Emergent constraints on TCR and ECS from historical warming in CMIP5 and CMIP6 models

Reposted from Dr. Judith Curry’s Climate Etc.

Posted on August 19, 2020 by niclewis

By Nic Lewis

This is a brief comment on a new paper[i] by a mathematician in the Exeter Climate Systems group, Femke Nijsse, and two better known colleagues, Peter Cox and Mark Williamson. I note that Earth Systems Dynamics published the paper despite one of the two peer reviewers recommending against acceptance without further major revisions. But neither of the reviewers appear to have raised the issue that I focus on here.

“Emergent constraints” methods relate observable climate trends, variations or other variables to climate system properties of interest, such as equilibrium climate sensitivity (ECS), in an ensemble of models. They then use the observed values of the variable(s) involved to estimate ECS or the other properties of interest. I’m not a great fan of emergent constraints studies, the results of which are often sensitive to the model ensemble used. Here the emergent constraint is the relationship, assumed linear, between transient climate response (TCR) and global warming from 1975 onwards.

The authors thereby derive, from a combined CMIP5 and CMIP6 54 model ensemble  a TCR estimate of 1.68 K (16-84% ‘likely’ range 1.29–2.05 K) using warming up to 2019.  Unfortunately, the study does not provide a results table for their TCR estimates and the 5-95% TCR range is not stated.

The paper states that using instead warming up to 2014, thereby enabling use of a larger set of CMIP6 models, reduces the TCR estimate to 1.54 K (5-95% range 0.76–2.30 K), but don’t mention that in their abstract or conclusions.

The authors also derive an estimated likely range for ECS of 1.9–3.4 K (5–95% range 1.5–4.0 K) from CMIP6 models, median estimate 2.6 K, from warming to 2019. Based on warming up to 2014 in the larger ensemble of CMIP6 models, the median ECS estimate is 1.9 K (5–95% range 1.0–3.3 K). Again, the result from the larger ensemble is not mentioned in the abstract or conclusions.

I am very doubtful about estimating ECS by comparing observed and simulated historical warming. Without also using observational data on ocean heat update, to estimate changes in the Earth’s energy imbalance, it is impossible to distinguish satisfactorily between ECS and ocean heat uptake both being high and them both being low – either combination can produce the same historical warming. So I would not place any reliance on their ECS ranges, even if they don’t look unreasonable.

On the other hand, one would expect historical warming in climate models to have a close to linear relationship with their TCR, since pre-1975 ‘warming in the pipeline’ is fairly negligible and post 1975 forcing is reasonably close to the quasi-linear ramp forcing used to measure TCR, and similarly of multidecadal length. The existence of episodic volcanic forcing, to which models and the real climate system may respond differently, is a possible confounding factor, although use of the difference between 1975–1985 and the 2009–2019 means to measure warming excludes years affected by the 1991 Mount Pinatubo eruption. There is also the issue that the mean change in effective radiative forcing (ERF) in climate models between those two periods may not equal the ERF change in the real climate system. For CMIP5 models at least, I suspect that their mean ERF change falls somewhat short of the actual change.  That would induce an upwards bias in the emergent constraint TCR estimate.

Regardless of the above considerations, there is a fatal problem with the regression method used to relate TCR with warming. If a model has a TCR of zero, then it would be expected to show zero historical warming. The authors appear to recognise this, writing “As no warming would be expected if climate sensitivity were zero, we expect the regression to pass through the intercept”. They actually mean pass through the origin (have a zero y-intercept), as their equations (A3) and (A4) make clear. And their equation (3) theoretical relationship between TCR and warming, TCR = s ΔT, has no offset term. It is therefore physically inappropriate to use regression with a y-intercept term being estimated.

However, despite admitting that a zero y-intercept is physically appropriate, the study estimates a regression fit using a y-intercept as well as a slope coefficient parameter. Moreover, the resulting best-fit line does not pass at all close to the origin. Their estimate implies that climate models with a TCR of ~0.7 K would have simulated zero post-1975 warming. Their Figure 4(a), reproduced as Figure 1 below, shows this.

