Guest Post by Willis Eschenbach

I got to thinking about the lack of progress in estimating the “equilibrium climate sensitivity”, known as ECS. The ECS measures how much the temperature changes when the top-of-atmosphere forcing changes, in about a thousand years after all the changes have equilibrated. The ECS is measured in degrees C per doubling of CO2 (°C / 2xCO2).

Knutti et al. 2017 offers us an interesting look at the range of historical answers to this question. From the abstract:

Equilibrium climate sensitivity characterizes the Earth’s long-term global temperature response to increased atmospheric CO2 concentration. It has reached almost iconic status as the single number that describes how severe climate change will be. The consensus on the ‘likely’ range for climate sensitivity of 1.5 °C to 4.5 °C today is the same as given by Jule Charney in 1979, but now it is based on quantitative evidence from across the climate system and throughout climate history.

This “climate sensitivity”, often represented by the Greek letter lambda (λ), is claimed to be a constant that relates changes in downwelling radiation (called “forcing”) to changes in global surface temperature. The relationship is claimed to be:

Change in temperature is equal to climate sensitivity times the change in downwelling radiation.

Or written in that curious language called “math” it is

∆T = λ ∆F                               Equation 1 (and only)

where T is surface temperature, F is downwelling radiative forcing, λ is climate sensitivity, and ∆ means “change in”

I call this the “canonical equation” of modern climate science. I discuss the derivation of this equation here. And according to that canonical equation, depending on the value of the climate sensitivity, a doubling of CO2 could make either a large or small change in surface temperature. Which is why it the sensitivity is “iconic”.

Now, I describe myself as a climate heretic, rather than a skeptic. A heretic is someone who does not believe orthodox doctrine. Me, I question that underlying equation. I do not think that even over the long term the change in temperature is equal to a constant time the change in downwelling radiation.

My simplest objection to this idea is that evidence shows that the climate sensitivity is not a constant. Instead, it is a function inter alia of the surface temperature. I will return to this idea in a bit. First, let me quote a bit more from the Knutti paper on historical estimates of climate sensitivity:

The climate system response to changes in the Earth’s radiative balance depends fundamentally on the timescale considered. The initial transient response over several decades is characterized by the transient climate response (TCR), defined as the global mean surface warming at the time of doubling of CO2 in an idealized 1% yr–1 CO2 increase experiment, but is more generally quantifying warming in response to a changing forcing prior to the deep ocean being in equilibrium with the forcing  …

By contrast [to Transient Climate Response TCR], the equilibrium climate sensitivity (ECS) is defined as the warming response to doubling CO2 in the atmosphere relative to pre-industrial climate, after the climate reached its new equilibrium, taking into account changes in water vapour, lapse rate, clouds and surface albedo. 

It takes thousands of years for the ocean to reach a new equilibrium. By that time, long-term Earth system feedbacks — such as changes in ice sheets and vegetation, and the feedbacks between climate and biogeochemical cycles — will further affect climate, but such feedbacks are not included in ECS because they are fixed in these model simulations. 

Despite not directly predicting actual warming, ECS has become an almost iconic number to quantify the seriousness of anthropogenic warming. This is a consequence of its historical legacy, the simplicity of its definition, its apparently convenient relation to radiative forcing, and because many impacts to first order scale with global mean surface temperature. 

The estimated range of ECS has not changed much despite massive research efforts. The IPCC assessed that it is ‘likely’ to be in the range of 1.5 °C to 4.5 °C (Figs 2 and 3), which is the same range given by Charney in 1979. The question is legitimate: have we made no progress on estimating climate sensitivity?

Here’s what the results show. There has been no advance, no increase in accuracy, no reduced uncertainty, in ECS estimates over the forty years since Carney in 1979. Let’s take a look at the actual estimates.

The Knutti paper divides the results up based on the type of underlying data upon which they were determined, viz: “Theory & Reviews”, “Observations”, “Paleoclimate”, “Constrained by Climatology”, and “GCMs” (global climate models). Some of the 145 estimates only contained a range, like say 1.5 to 4.5. In that case, for the purposes of Figure 1 I’ve taken the mean of the range as the point value of their estimate.

Next, I looked at the 124 estimates which included a range for the data. Some of these are 95% confidence intervals; some are reported as one standard deviation; others are a raw range of a group of results. I have converted all of these to a common standard, the 95% confidence interval. Figure 2 shows the maxima and the minima of these ranges. I have highlighted the results from the five IPCC Assessment Reports, as well as the Charney estimate.

The Charney / IPCC estimates for the range of the ECS values are constant from 1979 to 1995, at 1.5°C to 4.5°C for a doubling of CO2. In the Third Assessment Report (TAR) in 2001 the range gets smaller, and in the Fourth Assessment Report (AR4) in 2007 the range got smaller still.

But in the most recent Fifth Assessment Report (AR5), we’re back to the original ECS range where we started, at 1.5 to 4.5°C / 2xCO2.

In fact, far from the uncertainty decreasing over time, the tops of the uncertainty ranges have been increasing over time (red/black line). And at the same time, the bottoms of the uncertainty ranges have been decreasing over time (yellow/black line). So things are getting worse. As you can see, over time the range of the uncertainty of the ECS estimates has steadily increased. 

Looking At The Shorter Term Changes.

