The CO2 problem in six easy steps (2022 Update)

One of our most-read old posts is the step-by-step explanation for why increasing CO2 is a significant problem (The CO2 problem in 6 easy steps). However, that was written in 2007 – 15 years ago! While the basic steps and concepts have not changed, there’s 15 years of more data, updates in some of the details and concepts, and (it turns out) better graphics to accompany the text. And so, here is a mildly updated and referenced version that should be a little more useful.

Step 1: There is a natural greenhouse effect.

The Earth’s Energy Budget (NASA)

The fact that there is a natural greenhouse effect (that the atmosphere restricts the passage of infra-red (IR) 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 normally close to radiative equilibrium. This means that there is an upward surface flux of IR around sigma T^4 (~398 W/m2), while the outward flux at the top of the atmosphere (TOA) is roughly equivalent to the net solar radiation absorbed (~240 W/m2). Thus there must be a large amount of IR absorbed by the atmosphere (around 158 W/m2) – a number that would be zero in the absence of any greenhouse substances. Note that this IR radiation is sometimes called longwave (LW) radiation to distinguish it from the shortwave (SW) radiation coming from the sun.

Step 2: Trace gases contribute to the natural greenhouse effect.

A sample Earth spectra taken from the NIMBUS-4 satellite in 1970 along with the theoretical blackbody emissions at 280 and 220 Kelvin.

The fact that different absorbers contribute to the atmospheric infrared absorption is clear from spectra observed from space (right) which show characteristic gaps associated with water vapour, CO2, O3, clouds, methane, CFCs etc. The only question is how much total energy is blocked by each. This can’t be calculated by hand (the number of absorption lines and the effects of pressure broadening preclude that), but it can be calculated using radiative transfer codes. For some parts of the spectrum, the IR can be either absorbed by CO2 or by water vapour or by clouds, but taking those overlaps into account we find that 50% of the greenhouse effect is from water vapour, 25% from clouds, and about 20% from CO2 and the rest absorbed by ozone, aerosols, and other trace gases (Schmidt et al, 2010). Note that the main constituents of the atmosphere (N2, O2, and Argon) do not absorb significantly in IR wavelength range, and so do not contribute to the greenhouse effect.

Step 3: Trace greenhouse gases have increased markedly due to human emissions

Ice core and instrumental measurements of CO2 concentrations to 2021.

CO2 concentrations are up more than 50% since the pre-industrial, methane (CH4) has more than doubled and is accelerating once more, N2O is up 15%, and tropospheric O3 has also increased. New greenhouse gas compounds such as halocarbons (CFCs, HFCs) did not exist in the pre-industrial atmosphere. All of these increases contribute to an enhanced greenhouse effect.

The sources of these increases are dominated by the burning of fossil fuels, landfills, mining, oil and gas operations, agriculture (especially livestock for methane), and industry.

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*1361*0.7/4 = 4.8 W/m2 (taking albedo and geometry into account) (more energy would come in than was leaving). This would define the radiative forcing (RF). An increase in greenhouse absorbers, or a change in the albedo, have analogous impacts on the TOA balance (more energy would come in than leave). However, calculation of the radiative forcing is again a job for the radiative transfer codes that take into account atmospheric profiles of temperature, water vapour and aerosols. The IPCC AR6 report used the most up-to-date estimates from Etminan et al (2016) which are similar but slightly more complicated than the simplified, oft-used formula for CO2: RF = 5.35 ln(CO2/CO2_orig) (seen in Table 6.2 in IPCC TAR).

Note that the logarithmic form for the CO2 RF comes from the fact that some particular wavelengths 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 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 3.9±0.5 W/m2 – the same order of magnitude as an increase of solar forcing by 2%.

Effective Radiative Forcing (RF) from IPCC AR6.

There are a couple of small twists on the radiative forcing concept. There are a number of processes that react very quickly to a change of GHG or aerosol concentrations that aren’t related to changes in the surface temperatures. It turns out that calculating this “effective” forcing, after these adjustments have occurred, makes the ERF more predictive of the eventual temperature rise. One such process is the stratospheric adjustment that happens with CO2 since it has an important role in the stratospheric radiation balance while another is very fast changes to clouds after an aerosol change. 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 (to 2019) about 3.3 W/m2, and the net forcing (including cooling impacts of aerosols and natural changes) is 2.7±0.8 W/m2 since the pre-industrial (IPCC AR6 Chapter 7). Most of the uncertainty is still related to aerosol effects. Current growth in forcings is dominated by increasing CO2, with an increasing 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

Constrained pdfs for ECS from Sherwood et al (2020)

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 (~8 W/m2 from ice sheets, greenhouse gases, dust and vegetation) giving a large temperature response (~5 to 6ºC) 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 recently done by Sherwood et al (2020), and they come up with, you guessed it, 3ºC (and also a tighter uncertainty bound of 2.3 to 4.5ºC).

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 imply the planet would warm 2ºC (=2.7 W/m2 x 0.75ºC/(W/m2)) by the time the climate reaches equilibrium. Because the oceans take time to warm up, we are not yet there (so far we have experienced 1.2ºC), and so the remaining ~0.8ºC is ‘in the pipeline’ if we keep concentrations constant (equivalent to an immediate ~70% cut in emissions). Additional forcings in plausible future scenarios could reach 5 W/m2 and therefore additional warming (at equilibrium) could be more than 3ºC. Interestingly, if CO2 emissions were to cease entirely, the net heat uptake and decreasing radiative forcing would roughly balance, and we would not expect temperatures to rise any further. Thus our societal flexibility will allow us to end up somewhere between those two extremes.

From xkcd

These temperature changes might seem like small numbers, but on the scale of a planet they are a big deal. We are already seeing impacts from the warming so far in changing statistics of heat waves, extreme precipitation, and coastal flooding. Recall that the last ice age was only 5 to 6ºC cooler than the pre-industrial – and that was a massive shift. We have already warmed between a fifth and a quarter of an ‘ice age unit‘, and the worst case scenarios have a full ice age unit of warming in a couple of centuries, compared to the 10,000 years it took to warm before.

That is already significant and is going to get more so until emissions cease.



  1. G.A. Schmidt, R.A. Ruedy, R.L. Miller, and A.A. Lacis, “Attribution of the present-day total greenhouse effect”, Journal of Geophysical Research, vol. 115, 2010.

  2. M. Etminan, G. Myhre, E.J. Highwood, and K.P. Shine, “Radiative forcing of carbon dioxide, methane, and nitrous oxide: A significant revision of the methane radiative forcing”, Geophysical Research Letters, vol. 43, 2016.

  3. J. Hansen, “Efficacy of climate forcings”, Journal of Geophysical Research, vol. 110, 2005.

  4. S.C. Sherwood, M.J. Webb, J.D. Annan, K.C. Armour, P.M. Forster, J.C. Hargreaves, G. Hegerl, S.A. Klein, K.D. Marvel, E.J. Rohling, M. Watanabe, T. Andrews, P. Braconnot, C.S. Bretherton, G.L. Foster, Z. Hausfather, A.S. Heydt, R. Knutti, T. Mauritsen, J.R. Norris, C. Proistosescu, M. Rugenstein, G.A. Schmidt, K.B. Tokarska, and M.D. Zelinka, “An Assessment of Earth’s Climate Sensitivity Using Multiple Lines of Evidence”, Reviews of Geophysics, vol. 58, 2020.

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