How much warming can we expect this century?

This article is also published on Judith Curry’s blog, Climate Etc. Dr. Curry introduced the article as A comprehensive explainer of climate sensitivity to CO₂. Watts Up With That then reposted the article from Climate Etc. I wanted to also publish it here, since the articles at Climate Etc and Watts Up With That have problems with the links to and from the footnotes. There’s also missing some important background color and text color in those articles. So read it here, and if you want to make a comment, consider doing that in one of the other places, where more people are likely to see the comment.

A big Thank you to Dr. Curry for publishing! A big Thank you also to Dr. Nic Lewis for reviewing. The article is much better because of it!

Short summary

According to the Intergovernmental Panel on Climate Change (IPCC), the atmosphere’s climate sensitivity is likely between 2.5 and 4.0°C. Simply put, this means that (in the very long term) Earth’s temperature will rise between 2.5 and 4.0°C when the amount of CO₂ in the atmosphere doubles.

A 2020 study (Sherwood20) greatly influenced how the IPCC calculated the climate sensitivity. Sherwood20 has been “extremely influential, including in informing the assessment of equilibrium climate sensitivity (ECS) in the 2021 IPCC Sixth Assessment Scientific Report (AR6); it was cited over twenty times in the relevant AR6 chapter“, according to Nic Lewis. A Comment in Nature confirmed this view.¹⁾

Nic Lewis took a closer look at this study, and in September 2022, he published his own study (Lewis22) that criticizes Sherwood20. By correcting errors and using more recent data, including from AR6, Lewis22 found that the climate sensitivity may be about 30% lower than what Sherwood20 had found.

If we know what the climate sensitivity is, and if we also know approximately the amount of greenhouse gases that will be emitted going forward, then the amount of future warming that’s caused by greenhouse gases can also be estimated.

In terms of future emissions, a 2022 study (Pielke22) found that something called RCP3.4 is the most plausible emissions scenario. Traditionally, another scenario (RCP8.5), has been used as a business-as-usual scenario, but this is now widely regarded as an extremely unlikely scenario, with unrealistically high emissions.

Assuming that the climate sensitivity from Lewis22 is correct and that RCP3.4 is the most appropriate emissions scenario, then we find that global temperatures will rise by less than 1°C from 2023 to 2100 (not accounting for natural variability).

How much the Earth’s surface air temperature will rise this century depends, among other things, on how sensitive the atmosphere is to greenhouse gases such as CO₂, the amount of greenhouse gases that are emitted, and natural variations. It’s hard to predict natural variations, so the focus here will be on climate sensitivity and greenhouse gas emissions (in particular CO₂).

Climate sensitivity

Climate sensitivity is the amount of warming that can be expected in the Earth’s surface air temperature if the amount of CO2 in the atmosphere doubles. So if the climate sensitivity is 3°C, and the amount of CO₂ in the atmosphere quickly doubles and stays at that level, then the Earth’s surface air temperature will – in the long term – rise by 3°C.²⁾ In the long term, in this case, is more than 1000 years, but most of the temperature increase happens relatively fast.

The exact value for the climate sensitivity isn’t known, and the uncertainty range has traditionally been very large. In 1979, the so-called Charney report found the climate sensitivity to be between 1.5 and 4.5°C. 34 years later, in 2013, the IPCC reached the exact same conclusion – that it’s likely (66% probability) that the climate sensitivity is between 1.5 and 4.5°C. However, the uncertainty in the Charney report may have been underestimated. So even though the official climate sensitivity estimate didn’t change, it wouldn’t be correct to say that no progress was made during those 34 years.

In climate science, there are several different types of climate sensitivity. I won’t go into detail about the various types just yet, but I’ll have something to say about some of them later in the article – when it becomes relevant. The type of climate sensitivity referred to above – in the Charney report and by the IPCC – is called equilibrium climate sensitivity (ECS).

Why so much uncertainty? (Feedback effects)

There’s broad agreement that without so-called feedback effects, the equilibrium climate sensitivity (ECS) would be close to 1.2°C ³⁾, which is quite low and not particularly dangerous. The reason for the great uncertainty comes from how feedback effects affect the temperature.

A feedback effect can be either positive or negative. A positive feedback effect amplifies warming, contributing to a higher climate sensitivity. A negative feedback dampens warming and contributes to a lower climate sensitivity.

The strengths of feedback effects can vary based on the atmosphere’s temperature and composition, and how much of the Earth is covered by ice and vegetation, among other things. Earth’s climate sensitivity is thus not a constant. And for this reason, the equilibrium climate sensitivity, ECS, has been defined as the long-term increase in temperature as a result of a doubling of CO₂ from pre-industrial levels (which was about 284 parts per million (ppm)).

Atmospheric CO₂ concentration currently stands at approximately 420 ppm, which means there’s been a near 50% increase since the second half of the 19th century.⁴⁾ Since the concentration of CO₂ hasn’t yet doubled (and also since the long term is a long way away), the temperature has risen less than what the climate sensitivity is. To be more precise, the temperature increase has been approximately 1.2°C over the past 150 years.

Types of feedback mechanisms

There are several different feedback mechanisms. Here are some of the most important ones:

• Water vapor. Increased amounts of greenhouse gases in the atmosphere cause higher temperatures. A higher temperature then allows the atmosphere to hold more water vapor, and since water vapor is a strong greenhouse gas, the increased amount of water vapor in the atmosphere causes the temperature to rise even more.⁵⁾ The feedback effect from water vapor is therefore said to be positive.
• Lapse rate is how the temperature changes with altitude. The higher up you go in the lower atmosphere (troposphere), the colder it gets – on average about 6.5°C colder per kilometer up. So the lapse rate is said to be 6.5°C per kilometer in the lower atmosphere.
  The feedback from lapse rate is related to the feedback from water vapor, and the two are often considered together. More water vapor causes the temperature to rise more higher up in the atmosphere than closer to the Earth’s surface. This is because the air is generally drier higher up, and so at those altitudes the increased amounts of water vapor has a larger effect on the temperature. The increased temperature at higher altitudes then contributes to more radiation to space, which causes the Earth to cool more. This means that the feedback effect from lapse rate is negative. However, the combined effect of water vapor and lapse rate is positive.

  

• Clouds. Without clouds, the temperature on Earth would be significantly higher than today, but not all clouds have a net cooling effect. Different types of clouds have a different effect on the temperature. On average, high clouds have a warming effect, while low clouds tend to have a cooling effect. When assessing whether total cloud feedback is positive or negative, one must determine whether clouds in a warmer atmosphere on average will have a greater or lesser warming effect than they do now. There is some uncertainty about this, but according to the IPCC, it’s very likely (over 90%) that the feedback effect from clouds is positive, and that therefore changes in cloud cover as a result of increased temperature will amplify the temperature increase.
• Surface Albedo Changes. Earth’s surface albedo says how much solar radiation the Earth reflects directly back to space. Currently, it’s around 0.3, which means that the Earth reflects 30% of the incoming solar radiation. The part of the solar radiation that’s reflected does not contribute to warming.
  The Earth’s albedo can change, for example, when a larger or smaller part of the surface is covered by ice and snow. A higher temperature generally leads to less ice cover, which in turn leads to higher temperatures still, since less radiation is reflected (the albedo decreases). The albedo change resulting from changes in ice cover is a positive feedback effect.
  (Changes in albedo due to changes in cloud cover are included in the cloud feedback.)
• Planck Feedback. A warm object radiates more than a cold object. Or in the case of the Earth: A warm planet radiates more to space than a cold planet. As the Earth warms, it radiates more energy to space, which cools the planet and reduces the rate of warming. The Planck feedback is a strongly negative feedback.⁶⁾
  Actually, the Planck feedback is already included in the calculation of how much the temperature would rise in the absence of (other) feedback effects. In this sense, the Planck feedback is different than the other feedbacks, and it may be best not to think of it as an actual feedback effect, but rather as a fundamental property of physical objects. The Planck feedback is sometimes referred to as Planck response or no-feedback response.

