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Back of the envelope calculations

Hello all,
I hate to post so soon after joining, but this seems like the place to ask the question I've had for several years now. I used to follow John's postings on Usenet back before there was a WWW, and the sort of "physicist's reasoning" is what I'm looking for here.

Does anyone have (or know of) a back-of-the-envelope, semi-quantitative, calculation of the expected sizes of the major climate feedback loops? At the very least, one ought to be able to put together a physics colloquium style one hour presentation that "does the math" on climate change. There are so many screechy voices (on both sides) that it sure would be nice to have a ready, coherent argument that captures the physics and sets a scale to the effects.

I know that there are many detailed analyses, and no back-of-the-envelope is going to capture everything in a full-up computer model. But I'm a physicist and not a climatologist. It just seems that we ought to be able to capture the major features in a bit of math and physics reasoning. I'm mindful of Feynman's admonition that "we don't understand anything until we can explain it to a barmaid." How would Feynman's chapter on climate change have looked?

Thanks!
-Brian

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1.

Hello Brian,

I think that's an interesting question to which I would like to find an answer as well.

My first guess would be: burning of carbon -> rise of $CO_2$ (-> lagged sequestration by oceans) -> greenhouse effect. I'm already ignoring changes in cloud formation due to changing temperatures and no doubt there are other essentials I am not aware of. But perhaps we could chose our time scales conveniently to brush some loops under the carpet...

A small digression: for laypeople I usually compare climate change to the human body and food: if you would eat+exercise exactly the same as before (with temporal variations that average to zero), and then add a few biscuits to your daily consumption, most people immediately conclude that "you will get fatter". But the body is a complex system with many feedback loops as well and then they usually start to agree on the greenhouse effect... But if the laypeople appreciate science I then add: if one would eat several ounces of vegetables extra every day (with the amount of vegetables containing the same energetic value as the amount of biscuits) other feedbacks may be triggered - and perhaps you will lose weight! Nevertheless, I think it's reasonable to assume the rise in weight, as a first hypothesis for the consequence of the uptake of additional energy, especially if this is what you're measuring on the weighing scale!

Frederik

Comment Source:Hello Brian, I think that's an interesting question to which I would like to find an answer as well. My first guess would be: burning of carbon -> rise of $CO_2$ (-> lagged sequestration by oceans) -> greenhouse effect. I'm already ignoring changes in cloud formation due to changing temperatures and no doubt there are other essentials I am not aware of. But perhaps we could chose our time scales conveniently to brush some loops under the carpet... A small digression: for laypeople I usually compare climate change to the human body and food: if you would eat+exercise exactly the same as before (with temporal variations that average to zero), and then add a few biscuits to your daily consumption, most people immediately conclude that "you will get fatter". But the body is a complex system with many feedback loops as well and then they usually start to agree on the greenhouse effect... But if the laypeople appreciate science I then add: if one would eat several ounces of vegetables extra every day (with the amount of vegetables containing the same energetic value as the amount of biscuits) other feedbacks may be triggered - and perhaps you will lose weight! Nevertheless, I think it's reasonable to assume the rise in weight, as a first hypothesis for the consequence of the uptake of additional energy, especially if this is what you're measuring on the weighing scale! Frederik
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2.

Brian, I am not sure what you are looking for, but maybe it is already on the wiki at climate model or climate feedback. The former has links to Section 8.6 of the AR4 WG1 report for model estimates and Section 9.6 for observational estimates. A simple summary of those would be nice, extending what is at climate feedback.

Comment Source:Brian, I am not sure what you are looking for, but maybe it is already on the wiki at [[climate model]] or [[climate feedback]]. The former has links to Section 8.6 of the AR4 WG1 report for model estimates and Section 9.6 for observational estimates. A simple summary of those would be nice, extending what is at [[climate feedback]].
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3.
Graham,
Thanks for the links -- I thought I looked for stuff before I posted, but I obviously missed that.

It's close, but not really what I'm looking for. Why should dT/dt = k(F + LT), other than that is the simplest linear equation we can write? Maybe that's good enough, but I'd like something a little more physical.

I think the thing to do is to start with the energy conservation. If there's one thing we can count on, it's energy conservation, right? The feedback-free Stephan-Boltzmann relation gives an equilibrium temperature -- I've seen that done somewhere, and it comes out with something like -18C, if I recall. Then I'd like to build out the feedback terms, and show how the equilibrium point changes. It seems like one should be able to polish this line of reasoning into something very concise, but I haven't found it. Once in hand, it would readily end any debate with anyone who believes in math.

