Radiative forcing and CO2 emissions
February 25, 2010 by jason
Let me start by explaining what radiative forcing actually is and why it is the subject of so much debate, for those not familiar with the term. Radiative forcing is basically the change in radiation (including visible light) which the earth receives as a result of whatever gas we are talking about.
Another important term here is net irradiance which is the difference between the amount of light (I will just refer to all forms of electromagnetic radiation as light from now on, just to keep it simple) entering the earth, and the amount leaving it. Ignoring things like street lights, fires and cities (which are minimal compared to the amount of light hitting the earth), we can basically consider this net irradiance term to mean the amount of light which the earth is absorbing from the sun.
Put simply, radiative forcing is the change in Net Irradiance.
The Intergovernmental Panel on Climate Change created its own, more specific, definition of the term:
Quote:
Radiative forcing is a measure of the influence a factor has in altering the balance of incoming and outgoing energy in the Earth-atmosphere system and is an index of the importance of the factor as a potential climate change mechanism. In this report radiative forcing values are for changes relative to preindustrial conditions defined at 1750 and are expressed in watts per square metre (W/m2).
source:Climate Change 2007 - Synthesis Report
CO2 and Radiative Forcing
Carbon dioxide (CO2) has an effect on the atmosphere's ability to absorb light, because it is able to absorb radiation at frequencies not already absorbed by other gases in the atmosphere. It was actually only discovered during the 1950s, that CO2 was able to absorb frequencies not already absorbed by water. Let's take a look at the absorption bands of the most prominent gases in our atmosphere:
Absorption bands of the major gases in the Earth's atmosphere (source: Climate Change Science)
CO2 absorbs light at 2.5,4 and 20 micrometer wavelengths, giving rise to its label as a greenhouse gas. The gas in our atmosphere able to absorb the largest frequency ranges is water vapour. It should noted, that this also explains the phenomenon that more humid regions are less affected by recent temperature changes, as CO2 plays a smaller role. Cooler and drier regions have seen larger temperature increases in recent decades, which can be attributed to the larger role that CO2 plays in these areas (REFERENCE).
What about CO2 absorption saturation?
As a material, or gas, becomes denser, it absorbs more an more light. For example, a piece of glass 1cm thick does not appear to absorb anything, but if you look through it sideways (through the edges) it becomes very difficult to see the other side. A similar effect occurs with fluids, including CO2. However, unlike some substances, CO2 never actually experiences this saturation and continues to absorb more and more light as it gets denser and thicker. The change in the amount of light which CO2 absorbs (ie. the radiative forcing) can be represented empirically by the following equation:
source:Myhre et. al 1998
By setting the reference CO2 concentration value (C0) to 250ppmv, we can plot the resulting radiative forcing (change in net irradiation) resulting from the respective additions of CO2, shown below up to 1000ppmv:
Radiative forcing from additions of CO2 to the atmosphere
This graphical representation makes it much easier to see that the amount of potential warming which additional CO2 is by no means limited by the approach of a saturation point. This should put an end to the CO2 radiative forcing is saturated debates floating around of the global climate change forums, as it shows that radiative forcing is likely to continue to increase significantly over the next few decades.
For a more comprehensive discussions on CO2 concentrations and global temperatures, please see my blog on the relationship between CO2 and global temperature.
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Comments
One last time, for everyone
September 23, 2010 by jason
Yes, but only in the vertical axis. For the good of anyone else reading this, I'll reiterate one last time. As I said, this graph has no horizontal asymptote, there is no limit to the value that the concentration will reach. You say you have an engineering background, but you don't really seem to grasp the concept of an asymptote. The behavior you're "seeing" in the graph, is simply the decreasing gradient. A decreasing gradient is not the same thing as tending towards a limit. A good way to visualise this is to look at a log-log graph (just type log-log into google). There you'll see that a log function extends to infinity and never asymptotes. Mathematically one would say that log(x) tends to infinity as x tends to infinity.
