Estimating the impact of CO2 on global mean temperature

[Skyhunter]

CO2 concentration is not set (in part) by temperature? Ocean uptake and release in particular is dependent on temperature.

http://www.learner.org/courses/envsci/visual/animation.php?shortname=anm_geocarboncycle

The carbon cycle on geologic time scales.
http://www.learner.org/courses/envsci/visual/vis_bytype.php?type=animation

 

[mheslep]

http://www.learner.org/courses/envsci/visual/animation.php?shortname=anm_geocarboncycle

The carbon cycle on geologic time scales.
http://www.learner.org/courses/envsci/visual/vis_bytype.php?type=animation

Thank you

 

[chriscolose]

CO2 concentration is not set (in part) by temperature? Ocean uptake and release in particular is dependent on temperature.

Of course, although this impacts sources and sinks and not CO2 concentration directly, and the corresponding changes in CO2 generally occur over much longer timescales. This is a function of the underlying biogeophysical boundary conditions, and it generally happens that changing the climate will change the chemistry of the atmosphere (through ocean solubility or weathering, etc on longer timescales), although there is no physical law which mandates it to do such. We live in a very fortunate circumstance with oceans and other processes which can keep CO2 well constrained in its atmospheric concentration. In the case of water vapor which has a very short residence time in the atmosphere, changing the global temperature will result in a roughly exponential change in the saturation vapor pressure allowing the H2O to condense and precipitate out once it builds up enough. In the case of CO2, there is really no limit (aside from fossil fuel reserves and economic activity) as to how much we can release and build up its atmospheric concentration, and that concentration will rise even if the temperature doesn't change beforehand. The increase in atmospheric water vapor is dictated by the Clausius-Clapeyron relation, which is a well-founded principle of physics.

 

[skypunter]

"Dark Matter" and "Dark Energy" are basically a placeholders for an unknown factor in the prominent theory of the universe, the big bang. Astrophysicists are quite honest about this unresolved discrepancy.
That is why the analogy is appropriate in terms of the "forcing" equation.

 

[chriscolose]

http://www.learner.org/courses/envsci/visual/animation.php?shortname=anm_geocarboncycle

The carbon cycle on geologic time scales.
http://www.learner.org/courses/envsci/visual/vis_bytype.php?type=animation

Interesting site, thanks.

 

[skypunter]

None of the radiative forcing arguments address the fact that the atmosphere circulates. There are two each of the Hadley, Polar and Ferrell cells of circulation. Heat laden air is constantly being carried aloft, above the majority of greenhouse effect, where it freely radiates IR into space. Not to mention the tremendous energy carried aloft by tropical cyclones and thunderstorms. These mechanisms are dynamic and vary according to temperature.
http://ess.geology.ufl.edu/ess/Notes/AtmosphericCirculation/7-11.jpeg

The radiative forcing graphic in post 66 is often presented today as a global energy balance equation. It's probably less than half of the story.

the magnitude of the leak shows that it HAS to be a significant part of the total reservoir losses.
(Sorry, haven't figured out how to quote multiple times.)

Consider that other porus strata may be feeding the lake additional water.

 

[mheslep]

None of the radiative forcing arguments address the fact that the atmosphere circulates. There are two each of the Hadley, Polar and Ferrell cells of circulation. Heat laden air is constantly being carried aloft, above the majority of greenhouse effect, ...

I think this is backwards. My understanding is the CO2 greenhouse effect of interest happens primarily at higher altitudes, as the high water vapor content at the surface makes the surface atmosphere nearly opaque to infrared, or a very effective water vapor dominated greenhouse effect if you will. So near the surface a major heat transfer mechanism is in fact the convection you mention. Convection moves heat up to higher altitudes, and it is there that the greenhouse effect due to CO2 can have its impact.

 

[chriscolose]

Actually this kind of heat transfer was considered even in early radiative-convective models since at least Manabe

 

[sylas]

(Sorry, haven't figured out how to quote multiple times.)

It's the same as using color. You just add quote tags rather than color tags. To do your quoting, simply put tags around quote text as follows (but using square brackets, of course):
{QUOTE=author}...text...{/QUOTE}

If you are using the "advanced" message editor, then look for the little button that looks like a speech balloon: https://www.physicsforums.com/Nexus/editor/quote.png .[/URL] That will put QUOTE tags around selected text.

