By Andy May
This is an updated version of this post; the original post had incorrect figures as a result of a bug in my R program. The conclusions remain the same, but the figures and the text have changed (May 4, 2026).
The NCAR CERES EBAF satellite dataset has been adjusted to match upper ocean heat content changes. Thus, the EEI (Earth Energy Imbalance) from CERES EBAF (“Clouds and Earth’s Radiant Energy Systems, Energy Balanced and Filled”) is not estimated directly from satellite measurements. If upper ocean heat content were known accurately over a sufficiently long period, this would be fine, but it isn’t.
Even if CERES EBAF numbers are not accurate enough to derive EEI on their own, they are still useful. I’ve been going over the various CERES EBAF variables in some detail lately and noticed that one of the variables (“toa_net_all_mon”) provides the total net incoming radiation at the top of the atmosphere or TOA. All energy exchanged between space and the top of the atmosphere is via radiation so this variable can be used to estimate ECS (the Equilibrium Climate Sensitivity to a doubling of CO2) if we assume that CO2 and related anthropogenic greenhouse gases are the dominant factor in warming over the period studied.
Originally, ECS was defined as the ultimate warming due to an instantaneous doubling of atmospheric CO2 (IPCC, 1992, p. 73). ECS has always been tied to climate models and was explicitly used to compare climate models to one another (IPCC, 1992, p. xxv) & (Gregory et al., 2004). An instantaneous doubling of CO2 is almost impossible and, in any case, waiting for hundreds or thousands of years to determine the ultimate effect at a new equilibrium state is impractical, but it was a good single-number model metric, and an easy way to rank models from hot to cold.
However, as time went on, this convenient model metric began to be used as a predictive tool for the real world. People confused models with reality and claimed that the average model ECS told us how the world would warm. Attempts have been made to estimate ECS using real world measurements (see here and here), but due to the lack of adequate measurements over long enough time periods these estimates are considered inadequate. It is still difficult to estimate ECS using observations.
I used two approaches, when I applied conventional forcing values and CERES EBAF TOA observations, the resulting implied ECS values were physically implausible—5.6 to 7.4°C per doubling. Using newer AR6 constraints, I get a more reasonable ECS of 2.67. This relatively simple exercise reveals some contradictions in the AR6 ECS framework and real‑world data.
Defining ECS
To understand what CERES can and cannot tell us, we need to revisit how ECS is currently defined and how the definition shifted after AR5 (IPCC, 2013). The definition of ECS used by the IPCC through AR5 probably originated with Gunnar Myhre (Myhre et al., 1998).
Eq. 1: ΔF2xCO2 = α • ln(C / C0)
Where ΔF2xCO2 is the change in forcing due to a doubling of CO2. Myhre et al. specifies α = 5.35 and C / C0 = 2 (a doubling of the CO2 concentration), so ΔF2xCO2 is a fixed value of 3.71 W/m2. All IPCC reports, including AR6, then define ECS as:
Eq. 2: ECS = -ΔF2xCO2 /λ (IPCC, 2021, p. 993)
Myhre’s F2xCO2 value of 3.71 W/m2 is nearly identical to the value used in the IPCC AR5 report (IPCC, 2013, p. 818). The value of the net feedback parameter (λ, substituted for the AR6 α) can be determined as the slope of a fitted line through the change in net radiation at the top of the atmosphere (TOA) versus global mean surface temperature. Both F2xCO2 and λ were fixed global averages before AR6 and ECS was computed from them using equation 2. The concept of ERF, a varying effective radiative forcing, was introduced in AR5, but not used, and they still computed ECS with a fixed F, but in AR6 ERF was used and since it continuously varied, it could not be used to directly compute ECS without averaging it. In figure 1 I’ve plotted the CERES top of the atmosphere (TOA) net incoming radiation (both longwave and shortwave) on the y axis and the ERSST v5 SST anomaly on the x axis.
In the conventional scheme ΔF2xCO2 is defined as a positive number in the sense that doubling CO2 increases the energy retained in the climate system, thus it is warming. The TOA net radiation (“N” in figure 1) from CERES is also the downward net radiation. The global net feedback parameter (λ, units: W/m2/°C) is the negative of the slope of the best fit line through the CERES EBAF points plotted in figure 1 against the ERSST v5 SST anomaly on the x axis. The pink bands are the 95% confidence interval for the regression.
