UPDATE from Girma: “My title should have been ‘How to arrive at IPCC’s climate sensitivity estimate’ instead of the original”
Guest essay by Girma Orssengo, PhD
1) IPCC’s 0.2 deg C/decade warming rate gives a change in temperature of dT = 0.6 deg C in 30 years
IPCC:
“Since IPCC’s first report in 1990, assessed projections have suggested global average temperature increases between about 0.15°C and 0.3°C per decade for 1990 to 2005. This can now be compared with observed values of about 0.2°C per decade, strengthening confidence in near-term projections.”
Source: http://www.ipcc.ch/publications_and_data/ar4/wg1/en/spmsspm-projections-of.html
2) The HadCRUT4 global mean surface temperature dataset shows a warming of 0.6 deg C from 1974 to 2004 as shown in the following graph.
Source: http://www.woodfortrees.org/plot/hadcrut4gl/from:1974/to:2004/trend/plot/hadcrut4gl/from:1974/to:2005/compress:12
3) From the following Mauna Loa data for CO2 concentration in the atmosphere, we have CO2 concentration for 1974 of C1 = 330 ppm and for 2004 of C2=378 ppm
Source: http://www.woodfortrees.org/plot/esrl-co2/compress:12
Using the above data, the climate sensitivity (CS) can be calculated using the following proportionality formula for the period from 1974 to 2004
CS = (ln (2)/ln(C2/C1))*dT = (0.693/ln(378/330))*dT = (0.693/0.136)*dT = 5.1*dT
For change in temperature of dT = 0.6 deg C from 1974 to 2004, the above relation gives
CS = 5.1 * 0.6 = 3.1 deg C, which is IPCC’s estimate of climate sensitivity and requires a warming rate of 0.2 deg C/decade.
IPCC’s warming rate of 0.2 deg C/decade is not the climate signal as it includes the warming rate due to the warming phase of the multidecadal oscillation.
To remove the warming rate due to the multidecadal oscillation of about 60 years cycle, least squares trend of 60 years period from 1945 to 2004 is calculated as shown in the following link:
Source: http://www.woodfortrees.org/plot/hadcrut4gl/from:1945/to:2004/trend/plot/hadcrut4gl/from:1945/to:2005/compress:12
This result gives a long-term warming rate of 0.08 deg C/decade. From this, for the three decades from 1974 to 2004, dT = 0.08* 3 = 0.24 deg C.
Substituting dT=0.24 deg C in the equation for Climate sensitivity for the period from 1974 to 2004 gives
CS = 5.1* dT = 5.1* 0.24 = 1.2 deg C.
IPCC’s climate sensitivity of about 3 deg C is incorrect because it includes the warming rate due to the warming phase of the multidecadal oscillation. The true climate sensitivity is only about 1.2 deg C, which is identical to the climate sensitivity with net zero-feedback, where the positive and negative climate feedbacks cancel each other.
Positive feedback of the climate is not supported by the data.
UPDATE:
To respond to the comments, I have included the following graph
Source: http://www.woodfortrees.org/plot/hadcrut4gl/mean:756/plot/hadcrut4gl/compress:12/from:1870/plot/hadcrut4gl/from:1974/to:2004/trend/plot/esrl-co2/scale:0.005/offset:-1.62/detrend:-0.1/plot/esrl-co2/scale:0.005/offset:-1.35/detrend:-0.1/plot/esrl-co2/scale:0.005/offset:-1.89/detrend:-0.1/plot/hadcrut4gl/mean:756/offset:-0.27/plot/hadcrut4gl/mean:756/offset:0.27/plot/hadcrut3sh/scale:0.00001/offset:2/from:1870/plot/hadcrut4gl/from:1949/to:2005/trend/offset:0.025/plot/hadcrut4gl/from:1949/to:2005/trend/offset:0.01
I have got a better estimate of the warming of the long-term smoothed GMST using least squares trend from 1949 to 2005 as shown in the above graph, which shows the least squares trend coincides with the Secular GMST curve for the period from 1974 to 2005. For this case, the warming rate of the least squares trend for the period from 1949 to 2005 is 0.09 deg C/decade.
This gives dT = 0.09 * 3 = 0.27 deg C, and the improved climate sensitivity estimate is
CS = 5.1*0.27 = 1.4 deg C.
That is an increase in Secular GMST of 1.4 deg C for doubling of CO2 based on the instrumental records.