Different ways to calculate climate sensitivity

There are several ways to calculate climate sensitivity. We can base it on the historical record of the past 150 years, where we know approximately how temperature, greenhouse gases, aerosols etc have changed (historical evidence). Or we can estimate the strengths of the various known feedback mechanisms and sum them (process evidence). Or it can be calculated based on how much average temperature has changed since the last ice age glaciation or other warm or cold periods in the Earth’s history (paleo evidence). A fourth possibility is to use climate models – large computer programs that attempt to simulate Earth’s past and future climate under different assumptions.

Sherwood20

In 2020, a large study by 25 authors was published, and it combined the first three of the above-mentioned methods. So they did not calculate climate sensitivity from climate models directly, although the study oftentimes relies on climate models to substantiate some of their values and assumptions.

The study’s title is An Assessment of Earth’s Climate Sensitivity Using Multiple Lines of Evidence. Steven Sherwood is lead author, and so the study is often referred to as Sherwood et al 2020. To simplify further, I’ll just call it Sherwood20.

Sherwood20 concluded that the climate sensitivity is likely (66% probability) between 2.6 and 3.9°C, with 3.1 degrees as the median value. (It’s equally likely that climate sensitivity is higher (50%) or lower (also 50%) than the median.)

The latest IPCC scientific report (AR6) put great emphasis on Sherwood20, and the IPCC, in turn, concluded that climate sensitivity is likely between 2.5 and 4.0°C, a significant narrowing of their previous uncertainty range.
(Note, however, that Sherwood20 and the IPCC focused on different types of climate sensitivities, so their respective values aren’t directly comparable.⁷⁾)

Sherwood20 thoroughly examines all factors that they believe affect climate sensitivity and discusses sources of uncertainty.

Process evidence: Climate sensitivity calculated by adding up feedback effects

The feedback effects that Sherwood20 focused on were primarily the five that I listed earlier. Other feedbacks were estimated as having no net effect. To calculate the climate sensitivity based on feedback effects, the first step is to add up the strengths of each individual feedback effect, and then there’s a simple formula to convert from total feedback strength to climate sensitivity.

The cloud feedback has the largest uncertainty of the various feedback effects. This is true even though the uncertainty has been reduced in recent years.⁸⁾

Historical evidence: Climate sensitivity calculated from temperature and other data over the past 150 years

Within some margin of error, we know how the Earth’s surface air temperature has varied over the past 150 years. We also know roughly how the amount of greenhouse gases in the atmosphere has increased – at least since 1958, when the Mauna Loa observatory started measuring atmospheric CO₂. But in order to calculate the climate sensitivity to CO₂, we also need to know the effect that other drivers of climate change, including aerosols, have had on the temperature and ideally also how the temperature would have changed without human influence. In addition, there’s something called the pattern effect, which, along with aerosols, is what contributes most to the uncertainty in the climate sensitivity when it’s calculated from historical evidence.

• Aerosols: Translated from Norwegian Wikipedia, aerosols are “small particles of liquid or solid in the atmosphere, but not clouds or raindrops. These can have a natural origin or be human-made. Aerosols can affect the climate in various complex ways by affecting Earth’s radiation balance and cloud formation. Studies suggest that these have been released since the start of the Industrial Revolution and have had a cooling effect.”
  The uncertainty in how aerosols affect the temperature is surprisingly large, but they likely have a net cooling effect. The main reason for the large uncertainty is a lack of knowledge about how aerosols interact with clouds.⁹⁾ Along with greenhouse gases, certain aerosols are released during the combustion of fossil fuels, but with newer technologies, the release of aerosols from combustion is being reduced.
  If aerosols have a strong cooling effect, it means they’ve counteracted a significant part of the warming from greenhouse gases. If so, the climate sensitivity to CO₂ must be relatively high. If the cooling effect from aerosols is smaller, it implies a lower climate sensitivity.
• The pattern effect: Different geographical regions have experienced different amounts of warming since the 1800s.¹⁰⁾ Following some previous work, Sherwood20 assumes that areas that have experienced little warming will eventually “catch up” with areas that have experienced more warming, and that this will lead to cloud feedback becoming more positive. However, this may not necessarily happen this century.¹¹⁾ There are few climate sensitivity studies prior to Sherwood20 that take the pattern effect into account, and there’s considerable uncertainty about its magnitude. As a result, the uncertainty in the climate sensitivity as calculated from historical evidence is significantly larger in Sherwood20 than in the earlier studies.

Paleo evidence: Climate sensitivity estimated from previous warm and cold periods

Sherwood20 used one past cold period and one warm period to calculate the climate sensitivity based on paleo evidence (past climates). They also looked at one additional warm period (PETM – Paleocene-Eocene Thermal Maximum, 56 million years ago), but didn’t use the results from that period when calculating their main results.

The cold period that Sherwood20 looked at was the coldest period in the last ice age glaciation (Last Glacial Maximum, LGM), about 20,000 years ago (20 “kyr Before Present” in the graph), when, according to the study, Earth’s temperature was 5±1°C below pre-industrial temperature (so 6±1°C colder than today).

The warm period they looked at was the mid-Pliocene Warm Period (mPWP), about 3 million years ago (3 “Myr Before Present” in the graph), when the temperature was 3±1°C higher than pre-industrial (2±1°C warmer than today).

It may not be obvious that it’s possible to calculate the atmosphere’s climate sensitivity to CO₂ based on what the temperature was in previous warm or cold periods. The reason it is possible is that we can also talk about the atmosphere’s climate sensitivity in a more general sense, without specifically taking CO₂ into consideration.¹²⁾ I’ll try to explain.

If the Earth receives more energy than it radiates back to space, the Earth’s temperature will rise. If climate sensitivity is high, the temperature will rise by a relatively large amount. If climate sensitivity is low, the temperature will rise less.

Regardless of what non-temperature factor causes a change in the balance between incoming and outgoing energy – whether it’s due to more greenhouse gases or a stronger sun, or to ice sheets reflecting more sunlight – the result is (approximately) the same. What matters (most) is the size of the change, not what causes it.

So if we know how much warmer or colder Earth was in an earlier time period, and if we also know how much more or less energy the Earth received at that time compared to now, then it should be possible to calculate how sensitive the atmosphere is to a change in incoming energy.

When we know this general climate sensitivity, and when we also know what CO₂ does to the atmosphere’s energy balance, then it’s possible to calculate the atmosphere’s climate sensitivity to CO₂.

When it comes to what CO₂ does to the atmosphere’s energy balance, it’s been found that a doubling of CO₂ reduces radiation to space by about 4 watts per square meter (W/m²) over the entire atmosphere.¹³⁾ Less radiation to space means that more energy stays in the atmosphere, raising temperatures until outgoing radiation again balances incoming radiation.

All of this means that it’s possible (in theory) that the amount of CO₂ in the atmosphere was the same today and at an earlier time when temperatures were quite different from today, and even if CO₂ levels were the same (and some other factor(s) caused the temperature difference), it would be possible to calculate the atmosphere’s climate sensitivity to CO₂ – because we know approximately what a doubling of CO₂ does to the atmosphere’s energy balance.

When scientists estimate the climate sensitivity from past warm or cold periods, they’re looking at very long time spans. This means that all the slow feedbacks have had time to take effect, and we can then find the “real” long-term climate sensitivity. Based on what I’ve written earlier, you would probably think this is the equilibrium climate sensitivity, ECS. However, in the definition of ECS, the Earth’s ice cover is kept constant, so ECS is in a way a theoretical – not a real – climate sensitivity. The real long-term climate sensitivity is called Earth system sensitivity, or ESS for short.

The climate sensitivity that Sherwood20 calculated is called effective climate sensitivity (S) and is an approximation of ECS. ECS is likely higher than S, and ESS is likely significantly higher than ECS (so S < ECS < ESS).

Even though ESS is the true very long-term climate sensitivity, S is actually the most relevant climate sensitivity for us, since we’re most interested in what will happen in the relatively near term – the next century or two. Sherwood20 writes:

Crucially, effective sensitivity (or other measures based on behavior within a century or two of applying the forcing) is more relevant to the time scales of greatest interest (i.e., the next century) than is equilibrium sensitivity[.]