Van Wijngaarden and Happer derive 3.0 W/m2 for ΔF2xCO2 in the midlatitudes at the TOA and pointed out that the forcing changes with altitude (Wijngaarden & Happer, 2020, Table 3). AR6 “assessed” a value of 3.93 (IPCC, 2021, p. 993) for the period from 1750-2019 and they call it “ERF” or effective radiative forcing. They explain how they get from the AR5 value of 3.71 to 3.93 in Table 7.4 (IPCC, 2021, p. 945). Basically, they believe that the forcing of CO2 varies with temperature, stratospheric conditions, clouds etc. and try to compensate for these other factors. Using a CERES derived λ of -0.53 from figure 1 and these three values of ΔF2xCO2, equation 2 gives the ECS values listed in figure 1. They are all unreasonable values and above five °C/2xCO2. AR6 “assesses” a λ of -1.16 (AR6, Table 7.10, p 978), which results in an ECS of 3.39 using equation 2.
Strictly speaking, if both F and λ vary independently, as claimed by AR6, it is very hard, if not impossible, to determine ECS from them. Equation 2 only works when F2xCO2 is a fixed number, which is presumably why AR6 changed the ECS calculation and changed “F” to “ERF” or “effective radiative forcing” (IPCC, 2021, pp. 959, 1005). For a description of the new AR6 ECS calculation see (Sherwood et al., 2020) and for a critique of the method see (Lewis, 2023). They also introduce an “Effective Equilibrium climate sensitivity,” which is still is the surface temperature response to a doubling of CO2, but can be different from ECS. “ECS” has become very bewildering.
The global mean ERSST v5 global sea surface temperature anomaly is related to ocean heat content or OHC, which is used to tune the CERES EBAF TOA net radiation measurement plotted on the y axis in figure 1. Thus, the two numbers plotted are not completely independent of one another. Both means are area-weighted by latitude and only values from populated ERSST v5 cells are used, thus land (~29% of the Earth) is ignored in this study. The CERES grid is a 1°x1° latitude/longitude grid, but it was aggregated to match the 2°x2° ERSST grid. A plot of the slopes, that is the change in downward total radiation flux from the TOA per the change in SST, for each 2°x2° grid cell, is shown in figure 2.
Since ΔF2xCO2 in equation 2 is fixed, for any given value, ECS is a function of λ (the slope mapped in figure 2 is -λ). Figure 2 shows that both λ and ECS vary a lot with location, AR6 does a “spatial pattern effect” analysis to try and use these anomalies to determine both ERF (effective radiative forcing) and λ (IPCC, 2021, Section 7.3, page 941) & (Gregory et al., 2004). Normally, these studies involve comparing model results to observations spatially over the oceans because land observations are usually much more erratic (relative to model results) than ocean observations (IPCC, 2021, p. 942), although the eastern Pacific off South America is always a problem since it is cooling in recent years and the models predicted significant warming (IPCC, 2021, p. 990).
AR6 does consider observations. They study model-observation differences to evaluate model quality and to determine effective radiative forcing and λ. The large areal variability shown in figure 2 is problematic and may invalidate global λ estimates (including mine) over short periods of time. It suggests internal variability dominates the signal, at least over the period from 2001-2025, this is reinforced by known long-term ocean oscillations like the AMO. Such long-term internal variability, if not taken into account, may invalidate the AR6 pattern-effect methodology.
The Gregory Plot
Gregory et al. first described the new model-based “effective” forcing and climate sensitivity ideas used extensively in AR6 (Gregory et al., 2004). Gregory et al. devised a plot, since dubbed the “Gregory plot,” to evaluate model results. The plot is of modeled surface temperature versus the modeled change in downward flux where the intercept reflects ERF and the slope reflects the net feedback. I was curious what it would look like with real data, as opposed to model output. The plot is shown with CERES EBAF data and ERSST v5 SST data in figure 3.
Gregory et al. allows “ΔF2xCO2” or “F” to vary, it is still positive downward and here taken as Forster’s “Best ERF” (Forster et al., 2023). The standard Gregory equation is:
Eq. 3: N = F – λΔT
Where:
- N is the net downward TOA flux (CERES, positive downward)
- F is the effective radiative forcing (Forster “Best ERF”, positive downward)
The version of the equation plotted is:
Eq. 4: N – F = -λΔT
In figure 3 the slope is λ and the sign does not have to be reversed. Other than this the only real difference between this plot and figure 1 is that F varies and is populated with the Forster et al. ERF values. Forster et al. constructed their ERF values following the AR6 “methods as closely as possible” (Forster et al., 2023).