Figure 1. Reproduction of Figure 4(a) of Nijsse et al. (2020). Emergent constraint on TCR against historical warming ΔT . ΔT is calculated from the difference between 1975–1985 and 2009–2019 of a time series of GMSAT. Linear regression is performed with all CMIP5 and CMIP6 simulations. Shaded areas indicate a 90% prediction interval. The vertical dashed line is the mean value of the observations, and the y axis shows the probability distribution of both generations of ensembles.

A quite involved and not very clearly described hierarchical Bayesian model regression method is used, which makes it difficult to reproduce exactly the study’s results. Remarkably, the numerical value and uncertainty range of the observed warming estimate is nowhere stated. I therefore measured it off their Figure 4(a), as 0.606 K, and took the shading as showing a normally distribution 5–95% range, width 0.225 K. Based on a simple ordinary least squares (OLS) with-intercept regression of TCR on model-ensemble mean simulated historical warming, across the multimodel combined CMIP5 and CMIP6 ensemble, I estimate a median TCR estimate of 1.62 K, marginally lower than their 1.68 K.

If I repeat the exercise but without estimating a y-intercept, thereby forcing the regression fit to match a zero TCR with zero historical warming, the emergent constraint gives a TCR best estimate of 1.43 K. The regression fit is very good (R2 = 0.97). There is little regression dilution when no y-intercept  is estimated. Regressing warming on TCR rather than vice versa gives an emergent constraint TCR best estimate of 1.47 K. Regressing TCR on warming just across the CMIP5 ensemble gives a slightly lower TCR estimate of 1.37 K (R2 = 0.97). Doing so across the CMIP6 ensemble alone gives a TCR estimate of 1.50 K ((R2 = 0.98). The slope coefficient standard errors imply that there is only a 3.1% chance that the TCR–warming relationship is the same in the CMIP5 and CMIP6 ensembles.

It is unclear which regression method is more accurate. Using the geometrical mean of the estimates regressing each way, as is sometimes recommended, gives a TCR best estimate of 1.45 K from the combined CMIP5/CMIP6 ensemble. A crude estimate of uncertainty can be obtained by using, for each type of regression, the standard error in the slope estimate and the observational uncertainty to form a large number of randomly sampled TCR estimates, combining the two resulting sets of estimates and computing quantiles. Doing so gives a median TCR estimate of 1.45 K, with a 16–84% range of 1.29–1.62 K and a 5–95% range of 1.18–1.74 K. However, this does not account for all sources of uncertainty.

Interestingly, when fitting a relationship between ECS and post-1975 warming, and between ECS and TCR, the authors didn’t use a y-intercept term, resulting in those fits passing through the origin.

My key point is that an analysis method that results in a physically reasonable estimated relationship between the variables being studied should be used. An estimated relationship that implies zero warming with a positive TCR, and significant cooling with a zero TCR, is unphysical. Therefore, the results of the Nijsse et al. paper are unreliable and should be discounted.

Nicholas Lewis                                                           19 August 2020

[i] Njisse et al., 2020: Emergent constraints on transient climate response (TCR) and equilibrium climate sensitivity (ECS) from historical warming in CMIP5 and CMIP6 models, Earth Syst. Dynam., 11, 737–750, 2020 https://doi.org/10.5194/esd-11-737-2020

Originally posted here, where a pdf copy is also available

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August 20, 2020 2:21 pm

The rise in CO2 levels started after 1940, so observations should start in 1940. Unfortunately the measurements before 1979 are far from having global coverage and there’s too much infilling. In addition to haphazard and changing measurement methodologies, the cause of global warming is not known. It is only a worst case assumption that CO2 is the only cause of warming. With that worst case assumption, the TCS is unlikely to be over 1.0. Anyone who states a TCS, or the meaningless ECS — because our planet is NEVER in equilibrium — is just wild guessing with no way to verify they are correct. The physics of climate change are not known in enough detail to stare a TCS or ECS. Hwever, that does not stop the wild guessing. I suppose some of the wild guesses are better than others.

