What is climate sensitivity?

Sensitivity, in the parlance of climate science, refers to the change in air temperature resulting from a change in forcing. For a given amount of forcing, a more sensitive climate will see greater air temperature changes. If you want to know how much hotter our atmosphere will get as a result of climate change, you need to know how sensitive our climate is.

Since humanity’s main influence on climate has been our emissions of carbon dioxide, and the attendant increase in atmospheric concentrations of said gas, for reasons of convention ‘sensitivity’ refers to how much temperature increases as a response to rises in carbon dioxide concentrations. When someone wants to discuss the climate’s sensitivity to other forcing agents, it’s mentioned explicitly.

The warming effect of CO2 is approximately logarithmic, meaning that doubling concentration tends to result in the same temperature increase regardless of the absolute level of CO2 in the atmosphere. Before industrial-scale emissions started, the atmospheric concentration of CO2 was about 280 parts per million (ppm). So, by way of example, the warming one should expect when going from 280 to 560 ppm is about the same as the one we’d see going from 400 to 800 ppm. For this reason, when someone talks about climate sensitivity without adding any qualifier, he almost always refers to the warming that results from a doubling of CO2 concentrations.


The easiest-to-understand example of forcing is a volcanic eruption. Such an event affects climate, but is not caused by the climate system itself. When volcanic aerosols lead to a reduction in incoming sunlight (or solar radiation, to use the technical term), that is a negative forcing, i.e. one that leads to cooling.

Almost all energy received by Earth is solar radiation. The energy released by our planet is both infrared radiation and reflected sunlight. Externally-caused events, like volcanic eruptions, that lead to changes in either incoming or outgoing radiation levels are called forcings.

The planet’s energy imbalance is the difference between emitted and received radiation. Approximately, each square meter of the Earth’s surface both receives and releases 340 watts, and the forcing resulting from a doubling of CO2 concentrations is estimated to be about 3.8 watts per square meter. If the planet receives more energy than it releases, as is currently the case, then it will experience energy gain. Which is to say more heat.

(If you’re thinking that it may be difficult to determine what really counts as a ‘forcing’, because it’s not clear which changes in radiation levels are externally-caused and which are caused by the climate system itself… you’re right).

Talking about ‘radiative’ forcing is a bit redundant at the planet level, because all energy exchange between Earth and space is through radiation – there is no energy gain or loss from evaporation, conduction, etc. So this app will simply deal with ‘forcing’.

For a more technical description of forcing, the closely related concept of ‘feedback’, and the various forcings involved in the climate system, I recommend reading this chapter of the IPCC’s Assessment Report 5.

Energy imbalance

The bulk of the energy gained by the planet (90% or more) is stored in the ocean. Here, ‘stored’ means ocean temperatures have gone up… a little. The ocean’s heat capacity is so massive that it really makes no sense to talk in terms of degrees. Instead, we measure energy stocks in zettajoules and energy flows in watts per square meter.

Imagine that the current ocean heat uptake is 0.9 watts per square meter, while the Earth’s total energy imbalance is a bit larger, 1 watt per square meter (due to heat uptake other than the ocean’s). Imagine further that humanity has so far created a forcing of 3 watts per square meter. What that would mean, crudely speaking, is that 2 watts per square meter have so far acted to raise atmospheric temperatures – while the other watt hasn’t raised air temperatures yet. Instead, the remaining watt’s principal effect, currently, is to raise ocean temperatures.

Transient climate response

For the purpose of simplicity, imagine humanity’s only influence on the climate is our emissions of carbon dioxide. Starting from a level of 370ppm in the year 2000, we increase this concentration to 740ppm by year 2100. But then, thanks to major declines in emissions, concentrations stabilize.

The transient climate response, or TCR for short, is an estimate of how much temperatures will have risen by the time CO2 concentrations have doubled. In page 82 of this IPCC document you have a more technical description.

Equilibrium climate sensitivity

Think about the example we just mentioned. By the year 2100, CO2 concentrations are double their 2000 level. As a result temperatures have risen by, let’s say, 1.5ºC. But even if CO2 concentrations stabilize, temperatures will keep increasing. Equilibrium climate sensitivity (ECS) refers to this total, long-term warming coming from a doubling of CO2 concentrations.

To appreciate why ECS is almost certainly higher than TCR, think back to the concept of energy imbalance. A positive energy imbalance means the planet is gaining more energy than it releases – i.e. the planet is warming. Warming only stops when the imbalance disappears or, in other words, the climate system regains equilibrium. (Of course an energy imbalance of exactly zero is impossible, and we couldn’t measure it anyway – ‘equilibrium’ here just means the imbalance is small enough not to matter for global temperature).