The surface warming feedback factor (λ) is the slope from a regression of equation 4 in figure 3. If we assume an F of 3.71 (Myhre and AR5) and couple it with the Gregory AR6 compliant λ = -1.636, equation 2 gives us a realistic ECS of 2.26 °C/2xCO2. The Gregory method does not allow us to compute ECS directly because the ERF (effective forcing due to a doubling of CO2) varies, but we can plug in a reasonable fixed F as a reality check and the ECS is lower than what AR6 shows. Remember, AR6 recommends a λ of -1.16 (AR6, Table 7.10, p 978), which results in an ECS of 3.39 using equation 2.
Figure 3 overlays two Gregory plots. The red line is constructed so that the coefficient of F is forced to be one, which is the AR6 convention. In AR6 they assume that N = F + λT exactly. This is why the regression shown in figure 3 is (N-F) versus the SST anomaly. If we regressed “N = F + λSST” and allowed F to float (the “λ_full” in figure 3) then the F coefficient is decided by the CERES data and different from one and we get a λ=-0.776 and an ECS of 4.78, which is unreasonable.
So, the AR6 recommended ECS of 3.39 and λ of -1.16 is not consistent with their regression constraint (F coefficient of one) and the CERES net top of the atmosphere radiation measurements, even when using the AR6-style “ERF” (effective radiative forcing) from Forster, et al. While radiation-in versus radiation-out must immediately balance for blackbodies, this is not necessarily true for Earth over short (<100 years) periods of time where there are a lot of complicating factors involved, the most obvious being climate oscillations like ENSO and the AMO.
The blue line in figure 3 is a full unrestrained regression (N = F + λT) and tests the coefficient when both F and T are allowed to float, it results in a λ of -0.776. This full regression slope and the AR6-constrained slope are significantly different statistically as shown by the confidence intervals in figure 3. Unfortunately, the full regression does not pass a basic reality check. Using a Myhre/AR5 fixed F = 3.71 and couple it with the floating regression we get 4.78 °C/2xCO2 using equation 2. This suggests that either the CERES TOA net radiation data, the Forster ERF data, or the period of time (25 years) is too short to get meaningful data. Or perhaps a combination of all three.
AR6 did not do these calculations, instead they independently estimated the average 1750-2019 forcing as 3.93 W/m2 and the feedback (our λ and their α) to be -1.16, which results in an ECS of 3.39 (IPCC, 2021, p. 993). The AR6 λ of -1.16 is higher than the AR6 constrained CERES Gregory derived λ of -1.64 and much less than the conventional CERES λ of -0.53 (ECS=7, figure 1), which is difficult to explain.
Discussion
The model results in Gregory et al. look nothing like figure 3. Neither do the “idealized 2xCO2 response” plots in AR6 (IPCC, 2021, Ch. 7, Box 7.1, p 932). It could be that the CERES time period used (2001-2025) is too short even though it is only five years short of the normal 30-year definition of a climate period. The short period of data, the small range of SST values, the uncertainty in the CERES data all combine to make the regressions in figures 1 and 3 problematic and unstable. Further, the very important AMO climate oscillation is 60-70 years long and we are currently at an AMO warming peak (May & Crok, 2024), so things may change radically over the next few decades.
CERES EBAF is not accurate enough on an absolute basis to measure the EEI but is probably directionally correct. Thus, the trend shown in figure 3 from 2001-2025 should be close to correct. The variable Forster ERF values used in figure 3 are problematic, they result in an unreasonable λ and may be conceptually flawed. The AR6 changes in the definitions of ECS, λ, and ΔF2xCO2 have muddied the water and, in my opinion, unnecessarily complicate their story. Further, by their own admission, the changes did not help, and the AR6 results moved farther away from observations than in AR5 (IPCC, 2021, pp. 443-444) and here. It appears they are headed in the wrong direction.
