Calculating Sensitivity from the LGM

Despite the common misconception that estimates for equilibrium climate sensitivity (ECS) are only derived from model simulations (sometimes erroneously said to be model inputs), there are many ways to estimate ECS. Here on this blog, I've used the energy balance equation with empirical data, and despite varying levels of complexity in quantifying forcings, I keep coming up with a value for ECS of ~3.2°C for 2xCO2. I consider these back-of-the-envelope calculations, fitting for a blogpost to show IPCC estimates are plausible and realistic, but not really for much else. All these types of equations cover a relatively short time period (~175 years) and can be significantly impacted by the uncertainties in the relevant forcings, most importantly aerosols. Some recent evidence suggests that scientists may be underestimating the cooling effect of aerosol pollution and thus underestimating ECS. In fact, Hansen published a paper recently suggesting that ECS could be as high as 4.8°C.[1] 

The ΔT for the LGM

One important feature undergirding that high ECS estimate comes from a reevaluation of how much cooler the last glacial maximum (LGM) was compared to the preindustrial Holocene. Some early estimates from Shakun and a couple others placed the difference at ~3.5°C, but some later studies indicated that value may be too small. In 2020, though, Jessica Tierney[2] used her paleoDA approach (essentially a reanalysis where models are corrected by proxy data) and came up with a value of 6.1 ± 0.4°C (95% CI) for the difference between the LGM and the preindustrial Holocene (I'll refer to this simply as ΔT in this post). Her conclusions agreed with many of the more recent estimates for ΔT that hover around 6°C.

Calculating ECS

CO2 concentrations increased by about 100 ppm from the LGM to the HTM, so if we were to do a simple calculation based on CO2 data alone, we'd conclude that there was a radiative forcing increase (ΔR) of 5.35*ln(280/180) = 2.36 W/m^2. On these time scales, especially going between roughly stable temps of the LGM to the HTM, we can safely assume that EEI is 0. Calculating ECS on the basis of CO2 alone and temperature would yield ΔT/ΔR = 6.1/2.36 = 2.58 C/W/m^2, which would translate into an ECS of 2.58*3.71 = 9.6°C. That's way too high for any reasonable ECS estimate, and it's one reason why I'm skeptical of people making these kinds of simplistic calculations based on numbers without considering the Earth's climate history. We know, for instance, that coming out of the LGM warming was triggered by orbital forcings (which are small) with GHGs, ice-albedo and mineral dust-aerosols changing in response to the orbital "trigger." So in this case, we have to add all these forcings in order to make a proper estimate of a "Charney" definition of ECS.

Jessica Tierney calculated ECS from her estimate of the ΔT and ΔR estimates for GHGs (ΔRghg), ice-albedo (ΔRice) and mineral dust-aerosols (ΔRaer) and the forcing for 2xCO2. She came up with the following values in the published version of her paper.

ΔT = 6.1 ± 0.4°C (95% CI)

ECS = 3.4 ± 1°C (95% CI), or a range of 2.4 - 4.5°C

These results are very close to those used by the IPCC, and in fact, the IPCC's most recent AR6 report was significantly influenced by Tierney's work. The paper is behind a paywall, but I was able to see a prepub version of this paper on the Earth-arXiv, which had slightly different numbers for ΔT and ECS, but it also allowed me to see her ΔR values for the various radiative forcings she use for her calculations. Her prepub numbers were:

ΔT = 5.9 ± 0.4°C (95% CI)

ECS = 3.4 ± 1°C (95% CI), or a range of 2.2 - 4.3°C

ΔRghg = 2.81 ± 0.28 W/m^2 (90% CI)

ΔRice = 3.66 W/m^2 (2.59 to 5.20 W/m^2)

ΔRaer = 0 - 2 W/m^2

ΔR2xco2 = 3.80 ± 0.38 W/m^2 (90%CI)

I decided to play with this a little to sort out the differences between the prepub and published versions. Tierney says it was hard to get a definitive mean value for ΔRaer because the shape of the distribution is not well-defined. But given the ΔR values in the prepub paper, I decided to solve for the ~ΔRaer that would produce the ECS value in the prepub paper using the ΔT in the prepub paper. That turned out to be ~0.6 W/m^2:

ΔRtot = ΔRghg + ΔRice + ΔRaer 

ΔRtot = 2.81 + 3.66 + 0.6 = 7.07 W/m^2 

ECS = [ΔT/ΔRtot]*ΔR2xco2
ECS = [5.9/7.07]*3.8 = 3.2°C

And then I also solved for the ~ΔRtot using Tierney's published values for ΔT and Δ2xco2, I get a ΔRtot of ~6.8 W/m^2. That is,

ECS = [6.1/6.8]*3.8 = 3.4°C

So it would appear that her ΔR values became slightly smaller during responses to peer-review, and her ECS value increased slightly. However, these ΔR values will help me compare Tierney's results to Hansen's recent paper and offer my own thoughts at the end.

