How Much Warming Can We Expect in the 21st Century?

From Climate Etc.

by Hakon Karlsen

A comprehensive explainer of climate sensitivity to CO2

Short summary

According to the Intergovernmental Panel on Climate Change (IPCC), the atmosphere’s climate sensitivity to CO2is 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 than the magnitude of the equilibrium climate sensitivity. 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.

How temperature changes with altitude in the lower atmosphere. Image found on ScienceDirect (from the book Environmental Management).

  • 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.


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.

Screen Shot 2023-07-08 at 8.25.51 AM

Temperature trends for the past 65 million years. Figure from Burke et al 2018. The original image also contained different future projections, but I’ve removed that part of the image. Note that there are 5 different scales on the time axis.

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.)

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:

In (a), (b), and (d), dashed lines represent results from Sherwood20, while solid lines are from Lewis22. In (b), we see that the three lines of evidence for calculating the climate sensitivity coincide nicely for Lewis22, while the variation is slightly larger in Sherwood20. Additionally, the uncertainty is lower (the curves are narrower) in Lewis22, especially for historical evidence (data from the past 150 years). PETM is the warm period that Sherwood20 didn’t include in the calculation of the combined climate sensitivity (PETM = Paleocene-Eocene Thermal Maximum, about 56 million years ago, when temperatures were about 12°C higher than now).

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)

Screen Shot 2023-07-06 at 3.07.33 PM
ΔFOther well-mixed greenhouse gases0.9691.015
ΔFLand use-0.106-0.150
ΔFStratospheric water vapor0.0640.041
ΔFBlack carbon on snow and ice0.0200.109
ΔFContrails og induced cirrus0.048As Sherwood20
ΔF (sum, difference in forcing, W/m2)1.8242.390
ΔN (W/m2)0.600 ± 0.183As Sherwood20
ΔT (or ΔTGMAT, °C)1.03 + 0.0850.94 ± 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 ± 0,303.93 ± 0.30
Δλ (pattern effect, W/m2/°C)0.500 ± 0.3050.350 ± 0.305
Climate sensitivity, S (°C)5.822.16

ΔF, ΔN, and ΔTGMAT 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 ΔTGMST (0.94°C) to ΔTGMAT (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 ΔTGMAT that’s equal to ΔTGMST. (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 ΔF2xCO2. You can read more about this in Lewis22 under Climate Sensitivity MeasuresF2xCO2 and its scaling when using Eq. (4) and Supporting Information (S1).

The reason for the relatively large change in aerosol forcing (ΔFAerosols) 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):

λWater vapor + lapse rate1.15 ± 0.15As Sherwood20
λCloud0.45 ± 0.330.27 ± 0.33
λAlbedo0.30 ± 0.15As Sherwood20
λPlanck-3.20 ± 0.10-3.25 ± 0.10
λOther0.00 ± 0.18As 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 ± 0.303.93 ± 0.30
Climate sensitivity, S (°C)3.082.21

Lewis adjusted the cloud feedback (λCloud) 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 (λPlanck) 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)
ζ (how much higher ECS is than S)0.06 ± 0.200.135 ± 0.10
ΔFCO2-0.57 x ΔF2xCO2 = -2.28-0.57 x ΔF2xCO2 = -2.24
ΔFCH4-0.57As Sherwood20
ΔFN2O-0.28As Sherwood20
ΔFLand ice and sea level-3.20-3.72
ΔFVegetation-1.10As Sherwood20
ΔFDust (aerosol)-1.00As 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 ± 0.10As Sherwood20
λ (W/m2/°C)-1.522-1.992
ΔF2xCO2 (W/m2)4.00 ± 0.303.93 ± 0.30
Climate sensitivity, S (°C)2.631.97

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 (ΔF4xCO2) by 2 to find the climate forcing for a doubling of CO2 (ΔF2xCO2). 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 ΔFLand 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).

  1. Mid-Pliocene Warm Period (mPWP)
CO2 (ppm)375 ± 25As Sherwood20
ΔF2xCO2 (W/m2)4.00 ± 0.303.93 ± 0.30
ΔFCO2 (difference i forcing from CO2, W/m2)1.6041.576
ζ (how much higher ECS is than S)0.06 ± 0.200.135 ± 0.10
fCH40.40 ± 0.10As Sherwood20
fESS0.50 ± 0.250.67 ± 0.40
ΔT (°C)3.00 ± 1.002.48 ± 1.25
λ (W/m2/°C)-1.190-1.686
Climate sensitivity, S (°C)3.362.33

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. ΔFCO2 is the difference in climate forcing (from CO2) between mPWP and pre-industrial. fCH4 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). fESS 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 fESS 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.

  1. Paleocene–Eocene Thermal Maximum (PETM):

Using β = 0, we can simplify to:

ζ0.06 ± 0.200.135 ± 0.10
ΔT (°C)5.00 ± 2.00As Sherwood20
fCH40.40 ± 0.20As Sherwood20
CO2 (ppm)2400 ± 700As Sherwood20
β0.0 ± 0.5As Sherwood20
fCO2nonLogOmitted (1.00)1.117
Climate sensitivity, S (°C)2.381.99

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. fCH4 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 fCO2nonLog. 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.

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 ECS. 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 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.


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 (ΔF2xCO2 = 4.00 W/m2 and λPlanck = -3.20 W/m2/°C) we get that ECSnoFeedback = 1.25°C. For the other study, Lewis22 (ΔF2xCO2 = 3.93 W/m2 and λPlanck = -3.25 W/m2/°C) we get ECSnoFeedback = 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

[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 βlnL−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 ΔTLGM 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 ΔF2xCO2, 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 TLGM2 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 ΔTmPWP 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] ΔCO2PETM distribution. That covers, within its 90% uncertainty range, a concentration ratio range (1 + ΔCO2PETM) 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 + ΔCO2PETM) within 1.4 to 5. Using instead that range would lower PETM based S estimates. Nevertheless, I retain S20’s ΔCO2PETM 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 fCH4 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 fCH4 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[.]

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William Howard
July 9, 2023 6:18 am

sensitivity? so why has ther been no increase in temerature in the last 20 years while the amount of CO2 has dramatically increased? if a hypothesis isn’t confirmed by observed real world data it shoud be discarded

Boff Doff
Reply to  William Howard
July 9, 2023 6:42 am

I believe there is a proviso at the outset that states the temperature variation is subject to natural variation. The implication being there would have been some cooling over the last 20 years.

It is just speculation to assert that any forecast of temperatures longer than 3 days has any predictive skill. Producing an alternative study that suggests the alarmists are inaccurate just gives their arrogance a veneer of credibility that shouldn’t exist. Stop it.

Reply to  William Howard
July 9, 2023 6:55 am

Correct, the IPCCs consensus is based on amateurish modelling, which is probably why their 97% is really 2% and the almost 40,000 Clintel / Oregon Petition signatories have far more credibility

Frank from NoVA
Reply to  William Howard
July 9, 2023 8:44 am

Exactly. Dr. Feynman, please call your office.