But how can the imbalance be reduced? One way is by reducing incoming solar radiation (which is what all these ‘geoengineering’ proposals are about). The other is by increasing outgoing infrarred radiation. However, the only way for infrared radiation to increase significantly is for temperatures to increase: a body’s infrared emissions are directly linked to its temperature. And the bulk of this energy is radiated from the atmosphere, not the ocean (a small part of infrared emissions escape to space directly from the surface – mostly that happens in the poles).

Thus, if the planet is releasing more infrared energy to space, it’s because air temperatures have risen. The increase in atmospheric temperatures is precisely the mechanism by which climate reestablishes equilibrium.

The only way TCR could be equal to ECS is if, by the year 2100, the imbalance was already reduced to the equilibrium level. Without getting technical, there are reasons why this is implausible – first of all the fact that the world’s current energy imbalance is far from equilibrium.

The IPCC document linked to in the TCR section also has more technical detail on ECS.

Efficacy? Really?

It has been argued that the Earth’s climate may not be equally sensitive to all types of forcing. Perhaps a negative forcing of 1 watt per square meter, if coming from a volcanic eruption, reduces temperatures less than an equally-sized forcing coming from man-made aerosols.

The problem is that the IPCC’s and other figures about radiative forcing already refer to ‘effective’ radiative forcing. It would be very confusing to say that some kinds of effective radiative forcing are more effective than others. So instead in climatespeak we say that some forcings are more efficacious than others, i.e. that they have greater efficacy.

Since CO2 is the main object of study in climate forcings, the efficacy of others is expressed on that basis. If volcanic forcing is only half as efficacious as CO2 in changing air temperatures, then we say its efficacy is 0.5. If aerosols are twice as efficacious as CO2, then their efficacy is 2.

The app allows users to set different efficacy levels and see what happens. By default all the efficacy values are set to 1, except in the case of volcanoes and black carbon on snow, as there is evidence that their efficacies are, respectively, lower and higher than that of CO2. If the user has doubts about the reliability of the data for some forcing (or its very existence), he can exclude that forcing by setting the efficacy to zero.

So how is climate sensitivity calculated?

Ideally we’d have a laboratory Earth where we could double CO2 concentrations and see what happens. Climate models are a way to simulate that. But if we want to use real-world data, the main way to calculate (or should we say estimate) climate sensitivity is by looking at the evolution of temperatures, forcing, and energy imbalance over the historical record.

Suppose that, over a period of time, forcing has increased by 2 watts per square meter while temperatures have risen 1º C. These 2 w/m2 are actually a mix of forcings: 3 w/m2 of positive forcing from CO2, 1 w/m2 of negative forcing from aerosols.

In order to calculate TCR, we need to extrapolate this temperature change to the forcing level involved in a doubling of CO2 concentrations, which is to say 3.8 w/m2. Since 3.8 is 90% more than 2, we say TCR is 1ºC * 1.9 = 1.9ºC

But what if aerosols have 50% greater efficacy than CO2? Then, the ‘real’ forcing suffered by the climate system is not 3 – 1 = 2 watts per square meter, but 3 – 1.5 = 1.5 watt per square meter. So the extrapolation now gives a much different result: 3.8 is 153% more than 1, so TCR will be 1ºC * 2.53 = 2.53ºC

As for ECS, remember from our discussion of energy imbalance that part of the forcing has not yet affected air temperatures, because it’s been (mostly) taken up as heat by the ocean. The calculation of ECS thus accounts for the effect that this ‘remaining’ forcing, the energy imbalance, will have on air temperatures.

Suppose that, over a given period, the increase in energy imbalance has been 0.7 w/m2, while the increase in temperatures and forcing (as above) was 1º C and 2 w/m2, respectively. Then, the forcing that has affected air temperatures so far is 2 – 0.7 = 1.3 w/m2. Since 3.8 is 192% more than 1.3, ECS will be 1ºC * 2.92 = 2.92ºC

There is some evidence from climate models that sensitivity is not always the same. Rather, at least in model simulations, it increases over time. Thus, an extrapolation from historical data may underestimate true long-term climate sensitivity. However, the magnitude or even existence of this effect in the real world is unclear. The app may, in the future, allow the user to see what happens to ECS estimates if sensitivity changes over time.

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