The CO2 problem in 6 easy steps
Filed under: Climate Science Greenhouse gases — gavin @ 6 August 2007
We often get requests to provide an easy-to-understand explanation
for why increasing CO2 is a significant problem without relying on
climate models and we are generally happy to oblige. The explanation
has a number of separate steps which tend to sometimes get confused
and so we will try to break it down carefully.
Step 1: There is a natural greenhouse effect.
The fact that there is a natural greenhouse effect (that the
atmosphere restricts the passage of long wave (LW) radiation from the
Earth’s surface to space) is easily deducible from i) the mean
temperature of the surface (around 15ºC) and ii) knowing that the
planet is roughly in radiative equilibrium. This means that there is
an upward surface flux of LW around [tex]\sigma T^4[/tex] (~390 W/
m2), while the outward flux at the top of the atmosphere (TOA) is
roughly equivalent to the net solar radiation coming in (1-a)S/4
(~240 W/m2). Thus there is a large amount of LW absorbed by the
atmosphere (around 150 W/m2) – a number that would be zero in the
absence of any greenhouse substances.
Step 2: Trace gases contribute to the natural greenhouse effect.
The fact that different absorbers contribute to the net LW absorption
is clear from IR spectra taken from space which show characteristic
gaps associated with water vapour, CO2, CH4, O3 etc (Harries et al,
2001; HITRAN). The only question is how much energy is blocked by
each. This cannot be calculated by hand (the number of absorption
lines and the effects of pressure broadening etc. preclude that), but
it can be calculated using line-by-line radiative transfer codes. The
earliest calculations (reviewed by Ramanathan and Coakley, 1979) give
very similar results to more modern calculations (Clough and Iacono,
1995), and demonstrate that removing the effect of CO2 reduces the
net LW absorbed by ~14%, or around 30 W/m2. For some parts of the
spectrum, IR can be either absorbed by CO2 or by water vapour, and so
simply removing the CO2 gives only a minimum effect. Thus CO2 on its
own would cause an even larger absorption. In either case however,
the trace gases are a significant part of what gets absorbed.
Step 3: The trace greenhouse gases have increased markedly due to
human emissions
CO2 is up more than 30%, CH4 has more than doubled, N2O is up 15%,
tropospheric O3 has also increased. New compounds such as halocarbons
(CFCs, HFCs) did not exist in the pre-industrial atmosphere. All of
these increases contribute to an enhanced greenhouse effect.
Step 4: Radiative forcing is a useful diagnostic and can easily be
calculated
Lessons from simple toy models and experience with more sophisticated
GCMs suggests that any perturbation to the TOA radiation budget from
whatever source is a pretty good predictor of eventual surface
temperature change. Thus if the sun were to become stronger by about
2%, the TOA radiation balance would change by 0.02*1366*0.7/4 = 4.8 W/
m2 (taking albedo and geometry into account) and this would be the
radiative forcing (RF). An increase in greenhouse absorbers or a
change in the albedo have analogous impacts on the TOA balance.
However, calculation of the radiative forcing is again a job for the
line-by-line codes that take into account atmospheric profiles of
temperature, water vapour and aerosols. The most up-to-date
calculations for the trace gases are by Myhre et al (1998) and those
are the ones used in IPCC TAR and AR4.
These calculations can be condensed into simplified fits to the data,
such as the oft-used formula for CO2: RF = 5.35 ln(CO2/CO2_orig) (see
Table 6.2 in IPCC TAR for the others). The logarithmic form comes
from the fact that some particular lines are already saturated and
that the increase in forcing depends on the ‘wings’ (see this post
for more details). Forcings for lower concentration gases (such as
CFCs) are linear in concentration. The calculations in Myhre et al
use representative profiles for different latitudes, but different
assumptions about clouds, their properties and the spatial
heterogeneity mean that the global mean forcing is uncertain by about
10%. Thus the RF for a doubling of CO2 is likely 3.7±0.4 W/m2 – the
same order of magnitude as an increase of solar forcing by 2%.
There are a couple of small twists on the radiative forcing concept.
One is that CO2 has an important role in the stratospheric radiation
balance. The stratosphere reacts very quickly to changes in that
balance and that changes the TOA forcing by a small but non-
negligible amount. The surface response, which is much slower,
therefore reacts more proportionately to the ‘adjusted’ forcing and
this is generally what is used in lieu of the instantaneous forcing.
The other wrinkle is depending slightly on the spatial distribution
of forcing agents, different feedbacks and processes might come into
play and thus an equivalent forcing from two different sources might
not give the same response. The factor that quantifies this effect is
called the ‘efficacy’ of the forcing, which for the most part is
reasonably close to one, and so doesn’t change the zeroth-order
picture (Hansen et al, 2005). This means that climate forcings can be
simply added to approximate the net effect.
The total forcing from the trace greenhouse gases mentioned in Step
3, is currently about 2.5 W/m2, and the net forcing (including
cooling impacts of aerosols and natural changes) is 1.6±1.0 W/m2
since the pre-industrial. Most of the uncertainty is related to
aerosol effects. Current growth in forcings is dominated by
increasing CO2, with potentially a small role for decreases in
reflective aerosols (sulphates, particularly in the US and EU) and
increases in absorbing aerosols (like soot, particularly from India
and China and from biomass burning).
Step 5: Climate sensitivity is around 3ºC for a doubling of CO2
The climate sensitivity classically defined is the response of global
mean temperature to a forcing once all the ‘fast feedbacks’ have
occurred (atmospheric temperatures, clouds, water vapour, winds,
snow, sea ice etc.), but before any of the ’slow’ feedbacks have
kicked in (ice sheets, vegetation, carbon cycle etc.). Given that it
doesn’t matter much which forcing is changing, sensitivity can be
assessed from any particular period in the past where the changes in
forcing are known and the corresponding equilibrium temperature
change can be estimated. As we have discussed previously, the last
glacial period is a good example of a large forcing (~7 W/m2 from ice
sheets, greenhouse gases, dust and vegetation) giving a large
temperature response (~5 ºC) and implying a sensitivity of about 3ºC
(with substantial error bars). More formally, you can combine this
estimate with others taken from the 20th century, the response to
volcanoes, the last millennium, remote sensing etc. to get pretty
good constraints on what the number should be. This was done by Annan
and Hargreaves (2006), and they come up with, you guessed it, 3ºC.
Converting the estimate for doubled CO2 to a more useful factor gives
~0.75 ºC/(W/m2).
Step 6: Radiative forcing x climate sensitivity is a significant number
Current forcings (1.6 W/m2) x 0.75 ºC/(W/m2) imply 1.2 ºC that would
occur at equilibrium. Because the oceans take time to warm up, we are
not yet there (so far we have experienced 0.7ºC), and so the
remaining 0.5 ºC is ‘in the pipeline’. We can estimate this
independently using the changes in ocean heat content over the last
decade or so (roughly equal to the current radiative imbalance) of
~0.7 W/m2, implying that this ‘unrealised’ forcing will lead to
another 0.7×0.75 ºC – i.e. 0.5 ºC.
Additional forcings in business-as-usual scenarios range roughly from
3 to 7 W/m2 and therefore additional warming (at equilibrium) would
be 2 to 5 ºC. That is significant.
Q.E.D.?
http://www.realclimate.org/index.php/archives/2007/08/the-co2-problem-
in-6-easy-steps/