Reply to  William Howard
July 9, 2023 11:04 am

The CERES satellite data shows that the earth’s energy imbalance was zero about 25 years ago. Since the plants use some of the sun’s energy just to grow, that means there was not enough energy to keep the earth’s temperature stable. The imbalance has increased to the point where the plants are being kept alive and we’re very close to equilibrium.

Joseph Zorzin
July 9, 2023 6:33 am

“The exact value for the climate sensitivity isn’t known…”

but…but… I’ve been told that THE science is settled! /sarc

Joseph Zorzin
Reply to  Joseph Zorzin
July 9, 2023 7:02 am

Now that I’ve finished reading this article I have far less confidence in THE science than I did when I got out of bed. And this is only one topic within THE science. I suspect all the topics within THE science are just as dubious. Put them all together and what do you have but mysticism.

Tom Abbott
Reply to  Joseph Zorzin
July 10, 2023 4:21 am

All the topics are just as dubious. It’s all speculation, assumptions and assertions. And nothing else. No evidence of anything the climate alarmists claim.

Joseph Zorzin
Reply to  Tom Abbott
July 10, 2023 4:31 am

especially tree ring thermometers!

Reply to  Joseph Zorzin
July 11, 2023 6:12 pm

Witch doctors use more science than this topic.

Reply to  Joseph Zorzin
July 9, 2023 1:37 pm

Try listening to this balloon data analysis

The analysis given in the post is radiative….. but what if something else “controlled” the energy transfer in the atmosphere.

Joseph Zorzin
Reply to  bnice2000
July 9, 2023 1:50 pm

Apparently, I saw half of it a long time ago- I still see the red line under it- but maybe I didn’t finish it because of- the brief description under it which says:

Climate change refers to long-term shifts in temperatures and weather patterns, mainly caused by human activities, especially the burning of fossil fuels.

Reply to  Joseph Zorzin
July 9, 2023 4:34 pm

Climate change refers to long-term shifts in temperatures and weather patterns, mainly caused by human activities, especially the burning of fossil fuels.”

Michael (or was it Ronan), was quoting the IPCC mantra, as being nonsense.

Start at the 24 minute mark where Michael takes over with the balloon data analysis. (I think I have the time mark about right)

It is worth watching because it appears to prove that the atmosphere is controlled by the gas laws, not radiation.

Not saying radiation is not part of the overall energy transfer system of the atmosphere, as are convection, conduction, air movement etc etc…

… but how do you end up with a dead straight line for energy v molecular density if the gas laws are not the final control.?

Krishna Gans
Reply to  Joseph Zorzin
July 10, 2023 12:35 am

Climate sensitivity isn’t science obviously 😀

Tom Abbott
Reply to  Krishna Gans
July 10, 2023 4:24 am

No, climate sensitivity is guessing, not science. The estimates are all over the place from net warming to net cooling.

This is what we are wasting TRILLIONS of dollars on: Trying to fix something (CO2) that may not be broken.

Peta of Newark
July 9, 2023 6:42 am

Hello people: Welcome (back) to the 13th Century

Try not to worry too much about being in the dark, in a few hundred years Isaac Newton will be along and things can only go up from then on…..

Even tho he did poison himself trying to mix Sulphur and Mercury to make Gold

Richard Page
Reply to  Peta of Newark
July 9, 2023 8:16 am

Sheesh, amateurs eh? Everybody knows the best way to create gold is to mix politics and climate change….

Reply to  Richard Page
July 9, 2023 8:40 am

First LOL of the day, thank you.

BTW, 100% true in most previously industrialized countries, i.e. the western moronic “democracies”.

Reply to  Richard Page
July 9, 2023 9:13 am

Modern alchemy, brought to you courtesy of the IPCC.

Reply to  Richard Page
July 9, 2023 1:48 pm

I think you just nailed it, Richard!

Reply to  Peta of Newark
July 9, 2023 10:01 am

In the Beginning,
All was dark as night.
God said “Let Newton be”
And all was light.

It couldn’t last.
The Devil, howling “Ho,
Let Einstein be ”
Restored the status quo.

Reply to  Oldseadog
July 9, 2023 12:39 pm

Good poem. Says a lot about the end of the clockwork universe through relativity and, especially, quantum theory.

But it should be noticed that it has antisemitic undertones.

Reply to  MCourtney
July 9, 2023 5:24 pm

But it should be noticed that it has antisemitic undertones.

Only to those who are so obsessed with such silliness that they can only imagine their own neurosis behind every statement about virtually anything.

Joseph Zorzin
July 9, 2023 6:46 am

“according to the IPCC, it’s very likely (over 90%) that the feedback effect from clouds is positive”

What with them being scientists- they’re probably right- but, I like to sit in my back yard catching some rays to improve my tan- I notice on a cloudy day- when a cloud blocks the sun, the temperature drops quickly- of course this is more noticeable when the humidity is low because high humidity holds the heat (I’m not so dumb for a non scientist)- enough to feel a chill- then after a few minutes or so, the cloud moves on- I get the full sun – and the temperature shoots up several degrees. Just a layman’s perspective on this topic.

I’ve also noticed that on cloudy nights the temperature doesn’t drop as low as it would have if cloudless.

“but according to the IPCC, it’s very likely (over 90%) that the feedback effect from clouds is positive”

They may be right but I don’t think the 90% confidence is justified. Do they really have enough data to be so confident?

Reply to  Joseph Zorzin
July 9, 2023 9:16 am

according to the IPCC, it’s very likely . . .”

Hmmm, upon thorough review, nowhere in the scientific method do I find mention of use of probability theory.

Tom Abbott
Reply to  ToldYouSo
July 10, 2023 4:30 am

It’s not the scientific method, it’s guessing. If it was the scientific method they wouldn’t be using the word “likely”.

Of course, you obviously know that, but apparently a lot of others do not, including members of the IPCC.

Reply to  Joseph Zorzin
July 9, 2023 3:26 pm

Do they really have enough data to be so confident?

A resounding YES – all the climate models show that clouds cause warming and the models incorporate the latest climate phiisics that can never be wrong.

Joseph Zorzin
Reply to  RickWill
July 9, 2023 4:31 pm

OK, glad we got that resolved. 🙂

Tom Abbott
Reply to  RickWill
July 10, 2023 4:31 am

No, they don’t have enough data, and if they have any confidence in what they have, they are fooling themselves.

Frank from NoVA
July 9, 2023 6:47 am

There is no evidence from 65 million years of paleo data that CO2 acts as the Earth’s ‘control knob’. Neither Lewis 2022 nor Sherwood 2020 provide any evidence that our emissions of CO2 have contributed to the Earth’s warming since the Little Ice Age.

Reply to  Frank from NoVA
July 9, 2023 6:59 am

Anyone peddling CO2 as dangerous, is uneducated in basic established science, or is earning big bucks by doing so

Tom Abbott
Reply to  Energywise
July 10, 2023 4:37 am

Either way, they are not telling the truth.

Reply to  Frank from NoVA
July 9, 2023 9:23 am

As a matter of (paleoclimatology) “fact”, extensive periods have show anti-correlation of CO2 with global temperature.