Reply to  Richard Greene
August 20, 2020 2:31 pm

I should add that it seems some government bureaycrat climate sientists start by estimating how much global warming would scare the general public, and then work to get the needed TCS number !

Don’t buy a used car from a government bureaucrat climate scientist.

Reply to  Richard Greene
August 20, 2020 2:41 pm

Colloquially, it’s called putting lipstick on a pig.

Reply to  Richard Greene
August 20, 2020 3:06 pm

“our planet is NEVER in equilibrium”
If it was, the planet would be much warmer. The chaotic atmospheric and oceanic flows help the planet to reject heat.

Reply to  pochas94
August 20, 2020 5:14 pm

Yes totally agree. For one thing most of this warming is suppose to come from more water acting as greenhouse gas, but if say water vapor increases by x pct, will it increase everywhere in atmosphere by x pct ? Certainly not. There are many unknowns so I put little faith in these models.

Martin Cropp
Reply to  Stevek
August 20, 2020 6:04 pm

Looking at the chart below, there must be a large increase of CO2 and water vapor between 60 to 85 north latitudes and a significant decrease between 50 to 75 latitudes south. Shouldn’t be too hard for these emperors of knowledge and wisdom to explain it too us skeptical dimwits.

After all they just have to look into their kaleidoscope futuristic models. The chart was from one of Willis’s earlier posts.

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Reply to  Martin Cropp
August 21, 2020 1:04 am


Thank you for the links. If there is a way for extra heat to escape then the heat will escape that way. They haven’t modeled all different ways the heat can leave. It is like only insulating half your house and thinking this will keep heat in your house in the winter. The heat will leave through the un-insulated parts of the house.

Martin Cropp
Reply to  Martin Cropp
August 21, 2020 2:01 pm

The critical point of the 2 meter temperature record is that is measures the movement of both heat and cold. It records temperature movement and is not an absolute record of Earth’s temperature.

The Ceres data is absolute evidence of that.

Reply to  pochas94
August 20, 2020 9:47 pm

The calculation of an estimate of Equilibrium Climate Sensitivity (ECS) does not assume the planet is or ever will be in temperature equilibrium. Therefore your comment is irrelevant. However, the definition of ECS is the temperature change due to a doubling of CO2 in the atmosphere, then held constant until temperature equilibrium with the oceans is reached, which takes 1500 years for the upper 3 km of the oceans in the models. Of course, that can only happen in a model.

Reply to  Ken Gregory
August 21, 2020 4:09 am

Unless all man made CO2 emissions stop and remain at zero for centuries, how would an equilibrium ever be reached … not to mention variations of water vaoor. methane etc.

Reply to  Richard Greene
August 21, 2020 9:30 am

As I said above, it can only be done in a climate model simulation. ECS is a theoretical concept. It is useful for comparing climate models to esch other, and to energy balance models that use the historical temperature record.

Reply to  Richard Greene
August 23, 2020 5:21 am

Richard, I understand what Ken is saying is theoretically true, yet we have a massive media-promoted socio-political movement to cancel fossil fuels based on the belief that ECS will happen in the real world, and soon. In that context, it is necessary to look at reasonable forecasts of what is possible and what is not. Nic’s work in this regard is valuable.
Also your comment about reliable CO2 measures in the past is valid, but again the discourse is driven by Moana Loa record starting in 1954. Coincidentally, that period was in the middle of post-1930’s cooling, and so some comparison projections can be made. I did an analysis based on that baseline, and discovered that the ECS from the best-performing CMIP6 model, INMCM5, resembles closely a continuation of the mild 20th century warming to to end of this century.


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Reply to  Ron Clutz
August 23, 2020 5:24 am

Correction: Moana Loa starts in 1959.

Hans Henrik Hansen
August 20, 2020 2:33 pm

“Without also using observational data on ocean heat update, to estimate changes …” – shouldn’t ‘heat udate’ be ‘heat uptake’ for the statement to give any meaning??