RE: Ian W says: – May 19, 2013 at 3:20 am
Trying to fit a linear change or a cyclic variation/oscillation to a chaotic system is a nonsense. There may be brief periods where there is ‘a fit’ then the system will change due multiple unknown non-linear non-cyclic interactions and the pattern will not exist any more as expected. Just because we humans like to see a simple pattern doesn’t mean that there is one. Even doing Fourier analyses is just obfuscating the concept that there must be standard repeating patterns that make up the apparent random noise – well you may find some but they will be dependent on the algorithm used and the end points they won’t describe the chaotic system because by definition they expect repeating patterns at various scales from a chaotic system.
Random Walk from Wikipedia:
http://en.wikipedia.org/wiki/Random_walk
I’ve fooled around with random pattern generators on Excel and it’s surprising how often they nearly match those Hadcrut, GISS, RSS, UAH graphs we’ve all stared at.
IIan W says:
Trying to fit a linear change or a cyclic variation/oscillation to a chaotic system is a nonsense. There may be brief periods where there is ‘a fit’ then the system will change due multiple unknown non-linear non-cyclic interactions and the pattern will not exist any more as expected. Just because we humans like to see a simple pattern doesn’t mean that there is one. Even doing Fourier analyses is just obfuscating the concept that there must be standard repeating patterns that make up the apparent random noise – well you may find some but they will be dependent on the algorithm used and the end points they won’t describe the chaotic system because by definition they expect repeating patterns at various scales from a chaotic system.
===
What you caution is valid as a caution but it is incorrect to go to the other extreme and say that any order or pattern in a chaotic system is illusionary.
Calling a system chaotic is simply a statement of the lack of understand we have of how it works.
That is not a reason for not looking or calling everything “stochastic”
The climate system has many physical feedbacks which will lend to the creation of possible oscillatory behaviour. There are also many periodic drivers of which the daily and annual changes are the most obvious.
From Greg Goodman on May 19, 2013 at 3:26 am:
Yes, running means are so bad that you have repeatedly recommended a 30 month running mean, followed by a 22 month running mean, followed by a 17 month running mean, all on the same data. You say running means are bad, then heartily recommend three times the badness.
You’ve also complained about the simple WFT tools, then repeatedly used them. Even after it was demonstrated you were using them incorrectly.
But because you call your triple-badness 3x running means “filters”, somehow they are great and wonderful, and if someone familiar with WFT recognizes your “filters” are a crappy unneeded triple running means, they are obviously ignorant and needing of your “brief explanation”?
Fine, I’ll go read your “explanation”.
…
Nope, you’re still stupid. You are referring to the sinc(x) function, used for Fourier transforms, talking about frequencies. For example, bold added:
These are measurements of climate, an inherently chaotic system. You want to use tools suitable for perfect precise fixed frequencies. If you would have read Willis Eschenbach’s post that I linked to, or to what others have said, or even made an honest open-minded examination of that data, you would know that you are neck-deep in folly.
Now, feel free to insist I’m the idiot while you’re the expert, while I laugh at you like you were a freshly-graduated engineer who expects a 15mm hex nut to fit perfectly into the slot they precisely spec’d at 15.000mm.
Girma says “Willis, plotting the Secular GMST and ln (CO2) gives you a linear relationship given by T = 1.871*ln(CO2/320.09) ”
No, plotting does not give any relationship. What does that is doing a linear regression. Here you have done a linear regression of T on log of co2 ratio.
The thing is that log CO2 represents an additional “forcing” (W/m2) , that will produce a rate of change of temperature (temperature is a measure of energy not power !)
That is why , yesterday, I said you need to integrate. Then you need to account for how much of today’s dT is because of feedbacks to yesterday CO2 etc, etc.
Sorry, if it was as trivial as you are trying to make it , it would have been solved in the 19th century on the back of an envelop.
I consider all the claims regarding the ability to assess climate sensitivity disingenuous, even bordering on the dishonest.
It may be possible to calculate how CO2 behaves in laboratory conditions and hence to calculate a theoretical warming in relation to increasing CO2 levels in laboratory conditions. But that is not the real world.
