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.
UPDATE
To respond to the comments, I have included the following graph
http://bit.ly/16GPCm3
I have got a better estimate of the warming of the long-term smoothed GMST using a 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.
Greg
before calling CO2 “monotonic” you ought to have a look at:
I mean the annual CO2 concentration:
http://www.woodfortrees.org/plot/esrl-co2/compress:12
Greg
With that kind of baggage you should be able to fit a simple model without relying upon trivial detrending and runny mean filters available at WTF.org.
I want others to do it for themselves with available data and software online.
How many can determine for themselves a climate sensitivity of 1.4 deg C from the data and software easily available online as described in my essay?
“I mean the annual CO2 concentration:”
I’m working the the annual conc too. But once you look at the rate of change you start to realise that it’s not just random noise or “stochastic” variation. It’s highly correlated to temperature.
Now if you are supposedly investigating the relationship of CO2 and temperature that is not the sort of thing you can ignore.
“I want others to do it for themselves with available data and software online.”
Well that would be nice. But that is really not an acceptable excuse for not doing it properly. WTF.org is so basic you just can’t do this sort of analysis. Maybe there are better online tools or you could use a spreadsheet.
You’re taking the log of two points on the CO2 curve , that gives you the increased “forcing” at the end of the period. You seem to be applying that across the whole period.
What you need is the integral of the instantaneous forcing over the period. It’s not correct.
Greg
I have done the analysis as you suggested. Here is my final result, which shows the linear relationship between Secular GMST (after the multidecdal oscillation has been removed) and the logarithm of the CO2 concentration.
http://orssengo.com/GlobalWarming/ClimateSensitivityOfOnePointThreeDegC.png
From the above graph, the slope of the linear relationship for the period from 1974 to 2004 is
k = dT/(ln C2 – ln C1) = (0.31 – 0.06)/(ln 377 – ln 331) = 0.25 / ln(377/331) = 0.25 / 0.130 = 1.923
From k = dT/(ln(C2/C1)), for doubling of CO2 we have
k = CS/ln 2
Therefore CS = k * ln 2 = 1.923 * ln 2 = 1.923 * 0.693 = 1.3 deg C for doubling of CO2
“I have done the analysis as you suggested. ”
Well you haven’t. But it’s not my job to try and force you to do something you don’t want or are not capable of doing.
I’m tired. Bedtime.
Girma says:
May 18, 2013 at 6:36 pm
It looks like you’ve established that CO2 and temperature are running in parallel … but that’s not supposed to happen. Instead, temperature is supposed to vary with Log2(CO2). So already you are far afield from the IPCC (not that that is a bad thing.)
But in any case, what you have demonstrated is mere correlation. It’s been known for a while that in a vague hand-waving kind of fashion temperature is correlated with Log2(CO2) … but unfortunately, over the last fifteen years or so, they seem to have decoupled. Log2(CO2) continued to rise apace, but temperature has not cooperated.
That is, of course, if they were ever coupled in the first place …
w.
Wllis
The relationship between temperature and and CO2 is between the Secular GMST (the monotonously increasing long-term GMST that has similar shape as the CO2 concentration and the sea level rise) and the CO2 concentration. The multidecadal oscillation of about 63 deg C period should not be considered as they are transient.
Willis, plotting the Secular GMST and ln (CO2) gives you a linear relationship given by
T = 1.871*ln(CO2/320.09)
That is the relationship between HadCRUT4 and the Mauna Loa datasets. T is the simple fit to the 63-years moving average of the annual GMST and CO2 is the annual CO2 concentration.
Please try it and see if it works. It has worked for me.
The equation for T since 1869 is
T = 0.5*t1*(year-1895)^2 + t2*(year-1895) + t3
where
t1 = 5.477*10^(-5) deg C/year^2
t2 = 2.990*10^(-3) deg C/year
t3 = -0.344 deg C
Here is the graph for the relationship between the model and the annual GMST:
http://orssengo.com/GlobalWarming/GmstPatternOf20thCentury.png
Using the Hadcrut4 data and extrapolating the Keeling curve back to 1850 I find:
From 1850 to 1878 CO2 went up less than 1 ppm and temperature went up 0.4°C
From 1878 to 1911 CO2 went up nearly 6 ppm and temperatures dropped about -0.6°C.