If you are composing posts off-line (my preferred method) then you have to add the tags yourself directly, but you do need to watch that every {QUOTE} tag is followed by a {/QUOTE} tag at the end of the quoted material. It's not necessary, but you can also add the "=author" if you like, or even "=author;$#" where$# is the post number you are quoting. You get this for free if you just copy and paste of the quote tags given automatically when you first hit the "QUOTE" button to start your reply.

None of the radiative forcing arguments address the fact that the atmosphere circulates.

That is because this is not a source of energy, but a matter of how energy distributes.

It is most definitely considered in climate models; but you are now mixing up apples and oranges to a completely absurd degree. The circulation of the atmosphere makes no difference whatsoever to the simple physical fact that carbon dioxide is necessarily a crucial forcing driving current increases in global temperature.

Circulation shows up when you want to look at the consequences of temperature change and shifting climate patterns, and it is needed to model feedback processes within a dynamical system, and it is needed for looking at rates of change in response to forcing. But it doesn't do a damn thing for sorting out what forcings are driving the changes currently underway.

This is the red herring to end all red herrings. I am NOT trying to model climate here. I am simply giving a basic physical fact of the large impact of carbon dioxide. The effect of circulation is totally irrelevant to that topic. It's important for understanding climate. It is NOT a source of energy to force increasing temperatures. Stick to the topic.

The radiative forcing graphic in post 66 is often presented today as a global energy balance equation. It's probably less than half of the story.

It's a LOT less than half the story, if by the story you mean every last aspect of climate. That's why it only shows up in one chapter of the WG-1 report. But it is pretty much the whole story known at present if we are looking at what is forcing the changes in climate -- which is the topic of this thread.

You appear to be completely confused about following the different parts of this problem. No wonder you are so unable to distinguish what is known to high confidence from what is open research questions with high uncertainty.

the magnitude of the leak shows that it HAS to be a significant part of the total reservoir losses.

Consider that other porus strata may be feeding the lake additional water.

Still a red herring. It DOESN'T MATTER what other factors are involved, either positive or negative. If you have found one factor which has a total impact comparable to the total effect, then you HAVE to take that factor into account to get anywhere close to an explanation for the effect being considered. The comparison of magnitudes with the total effect is sufficient to show that the leak is necessarily significant. Stop trying to invent spurious analogies. It's a distraction. The role of an analogy is to help explain some concept with a related simpler example. It is NOT to invent new associations out of thin air and draw conclusions. It's for explanation, not for inference.

Can't you see that if you have an effect of about 5 Megalitres per day, and some factor which has an impact of about that magnitude, then this factor HAS to be significant? It's not a proof of being the "most" significant -- which is why the argument set out for discussion in this thread makes no attempt to prove CO2 is most significant.

Now in fact, as I have shown, if you are willing to go further and look at actual honest science attempting to consider at all the forcings involved, then you DO find that carbon dioxide is the largest single heating influence, by a substantial margin.

That's a fact as much as anything is a fact. It is not impacted in the slightest by irrelevant distractions such as circulation, or pushing analogies into something completely divorced from what we SEE when we honestly look at climate itself.

Cheers -- sylas

 

[sylas]

CO2 concentration is not set (in part) by temperature? Ocean uptake and release in particular is dependent on temperature.

Yes, that is true, but it is a rather long time scale effect. Chris Colose (in [post=2216203]msg #73[/post]) has given a good account of how time scales matter. The animations linked by skyhunter (in [post=2216169]msg #71[/post]) take this even further to the extremely long scales of the geological carbon cycle.

Here's a bit more detail, looking at a couple of examples that have shown up in the thread.

Climate is so complicated because there are a lot of interacting processes and they work on all kinds of different time scales. Speaking of the "equilibrium" makes a certain amount of good sense; but when you have a perturbation in the system, some things come to equilibrium faster than others.

(1) Very fast: stratospheric response

The temperature of the stratosphere responds very rapidly indeed to any change in radiant energy balance. There's not much circulation or heat capacity to complicate things. Hence, the formal definition of "radiative forcing" is a change in energy balance after the stratosphere has come to equilibrium. (See [post=2199572]msg #69[/post] of thread "Physics of Global Warming" for the formal definition and references.)

