From Watts Up With That?

Guest Post by Willis Eschenbach (@weschenbach on X, blog at Skating Under The Ice)

Like Don Quixote suffering a coffee overdose, once again I mount my steed, take up my lance, and go tilting at windmills.

Here’s a thought experiment. Consider the Earth with no atmosphere and with the same surface albedo of 12.5% that it has now. How warm would it be?

In this condition, because there is no atmosphere, there are no heat losses from the surface by sensible or latent heat. For the same reason, there’s no reduction in incoming solar power as a result of reflection from clouds or solar radiation absorbed by the atmosphere. Solar radiation absorbed at the surface is radiated straight back to space. So, we can calculate the temperature directly from the absorbed radiation using the Stefan-Boltzmann equation. This equation relates watts per square meter of surface radiation to the corresponding temperature of the radiating surface. I used the S/B equation with the average emissivity of the Earth, which is ~ 0.98, to calculate the surface temperature. All values are in watts per square meter (abbreviated variously as W/m2 or W/m²).

Minus two degrees C. What you might call totally chill. Just below freezing, in fact.

Now, over millions of years, let’s slowly add in an atmosphere and when it matches the modern atmosphere in all respects, let it percolate for another few million years.

After adding the atmosphere, there are lots of changes. Atmospheric absorption cuts down on the amount of solar radiation hitting the surface, which cools the surface. Of course, reduced surface radiation also reduces the amount reflected. However, this reduction in solar radiation at the surface is more than compensated for by the atmosphere adding in 340 W/m² of downwelling longwave (thermal) radiation from the atmosphere to the surface (yellow arrow in Figure 2 below), which provides significant warming.

And back to the chill side, having an atmosphere allows for sensible and latent heat loss to the atmosphere, which cools the surface. In addition, with an atmosphere we get atmospheric absorption of sunlight, emergent phenomena like thunderstorms, and cloud radiative effects, all of which cool the surface.

It’s a mixed atmospheric bag that ends up with about 20°C less temperature change from the no-atmosphere to the with-atmosphere condition than you’d expect based on the large increase of ~ 212 W/m² in absorbed radiation at the surface.

With that as prologue, here’s the surface radiation absorption with our current atmosphere to the same scale as Figure 1.

OK. Some simple math.

The amount of radiation absorbed by the surface increased from 298 W/m² with no atmosphere, to 510 W/m² with an atmosphere, an increase of 212 W/m².

Due to surface cooling from reduced solar hitting the surface as well as sensible and latent heat loss to the atmosphere, when the atmosphere was added, the temperature only went from -2°C to 18°C, an increase of 20°C.

This means that for each additional W/m² absorbed by the surface, including all possible influences and feedbacks from clouds, water vapor, sensible and latent heat loss, etc., in the long term the temperature increased by 20°C / 212 W/m² = 0.09°C per W/m²

If we use the IPCC canonical value of 3.7 W/m² per doubling of CO₂, this would mean that the equilibrium climate sensitivity at the surface is 0.35°C per doubling of CO₂.

“But wait”, I hear you thinking. “Climate sensitivity is how much the temperature changes, not with downwelling longwave radiation at the surface, but how much temperature changes with the “greenhouse effect” radiation (GHE) from the atmosphere and the clouds, as measured at the top of the atmosphere (TOA)”.

And you’d be right. That’s the definition.

However, we can allow for this by understanding the relationship of surface downwelling longwave and downwelling “greenhouse radiation” from the atmosphere and clouds.

When we look at the current global correlation between the poorly named atmospheric “greenhouse radiation” measured at the top of the atmosphere (TOA) and the surface downwelling longwave radiation, when the TOA-measured greenhouse radiation changes by 1 W/m², due to internal feedbacks, the surface downwelling longwave radiation changes by 1.26 W/m². Or vice versa. In either case, they move in synchrony.

Multiplying the surface sensitivity by 1.26 to convert to sensitivity to greenhouse gases increases the equilibrium climate sensitivity from the surface value of 0.35°C per doubling of CO₂ calculated above, to a final figure of 0.44°C per CO₂ doubling.

OK, that’s one way to get there. Interestingly, for verification of the sensitivity estimate, we can calculate the equilibrium climate sensitivity in a totally different manner. Consider the same thought experiment as above.

With no atmosphere, the GHE radiation is zero W/m². Currently, the GHE radiation is 158 W/m². That gives us 20°C / 158 W/m² * 3.7 W/m²_per_CO₂_doubling = 0.47°C per CO₂ doubling … compared to the 0.44°C from the previous calculation using a different method, that’s excellent agreement. So to be conservative, let me call the warming on the order of half a degree C from a doubling of CO₂.

