# Any Climate Change from Doubled CO2?

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In our exploration of blackbody radiation we have been led to the idea that the temperatures of different blackbodies in radiative contact are measured by comparison with a reference blackbody used as a thermometer defining the temperature scale for each blackbody. Effectively, this gives a Planck law of the form (with simplified cut-off)

• $R(T,\nu )=\gamma T\nu^2$ for $\nu$ $<\frac{T}{h}$,
• $R(T,\nu )= 0$ for $\nu$ $>\frac{T}{h}$,,

where the  constants $\gamma$ and $h$ are independent of the composition of the blackbody and thus can be viewed as universal constants. This is the universality of blackbody radiation which attracted Planck’s universal mind, see Chap 12 of Mathematical Physics of Blackbody Radiation.

The temperature $T$ for a given blackbody can then be seen as a measure of the energy of each internal degree of freedom as a vibration mode of a certain frequency, assuming all frequencies have the same temperature. Temperature will be a measure of radiation capacity rather than an intrinsic measure of internal energy.

Assume now for the discussion that atmospheric CO2 acts as a blackbody (in a certain frequency range). We are then led to the following conclusions, since by universality the radiative effect of CO2 would be independent of concentration:

1. Even if CO2 is only a trace gas it can have an effect on the radiative balance of global climate.
2. This effect does not change with the concentration of CO2.

Here, 1 is used by alarmists to send the alarm that a trace gas can upset the whole climate system.

On the other hand, 2 tells us that doubling CO2 will not give more effect than the present effect and if the present effect is not worrisome, then there is nothing to worry about.

This discussion connects to the dip in the spectrum of OLR shown in the above figure, which can be viewed as a measure of the radiative effect of CO2, and the fact that the dip changes very little with doubled CO2: The bottom remains fixed (saturation) while arguments are put forward that the “shoulders” possibly could get a bit broader by more CO2 expressed by a weak logarithmic dependence.

Conclusion: CO2 as a trace gas has an effect on global climate, but the effect is independent of the concentration of CO2 and thus will not change by doubling. Thus no climate change from doubled CO2.

This is one argument of many indicating that climate sensitivity as global warming by doubled CO2 is so small that it cannot be detected.