Pondering all of this, I got to thinking about a related matter. The charts above show equilibrium climate sensitivity (ECS), the response to a CO2 increase after a thousand years or so. There is also the “transient climate response” (TCR) mentioned above. Here’s the definition of the TCR, from the IPCC:

Transient Climate Response (TCR)

TCR is defined as the average global temperature change that would occur if the atmospheric CO2 concentration were increased at 1% per year (compounded) until CO2 doubles at year 70. The TCR is measured in simulations as the average global temperature in a 20-year window centered at year 70 (i.e. years 60 to 80).

The transient climate response (TCR) tends to be about 70% of the equilibrium climate sensitivity (ECS). 

However, this time I wanted to look at an even shorter-term measure, the “immediate climate response” (ICR). The ICR is what happens immediately when radiation is increased. Bear in mind that the effect of radiation is immediate—as soon as the radiation is absorbed, the temperature of whatever absorbed the radiation goes up.

Now, a while back Ramanathan proposed a way to actually measure the strength of the atmospheric greenhouse effect. He pointed out that if you take the upwelling surface longwave radiation, and you subtract upwelling longwave radiation measured at the top of the atmosphere (TOA), the difference between the two is the amount of upwelling surface longwave that is being absorbed by the greenhouse gases (GHGs) in the atmosphere. It is this net absorbed radiation which is then radiated back down towards the planetary surface. Figure 3 shows the average strength of the atmospheric greenhouse effect.

The main forces influencing the variation in downwelling radiation are clouds and water vapor. We know this because the non-condensing greenhouse gases (CO2, methane, etc) are generally well-mixed. Clouds are responsible for about 38 W/m2 of the downwelling LW radiation, CO2 is responsible for on the order of another twenty or thirty W/m2 or so, and the other ~ hundred watts/m2 or so are from water vapor.

So to return to the question of immediate climate response … how much does the monthly average surface temperature change when there are changes in the monthly average downwelling longwave radiation shown in Figure 3? This is the immediate climate response (ICR) I mentioned above. Figure 4 below shows how much the temperature changes immediately with respect to changes in downwelling GHG radiation (also called “GHG forcing”).

There are some interesting things to be found in Figure 4. First, as you might imagine, the ocean warms much less on average than the land when downwelling radiation increases. However, it was not for the reason I first assumed. I figured that the reason was the difference in thermal mass between the ocean and the land. However, if you look at the tropical areas you’ll see that the changes on land are very much like those in the ocean. 

Instead of thermal mass, the difference in land and sea appears to be related to land and sea snow and ice. These are generally the green-colored areas in Figure 4 above. When ice melts either on land or sea, much less sunlight is reflected back to space from the surface. This positive feedback increases the thermal response to increased forcing. 

Next, you can see evidence for the long-discussed claim that if CO2 increases, there will be more warming near the poles than in the tropics. The colder areas of the planet warm the most from an increase in downwelling LW radiation. On the other hand, the tropics barely warm at all with increasing downwelling radiation.

Seeing the cold areas warming more than the warm areas led me to graph the temperature increase per additional 3.7 W/m2 versus the average temperature in each gridcell, as seen in Figure 5 below.

The yellow/black line is the amount that we’d expect the temperature to rise (using the Stefan-Boltzmann equation) if the downwelling radiation goes up by 3.7W/m2 and there is no feedback. This graph reveals some very interesting things.

First, at the cold end, things warm faster than expected. As mentioned above, I would suggest that at least in part this is the result of the positive albedo feedback from the melting of land and sea ice.

There is support for this interpretation when we note that the right-hand part of Figure 5 that is above freezing is very different from the left-hand part that is below freezing. Above freezing, the temperature rise per additional radiation is much smaller than below freezing. 

It is also almost entirely below the theoretical response. The average immediate climate response (ICR) of all of the unfrozen parts of the planet is a warming of only 0.2°C per 3.7 W/m2.

Discussion

We’re left with a question: why it is that forty years after the Charney report, there has been no progress in reducing the uncertainty in the estimate of the equilibrium climate sensitivity?

I hold that the reason is that the canonical equation is not an accurate representation of reality … and it’s hard to get the right answer when you’re asking the wrong question. 

From above, here’s the canonical equation once again: 

This “climate sensitivity”, often represented by the Greek letter lambda (λ), is claimed to be a constant that relates changes in downwelling radiation (called “forcing”) to changes in global surface temperature. The relationship is claimed to be:

Change in temperature is equal to climate sensitivity times the change in downwelling radiation.

Or written in that curious language called “math” it is

∆T = λ ∆F                                               Equation 1 (and only)

where T is surface temperature, F is downwelling radiative forcing, λ is climate sensitivity, and ∆ means “change in”

I hold that the error in that equation is the idea that lambda, the climate sensitivity, is a constant. Nor is there any a priori reason to assume it is constant.

Finally, it is worth noting that in areas above freezing, the immediate change in temperature per doubling of CO2 is far below the amount expected from just the known Stefan-Boltzmann relationship between radiation and temperature (yellow/black line in Figure 5). And in the areas below freezing, it is well above the amount expected.

And this means that just as the areas below freezing are showing clear and strong positive feedback, the areas above freezing are showing clear and strong negative feedback.

Best Christmas/Hannukah/Kwanzaa/Whateverfloatsyourboat wishes to all,

w.

AS USUAL, I ask that when you comment you quote the exact words you are discussing, so we can all be certain what you are referring to.