(2) Fast: water vapour

The humidity of the atmosphere depends largely on temperature. Industry adds a lot of water vapour to the atmosphere, and this doesn't actually have all that much effect; nothing like the effect of carbon dioxide -- even though the carbon dioxide is a weaker greenhouse gas. That is because when water levels are raised much above, or below, the natural equilibrium level, you rapidly get the equilibrium restored, as water evaporates back into the atmosphere or is precipitated out again.

This is the key to why water vapour is not treated as a "forcing" at all. When you add water vapour directly, it rains out again too quickly to have any extended climate effect. On the other hand! If you raise temperatures by some other means, then you change the natural equilibrium level of specific humidity... and the ocean adds the water vapour to match; and because this change is persistent, the additional water vapour contributes to the extended increase in temperature. That is -- this is a feedback process, not a forcing.

(3) Slow. The carbon cycle in the biosphere.

Just like there is a natural equilibrium of water vapour, so too there is a natural equilibrium for carbon dioxide, between atmospheric and oceanic carbon levels. The time it takes for atmosphere and ocean to relax back to equilibrium, however, is measured in many centuries. If this process was as fast as the water cycle, then all our industrial CO2 emissions would have only a small effect on atmospheric CO2 levels, because about 99% of what we added to the atmosphere would end up absorbed into the ocean.

What happens in practice is that about half of all the CO2 we have added since the development of industry has ended up in the ocean or other carbon sinks; and about half has ended up in the atmosphere. If we stopped adding CO2 tomorrow, most of the elevated CO2 levels would gradually relax back down into the ocean... but this would take at least a thousand years. There are multiple processes involved in restoring this equilibrium, each with their own characteristic time constant, and that makes the net relaxation time a rather complicated mathematical function.

This is where there is an important temperature impact. The natural equilibrium between ocean and atmosphere is temperature dependent. Now at present the atmosphere is a long way out of balance with the ocean; and so there is a steady net flux of CO2 into the oceans, at about half the rate of the flux of CO2 into the atmosphere from human industry. The temperature effect in the present, therefore, is mainly about the rate at which the ocean takes up carbon, and not about the equilibrium level, since it be at least another thousand years before there's any equilibrium.

For climate studies of interest to human society, therefore, carbon dioxide is treated as a forcing; and you estimate atmospheric carbon dioxide levels based on emissions and on models of how carbon is flushed back out into other sinks.

If someone wanted to make a very long scale model of climate for the ice ages of the quaternary period (time span of a million years or so, and time steps of a century or so) then carbon dioxide would show up as a feedback rather than a forcing; much like water vapour shows up as a feedback on scales of interest to us in the present. The difference between "feedback" and "forcing" is not hard and fast, but depends on the scale of interest.

(4) Insanely slow. The geological carbon cycle

This is what skyhunter's link was talking about. On really long time scales, from around millions of years to hundreds of millions of years, what counts is the transfer of carbon in and out of geological reserves, which are enormously more than what is seen in oceans or atmosphere. These cycles are too slow even to explain the cycles of ice ages in the quaternary period; but they become critical for explaining changes between "greenhouse" and "icehouse" conditions on very long times scales of hundreds of millions of years, and can involve much larger levels of atmospheric carbon than anything considered for climate in modern times or the foreseeable future.

The most drastic example of this is "Snowball Earth" theory, which by now is pretty much mainstream. There have been episodes in Earth's long history (the most recent of which was about 650 million years ago) in which we had ice ages of such intensity that the entire Earth was frozen, right into the tropics. Such a condition is self-perpetuating, because ice and snow are so reflective, and with most of sunlight being reflected, there is not enough energy coming into melt the ice.

