# Beginners question: is my calculation CO2 temp. increase correct?

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Posted (edited)

Hello all,

I live in Netherland, Europe. I dive a hybrid car and I have 3.2 kWp of solar panels on my roof. I do not use natural gas for heating but an air/air heatpump with a COP of 5.0. So yes, I do believe in climate change and that it is (at least partially) caused by human activity.
At a party I met some one who called himself a climate skeptic, he did believe that climate change was a fact but not that it was significantly influenced by mankind. He challenged me to calculate what effect (increase in temperature) a doubling of CO2 would have on the climate. And that is what I did, or at least tried to do, a few days later. And to my surprise it was very little, much less than I had expected at least.

I am probably making a mistake somewhere along the way. Hopefully you can point me in the right direction. Just to be clear: this is only the rise in temperature caused by CO2. Not the effect this in turn would have on water vapor or anything else. I know the atmosphere consist of various layers and is much more complex in reality but I would like to keep this example as simple as possible, so I also use nice round numbers. We use the metric system here so I will use degrees Celsius.

The average temperature (summer/winter) on earth is about 15 degrees. Up into the tropopause the lowest temperature can reach –58 degrees. If you go higher, into the stratosphere it gets warmer again. So within this range of approx. 72 degrees Celsius an increase of CO2 would have an effect on the temperature. CO2 reflects infrared light more and thus slows down heat from traveling into space. The thermal conductivity of CO2 is about 36% lower than that of oxygen or nitrogen en therefor it is a greenhouse gas.
So let’s assume there is an increase of 400 ppm CO2. That would mean 400/1000000th part of the atmosphere conducts heat 36/100th less over a total of 72 degrees that would result in a temperature difference of 0.010368 degrees Celsius.
In my highly simplified atmosphere, it would cool down near the stratosphere by half of that and in the lower troposphere is would heat up by about 0.005 degrees Celsius.

That is much less than I had expected but maybe it is correct. If not, where am I going wrong? Please keep in mind that I am new to this subject. Maybe this question has been asked before but I could not find it on the forum. If so please put a link to the thread. Thanks!

Edited by Herman

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swansont    6248

The effect of CO2 is not conduction, so the conductivity is not the right parameter to look at. It's radiation: re-radiating infrared that's emitted by the earth.

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Posted (edited)

The effect of CO2 is not conduction, so the conductivity is not the right parameter to look at. It's radiation: re-radiating infrared that's emitted by the earth.

Thanks. But wouldn't a re-radiation of, let's say a third of infrared particals, result in a reduction in heat conductivity of 33%?

Edited by Herman

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swansont    6248

Thanks. But wouldn't a re-radiation of, let's say a third of infrared particals, result in a reduction in heat conductivity of 33%?

It's not conduction.

The earth is radiating some amount of power. CO2 absorbs some and sends some of the back to earth. If you increase the concentration, more radiation is intercepted, closer to the earth, and some radiation that previously escaped does not.

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...CO2 absorbs some and sends some of the back to earth. If you increase the concentration, more radiation is intercepted, closer to the earth, and some radiation that previously escaped does not.

Because radiation in itself is not dependent on a medium (it can travel though a vacuum) I assumed it had to be the ability to, either more or less, absorption of infrared radiation within a gas. Meaning: the abilty to pass on energy of molecular motion on to other molecules. Thus, thermal conductance of gases. That was my reasoning, it seems I have gone wrong there. Is there another way I can calculate the increase in temperature?

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swansont    6248

Another way of looking at why it's not conduction is that the mechanism doesn't involve heating up the CO2 molecules.

The calculation of whether or not a photon is absorbed (probability) is straightforward. The issue here, though, is that in the absorption bands, the atmosphere is already "optically thick", i.e. the chance of absorbing a photon is already essentially 100%. A photon will scatter many times along its way, whether that leads to escape or re-absrpotion by the earth. What you are doing by adding more CO2 is shortening the average distance a photon goes before absorption, leading to more scatters. It's a much more complicated situation than if you were going from e.g. 10% absorption to 20%.

This analysis might be described in detail in some paper, but I can't point you toward which one.

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Posted (edited)

....What you are doing by adding more CO2 is shortening the average distance a photon goes before absorption, leading to more scatters. It's a much more complicated situation than if you were going from e.g. 10% absorption to 20%....

I'm beginning to understand now. Thanks a lot swansont, I really appreciate your patience. I was basically trying to calculate it using 'old fashioned' thermodynamics and that simply does not explain global warming. At my age, 58 yo, high school is a long time ago and a lot has changed since then. But new things always interest me.

I could not find a website which can explain GW clearly in laymen's term so everybody can understand it. In this part of the world there are not many people who doubt global warming. Maybe a few who think human activity is not as much an influence as expected but they will still agree it is better for the invironment to switch to durable energy sources. In this country the feed-in tariff is the same a you pay per kWh and the government just deceided to extend that to at least 2023. Wind power is also getting a boost, they plan to add two big wind farms in the sea just off the shore.

Thanks again, I have a lot to read and catching up to do. If you know of a website that is great for beginners on this subject, please let me know.

Edited by Herman