This ~ half degree C of surface warming per doubling of CO₂ represents a long-term equilibrium calculation, because it includes all known and unknown atmospheric factors and feedbacks involving water vapor, cloud radiative effects, latent and sensible heat losses, atmospheric absorption of solar radiation, all of that. The climate system during the Holocene is basically in a long-term (millennia) dynamic steady-state.

One advantage of using this method to calculate climate sensitivity is that the radiation numbers are large. As a result, small variations or uncertainties in them don’t change the answer much. For example, the current calculated ~ 2 W/m² increase in “greenhouse radiation” since “pre-industrial” times is not significant because it is only ~ 1% of the change in downwelling longwave radiation from the no-atmosphere to the with-atmosphere condition. Basically, the answer is the same whether it’s included or not.

And while my estimate of the equilibrium climate sensitivity of ~ half-degree per CO₂ doubling is well below the three degrees per doubling that the IPCC uses as the sensitivity, it’s not outside historical estimates.

Here are the authors, dates, and values of the best estimates shown in Figure 4 that are under 1 W/m2.

       Author             Year ECS      Class
1  Specht et al.        2016  0.37 Theory & Reviews
2 Idso                       1998  0.42 Theory & Reviews
3 Lindzen and Choi 2009  0.47   Observations
4 Harde                   2017  0.65 Theory & Reviews
5 Lindzen and Choi  2011  0.72   Observations
6 Bates                    2016  0.92   Observations

References are in the paper here.

In closing, in my post “Testing A Constructal Climate Model“, I described how the Constructal model estimates a climate sensitivity of 1.1°C per doubling of CO₂. However, in that post I said:

Finally, this is a maximum sensitivity which does not include the various emergent thermoregulatory mechanisms that tend to oppose any heating or cooling. This means the actual sensitivity is lower than ~1.1°C per 2xCO₂.

This latest result, of ~ half a degree warming per doubling of CO₂, which includes not only emergent phenomena but all atmosphere-related phenomena, is in line with that assessment.

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In related news, providing this method holds up, this means

“APOCALYPSE CANCELLED! SORRY, NO REFUNDS!”

It’s very unlikely that we will double the current CO₂ level. Burning all total known reserves, not just the proven reserves, but all known reserves, will emit about 4,800 gigatonnes of CO₂. This will raise the CO₂ level in the atmosphere by ~ 280 ppmv. That’s far from doubling the current 420 ppmv atmospheric CO₂ level.

This means that about a third of a degree of future warming lies in the ground in the form of fossil fuels.

Sadly, I fear the chance that this analysis will convince any true believers is small. They’re caught in the Upton Sinclair Trap. He famously said:

“It is difficult to get a man to understand something, when his salary depends on his not understanding it.”

It does seem recently, however, that more and more people are seeing through the climate grift. At least the US Government seems to be getting off the climate merry-go-round of endless failed predictions.

And to return to my analysis, what am I missing here? Where are my math mistakes or the holes in my logic? Why isn’t this a solid estimate of the equilibrium climate sensitivity, giving the same answer when calculated in two different ways?

Regards to all on a cloudy fall day,

w.

[UPDATE] In response to comments, a clarification.

A general comment for all, to clarify my position.

I do think that radiatively active gases affect the temperature. But I don’t think that small variations of a few watts per square meter in the resulting downwelling radiation change the temperature anywhere near as much as the conventional wisdom would have you alarmed to believe.

In addition to theoretical arguments and other evidence, my own climate model is able to do a very good job of emulating the real-world temperature using only albedo and the Ramanathan “greenhouse factor”, the percentage of upwelling surface radiation that is absorbed in the atmosphere.

Here is a more recent graphic from my ever-evolving Constructal climate model, showing how those two measurable environmental variables, albedo and greenhouse factor, are all you need to emulate the absolute temperature.

This also makes physical sense. Albedo controls how much energy is entering the system at any time. The greenhouse factor controls how much energy is leaving the system at any time. Any imbalance between those two will be reflected in a temperature change … just not as much as folks think.

This excellent goodness of fit of the Constructal climate model is further evidence that the greenhouse factor, the percentage of upwelling radiation absorbed by radiatively active gases in the atmosphere, does in fact affect the surface temperature.

Regards to everyone,

w.

As Is My Habit: I ask that when you comment, you QUOTE THE EXACT WORDS you are discussing. This is essential to prevent misunderstandings.