Reply to  Hans Henrik Hansen
August 20, 2020 9:30 pm

When reporting a typo, please avoid making a typo in your comment!

Hans Henrik Hansen
Reply to  Ken Gregory
August 21, 2020 2:39 am

So sorry for the missing ‘p’! 😉

Hans Henrik
Reply to  Ken Gregory
August 21, 2020 2:41 am

So sorry for the missing ‘p’! 😉

Hans Henrik Hansen
Reply to  Hans Henrik
August 21, 2020 2:43 am

…and for the duplication of my comment: My first entry was seemingly omitted(?).

Reply to  Hans Henrik
August 22, 2020 12:02 pm

No need for an apology Hans. There are LOTS of posts, mostly on other sites, that are really hard to interpret due to mispelling, misuse of words, lack of knowledge of definitions, vague grammar in supposed sentences, and more.

Single letter typo’s are common and really don’t need to be changed. Its very rare that one will confuse the post so badly people can’t understand it.

Reply to  Ken Gregory
August 21, 2020 6:36 am

I always assume my readers are smart enough to correct my typos as they read.

Reply to  pochas94
August 21, 2020 8:49 am

Me two.

August 20, 2020 2:35 pm

An estimated relationship that implies zero warming with a positive TCR, and significant cooling with a zero TCR, is unphysical. Therefore, the results of the Nijsse et al. paper are unreliable and should be discounted.

Yes. Your model can be deterministic or stochastic. Either has a place. However a deterministic model should be truly deterministic. If, anywhere in the model, there are unphysical processes, the model is junk.

This is the second time recently when I’ve heard the criticism that unphysical processes are hidden away in models.

I think Edward Norton Lorenz would disapprove. Words of Wisdom As far as I can tell Lorenz rejects any hybrid of deterministic and stochastic models.

Carlo, Monte
August 20, 2020 2:43 pm

Meaningless statistics, especially these “5-95% ranges”.

August 20, 2020 2:47 pm

If a model has a TCR of zero, then it would be expected to show zero historical warming.

This assumes only GHGs cause warming, which is nuts.

Michael Jankowski
Reply to  Javier
August 20, 2020 3:52 pm

Not as nuts as a TCR of 0.7K resulting in no warming at all.

Robert of Texas
August 20, 2020 3:56 pm

A “worst case scenario” is by itself just a guess, and one does not just assume it will happen, but only that it is slightly possible. Given that we have 100 years (or so) to adapt, a worst case scenario is pretty much meaningless – it assumes that nothing is changing in the 100 years, stuff that is not possible to predict (we don’t know what we don’t know).

I just cannot fathom why anyone puts any credence into these model scenario’s. That have never been right and if they keep averaging them – never will be. If the models are not right, no amount of analyzing their output will provide correct results either.

A few degrees of heat “on average” will not kill anyone directly. Remember most of the warming is where it is cold today – very little where it is already hot – so lives may be saved. If you worry about sea level rise then require new construction to be elevated and away from the shore lines. In 100 years you have already adapted to the higher sea level by doing this. That’s ***IF*** the worse case happens, which is unlikely.

August 20, 2020 4:00 pm

Nevertheless, their TCR and ECS estimates are fairly benign, suggesting that any mitigation effort would be foolish and unnecessary. Valid or not, the lunatic fringe will cancel these guys. Have to stay with the script.

Bob boder
Reply to  Pflashgordon
August 20, 2020 4:13 pm

I agree the paper is ridiculous but you are correct they are establishing a very benign scenario

Reply to  Bob boder
August 20, 2020 5:20 pm

That is probably why the one reviewer didn’t like it, not enough warming. Rearrange things and try a new regression method to get more warming, then it would be unanimously accepted. In finance companies change their accounting methods to book more profits to boost the stock price.