In this condition, the processes discussed in Skyhunter's link become important. Weathering is much reduced, but outgassing is not. The result is a steady increase in levels of carbon dioxide, up to levels many times greater than what we have at present. Eventually -- and this can take a long long time -- the greenhouse effect becomes so strong that ice can begin to melt around the tropics. In this condition, a runaway feedback process occurs, because as ice melts, the albedo rises, and you start to get more absorbed sunlight. Over a geological eyeblink (as little as a thousand years) ALL the ice melts, and the Earth flips over into a "greenhouse" state, with very high carbon dioxide levels and a temperature rise from the "showball" state of as much as 50 degrees. It would have been the mother of all climate shifts. From there, of course, carbon dixoxide levels begin to fall again... rapidly at first, and then slowly, slowly... as carbon is taken up into the geological reserves once more.

For more details on this fascinating idea, see the website Snowball Earth, and in particular the FAQ question How did the snowball Earth's end?. There is now an extensive scientific literature on this. See, for example:

• Hoffman, P.F. et. al. (1998) A Neoproterozoic Snowball Earth, in Science Vol 281, 28 Aug 1998, pp 1342-1346.

Note that coming out of the snowball Earth condition may not occur until CO2 levels are as much as 350 times current levels, as described in the abstract of the above paper. That’s an atmosphere of about 12% carbon dioxide. From there, once the ice melted, deposition of carbon into geological reserves would begin, quite rapidly at first. This is the focus of the paper by Hoffman et al.

There's a lot of ongoing work with modeling the geological carbon cycle on long time scales like this, but the broad picture is now fairly solid, of a snowball Earth state in the Neoproterozoic, ending with a rapid transition to a hot greenhouse state with enormously elevated atmospheric carbon dioxide levels, followed by a return of carbon into geological reserves as carbonates precipitate out of the warmer ocean and a corresponding decline of temperatures -- although still a hot greenhouse state much warmer than prevailing conditions in the present, and well beyond anything predicted as a result of anthropogenic global warming.

I have in mind a new thread sometime in which I look at a really simple toy model that illustrates some of the basic ideas of feedback and hysteresis as they apply for snowball Earth. In the meantime, here's a diagram of how it works, from the snowball Earth site:

Basically, there is a kind of runaway albedo feedback that occurs as you move into and out of the snowball state, moving the Earth between two different stable equilibrium conditions. This effect is called hysteresis.

Cheers -- sylas

 

[skypunter]

Sorry, I'll be on my way now.

 

[sylas]

Sorry, I'll be on my way now.

And my apologies in turn for allowing myself to get a bit frustrated! Sorry! I'm glad to have had you in the thread, and you are welcome back anytime.

Since I am mainly interesting in contributing to basic education on particular points where there is a lot of public confusion, I need to watch myself more and not be rude to people who are making a sincere attempt to follow along. I was too rude to you just now, and I apologise.

I still stand by all the substantive remarks, of course. There's nothing in climate that sensibly corresponds to dark energy or dark matter in cosmology. That analogy only confuses the state of play; the nature of what is unknown in climate is not unknown forcings, but hard to model consequences.[*] Atmospheric circulation is important, but it really doesn't make any meaningful difference for sorting out the the forcings. It's part of the complexity of climate modeling... though actually one of the parts we can manage quite effectively. If you want to look at where we have much less of an idea of what is going on, look at circulation in the ocean, not the atmosphere! This has a major impact on the rate at which climate responds to forcings, and can give very strong effects on short term temperature variability. In some respects the ocean sometimes looks a bit like a forcing, because of the large heat capacity involved.

Cheers -- sylas

 

[sylas]

This thread seems like a good place to leave this note. A recent letter to Nature has proposed a simple metric: the "climate carbon response" (CCR). Basically, this is the the temperature rise per unit carbon emissions. This will depend on both carbon cycle and climate sensitivity estimates, both of which are uncertain; and so the value of the CCR is also uncertain. But it can be estimated with uncertainty bounds, and the number gives a convenient number for quantifying the number that was the topic of this thread. However, in the thread I have been comparing CO2 in the atmosphere to temperature; this new measure is relating carbon in emissions to temperature, which is potentially a more useful number for those who want a quick way to estimate to effects of changes to emissions.