See attached graphic attributed to Royer,

Reply to  ToldYouSo
July 9, 2023 9:25 am

Ooops . . . here’s the graphic.

And the attribution should be to Scotese and Berner, as noted . . . not to Royer . . . mea culpa

Reply to  Frank from NoVA
July 9, 2023 4:33 pm

There is no evidence from 65 million years of paleo data that CO2 acts as the Earth’s ‘control knob’.”
Is their any proof that co2 does or has ever done anything to temperature which is measurable?

Frank from NoVA
Reply to  Mike
July 9, 2023 7:38 pm

The word ‘proof’ doesn’t apply to science. There’s plenty of evidence that CO2, like water vapor, is a so-called greenhouse gas that absorbs and emits LWIR, but there’s no evidence that our emissions of CO2 have contributed to the current post-LIA warming or will otherwise endanger mankind.

Conversely, there is a preponderance of evidence that the use of cheap and reliable energy from fossil fuels has allowed billions of people to achieve material abundance that would have been inconceivable to even the wealthiest individuals only a few generations earlier.

Given that we know that photosynthesis stops below 150 ppm, and that CO2 levels when modern life first evolved on Earth were considerably higher than today’s level of 400+ ppm, any manifestation of climate alarmism would be laughable but for the knowledge that it’s being used by the Left to collapse civilization.

Tom Abbott
Reply to  Mike
July 10, 2023 4:46 am

“Is their any proof that co2 does or has ever done anything to temperature which is measurable?”

No, there is not. Not in the real world.

Climate Alarmists are invited to rebut this claim.

You will note if you come back later, that no Climate Alarmists have rebuted this claim because they can’t, because there is no evidence they can cite.

When you say to climate alarmists: Prove it!, they can’t do it. That ought to tell you all you need to know about the state of CO2 science.

The best climate alarmist can do is “CONfidence” levels, which are meaningless in climate science. A confidence level is an educated GUESS. It is not an established fact. And these educated guesses are based on other educated guesses which makes it even worse.

Nothing is an established fact about CO2 other than it is a greenhouse gas. It’s interaction with the Earth’s atmosphere has definitely not been established

Tom Abbott
Reply to  Frank from NoVA
July 10, 2023 4:36 am

You are exactly right, Frank. There is no evidence of there ever being a runaway greenhouse effect due to CO2, and CO2 levels have been much higher in the past than they are now (7,000ppm in the past verses 420ppm today), and there is no evidence that CO2 has contributed to Earth’s warming. CO2 may actually net cool the Earth’s atmosphere, and the experts cannot say that is not the case with any confidence.

The current state of climate science is a joke. A really bad joke on humanity. A really destructive joke on humanity.

Joseph Zorzin
July 9, 2023 6:49 am

“There are several ways to calculate climate sensitivity.”

But we’ll never know for sure until we get the results- after the fact. All those “ways to calculate” aren’t really calculations in the sense of actual measurements, they’re really just estimates and prophecies/predictions.

Reply to  Joseph Zorzin
July 9, 2023 1:49 pm

My understanding, is that it is basically impossible for CO2 to affect atmospheric temperature at all…

It absorbs a thin band of surface radiation, by does not re-emit until some 11km altitude.

Its frequency when it does re-emit is too weak to warm anything. (some -80C iirc)

It thermalises in the atmosphere and the tiny amount energy released is easily dealt with immediately by normal atmospheric balances.

Just like bushfire heat is not retained in the atmosphere for long,

CO2 is just another path for energy to be balanced in the atmospheric system.

Reply to  bnice2000
July 9, 2023 5:27 pm

what if its altimeter gets broken?

July 9, 2023 6:53 am

Basically, as much, or as little, as Mother Nature wants to give us

July 9, 2023 6:58 am

LiG Metrology, Correlated Error, and the Integrity of the Global Surface Air-Temperature Record — Patrick Frank 

Abstract: The published 95% uncertainty of the global surface air-temperature anomaly (GSATA) record through 1980 is impossibly less than the 2σ = ±0.25 ◦C lower limit of laboratory resolution of 1 ◦C/division liquid-in-glass (LiG) thermometers. The ~0.7 ◦C/century Joule-drift of lead- and soft-glass thermometer bulbs renders unreliable the entire historical air-temperature record through the 19th century. A circa 1900 Baudin meteorological spirit thermometer bulb exhibited intense Pb X-ray emission lines (10.55, 12.66, and 14.76 keV). Uncorrected LiG thermometer non-linearity leaves 1σ = ±0.27 ◦C uncertainty in land-surface air temperatures prior to 1981. The 2σ = ±0.43 ◦C from LiG resolution and non-linearity obscures most of the 20th century GSATA trend. Systematic sensor-measurement errors are highly pair-wise correlated, possibly across hundreds of km. Non- normal distributions of bucket and engine-intake difference SSTs disconfirm the assumption of random measurement error. Semivariogram analysis of ship SST measurements yields half the error difference mean, ± 12 ∆ε1,2 , not the error mean. Transfer-function adjustment following a change of land station air-temperature sensor eliminates measurement independence and forward-propagates the antecedent uncertainty. LiG resolution limits, non-linearity, and sensor field calibrations yield GSATA mean ±2σ RMS uncertainties of, 1900–1945, ±1.7 ◦C; 1946–1980, ±2.1 ◦C; 1981–2004, ±2.0 ◦C; and 2005–2010, ±1.6 ◦C. Finally, the 20th century (1900–1999) GSATA, 0.74 ± 1.94 ◦C, does not convey any information about rate or magnitude of temperature change.

Reply to  karlomonte
July 9, 2023 7:34 am

It has to have warmed in the past century.

Trillions depend on it.

Reply to  karlomonte
July 12, 2023 3:20 pm

Back in 2018 I published an error analysis in WUWT, comparing ship’s bucket, engine intake, ARGO, XBT sondes, moored buoys. Desired error+/- 0.1 degrees C. Error results: Bucket 1.54 deg., Engine intake 1.6 deg., XBT 0.4 deg., ARGO 0.12 deg. Engineering rule of thumb says the measuring device needs to be at least three times better than the desired accuracy. The numbers speak for themselves.

Dietrich Hoecht

Richard Page
July 9, 2023 7:10 am

All of this is simply lovely and good to see a robust scientific debate as well as corrections of past calculations. However this is all predicated on an untested hypothesis that CO2 rise causes a subsequent rise in temperatures. Ice core data shows that a rise in temperature occurs first, THEN a rise in CO2 – in other words; if the 2 are linked then it is the reverse of this global warming hypothesis. I have to admit, I agree with the temperature first hypothesis simply because of what happens with plants at warmer temperatures – add in areas where plant growth is a net emitter, rather than neutral or a net sink and it becomes obvious that temperature is the control knob of CO2 increase. One of the problems, as I see it, is that climate scientists are trying to view the world as a single homogenised object, rather than as a series of linked regions which do different things at different times – which is what the data on regional specific studies of past warm periods show us, and is even referenced in the above article.
Now, whilst I applaud articles discussing the specifics of one hypothesis like these, in principle, where are the opposing viewpoints? The discussions of alternative hypotheses? Where is the data-driven science?