August 20, 2020 5:30 pm

There will be some upcoming cooling this winter from the building La Nina in the Pacific, but will also probably result in an overactive storm season in the Atlantic Basin this fall. So any increased hurricane activity will be blamed on global warming, even though it is well known that wind shear is lesser in an La Nina season than an El Nino, which tends to blow the tops of the budding storms off before they begin a massive rotation and subsequent tropical depression that may turn into a hurricane. So the optics with more storminess this season, heat waves in California with rolling blackouts and whatever inclement normal weather that makes it into the news will keep the CAGW industry going strong. At least until the election, which will have the scarce tactics turned up on steroids by the lane stream media.

The only thing possible in the short term to quell this misinformation about man made climate change will be the reelection of DJT. If that doesn’t work out successfully, especially being able to retain the Senate and take back the House, will result in the Democrat CAGW climate agenda to severely tax and reduce our use of fossil fuels, at least in the West. Elections have consequences, and this one is especially consequential, with rabid socialism/marxism showing its teeth in the USA. That will hopefully be enough to have the majority sit up and take notice that we need 4 more years to sort this mess out. The silent majority has to get out and vote in person.

Tom Abbott
Reply to  Earthling2
August 21, 2020 5:53 am

“The only thing possible in the short term to quell this misinformation about man made climate change will be the reelection of DJT.”

Joe Biden proved last night that he can read a telepromter, but he was particularly uninspiring and gave no details about his plans for the United States. The Democrats don’t want to discuss what they have in mind because it is so radical it is going to turn a lot of people off when they hear about it.

Joe China has turned out to be a big advocate for the Green New Deal, calling Human-caused climate change an existential threat to the world. Biden and Trump will have three debates beginning September 29, 2020, and so maybe for the first time, we will get a national debate on Human-caused climate change. Trump will have to address the issue directly and take a stand, and Biden will have to try to address the issue directly.

I’m not sure Biden is mentally agile enough to debate the issue. We’ll just have to see. Biden does still retain his ability to do personal attacks on Republicans. He hasn’t lost his nastiness. I know a person who had a massive stroke which severely affected his ability to speak, but he says every curse word clearly. Reminds me of Biden. Biden has been attacking Republicans as being racist so long he can do it automatically, without thinking.

The first thing out of Biden’s mouth is the charge that Trump is a racist This is standard operating procedure for Democrats. They always claim Republicans are racist. They do this to deflect attention from the racist past and present of the Democrats. The KKK was a Democrat organization. The Democrats filibustered the Civil Rights and Voting Rights bills. The governor who stood in front of the Univeristy door to prevent a black student from entering was a Democrat. The Jim Crowe law was from Democrats. The Democrats don’t want you thinking about all that. They want to pretend that Trump is the racist.

Just about everything the Democrats say is a distortion of reality. They live in a false reality of their own making, and they want us to live in that false reality, too. The Delusional Democrats are not fit to govern us. In fact, they, and their delusions, are a great danger to everyone’s personal freedoms. Don’t give them the power to inflict their insanity on the rest of us. Vote them out of Office at the next opportunity.

Carlo, Monte
Reply to  Tom Abbott
August 21, 2020 6:13 am

Amen to all of this.

One of the phases of Alzheimer’s/dementia is the anger phase, I’ve personally seen this happen to people afflicted. Biden has always been nasty but now it seems anything can set him off.

M Seward
August 20, 2020 5:35 pm

If you gave these people cameras with zoom lenses to film ant’s nests then pretty soon there would be a concensus that we have been invaded by spiders from Mars or some asteroid. Why? Becuse the funding would far outweigh that that would flow from the study of ants going about their daily business. and the media would slurp it up, snort it and inject it at their usual frenzied pace.

August 20, 2020 7:34 pm

More about the TCRE


Note: For carbon budget issues of the TCRE please visit the “Related Post” links at the top of the TCRE post.