• Matthews, D.H. et. al. (2009) The proportionality of global warming to cumulative carbon emissions, in Nature, 459, 829-832 (11 June 2009) | doi:10.1038/nature08047

Extract:

From observational constraints, we estimate CCR to be in the range 1.0–2.1 °C per trillion tonnes of carbon (Tt C) emitted (5th to 95th percentiles)​

What I found most interesting about this proposal is that it suggests a way to avoid a problem with "equilibrium sensitivity" and "transient response sensitivity". Basically, if you increase CO2 levels, then it may take a long time for the climate to respond. So there is a "transient" response (which is what you get when CO2 is increased gradually to a final level) and the "equilibrium" response (which is what you get when you keep waiting after CO2 has stabilised until the temperature come to equilibrium. The equilibrium response is larger than the transient response, by these definitions.

However, if you are interested in emissions, then as you wait the atmospheric CO2 levels also start to decay. It's rather artificial to simply hold atmospheric CO2 fixed and let temperature equilibriate, because there is at the same time an equilibriation of the carbon cycle.

Lets compare with the expected value you might get from considerations in this thread. I've proposed about 3 degrees per doubling, which would be 3/Ln(2) = 4.3 degrees per natural log, and at present the atmosphere contains about 8.2*10¹¹ tons of carbon, or 0.82 trillion tons. Assuming the logarithmic relation, we have dT/dC=4.3/C which works for any unit of carbon content C in the atmosphere.

Now if we just consider carbon in the atmosphere, the value is about 5.2 degrees per trillion tons carbon. But this is the equilibrium response, and appropriate for looking at the long term effect of a given atmospheric concentration.

On the other hand, if we are specifically interested in anthropogenic factors, then we can try to look at emissions rather that atmospheric concentrations. The results of this paper suggest that we can do this by using the transient sensitivity.

Transient sensitivity also called transient climate response (TCR) is about 1 to 3 degrees per doubling, with a best value of around 2. Using 2/Ln(2) we get about 2.9 degrees per natural log.

We also need to consider how much of emissions actually end up in the atmosphere. Much of it gets cycled into the ocean and other reservoirs of the carbon cycle. Off the top of my head I believe we are in the right ball part to assume about half of emissions actually end up in the atmosphere.

Using this approximation we have about 1.6 trillion tons of emissions equivalent, in the atmosphere, and the CCR would be about 2.9/1.6 = 1.8 degrees per trillion tons emission. This estimate was really crude, but I've ended up inside the bounds of 1.0 to 2.1 quoted in the published letter.

The letter emphasizes that there is a lot of uncertainty in the magnitude of this number. What is impressive is that the value is comparatively insensitive to how rapidly this is emitted or when! This gives a much more clearly understandable basis for people interested in policy or mitigation proposals focused on carbon footprints.

Cheers -- sylas

 

[joelupchurch]

Frankly, I have some trouble believing that the fundamental constraint isn't the concentration of CO₂ in the atmosphere. They seem to be arguing that even if we stabilized CO₂ at say 450ppm, that the temperature would continue to increase if we emitted any CO₂. This seems to violate some pretty basic physics.

BTW, didn't Nature publish a rather similar paper in April?

"Warming caused by cumulative carbon emissions towards the trillionth tonne"
Nature 458, 1163-1166 (30 April 2009) | doi:10.1038/nature08019; Received 25 September 2008; Accepted 25 March 2009
Myles R. Allen, David J. Frame, Chris Huntingford, Chris D. Jones, Jason A. Lowe, Malte Meinshausen & Nicolai Meinshausen
https://regtransfers-sth-se.diino.com/download/f.thompson/migrated_data/EandH/nature08019.pdf"

 

[sylas]

Frankly, I have some trouble believing that the fundamental constraint isn't the concentration of CO₂ in the atmosphere. They seem to be arguing that even if we stabilized CO₂ at say 450ppm, that the temperature would continue to increase if we emitted any CO₂. This seems to violate some pretty basic physics.

I don't understand the comment. There's no physical problem here.

All that matters for temperature, physically, is what carbon is in the atmosphere; but it still takes time to get the response. Suppose we stabilise at 450ppm. In that case, what we emit or not is beside the point; the premise of the comment is that the atmosphere has been stabilised, and that is all you need to know for the temperature estimates.

In the event that the atmosphere is stabilised at a certain concentration, the temperatures will indeed continue to increase. The reason for this is that there is a large time lag in the climate system, as a consequence of the heat sink in the ocean.