In the real world, increased concentrations of CO2 would theoretically block a certain proportion of incoming solar insolation so that less solar radiance is absorbed by the ground and oceans, and it would also increase the rate of out going radiation at TOA. Both of these are potentially cooling factors. Thus the first issue is whether in real world conditions the theoretical laboratory ‘heat trapping’ effect of CO2 exceeds the ‘cooling’ effects of CO2 blocking incoming solar irradiance and increasing radiation at TOA and if so, by how much? The second issue is far more complex, namely the inter-relationship with other gases in the atmosphere and what effect it may have on the rate of convection at various altitudes and/or whether convection effectively outstrips any ‘heat trapping’ effect of CO2 carrying the warmer air away and upwards to the upper atmosphere where the ‘heat’ is radiated to space. None of those issues can be assessed in the laboratory, and can only be considered in real world conditions by way of empirical observational data. This is a hapless task since the data sets are either too short and/or have been horribly bastardised by endless adjustments, siting issues, station drop outs and polluted by UHI. Quite simply data sets of sufficiently high quality do not exist.
It is simply impossible to determine a value for climate sensitivity from observation data until absolutely everything is known and understood about natural variation, what its various constituent components are, the forcings of each and every individual component and whether the individual component concerned operates positively or negatively, and the upper and lower bounds of the forcings associated with each and every one of its constituent components.
This is logically and necessarily the position, since until one can look at the data set (thermometer or proxy) and identify the extent of each change in the data set and say with certainty to what extent, if any, that change was (or was not) brought about by natural variation, one cannot extract the signal of climate sensitivity from the noise of natural variation.
I seem to recall that one of the Team recognised the problem and at one time observed “”Quantifying climate sensitivity from real world data cannot even be done using present-day data, including satellite data. If you think that one
could do better with paleo data, then you’re fooling yourself. This is
fine, but there is no need to try to fool others by making extravagant
claims.”
We do not know whether at this stage of the Holocene adding more CO2 does anything, or, if it does, whether it warms or cools the atmosphere (or for that matter the oceans). Anyone who claims that they know and/or can properly assess the effect of CO2 in real world conditions is being disengenuous.
Jim Cripwell says: May 18, 2013 at 6:33 am
“Baa Humbug says”Alert me when you get to climate sensitivity of zero and I’ll pay attention”
You may be interested in my extremely simplistic approach to this issue. Since no-one has measured a CO2 signal in any modern temperature/time graph, from standard signal to noise ratio physics, there is a strong indication that the climate sensitivity of CO2 is indistinguishable from zero.”
As noted above, we do not know enough about natural variation to extract the so called climate sensitivity from the noise.
For what it is worth, 33 years worth of satellite data (which shows that temperatures were essentially flat between 1979 and 1997 and between 1999 to date and demonstrates no correlation between CO2 and temperature) suggests that the climate sensitivity of CO2 is so low that it is indistinguishable from zero.
Surely the best evidence we have comes from the ice cores, which record the temperature and CO2 cycles over nearly the last million years.
As far as I’m aware, the ice cores show no trace of CO2 changes causing corresponding temperature changes. But they consistently show that CO2 changes are driven by temperature changes.
If so, then it strongly suggests that the warming effect of CO2 is close to zero. As the greenhouse effect does – presumably – work in the laboratory, then it also suggests that strong negative feedbacks are dominant in the climate system.
Chris
“But because you call your triple-badness 3x running means “filters”, somehow they are great and wonderful, and if someone familiar with WFT recognizes your “filters” are a crappy unneeded triple running means, they are obviously ignorant and needing of your “brief explanation”?”
No, if someone who is not familiar with filters wades in telling me “you don’t do this … you don’t do that … you never do blah” simple because they do not understand squat, I will point out that they are shouting about something they do not understand.
Running means have serious deficiencies but with a little knowledge these can be over come. I have explained the origin of the problem, and detailed how to correct it. That may be useful to others who are willing to learn.
“Nope, you’re still stupid. You are referring to the sinc(x) function, used for Fourier transforms, talking about frequencies.”
You have not understood a word of it have you? You are clearly unable and unwilling to learn anything and will keep ignoring everything I show you so that you can keep waving your arms and shouting insults.
Enough with the insults. I’m bored.
richard verney says: It is simply impossible to determine a value for climate sensitivity from observation data until absolutely everything is known and understood about natural variation, what its various constituent components are, the forcings of each and every individual component and whether the individual component concerned operates positively or negatively, and the upper and lower bounds of the forcings associated with each and every one of its constituent components.