August 20, 2020 9:20 pm

“If I repeat the exercise but without estimating a y-intercept, thereby forcing the regression fit to match a zero TCR with zero historical warming, the emergent constraint gives a TCR best estimate of 1.43 K.”
This paper and Nic’s recalculated TCR estimate both falsely assume that almost all of the warming since 1975 was caused by greenhouse gases (GHG). There several hundreds of technical papers that show that a significant amount of the recorded global warming was caused by natural climate change. There is an obvious 60-year temperature oscillation related to the AMO that started increasing around 1975. There is also an obvious millennium scale temperature oscillation, which began to increase at about 1700, which was also the end of the Maunder Minimum. Solar activity increased to a maximum at 1992 which would cause a maximum temperature response two or more decades later. Several studies show that the urban heat island effect (UHIE) caused about half of the warming from 1980 over land. The non-GHG warming 1975 – 2019 due to the 60-year cycle, the millennium cycle and the UHIE, is 0.204 °C, 0.037 °C and 0.176 °C, respectively. The sum of 0.417 °C of non-GHG warming must be removed from the temperature record for an appropriate comparison to the climate model results.

Reply to  KenGregory
August 21, 2020 12:09 am

“KenGregory August 20, 2020 at 9:20 pm
“If I repeat the exercise but without estimating a y-intercept, thereby forcing the regression fit to match a zero TCR with zero historical warming, the emergent constraint gives a TCR best estimate of 1.43 K.”
This paper and Nic’s recalculated TCR estimate both falsely assume that almost all of the warming since 1975 was caused by greenhouse gases (GHG). ”

Also falsely assume that the TCRE correlation shows that temperature is responsive to emissions.
Pls see


August 20, 2020 9:23 pm

The Lewis & Curry 2018 paper calculated a TCR best estimate of 1.20 °C, which is far less 1.43 °C Nic calculated above using the assumption that TCR would be 0 when the temperature change is 0. The LC18 paper effectively accounted for the 60 year cycle by using a long time period (136 years between the midpoints of the start and end periods, which were at similar parts of the oscillation).

Unfortunately, the LC18 analysis was deficient in that the natural climate change from the base to final periods were not considered and no correction was applied to remove the urban heat island effect (UHIE) from the temperature record. This study https://friendsofscience.org/index.php?id=2519 presents corrected estimates of ECS and TCR with uncertainty estimates by including the UHIE and natural warming. The median (best estimate) of ECS and TCR are estimated at 1.04 °C and 0.83 °C, respectively. Global average temperatures are forecast to increase by 0.63 °C from 2019 to 2100, assuming the GHG concentrations in the atmosphere increase exponentially and no natural climate change. The FUND economic model, using updated energy impacts and CO2 fertilization effects and assuming an ECS of 1.0 °C, calculates that a 2 °C GMST rise from 2000 would increase global wealth by 1.45% by 2147, equivalent to 2019US$1.26 trillion.

Reply to  Ken Gregory
August 21, 2020 1:16 am

“Ken Gregory August 20, 2020 at 9:23 pm
The Lewis & Curry 2018 paper calculated a TCR best estimate of 1.20 °C.”

The TCRE is a regression coefficient supported by a spurious correlation. It has no interpretation in terms of the phenomena under study it apparently represents.

Reply to  chaamjamal
August 21, 2020 6:51 pm

Don’t you know that TCRE is a different metric than TCR?
The E in TCRE is ’emissions’. TCRE means “transient climate response to cumulative carbon emissions”. TCR is about CO2 concentrations at a doubling versus the temperature change at the time of the doubling. TCRE is also an important metric for GHG-caused global warming.
Your comment that “It has no interpretation” is nonsense. TCRE is the global temperature change per change is cumulative CO2 emissions, and is usually expressed in deg. C/TtC, where TtC means a trillion tonnes of the carbon portion of CO2, or 3667 GtCO2.

August 21, 2020 2:32 am


Both sides of the climate debate have been drinking magnums of the same over-proof rum for decades, and have spent their time arguing about the magnitude of ECS (and TCS) as if it actually exists.

There is significant evidence that ECS/TCS is an imaginary concept that does not exist in reality, but is a fiction – a result of long-term alcohol abuse, an apparition caused by a bad case of the DTs.