As we’ve seen, Sherwood20 combined climate sensitivities from three different lines of evidence (meaning that they combined climate sensitivities that had been calculated in three different/independent ways). For historical and process evidence, Sherwood20 calculated effective climate sensitivity (S). But the type of climate sensitivity that is most easily calculated from paleo evidence is Earth system sensitivity (ESS). So to be able to directly compare, and then combine, the climate sensitivities from all three lines of evidence, they needed to convert from ESS to S.

According to Sherwood20, ESS was around 50% higher than ECS during the mPWP warm period. During the much warmer PETM, Sherwood20 assumed that ESS and ECS were approximately the same since there weren’t any large permanent ice-sheets during that warm period – and hence no significant changes in ice-cover.

For the more recent LGM, however, it was actually possible to calculate ECS directly (instead of ESS), by treating slow feedbacks as forcings rather than feedbacks.¹⁴⁾

Naturally, there’s significant uncertainty involved when calculating climate sensitivity based on previous warm and cold periods (paleo evidence). We don’t know what the Earth’s exact average temperature was, and we also don’t know exactly how much more or less energy the Earth received at that time compared to today (or surrounding time periods). Still, according to Sherwood20, the uncertainty in the climate sensitivity as calculated from paleo evidence isn’t necessarily greater than for the other lines of evidence.

Sherwood20’s conclusion

According to Sherwood20, “there is substantial overlap between the lines of evidence” used to calculate climate sensitivity, and the “maximum likelihood values are all fairly close”, as can be seen in the graph (b) below. (However, the median value for historical evidence has a surprisingly high value of 5.82°C).

This is Figure 20 from Sherwood20 and shows their main results. The figure shows how likely different climate sensitivities (S) are for each of their three lines of evidence – in addition to the combined likelihood (black curve). The higher the curve goes, the greater the likelihood. We see that the most likely value is just under 3°C, but the median value is 3.1°C.

Gavin Schmidt, one of the co-authors of Sherwood20, has also written a summary of the study on RealClimate.

Critique of Sherwood20

Nic Lewis is a British mathematician and physicist who entered the field of climate science after being inspired by Stephen McIntyre. McIntyre had criticized the perhaps most important study behind the hockey stick graph used in IPCC’s third assessment report from 2001. (See this earlier post I wrote, which talks about the hockey stick controversy, among other things.)

So Nic Lewis isn’t quite like other climate scientists. You may call him a “skeptical” climate scientist. Not skeptical in the sense that he doesn’t believe CO₂ is a greenhouse gas, but skeptical at least in the sense that he doesn’t believe there’s a major climate emergency. In general, Lewis’ research points to a lower climate sensitivity than IPCC’s estimates.

Here’s a 2019 talk by Nic Lewis on the topic of climate sensitivity. I highly recommend it:

Lewis has published a total of 10 studies related to climate sensitivity, and Sherwood20 referenced studies where Lewis was the main (or only) author 16 times. In September 2022, Lewis published a study, Objectively Combining Climate Sensitivity Evidence, where he discusses and corrects Sherwood20. I will refer to this new study as Lewis22.

In an article that summarizes Lewis22, Lewis argues that Sherwood20’s methodology of combining different lines of evidence to calculate the climate sensitivity is sound:

This is a strong scientific approach, in that it utilizes a broad base of evidence and avoids direct dependence on [Global Climate Model] climate sensitivities. Such an approach should be able to provide more precise and reliable estimation of climate sensitivity than that in previous IPCC assessment reports.

Lewis writes in the article that since 2015, he has published several studies that describe how to combine “multiple lines of evidence regarding climate sensitivity using an Objective Bayesian statistical approach”. Although Sherwood20 was well aware of Nic Lewis’ studies, Sherwood20 had chosen a (simpler) subjective method instead. According to Lewis, the subjective method “may produce uncertainty ranges that poorly match confidence intervals”. Lewis therefore decided to replicate Sherwood20 using the objective method. He also wanted to check Sherwood20’s estimates and data.

The authors of Sherwood20 had, however, made a deliberate choice to use the subjective method. In Schmidt’s article on RealClimate, we can see that Sherwood20 thought the subjective method was more appropriate:

Attempts to avoid subjectivity (so-called ‘objective’ Bayesian approaches) end up with unjustifiable priors (things that no-one would have suggested before the calculation) whose mathematical properties are more important than their realism.

By using the objective method instead of the subjective one, and by also using an appropriate likelihood estimation method,¹⁵⁾ the result was actually a slightly higher climate sensitivity. The median climate sensitivity increased from 3.10 to 3.23°C. Lewis comments:

As it happens, neither the use of a Subjective Bayesian method nor the flawed likelihood estimation led to significant bias in Sherwood20’s estimate of [the climate sensitivity] S when all lines of evidence were combined. Nevertheless, for there to be confidence in the results obtained, sound statistical methods that can be expected to produce reliable parameter estimation must be used.

However, after correcting some other errors and using newer data, including from IPCC’s latest scientific report from 2021 (AR6), the most likely value for the effective climate sensitivity fell to 2.25°C. By also using data that Lewis considered as better justified (not newer), the climate sensitivity was revised down by another 0.09°C, to 2.16°C.

The data changes made by Lewis22 are in part explained in the study and in part in an appendix to the study (Supporting Information, S5). In addition to discussing data values that he changed, in the appendix, Lewis also discusses some data values that he conservatively chose not to change – even though he thought Sherwood20’s values weren’t optimal. So a case could actually be made for an even lower effective climate sensitivity than the 2,16°C that Lewis found in his study.

The figure below is taken from Lewis’ summary of Lewis22 and shows Lewis’ results compared to Sherwood20’s:

The details: Why Lewis22 found a lower climate sensitivity than Sherwood20

In this section, I’ll try to explain in more detail why Lewis22 found a lower climate sensitivity than Sherwood20. This is the most technical part of this article, and if you’re not interested in the details, you may want to skip ahead to the section on future emissions.

Values with blue text are the same as in IPCC’s latest assessment report (AR6). Values with yellow background in Lewis22 are conservative choices.¹⁶⁾ Less conservative choices would have resulted in a lower climate sensitivity. The data changes in Lewis22 are discussed under Review and revision of S20 data-variable assumptions in Lewis22 and in section S5 of Supporting Information.

Historical evidence (data from the past 150 years)

	Sherwood20	Lewis22
ΔFCO2	1.731	1.724
ΔFOther well-mixed greenhouse gases	0.969	1.015
ΔFOzone	0.298	0.400
ΔFLand use	-0.106	-0.150
ΔFStratospheric water vapor	0.064	0.041
ΔFBlack carbon on snow and ice	0.020	0.109
ΔFContrails og induced cirrus	0.048	As Sherwood20
ΔFSolar	0.017	0.019
ΔFVolcanic	-0.113	0.044
ΔFAerosols	-1.104	-0.860
ΔF (sum, difference in forcing, W/m2)	1.824	2.390
ΔN (W/m2)	0.600 ± 0.183	As Sherwood20
ΔT (or ΔTGMAT, °C)	1.03 + 0.085	0.94 ± 0.095
λhist (W/m2/°C)	-1.188	-1.915
𝛾 (scaling factor)	Omitted (1.00)	0.86 ± 0.09
ΔF2xCO2 (W/m2)	4,00 ± 0,30	3.93 ± 0.30
Δλ (pattern effect, W/m2/°C)	0.500 ± 0.305	0.350 ± 0.305
Climate sensitivity, S (°C)	5.82	2.16

ΔF, ΔN, and ΔT_GMAT refer to differences between 1861-1880 and 2006-2018. ΔF is the difference in climate forcing (climate forcing (or radiative forcing) is something that forces the Earth’s energy balance to change, e.g. a stronger/weaker sun or more/less greenhouse gases in the atmosphere). ΔN is the change in radiative imbalance at the top of the atmosphere, measured in W/m². A positive ΔN means that the radiative imbalance is greater now than at the end of the 19th century, and that the Earth is receiving more net energy now than then.