Comparing Tierney with Hansen

So the question is, how does Hansen come to a higher estimate for ECS based on the climate changes coming out of the LGM? To get a value approaching 4.8°C, ΔT must be higher, ΔR2xco2 must be higher, and/or ΔRtot must be lower. It turns out that Hansen's values for all three differed in the direction of a higher ECS estimate. 

Hansen used a higher values for ΔT and ΔR2xco2. After mentioning Tierney's results, Hansen writes:

A similarly constrained global analysis by Osman et al. [50] finds LGM cooling at 21–18 kyBP of 7.0 ± 1°C (95% confidence). Tierney (priv. comm.) attributes the difference between the two studies to the broader time interval of the former study, and concludes that peak LGM cooling was near 7°C.

If we take 7°C as a "friendly amendment" to Tierney's paper and adjust Tierney's ΔT to 7°C then ECS jumps up to [7/6.8]*3.8 = 3.9°C. However, Hansen also used 4 W/m^2 for ΔR2xco2 instead of 3.8 W/m^2 in Tierney's paper. That pushes ECS higher again to [7/6.8]*4 = 4.1°C

Hansen used a lower value for ΔRtot, and I think much of this has to do with the fact that he did more work quantifying surface forcings other than ice-albedo and sea level change. For instance, Tierney's paper didn't include forcings for vegetation changes, and Hansen's paper did. Here's as summary of their values:

Evaluation is ideal for CMIP [53] (Coupled Model Intercomparison Project) collaboration with PMIP [54] (Paleoclimate Modelling Intercomparison Project); a study of LGM surface forcing could aid GCM development and assessment of climate sensitivity. Sherwood et al. [21] review studies of LGM ice sheet forcing and settle on 3.2 ± 0.7 W/m2, the same as IPCC AR4 [55]. However, some GCMs yield efficacies as low as ∼0.75 [56] or even ∼0.5 [57], likely due to cloud shielding. We found [7] a forcing of −0.9 W/m2 for LGM vegetation by using the Koppen [58] scheme to relate vegetation to local climate, but we thought the model effect was exaggerated as real-world forests tends to shake off snow albedo effects. Kohler et al. [59] estimate a continental shelf forcing of −0.67 W/m2. Based on an earlier study [60] (hereafter Target CO2), our estimate of LGM-Holocene surface forcing is 3.5 ± 1 W/m2. Thus, LGM (18–21 kyBP) cooling of 7°C relative to mid-Holocene (7 kyBP), GHG forcing of 2.25 W/m2, and surface forcing of 3.5 W/m2 yield an initial ECS estimate 7/(2.25 + 3.5) = 1.22°C per W/m2. We discuss uncertainties in Equilibrium climate sensitivity section.

Hansen et al also do not contain a ΔRaer forcing, since they consider natural aerosols, including dust, to be a feedback, not a forcing.

Glacial-interglacial aerosol changes are not included as a forcing. Natural aerosol changes, like clouds, are fast feedbacks. Indeed, aerosols and clouds form a continuum and distinction is arbitrary as humidity approaches 100%. There are many aerosol types, including VOCs (volatile organic compounds) produced by trees, sea salt produced by wind and waves, black and organic carbon produced by forest and grass fires, dust produced by wind and drought, and marine biologic dimethyl sulfide and its secondary aerosol products, all varying geographically and in response to climate change. We do not know, or need to know, natural aerosol properties in prior eras because their changes are feedbacks included in the climate response.

So Hansen's paper revises virtually all of Tierney's estimates in the direction of a higher ECS estimate. Hansen et al combine ice-albedo, continental shelf and vegetation into what I'm going to call ΔRsurf, and they revise Tierney's ΔRghg value downward. So for Hansen:

ΔRsurf = 3.5 W/m^2

ΔRghg = 2.25 W/m^2

ΔRtot = 5.75 W/m^2

Therefore, for Hansen et al, ECS calculated from the ΔT from the LGM is:

ECS = [7/5.75]*4 = 4.9°C

This appears to account for the entirety of the discrepancy between Tierney's estimate and Hansen's estimate for ECS. 

My Take

So now for my personal take on this (take the following with a grain of salt; I'm not a climate scientist). While I think Hansen has made a case that paleoclimate evidence means we should not entirely rule out high ECS values (even those higher than the IPCC range), I'm not sure I'm ready yet to abandon the more "consensus" value of ~3°C yet. As it stands right now, I think there may be some cause for caution about Hansen's calculations.

