Reconciled climate response estimates from climate models and the energy budget of Earth

Mark Richardson, Kevin Cowtan, Ed Hawkins, Martin Stolpe


Climate models are used to estimate the likely range of warming we will see in the future for a given level of fossil fuel emissions. The size of the effect of human activity on global temperature is often summarized by a single number, the "climate sensitivity", which measures how much the Earth will warm in response to a doubling of atmospheric CO2.

The climate system takes time to respond to changes, and so different measures of climate sensitivity are used for different timescales. Most relevant to policy is the "Transient Climate Response", or TCR, which measures how much warming will occur over the span of a human lifetime.

Transient Climate Response has traditionally been determined from climate models, which yield values of around 1.8 Celsius of warming for a doubling of CO2. However in the lead up to the last IPCC report, a paper by Otto and colleagues produced an estimate of TCR using the historical temperature record which was 25% lower than the values from the climate models. Lewis & Curry (2015) and Bengtsson & Schwartz (2013) obtained similar results.

In our paper we redid the calculation of Otto and colleagues, taking special care to ensure that the temperature data from the models were treated in the same way as the temperature data from the observations. When we do an apples-to-apples comparison, the discrepancy between the models and the observations is largely resolved, as shown in Figure 1.

Figure 1: Like-with-like comparisons of climate sensitivity (TCR) estimates between models and observations. In the upper two bars, the observed estimates are adjusted to match the method used for the models. In the lower two bars the model outputs are treated in the same way as the observations.

The lower two bars in Figure 1 show what happens when the model temperatures are treated in the same way as the observations, in particular the coverage of the globe is reduced to match the coverage of the historical observations for that month, and air and sea temperatures are merged using the same method as from the observations. The upper two bars show what happens if the observed estimates of climate sensitivity are corrected to account for the errors introduced by not treating the model outputs in the same way as the observations. In both cases, the climate sensitivity estimates from both models and observations agree.

Which climate sensitivity is right?

When we treat the models like the observations, we get a lower estimate of climate sensitivity. When we treat the observations like the models, we get a higher value. In both cases the models and the observations agree. But which is right?

Climate sensitivity has always been defined in terms of global air temperature, so the larger value is correct in terms of the formal definition. However the lower value is also of use, because it is more convenient to calculate from the observational data. To avoid confusion we recommend that this value should not be referred to as climate sensitivity or TCR. This new parameter will also differ for different versions of the temperature record.

What factors contribute to the lower value of observational estimates of TCR?

The largest contribution to the low observational estimates of TCR is the incomplete global coverage of historical temperature observations (Figure 2). Applying historical coverage to climate model outputs reduces the temperature change by about 15%. (This is larger than the change estimated by infilling the unobserved regions as in Cowtan and Way 2013, because the early record is too incomplete for infilling to be fully effective.)

Figure 2: Change in near-surface air temperature from 1861-1880 to 2000-2009 seen globally (left), seen by typical HadCRUT4 data coverage over 2000-2009 (centre) and by typical HadCRUT4 data coverage over 1861-1880 (right). Typical coverage refers to cases where more than 25% of months within that period report data.

The next largest effect is the use of sea surface temperatures rather than air temperatures in the observational record. If the climate models are analyzed using both sea and air temperatures rather than air temperatures alone (as required by the formal definition of TCR), the temperature change is reduced by a little under 5%.

The final effect arises from the blending of air and sea temperatures in regions where the sea ice edge has changed. This effect is the most uncertain, but has the smallest effect; less than 5%.

When combined, these three factors reduce the temperature change in the climate model outputs by about a quarter. The different handling of the temperature data between the models and observations therefore explains almost all of the difference between the estimates of climate sensitivity from models and observations.


The largest uncertainty in estimates of climate sensitivity from historical data comes from the climate forcings. A recent study, Marvel et al 2015 and prior works suggest that cooling effect of non-CO2 pollution may have been underestimated. This also suggests that climate sensitivity is underestimated (since the net direct impact of human activity would be reduced, requiring a greater sensitivity to achieve the observed temperature change).

The results of Marvel et al are independent of this work. If both studies are correct, climate sensitivity from the historical record could be higher than climate sensitivity from the models. However we are not in a position to comment on that paper, and so draw the weaker conclusion that the historical record offers no reason to doubt the estimates of climate sensitivity from climate models.