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.
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Two comments:
1. The assumption that a complete quasi-60 year oscillation just happens to be within the temperature range being studied is silly. Did you capture one? And on what observational data do you stand on regarding that oscillation capture?
2. Furthermore, the measurement error related to any OLS trendline through such highly variable data must be calculated and reported. Easily done: Excel it.
Willis you beat me to it. Damn.
In 1896 Arrhenius estimated that a halving of CO2 would decrease temperatures by 4-5°C and a doubling of CO2 would cause a temperature rise of 5-6°C. In his 1906 publication, Arrhenius adjusted the value downwards to 1.6°C (including water vapor feedback: 2.1°C). Recent estimates from IPCC (2007) say this value (the Climate Sensitivity) is likely to be between 2 and 4.5°C. But Sherwood Idso in 1998 calculated the Climate Sensitivity to be 0.4°C, and more recently Richard Lindzen at 0.5°C. Roy Spencer calculated 1.3°C in 2011.
Willis, I think what he’s doing is assuming that the period of natural variation is (exactly) 60 years and thus by looking at (any) 60 period you should average out the cycle and get a more representative slope.
It’s a pretty crude way of fitting a 60y cosine + linear trend model to the data.
Crude but effective.
I would not say it was that rigorous and it has a lot of obvious weaknesses but it is a way to show what I have called “cosine warming”:
http://climategrog.wordpress.com/?attachment_id=209
Climate sensitivity is not a constant. It is variable and dependent upon other factors. That is due to the chaotic nature of climate. When near an attractor state it will be small. The further away it gets the higher it will be for any forcing.
Don Easterbrook says:
May 18, 2013 at 6:51 am
“…..Why don’t we do the same analysis for the period 1945 to 1977 and calculate how much COOLING occurs with increase in CO2? And why don’t we calculate for the period 1880 to 1915 how much COOLING occurs with increase in CO2?…”
Don, a good point. I believe if there is a CO2 signal and it is is concentrated in the last 60 years, then the downslopes of cooling periods should be reduced by the effect and the upslopes increased. Nowhere have I seen even this simple analysis because it looks like the slopes pre- CO2 main effect and post remain about the same.
Willis
“And just what is the “multidecadal oscillation” when it is at home? How are you “removing the warming rate due to the multidecadal oscillation” by calculating its linear trend? And how have you determined that we are in the “warming phase of the multidecadal oscillation”? Exactly when did said warming phase start, and when will it end?”
Willis
Here is the 21-years moving average GMST showing the multidecadal oscillation since 1880.
http://bit.ly/15WbhXW
The above result shows during the period from 1975 to 2005 the multidecadal oscillation (the 21-years moving average) was during its warming phase. It also shows the period for one complete oscillation is about 60 deg C. As this oscillation is natural, it must be removed from climate sensitivity calculation. This is done by calculating the trend for the secular long-term trend that is monotonic, not based on the 30-years least squares trend. For this, there are published results:
“…the rapidity of the warming in the late twentieth century was a result of concurrence of a secular warming trend and the warming phase of a multidecadal (~65-year period) oscillatory variation and we estimated the contribution of the former to be about 0.08 deg C per decade since ~1980.”
http://bit.ly/10ry70o
The secular (long-term non-period) warming rate of 0.08 deg C/decade above is identical to my approximate estimate given in my essay.
When the warming phase starts and ends can be seen as the 21-years moving average GMST crosses the secular GMST curve.
According to Nicola Scafetta:
“The climate system is clearly characterized by a 60-year cycle. We have seen statistically compatible periods of cooling during 1880-1910, 1940-1970, 2000-(2030 ?) and warming during 1850-1880, 1910-1940, 1970-2000.”
[See HadCRUT4 Global monthly mean temperature anomalies 1850-2013.09 (°C) + linear trends + 13 months mean (WoodForTrees – Observatorio ARVAL)]:
http://www.woodfortrees.org/plot/hadcrut3gl/from:1850/to:2012.84/plot/hadcrut3gl/from:1850/to:1880/trend/plot/hadcrut3gl/from:1880/to:1910/trend/plot/hadcrut3gl/from:1910/to:1940/trend/plot/hadcrut3gl/from:1940/to:1970/trend/plot/hadcrut3gl/from:1970/to:2001/trend/plot/hadcrut3gl/from:2001/to:2012.84/trend/plot/hadcrut3gl/mean:13
“Shouldn’t the trend over a complete 60 year cycle be zero?” Unfortunately not. The mean yes , not the “trend”. Again see the warming cosine.
http://climategrog.wordpress.com/?attachment_id=209
Girma’s calculation certainly will not give the correct result and it is a misrepresentation to say that is how the IPCC does it, though thier focusing on the last half of 20th c. is not far from the same thing.
It could be said that this is a parody of IPCC rather than a correction.
I would certainly hesitate to present such trivial and dubious calculation with a PhD nailed to the masthead.
BTW, I’ve never found out what Girma has a PhD in, maybe he would like to tell us.