Works Cited
Forster, P. M., Smith, C. J., Walsh, T., Lamb, W. F., Lamboll, R., Hauser, M., . . . von Schuckmann, K. (2023). Indicators of Global Climate Change 2022: annual update of large-scale indicators of the state of the climate system and human influence. Earth System Science Data, 15(6), 2295–2327. https://doi.org/10.5194/essd-15-2295-2023
Gregory, J. M., J.Ingram, W., A.Palmer, M., S.Jones, G., A.Stott, P., B.Thorpe, R., . . . D.Williams, K. (2004). A new method for diagnosing radiative forcing and climate sensitivity. Geophys. Res. Lett., 31. https://doi.org/10.1029/2003GL018747
IPCC. (1992). Climate Change: The IPCC 1990 and 1992 Assessments. Canada: IPCC. Retrieved from https://www.ipcc.ch/report/climate-change-the-ipcc-1990-and-1992-assessments/
IPCC. (2013). In T. Stocker, D. Qin, G.-K. Plattner, M. Tignor, S. Allen, J. Boschung, . . . P. Midgley, Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge: Cambridge University Press. Retrieved from https://www.ipcc.ch/pdf/assessment-report/ar5/wg1/WG1AR5_SPM_FINAL.pdf
IPCC. (2021). Climate Change 2021: The Physical Science Basis. In V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, . . . B. Zhou (Ed.)., WG1. Retrieved from https://www.ipcc.ch/report/ar6/wg1/
Lewis, N. (2023, May). Objectively combining climate sensitivity evidence. Climate Dynamics, 60, 3139-3165. https://doi.org/10.1007/s00382-022-06468-x
May, A., & Crok, M. (2024, May 29). Carbon dioxide and a warming climate are not problems. American Journal of Economics and Sociology, 1-15. https://doi.org/10.1111/ajes.12579
Myhre, G., Highwood, E. J., Shine, K. P., & Stordal, F. (1998). New estimates of radiative forcing due to well mixed greenhouse gases. Geophysical Research Letters, 25(14), 2715-2718. https://doi.org/10.1029/98GL01908
Sherwood, S. C., Webb, M. J., Annan, J. D., Armour, K. C., J., P. M., Hargreaves, C., . . . Knutti, R. (2020, July 22). An Assessment of Earth’s Climate Sensitivity Using Multiple Lines of Evidence. Reviews of Geophysics, 58. https://doi.org/https://doi.org/10.1029/2019RG000678
Wijngaarden, W., & Happer, W. (2020, June 4). Dependence of Earth’s Thermal Radiation on Five Most Abundant Greenhouse Gases. arXiv. Retrieved from https://arxiv.org/abs/2006.03098
e 4). Dependence of Earth’s Thermal Radiation on Five Most Abundant Greenhouse Gases. arXiv. Retrieved from https://arxiv.org/abs/2006.03098
The best estimates of CO2’s forcing comes from molecular heat transfer physicists’ line by line radiative transfer calculations. Those center around 0.6C for a stand alone doubling. The reason why the strong water vapor feedback assumed in climate models has never been observed in the real world is that CO2’s initial forcing is too weak to produce those.
Never mind that most of modern warming was from fewer clouds which allowed more of the suns energy to reach the surface and heat the oceans to depth. That is the primary cause of the TOA imbalance not CO2.
Yes, and that 0.6C calculation is likely even a “worst case scenario” as it doesn’t take into account the multiple negative feedbacks in the earth’s oceans and atmospheric circulation consistent with Le chatelier’s principle, including changes in clouds and the polar vortex, so the ECS for doubling CO2 is more likely no more than 0.1-0.2C, ie, less than the precision of the thermometers used to measure air temperatures.
The geologic record strongly suggests that CO2 has a negligible impact on climate. ECS is a hypothetical construct with no real world meaning because of that.
Yes, ECS and EEI are all well and good, but they don’t explain recent weather history.
After the end of the Little Ice Age, the temperatures warmed by about 2.0C in the 1880’s.
It is no warmer today than it was in the 1880’s, or the 1930’s.
In the 1880’s, CO2 levels were at about 280ppm.
Today, CO2 levels are at about 420ppm.
Yet it is no warmer now than it was in the recent past with less CO2 in the air.
Therefore, CO2 has had no discernible effect on the temperature of the Earth’s atmosphere.
Whether CO2 is 280ppm or 420ppm, the temperatures are the same.
What I have never understood is why the historical, written temperature record is not considered a real-world examples of temperatures around the world. If you believe the historical temperature record represents reality, then you cannot believe CO2 has any measurable effect on the temperatures.
The historical temperature records refute the notion that we need to worry about CO2.
CO2 warming does not explain the historical temperature records.
It’s seems obvious to me. One has to deny the written, historical temperature records to believe CO2 is anything other than a benign gas, essential for life on Earth.
