by J Storrs Hall
In my previous post, I argued that sea-surface temperatures hadn’t shown an inflection in the mid-twentieth century, and that the post-50’s rise was essently a land-based phenomenon. To take the analysis further, I thought I could try to find just what the climate signal from CO2 was. The method is to find a fit to the temperature record that included the CO2 forcing signature as a component, and see how big its contribution was compared to the other components of the fit.
First, the CO2. To get a curve since 1850, I got the estimated emissions from here, integrated for accumulation, scaled by matching to the Mauna Loa measured CO2 (red), and took the log for forcing. (No arguments, please; this is the bog-standard story. Let’s assume it’s true for the sake of argument.)
There’s clearly a knee in the curve ca. 1960. Also note that it’s been essentially straight since the 70’s — it’s the log of an exponential.
For components of the fit function, I used a cosine to capture the cyclicity we already know is in the record, a quadratic, and the forcing curve. I had used a second cosine before, and we know it produced two inflections in the result. The quadratic can only produce one, so the forcing curve has a better chance of matching the other one.
The idea is to find the overall best match and then look at the components to see how big the signal from the forcing is in comparison with the other components, which we will assume represent natural variability. We’ll plot each curve with the amplitude the optimizer gives it. Here’s what we get:
The blue line is the overall fit. Cyan is the 61-year oscillation, as before. No surprises here. Magenta is the quadratic, looking a lot like the sinusoid of the previous fit. Red is the CO2 forcing.
The CO2 forcing is upside down.
I gave the optimizer an initial guess for the forcing coefficient of 1; it came back with -1.67. This was, frankly, unexpected. I had seriously thought I would find some warming contribution from the forcing component.
So what on earth is going on? Here’s what we get if we add just the quadratic and the forcing curve:
For comparison, I’ve also plotted the second sinusoid from last time (green). It seems that the secular trend that the optimizer really, really wants is the shape of a Nike swoosh. If given only a quadratic to work with, it has to subtract the forcing curve to straighten out the twentieth-century rise. And it really, really wants the knee of the curve to be in 1890.
Does this mean that CO2 is actually producing a cooling effect? Absolutely not. It simply means that the secular rise in the twentieth century was a straight line, and the fit would do whatever it took to produce that shape. (This is why Pat Frank’s linear fit worked so well. As he noted, the linearity of sea-level rise would tend to confirm this.) What it does mean, though, is that there is no discernable CO2 warming signal in the HadSST temperature record. The (very real) twentieth century warming trend appears to have started about the time Sherlock Holmes was investigating the Red-Headed League.
Why are CO2 outputs always given as the mass not, more importantly, as the proportion of total CO2 output compared to the natural emitters. Victorian atmospheric CO2 levels are guessed at and given as 280ppmv or so. Problem is that measurements taken back then, by several scientists round Europe, gives a value of 400-500 ppmv. Nearly twice that of the stated Victorian values.
There are also inbuilt errors because models use 100-200 years as the figure for CO2 residence time when in fact it is between 5-10 years. Thus the imagined IPCC ‘buildup’ of CO2 in the atmosphere does not happen.
Oh, you’re going to be a very unpopular guy with this sort of analysis–warming starts w/ Sherlock Holmes; CO2 makes no contribution whatsoever to a warming Earth. I certainly hope you weren’t expecting some sort of government funding or any accolades from accademia!
/sarc off.
“You will not apply my precept,” he said, shaking his head. “How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?” – Sherlock Holmes
Oh, please do consider CO2 cooling. Enhanced radiation to the Outer Deeps is quite plausible, IMO.
What it does mean, though, is that there is no discernable CO2 warming signal in the HadSST temperature record. We are 13 days from the summer solstice. The native vegetation is three weeks later than usual. I’ve always been able to plant a garden in May, and I’m tired of shuffling 4 dozen plants inside every night, waiting until it seems safe to put them in the ground. It is 33°F right now, not a confidence builder. I want my global warming back!
HadSST is a best guess estimate extrapolated from a sampling of less than 1% of the ocean surface and that was not even the same 1% over time. I do not doubt your tests and end results but you are basing the tests on the Garbage that is HadSST! Even basing it on the 200 plus years of surface temperatures available would give the same end results. GIGO!
While the fittings you did are well done, I am not convinced that they have much in real world meaning. CO2 is (used to be) sensitive to the SST and the warming out of the LIA would result in increasing CO2 levels. If the SST’s are increasing, so are CO2 levels.
I used Moberg-2005 to build a rate of temperature change and his reconstruction showed mostly positive “rate of warming” for the 1800’s. That would indicate that most of the 1800’s had positive increases in CO2 levels.
http://theinconvenientskeptic.com/2011/04/2000-years-of-rate-of-temperature-change/
There you go again!
Relying on mathematics.
Can’t you just trust your feelings?
So what if the forcing is negative?
We all KNOW that we are at fault. Our hearts tell us so.
So there.
Very interesting, and Steve Keohane, I agree. Cold kills. Warmer is better.