The exact ΔF values that Lewis22 uses can’t be found in IPCC AR6. The reason for this is that Sherwood20 and Lewis22 look at the period from 1861-1880 to 2006-2018, while the IPCC has been more interested in the period 1750 to 2019. Fortunately, though, IPCC has also included forcing values for 1850 and also for several years after 2000, so Lewis has been able to calculate ΔF values with good accuracy (derived from official IPCC values, see table AIII.3 here).

GMAT (Global Mean near-surface Air Temperature) is average air temperature above ground. GMST (Global Mean Surface Temperature) is the same but uses sea surface temperature instead of air temperature over the ocean. Sherwood20 converted ΔT_GMST (0.94°C) to ΔT_GMAT (1.03°C) based on results from climate models, which suggest that GMAT is higher than GMST. Lewis, however, points out that a higher GMAT than GMST hasn’t been observed in the real world, and that, according to the IPCC AR6, the best estimate median difference between GMST and GMAT is 0. Lewis22 therefore uses a value for ΔT_GMAT that’s equal to ΔT_GMST. (See Supporting Information, 5.2.1.)

When estimating effective climate sensitivity (S) from climate feedback (λ), a scaling factor 𝛾 (gamma) is needed (for historical and process evidence). This is because Sherwood20 used linear regression to estimate S based on the ratio of ΔN to ΔT, a relationship that isn’t strictly linear. The reason it’s not linear is that, according to most climate models, climate feedback (λ) weakens during the first decade following a sudden increase in CO₂. (That λ weakens means it gets closer to 0 (less negative), which means that climate sensitivity, S, increases.)

[Sherwood20] recognize this issue, conceding a similar overestimation of S, but neglect it, asserting incorrectly that it only affects feedback estimates from [Global Climate Models]. This misconception results in [Sherwood20]’s estimates of S from Process and Historical evidence being biased high.

Lewis22 used numbers from the two most recent generations of climate models (CMIP5 and CMIP6) to determine that 𝛾 = 0.86.

More technically, 𝛾 is the ratio of to ΔF_2xCO2. You can read more about this in Lewis22 under Climate Sensitivity Measures, F_2xCO2 and its scaling when using Eq. (4) and Supporting Information (S1).

The reason for the relatively large change in aerosol forcing (ΔF_Aerosols) is quite elaborate and advanced, so for that I’ll have to refer you to the Supporting Information (5.2.3, starting from the third paragraph).

The change Lewis22 made for the pattern effect (Δλ) is in large part done because most datasets for sea surface temperature point to the so-called unforced component of the pattern effect (having to do with natural variation, see footnote 8) being very small. See Supporting Information, 5.2.4.

Process evidence (Adding up feedback effects):

	Sherwood20	Lewis22
λWater vapor + lapse rate	1.15 ± 0.15	As Sherwood20
λCloud	0.45 ± 0.33	0.27 ± 0.33
λAlbedo	0.30 ± 0.15	As Sherwood20
λPlanck	-3.20 ± 0.10	-3.25 ± 0.10
λOther	0.00 ± 0.18	As Sherwood20
λ (Sum, feedback effects, W/m2/°C)	-1.30 ± 0.44	-1.53 ± 0.44
𝛾 (Scaling factor)	Omitted (1.00)	0.86 ± 0.09
ΔF2xCO2 (W/m2)	4.00 ± 0.30	3.93 ± 0.30
Climate sensitivity, S (°C)	3.08	2.21

Lewis adjusted the cloud feedback (λ_Cloud) down based on data from Myers et al 2021 (a more recent study than Sherwood20), which found a lower value for low-cloud feedback over the ocean (0-60° from the equator). According to Myers et al 2021, the low-cloud feedback strength is 0.19 W/m²/°C, while Sherwood20 had used 0.37. The difference of 0.18 is how much the total cloud feedback strength was adjusted down in Lewis22. See Supporting Information (5.1.3) for more details.

According to physical expectation (calculated from a formula) and also the latest climate models (CMIP6), the Planck feedback (λ_Planck) is -3.3 W/m²/°C. Sherwood20 acknowledged that the physical expectation for the Planck feedback is -3.3, but they put more weight on the previous generation of climate models (CMIP5) and used -3.2 as the value for the Planck feedback. Lewis22 adjusted the Planck feedback halfway from Sherwood20’s estimate towards the value from physical expectation and CMIP6. See Supporting Information (5.1.2).

As a curiosity, the strength of the albedo feedback here has the same numerical value as the Earth’s albedo, namely 0.30. That’s merely a coincidence.

Paleo evidence (past cold and warm periods)

1. The coldest period during the last ice age glaciation (Last Glacial Maximum, LGM)

	Sherwood20	Lewis22
ζ (how much higher ECS is than S)	0.06 ± 0.20	0.135 ± 0.10
ΔFCO2	-0.57 x ΔF2xCO2 = -2.28	-0.57 x ΔF2xCO2 = -2.24
ΔFCH4	-0.57	As Sherwood20
ΔFN2O	-0.28	As Sherwood20
ΔFLand ice and sea level	-3.20	-3.72
ΔFVegetation	-1.10	As Sherwood20
ΔFDust (aerosol)	-1.00	As Sherwood20
ΔF (difference i forcing, W/m2)	-8.43 ± 2.00	-8.91 ± 2,00
ΔT (difference in temperature, °C)	-5.0 ± 1.00	-4.5 ± 1,00
α (state dependence)	0.10 ± 0.10	As Sherwood20
λ (W/m2/°C)	-1.522	-1.992
ΔF2xCO2 (W/m2)	4.00 ± 0.30	3.93 ± 0.30
Climate sensitivity, S (°C)	2.63	1.97

Sherwood20 calculated ζ (zeta; how much higher equilibrium climate sensitivity, ECS, is than the effective climate sensitivity, S) by looking at abrupt 4xCO₂ simulations – computer simulations where the atmosphere’s CO₂ level is instantaneously quadrupled. Sherwood20 then divided the resulting climate forcing (ΔF_4xCO2) by 2 to find the climate forcing for a doubling of CO₂ (ΔF_2xCO2). Lewis22 notes that the scaling factor of 2 “while popular, is difficult to justify when the actual [scaling factor] has been estimated with reasonable precision to be 2.10”. However, Lewis did not use this method to calculate ζ – instead, he extracted the ζ value (0.135) directly from the results of climate models (or, to be more precise, from long-term simulations by climate models of warming after CO₂ concentration was doubled or quadrupled, finding the same value in both cases). More details can be found under Climate Sensitivity Measures in Lewis22.

ΔF is the difference in climate forcing between the coldest period of the last ice age glaciation and pre-industrial times. ΔT is the temperature difference between these periods.

Sherwood20’s ΔT estimate was 5.0°C. However, the mean ΔT value for the studies that Sherwood20 based their estimate on was only 4.2°C (after, where necessary, adjusting values given in the studies to fairly reflect an observational (proxy-based) estimate of the temperature (GMAT) change). Lewis22 therefore adjusted Sherwood20’s ΔT estimate towards that value, from 5.0 to 4.5°C. See Supporting Information, 5.3.2.

The reason for Lewis22’s revision of ΔF_{Land ice and sea level} was that Sherwood20 had omitted albedo changes resulting from lower sea levels. (The sea level was approximately 125 meters lower during the LGM than now, so Earth’s land surface was larger during the LGM than now. Land reflects more solar radiation than water, so the Earth’s albedo might have been higher during the LGM than what Sherwood20 assumed.) See Supporting Information, 5.3.2.

α (alpha) says something about how climate sensitivity varies based on the state of Earth’s climate system. What we’re most interested in is the climate sensitivity for the current and near-future states of the climate system. Since climate sensitivity may be different for warm periods than cold periods (possibly higher in warm periods), we need to convert the climate sensitivity for any past warm or cold period to the current climate sensitivity. The α parameter is included in an attempt to translate the climate sensitivity for the LGM cold period into the current climate sensitivity.