From 1911 to 1944 CO2 went up over 16 ppm and temperatures went up 0.7°C.
From 1944 to 1976 CO2 went up over 29 ppm and temperatures dropped almost -0.4°C.
From 1976 to 2012 CO2 went up about 48 ppm and temperatures are up nearly 0.8°C.
Looks like this:
http://oi44.tinypic.com/4ikn78.jpg
You can take any two functions that increase over time and make it look like one causes the other but it isn’t necessarily the case.
stacase
The annual CO2 is related to the 63-years moving average GMST with an R^2 = 0.99
Here is the correlation:
http://www.woodfortrees.org/plot/hadcrut4gl/mean:732/from:1901/normalise/plot/esrl-co2/compress:12/normalise/offset:0.615/detrend:-0.125
Jim;
Can you elaborate on the fascinating “singal to nosie” physics? Does it require handkerchiefs?
😀
“””””…..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.”……””””””
So how does that jibe with the CRU public declaration that there has been NO statistically significant warming in the last 17 (now 18 ) years.
So if there was all of 0.6 deg. C rise since 1974, it must all have happened before 1995, because there has been none since.
Why do people keep on insisting on a link to CO2, when the data (real observed measurements) show there is no cause/effect connection (either way) whatsoever..
Keeping on repeating that old mantra under the authority of a PhD shingle doesn’t make it any more believable. The data tells the story; CO2 and Temperature can and do move in either the same or opposite directions, or both, and there is no link.
george e. smith
CO2 and Temperature can and do move in either the same or opposite directions, or both, and there is no link.
As the temperature increases, more CO2 is released from the oceans (where it is about 50 times than in the atmosphere) increasing the CO2 concentration in the atmospheric.
As the temperature decreases, more CO2 is dissolved in the oceans decreasing the CO2 concentration in the atmosphere.
That is what the Vostok ice core data shows for thousands of years as shown below:
http://www.climatedata.info/Proxy/Proxy/icecores.html
“””””……Girma says:
May 18, 2013 at 7:50 pm
Greg
I have done the analysis as you suggested. Here is my final result, which shows the linear relationship between Secular GMST (after the multidecdal oscillation has been removed) and the logarithm of the CO2 concentration.
http://orssengo.com/GlobalWarming/ClimateSensitivityOfOnePointThreeDegC.png
From the above graph, the slope of the linear relationship for the period from 1974 to 2004 is
k = dT/(ln C2 – ln C1) = (0.31 – 0.06)/(ln 377 – ln 331) = 0.25 / ln(377/331) = 0.25 / 0.130 = 1.923
From k = dT/(ln(C2/C1)), for doubling of CO2 we have
k = CS/ln 2
Therefore CS = k * ln 2 = 1.923 * ln 2 = 1.923 * 0.693 = 1.3 deg C for doubling of CO2…..”””””
So Girma, have you tried to fit the data, since say IGY in 1957/8 into a mathematical relationship of the form:-
y = mx + c, where y and x represent mean global surface Temperature, and Mauna Loa atmospheric CO2 abundance, either in that order, or in the reverse order (flip T and CO2), and show that it is any less likely to be true that your logarithmic form. For that matter, have you tried to fit the T and CO2 data to a formula of the form:-
(CO2)2 – (CO2)1 = a log (T2/T1) and shown it is any less plausible than your formula.
And for the piece de resistance try fitting the GMST and MLCO2 to an equation of the form:-
y = a.exp (-1/mx^2) +y0 since 1957/8, and of course x and y represent GMST and MLCO2 in either order (or both).
And show that is any less plausible than your logarithmic relationship.
remember only real measured data between 1957 and 2013; no computer simulated estimates, running averages, filtration residues or any such crap.; just the actual data.