Try substituting a 309 year cycle for your long term and forget about man-made “forcing”. This “natural” change projected into the future suggests a max of around 500 ppm about 2070.
I fully agree with John Marshall. Very important points.
John: There’s at least a little evidence that the 19th was flatter than the 18th or 20th here:
http://wattsupwiththat.com/2010/09/28/loehle-vindication/
Both reconstructions agree on that point, though of course they are NH and mostly land, where I was looking at SSTs.
The CO2 levels before the 1960’s from the Keeling curve and reproduced for this analysis are nothing more than an artifact of the mixing of apples (Hawaiian direct measurements) and oranges (Ice core measurements from trapped gas bubbles). They have no basis in reality and any conclusions drawn upon them can not be regarded as reliable.
“RockyRoad says:
June 8, 2011 at 4:27 am”
Just watched a program called “Catastrophy: Snow Ball Earth” narrated and presented by Tony Robinson (Baldrick in Blackadder). In this episode it is claimed that so much CO2 was removed from the atmosphere by bacteria 650mya resulted in a tipping point leading to “runaway” cooling. Ice built up and spread from the poles to the equator, covering the whole planet in thousands of meters of ice. Then super volcanoes errupted spilling CO2 into the atmosphere causing the planet to warm, melting the ice sheets leading to the warm planet we, and all other life as we know it, live on today. I had to laugh! If “Baldrick” says CO2 did it, it must be true.
If we extrapolate from this formula then it would predict the next 20 years will see definite mild cooling, as the downward part of the sinusoid briefly overpowers the upward quadratic, followed by a return to every warmists favourite trend – and warming stronger than ever.
This would seem to mean that the last decade of ocean cooling is not an indicator that the warming has gone and so is of little value when debating AGW theists.
How did you account for changes in aerosols in the atmosphere, which could have a significant forcing as well?
How did you account for changes in CH4 in the atmosphere, which could have a significant forcing as well?
How did you account for changes in the sun, which could have a significant forcing as well?
In the field that used to be my profession, data points (surveyed ground locations, including elevation) are difficult and expensive to collect. It is therefore useful, from the standpoint of cost-effectiveness, to collect a few points and interpolate the intermediate values.
The original state of the art for that interpolation relied on polynomial and/or cosine-curve fits. Workers quickly found that that system is sensitive to errors and the specific configuration of the input data. In one memorable case, the procedure reported to us that the swamps north and east of Mobile, AL. had an elevation of roughly 2,300 ft AMSL, with a calculated confidence >90%.
Polynomial fitting was abandoned with great glee when a newer procedure was developed, viz., linearization of the equations by partial differentiation, followed by solving the linear equations by iteration using the method of least squares. It isn’t perfect, but it does have the virtue of damping, rather than accentuating, the effects of data point errors and pathological configurations of the input data.
As a result, whenever I see “cosine fit” or references to polynomials (including “exponentials”) I stop reading except as a matter of amusing interest. I never had much to do with the mathematical formulations themselves, but I got intimately acquainted with the results. If garbage in gives garbage out, polynomial and cosine fits are the garbage truck.
Regards,
Ric
I am neither scientist nor mathematician but I have read a lot of the scientific papers on the whole climate change subject. Seems that CO2 concentrations follow temperature fluctuations by 800 years +/- according to the ice cores etc. What totally baffles me is that everyone seems to be trying to correlate today’s numbers when it strikes me that today’s increase in CO2 would more likely be caused by temperature increases during the mediaeval warm period, no? Seems to me that the 800 +/- years would line up fairly close.
“As he noted, the linearity of sea-level rise would tend to confirm this.”
Church and White, the classic purveyors of an exponentially shaped sea level curve, in their latest article update of 2011 (which eliminated the word “accelerating” from the title) plots, in hard-to-see yellow, a simple average of tide gauges, which, once I clean all the dark plots behind it away, shows stark linearity.
Graph: http://oi51.tinypic.com/28tkoix.jpg
Reference: http://www.springerlink.com/content/h2575k28311g5146/fulltext.pdf
what’s the justification for adding the quadratic?
i mean, what is it supposed to model? seems like that’s the forcing AGW proponents ascribe to CO2.
OK, the sinusoid I think I get. Some natural cycle or another. But what on earth is the quadratic supposed to represent? Surely there is no physical reality to a quadratic temperature signal centered in the 1880s. So then you need a negative coefficient on the CO2 signal to keep the quadratic from running away. Who cares what you get when you include the blatantly unphysical quadratic? Or are you suggesting that temperatures in1750 were similar to today, and before that it was hotter than hell?
Take out the unphysical quadratic and what coefficient are you left with on the CO2 fit? (I don’t know what it is, but I’ll go ahead and assert that it will be positive.)
J,
Are there studies that replace your proxy for natural variation with the actual natural variables and then regress delta temp = a + b1*CO2 + b2*var2 + …. + bN*varN + e, logged, or appropriately transformed as needed?
If natural variability, as captured by Variable2 thru VarialbeN, explain the change in temp, then the coefficient on CO2 would not differ statistically from zero.
