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Doubling CO2 log curves 
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#1
Jun2314, 09:39 AM

P: 143

The IPCC uses a figure 1.2°C for the direct response to a doubling of CO2,
from 280 ppm to 560 ppm. http://www.grida.no/climate/ipcc_tar/wg1/pdf/tar01.pdf I came up with an equation of 4(log 560)4(log 280)= 1.2041199. Is this the best way to fit this curve? 


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#2
Jun2414, 11:44 AM

P: 1,398

To compute the direct response for a doubling of CO2, you have to calculate the radiative forcing first, and then the temperature increment using the fact that the radiaton is proportional to the 4th power of the temperature The second calculation isn't too hard, but the first calculation involves detailed calculations, involving  different wavelengths  the temperature and pressure at different heights.  averaging seasons  averaging different latitudes  other greenhouse gases, espescially water vapour.  clouds. A really simple model of this process doesn't seem to work. A program used for the radiation calculations is called MODTRAN. According to chapter 6 of the IPCC report this comes to 3.7 W/m^2 Since the total outgoing IR radiation is 240 W/m^2, this means that the outgoing radiation has to go up by a factor 3.7/240 = 1.0154 and the absolue temperature has to go up by a factor (1.0154)^(1/4) = 1.0038. Multiplying this with the absolute temperature in kelvin you get 1.0038 * 288 = 289.1 K, so the temperature has to go up by 1.1 K. 


#3
Jun2414, 12:55 PM

P: 143

The 1.2°C number is from the IPCC cited Baede et al, and is based their radiative forcing calculation.
log equation was the best way to fit the doubling curve. 


#4
Jun2414, 03:19 PM

P: 1,398

Doubling CO2 log curves



#5
Jun2414, 03:37 PM

P: 143

based on the described response of CO2 of 1.2 °C for each doubling,
it would look like this, increase from 140 to 280 ppm 1.2 °C from 280 to 560 ppm 1.2 °C from 560 to 1120 ppm 1.2 °C The function is not a straight line. The log function I used seems to fit (within the ±10% anyway) I am wondering if there is a better way to fit a function to this curve? 


#6
Jun2414, 05:55 PM

P: 1,398

[tex] \Delta T = (1.2) \frac { log\frac{C}{280}} {log 2}[/tex] where C is the CO2 concentration in ppm exactly fits all the data points you mentioned. You can even use logarithms to any base. I think the idea of CO2 doubling was only introduced because more detailed calculations show that the radiative forcing is approximately proportional to the log of the CO2 concentration. 


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