Looking at derivates of SST and co2 is much more informative.
http://climategrog.wordpress.com/?attachment_id=223
Most of the inter-annual changes is explained by temperature causing CO2 out-gassing , not CO2 changing temperature.
http://climategrog.wordpress.com/?attachment_id=233
The short term proportionality between temp and rate of change of SST shows 1 degree deviation from equilibrium conditions causes 8 ppm/year of CO2 out-gassing from the oceans.
It also shows that there is a very rapid response time that pretty much destroys the IPCC’s claim of 100-1000 year residency of anthropogenic CO2.
Greg Goodman
Girma’s calculation certainly will not give the correct result
The fact is IPCC’s climate sensitivity estimate is 3 deg C and the non-feed back estimate is 1.2 deg C, and you can calculate these values directly from the data as described in my essay.
Girma,
In your third figure you display a straight line fit to curvy data; why not add the model fit on which you base your calculation, that is, the linear trend plus the 60 yr. oscillation?
Your title is misleading. What you have is a different estimate of climate sensitivity to CO2, not “how” the IPCC derived their estimate.
From richard telford on May 18, 2013 at 5:35 am:
But that section speaks of equilibrium climate sensitivity, while Dr. Orssengo is calculating dynamic values.
If you’re going to clutter up our comments with your theoretical debunkings, please do our host Anthony the courtesy of at least addressing the same topic.
Girma Orssengo rightly demonstrates that one cannot determine climate sensitivity empirically from observed changes in CO2 concentration and in global mean surface temperature unless one either studies periods that are multiples of ~60 years to cancel the transient effects of the warming and cooling phases of the Pacific and related ocean oscillations or studies periods centered on a phase-transition in the ocean oscillations.
However, one should hesitate to draw conclusions empirically over as short a period as 60 years: for it is the cry-babies’ contention that temperature feedbacks operate over various timescales out to 1000-3000 years (Solomon et al., 2009). This was one of the reasons why they sneered at Lindzen & Choi (2009, 2011), who studied sensitivity empirically over about 25 years.
You all are asking me the same question.
My result is based the following climate pattern of the 20th century:
http://bit.ly/15FKX0n
Another interesting feature of the rate of change plot is that d/dt( CO2 ) has a also taken a “pause” since 1997:
http://climategrog.wordpress.com/?attachment_id=223
ie CO2 is still rising but no longer accelerating. So if CO2 was driving temperature we would still be seeing rising temps.
On the other hand since is it rate of change of CO2 that is affected by temperature, this period confirms it is temp driving CO2 and not the opposite.
There is more to be gained from the long term relationship that shows a ratio of 4 rather than 8 between dT/dt and d2/dt2(CO2) .
That should tell us more about the proportion of emissions that do/don’t get absorbed and possible inverse effect on temps. This is probably a proportional+differential relationship that needs more thought and study.
I don’t think this is going to be explained by hacking about of WTF.org.
The problem with ‘averaging out’ the 60 year cycles is that it still doesn’t validate temperature as a function of CO2. We’ve been thawing out from the Little Ice Age for about 5 centuries, and most of that warming occurred BEFORE the sharp rise in CO2 emissions after 1945. The GISP2 Greenland ice core shows that temperatures in Greenland from 10,000 years ago to 1500 years ago were virtually all 1 to 2.5 degrees C warmer than present with ‘normal’ CO2 levels. These temperatures are for Greenland, not global, but they correlate very well with fluctuation of the world’s glaciers so they reflect global temperatures. How can anyone possibly defend calculating a global temp/CO2 function when temperature is clearly NOT a function of CO2 for 8,500 years? Such calculations are total nonsense!
Don Easterbrook
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.
It’s the drugs !
This is a fundamentally wrong calculation. You must take account of the thermal inertia. Otherwise, you largely underestimate the sensitivity. This is first year heat transfer physics by the way,
In addition, fitting a long period oscillation will remove some energy form the linear component even if the true periodic signal is zero because both function are not necessarily orthogonal on such period of time. Basic, Fourier analysis. First year again.
plakat1 says:
May 18, 2013 at 6:45 am
The point was that the IPCC are making things look bad to stop us ordinary people using up the worlds resources. The super rich want it all for themselves.
Monckton of Brenchley says: “This was one of the reasons why they sneered at Lindzen & Choi (2009, 2011), who studied sensitivity empirically over about 25 years.”
LC2011 looked at very short snippets of time within that period. That probably tells us something useful but should not be read as being representative of longer periods.
I think the method was rigorous but care is needed in interpreting what it shows.
Girma says:
May 18, 2013 at 8:59 am
Don Easterbrook
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.
… then you should be looking at the derivative of CO2 not plain ppm 😉
http://www.woodfortrees.org/plot/hadsst2gl/from:1958/mean:12/mean:9/mean:7/derivative/normalise/plot/esrl-co2/derivative:0.003/derivative:-1.03/mean:12/mean:9/mean:7/normalise
Girma says:
Greg Goodman
Girma’s calculation certainly will not give the correct result
The fact is IPCC’s climate sensitivity estimate is 3 deg C and the non-feed back estimate is 1.2 deg C, and you can calculate these values directly from the data as described in my essay.
===
That does not mean that is how IPCC got there , neither does it mean the second result gives the correct sensitivity.
You are still including ‘cosine warming’.