For a bonus, try fitting either GMST or CO2, or both since 1957, to the average Telephone number in the Manhattan Telephone directories published between 1957, and 2013.
stacase says:
May 18, 2013 at 9:33 pm
Excellent! (But you knew this was coming, didn’t you?)
But, I would amend this summary slightly.
What this change does is highlight the very short duration of any possible rising-CO2=rising-temperature effect, and highlight even more the length of the rising-CO2=no-change-in-temperature relationship we see right now in today’s climate.
(1)Your value of +0.8 C between 1976 and 2011 is off: We were about 0.3 above baseline of the mid-70’s in 2011. We have been at 0.0 change (or declining slightly since 1996.) Right now, at 2013 May, we are only 0.1 degree higher than the baseline of the mid-1970’s, so going up 0.8 between 1970 and2011 isn’t possible.
(2) Please, verify my (approximated) value of CO2 change at the 1996 and 2013 dates also.
Don Easterbrook says:
May 18, 2013 at 6:51 am
“…the notion that temperature is a function of CO2 is invalided [sic] until you first show a cause-and-effect relationship between the two!”
The cause/effect of CO2 and temperature has been known for 150 years. What is it about variation around a secular trend that seems to elude you? JP
Don Easterbrook says:
May 18, 2013 at 11:52 am
Girma
“I am not saying CO2 is causing the warming. I believe it is the warming that is causing the increase in CO2 concentration, as the vostok ice cores show. The CO2 concentration will drop when the temperature falls.”
You, Girma and many others in the skeptic community seem to have a problem discerning when CO2 increase acts as a radiative forcing and when it acts as a feedback. Of course the Vostok cores show CO2 increasing after warming. It’s a feedback. JP
@ur momisugly Greg Goodman on May 18, 2013 at 3:56 pm:
Okay, you’re agreeing you screwed up on the “doubled differential” part. That’s a start. Now to the rest.
From A Handbook of Numerical and Statistical Techniques: With examples mainly from the life sciences by J.H. Pollard, 1977, starting at pg 26, Simple methods of smoothing crude data:
From Leif Svalgaard to Willis Eschenbach to Roy Spencer, the dangers of repeated averaging are known and warned against. I have known such for a long time. You have already smoothed the data once, and want to do it again, twice. I will need better justification than “You’re stupid, shut up until you learn something.”
I did not ignore it, but you are speaking from arrogance thus it is understandable you will make all sorts of assumptions about me, that will invariably be in whatever direction further inflates your self-aggrandizement.
Let’s look at running means in smaller bites:
http://www.woodfortrees.org/plot/rss/from:1980/plot/rss/from:1980/mean:15/plot/rss/from:1980/mean:30/plot/rss/from:1980/mean:45/plot/rss/from:1980/mean:60/plot/rss/from:1980/mean:30/mean:22/mean:17
We’ll get rid of the noisy main signal for clarity, the 15-mo running mean shows its shape well enough:
http://www.woodfortrees.org/plot/rss/from:1980/mean:15/plot/rss/from:1980/mean:30/plot/rss/from:1980/mean:45/plot/rss/from:1980/mean:60/plot/rss/from:1980/mean:30/mean:22/mean:17
Your wonderful “triple filter” hugs no better than a simple 30-mo running average, said value being the largest of the ones you specified, while it loses much detail, for no benefit.
As seen in the 15-mo running average, there appears to be an underlying pattern of about five years, often just shorter. Thus 60-mo is a bad choice for a running average, as for example at the trough at approx. 1989.5, it’s averaging the 1987 and 1992 peaks.
Thus the usual sage advice is to only use a running average big enough to “smooth” noisy graph data, as for visual clarity, but stop before you introduce artifacts.
You are trumpeting the marvels of your miraculous “triple filter”, using that graph you said I ignored, when all you’ve basically shown is it’s better to stop at a 30 month running average than to enlarge to 60 months.
I must assume you are very new to this site, to think a blanket appeal to your authority should mean anything. Especially with the obvious errors you’ve made.
