How does CO2 respond to temperature ?

The response of co2 on temperature is approximately 10 ppm/degC

Quick and dirty approach:

Vostok ice core:
  minco2 183.9 ppm
  maxco2 299.5 ppm
  mintemp -8.49 degC
  maxtemp 3.26 degC

  temprange 11.75  degC
  co2range 115.6  ppm

  response 9.838298  ppm/degC

The effect of CO2 on temperature is the Arrhenius law.
dE=[alpha]ln([CO2]/[CO2}orig), where alpha is 5.35 (Myhre et al.)

E is change in forcing
using the derivative of Stefan-Boltzmann:
dT/dE = 1/(4[sigma] T^3)
dT=[alpha]ln([CO2]/[CO2}orig)/(4[sigma] T^3)

This is the equation without all feedbacks.

(Scroll down for "corrigendum" :-D )
Substituting a doubling CO2 level (unrealistic, according to Lomborg)
and substituting T= 15 degreesC = 288.16K
dT=0.6833 centigrade for a doubling of CO2 !!

That's physics. All the rest is models and hype.

Adding to the fact that [alpha] is derived from historic
surface temperatures, which trend is imho grossly overestimated.
This will bring [alpha] down even further, and so dT.

see for comments

Hans Erren 19 feb 2002

Note added 19 march 2003:
If we take the Mauna Loa CO2 data and assume a lower troposphere temperature of 250K
we get:

Which matches the "unknown linear effect L" of Douglas and Clader, 2002.
ref: Myhre, G., E.J Highwood, K.P Shine and F. Stordal, 1998, New Estimates of radiative forcing due to well mixed greenhouse gases, Geophys. Res Lett. 25, 2715-2718 Keeling, C.D. and T.P. Whorf. 2002. Atmospheric CO2 records from sites in the SIO air sampling network. In Trends: A Compendium of Data on Global Change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A. Douglass, D.H. and B.D Clader, 2002, Climate sensitivity of the earth to solar irradiance, Geophys. Res Lett. vol 29, no. 16, 10.1029/2002GL015345 Note added 7 august 2003: The water vapour feedback by Arrhenius is only a factor 1.3. This was explained by him in 1901 and confirmed by Ramanatan and Vogelmann in 1997. Taking 3.7 W/m2 for CO2 doubling and the Stefan- Boltzmann equation gives us 0.6833 degrees warming (Erren, 2002). Including the water feedback gives 0.6833*1.3= 0.888 K Wich fits beautifully in Douglas Hoyt's empirical range of 0.5 - 0.9 K for CO2 doubling. Note added 7 February 2004:
Unit no trend Dietze / Hoyt Stefan-Boltzmann Hansen Arrhenius
K/2xCO2 0.00 0.70 1.05 2.781 4.00
K 1979-2003 0.00 0.11 0.160.42 0.61
K/Wm-2 0.000 0.189 0.282 0.750 1.079
mK/decade 0 44 65 173 254
Climate sensitivity expressed in different units and originating from different authors

Note: Arrhenius value is the water-free value, including water feedback his value becomes 5.3 K/2xCO2.

Now if we look at the recent report from the Exeter conference (page 4)

For example, limiting warming to a 2 C increase with a relatively high certainty requires the equivalent concentration of CO2 to stay below 400 ppm. Conversely if less certainty was required concentrations could rise to 550 ppm equivalent.
Which climate sensitivities are used by the Steering group? Taking a pre-eindustrial level of 275 ppm (generously low) a 400 ppm level amounts to a CO2 factor of 1.454545, using Myhre, yields a forcing of 1.985 W/m2. Claiming that a forcing of this strength yields a warming of 2 C implies a climate sensitivity of 1 K/Wm-2. Which exactly matches Arrhenius' dry value of 4K for CO2 doubling.. The 550 ppm value by the steering commitee equals a doubling of CO2, or a climate sensitvity of 2K/2xCO2. Which still needs a huge (water vapour) feedback. Refs: Arrhenius, S, 1901, Ueber die Wärmabsorption durch Kohlensäure, Annalen der Physik Bd 4. 1901, p690-705. Hoyt, Douglas, 2004, A Critical Examination of Climate Change, Ramanathan, V. and A.M. Vogelmann. Greenhouse effect, atmospheric solar absorption and the Earth's radiation budget: From the Arrhenius/Langley era to the 1990s. AMBIO, 26(1):38-46, 1997. International symposium on the stabilisation of greenhouse gases Hadley Centre, Met Office, Exeter, UK 1-3 February 2005, Report of the Steering Committee 3 Feb 2005 Hans Erren, Arrhenius was wrong, Note added 6 march 2005:
Another approach to calculate the climate sensitivity for CO2 doubling is using Modtran.

