Central UK Max Temp vs Sunshine Hours for the idea.
Alfred Alexander says:
Who’s Pegleg? (I’ve heard of Peleg 🙂
M@WW says:
Regarding the sensitivity of CO2 to temperature, you’re comparing apples and oranges. There’s no reason that the sensitivity on time scales of tens of thousands of years (Vostok record) should be the same as the sensitivity on time scales of decades (modern record).
I don’t see the sensitivity should change if we’re talking about how much CO2 brine with contain. This is a function of T^5 not of time.
There will be different time constants for different magnitudes of change due to the different depth, hence volumes of water concerned.
You seem to be confusing the two.
M@WW says:
January 4, 2013 at 11:00 am
W,
Regarding the sensitivity of CO2 to temperature, you’re comparing apples and oranges. There’s no reason that the sensitivity on time scales of tens of thousands of years (Vostok record) should be the same as the sensitivity on time scales of decades (modern record).
There’s no particular reason to think it shouldn’t be the same, unless the goal is to hang onto a crumbling ideology. In addition, there is no evidence of a greater sensitivity in the modern record.
Hi Willis, Anthony and mods. You might enjoy this, though not strictly relevant to the thread!
On Positive Feedbacks in Climate
(Hat tip to Augustus de Morgan)
Great heats have lesser heats which grow before to cause ’em,
And little heats have lesser heats, and so ad nause-ausam.
The great heats themselves in turn cause greater heats in future,
And greater heats give “reasons” for politicals to loot yer.
(You can substitute “droughts,” “rains,” or “colds” for “heats” in the above).
Bill Illis is spot on:
‘You cannot estimate CO2 sensitivity in the ice ages or in the paleoclimate without having good Albedo estimates. In fact, you need this for every 500 year tranche of time going back 4.4 billion years in order to answer the question. Maybe there is also a CO2 to Albedo feedback and maybe there is a Albedo to CO2 feedback. We have the CO2 estimates but climate science refuses to put the Albedo numbers on paper in a transparent way. My estimate for the ice ages Albedo is -17 W/m2 based on my Albedo model.
Ice Age forcing = -17 W/m2 Albedo + -2.7 W/m2 GHGs = -19.7W/m2/6.0C = 0.3C/W/m2
Implying 0.3C/W/m2 * 4.2 W/m2 (CO2/GHG doubling) = 1.3C CO2 sensitivity
But this should not be such a big surprise to anyone – believe it or not, you can get the same result from IPCC Working Group documents – they just don’t make it into the Summary for Policy Makers! For example, IPCC have access to the HIGHTRANS suite of computer calculations that give the watts/square metre read out for each part of the log -curve of CO2ppmv….and that gives you roughly the 2 watts for CO2 for the 180-280 deglacial transition. The shortest cut is then to apply a factor (known as Lambda. L) to the equation T= L (watts per sq metre)…and at its outset IPCC argued for 0.8 as the likely factor. Thus, for 2.7 watts, the forced temperature would be 2.16 C. If you take the global shift as 6 degrees, that gives you a 36% amplification…and that is roughly what the ice-core literature of two or more decades assumes. However in IPCC4, Keith Shine argues that Lambda could be as low as 0.4, thus halving the previous estimate. I guess this lower factor might account for the low estimates of the IPCC model runs (who knows?).
Thus, for the CO2 effect, 2 watts per square metre would lead to 0.8 C and therefore about 13% amplification.
My own view is that the initiating mechanism is not small shifts in insolation hitting some kind of trigger related to snow albedo (the land-sea snow-ice area is relatively small compared to potential shifts in cloud amount and spatial distribution ) – rather it is shifts in global winds which likely relate to shifts in the jetstream (linked to…? UV radiation? Magnetic flux? Cloud Electrics?) – these shifts can be observed right now with the latest solar minimum….but the global picture is confusing….with cloud free areas of high pressure leading to record highs and other areas record lows, depending on the season.
The modern CO2 rise is about 100ppmv…and the curve is close to linear once the CO2 level rises above 50ppmv…so this latest 100ppmv should have delivered another 2 watts per square metre, as indeed IPCC calculate it has. Clearly we have not seen 6 degrees, nor is that expected. Their calculations show 0.8C to 0.4 C at equilibrium (assuming they acknowledge Shine’s work). And for the ‘doubling’ they calculate using HIGHTRANS…3.7 watts per square metre….which without alarming feedbacks, wouldl deliver at maximum, 2.96 C, or if Shine is right…then 1.48 (and no alarm!).
The modern record of 0.8 C would have to have no natural (cyclic) component at all if it reflected the effects of CO2, and we know this is not right because there was no expected CO2 effect before 1950, when half the warming had already occurred. So – IPCC are still just about in the ballpark with Shine’s Lambda of 0.4 but only IF all the warming since 1950 is a consequence of the CO2, or there is more warming in the (ocean) pipeline. I doubt this is correct and hence the Lambda is lower still – perhaps lower than Bill’s 0.3 (which would deliver 1.11 C for the doubling in 2050…..and that is where the EVIDENCE is pointing, and evidence that is IN the working group reports, but does not get through the filters to the SUMMARY FOR POLICY MAKERS.
Re: the video posted by Stephen Mosher.
At 9:27 the video references a paper, which says.
‘The radiative forcing due to CO2 may serve as an amplifier of initial orbital forcings’
The narrator then says, ‘Could the authors have made it any clearer.’
Well, yes they could. They could have left out that pesky ‘may’.
‘May’ in a scientific paper means, ‘we think this could be the mechanism, but don’t have evidence.’
This video is doing exactly what it purports to debunk by (so called) deniers. It distorts the science.
For me, the biggest giveaway has always been the turning points. The points where CO2 is following temperature up or down, then suddenly, temperature changes direction with no regard to the fact that CO2 is continuing in the same direction. If climate sensitivity were large such reversals in temperature, in direct contradiction to the direction of CO2, would be impossible. And yet they are what almost always happens.
Fred McCleney says:
”From the Greenland cores there are two really important considerations; (1) ~130k DOES NOT get us back to the start of the last interglacial, from which one can infer that the Greenland sheet may have completely melted away during the inception and early millenia of the Eemian!”
130 K DOES get us back to the very beginning of the Eemian, and in any case if the Greenland Icecap melted during the earliest Eemian, how did it manage to re-grow and cover most of Greenland to a depth of a couple of kilometres in just a few of thousand years with temperatures warmer than at present? Remember that the Eemian ice from GISP/GRIP/NGRIP/NEEM was deposited at approximately the same altitude and temperature as top of the current icecap.
Furthermore the latest (NEEM) ice-core did recover some MIS 6 ice (and probably the GISP2 core did as well). Also the youngest organic materials ever found under the Greenland icecap are 450 – 800 000 years old and beryllium exposure ages of subglacial rocks are similar.
Actually the reason it is so hard to get ice older than MIS 5e from Greenland is pretty simple. To get very old ice you have to drill down at an ice-divide, i. e. a place where the ice lies still because it flows away equally in two or more directions. Anywhere else the really old ice is long gone, having flowed down to the sea and melted. However it is clear that the Greenland ice did partly melt during the Eemian, which almost certainly means that the ice divide shifted considerably, and most of the older is therefore gone. Things are much easier in Antarctica where the ice is extremely stable, very thick, very sluggish and acccumulates very slowly. Even so it is only near the center of East Antarctica that very old ice is found.
Willis
There is still a “twenty” at the end of one paragraph where it (now) should be ‘only’ seven degrees.
[Thanks, fixed. -w.]