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.) http://www.grida.no/climate/ipcc_tar/wg1/222.htm E is change in forcing using the derivative of Stefan-Boltzmann: dT/dE = 1/(4[sigma] T^3) gets: 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=5.35ln2/(4*5.6705E-08*(288.16^3)) or 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 http://www.escribe.com/science/ClimateChangeDebate/m13965.html~~Hans Erren 19 feb 2002Note 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, 10.1029/2002GL015345Note 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 | 0.16 | 0.42 | 0.61 |

K/Wm-2 | 0.000 | 0.189 | 0.282 | 0.750 | 1.079 |

mK/decade | 0 | 44 | 65 | 173 | 254 |

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.

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

http://geoflop.uchicago.edu/cgi-bin/modtran3a.cgi?pco2=370&ch4=1.7&trop_o3=28&strat_o3=1&Toffset=0&h2otscaled=0&h2orat=1&model=1&icld=0&altitude=100&i_obs=180&runlabel=start370ppm&i_save=0

2) CO2 Doubling 740 ppm

http://geoflop.uchicago.edu/cgi-bin/modtran3a.cgi?pco2=740&ch4=1.7&trop_o3=28&strat_o3=1&Toffset=0&h2otscaled=0&h2orat=1&model=1&icld=0&altitude=100&i_obs=180&runlabel=double740ppm&i_save=0

3) 740 ppm surface increased 0.9 K

http://geoflop.uchicago.edu/cgi-bin/modtran3a.cgi?pco2=740&ch4=1.7&trop_o3=28&strat_o3=1&Toffset=0.9&h2otscaled=0&h2orat=1&model=1&icld=0&altitude=100&i_obs=180&runlabel=constantH2O&i_save=0

The 0.9 K is exclusive water vapour feedback.

But try this...

4) 740 ppm with constant RH increased 0.98 K

http://geoflop.uchicago.edu/cgi-bin/modtran3a.cgi?pco2=740&ch4=1.7&trop_o3=28&strat_o3=1&Toffset=0.98&h2otscaled=1&h2orat=1&model=1&icld=0&altitude=100&i_obs=180&runlabel=constantRH&i_save=0

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.

(?)

Noteadded 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. http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org: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=5.35ln2/(4*5.6705E-08*(255.15^3))

or

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 ? http://http://home.casema.nl/errenwijlens/co2/howmuch.htm homepage: http://home.casema.nl/errenwijlens

page updated 13 march 2008