"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." - Gavin Schmidt
And Mr. Romm adds his 7th step;
"And let me add Step 7: On our current emissions path, we’re going to blow past 550 ppm, a doubling of CO2 (See U.S. media largely ignores latest warning from climate scientists: “Recent observations confirm … the worst-case IPCC scenario trajectories (or even worse) are being realised” — 1000 ppm and M.I.T. doubles its 2095 warming projection to 10°F — with 866 ppm and Arctic warming of 20°F)."