Sniff Test to Refute Claims of Low Climate Sensitivity

There is no shortage of contrarian claims that equilibrium climate sensitivity (or ECS) is so low that global warming can't be considered a threat to human civilizations. Sometimes you'll find them using simple math to "prove" that this is the case. Almost always these "proofs" involve calculations of Planck sensitivity along with assertions that positive feedbacks are impossible (a common refrain is that they violate Le Chatelier's Principle, which they don't) or that they are trumped up lies to create scare stories about global warming. What I want to do here is share what should work as an effective "sniff test" for most (if not all) of these claims using the energy balance equation. First I'll show how the energy balance equation works for a rough estimate for ECS. Then I'll show how you can rearrange terms to show that low sensitivity claims simply don't account for empirical data.

To begin, let's start with the fact that at thermal equilibrium absorbed solar radiation (ASR) equals outgoing longwave radiation (OLR). When these two are not equal, the climate warms or cools until an equilibrium is reached. So when ASR > OLR, there is an earth energy imbalance (EEI), and the surface must warm until ASR = OLR again. So we can expand our equation to account for this: ASR = OLR + EEI, which shows that energy is conserved when climate is warming or cooling.

When a perturbation of the Earth's energy balance occurs (ΔF), some external forcing causes a radiative imbalance (or radiative forcing), and surface temperature changes (ΔT) until balance is restored. The temperature change is proportional to the change in forcing, so ΔT = λ*ΔF, where λ is a constant of proportionality we call "sensitivity." As temperature changes, EEI shrinks until it reaches zero. This allows us to construct the energy balance equation:

ΔF = ΔT/λ + EEI

A forcing change (ΔF) causes an imbalance (EEI) and temperature changes to reduce EEI until it reaches 0. We can rearrange these terms to solve for λ.

λ = ΔT/(ΔF - EEI)

Since forcings add, we can quantify both natural (ΔFn) and anthropogenic (ΔFa) forcings (ΔF = ΔFn + ΔFa) to account for both and solve for λ. I'll use values from the 2025 Indicators of Global Climate Change (IGCC25): ΔFa = 3.1 W/m², ΔFn = ~0 W/m², ΔT = 1.4°C and EEI = 1.4 W/m² 

λ = ΔT/(ΔFa + ΔFn - EEI)

λ = 1.4/(3.1 + 0 - 1.4) = 0.82°C/W/m²

In other words, in order to solve the energy balance equation λ must be near 0.82°C/W/m². Since the forcing for doubling CO2 (ΔFc) in AR6 is 3.93 W/m², we can calculate ECS to be 

ECS = λ* ΔFc = 0.82*3.93 = 3.24°C

That value is of course affected by the uncertainties associated with temperature, forcings, and EEI, so the true value for ECS may be a little higher or lower. In another post, I made a table (reproduced below) using values from HadCRUT5 for temperature, IGCC25 for forcings, and CERES data for EEI for two date ranges (2022-2025 and 2013-2025). I used two date ranges the effects of my choice; I just averaged the results of both.

I should caution that this should be seen as a back-of-the-envelope calculation, but doing this reliably puts you in the ballpark of the central estimate for ECS used by the IPCC (usually between 3°C and 3.5°C). Note here that you don't have to quantify feedbacks to solve the equation, but you can calculate the total of all feedbacks using the formulas in the chart above. So this approach avoids the pitfall that contrarian estimates always seem to fall into, which is deciding a priori that feedbacks must be small (or even negative) and then take that assumption into their calculations. This is the only way they can calculate ECS to be small, but it's fairly easy to show that this approach produces implausible results when compared to empirical data.

When someone makes a claim that ECS is too small to become problematic, we can test whether their claims turn out to be realistic. To do this, we can rearrange our terms to solve for ΔFn:

ΔFn = ΔT/λ + EEI - ΔFa

With this equation, we can show that extremely low ECS values require implausibly high values for ΔFn. I'll provide two examples of this. First, in a recent comment published by the CO2 Coalition and written by Happer and Lindzen, we're told that ECS is 0.538°C. From this we can calculate λ to be 0.538/3.93 = 0.137°C/W/m². Now we can solve for the natural forcings needed to solve the energy balance equation:

ΔFn = 1.4/0.137 + 1.4 - 3.1 = 8.52 W/m²

This means that if Happer and Lindzen are correct that ECS is only 0.54°C, given that human forcings total 3.1W/m², there must be 8.5 W/m² of natural forcings in order for the energy balance equation to actually balance. And this is important to recognize. It's not enough for Happer and Lindzen to perform a simple calculation with a priori assumptions about feedbacks. They have to show that their results are plausible and consistent with empirical data. But neither Happer nor Lindzen can find natural forcings totaling anywhere near 8.5 W/m². A generous assessment would be closer to 0.1 W/m², leaving 8.4 W/m² of unaccounted for natural forcings. Happer and Lindzen's political tract for the CO2 Coalition therefore fails a simple sniff test for plausibility. Unless they can come up with giant natural forcings never discovered by any scientist anywhere ever, their claim that ECS is 0.54°C makes no sense.

Second, let's use this same sniff test on John Shewchuk's claim in the following chart.

Shewchuk's value of 0.237°C/W/m² is slightly less ridiculously low, but it still fails the sniff test:

ΔFn = 1.4/0.237 + 1.4 - 3.1 = 4.21 W/m²

Shewchuk only needs to discover 4.1 W/m² of natural forcings not found by any scientist anywhere ever. This is still an insurmountable task.

Without a λ near 0.8°C/W/m², it's difficult if not impossible to get plausible values that solve the energy balance equation, and this of course requires feedbacks totaling ~2.1 W/m²/°C. If you're determined to keep λ small, there are only a few ways that contrarians can hope to overcome this problem. They could:

1. Try to show that forcings are underestimated, either ΔFn or ΔFa, or both,
2. Try try to show that ΔT and/or EEI are overestimated, or
3. Deny that the energy balance equation (and thus energy conservation) is valid.

There aren't any successful attempts at strategy 1, since ΔFa is well-quantified, and there is no plausible evidence for ΔFn being large. The most common attempt at choosing strategy 1 is to count cloud feedbacks as forcings, but by definition clouds are an internal response, not an external forcing. There are some loud claims taking strategy 2, claiming that ΔT (and even EEI) are fabricated, but none of these claims have any merit and would involve a global-scale conspiracy. So contrarians have to either 1) believe tinfoil hat conspiracy theories or 2) reject the conservation of energy in order to continue to believe their low ECS estimate. They can't have both low ECS and energy conservation unless there's some global conspiracy to fabricate data, which I guess is why virtually all climate contrarians end up being conspiracy theorists of some sort.