===
Interesting thoughts. That is certainly true if you hit everything with a 60 filter.
However, I do not think it is as black and white as that. It must be possible to rule out certain extreme values. From there the task is to narrow it down by closer inspection. Until we have a much better understanding that will likely remain very large.
Geologically CO2 has always lagged, this does preclude it acting as a positive feedback. This could be one reason climate tends to flip between glacial and interglacial states.
On a short time-scale temperature seems to determine atmospheric CO2 by out-gassing from oceans:
http://climategrog.wordpress.com/?attachment_id=233
The key question remains at the interdecadal scale and that is where data reliability and politically motived adjustments make an honest scientific enquiry a lot more difficult.
stacase: I’ve fooled around with random pattern generators on Excel and it’s surprising how often they nearly match those Hadcrut, GISS, RSS, UAH graphs we’ve all stared at.
Yes, that’s worth doing to get a feel for it can look like. Roy Spencer gave out an xls a couple of years back on his site if anyone wants to look at that.
Greg
I have reproduced your result:
http://www.woodfortrees.org/plot/rss/compress:12/derivative/normalise/plot/esrl-co2/compress:12/derivative/derivative/from:1979/normalise
Excellent correlation between global mean temperature and CO2 concentration.
Amazing.
But they are telling us the increase is due to human emission of CO2.
What a ……?
Greg Goodman says:
May 19, 2013 at 4:15 am
The climate system has many physical feedbacks which will lend to the creation of possible oscillatory behaviour. There are also many periodic drivers of which the daily and annual changes are the most obvious.
I would be interested how you find a diurnal or even annual pattern after 3 multimonth smoothings looking at a 60 year oscillation. 😉 especially as the inputs may not correlate at all with the outputs due to mulltiple different feedback lags and the chaotic interactions between those feedbacks and the inputs.
Girma says:
May 19, 2013 at 6:52 am
Greg
I have reproduced your result:
http://www.woodfortrees.org/plot/rss/compress:12/derivative/normalise/plot/esrl-co2/compress:12/derivative/derivative/from:1979/normalise
Excellent correlation between global mean temperature and CO2 concentration.
Amazing.
But they are telling us the increase is due to human emission of CO2.
What a ……?
Perhaps it is a good empirical proof of Henry’s Law.
G: But they are telling us the increase is due to human emission of CO2.
Ian: Perhaps it is a good empirical proof of Henry’s Law.
yes, I think this relationship is fairly clearly temp driving d/dt(CO2) with no discernible lag. That is basic chemistry/physics laws.
That is telling us that the short term response is ocean out-gassing and little to do with emissions.
That had a ratio of 8 ppm/K
It should be remembered that this is a dynamic response where T represents a temporary deviation from the temperature that would be at equilibrium with the instantaneous ocean pCO2 level.
The other factor was the mean dT/dt over that period of 0.7K/century ( this is SST, interesting to compare to hadCrut) . CO2 shows mean accel of 2.8 ppm/year/century.
That is a ratio of 4 ppm/K for the 50 year means, most of that was a warming period so this gives an estimation of the long term response.
If this is still “dynamic” it must be a very deep water response. and it is likely we need to take a variation in temp gradient into account. If the deep temperature change is , for example , half that seen at the surface that could correspond to the same 8 ppm/K seen in short term.
There may be another way to interpret the 50 year means.
There is also an interesting repetition in d/dt CO2: 1998 is a perfect replay or 1974
http://climategrog.wordpress.com/?attachment_id=232
That plot gives a slightly different acceleration of CO2 but not far off.
The finite, positive dT/dt means something is warming the ocean system and causing it to be generally slightly ahead of equilibrium at least during this warming segment.
BTW it takes less than a hour to re-equilibrate to a change on temp/CO2 in agitated water. In this context it is instantaneous at the surface.
Deeper there will be delays associated with mixing of water volumes but not CO2 concentration itself.
http://climategrog.wordpress.com/?attachment_id=254
Same data with four year low pass filter applied.
Here the decadal scale variations show CO2 acceleration lagging rate of change of temperature .
The lag is larger at the beginning and end of the record. Varying between about 0.5 years around 1990-95 to >1.5 years at the end.
It seems that as we move into “the pause” lag increased, similar to what is was pre 1975 at the end of the last cooling period.
Observation => WAG: greater lag in deep water exchanges during cooling periods.
