Arrhenius was wrong

It is widely believed that Svante Arrhenius correctly predicted
the rise in temperature. Perhaps you are unaware that he did this 
based on seriously flawed spectroscopic data.

His basic formula was derived from the Stefan-Boltzmann equation

Equation (3) in (Arrhenius, 1896) reads:



eqn3 
 Where K = a constant

   n = 1-albedo

   b = atmospheric IR absorption

for transparency (1-b) he used table III 
Table III 


see also: http://hps.elte.hu/~zagoni/Arrh2.htm


Arrhenius assumed that n is 0.925 for the "water covered parts". 
Quote: "For the earth's solid crust we may without sensible error
put n equal to 1, if we except the snowfields, for
which we assume n=0.5."

The present accepted value for the earth's albedo is 0.39, 
which corresponds to n = 0.61.

I calculated spectral emissivity using modtran 3 
for [CO2]=370ppm and [CO2]=740ppm, using a tropical temperature profile
http://geosci.uchicago.edu/~archer/cgimodels/radiation.html

CH4 = 1.7 
Tropospheric Ozone (ppb) = 28 
Stratospheric Ozone Scale Factor = 1 
T offset = 0 
Constant Water Vapor Pressure 
H2O vapor twiddle factor = 1 
Tropical Atmosphere Model 
No Clouds 
Sensor Altitude = 100 Looking down 

[CO2] = 370 ppm
INTEGRATED RADIATION ENERGY FLUX= 287.875W/m2 
BOUNDARY TEMPERATURE = 299.70 K
EMISSIVITY = 0.6293 

[CO2]=370 ppm 


[CO2] = 740 ppm
INTEGRATED RADIATION ENERGY FLUX= 284.672W/m2 
BOUNDARY TEMPERATURE = 299.70 K 
EMISSIVITY = 0.6223 

[CO2]=740 ppm 


BLACKBODY: 
T=299.7 K FLUX 457.44W/m2 

Using Arrhenius with these modern day spectra: 


T4 = K/(1+ne)
 
where n = 1-albedo = 0.61 and e emissivity,
follows K= 9540491123 for T=288.15 K (15 oC)







[CO2](ppm) 
e 
T (oC) 





370
0.6293 
15




740
0.6223 
15.22270447





We see that Arrhenius gives us a temperature increase of 0.22 K
for CO2 doubling....

Arrhenius was convinced that the atmosphere would be 
opaque for IR at levels of 40x C02. He clearly based himself on 
the wrong CO2 IR spectrum:

Spectrum comparison 

Finally a comparison between the absorption values for CO2 for different
publications: Arrhenius 1896 (derived from Lunar spectrum), Arrhenius 1901
(laboratory measurements) and a modern calculation using Modtran3.
The 1896 values are clearly to high.

Arrhenius vs. Modtran 

 
see also
http://home.casema.nl/errenwijlens/co2/arrhweart.htm
and
http://home.casema.nl/errenwijlens/co2/arrhenius.html

Hans Erren
 
 Ref:
Svante Arrhenius, 1896, On the Influence of Carbonic Acid in the Air upon the
Temperature of the Ground, The London, Edinburgh, and Dublin Philosophical
Magazine and Journal of Science [fifth series] April 1896. vol 41, p237-275

Svante Arrhenius, 1901, Ueber die Wärmeabsorption durch Kohlensäure, Annalen
der Physik Bd 4. 1901, p690-705.




this page:
http://home.casema.nl/errenwijlens/co2/arrhrev.html

homepage:
http://home.casema.nl/errenwijlens