Technical question: Present concentration of CO2-eq and expected warming

[Nils Simon]

I have come across a small puzzle, but am unable to solve it myself. I
was looking around a bit to find our present concentration of GHGs
measured in CO2-equivalents. I took all following numbers from the 4AR
or calculated them from these. Here's what I found, and I'm only
looking at the three most important GHGs:

CO2 - 380ppm
CH4 - 1,774 ppb, or 1.774 ppm, with a global warming potential (GWP)
of 25 equals 44.35 ppm CO2-eq
N2O - 319 ppb, or 0.319 ppm, with a GWP of 298 equals 95.06 ppm CO2-eq

Together, I get about 519 ppm CO2-eq, a surprisingly high figure.
(GWP figures are from p. 33 in the Technical Summary)

Now another table gives expected temperature increase for certain
concentrations of GHGs, also measured in CO2-eq. You can find it on p.
66. It says that for the following concentrations, we could expect the
following temperatur increase:

CO2-eq Best guess temperature increase (+ likely range)
350 ppm 1.0 (0.6-1.4) °C
450 ppm 2.1 (1.4-3.1)
550 ppm 2.9 (1.9-4.4)
650 ppm 3.6 (2.4-5.5)
750 ppm 4.3 (2.8-6.4)
and so on

Now I was in the belief that we would already have crossed or nearly
crossed the 2°C threshold (with 0.74 already realised and the rest in
the pipeline), since the Stern Review says our present GHG
concentration is about 430ppm CO2-eq, while George Monbiot gives a
figure of 440-450 ppm CO2-eq (don't ask for his source). I don't have
the faintest idea why my simple calculation gives me 519 ppm, which
would mean that we'd soon be commited to about 3°C, and all that just
for the three top gases. Anyone able to help me out on this? If
anywhere, I would guess I've made a mistake with the nitrous oxide
figure since it seems unlikely high, but I can't find it.

Btw, what puzzles me even more is that the pre-industrial
concentration appears to have been 280 ppm + 18.25 ppm + 80.46 ppm =
378.71 ppm CO2-eq. That's strange.

[James Annan]

CO2-eq is used to mean the equivalent CO2 concentration, holding other
gases fixed at the pre-industrial level. So you have to subtract off the
pre-ind level off CH4 and N2O from your sums. I think what you have
effectively done is work out the CO2-equivalent if all other gases were
zero.

James

[gerh...@aston.ac.uk]

> CO2-eq is used to mean the equivalent CO2 concentration, holding other
> gases fixed at the pre-industrial level. So you have to subtract off the
> pre-ind level off CH4 and N2O from your sums. I think what you have
> effectively done is work out the CO2-equivalent if all other gases were
> zero.

So far so good, but:

Can we really just add up like that? I understand that for CO2
concentration the effect is logarithmic, presumably that's also the
case for other GHG's and then isn't there such a thing as overlap
between the absorption bands of different GHG's?

I don't really understand the basic physics of spectroscopy very well,
but from what I've read I thought it was a lot more complicated than
simple addition?

[Michael Tobis]

For very large perturbations it is a tedious and complex calculation,
but for relatively small perturbations a linear approximation
suffices. It is true that the correction for large perturbations
reduces the contribution to slower than linear. The definition of
"large" depends on the particular constituent and the particular
atmosphere.

I think the 'global warming potentials" are some sort of
linearization, but the chemical lifetimes of the constituents are
taken into account in some way I don't understand. As a consequence I
am not sure that even with James' correction that Nils' calculation is
the right one, though something like it should be doable.

mt

[James Annan]

Michael Tobis wrote:
> For very large perturbations it is a tedious and complex calculation,
> but for relatively small perturbations a linear approximation
> suffices.

For CO2, it is of course logarithmic (to a close approximation) but AIUI
CH4 and N2O are both in the linear range.

I agree with both mt and gerhaus that in detail it is more complicated
than merely adding up separate components (even when accounting for the
logarithmic effect of CO2). I was just pointing out what I saw as the
over-riding misunderstanding in Nils' original calculation, a failure to
account for the pre-industrial level of these other trace gases.

James

[Roger Coppock]

On Aug 16, 5:07 pm, "Michael Tobis" <mto...@gmail.com> wrote:
[ . . . ]

> I think the 'global warming potentials" are some sort of
> linearization, but the chemical lifetimes of the constituents are
> taken into account in some way I don't understand.

"Global Warming Potentials" are explained in note 3 of this:
http://cdiac.esd.ornl.gov/pns/current_ghg.html

References are given to the IPCC TAR

[gerh...@aston.ac.uk]

> I have come across a small puzzle, but am unable to solve it myself. I
> was looking around a bit to find our present concentration of GHGs
> measured in CO2-equivalents.

What you can do is the following. Take the GHG forcing figures from
the AR4:

http://www.ipcc.ch/SPM2feb07.pdf

1.66 (CO2)
0.48 (Methane)
0.16 (N2O)
0.34 (Halocarbons)

Add them up and you get 2.64 W/m2

You then divide that by 3.7 W/m2 (the forcing for doubled CO2) and get

0.71 or 71%

ie total GHG forcing is 71% of doubled CO2.

Now raise 2 to the power of 0.71 and you get 1.64 (or in other words
to get 71% of the forcing we only need 64% of the CO2 concentration
increase)

and multiply that with 280 ppm, to give you:

459 ppm CO2 equ

And instead of your table, you could stick to James Annan's well known
theme (climate sensitivity is 3C).

Just multiply 71% with 3C and you get 2.14C as the equilibrium
response to present GHG forcing.

But, total GHG forcing is currently offset by aerosols to a poorly
known degree.

If you stick in total forcing compared to pre-industrial, namely 1.6 W/
m2, things look considerably better. 1.6 W/m2 is less than half of 3.7
W/m2, and gives you an equilibrium response of 1.3C. Due to thermal
lag, only about 0.7C are already realised and another 0.6C are in the
pipe-line.

One of my pet themes is aerosols. What you'll notice from these
figures is the consequences of reducing sulfate emissions towards
zero, while say reducing CO2 emissions just enough to keep
concentrations constant. As about half the CO2 is sunk at the moment,
that's also roughly the reduction required to keep concentration
constant.

If we do that instantaneously, and simultaneously eliminate aerosols,
we've got a slightly better than 50% chance of missing a 2C target.

If we keep all forcings constant, however, I get that the climate
sensitivity would have to be above 3 times 2/1.3 or more than 4.5 C,
which means I think that a 2C target could be met with greater than
95% probability.

The critical importance of aerosols is something that is completely
lost in the public debate.

But it is the loss of aerosol cooling from emissions reductions that
means we likely need huge cuts in GHG emissions to avoid 2C with
greater than 90% probability. And huge means something like a 50%
within 20 years and a 90% within 50. If you combine that with converge
and contract for equity reasons, Europe needs 80% cuts by 2020, the US
90% cuts by 2020, and both need 95%plus reductions by 2050.

These are fantastical reductions, and I think, mean that either we'll
have to accept that 2C isn't so dangerous we couldn't accept a 50%
probability of it happening, or we'll have to do some aerosol /
tropical cloud albedo geoengineering to compensate for current
unintended side effect aerosol geoengineering. We could also continue
current sulfate emissions levels, in spite of the fact that the
sulfates are emitted right where people live.