Reply to  Richard Page
July 9, 2023 8:37 am

My starting point in considering any hypotheses about climatic behaviors is –
which climate, and when are we talking about?

There are hundreds if not thousands of unique climates in regions and areas all around the world, all doing their own special things, influenced by their local geographies and where they sit in the pathways of atmospheric fluid dynamics and many other significant meteorological influences.

So to plonk all the scant available metrics of these hundreds, thousands of climates into a spreadsheet and “average” their combined total influences into a “climate model” with one “answer” is nothing short of arrant irrationality and stupidity.

In my opinion.

Jan Kjetil Andersen
Reply to  Richard Page
July 9, 2023 11:07 am

Richard, it is well known by all scientists that temperature is driving the CO2 level. The amount is also well known. it is about 10 to 15 ppm per degree Celsius.

However, the opposite effect is also well established; that CO2 is a greenhouse gas that drives the temperature.

Increase in temperature leads to increase in CO2, and increase in CO2 leads to increase on temperature.

Both are correct. This situation is not so uncommon in nature. It means that there is a direct positive feedback loop.

This feedback loop is not very strong though since 1 degree Celsius just give 10 to 15 ppm CO2. The current CO2 level is about 140 ppm above pre-industrial level and the temperature has risen only 1 degree. That means that without the feedback, the CO2 level could be 10 – 15 ppm lower and the tempreature about 0.1 degree lower.

Tim Gorman
Reply to  Jan Kjetil Andersen
July 9, 2023 11:19 am


Because of measurement uncertainties it’s going to be difficult, if not impossible, to distinguish 0.1C degree in the average global temperature. The uncertainty interval is far wider than that so we really don’t know if we are 0.1C higher than otherwise.

Jan Kjetil Andersen
Reply to  Tim Gorman
July 9, 2023 12:28 pm

My point is that the well-established historical correlation between CO2 level and temperature can have a causation in both directions.

Higher temperatures leads to higher atmospheric CO2 level and higher CO2 level leads to higher temperatures.

Reply to  Jan Kjetil Andersen
July 9, 2023 2:45 pm

The causation of warmer oceans giving out CO2 is well established , under Henry’s Law.

There is no evidence of causation for CO2 causing warming.

Did you know that the Vostok cores show that whenever CO2 was at a peak level… it was always cooling.

Richard Page
Reply to  Jan Kjetil Andersen
July 9, 2023 11:29 am

Once again Jan, with respect, there is zero evidence that CO2 has any effect on temperatures – and unless or until you can separate the natural warming from any CO2 caused warming it will remain that way. Atmospheric interference in certain wavelengths may have some miniscule effect but it is too small to measure accurately and may just result in indirect natural warming. Still far too many unknowns and the ‘best guesses’ appear to be mostly incorrect.

Jan Kjetil Andersen
Reply to  Richard Page
July 9, 2023 12:22 pm

There is no disagreement among scientists that CO2 is a greenhouse gas.

Every scientist is also well aware that the historical data shows a correlation beween CO2 level and temperature, and that the temperature is lagging some years behind the CO2 level. This indicate that historically tempetature has driven the CO2 level.

Every scientist knows that.

My point is that this does not mean that CO2 cannot also cause a rise in temperature.

I disagree with your claim of zero evidence that CO2 has any effect on temperatures.

The evidence starts with laboratry tests which shows the absorbsion of infrared wavelengts. Mathemathical models shows how much this insulating effect will have on the surface temperatures. These models are confirmed by atmosphric obervations.


Richard Page
Reply to  Jan Kjetil Andersen
July 9, 2023 1:23 pm

“There is no disagreement among climate scientists that CO2 is a greenhouse gas.” True, Jan, but there is immense disagreement on how a laboratory experiment applies to the real world or if it does at all – a lot of disagreement on how exactly it could work on a planetary scale and what effects it might have, if any at all. With that theoretical and experimental hypothesis in mind, there is still zero real-world proof of any causative relationship between temperature and CO2. And no, Jan, they are not ‘confirmed by atmospheric observations.’

Tom Abbott
Reply to  Richard Page
July 10, 2023 5:00 am

“there is still zero real-world proof of any causative relationship between temperature and CO2. And no, Jan, they are not ‘confirmed by atmospheric observations.’”

That is correct. No evidence, Jan. It’s all speculation.

Reply to  Jan Kjetil Andersen
July 9, 2023 1:54 pm

Lab experiments of enclosed gases..

They prove that CO2 is a radiative gas… that is all

They prove absolutely nothing about what happens in an open convective atmosphere.

Reply to  Jan Kjetil Andersen
July 9, 2023 2:47 pm

historical data shows a correlation between CO2 level and temperature, “

No it doesn’t. Certainly nothing that indicates CO2 causes warming.

“These models are confirmed by atmosphric obervations.”

Again.. No, they are not.

Tim Gorman
Reply to  bnice2000
July 10, 2023 4:04 am

There may very well be a correlation between CO2 and temperature. Both go up or go down. But correlation doesn’t consider *time*. It is important which leads and which lags when trying to decide if there is physical causation. it is the physical causation that is important and climate science *assumes* there is a direct causal link. The problem is that both may actually be correlated to a a third, confounding, variable that has yet to be identified. Neither may be caused by the other but by something else entirely – something which climate science has yet to identify.

Reply to  Jan Kjetil Andersen
July 9, 2023 1:51 pm

“and increase in CO2 leads to increase on temperature.”

There is no empirical evidence of that. CO2 warming has never been observed or measured anywhere on the planet.

Reply to  Jan Kjetil Andersen
July 9, 2023 4:42 pm

However, the opposite effect is also well established; that CO2 is a greenhouse gas that drives the temperature.

If that is true where is the proof?
I looked up ”well established” here is what I got…..
”entrenched, fixed, ingrained, firm, unshakable, deep-rooted, common, accepted, conventional, mainstream”.

I can’t see anything about proven there. Can you?

July 9, 2023 7:30 am

We are doomed! 100 year storms will occur every 11 years….it’s that feedback cycle….call it the Doom Cycle….what to do? Call the IPCC – who else?

David Wojick
July 9, 2023 8:11 am

Regarding this: “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.”

Sensitivity is not a prediction. It is the supposed amount of warming if nothing else happened, hence an abstraction. Temperature is not determined solely by CO2, which is a necessary condition for sensitivity being a prediction. That condition is far from met. Even the IPCC lists ten or so anthro forcings with CO2 being just one of them. (Then there are the natural forcings which they ignore.)

This also means sensitivity cannot be found by observation as that would require first knowing all the other forcings, which we do not.

Rud Istvan
July 9, 2023 8:14 am

There are several alternative methods to guesstimate ECS.

