Not All That Sensitive

Guest Post by Willis Eschenbach

For no particular reason, I got to thinking about the non-global nature of the incoming energy. And this led me to consider the sensitivity of the surface to changes in the radiation absorbed by the surface.

The sensitivity of the surface to changes in absorbed radiation is a central, critical question in climate science. The claim is that the change in global average temperature is equal to the change in absorbed radiation times the “equilibrium climate sensitivity”, abbreviated as ECS. The ECS is assumed to be a constant.

However, despite hundreds of thousands of dollars, work-hours, and computer-hours dedicated to determining the value of the ECS, the uncertainty about its value has only continued to increase.

Figure 1. This figure shows a variety of ways that the Equilibrium Climate Sensitivity (ECS) has been estimated. The dotted lines show the uncertainty of the earliest estimates of the ECS, which was said to be between 1.5 and 4.5 degrees C per doubling of CO2 (2xCO2).

Initially, back in the 1970s, the equilibrium climate sensitivity was claimed to be between 1.5 and 4.5 °C of warming from an increase of 3.7 W/m2 in downwelling radiation. This 3.7 W/m2 is the assumed value of the increase in downwelling radiation from a doubling of CO2 (2xCO2).

This can also be expressed as the change of temperature from a one watt per square meter increase in downwelling radiation. The original central estimate of 3 W/m2 per 2xCO2 is the same as 3/3.7 ≈ 0.8 °C for each radiation increase of 1 W/m2.

However, as you can see in the graphic above, over time, the estimates of the ECS have grown wider and wider. Now, they range from 0.37 degrees C warming resulting from a doubling of CO2 (2xCO2), up to 8.1 degrees C per 2xCO2. This is the same as a range of 0.1 to 2.2 W/m2 for each additional 1 W/m2 of radiation.

I know of no other field of science where this is true, where endless studies of a central constant in the field only show wider and wider uncertainty. To me, this can only mean that the underlying theory is incorrect … but I digress.

Now, the ECS is said to be the climate sensitivity after years of adjusting to the change in radiation. This is because the claim is that the warming is much larger and slower than direct calculations indicate. Mainstream scientists say that various feedbacks increase the warming due to increased radiation, with cloud feedbacks and water vapor feedbacks being the main culprits.

This is discussed in the IPCC AR6 Working Group 1 Chapter 7. They say that the central estimate for the net cloud feedback is 0.42 W/m2 for every 1°C of warming, and that the central estimate for water vapor feedback is another 1.8 W/m2.

In other words, the IPCC says that for every 1°C increase in temperature, the feedbacks increase increase the forcing by another 2.22 W/m2. This means that the warming should be far larger than you’d expect just from the underlying increase in radiation. Using the IPCC central estimate of 3°C/3.7 W/m2 of forcing from 2xCP2, the feedbacks would increase this by 6.66 W/m2 …

Keep this in mind—the standard theory says that the warming should be greater than no-feedback warming.

So to start with … if there were no feedbacks, what warming would we expect to occur?

To investigate this question, I started by taking a look at the total radiation being absorbed by the surface. This is the sum of the absorbed sunlight, which is the total sunlight hitting the surface less reflections from the surface, along with the downwelling thermal radiation from the atmosphere. Here’s a map of the global distribution of the total surface absorbed radiation.

Figure 2. Average Mar 2000 – Feb 2024 of the total absorbed surface radiation, which is the sum of longwave radiation (“LW”, thermal radiation from the atmosphere) and shortwave radiation (“SW”, solar radiation).

As a 24/7 average, the surface gets about half a kilowatt per square meter. In Figure 2, you can see the reflective nature of the desert and the poles, which lead to less radiation being absorbed.

Next, I looked at the total change in absorbed surface radiation over the 24-year period of the CERES dataset. Below you can compare the changes in absorbed radiation (top) with the changes in temperature.

Figure 3. Changes in total absorbed surface radiation (top) and changes in surface temperature (bottom) over the period March 2000 to February 2024.

Note that in a number of areas, the changes in absorbed radiation correlate with the surface temperature changes. Also note that, as expected, increasing radiation leads to increasing temperature.

How much would we expect this increase in radiation to increase the temperature? This can be determined from the Stefan-Boltzmann equation, which states that radiation is proportional to the fourth power of the temperature. Using the CERES data and the S-B equation allows us to calculate just what heating we’d expect to occur from that increase in absorbed radiation. Below is the result.

Figure 4. Theoretical change in temperatures from a uniform 1 W/m2 increase in absorbed surface radiation.

This shows that the expected warming is 0.19°C for each 1 W/m2 increase in absorbed radiation (or 0.7 W/m2 per 2xCO2). However, because a given increase in radiation warms cold areas more than warm areas, the warming ranges from 0.15°C per 1 W/m2 (0.6°C per 2xCO2) in the warmest ocean areas up to 0.44°C per 1 W/m2 (1.6 W/m2 per 2xCO2) in Antarctica.

So that’s our theoretical warming. And the prevailing theory says we should see much greater warming than the theoretical warming due to the feedbacks described above.

To gain further understanding, I looked at how much the observed temperature actually changed in response to the changes the absorbed radiation. Figure 5 below shows the change in temperature that corresponds to a one W/m2 increase in radiation.

Figure 5. Change in the surface temperature for each 1 W/m2 increase in absorbed surface radiation. CERES data from March 2000 – February 2024.

Now, this reveals a surprise. The climatastrophists keep saying that as the radiation absorbed by the surface increases, the temperature perforce must increase.