In contrast to Sherwood20’s assumption about the state dependence, Lewis22 writes that a 2021 study by Zhu and Poulsen “found that ocean feedback caused 25% higher LGM-estimated ECS.” This would bring the LGM climate sensitivity closer to the current climate sensitivity. For this reason (and one other) Lewis thought Sherwood20’s estimate for α was questionable. Still, he retained it. See Supporting Information, 5.3.2 (last paragraph).

2. Mid-Pliocene Warm Period (mPWP)

	Sherwood20	Lewis22
CO2 (ppm)	375 ± 25	As Sherwood20
ΔF2xCO2 (W/m2)	4.00 ± 0.30	3.93 ± 0.30
ΔFCO2 (difference i forcing from CO2, W/m2)	1.604	1.576
ζ (how much higher ECS is than S)	0.06 ± 0.20	0.135 ± 0.10
fCH4	0.40 ± 0.10	As Sherwood20
fESS	0.50 ± 0.25	0.67 ± 0.40
ΔT (°C)	3.00 ± 1.00	2.48 ± 1.25
λ (W/m2/°C)	-1.190	-1.686
Climate sensitivity, S (°C)	3.36	2.33

ΔT is the difference in temperature between the mid-Pliocene Warm Period (mPWP) and pre-industrial times. A positive value for the temperature difference means that mPWP was warmer. ΔF_CO2 is the difference in climate forcing (from CO₂) between mPWP and pre-industrial. f_CH4 is the estimated forcing change from methane (and actually also N₂O/nitrous oxide) relative to the forcing change from CO₂ (so if the forcing change from CO₂ is 1.6, then the forcing change from CH₄ (and N₂0) is 0.64). f_ESS is how much higher the climate sensitivity ESS is compared to the climate sensitivity ECS. The number 284 in the formula represents the pre-industrial CO₂ level (measured in parts-per-million).

Lewis22 used a newer value for f_ESS than Sherwood20. Sherwood20 obtained the value of 0.50 (or 50%) from The Pliocene Model Intercomparison Project (which focuses on the Pliocene era) version 1 (PlioMIP1). The value of 0.67 (or 67%) used by Lewis22 was taken from PlioMIP2, a newer version of the PlioMIP project. See Supporting Information, 5.3.3.

The change Lewis22 made to ΔT was also based on PlioMIP2. Tropical temperatures during the mPWP were about 1.5°C higher than pre-industrial tropical temperatures. To determine the change in global temperature, Sherwood20 multiplied the change in tropical temperatures by 2 on the grounds that average global temperature has changed about twice as much as tropical temperature over the last 500,000 years. However, conditions on Earth were different during the mPWP three million years ago, with much less extensive ice sheets than at present. The PlioMIP2 project has used climate models to estimate that changes in global temperature may have been about 1.65 times higher than changes in tropical temperature during the Pliocene. Lewis22 used this value and consequently multiplied the tropical temperature change (1.5°C) by 1.65 instead of by 2. This changes ΔT from 3.00°C down to 2.48°C. See Supporting Information, 5.3.3.

3. Paleocene–Eocene Thermal Maximum (PETM):

Using β = 0, we can simplify to:

	Sherwood20	Lewis22
ζ	0.06 ± 0.20	0.135 ± 0.10
ΔT (°C)	5.00 ± 2.00	As Sherwood20
fCH4	0.40 ± 0.20	As Sherwood20
CO2 (ppm)	2400 ± 700	As Sherwood20
β	0.0 ± 0.5	As Sherwood20
fCO2nonLog	Omitted (1.00)	1.117
Climate sensitivity, S (°C)	2.38	1.99

ΔT refers to the difference in temperature between the Paleocene-Eocene Thermal Maximum (PETM) and the time just before and after the PETM. During the PETM, temperatures were about 13°C higher than pre-industrial temperatures. Just before and after the PETM, temperatures were about 5°C lower than this (8°C higher than pre-industrial). The number 900 in the formula represents the approximate CO₂ level before and after the PETM. f_CH4 is again the estimated difference in climate forcing from methane (and nitrous oxide) relative to the forcing change from CO₂.

Sherwood20 assumes that the relationship between CO₂ concentration and CO₂ forcing is logarithmic. Lewis refers to Meinshausen et al. 2020, the results of which were adopted by the IPCC in AR6, which found that at high CO₂ concentrations (such as during the PETM), the climate forcing is higher than if the relationship had been purely logarithmic. By using a formula from Meinshausen, Lewis found that the CO₂ forcing during the PETM would have been some 11.7% higher than Sherwood20’s assumption of a purely logarithmic relationship. Therefore, Lewis22 used a value of 1.117 for f_CO2nonLog. See Supporting Information, 5.3.4.

One would think that a higher CO₂ forcing at high temperatures would imply a higher climate sensitivity during warm periods, but that’s not necessarily true, since feedback strengths may be different in warm and cold periods. However, if feedback strengths are the same in warm and cold periods, then a higher CO₂ forcing implies a higher climate sensitivity.

Sherwood20 then assumes that the climate sensitivity ESS during the PETM is roughly the same as today’s equilibrium climate sensitivity, ECS. Uncertainty is accounted for with the parameter β, whose mean value is set to zero. Lewis agrees that “[a]ssuming zero slow feedbacks in the PETM (so ESS equals ECS) may be reasonable, given the lack of evidence and the absence of major ice sheets.” However, some studies (that rely on climate models) suggest that climate sensitivity during the PETM may have been higher than it is today. For this reason, Lewis thinks a positive mean value for β would be better. He nonetheless retained Sherwood20’s estimate of zero. See Supporting Information, 5.3.4.

This concludes the most technical part of this article. Next up: greenhouse gas emissions.

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To determine how much the temperature will rise in the future (disregarding natural variability), it’s not enough to know what the climate sensitivity is – we also need to know approximately how much greenhouse gases will be emitted, so:

What will the emissions be?

The media and many scientists have long used something called RCP8.5 as a business-as-usual scenario for the effect of human activity (including emissions of greenhouse gases), and many still do. RCP stands for Representative Concentration Pathway, and the number (8.5 in this case) is how much greater the net energy input to the atmosphere is in the year 2100 compared to pre-industrial levels, measured in W/m².

But RCP8.5 was never meant to be a business-as-usual scenario. In a 2019 CarbonBrief article about RCP8.5, Zeke Hausfather, another co-author of Sherwood20, writes:

The creators of RCP8.5 had not intended it to represent the most likely “business as usual” outcome, emphasising that “no likelihood or preference is attached” to any of the specific scenarios. Its subsequent use as such represents something of a breakdown in communication between energy systems modellers and the climate modelling community.

Sherwood20 also mentions that RCP8.5 should not be seen as a business-as-usual scenario, but rather as a worst-case scenario:

Note that while RCP8.5 has sometimes been presented as a “business as usual” scenario, it is better viewed as a worst case (e.g., Hausfather & Peters, 2020).

RCPs are often referred to as scenarios, which I also did earlier. But it may be better to think of an RCP as a collection of scenarios that all result in roughly the same net change in incoming energy in the year 2100. Thousands of different scenarios have been developed, and these can be used as inputs to climate models when they simulate future climates.

Plausible emissions scenarios

Roger Pielke Jr, Matthew Burgess, and Justin Ritchie published a study in early 2022 titled Plausible 2005–2050 emissions scenarios project between 2 °C and 3 °C of warming by 2100. In Pielke22, the different scenarios used in IPCC’s 2013 assessment report were categorized based on how well they were able to predict actual emissions from 2005 to 2020, in addition to how well their future emissions matched the International Energy Agency’s projections until 2050. Assuming that the scenarios that best matched actual and projected emissions will also be the ones that will be best at predicting emissions in the second half of the century, they found that RCP3.4 is the most likely (or plausible) RCP.

These scenarios (RCP3.4) are largely compatible with a temperature increase of between 2 and 3°C from pre-industrial times to 2100, with 2.2°C as the median value. Earth’s average temperature has increased by about 1.2°C since pre-industrial, so the median of 2.2°C corresponds to a temperature increase from today to 2100 of about 1.0°C.