Why don’t we see these kinds of studies?
thanks
Any reason I can’t paste in a quote ?
(suddenly new WUWT version appeared with ‘ W Log In, t Log In & f Log In, with my name and details already there) .
Some folk require no science at all to convince themselves we are all just wicked and guilty . .
http://www.smh.com.au/business/denying-the-earths-growth-and-depleting-resources-is-just-eating-into-our-future-20110608-1ft6i.html
@Hall
The result is unexpected because you have flaws in your assumptions.
You need to adjust your curve labeled “CO2 Forcing” to reflect the fact that the IR absorption characteristics of CO2 is not linear across the range of atmospheric concentrations in the graph. This is why the climate boffins talk about surface temperature rise being a constant amount per CO2 doubling. The constant amount per doubling is usually given at 1.1C (absent the mythical water vapor amplification). Thus going from 280ppm to 560ppm gives a rise of 1.1C and then going from 560ppm to 1120ppm also results in a rise of 1.1C. If you take this into account there is no longer a “knee” and you’ll find that the forcing is a straight line not an exponential.
I agree it is largely a land based phenomenon. CO2 acts as insulator by absorbing upwelling LWIR (long wave infrared) from the surface and re-emitting it equally in all directions. Land surfaces can absorb downwelling CO2 and the net effect is that the rate of emission from surface to space is decreased i.e. the ground doesn’t cool down as fast. If daytime heating via SWVR (short wave visible light) remains constant the result is that the surface temperature will rise. This increases the rate of emission from surface to space establishing a new, higher surface equilibrium temperature.
Water is very different than land. H20 has many properties that when taken together make it a very unique substance. One of those properties that it’s almost perfectly transparent to SWVR and perfectly opaque to LWIR. Downwelling LWIR from CO2 cannot be absorbed by a body of water. LWIR absorption and emission takes place in a water surface layer of just a few micrometers. It results in no rise in water temperature but rather a rise in evaporation rate. This in combination with another property of water called “latent heat of vaporization”, which unique in how large it is in water, means that the lion’s share of the energy from downwelling IR results in water vapor of the same temperature as the water surface. Water vapor being far lighter than oxygen and nitrogen it tends to rise faster and get mixed into the atmosphere above. Like CO2 it has no greenhouse effect over the ocean. The effect it does have is increasing cloud cover which lowers daytime heating of the ocean by reflecting away more SWVR before it ever reaches the ocean surface. This then works as a negative feedback. The elevated evaporation rate caused by greenhouse gases is nullified by elavated albedo. This is the basis of my agreement with you on CO2 greenhouse effect being a land (or ice!) based phenomenon.
@John Marshall
You appear to making the same mistake as Hall in that you are assuming a linear CO2 “build-up” when in fact the rate at which natural sinks take up anthropogenic CO2 is dependent on how far out of equilibrium it is. The farther out of equilibrium the faster the sinks work to restore it. The current rate of CO2 emission is rougly 2ppm/year yet the rate of accumulation in the atmosphere is 1ppm/year. This ratio of only 1/2 the anthropogenic CO2 emitted taking up residence in the atmosphere has remained constant since the beginning of the industrial era.
For the sake of argument let’s presume that the CO2 equilibrium point is that found in ice cores through the last 3 million years of ice age conditions. That would be about 280ppm in interglacial periods and 200ppm during the glacial periods. If we presume 280ppm is an equilibrium point for natural CO2 sources and sinks in the current interglacial and that the farther out of equilibrium it becomes the harder the natural sources work to restore it then we should expect exactly what we observe: a constant rate of accumulation in the atmosphere. In other words as anthropogenic CO2 emissions has grown on an exponential curve the ability of natural sinks to absorb it also grows exponentially.
So when it comes to “residence” time it depends on how far out of equilibrium it is. If the above description of a natural equilibrium is correct then if we were to somehow cease anthropogenic CO2 production today it would be removed by natural sinks at the same rate and thus take about 150 years to return to 280ppm. But it’s not a linear decrease. In the first 50 years it would have already decreased from 390ppm to 315ppm. So you get 2/3 of the way back to 280ppm in the first third of the 150 years. It take the next century to remove the remaining 35ppm above equilibrium.
So “residence” time isn’t a fixed amount and you really can’t say things like 15 years or 150 years because the residence time depends on how far out of equilibruim it is in any given year.
In regard to some anomalously high CO2 measurements in the past no one argues that local CO2 levels can’t vary by quite a margin close to the surface in calm air. After all CO2 is heavier than both O2 and N2 and the sources are all near the surface. This is why we use as our gold standard for atmospheric CO2 level data obtained from balloon soundings, high atop frozen mountains, and in permanently frozen Antarctic. These different methods of obtaining “well mixed” air samples have all been in perfect agreement. Moreover another method of measuring CO2, entrainment in glacial ice, is also in perfect agreement. Essentially all the evidence is that CO2 is well mixed in the turbulent troposphere with the exception of local situations close to the surface in exceptionally calm air with active sources and sinks (i.e. not barren desert or ice).