Think of it like this. Image the atmosphere suddenly jumps to 450ppm overnight. This will result, almost immediately, in an excess of energy being received at the surface, and the surface will start to heat up. The surface will continue to heat up until it gets to an equilibrium of the energy balance. Now the main reason the surface does't heat up in a month is the ocean. It takes a long long time for the ocean to heat up; and until this occurs, there is a flux of energy from the surface going down into the ocean. Once the ocean temperature has come to the equilibrium, this net flux is gone, and the surface has to be in balance with the top of the atmosphere again.

There's a long approach of temperature to the equilibrium value.

The Earth at present has an excess of energy flowing into the ocean. It's not clear how much this is. It is almost certainly less than 1 W/m². An estimate of 0.5 is probably close, but it could be less; and is unlikely to be more IMO. If the atmosphere remains fixed at the present composition, right now, then this excess of 0.5 W/m² will gradually be realized as a temperature increase at the surface, which is probably in the ball park of 0.4 degrees. This is often called temperature rise "in the pipeline".

There are some larger estimates for this published. In particular, a recent paper in Science proposed 0.85 W/m². I've commented before on why I think the smaller estimates are a bit more accurate. See [post=2186640]msg #3 of "Ocean Heat Storage" thread[/post]. Nailing this down is an open question as well, of course.

Suppose we put a pulse of CO2 into the atmosphere. If you wait a long time, then most of that pulse will come back out of the atmosphere, since the largest reservoirs of carbon in our carbon cycle are in the ocean. In the meantime, temperature will take a long time to come up to the equilibrium value. One point of this paper is to argue that these two opposing effects nearly cancel.

It's physically sensible; and the hypothesis seems very credible.

BTW, didn't Nature publish a rather similar paper in April?

"Warming caused by cumulative carbon emissions towards the trillionth tonne"
Nature 458, 1163-1166 (30 April 2009) | doi:10.1038/nature08019; Received 25 September 2008; Accepted 25 March 2009
Myles R. Allen, David J. Frame, Chris Huntingford, Chris D. Jones, Jason A. Lowe, Malte Meinshausen & Nicolai Meinshausen
https://regtransfers-sth-se.diino.com/download/f.thompson/migrated_data/EandH/nature08019.pdf"

Thanks for the reference! Great catch. I've had a quick look, and I agree. They are very closely related. Matthews et al cite this paper, and credit the authors in the acknowledgments as people who have provided useful commentary and discussion on the work. The citation you have given for Allen et al likewise references the paper by Matthews et al, though it is marked as "in press" as Allen et al came out a few months earlier.

Cheers -- sylas

 

[chriscolose]

I think the Hansen et al number of 0.85 W m^-2 was based on the year 2005 relative to some pre-industrial baseline, not a long-term value.

 

[skypunter]

Pardon me if this is a stupid question.
Does this formula take into account the logarithmic reduction in the effect of additional CO2 in the atmosphere?
For example, it takes a doubling to increase temperature a certain amount, but it takes another doubling of the new base to increase temperature the same amount as the first doubling. That is logarithmic, correct?
This simple formula does not appear to have a logaritmic component, and that makes me skeptical.

 

[skypunter]

"Now if we just consider carbon in the atmosphere, the value is about 5.2 degrees per trillion tons carbon."

Here is another stupid question.
Why are CO2 emissions referred to as "carbon" emissions, when the chemical contains more oxygen atoms than carbon. Shouldn't CO2 emissions be referred to as "Oxygen" emissions?

 

[sylas]

Three replies in one here; to chris and skypunter.

I think the Hansen et al number of 0.85 W m^-2 was based on the year 2005 relative to some pre-industrial baseline, not a long-term value.

The value was based on a model; and even in the 2005 paper it is apparent that the model value is greater than what is obtained from ocean data. A later lecture by Hansen uses smaller values for model based estimate, and clearly distinguishes the ocean data based estimates. The estimates in the 2005 paper were based on the decade 1993-2003. Here is the content of a chart in a lecture he gave earlier this year.

Chart 14:

Modeled Imbalance: +0.75 +/- 0.25 W/m²
Ocean Data Suggest: +0.5 +/- 0.25 W/m²​

Now, the ultimate question: can we stabilize climate? We would need to restore the planet’s energy balance. The underlying imbalance (averaging over short-term fluctuations) is probably close to 0.5 W/m².