A doubling of CO2 from 370 to 740 ppm decreases outgoing flux from 287.875 W/m2 to 284.672W/m2, that's 3.2 W/m2. To restore this flux, a surface temperature increase of 0.9 K is needed. Which BTW means a dry CO2 doubling corresponds to 3.2 W/m2, which is substantially lower than Myhre(?)

Try these three modtran3 runs:

1) start run 370 ppm

2) CO2 Doubling 740 ppm

3) 740 ppm surface increased 0.9 K

The 0.9 K is exclusive water vapour feedback.

But try this...
4) 740 ppm with constant RH increased 0.98 K

Doubling leads to 0.9 K increase, water vapour feedback is 0.08K

So 0.98 K temperature increase for CO2 doubling inclusive water vapour feedback !

ref: UKweatherworld forum

Now have a look at this...
The most warming in the 20th century occured over central Siberia and Canada in winter.

This is how a vertical temperature profile looks over Barrow (Alaska) and Oimjakon (Siberia) in mid winter:

data from University of Wyoming

When a large temperature inversion near ground is occuring, this leads to the following observed infrared spectrum (look carefully at the bottom frame over the Antarctic):

In deep winter conditions the atmosphere spectrum has emission bands for CO2, so adding more CO2 leads to higher emission in winter, and subsequent cooling.


Note added 23 October:
Here is the update of Douglass et al. with a downloadable pdf
Douglass, David H, B. David Clader, and R.S. Knox , 2004, Climate sensitivity
of Earth to solar irradiance: update. Physics, abstract physics/0411002.

Note added 2 february 2006:
I've received several comments that the cental temperature should not be 15 degreesC, but the blackbody equilibruim temperature for incoming radiation. -18 degreesC
Applying this to the Myhre Stefan-Boltzmann equation yields:
T= -18 degreesC = 255.15K
dT=0.9843 centigrade for a doubling of CO2, agreeing with the above modtran results.

That's (better) physics. Still: all the rest is models and hype.

Note added 31 may 2007:
If we calculate the contribution of CO2 on the warming and cooling of the ice ages using a climate sensitivity of 1K/2xCo2 and 3K/2xCO2, this is the result:

So even with a high climate sensitivity the bulk of the warming in the ice ages is not caused by CO2(!)

Note added 28 december 2007:
A summary of the major published numbers on climate sensitivity as function of reference period.

For Shaviv see On Climate Sensitivity and why it is probably small

Shaviv, N.J., 2005. On climate response to changes in the cosmic ray flux and radiative budget. J. Geophys. Res. 110, A08105.

Stephen E. Schwartz, 2007, Heat capacity, time constant, and sensitivity of Earth's climate system, J. Geophys. Res., 112, D24S05, doi:10.1029/2007JD008746

Chylek P., U. Lohmann, M. Dubey, M. Mishchenko, R. Kahn, and A. Ohmura, 2007: Limits on climate sensitivity derived from recent satellite and surface observations. J. Geophys. Res., 112, D24S04, doi:10.1029/2007JD008740.

Petr Chylek & Ulrike Lohmann, 2008, Aerosol radiative forcing and climate sensitivity deduced from the Last Glacial Maximum to Holocene transition, Geophysical Research Letters, VOL. 35, L04804, doi:10.1029/2007GL032759

this page:
Erren, Hans, 2002-2008, How does CO2 respond to temperature ?


page updated 13 march 2008