I'll try to work it out myself (unless anyone wants to collaborate with me) but as I have a day job, I may not get to it very quickly. I was hoping to cheat by copying off of someone else's paper. :)
Comment Source:Graham, Thanks for the links -- I thought I looked for stuff before I posted, but I obviously missed that. It's close, but not really what I'm looking for. Why should dT/dt = k(F + LT), other than that is the simplest linear equation we can write? Maybe that's good enough, but I'd like something a little more physical. I think the thing to do is to start with the energy conservation. If there's one thing we can count on, it's energy conservation, right? The feedback-free Stephan-Boltzmann relation gives an equilibrium temperature -- I've seen that done somewhere, and it comes out with something like -18C, if I recall. Then I'd like to build out the feedback terms, and show how the equilibrium point changes. It seems like one should be able to polish this line of reasoning into something very concise, but I haven't found it. Once in hand, it would readily end any debate with anyone who believes in math. I'll try to work it out myself (unless anyone wants to collaborate with me) but as I have a day job, I may not get to it very quickly. I was hoping to cheat by copying off of someone else's paper. :)
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4.

Hi Brian,

what you mention sounds like an energy balance model, I've been learning about this stuff from the book "A Climate Modelling Primer", see Recommended reading.

Comment Source:Hi Brian, what you mention sounds like an [[energy balance model]], I've been learning about this stuff from the book "A Climate Modelling Primer", see [[Recommended reading]].
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5.

Hi Brian,

I think I misunderstood your question, I thought you were rather looking at the fast response of the temperature due to human carbon emissions (for which I thought we would not need all feedback mechanisms). So if I'm correct you want a "long term" model with the major feedback loops (but not too long such that plate tectonics can be neglected) depending on atmospheric carbon dioxide concentration, among others?

The feedback-free Stephan-Boltzmann relation gives an equilibrium temperature -- I've seen that done somewhere, and it comes out with something like -18C, if I recall. Then I'd like to build out the feedback terms, and show how the equilibrium point changes.

I think it would be very interesting to have such a calculation here, but I'm unsure how precise you could get the temperature (-18°C seems quite close). Given that a few degrees difference already have drastic ecological consequences, the physical back-of-the-envelope may be insufficient to convince people that human emissions can lead to a few degrees difference. (I guess they may say that the proposed model isn't good enough either to discuss centidegrees' differences)

Frederik

Comment Source:Hi Brian, I think I misunderstood your question, I thought you were rather looking at the fast response of the temperature due to human carbon emissions (for which I thought we would not need all feedback mechanisms). So if I'm correct you want a "long term" model with the major feedback loops (but not too long such that plate tectonics can be neglected) depending on atmospheric carbon dioxide concentration, among others? > The feedback-free Stephan-Boltzmann relation gives an equilibrium temperature -- I've seen that done somewhere, and it comes out with something like -18C, if I recall. Then I'd like to build out the feedback terms, and show how the equilibrium point changes. I believe I've heard about this -18°C too... This was with the atmosphere already included? I think it would be very interesting to have such a calculation here, but I'm unsure how precise you could get the temperature (-18°C seems quite close). Given that a few degrees difference already have drastic ecological consequences, the physical back-of-the-envelope may be insufficient to convince people that human emissions can lead to a few degrees difference. (I guess they may say that the proposed model isn't good enough either to discuss centidegrees' differences) Frederik
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6.

I think it would be very interesting to have such a calculation here, but I'm unsure how precise you could get the temperature (-18°C seems quite close).

This is a calculation using a zero-dimensional energy balance model from the primer, I've been planning to add it to the EBM page, but became distracted - maybe I'll do it today, unless I'm too tired when I get home :-)

Comment Source:<blockquote> <p> I think it would be very interesting to have such a calculation here, but I'm unsure how precise you could get the temperature (-18°C seems quite close). </p> </blockquote> This is a calculation using a zero-dimensional energy balance model from the primer, I've been planning to add it to the EBM page, but became distracted - maybe I'll do it today, unless I'm too tired when I get home :-)
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7.
I calculated the -18C last night; I'll post after I learn the difference between Itex and LaTeX. Found the help page, just gotta read it...
Comment Source:I calculated the -18C last night; I'll post after I learn the difference between Itex and LaTeX. Found the help page, just gotta read it...