—Air Pollutant Climate Forcings within the Big Climate Picture, Talk given by J. Hansen at the Climate Change Congress, “Global Risks, Challenges & Decisions”, Copenhagen, Denmark, March 11, 2009​

This is not an "anomaly" in the sense that it is measured with respect to a baseline of any kind. It is an absolute value for a total energy flux. The flux will vary from year to year, so you can certainly look for averages over a time span. The very long term average is effectively zero, because there's no significant source of energy in the ocean; it is almost all ultimate a redistribution of energy from the Sun.

I discuss this in more detail in [post=2194788]msg #31[/post] of thread "Ocean Heat Storage". In my opinion, this is a quantity where we are likely to get better estimates in time. I've stuck my neck out in that post to suggest that something a bit less than 0.5 is probable; but that's just my guess. 0.5 works for back of the envelope approximations.

Pardon me if this is a stupid question.
Does this formula take into account the logarithmic reduction in the effect of additional CO2 in the atmosphere?
For example, it takes a doubling to increase temperature a certain amount, but it takes another doubling of the new base to increase temperature the same amount as the first doubling. That is logarithmic, correct?
This simple formula does not appear to have a logaritmic component, and that makes me skeptical.

The answer to this is yes and no. You are quite right that it is not consistent with the logarithmic relation in the sense that you couldn't use this number over a very wide range of concentrations. For example, if you calculate this value again in a condition of substantially greater concentrations, you'd get a smaller value, for precisely the reason you identify.

However it is consistent in the sense that the underlying mathematical models used to calculate the number do indeed have this logarithmic relationship, and the number given works for estimating impacts in the present. Current CO2 values are approaching 400ppm. This number is a guide for the effects emissions on temperature in this case. There are substantial uncertainties in the number (the range is 1.0 to 2.1 at the 5th and 95th percentiles) and the consequences of the logarithmic relation are not particularly significant in this range.

Here is figure 2 from Allen et al (2009). What we are looking at here is temperature on the vertical axis, being the peak in warming over a pre-industrial average; and total carbon emissions on the horizontal axis. Currently we are at a bit over 0.4 trillion tons. The white crosses are best fit values, where each cross is a difference scenario. The grey shading represents a likelihood distribution.

You can see the logarithmic relation pretty clearly in how the white crosses lie. If you go over to 3 or 4 trillion tons, then the effect is clearly dropping off, as you should expect from the logarithmic relation of atmospheric carbon to temperature. But for total emissions of up to 1 trillion tons (basically emit in the future a bit more than what we've emitted since the start of the industrial revolution), the value proposed works well. It's not bad over higher values up to 1.5 or (yeesh) 2 trillion.

Note that this is only looking at carbon dioxide effects. This is one of the largest factors, but there are many other significant anthropogenic factors involved with industrial emissions as well. This is also noted in the papers cited.

Why are CO2 emissions referred to as "carbon" emissions, when the chemical contains more oxygen atoms than carbon. Shouldn't CO2 emissions be referred to as "Oxygen" emissions?

That's a point well worth emphasizing when looking at numbers. Numbers that get thrown around are sometimes for carbon, sometimes for CO₂, sometimes for mass and sometimes for volume. The conversions are not hard, but I've tripped up before this by mixing up the actual quantities being used in some report.

We don't refer to oxygen emissions because the oxygen involved comes from the atmosphere anyway. Burning of carbon based fuels takes oxygen out of the air, and carbon out of the fuel, and returns CO2 to the air.

It's useful to focus on the carbon, because what matters is the carbon content of the various fuels we use. Also, the Earth's carbon cycle involves various chemical reactions where carbon moves in and out of different compounds. The one common factor is the carbon; and so we speak of the carbon cycle and the carbon content of various reservoirs, without worrying about whether the carbon is there as CO₂, or (C₆H₁₀O₅)_n (cellulose, in wood), or H₂CO₃ (carbonic acid, in the ocean), or any number of other forms.

Cheers -- sylas

 

[skypunter]

this new measure is relating carbon in emissions to temperature, which is potentially a more useful number for those who want a quick way to estimate to effects of changes to emissions.

Such as the press.