After Pielke22 was published, Pielke Jr also looked at the scenarios used in IPCC’s latest assessment report (from 2021). He spoke about this in a talk in November 2022 (54:03-1:06:16), and, according to Pielke Jr, the median value for these newer scenarios is 2.6°C (rather than 2.2°C). This corresponds to a temperature rise of 1.4°C from today until 2100. In the following, I will use this more recent value.

In the talk, Pielke Jr says that RCP4.5 should now be considered a high-emissions scenario, while RCP8.5 and RCP6.0 are unlikely (58:12):

The high emissions scenarios are clearly implausible […]. What’s a high emissions scenario? Anything over 6 W/m² […].

RCP 4.5 and the SSP2-4.5 are plausible high emissions scenarios. I know in the literature they’re often used to represent mitigation success. Today I think we can say based on this method that they’re in fact high-end scenarios. A business as usual – or consistent with current policy – scenario is a 3.4 W/m² scenario. I will say that scenario is almost never studied by anyone.

Pielke22 doesn’t mention climate sensitivity explicitly, but the median equilibrium climate sensitivity (ECS) used in the latest generation of climate models is 3.74°C. ECS is likely higher than the effective climate sensitivity (S), which is the type of climate sensitivity that Sherwood20 and Lewis22 calculated. According to Sherwood, ECS is 6% higher than S. According to Lewis22, ECS is 13.5% higher. Using Lewis22’s value of 13.5%, an ECS of 3.74°C corresponds to an effective climate sensitivity (S) of 3.30°C.

If the climate sensitivity S is closer to 2.16°C, as Lewis22 found, then the temperature increase from today to 2100 will be approximately 35% lower than what Pielke Jr found. This means that the temperature increase from today will be 0.9°C instead of 1.4°C (0.9°C higher than today will be 2.1°C above pre-industrial).

An assumption in the RCP3.4 scenarios is widespread use of CO₂ removal from the atmosphere in the second half of the century. Pielke22 did not assess whether that’s feasible:

Importantly, in the scenarios our analysis identifies as plausible, future decarbonization rates accelerate relative to the present, and many include substantial deployment of carbon removal technologies in the latter half of the century, the feasibility of which our analysis does not assess.

Given the recent rapid pace of technological development, I believe it to be highly likely that potent CO₂ removal technologies will be developed this century. However, other methods may be more economically effective in limiting an unwanted temperature rise, e.g. manipulating the cloud cover, as Bjørn Lomborg suggests in an interview on Econlib (skip forward to 8:35 and listen for 2 minutes or read in footnote 17)).

In October 2022, The New York Times published an extensive article titled Beyond Catastrophe – A New Climate Reality Is Coming Into View. According to the author, David Wallace-Wells, recent evidence shows that the Earth is on track for a 2-3°C warming from the 1800s until 2100 instead of the previously feared 4-5°C. 2-3°C is the same as Pielke22 found.

According to The New York Times article, Hausfather contends that about half of the reduction in expected temperature rise is due to an unrealistic scenario being used previously (RCP8.5). The other half comes from “technology, markets and public policy”, including faster-than-expected development of renewable energy.

How much will temperatures rise by 2100?

Figure 1 (b) in Sherwood20 (graph (b) below) shows how much the temperature is likely to rise between 1986-2005 and 2079-2099, depending on effective climate sensitivity (S) and RCP scenario. This period is about 16 years longer than the 77 years from today until 2100, so the temperature rise for the remainder of the century will be less than the graph suggests – about 18% lower if we assume a linear temperature rise.

We can see in the graph that if RCP4.5 is the correct emissions scenario and the effective climate sensitivity is 3.1°C, then the temperature will rise by about 1.8°C between 1986-2005 and 2079-2099. To estimate the temperature rise from today until 2100, we subtract 18% from 1.8°C, resulting in an estimated increase of about 1.5°C.

Using instead Lewis22’s effective climate sensitivity of 2.16°C with the RCP4.5 scenario, we can see from the graph that the temperature increase will be approximately 1.25°C. This corresponds to a temperature rise of 1.0°C from today until 2100.

RCP3.4 is not included in the graph, but we can assume that the temperature increase for RCP3.4 will be a few tenths of a degree lower than for RCP4.5, so perhaps 0.7-0.8°C, which also agrees quite well with what Pielke Jr found (0.9°C) after we adjusted for the climate sensitivity from Lewis22.

0.8°C corresponds to a temperature rise of 2.0°C since the second half of the 19th century and is identical to the Paris agreement’s two degree target. 2.0°C is also within the New York Times interval of 2-3°C, where – as for the two degree target – pre-industrial is the starting point.

Although Lewis22’s estimate of climate sensitivity may be the best estimate as of today, it’s not the final answer. Much of the adjustment made to Sherwood20’s estimate was based on more recent data, and as newer data becomes available in the future, the effective climate sensitivity estimate of 2.16°C is going to be revised up or down.

And Nic Lewis himself points out that:

This large reduction relative to Sherwood et al. shows how sensitive climate sensitivity estimates are to input assumptions.

But he also criticizes the IPCC for significantly raising the lower end of the climate sensitivity likely range (from the previous to the latest assessment report, the lower end of the likely range was raised from 1.5 to 2.5°C):

This sensitivity to the assumptions employed implies that climate sensitivity remains difficult to ascertain, and that values between 1.5°C and 2°C are quite plausible.

It will be interesting to see what the authors of Sherwood20 have to say about Lewis22.

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Footnotes

¹⁾ From the Comment in Nature (which is written by five authors, four of whom are co-authors of Sherwood20):

On the basis of [Sherwood20] and other recent findings, the AR6 authors decided to narrow the climate sensitivity they considered ‘likely’ to a similar range, of between 2.5 and 4 °C, and to a ‘very likely’ range of between 2 °C and 5 °C.

The Comment in Nature is titled Climate simulations: recognize the ‘hot model’ problem, but it’s behind a paywall. Luckily, however, it’s also published on MasterResource.

²⁾ Zeke Hausfather has written on CarbonBrief that for CO₂ levels to remain at the same high level after a doubling of CO₂, it’s necessary to continue emitting CO₂. If humans stop emitting CO₂, the atmosphere’s CO₂ level will fall relatively quickly. Temperature, however, is not expected to fall, but will likely remain constant for a few centuries (disregarding natural variability).

³⁾ It may not be entirely correct to say that the temperature will increase by 1.2°C if there are no feedback effects. The reason is that the so-called Planck feedback is included in the formula for the “no feedback” climate sensitivity:

However, the Planck feedback can be seen as a different kind of feedback than the other feedbacks mentioned here, and it’s sometimes called the Planck response or no-feedback response. Anyway, if we insert the values from the studies we’re going to discuss in this article, then for Sherwood20 (ΔF_2xCO2 = 4.00 W/m² and λ_Planck = -3.20 W/m²/°C) we get that ECS_noFeedback = 1.25°C. For the other study, Lewis22 (ΔF_2xCO2 = 3.93 W/m² and λ_Planck = -3.25 W/m²/°C) we get ECS_noFeedback = 1.21°C.

⁴⁾ Pre-industrial has traditionally been defined as the average of 1850-1900. Sherwood20 and Lewis22 have used the average of 1861-1880 as pre-industrial, since it is far less affected by volcanic activity. IPCC has started to use 1750.

⁵⁾ This is the theory, at least. However, Andy May has shown that the relationship between temperature and the atmosphere’s water content may be more complicated. His argument is presumably based on the best available data, but he also notes that the data for atmospheric water content is somewhat poor.

⁶⁾ If we add up the strengths of all the feedback effects including the Planck feedback, we get a negative number. But when the Planck feedback is not included, then the sum is very likely positive. And if this sum is positive, it means that the climate sensitivity (ECS) is higher than 1.2°C (which is what the climate sensitivity would be with no feedback effects except the Planck feedback, see footnote 2).