There are authorities on this site I do respect, because they do not have your “shut up and accept my authority” attitude, and are willing to explain things. They have warned against repeated averages as you are advocating, as I have been warned decades ago. You are discussing “filter design ,frequency response, and phase distortion” as if fixed frequencies were involved. Willis Eschenbach warned us about people like you.
If you can get one of them to sign off on your particular number-mangling, I will consider it to have worth, within its obvious demonstrated limited usefulness. But your appeal to your own authority? Your “Cease your ignorant whining, learn something elsewhere, then come apologize to me!” attitude? This site wouldn’t exist if Anthony Watts had accepted that. Neither would Climate Audit, or Jo Nova’s site, or many others.
Climate skepticism wouldn’t have gotten this far if we had adopted the attitude of the opposition as you have done, assuming you are “on our side”. And from the obvious mistakes you are making, I’ll need more assurances that you’re an authority, on much of anything, than your imperious decree.
with regard to the formulated relationship between Temperature and CO2 I believe I have seen both the symbols LN and LOG used, where the base has not been made explicit, at least to the extent I have examined. I typed both as CAPS simply to make clear of the letters I used, the two variants are shown in formulas as lower case.
thus, I think the natural log ( base e ) is correct with regard to this formulated relationship.
yes, or no ?
Whoops, I said on May 19, 2013 at 1:39 am:
I pulled the same mistake as you, that should be “doubled derivative“, not “differential”. Sorry about that, Greg!
From Steve on May 19, 2013 at 1:39 am:
ln(2)/ln(10) = 0.301029996
log(2)/log(10) = 0.301029996
ln(15)/ln(8) = 1.302296865
log(15)/log(8) = 1.302296865
ln(1)/ln(2) = 0
log(1)/log(2) = 0
(trivial case)
As Dr. Orssengo’s equation used a log over a log of the same base, although I’d agree “ln” should indicate base e, it doesn’t matter. You could use logs of base 7 or base pi, you’d get the same result, when the base is the same it “cancels out”.
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.
kadaka “From A Handbook of Numerical and Statistical Techniques: With examples mainly from the life sciences by J.H. Pollard, 1977, starting at pg 26, Simple methods of smoothing crude data:”
Well if your understanding of data processing and filter design is based on “life sciences” text books I am not surprised you do not understand the subject.
I try avoid the use of the word arrogant , it can easily backfire.
“Thus the usual sage advice is to only use a running average big enough to “smooth” noisy graph data, as for visual clarity, but stop before you introduce artifacts.”
“Your wonderful “triple filter” hugs no better than a simple 30-mo running average, said value being the largest of the ones you specified, while it loses much detail, for no benefit.”
Filters are not designed to “hug” neither is their only function “visual clarity”. Your whole language and attitude shows you have no understanding of data processing or filtering yet you continue to get excited and call me arrogant because I do.
I told you why running mean was bad but it obviously was beyond your comprehension, so you just ignored what I explained and carry on shouting even louder.
This subject was one I have wanted to write a post about for a while so here is a brief explanation
http://climategrog.wordpress.com/2013/05/19/triple-running-mean-filters/
Re: RACookPE1978 – May 19, 2013 at 12:04 am
You added the span of years for each epoch in my post. They would have ranged from 28 to 37 years except that you broke the last and most recent span of 37 years down to 20 and 17 respectively. Obviously you wanted to point out the lull that’s been going on for a long time now. But yes, adding the span of years is a good idea.
Hadcrut4 has 2010 as the high point which is what I used. So I should have said 2010 instead of 2012. The 1976 value is -0.24 and 2010 is 0.54. The difference is 0.78 which I rounded off to 0.8. Had I used the very last year in the time series, 2012, I would have gotten 0.7, but I was picking off high & low points.
Yes, I see I have a typo! CO2 for 1976 is 332 ppm and for 2010 it’s 390 ppm for a difference of 58 ppm not 48.
Thanks for your comments, I’ll correct the ppm error since 1976 and stew about what to use as an end point if I post this elsewhere.