If one focuses on periods of observed global warming (e.g. 1979 to 2017) one can calculate a hypothetical ECS value of approx. 1C/(2*CO2).

If one focuses on periods of observed global cooling (e.g. 1940 to 1977), one can calculate a hypothetical ECS value of approx. MINUS 1C/(2*CO2).

Both hypothetical values of ECS are too low to cause alarm – end of the very-scary global warming (CAGW)/climate-change story – a satisfactory result, as far as it goes.

But scientifically, atmospheric CO2 changes lag atmospheric temperature changes at all measured time scales, from ~9 months in the modern data record to ~~800 years in the ice core record – aka “cart before horse”.

Kuo et al (1990) and Keeling (1995) both observed that “CO2 changes lagged temperature changes” in the modern data record. That reality has been studiously ignored in the current climate debate. I independently re-discovered that observation (temperature changes lead, CO2 changes lag) in January 2008 and have provided the details of the physical mechanism in papers published from January 2008 to June 2019.

That observation does not preclude other sources of increasing atmospheric CO2 such as fossil fuel combustion, deforestation, etc. but it does provide further evidence that THE ENTIRE GLOBAL WARMING/CLIMATE CHANGE STORY IS A SCARY FICTION, FOR WHICH THERE IS NO CREDIBLE EVIDENCE.

by Allan M.R. MacRae, B.A.Sc., M.Eng., June 15, 2019
Excel: https://wattsupwiththat.com/wp-content/uploads/2019/07/Rev_CO2-Global-Warming-Climate-and-Energy-June2019-FINAL.xlsx

Carlo, Monte
August 21, 2020 6:20 am

Therefore, it would be my observation that neither of these quantities (Ecs & Tcs) is a constant, yet they are treated and used as if they were constants.

Is this a fair assessment?

Reply to  Carlo, Monte
August 21, 2020 7:03 am

Think of ECS and TCS as Imaginary Numbers.

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i² = −1. 🙂

August 22, 2020 6:52 am

The ‘smiley” apparently does not show in my above message about “imaginary numbers.” 🙂

Seriously, I regards ECS and TCS as parameters of religious faith – in a religion based on the belief that increasing atmospheric CO2 significantly drives atmospheric temperature.

Where is the global-scale evidence that that increasing atmospheric CO2 significantly drives atmospheric temperature? Molecular-scale arguments are not convincing, since we know that scale-up to global scale from molecular scale is huge, and many of the physical phenomena that impact this scale-up are not well-understood or quantified.

What we do understand is that atmospheric temperature changes precede atmospheric CO2 changes at all measured time scales – thus the above religious belief assumes that the future causes the past – so that belief is disproved via precedence.

If we do accept the above religious belief, and calculate temperature sensitivity based on that belief, we get a sensitivity of about 1C/[hypothetical doubling of CO2) based on warming intervals (Christy and McNider 2017, Lewis and Curry 2018) and the alleged global warming crisis disappears to insignificance. If we similarly analyze the cooling period 1940 to 1977 we calculate a hypothetical climate sensitivity of approx. MINUS 1C/(2*CO2). Again, the global warming crisis disappears to insignificance.

The alleged global warming is averted due to lack of any credible evidence that it exists. It is an imaginary crisis, based on imaginary numbers! [insert smiley face]

Regards, Allan

August 21, 2020 7:09 pm

There is nothing “imaginary” about the ECS or TCR concepts. However, there is considerable debate about their values in the real world.
What is critically important is that when calculating either value, one must compare only that part of the temperature rise caused by greenhouse gases to the forcings of those greenhouse gases. That is, one must remove the temperature change caused by natural climate change and that caused by urban warming (UHIE) from the temperature record before comparing to the GHG forcings over the time period considered.

If one attempt to use a period of global cooling (e.g. 1940 to 1977) to calculate the ECS, you would have to remove the natural cooling and aerosol cooling during the period before comparing to the GHG forcings. Then you would get a positive ECS.