  1. Lindzen’s Bode feedback Curve. The IPCC estimate is ~3C, so Bode 0.65. The no feedback is 1.2C. AR4 said water vapor feedback (WVF) doubles this, so 2.4C, so Bode 0.5. The remainder 0.15 is clouds as IPCC says everything else sums to zero. But Dessler showed in 2010 that cloud feedback is about zero. And ARGO finds twice the ocean rainfall as CMIP5
  2. /6 models, so WVF ~ 0.25. Bode 0.25==> ECS 1.8.
  3. Guy Callendar’s 1935 curve implies 1.68C
  4. Lewis and Curry energy budget methods say ~1.65C. I prefer their second paper because it specifically responds to 5 criticisms of their first.
  5. The Russian climate model INM CM5 is the only CMIP6 model that does NOT produce a tropical troposphere hotspot. So arguably more realistic than all the rest, as there is no tropical troposphere hotspot. It’s ECS is 1.8C

So I think something between 1.65 -1.8C is the most likely ‘true’ ECS. Precision doesn’t matter because anything in that range means there is NO climate alarm.

Javier Vinós
Reply to  Rud Istvan
July 9, 2023 9:21 am

The Russian climate model has the same problems as all the rest. With a climate model, agreement with observations cannot be taken as a sign of model correctness. All models are structurally flawed and none reproduces natural variability. They are very useful learning tools, but their predictions are detrimental to society.

If you were to construct hundreds of random models, some would show better agreement with observations. If you then allow scientists to tune them, the agreement would become convincing. Model climate and real climate have little in common.

Rud Istvan
Reply to  Javier Vinós
July 9, 2023 10:41 am

Partly agree and partly disagree.
The climate models are not intended to reproduce natural variability. That leads directly to the parameter tuned hindcast attribution problem (the observed data for the hindcast must have some natural variability but you don’t know how much or what sign.)

They are intended to estimate the impact of CO2. The Russian INM CM5 does a provably better job of this than the rest of CMIP6. No tropical troposphere hotspot. The reason is that INM CM6 ocean rainfall was parameterized from ARGO, meaning more rainfall and less WVF, hence no tropical troposphere hotspot. And it’s ECS matches fairly well with 3 other methods.

Javier Vinós
Reply to  Rud Istvan
July 9, 2023 12:23 pm

The climate models are not intended to reproduce natural variability. They are intended to estimate the impact of CO2. 

I can’t agree with that. Nor does NASA when they talk about their model.

The climate modeling program at GISS is primarily aimed at the development of coupled atmosphere-ocean models for simulating Earth’s climate system. Primary emphasis is placed on investigation of climate sensitivity —globally and regionally, including the climate system’s response to diverse forcings such as solar variability, volcanoes, anthropogenic and natural emissions of greenhouse gases and aerosols, paleo-climate changes, etc.

Earth system models even include biological, geological, and chemical processes.

The IPCC AR6) also talks about how models represent natural variability.

To understand how much of observed recent climate change has been caused by natural variability (a process referred to as attribution), scientists use climate model simulations. When only natural factors are used to force climate models, the resulting simulations show variations in climate on a wide range of time scales in response to volcanic eruptions, variations in solar activity, and internal natural variability. However, the influence of natural climate variability typically decreases as the time period gets longer, such that it only has mild effects on multi-decadal and longer trends (FAQ 3.2, Figure 1).

comment image

FAQ 3.2, Figure 1 | Annual (left), decadal (middle) and multi-decadal (right) variations in average global surface temperature. The thick black line is an estimate of the human contribution to temperature changes, based on climate models, whereas the green lines show the combined effect of natural variations and human-induced warming, different shadings of green represent different simulations, which can be viewed as showing a range of potential pasts. The influence of natural variability is shown by the green bars, and it decreases on longer time scales. The data is sourced from the CESM1 large ensemble.

They are trying to get natural variability, but they are failing. All of them. Russian model included. I don’t buy that it is a better model. You assume the reasons why it gets closer to observations are correct, but we don’t know that.

Reply to  Javier Vinós
July 9, 2023 2:50 pm

Please don’t use the GISS temperature fabrications (or whichever it is in chart 1) as an indicator of actual real global temperatures.

They are part of the general climate scam, with deliberate manipulations and adjustments to get them nearer the fake model outputs.

Reply to  Javier Vinós
July 9, 2023 5:56 pm

However, the influence of natural climate variability typically decreases as the time period gets longer

That must explain glacial cycles.

Tim Gorman
Reply to  AndyHce
July 10, 2023 5:19 am


July 9, 2023 8:16 am
Pat from Kerbob
Reply to  JohnC
July 9, 2023 8:47 am

The bbc doesn’t do need any more.
So this isn’t a news tip.

Joseph Zorzin
Reply to  JohnC
July 9, 2023 9:14 am

That item says:

“There is a similar story of unprecedented hot weather in North Africa, the Middle East and Asia.”

unprecedented hot weather in those areas? a big duh!

Reply to  Joseph Zorzin
July 9, 2023 1:32 pm

Unprecedented in the last glacial period, maybe, that’s what I assume they mean, after all that is the ultimate aim isn’t it?/sarc

Richard Page
Reply to  JohnC
July 9, 2023 11:32 am

Given the new scandal the BBC is involved in you’d have thought they’d be running scared.

Reply to  Richard Page
July 9, 2023 1:33 pm

I’d agree, I think they have more internal concerns that they need to be concerned about.

Reply to  JohnC
July 9, 2023 4:40 pm

So, the BBC are basically admitting that it is solar energy charging the oceans (with maybe some sub-ocean volcanics) that is causing the temperature change.


Pat from Kerbob
July 9, 2023 8:46 am

Gobbledegook plus twaddle plus narrative, reporting poor correlation as causation.
As we now know, everything is censored, information is controlled, the government has been working to prevent you knowing things they don’t want you to know.

It’s been warming for over 200 years, some say since 1750, 270 years.
Glaciers have been noticeably melting for 200 years, sea level rise has been steady in that time frame, and yet we are told that since 1950 any warming is primarily or completely human caused.
But those that tell us this cannot state why we started warming 200+ years ago, or why that stopped and how they know everything recent is AGW. We are just supposed to believe.
All feedbacks are positive even though co2 was much higher in the distant past with no tipping points.

Lies on top of lies on top of BS, that’s science today.

Joseph Zorzin
Reply to  Pat from Kerbob
July 9, 2023 9:16 am

“the government has been working to prevent you knowing things they don’t want you to know”

Such as UAPs and aliens.

Reply to  Pat from Kerbob
July 9, 2023 9:30 am

Well I’ve now lived through 2 and a half of those 30-year climate phase WMO constructs, in sub-topical, marine, alpine, temperate and desert climates in all hemispheres, and from my observations, nothing sensible to a human body has changed, or is changing.

(Big cities excepted – they just get busier, more congested, hotter, hazier, smellier, noisier, crazier and more expensive. For me, big cities don’t count as part of Earth’s natural environment or eco-system.)

Reply to  Pat from Kerbob
July 9, 2023 11:34 am

Pat, on liars…..
Unfortunately, it is much harder to change the mind of someone who believes what ain’t so compared to a mere liar.