⁷⁾ The IPCC estimated equilibrium climate sensitivity (ECS). Sherwood20, on the other hand, calculated effective climate sensitivity (S). ECS is likely higher than S – 6% higher according to Sherwood20, 13.5% higher according to Lewis22 (which is the study that corrects Sherwood20).

⁸⁾ From Sherwood20:

Among these distinct feedbacks, those due to clouds remain the main source of uncertainty in λ, although the uncertainty in the other feedbacks is still important. 

λ (lambda) is the strength of a feedback effect. A positive λ means that the corresponding feedback effect increases climate sensitivity. Negative λ does the opposite. If the value of λ is known for every type of feedback, then the climate sensitivity can easily be calculated from the sum of the feedback strengths:

⁹⁾ Sherwood20 writes:

However, uncertainty in radiative forcing [during the past 150 years] is dominated by the contribution from anthropogenic aerosols, especially via their impact on clouds, which is relatively unconstrained by process knowledge or direct observations (Bellouin et al., 2020).

¹⁰⁾ Andrew Dessler has been lead author and co-author in several studies on the pattern effect. In a couple of youtube-videos (one short and one long), you can watch his explanation of the pattern effect in relation to committed warming (however, he doesn’t use the term pattern effect in the short video).

An example Dessler uses to illustrate the pattern effect is from the oceans around Antarctica:

The existence of present day cold sea surface temperatures in these regions while the overlying atmosphere is warming due to global warming favors the buildup of low clouds over the region. These clouds reflect sunlight back to space and tend to cool the planet.

From Dessler’s short video (3:08)

When the ocean temperature eventually increases, less clouds are expected, which will lead to faster warming.

Nic Lewis (who criticized Sherwood20) has written an article which criticizes the study that Dessler talks about in the videos (Zhou et al 2021, titled Greater committed warming after accounting for the pattern effect). Although Lewis’ article, which was published on Judith Curry’s climate blog (Climate Etc), isn’t peer reviewed, he has also published a study on the pattern effect, which is peer reviewed.

The dataset for sea surface temperature (SST) used in Zhou et al implies a relatively large pattern effect. However, Lewis notes that other sea surface temperature datasets imply a much smaller pattern effect. The reason for the discrepancy is that sea surface temperature measurements historically have been quite sparse. The uncertainty is therefore substantial.

Lewis also criticizes Zhou et al for not distinguishing between the forced and unforced pattern effect. The component of the pattern effect that is forced has to do with the effect of greenhouse gases. The unforced component, on the other hand, has to do with natural variability. And the two components have different implications for future committed warming. Whereas the greenhouse gas-related component will have little effect on warming this century, the natural variations-component may have a larger effect on warming this century.

Lewis found that the natural variations-component is very close to zero if the following two conditions are met: (1) a different sea surface temperature dataset is used than the dataset Zhou et al used, and (2) a reference period is used that’s outside of the hiatus (1998-2014) – a period of relatively low temperature rise, which may have been caused by a cooling effect from natural variability. It’s thus uncertain whether the pattern effect will have any significant impact on temperatures this century.

¹¹⁾ IPCC on the pattern effect (latest assessment report, section 7.4.4.3):

[T]here is low confidence that these features, which have been largely absent over the historical record, will emerge this century[.]

¹²⁾ From Wikipedia:

Although the term “climate sensitivity” is usually used for the sensitivity to radiative forcing caused by rising atmospheric CO₂, it is a general property of the climate system. Other agents can also cause a radiative imbalance. Climate sensitivity is the change in surface air temperature per unit change in radiative forcing, and the climate sensitivity parameter is therefore expressed in units of °C/(W/m²). Climate sensitivity is approximately the same whatever the reason for the radiative forcing (such as from greenhouse gases or solar variation). When climate sensitivity is expressed as the temperature change for a level of atmospheric CO₂ double the pre-industrial level, its units are degrees Celsius (°C).

¹³⁾ Sherwood20 uses the value 4,00±0,30 W/m², while Lewis22 uses 3,93±0,30 W/m² for the climate forcing for doubled CO₂, which accords with the AR6 assessment (uncertainties here are ± 1 standard deviation).

Some skeptics argue that the atmosphere’s absorption of CO₂ is saturated. This presumably means that the climate forcing for doubled CO₂ would be close to zero, but according to Nic Lewis, this is wrong. The following quote is from a 2019 talk by Lewis (14:00):

Another point that is often argued is that the absorption by carbon dioxide is saturated – that it can’t get any stronger. Unfortunately, that is not the case. However, it is a logarithmic relationship, approximately, so it increases slower and slower. Roughly speaking, every time you double carbon dioxide level, you get the same increase in the effect it has in reducing outgoing radiation. And this decrease in outgoing radiation is called a radiative forcing, and it’s just under 4 W/m² of flux for every time you double carbon dioxide. And again, this is pretty well established.

And a little earlier in the same talk (11:12):

The black is the measured levels – this is measured by satellite at the top of the atmosphere. […] And the red lines are from a specialized radiative transfer model, and you can see how accurately they reproduce the observations. And what that reflects is that this is basic radiative physics, it’s very soundly based. There’s no point in my view disputing it because the evidence is that the theory is matched by what’s actually happening.

The figure that he’s talking about is this one:

The figure shows how CO₂ and other (greenhouse) gases in the atmosphere absorb infrared light from the ground at various wavelengths in the absence of clouds (above the Sahara). Without an atmosphere, the outgoing radiation would follow the top dashed line marked by the temperature 320 K (47°C).

¹⁴⁾ Lewis writes:

A significant advantage of the LGM transition is that, unlike more distant periods, there is proxy evidence not only of changes in temperature and CO₂ concentration but also of non-CO₂ forcings, and that enables estimation of the effects on radiative balance of slow (ice sheet, etc.) feedbacks, which need to be treated as forcings in order to estimate ECS (and hence S) rather than ESS.

¹⁵⁾ The method that Sherwood20 had used to calculate the likelihood of different climate sensitivities was invalid in some circumstances. Among other things, the method assumed a normal (Gaussian) distribution of all input parameters. But for historical evidence (data for the past 150 years), this wasn’t the case since the climate forcing from aerosols wasn’t normally distributed.

To triple-check that Sherwood20’s method was invalid, Lewis calculated the probability distribution using three different methods, and they all gave the same result.

The method used by Sherwood20 led to an underestimation of the probability of high climate sensitivity values:

The dashed lines here show Sherwood20’s results for historical evidence, while the solid lines show Lewis22’s correction.

Correcting this error in Sherwood20 caused the median for the combined climate sensitivity to increase from 3.10 to 3.16°C. (The further increase from 3.16 to 3.23°C, was due to Lewis applying the objective Bayesian method rather than the subjective Bayesian method.)

See Likelihood estimation for S in Lewis22, Supporting Information (S2) and Appendix B in Lewis’ summary of Lewis22 for more details.

¹⁶⁾ Conservative choices in Lewis22 (Supporting Information) – S20 is Sherwood20:

I make no changes to S20’s assessments of other cloud feedbacks. However, I note that Lindzen and Choi (2021) cast doubt on the evidence, notably from Williams and Pierrehumbert (2017), relied upon by S20 that tropical anvil cloud feedback is not, as previously suggested (Lindzen and Choi 2011; Mauritsen and Stevens 2015), strongly negative.

The resulting median revised total cloud feedback estimate is 0.27 − almost double the 0.14 for nine CMIP6 GCMs that well represent observed interhemispheric warming (Wang et al. 2021).

S20’s GMST [=Global Mean Surface Temperature] estimate was infilled by kriging, which does not detect anisotropic features. Recently, a method that does detect anisotropic features was developed, with improved results (Vaccaro et al. 2021a,b). Infilling the same observational dataset as underlies S20’s infilled estimate, the improved method estimates a 9% lower GMST increase. Nevertheless, I retain S20’s estimate of the GMST rise, resulting in a GMAT [=Global Mean Air Temperature] ΔT estimate of 0.94 ± 0.095 [°C].

