## Wednesday, May 19, 2010

### CO2 Doubling Temperature

One claim made by climatologists is that each doubling in the concentration of CO2 will cause the same increase in the Earth's surface temperature. So far as we can tell, the basis for this claim is that the absorption of radiation by greenhouse gases is "logarithmic". See Nelson, Earthguide and Wikipedia for examples. We never understood this "logarithmic" argument. We have never seen any calculations to back it up.

The greenhouse effect in our Planetary Greenhouse example is the result of logarithmic absorption by a greenhouse gas. The atmosphere contains a hypothetical gas that is opaque to some, but not all, long-wave radiation. As we showed in our previous post, successive doublings in the concentration of this gas do not cause the same increase in surface temperature. Indeed, the graph produced by our computer program shows that each successive doubling causes half as much warming as the previous doubling.

Thus logarithmic absorption alone is not sufficient justification for the existence of a "CO2 Doubling Temperature".

1. Tom Nelson, author of The Cold Facts About Global Warming was kind enough to comment upon my bold claim about CO2 doubling temperature, and I include the text of his letter below.

Dear Mr Hashemi,

Thanks for your feedback. I looked at the blog page you mentioned.
It was not 100% clear to me from reading these blog-style pages exactly what went into your calculations, but it seems to me that your conclusion that doubling CO2 would cause a 13K increase is too high. Even the wildest projections of the IPCC at the height of the CO2 mania never exceeded 9 degrees.

Does your program take water vapor into account? All greenhouse gases together, including water vapor, only raise the temperature 33 degrees.
Consider what happens in your model if you halve CO2 a few times. Even halving it once would cause a decrease of at least 24 degrees. In fact,
your curve appears to have an asymptote at CO2=0.

You also assume that water molecules absorb infrared radiation the
same way in water vapor and liquid water. This is not true: the
absorption spectra of gases are qualitatively quite different from liquids. Many people have tried to treat the Earth as a black body and reached wildly different conclusions from you and from each other. That's not to say yours are necessarily wrong, but it may be that
small changes in your assumptions will produce dramatically different conclusions.

Tom Nelson

2. Dear Dr. Nelson,

Thank you for your attention to my claim.

> it seems to me that your conclusion that doubling CO2 would
> cause a 13K increase is too high.

I'm not modeling the Earth yet. I'm approaching the problem in steps, starting with the simplest Extreme Greenhouse and now moving on to a Planetary Greenhouse, which contains a hypothetical simplified greenhouse gas in an atmosphere that drops in pressure to infinity. The gas is transparent below 13 um and has a constant absoption lenght above 13 um.

What I show is that the logarithmic nature of absorption is not a sufficient argument for a constant doubling temperature.

> Does your program take water vapor into account?

As you can see: it does not, but that is deliberate and water vapor is not necessary for my claim.

> In fact, your curve appears to have an asymptote at CO2=0.

The graphs are labeled according to the tropopause pressure in kPa, which is inversely proportional to the greenhouse gas concdentration in ppm. And, for the record, the gas is not CO2, it's the hypothetical greenhouse gas I mentioned.

The tropopause is the layer of the atmosphere that radiates heat into space, by virtue of the fact that the air above is so thin that it is transparent. The higher the greenhouse gas concentration, the less the weight of air above the tropopause. And the weight per square meter is the pressure.

Thus the tropopause pressure drops with increasing greenhouse gas concentration. Air rising by convection to the tropopause cools more by adiabatic expansion because it drops more in pressure. The tropopause temperature drops. The power radiated by the tropopause drops as the 4th power of the temperature. Eventually the heat radiated by the tropopause is negligible compared to the heat radiated directly through the atmosphere by the planet. Further doubling in greenhouse gas concentration brings successively smaller rises in surface temperature.

> You also assume that water molecules absorb infrared radiation the
> same way in water vapor and liquid water.

I discuss that assumption in one post, but later present plots from my astronomer friends that show how water vapor behaves differently. I will start to discuss water vapor in the context of the Planeteray Greenhouse soon.

Yours, Kevan