Right-Handed Shark
July 9, 2023 8:53 am

“Equilibrium Climate Sensitivity”.. the very term is word salad.

Joseph Zorzin
Reply to  Right-Handed Shark
July 9, 2023 9:19 am

good point!

Reply to  Right-Handed Shark
July 9, 2023 1:59 pm

That assumes that radiation controls atmospheric temperature.. but does it ?

Balloon data analysis seems to indicate otherwise.

Gregory Woods
July 9, 2023 9:08 am

You can message all the numbers you want, but we are still in the Alchemist stage of climate knowledge.

Reply to  Gregory Woods
July 9, 2023 10:04 am

Well we certainly do have legions of “sorcerer’s apprentices”.

(also called “useful idiots”)

Richard Page
Reply to  Gregory Woods
July 9, 2023 11:33 am

I thought we were still in the deification stage, just swapping one deity for another.

July 9, 2023 9:10 am

First sentence in the above article’s short summary:
“According to the Intergovernmental Panel on Climate Change (IPCC), the atmosphere’s climate sensitivity to CO2 is likely between 2.5 and 4.0°C.”

Hah! I cannot think of a less-scientific source to reference than the IPCC, that among other things refuses to admit that its gathered ensemble of multi-million dollar computer models of future Earth “climate” (expressed as °C “global warming”) have average predictions some 3x higher than observations . . . and the IPCC has known about this discrepancy for more than the last five years and done NOTHING to correct it.

Reply to  ToldYouSo
July 9, 2023 6:03 pm

She said she would be here. I know she is way late but if we just wait a little longer she will surely show up. I know she really loves me.

Richard M
July 9, 2023 9:11 am

Once again the same major error in understanding atmospheric energy flow shows up due to not understanding boundary layer effects. When these effects are applied, CS is zero. These two key effects lead to CO2 increases not warming the surface. :

The increase in downwelling IR leads to increased evaporation. The energy that goes into evaporation will increase convection which takes energy out of the lower atmosphere. This cools the lower atmosphere. The rest of the energy is conducted back into the atmosphere due to the 2LOT. The effect of low level saturation means almost all the energy directed at the surface comes from within the boundary layer. This layer continually exchanges energy with the surface via conduction. If the surface warms and the boundary layer cools (the result of an IR transfer), this will increase conduction from the surface to the boundary layer.
Fortunately, we are not done. Otherwise, increases in CO2 would be a cooling effect. However, we do get increases in energy absorption caused by widening the frequency range near the 15 micron absorption band. This compensates for the evaporative cooling described above. The net result is no change.

This is the first step in understanding the overall effects of CO2. There are also effects high in the atmosphere that are important. The enhanced evaporation and convection drive up the water vapor content low in the atmosphere but since the convective currents are stronger, the water vapor is driven higher into the colder upper atmosphere. This increases condensation which also releases the extra energy collected at the surface.

The net result is thicker clouds, more rain and less left over water vapor. That’s right, all of these are cooling effects in the upper atmosphere. These are offset by that increase in latent heat released during condensation. Once again the net effect is no warming or cooling, just an increase in the amount of precipitation.

The 3 w/m2 that radiation models compute from doubling CO2 leads to 3 w/m2 of energy lost in the water vapor bands. This is not seen in typical studies because they keep relative humidity constant at all altitudes. They then claim this increase in water vapor will trap more energy and cause even more warming. Instead, water vapor works as a negative feedback.

July 9, 2023 9:32 am

>> If humans stop emitting CO2, the atmosphere’s CO2 level will fall relatively quickly. Temperature, however, is not expected to fall

(I looked at Zeke´s CarbonBrief article and he simply assert this, without giving any explanation)

That seems to contradict the notion that CO2 affects the radiation balance, which I thought is the basis of the CO2 effect.
That would work with light speed +CO2 emission time constants or at the lower atmosphere the thermalization time.. over all less than micro seconds.
The main feedback mechanism for a changed radiation balance is by water and clouds which are supposed to react to changes of the radiation balance within weeks

Reply to  morfu03
July 9, 2023 4:09 pm

The only way humans can stop emitting CO2 is to disappear from the earth. each of the 8 billion humans breathe out 2.2lb`s of CO2 every day. So we’ve had a 550% increase in human emitted CO2 since 1850. I would put to you that it is impossible to stop those emissions without eradicating the population, in which case the temperature is not a material issue. Zeke should be more careful with the language.

Reply to  Nansar07
July 9, 2023 7:14 pm

Maybe he should be careful about language too, but you seem to be missing the point of my post..

John Oliver
July 9, 2023 10:53 am

Don’t worry. The government will buy us all personal water craft and we will be required to zip around the coast in rooster tail mode “seeding” the atmosphere. Problem solved!

Reply to  John Oliver
July 9, 2023 6:09 pm

Do battery powered ‘watercraft’ actually float?

Richard Page
Reply to  AndyHce
July 10, 2023 8:48 am

Toys do, there’s a whole sector of the toy industry producing toy rc boats. Entirely unsure how that would scale up to real boats, but if the toy rc cars scaled up to ev’s is any example, not well.

July 9, 2023 11:16 am

according to the IPCC, it’s very likely (over 90%) that the feedback effect from clouds is positive

This is WRONG. Cloud bottoms are warmer than outer space so they DO contribute some IR “back radiation” to the surface, about 20 watts/sq.M of IR, the effect of which we can sense mostly on cloudy nights. However clouds are very reflective of sunlight and especially low thick clouds can locally reflect 80% of incoming sunlight, which can easily locally reflect a few hundred watts of SW back to outer space. Reflective clouds are the result of water evaporating from the surface of our predominantly wetted surface planet.
A degree warmer is 7% more water vapor at low elevations, therefore probably 7%x .5 more cloud cover (rising moist air=falling dry air). The planet is already about 65% cloud cover which controls it’s average temperature to about 15 C. An extra 3.5% cloud cover somewhere is HUGE when it comes to reflecting an incoming 1361 watts/sq.M. even if you multiply by 50% for day/night and 25% for zenith angle cosine….compared to a puny 3 watts per doubling of CO2….
So basically a warmer surface no matter what the cause, land use, CO2, or just a sunny day ends up being strongly opposed by evaporation and cloud cover. This is what should be taught in high schools instead of enviro-doom CO2 dogma….

July 9, 2023 12:36 pm

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.

If you say your range is a-b in 1979 and say it’s a-b a third of a century later you have made no progress. You are still at the same range. No improvement in uncertainty.

Claiming that the 1970s did not know how to assess the uncertainty may be true. But for the same reasons (unknown unknowns) saying that now we do know how how to assess the uncertainty is untrue.

It’s the most important finding in climate science and should not be waved away:

No progress in understanding of climate sensitivity despite decades of research, improved measurements (satellites, sea buoys) and thousands more researchers is a real issue and has a cause; either we have no way to model a chaotic system, we have no way to measure a meaningful initial state or our premise of how the climate works is fundamentally wrong.

Tim Gorman
Reply to  MCourtney
July 10, 2023 3:51 am

You are still at the same range. No improvement in uncertainty.”