S20’s 0.60 Wm⁻² estimate of the change in planetary radiative imbalance equals that per AR6. However, AR6 (Gulev et al. 2021 Figure 2.26(b)) shows that, excluding series that are outliers, the AR6 0-2000m [Ocean Heat Content] estimate is middle-of-the-range in 2018 but at its bottom in 2006, hence yielding an above average increase over that period. Nevertheless, I retain S20’s estimate.

Moreover, Golaz et al. (2019) found that an advanced [Global Climate Model] with historical aerosol [Effective Radiative Forcing] of −1.7 Wm⁻², tuned on the pre industrial climate, would only produce realistic GMAT projections if the aerosol forcing is scaled down to ~−0.9 Wm⁻² (and, in addition, its climate sensitivity is halved).

Conservatively, in the light of the foregoing evidence pointing to aerosol forcing being weaker than implied by simply revising B20’s β_lnL−lnN estimate, I adopt a modestly weakened aerosol ERF estimate of −0.95 ± 0.55 Wm⁻² over, as in B20, 1850 to 2005-15. This implies a 5–95% uncertainty range of −1.85 to −0.05 Wm⁻², which has the same lower bound as AR6’s estimate, and is likewise symmetrical.

Scaled to the period 1861-1880 to 2006-2018, the median then becomes 0.86 instead of 0.95, according to Lewis22.

In two [Global Climate Models], Andrews et al. (2018) found a 0.6 weakening in [the pattern effect] when using [a newer sea-ice dataset]. Although the [newer] sea-ice dataset […] is no doubt imperfect […], its developers argue that it is an improvement on [the earlier version]. However, I consider that there is too much uncertainty involved for any sea-ice related reduction to be made when estimating the unforced Historical pattern effect.

In view of the evidence that pattern effect estimates from [Atmospheric Model Intercomparison Project II]-based simulations are likely substantially excessive, and that the unforced element is probably minor and could potentially be negative, it is difficult to justify making a significantly positive estimate for the unforced element. However, a nominal 0.1 ± 0.25 is added to the 0.25 ± 0.17 forced pattern effect estimate, which reflects the substantial uncertainty and allows not only for any unforced pattern effect but also for the possibility that some other element of the revised Historical evidence data-variable distributions might be misestimated.

I revise S20’s central LGM [=Last Glacial Maximum] cooling estimate of −5 [°C] to −4.5 [°C], primarily reflecting, less than fully, the −4.2 [°C] adjusted mean ΔT_LGM estimate of the sources cited by S20, and increase the standard deviation estimate to 1.25 [°C] so as to maintain the same –7 [°C] lower bound of the 95% uncertainty range as S20’s.

S20 use the single year 1850 as their preindustrial reference period for GHG concentrations, whereas for observational estimates of temperature change preindustrial generally refers to the average over 1850−1900. For consistency, the S20 GHG [=Greenhouse Gas] forcing changes should therefore use mean 1850−1900 GHG concentrations. Doing so would change the CO₂ ERF from –0.57x to –0.59x ΔF_2xCO2, as well as marginally changing the CH₄ and N₂O ERFs. However, conservatively, I do not adjust S20’s LGM forcing estimates to be consistent with the LGM ΔT measure.

S20 adopt the estimate of vegetation forcing in the Kohler et al. (2010) comprehensive assessment of non-greenhouse gas LGM forcing changes, but use a central estimate of –1.0 Wm⁻² for aerosol (dust) forcing in place of Kohler et al.’s –1.88 Wm⁻². This seems questionable; Friedrich and Timmermann (2020) adopt Kohler et al.’s estimate, while pointing out that estimates of its glacial-interglacial magnitude vary from ~0.33 to ~3.3 Wm⁻². I nevertheless accept S20’s estimate of dust forcing[.]

S20 assume that climate feedback in equilibrium (λ’) strengthens by α for every -1 [°C] change in ΔT, resulting in the 0.5 α T_LGM² term in (11), reducing LGM-estimated ECS. Contrariwise, Zhu and Poulsen (2021) found that ocean feedback caused 25% higher LGM-estimated [climate sensitivity] ECS. Moreover, a significant part of the reduction in mean surface air temperature at the LGM is due to ice-sheet caused increased land elevation, which would weaken λ’ compared to in non-glacial climates. Although S20’s [α = 0,1 ± 0,1] estimate appears questionable, I retain it.

Although the Tierney et. al (2019) 1.4 [°C] tropical SST warming estimate appears more reliable than S20’s 1.5 [°C], I retain the latter but multiply it by the 1.65 PlioMIP2 ratio, giving a revised GMAT ΔT_mPWP of 2.48 [°C].

S20 assessed a [2400 ± 700] ppm distribution for CO₂ concentration in the PETM relative to a baseline of 900 ppm, implying a [1.667 ± 0.778] ΔCO2_PETM distribution. That covers, within its 90% uncertainty range, a concentration ratio range (1 + ΔCO2_PETM) of 1.39 to 3.95. The CO₂ concentration estimates considered by S20, even taking extremes of both their PETM and Eocene ranges, constrain (1 + ΔCO2_PETM) within 1.4 to 5. Using instead that range would lower PETM based S estimates. Nevertheless, I retain S20’s ΔCO2_PETM distribution.

While Meinshausen et al. assume a fixed ratio of CO₂ ERF to stratospherically-adjusted radiative forcing, there is modeling evidence that fast adjustments become more positive at higher temperatures (Caballero and Huber 2013), which would further increase CO₂ ERF change in the PETM. I make no adjustment for this effect.

To account for forcing from changes in CH₄ concentrations, S20 apply the same 0.4 f_CH4 factor to the CO₂ forcing change as for the mPWP, with doubled uncertainty, although noting that the tropospheric lifetime of CH₄ could be up to four times higher given sustained large inputs of CH₄ into the atmosphere (Schmidt and Shindell 2003). I retain S20’s f_CH4 distribution, although doing so may bias estimation of S upwards.

S20 assume that ESS [=Earth System Sensitivity] for the PETM was the same as present ECS, representing uncertainty regarding this by deducting a [0 ± 0,5] adjustment (β) from ESS feedback when estimating ECS feedback, λ’. Assuming zero slow feedbacks in the PETM (so ESS equals ECS) may be reasonable, given the lack of evidence and the absence of major ice sheets. However, Caballero and Huber (2013) and Meraner et al. (2013) both found, in modeling studies, substantially (~50%) weaker climate feedback for climates as warm as the PETM. Zhu et al (2019) found, in a state-of-the-art GCM, that ECS was over 50% higher than in present day conditions, with little of the increase being due to higher CO₂ ERF. I therefore consider that it would be more realistic to use a positive central estimate for β. Nevertheless, I retain S20’s estimate.

¹⁷⁾ Here’s (roughly) what Bjørn Lomborg said:

If [you] want to protect yourself against runaway global warming of some sorts, the only way is to focus on geoengineering, and […] we should not be doing this now, partly because global warming is just not nearly enough of a problem, and also because we need to investigate a lot more what could be the bad impacts of doing geoengineering.

But we know that white clouds reflect more sunlight and hence cool the planet slightly. One way of making white clouds is by having a little more sea salt over the oceans stirred up. Remember, most clouds over the oceans get produced by stirred-up sea salt — basically wave-action putting sea salt up in the lower atmosphere, and those very tiny salt crystals act as nuclei for the clouds to condense around. The more nuclei there are, the whiter the cloud becomes, and so what we could do is simply put out a lot of ships that would basically [stir] up a little bit of seawater — an entirely natural process — and build more white clouds.

Estimates show that the total cost of avoiding all global warming for the 21st century would be in the order of $10 billion. […] This is probably somewhere between 3 and 4 orders of magnitude cheaper — typically, we talk about $10 to $100 trillion of trying to fix global warming. This could fix it for one thousandth or one ten thousandth of that cost. So, surely we should be looking into it, if, for no other reason, because a billionaire at some point in the next couple of decades could just say, “Hey, I’m just going to do this for the world,” and conceivably actually do it. And then, of course, we’d like to know if there’s a really bad thing that would happen from doing that. But this is what could actually avoid any sort of catastrophic outcomes[.]