This should gives clues as to the origin of the warming. More on that once I’ve thought it through…
Greg Goodman at May 19, 2013 at 8:38 am
Around 1990 the graph reveals a dramatic negative acceleration in CO2 and a corresponding negative SST trend. I would have expected to see this dip in 1992 due to the Pinatubo eruption. Does the smoothing cause a shift in dating?
Also – and it may be only me – but I strongly associate CO2 with green and temp with red. For a time, the graph’s reversed expected colors were somewhat disconcerting, a mental illusion which flipped the meaning of the colors back and forth between actual and conditioned.
Girma.
IMO, your attempt to isolate secular variance by removing 60 yr pseudo-cycle noise is far more honest (and IMO accurate) than to leave it in and claim that the trend from mid-70’s onward is “mostly” due to anthro CO2. We have had far too much of the latter from media and activists over the past 17 years.
You are open to suggestions and progressive improvement. Therefore your “back-of-the-envelope” does not offend me. (I think the title is a stretch.)
Thanks and good luck.
blueice2hotsea
No the filter will not introduce a spurious shift, it is centred correctly. There will be a slight spreading in width of the peak. However, bear in mind that rate of change drops before the actual temperature.
Max negative rate of change is about when temp goes through zero on the way down.
Having said that even dT/dt can’t drop before the eruption, if is the cause. This shows there’s no significant drop from El Chicon or Mt Pinatubo. Nothing that stands out from the usual ups and downs.
However, there is a very noticeable negative acceleration in CO2 at about the right time for Mt Agung around 1963/64. This stands out as one of the few deviations of the two datasets. A paper was published looking at that in detail which concluded the drop in CO2 could probably be attributed to the eruption.
That is also an explicit recognition of the effect of sea temperature on atmospheric CO2.
CO2 is colourless and temps are only red in alarmist literature. Seems they’ve got you trained with that preconception. 😉
If I had thought about attributing colours, I would have made the sea blue.
to KD, above:
thanks, and I should have been more ‘clear’ – yes, i do understand the cancel out in this particular equation – I was trying to indicate “log” vs “ln” i have read in other discussions and articles as well as this one – it’s , for me , a matter of there is so much “to forget” that I need to be remembering.
Girma says:
May 18, 2013 at 10:00 pm
Girma, you have not considered a couple of things. One is the pernicious side of smoothing. This is the increasing autocorrelation that occurs when you smooth a dataset. You need to, have to, absolutely must take autocorrelation into account when considering whether a given R^2 is significant or not. I use the method of Quenouille, which is as follows:
The other is the small size of your dataset. You are using annual CO2 figures, and you show an overlap in your two datasets of 25 years … which means that N is only equal to 25, an absurdly small dataset to analyze.
As a result of these two things, the fact that your R^2 is greater than 99% is MEANINGLESS. There’s not even enough data to calculate the statistical significance of the relationship between the two tiny datasets, much less determine its meaning.
I am somewhat surprised, given your PhD and your list of programs you use (Mathematica, Excel, etc.) that you seem to be so woefully unaware of even these rudimentary issues of sample size and autocorrelation when analyzing climate data … truly, you have demonstrated beyond question that are out of your depth here.
You need to read up on the handling of autocorrelated datasets, because at present, unfortunately, your statistical claims are … well … let me call them charmingly naive at best, and unintentionally misleading at worst,
w.
Why do we constantly assume that all warming post LIA is due to CO2 and not due to the end of whatever condition caused the LIA in the first place and a recovery from that event? Why are all climate graphs starting with the end of the LIA and do not go back to around 1100 or so and show the drop into the LIA in context with the recovery out of it?
Did we have some global reduction of CO2 leading into the LIA? I don’t think we did.
Greg Goodman –
When I attempt a similar graph as yours, there is a sharp inflection at 1992. This does not square with 1990 in your graph.
Is there something wrong at WFT? Or what am I doing wrong? I must say that the closer alignment with Pinatubo event is interesting.
Or what am I doing wrong?
WTF.org says: “Compress Reduces the number of samples by averaging across the given number of months and replacing with the average. Use this to simplify a dataset before doing complex operations on it ”
You also seem have reduced a monthly series to annual. Why would you want that?
http://climategrog.wordpress.com/2013/05/19/triple-running-mean-filters/
Try again using a 12, 9, 7 triple running mean to remove the annual cycle instead of “isolate”.