Yep! Uncertainty is the interval where we simply DO NOT KNOW the true value. It can be anywhere in the interval. CAGW alarmists *subjectively* choose to believe it has to be on the high side. Everyone else understands “we don’t know”.

Reply to  Tim Gorman
July 10, 2023 9:13 pm

When ever I’m uncertain about a certain subject, I ask all my friends for their opinion. When 97% of them agree about the uncertainty, I am no longer uncertain about their opinions anymore. But they still have not demonstrated any improvement in the actual uncertainty.

David Dibbell
July 9, 2023 12:37 pm

I read the whole article and many of the foregoing comments before commenting myself.

The entire discussion of a climate system response (ECS, ESS, S, TCR, whatever) to incrementally increased concentrations of CO2 and other non-condensing GHGs arises from the “forcing + feedback” framing of the issue. I consider this framing to be a misdirection, a misconception.

Rather, “watch” from space to grasp that the planet is a huge array of highly variable, powered longwave emitter elements. The surface is mostly obscured. The emitter that matters most is the atmosphere itself (including clouds), and the characteristic seen most obviously from space is dynamic self-regulation in response to absorbed and stored energy. And if so, then the climate system response to rising concentrations of CO2 cannot be reliably distinguished from zero by any means we have available to us.

More here.

And here.

(And yes, karlomonte above gets it right in referring to Pat Frank’s work recently published and posted here at WUWT about the uncertainty that should be applied to surface temperature records.)

Tim Gorman
Reply to  David Dibbell
July 10, 2023 3:56 am

(And yes, karlomonte above gets it right in referring to Pat Frank’s work recently published and posted here at WUWT about the uncertainty that should be applied to surface temperature records.)”

Far too many in climate science are *not* physical scientists or engineers. They believe they can increase the resolution of measurements by averaging and can also reduce uncertainty by averaging. They’ve never been in a situation where such assumptions could bring civil or legal liability should harm be caused by such assumptions.

Reply to  Tim Gorman
July 10, 2023 9:16 pm

Which is why climate scientists are not licensed and never will be.

Ed Zuiderwijk
July 9, 2023 1:32 pm

The Charney sensitivity is smaller than the 1.5C lower boundary mentioned and likely smaller than 1C.

The ‘Planck response’ is a non-concept. If you look at the way the formula is derived at, then you will see the work of a schoolboy who has heard the bell’s chimes but doesn’t know where the clanger is.

Reply to  Ed Zuiderwijk
July 9, 2023 2:40 pm

Huh ? The “Planck response” is that if the surface warms up from 288 to 289 K, it will emit 5.44 watts more energy upwards (in planet Earth’s case, thus cooling back down overnight). It’s not a non-concept but a basic concept.

Jim Gorman
July 9, 2023 1:53 pm

“””””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.”””””

Someone explain to me how water vapor “causes the temperature to rise”? Water vapor contains latent heat which does not evidence itself with measurable temperature. When it loses the latent heat it precipitates into liquid H2O. Something amiss here.

Reply to  Jim Gorman
July 9, 2023 2:45 pm

Yes Jim, and an hour or day later, the warm water vapor rises and becomes a cloud…suddenly increasing the local Albedo from say .1 for ocean surface to .7 for stratus clouds…..reflecting many more watts of SW back to outer space than the IR the water vapor ever absorbed.

July 9, 2023 3:21 pm

The exact value for the climate sensitivity isn’t known

Anyone who understands convective instability and the persistence of resulting cloud know that the tropical ocean surface temperature cannot sustain more than 30C. Once you realise this, you understand that there is no delicate radiation balance influencing Earth’s climate and the influence of trace amount of CO2 is unmeasurable. The exact value is so close to zero that it is lost in the noise.

Convection currently in high gear off the wet coast of Mexico pulling the surface temperature below 30C:,9.50,529/loc=-95.725,10.842

July 9, 2023 4:01 pm

Because natural variability dwarfs the tiny human forcing, sensitivity discussions are hypothetical exercises in mental masturbation. Pretending future climate states/temperature can be determined by a single variable is preposterous nonsense.

July 9, 2023 4:20 pm

The warming effect of greenhouse gases on the surface is governed by gravity and solar radiation not their concentration. There is no ECS. Prove me wrong.

ideal gas law.JPG
Reply to  Mike
July 9, 2023 4:42 pm

“The warming effect of greenhouse gases on the surface is governed by gravity and solar radiation not their concentration.”

Balloon data analysis seems to support this theory.

The analysis appears to indicate that the atmosphere remains, always, in thermodynamic equilibrium under the gas laws, with the lower moisture affected boundary layer being in a slightly different state of equilibrium.

Reply to  Mike
July 9, 2023 6:07 pm

There is no ECS. Prove me wrong.

The upper limit on ocean surface is presently close to 30C. That limit is a function of atmospheric mass. It increases approximately 1C for every 5% increase in atmospheric mass. The atmospheric mass increase through burning fossil fuels is not easy to calculate because both carbon and hydrogen are being added and some of that which is added does not remain in the atmosphere.

Taking a rough assumption that doubling CO2 from 285ppm by adding 285ppm increases mass by 0.03%, the resulting warming will be 0.006C. Unmeasurable but still warming. That is the upper limit of ocean surface temperature increases. The lower limit does not change from the present -1.7C so actual increase averaged over the globe will be close to 0.004C

You even state that gravity plays a role and I expect that field is working on the atmospheric mass. Increasing the atmospheric mass increases the surface pressure as well as the upper temperature limit.

Reply to  RickWill
July 9, 2023 8:11 pm

0.006 Unmeasurable but still warming.

Let’s just call it zero and move on…..

Geoff Sherrington
July 9, 2023 7:29 pm

The author, Hakon Karlsen, udopts a pre-industrial CO2 air level of 284 ppm.
Many of the sensitivity calculations involve this figure.
There were many,many determinations of CO2 in air performed in the last 180 years.

There have been many attemps toignore values above 280 ppm because The Establishment has decreed that 280 ppm is correct.
It is not.
It follows that estimates of ECS, TCS etc that involve that assertion of correct 280 ppm are suspect or invalid. Some historic measurements are plausibly wrong, but that does not mean that all should be dismissed.
There can be no argument about that. You cannot dismiss scientific work because it is inconvenient.
Geoff S

Jan Kjetil Andersen
July 9, 2023 9:36 pm

Thank you for the good overview Hakon.

However, I miss a little summary of your conclusion vs the AR6.

I have therefore formulated what I think you say below, do you agree?

The RPC4.5 is described by the IPCC as an intermediate scenario. Emissions in RCP 4.5 will not increase much from todays 37 Gigaton and they will peak at about 40 Gigaton around 2040, then decline.

The CO2 concentration in 2100 will then be approximately 600ppm.

In this scenario the IPCC AR6 estimate for temperature increase from the 1850-1900 level is 2.1 to 3.5 degrees Celsius (up 0.9 to 2.3 degrees from todays 1.2).

Your conclusion is that you agree that the RPC4.5 is the most probable scenario, but you end up with a most probable temperature increase of 2.2 degrees from 1850-1900 level?