The atmospheric CO2 changes lag atmospheric temperature changes by ~9 month due to the seasonal cycle. This is irrelevant to the calculation of ECS or TCR as we are concerned about the long-term effects of increasing CO2 concentrations, not the seasonal cycle.

Reply to  Ken Gregory
August 22, 2020 6:26 am

Of course they are imaginary. If CO2 caused warming it would be mentioned in specific heat tables, or Shomate equation, or in the NIST data sheet. According to climate science there are two values when calculating dT when using Q = Cp * m * dT. One with IR included and one without IR which is against thermodynamics saying the energy can be in any form.

Reply to  Ken Gregory
August 22, 2020 8:01 am

By some accounts, medieval scholars used to debate “How many angels can dance on the head of a pin?”

I view the debate to quantify “climate sensitivity to increasing atmospheric CO2” as similarly dysfunctional – an utter waste of time and resources, as is the entire very-scary human-made global warming false narrative.

Would not the Null Hypothesis be that “climate sensitivity to increasing atmospheric CO2 does not exist, or is too small to accurately measure”, since “climate sensitivity to increasing CO2” has never been scientifically demonstrated to exist at global scale and has never been accurately quantified?

This statement would be consistent with the greater Null Hypothesis that has yet to be disproved: “The alleged dangerous humanmade global warming crisis does NOT exist.”

The false global warming crisis has cost global society trillions of dollars and harmed billions of lives. Those who have promoted this fiction for so many decades must know it is false – no rational person could be this stupid for this long. Some of the global warming proponents have now admitted that it was always a smokescreen for their extreme-left political objectives – it’s time we believed them.

Matthew Sykes
August 21, 2020 3:02 am

The difference between TCR and ECS is ocean heat uptake, according to the IPCC. Yet the oceans are:
1) 3 C warmer than the air
2) Incapable of absorbing LW radiation

Ocean heat uptake of LW energy is impossible. The icean can not slow the atmospheric warming from CO2. TCR and ECS are therefore one and the same thing, and rather low, about 1C

slow to follow
August 21, 2020 3:16 am

Nic’s addition at the Climate etc version:
Update 20 August 2020

Thanks to a commenter pointing out that it was erroneous, in the third paragraph I have removed the statement ‘Unfortunately, the study does not provide a results table for their TCR estimates and the 5-95% TCR range is not stated.’, stated that range and also corrected the reference to the model ensemble involved. In the fifth from last paragraph I have added the TCR estimate that I derive using the CMIP6 ensemble on its own.

August 21, 2020 3:17 am

Correct this poor ignorant layman if he’s got it wrong but it seems that by modelling the models you create a model that gives you an answer similar to the models you modelled in the first place +/- a bit.

As someone whose models are confined to 2mm/ft and simply do what they’re told (provided I keep the track clean) I am in awe of such scientific genius!

Alasdair Fairbairn
Reply to  Newminster
August 21, 2020 11:58 am

Precisely. If you start off with dubious assumptions such as CMIP5 &6 you wind up with usually even more dubious conclusions no matter how sophisticated the calculations are.

Incidentally I would like to see a zoomed out presentation of the the graph (figure 1) to include negative values of TCR. After all it could well happen with a Solar Minimum waiting in the wings.

Just a reminder: At evaporative phase change of water the sensitivity coefficient is ZERO and there is a lot of water in the atmosphere.

August 21, 2020 4:15 pm

CMIP5 and CMIP6 initiatives show how stupid the whole idea is! So much money, effort, man power is involved on those meaningless study. That initiatives show the level of emptiness among climate science communities. All third grade scientists, those have indeed certain leadership qualities are now leading the climate science. They are involved in promoting and convincing other people all false things to be true and misleading the whole climate science.

Gerald Browning
August 23, 2020 4:12 pm

A peer reviewed manuscript has shown that all climate models are based on the wrong dynamical.system of equations (DAO September issue). Therefore any conclusions drawn from these models are nonsense.


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