And for most of the world this is true, although at greatly different rates as we can see in Figure 5.

But in the area of the “Pacific Warm Pool” north of Australia, and the area of the Inter-Tropical Convergence Zone (ITCZ) just above the Equator, the opposite is true—as the amount of radiation absorbed by the surface increases, the temperature goes down, not up.

I say this is a result of the combined effects of the temperature-threshold driven emergence of both tropical cumulus cloud fields and tropical thermally driven thunderstorms. These cool the surface in a host of ways, and exert a huge negative feedback on temperature increases.

But for the purposes of this post, the mixture of phenomena driving this important oddity are not the focus. I’m simply looking at the actual response of the surface temperature to changes in absorbed surface radiation. Most places it increases … but not everywhere.

Next, I looked at the trend data in a different way. I looked at a scatterplot of the trend shown in Figure 5 versus the average surface temperature. I also included the theoretically expected temperature change versus the average surface temperature.

Figure 6. Scatterplot, sensitivity of surface temperature to surface absorbed radiation. Actual average, actual land, and actual sea are calculated based on the CERES data. Theoretical results and average are based on the use of the Stefan-Boltzmann equation on the CERES data.

Now, this is quite interesting for a number of reasons.

First, in every case, the results are below the theoretical calculations. This is a clear indication that far from the globe having a strong positive net feedback to any warming, the net feedback is negative.

Next, this data covers 24 years, nearly a quarter century. So this is not the instantaneous sensitivity of the surface to absorbed radiation.

However, it’s likely that the longer-term warming would be greater than shown in Figure 4. In other words, if the amount of absorbed surface radiation were to suddenly stop increasing, the world would continue to warm for a bit.

So … how much will it warm? Well, in my post Lags and Leads, I showed that we can calculate the warming based on the length of time by which the surface warming lags the absorption of the radiation at the surface. As you might expect, this is greater for the ocean than for the land, due to the greater thermal mass of the ocean.

Per the CERES data, the lag in the land warming is about ten days, and the lag in the ocean warming is much larger, about four times that. Using the formula from “Lags and Leads” linked to above, this would increase the land warming by about 2%, and it would increase the ocean warming by about 30%.

So here is the data shown in Figure 4 above, but with the values adjusted as discussed above to account for delayed warming. I’ve also included the lowest four ECS values from Figure 1 at the head of the post. (The values in that figure have been divided by 3.7 to give them in units of °C per W/m2 rather than °C per 2xCO2.)

Figure 7. As in Figure 6, but with the values adjusted to give the eventual change in the temperature. Purple dots show the lowest four of the ECS estimates shown in Figure 1 at the head of the post (values converted from °C/2xCO2 to °C per W/m2).

Even with these adjustments, the sensitivity of the temperature to absorbed radiation is still well below the theoretical global average. In addition, the four lowest values from Figure 1 are also below the theoretical blackbody values.

And because it is based on observations, this graph includes all possible feedbacks, including cloud feedbacks, cloud aerosol feedbacks, water vapor feedbacks, and all the rest. It is based on how much the surface temperature actually has changed with an increase of 1 W/m2 in absorbed surface radiation.

So I’ll go out on a limb and say that this value of 0.11°C per W/m2 (0.4°C per doubling of CO2) is a reasonable estimate for the Equilibrium Climate Sensitivity. It includes all feedbacks known and unknown, is adjusted for the different thermal lags in the ocean and the land, it is in the range of the four smallest ECS estimates from mainstream climate studies, and it is quite close to three of those ECS estimates.

As Figure 5 shows, like the four smallest ECS estimates in Figure 1, the net feedback to the warming is negative. We know this because everywhere on the Earth, the warming is less than we’d experience with a blackbody planet.

This negative feedback is as we’d expect, given the remarkable stability of the global surface temperature, which only increased by about 0.2% over the entire 20th Century. Twenty-five years ago, that surprising stability was what first drew me to start studying the climate. If the feedback were positive, there would be much larger variations in the Earth’s temperature.

Finally, it could be argued that this is NOT the equilibrium climate sensitivity (ECS), because I’ve used the change in radiation absorbed at the surface, while the ECS is based on the change in top-of-atmosphere (TOA) downwelling “greenhouse effect” radiation (GHE).

As Ramanathan first noted, the TOA GHE radiation can be calculated as the amount of surface upwelling thermal radiation minus the amount of TOA upwelling thermal radiation. And this GHE radiation is closely related to the downwelling radiation absorbed by the surface. Figure 7 shows that relationship.

Figure 7. Absorbed downwelling longwave radiation at the surface, and top of atmosphere (TOA) “greenhouse effect” downwelling longwave radiation

Because they are so similar, and because the downwelling longwave radiation at the surface is only part of the total absorbed radiation, this will make little difference to the ECS I calculated.

 The CERES data shows that for every 1 W/m2 increase in TOA downwelling greenhouse radiation, as we’d expect, the surface downwelling radiation increases by on the order of one W/m2 (1.1 ± .14 W/m2 per W/m2). So any change in my calculated ECS will be small.

And with that, further affiant sayeth naught.

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Fog this morning, which is good news because it’s been hot and I still have another acre to mow. Protip: When your age has two digits and starts with a 7 or above, if you slow down …

… you stop.

And wonder of wonders, a bobcat just walked into the back acreage, what a lovely being!

My very best to all,

w.

You’ve Heard It Before: Quote the exact words you are commenting on. I can defend my words. I can’t defend your interpretation of my words.