A ‘new’ measurement of climate sensitivity?

This was first posted on and Then There's Physics by SkS contributor Mark Richardson, who is currently a Caltech Postdoctoral Scholar at the NASA Jet Propulsion Laboratory. Mark has a particular interest in the role of clouds in climate change. This post is a response to a suggestion that it is possible to more tightly constrain Equilibrium Climate Sensitivity (ECS). This article is all personal opinion and does not represent NASA, JPL or Caltech in any way.

The oceans are massive and their deeper layers haven’t caught up with today’s fast global warming. Unfortunately we don’t know exactly how far behind they are so it’s hard to pin down “equilibrium climate sensitivity” (ECS), or the eventual warming after CO2 in the air is doubled.

Blogger Clive Best proposes that data support an ECS range of 2–3°C, with a best estimate of 2.5°C. The 2013 Intergovernmental Panel on Climate Change (IPCC) consensus range was 1.5–4.5°C with a best estimate of 3°C. He asks “why is there still so much IPCC uncertainty?” Here we’ll see that part of the reason relates to the oceans, and that surprisingly Best’s results actually agree with IPCC climate models.

Clive Best mixes temperature data with a record of heating due to changes in gases in the air, solar activity, volcanic eruptions, air pollution and so on. Apparently without realising it, he accurately reproduced a textbook calculation including a reasonable way to try and account for the oceans lagging behind surface warming. This is a good start!

This calculation is often called a “one-box energy balance model” but by 2010 it was known to have issues with calculating ECS. Clive Best misses some of these because he uses a 1983 climate model to estimate that the oceans lag about 12 years behind the surface, which combined with the HadCRUT4 data gives an ECS of about 2.5°C.

Figure 1: Temperature change over 150 years in abrupt 4xCO2 simulations of four climate models. Black lines are a one-box fit with ECS and response time (τ) allowed to vary. Legend lists model name, true ECS and fit parameters.

The reliance on a 1983 model is the explanation. The 1983 NASA GISS Model II was mostly designed for the atmosphere and had a simple ocean. For example, its ocean currents couldn’t change. Modern models are more realistic and the graphs to the right (Figure 1) show their temperature after an immediate 300 % increase in CO2. Each legend has the known model ECS, along with the ECS and time lag (labelled τ) calculated for the one-box model.

The ECS is off and the time lag can be as long as 21 years instead of 12! On top of that the fits are bad because the oceans aren’t just 12 years “behind”, instead the system acts as if the ocean has multiple layers and each one can respond on a different timescale. Now let’s look at simulations of the climate since 1861 and the one-box fits.

Figure 2: Simulated temperature change from 1861–2015 inclusive in 4 climate models using historical-Representative Concentration Pathway 8.5 scenarios (RCP8.5, blue). Model output is sampled in the same way as HadCRUT4. The thicker lines are fits using a one-box model with either the lag from Figure 1 or assuming a 12-year lag. Radiative forcing is the Forster et al. historical-RCP8.5 in all cases.

Consider the Figure on the left (Figure 2). Imagine living in the world of the top left panel. In this world we might read a blog that says ECS is around 1.7°C but in reality it would be 3.8°C. Now let’s compare the one-box and true ECS values for 18 models.

Figure 3: Model true equilibrium climate sensitivity (True ECS) as a function of that calculated as in Figure 2, using historical-RCP8.5 temperature change with the Forster forcing and a one-box model with a 12-year lag. All of the points are above the 1:1 black dashed line, showing that the one-box model underestimates true ECS in all 18 cases. The red line is a best fit to the models, although the fit is weak.

If this one-box calculation works, then it should give the right answer when applied to complex climate models where we know the answer (e.g. Geoffroy et al. (2013) do this sort of test). With this data being free online, anyone can work out that climate models with ECS from 2.3–3.8°C are consistent with the data & one-box approach. A little exploration shows us that the climate’s response time matters, and measured ocean heatingshows a single 12-year lag doesn’t make sense (Figure 3).

Clive Best asked why the IPCC give a range for ECS that’s bigger than his calculated 2–3°C. This post shows that partly this is because his approach missed lots of uncertainty related to ocean layering. A 2013 paper found that the way in which oceans delay warming could even affect future sea ice and clouds while a 2017 study brought together the key physics and data. The conclusion? Observational data support a “best estimate of equilibrium climate sensitivity of 2.9°C”, with a range of 1.7–7.1°C.