1. Gavin Schmidt has pointed out that no model with an ECS > 4.5 has been able to reproduce the LGM. They make the LGM too cold.
2. Osman's estimate of 7°C is on the high end of recent estimates for ΔT, and I suspect using a value nearer to 6°C will take into account more of the published evidence on ΔT.  
3. Forcings from CO2 alone may be higher than Hansen's value for ΔRghg.
4. Hansen did more (and better) work for his ΔRsurf, value, imho.
5. Hansen's value for ΔR2xco2 is higher than the IPCC's most recent estimate, which is 3.93 ± 0.47 W/m^2. Tierney's value came from an older IPCC report. 
6. I'm not sure it's fair to say that mineral dust changes are only a feedback, and I suspect mineral dust should be added to ΔRtot. I want to research this further, but I'm suspicious that ΔRaer should not be 0. Afterall, GHG and ice-albedo forcings are also triggered by orbital forcings.

Friedrick et al 2016[3] placed ΔT at ~6°C and also counted mineral dust aerosols as a forcing, not just a feedback, though they also point out that dust is the largest source of uncertainty in their calculations. Their results indicated that sensitivity actually increased with warming, but the average sensitivity agreed more with Tierney's ECS estimate.

The resulting mean of S for cold climates (Scold) amounts to 0.48KW−1m2,which corresponds to 1.78K per CO2 doubling. For warm climates, the value (Swarm) is more than two times larger, attaining 1.32 KW−1m2 or 4.88K per CO2 doubling. The average of S over the entire 784 ka range can be calculated from a linear regression of the SAT/radiative forcing dataset. It amounts to 3.22 K per CO2 doubling.

It's probably worth noting that Friedrick's value for ΔR2xco2 is 3.7 W/m^2. If we scale his numbers to Tierney's 3.8 W/m^2, Friedrick's ECS would be 3.31°C for 2xCO2. That said, Friedrick cautions against using S over Swarm for future projections. "Comparing the mean of S to Swarm, it becomes apparent that this long-term mean value substantially underestimates Swarm and thus should not be used to assess future anthropogenic warming." In a sense, Friedrick agrees with both Tieney and Hansen; he agrees with Tierney that ECS from the LGM to HTM averages ~3.3°C; he agrees with Hansen that future anthropogenic warming will likely be closer to 4.8°C.

So let's redo the calculation for ECS from the LGM to HTM with a cautious and conservative reading of Hansen tempered by Tierney's and Friedrick's work. My tentatively revised estimates:

ΔRsurf = 3.5 W/m^2 (Hansen)

ΔRghg = 2.8 W/m^2 (Tierney)

ΔRaer = 0.5 W/m^2 (Tierney)

ΔRtot = 6.8 W/m^2 (Combination)

ΔR2xco2 = 3.93 W/m^2 (IPCC)

ΔT = 6.1°C (Tierney, Friedrick, others)

ECS = [6.1/6.8]*3.93 = 3.5°C

Hansen and his colleagues have somewhat put themselves outside of what mainstream climate science is currently concluding. Michael Mann has published a cordial criticism of Hansen's paper that I would recommend to people interested in investigating this further. Personally I think we need good scientists investigating possibilities that the "consensus" values for ECS are too high and too low. From what I've read, I still think that an ECS between 3.0°C and 3.5°C best represents the data we have. But the notion that ECS is not constant is also intriguing. Tierney also acknowledges that ECS is not constant with warming. "ECS is unlikely to remain constant across climate states; rather, paleoclimate and modeling evidence suggest that it scales with background temperature, with lower values during cold climates and higher values during warm states." In another paper, she argues that ECS was ~6.5°C during the PETM. It may well be that the LGM to HTM climate changes contain compelling evidence that ECS is significantly larger than 3°C, and even if it doesn't support an average value near 5°C, that doesn't necessarily mean that we won't see that in the future; in fact, even though I remain skeptical of that, we should do our best to not find out.

References:

[1] James E Hansen, Makiko Sato, Leon Simons, Larissa S Nazarenko, Isabelle Sangha, Pushker Kharecha, James C Zachos, Karina von Schuckmann, Norman G Loeb, Matthew B Osman, Qinjian Jin, George Tselioudis, Eunbi Jeong, Andrew Lacis, Reto Ruedy, Gary Russell, Junji Cao, Jing Li, Global warming in the pipeline, Oxford Open Climate Change, Volume 3, Issue 1, 2023, kgad008, https://doi.org/10.1093/oxfclm/kgad008

[2] Tierney, J.E., Zhu, J., King, J. et al. Glacial cooling and climate sensitivity revisited. Nature 584, 569–573 (2020). https://doi.org/10.1038/s41586-020-2617-x

[3] Tobias Friedrich et al. Nonlinear climate sensitivity and its implications for future greenhouse warming. Sci. Adv.2,e1501923(2016).DOI:10.1126/sciadv.1501923