Is this what you are saying?


Reply to  Jan Kjetil Andersen
July 14, 2023 11:59 am

And thank you!
Based on Pielke22, I used the RCP3.4 scenario.
I used Lewis’ downwards adjusted climate sensitivity.
These two items explain why I ended up with a lower temperature increase than AR6.

July 10, 2023 1:51 am

Here’s a 2019 talk by Nic Lewis

There’s no link there. Sorry to be difficult.

Reply to  Hivemind
July 14, 2023 12:02 pm

Here’s the missing link:
The video was supposed to be embedded.

Simon Derricutt
July 10, 2023 4:15 am

I’ll quote an important section here:
“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 (ΔF4xCO2) by 2 to find the climate forcing for a doubling of CO2 (ΔF2xCO2). 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.”

Basically, I read this as saying that they used the climate models to determine the sensitivity to CO2 concentration. Since of course the models have each built-in the sensitivity to CO2 concentration and the multiplication-factor believed to be due to the increased water vapour that produces, and they use different sensitivities and multiplication factors, this is a circular argument. I use the term “recursive” for this type of argument. Of course, if you hide something in the basic assumptions, it’s going to be shown in the final results.

Willis Eschenbach has often shown here the disconnect between CO2 levels and temperature over longer periods than the 30 years required to define “climate” rather than “weather”. In fact, with the “pause” over the last 10 years or so with CO2 levels rising at about the same rate as before, you don’t even need to go back far to show that lack of correlation. It’s just far more obvious if you go back a few thousand years where during the Mediaeval Warm Period and the Roman Warm period we have archaeological evidence that crops were grown much further North than today, thus even if we’re not really sure of the temperature then to 1/100th of a degree, it’s pretty obvious that it was several degrees warmer than today.

There can’t really be any doubt that extra “greenhouse gases” in the atmosphere will change the downwelling LWIR radiation – we can measure it. There is however a question on whether that will change the measured surface temperature by a certain amount, given that we’re dealing with many equilibrium situations that are always disturbed and thus never at equilibrium but instead moving towards one. A change in local temperature will change the rate of advection and thus the movement of heat around the system, and the very stability of the average temperature over time implies that there is a significant negative feedback in the system.

One of the simplifications assumed in the modelling is that the weather system is in equilibrium. That is, the heat in from solar radiation and heat out from reflected solar radiation and the LWIR emitted from the ground and atmosphere will be the same. It is obviously never true – look at a daily temperature curve. After sunset, the temperature drops, and it’s coldest just before Dawn – we’ve known that for a long time. The approach to that coldest point is however an asymptote, and thus a large difference in starting temperature will result in a very small (and unmeasurable) difference in lowest temperature if other parameters (cloudiness and wind) remain the same. Thus each day is effectively separate from each other, and very little heat can accumulate over time. In the models, if you have an extra few watts per m² from downwelling LWIR it will accumulate and make the next day warmer, but this does not happen in reality – it will be removed overnight. Yep, the degree of cloudiness will affect how much heat gets removed, but the amount of CO2, CH4, and even water vapour in the air will have very little effect. The nights are too long to allow greenhouse gases to have much influence on energy storage.

This problem of averaging out the energy inputs and outputs is obvious in the Trenberth diagram. Incoming solar radiation of 341.3 W/m², averaged over the whole surface area over the year. In fact, for each location, that incoming solar radiation will be around 4 times that at midday and almost-zero at night, and the period of insolation per day will vary through the year. If you take that average value, then an extra 4W/m² will give over 1% more input energy and thus a change in surface temperature of around 1% of the absolute temperature – 3-4°C. In reality, though, the percentage change in peak radiation received is about 1/4 of that, leading to a temperature change of around 1°C instead, and even that will probably be reduced by the obvious negative feedback in the somewhat-complex weather system.

The real answer to “how much warming can we expect in the 21st century” is that we don’t know and can’t predict it. The problem is not computable. Pat Frank has noted the accumulation of errors involved in iterative calculations, and that the range of possible error soon exceeds any reasonable limits. We may as well argue how many angels can dance on a pinhead. Even the concept of a definable Global Average Temperature has big problems in that we don’t have an even grid of measured points, and that homogenisation is used to infill the places where we do not measure. I can measure variations of local temperature at ground level of multiple degrees, depending on vegetation and conditions – what’s the average temperature over my land? I can only give a rough estimate.

Probably the best guesses as to future climate are from people such as Rick Will (Richard Willoughby), looking at cycles of past estimated variations, but given that in the past we adapted to them and that our technology has improved since then, I expect we’ll adapt to what happens in future. If we have cheap-enough energy, that makes adaptation a lot easier.

Larry Kummer, Editor
July 10, 2023 2:10 pm

Is there research showing how the sensitivity of temperature to CO2 varies with the amount of CO2 in the atmosphere?

Do studies computing sensitivity using historical data take this into account?

July 12, 2023 12:45 pm

I have to agree with Nic Lewis.
I’m a rank amateur and I get results consistent with his:
We have excellent data on CO2 since 1979 and pretty good data on the underlying temperature increase during the same period.
An equation using .51% growth in CO2 per year results in a good curve fit over 44 years and I assumed that would continue into the next century.
For temperature, it was only slightly more complicated. Since science agrees that “delta T” vs “delta CO2” is logarithmic, I used the natural log of that ratio to back into a factor for the temperature increase compared to 1979. That also results in a pretty good curve fit.

I did it based on two different assumptions:

  1. Using UAH historical data from Spencer at .13C per decade.
  2. Using NOAA historical data at .18C per decade

With the UAH approach I get 1.17C above 2023 by 2100.
With the NOAA approach I get 1.39C above 2023 by 2100.

True, they’re both a bit higher than Lewis but remember I assumed the CO2 would continue to increase to 2100 and beyond. Most analysis assume it stops increasing during this century.

More importantly, the value of “Climate Sensitivity” from my half-ass equations varies from 2.09C to 2.47C for the two different assumptions; exactly in agreement with Lewis’ paper. This is based on CO2 doubling from 1979 to 2116.

I agree my approach is really rough. But withe the magnitude of uncertainty in the science and data, who’s to say the results are wrong.

The whole history of the value of “Climate Sensitivity” beggars questions. In modern times it started with the Charney” report in 1979. An excerpt from my paper:

The most credible input for “Climate Sensitivity” came from Syukuro Manabe a Nobel Prize winner in climate science. His model indicated a value of 2ºC for a doubling of CO2. The activist James Hansen from NASA, using data from studying the planet Venus, claimed a value of 4ºC . Another climate modeler, AkioArakana, thought at the time that the real value was somewhere between the two values. Charney cleverly steered the panel to a value of 3ºC ± 1.5ºC for a range of 1.5 to 4.5 ºC which accomodated all the opinions. Many years later Arakana predicted a value of 2ºC , less than the Charney report and Hansen’s prediction. But the climate science “industry” has not moved away from the 3ºC. (Source: Pulitzer Center and oral history with Akio Arakana)

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