The CO2 problem in 6 easy steps

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

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