Asymptotic behavior is only exhibited by functions which have a limit to their value in that axis. An example of this is exp(-x), which tends towards 0 as x approaches infinity, and thus has a horizontal asymptote at y=0. Another example, which you seem to be confusing with the CO2 case, is log(x), which does NOT have a horizontal asymptote, that is to say, the domain of log(x) is the domain of all real numbers for x for all x>0. That is to say, if x tends to infinity, so does log(x). There is no limit so there is no asymptote. In the same way, according to that graph, as CO2 concentration increases, so does radiative forcing, and this occurs to infinity. Of course, that's not physically meaningful, but mathematically it's what would happen.
Having said that, as x tends towards 0, log(x) tends towards negative infinity, so a log graph does asymptote, but on a vertical axis. This is probably where you got the idea from that a asymptotic behavior is implicit in log functions. However, in the case of CO2 concentrations this has no physical meaning.
Asymptotes.
September 23, 2010 by Catweazel (not verified)
"Yes, it is, but this graph unfortunately does not tend towards a horizontal asymptote."
Of course it does.
That's obvious from looking at even the bit you've posted.
Asymptotic behaviour is implicit in the logarithmic function.
Asymptotes.
September 23, 2010 by Catweazel (not verified)
Yes, it is, but this graph unfortunately does not tend towards a horizontal asymptote.
No asymptote in radiative forcing...
September 22, 2010 by jason
No. There is no upper limit in that graph. There is no asymptote, and assuming so is not good enough for government work. As I mentioned before, you could use a tolerance, and state that a certain increase rate is acceptable, although this has no realistically useful application.
Yes, it is, but this graph unfortunately does not tend towards a horizontal asymptote.
Yes, the graph is an empirical relation, and - like all empirical relations - has a limited scope and only applies to realistic atmospheric values. It's good enough for government work, as you might say...
Radiative forcing
September 22, 2010 by Catweazel (not verified)
"Sorry to disappoint you, but the idea of CO2 "saturation" is little more than a myth..."
Yes, I should have used "clearly tend towards zero".
Hence there is obviously an absolute upper limit to the amount of warming that CO2 can ever accomplish, and from your graph that will be achieved at around 2000ppm.
Tending towards asymptotic is close enough to a zero gradient for all useful purposes.
As I come from an engineering as opposed to a scientific background, as far as I'm concerned that's close enough for government work, as the old saying goes.
To state otherwise is just plain disingenuous.
Further, in actuality there are physical constraints on the absorption of photons by bipolar molecules that do in fact infer saturation will occur at some point.
Check your quantum mechanics.
There is no saturation...
September 22, 2010 by jason
What smithens said is correct; the graph will continue to increase indefinitely. However, since it is a logarithmic relationship, the rate at which the absorption increases will decline. This means that each increment in CO2 concentration will have a smaller effect on the overall atmospheric warming than the previous addition. You cannot however state that saturation occurs at any particular point, since adding more CO2 will always increase the radiative forcing.
What you can do, is define a point at which the increase in heating caused by a realistic addition of CO2 becomes negligible. You would need to define tolerances to limit how much heating you would consider negligible, which is beyond the scope of what I was writing in this article.
Sorry to disappoint you, but the idea of CO2 "saturation" is little more than a myth...
The graph will not become 0,
September 22, 2010 by smithens (not verified)
The graph will not become 0, ever. It just looks like it will...
CO2 saturation
September 14, 2010 by Catweazle (not verified)
Your gradient of your graph will clearly become zero (by a back of fag packet calculation) somewhere well short of 2000 ppm CO2.
Does that not indicate saturation?
Catweazle
Ref
August 11, 2010 by Clive (not verified)
Hi Jason. I see that you have referenced the source for the radiative forcing equation. Unfortunately your link only leads to an abstract. Do you know where I can download the whole scientific paper for free?
Re: Ref
November 3, 2010 by jason
Better late than never; you can find mention of the empirical CO2 radiative forcing relationships in the IPCC's Climate Change 2007 Synthesis Report, although this report only gives the formula and then cites the same source I gave in the article.