The Equilibrium Climate Sensitivity (ECS) has remained stubbornly uncertain for more than 40 years. A new study by Peter Cox and colleagues reduced the uncertainty, considerably, while retaining a similar central estimate. Another study by Brown and Caldeira (2017) led to a similar reduction in uncertainty, but with a higher median.

I am sure a debate will rage on whether these new uncertainty ranges will stand the test of time. The point of this blog is not to question the studies, I will leave that to others, but to consider the implications of the studies on the carbon budget. I will focus here on the study by Cox et al, as it conveniently does not change the central estimate.

We have all been absorbed by the concept of the carbon budget, the total amount of carbon we can emit to stay below (or exceed) a given temperature target. One can question the policy utility of the carbon budget concept, its uncertainty, and its implications, but we have to admit the concept has a few nice features.

One strength of the carbon budget is that it is amenable to simple manipulations. And this blog is about simple manipulations!

Damon Matthews and colleagues showed earlier that the Transient Climate Response to cumulative Emissions (TCRE) can be decomposed into a carbon and climate sensitivity.

This simple relationship is useful. It means that the uncertainty in TCRE scales with the uncertainty in the ECS. Cox et al argued that the ECS range has reduced from (4.5-1.5)=3.0°C to (3.4-2.2)=1.2°C. One could argue that the TCRE range goes down a similar proportion, depending on how the climate and carbon sensitivity interact. One can squabble about the size of the change, but since the equations are simple, we can look at all options!

It is straightforward to translate simple changes in the parameters of the TCRE into new estimates of the carbon budget.

where *Q* is the carbon budget for temperature *T* and probability *p*, *F* is the TCRE distribution, *μ* is the mean TCRE (1.65°C/1000PgC), and *σ* is the standard deviation (0.85°C/1000PgC). The TCRE distribution is taken as Gaussian, which is a strong assumption and will particularly effect the tails of the distribution.

Since the TCRE is uncertain, the use of the probability (greater than 50%) is analogous to applying the precautionary principle, giving extra confidence that a temperature goal may be achieved given the uncertainty.

If we fix the temperature and probability, say 2°C with a 66% chance, as is common in the IPCC, then we can see how the carbon budget will change as the TCRE uncertainty is reduced.

If we assume the TCRE uncertainty is reduced in the same proportion as the ECS uncertainty, 1.2/3.0=0.4, then the total carbon budget will be increased from 3670GtCO_{2} to 4150GtCO_{2}, a 430GtCO_{2} (12%) increase. Of course, if you don’t like that choice, then the figure gives all other choices. Take your pick!

The carbon budget for 2°C with a 50% chance (the median) will not change as we have assumed a symmetric TCRE distribution, which of course could be questioned.

The total carbon budget needs to be adjusted for non-CO_{2} emissions and historical emissions. If we take the adjustment of non-CO_{2} for RCP2.6 from IPCC AR5 Working Group 1 (770GtCO_{2}, in reality there is a range) and the latest historical emissions from the Global Carbon Budget from 1870 to 2016 (2075±205GtCO_{2}), then the remaining budget from 2017 is increased from 820GtCO_{2}to 1250GtCO_{2}, a 430GtCO_{2} (52%) increase.

The figures allow you to decide on the uncertainty range of the TCRE, and then read off how big the change will be in the carbon budget.

### Putting the numbers in context

The main point is that reducing the uncertainty on the ECS will reduce the uncertainty on the TCRE, which makes the carbon budget bigger if the probability is greater than 50%. **This is great news, of course, if the Cox et al ECS estimate stands the test of time!**

A key point is whether the uncertainty ranges presented by Cox et al and Brown and Caldeira are robust, and it is important to note that they may be lower bounds as they don’t consider all uncertainties.

Even if the climate sensitivity has a smaller range than previously thought, the carbon budgets will remain highly uncertain. The main reason for the uncertainty is that non-CO_{2} emissions are important for the carbon budget and depend on the pathway, and negative emissions make it rather ambiguous how to define the carbon budget.

The uncertainty of the carbon budget is something that we as a community have not been sufficiently clear about, which is one reason why we have debates when estimates change!

**Watch a video discussing the uncertainty in the carbon budget:**

**Or look at my presentation:**

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