“One has to deny the written, historical temperature records to believe CO2 is anything other than a benign gas, essential for life on Earth.”
CO2 was 3x as high during the age of the dinosaurs as it is today. Yet both flora and fauna flourished then. Massive amounts of food up and down the chain had to be available to support the amount of life that existed – meaning the earth didn’t become a sphere of deserts, hurricanes, and tornadoes because of “trapped heat”.
Freeman Dyson so eloquently pointed out long ago that climate science and its models are not holistic at all. Climate science and its models remind me so much of ancient soothsayers trying to foretell the future based on throwing a handful of chicken bones on the ground and “reading” what they predict. Don’t study the chickens themselves or the environment in which they exist – that would just be a distraction!
Climate models are those chicken bones. And because of the measurement uncertainty associated with the models the soothsayers (read climate scientists) don’t even really know if they *are* chicken bones!
Also the other reason the strong (positive) water vapor feedback has never been observed is that it is based on a dubious assumption that relative humidity remains constant as the world warms, so that absolute humidity or water vapor increases, consequently increasing the greenhouse effect of water vapor. This was part of the work that yielded the Nobel Prize for Syukuro Manabe in 2021. BUT that assumption of fixed relative humidity has not been shown to persist throughout the atmosphere, debunking the entire positive water vapor feedback concept from increases in CO2.
This item may be well informed and accurate but my lack of advanced mathematical knowledge limits it’s usefulness to me
I apologize for the equations; I normally avoid them like the plague. But ECS is the result of an equation, and I had to include them for that reason. Primary point, ECS is a climate model metric, it has nothing to do with the real world and never will. I hope the main takeaway for people who don’t like equations is just that. Secondary takeaway: AR6 made a complete mess of the whole ECS paradigm.
ECS is a made up number that has no real world significance because natural variability dominates the climate system and will determine future conditions. Nobody can know what those future conditions will be. The caveat about all other variables remaining constant is an absurd condition that never happens in Earth’s climate system so the house of cards has no base.
For me, it’s more accurate to say that equations don’t like me.
He doesn’t like you. I don’t like you either.
I agree Anthony but all of that scientific/mathematical stuff is necessary. Andy has a whole lot of information people like you and me need to know. The important thing is at the end of the article we need a conclusion laying out in plain English what we should take from the post.
This is the main point, and it is near the beginning:
My main point is that the IPCC has “out-scienced” themselves. Their reasoning is so complicated in AR6 as to be unbelievable. I finish with this:
When a model meets observations, the observations always win, to paraphrase Feynman.
I hope that helps.
Anthony,
The mathematics used here are not “advanced” as you claim. They are little more than adding up, taking away, multiply and divide. If you cannot comprehend the mathematics, you should ask yourself why you try to follow the science because you might be incapable of advancing it.
Geoff S
Look at the graphs. Take the lines and shading off Fig 1 and 3…basically a curve fit through those points shows no predictabilty whatsoever…so technically are random despite someone “best-fitting” a line….Fig 1 a slight but statistically meaningless (because no predictability) increase over time….Fig 3…fly specks on a calendar come to mind….
Yes! The uncertainty (shaded area) contains many possibilities, any one of which may be the “correct” one. The best fit line does not have a 100% possibilty of being correct.
First of all, Anthony, my guess is that you might have gotten confused by the naming of variables
_DeltaF-CO2 sounds fancy (and is named such for a good reason), but when you look at the equations they are to a large extent simple divisions.
I have some trouble with this statement:
Andy wrote “”Strictly speaking, if both F and λ vary independently, as claimed by AR6, it is very hard, if not impossible, to determine ECS from them. “‘
Well, at least as an estimate it is straightforward to divide the outer limits of each of those parameters and get a range of ECS as a result (trusting the the procedure to find the values is good.. which of course is a point of this article.)
Also, uhm if you take real world values and pluck them into equation 2 you get an unrealistic ECS.
The conclusion can only be that the equation then goes not describe reality??
ECS is supposed to be the sensitivity of surface temperature to an instantaneous doubling of CO2. In a real-world sense, as opposed to a model, if both the forcing (due to CO2) and the feedback vary, you can’t really determine ECS.
If working in the model world, you can take the values from the initial state and the end state and compute an ECS. But one of the points of the post is that ECS is really a model metric and has little to do with the real world.
“If working in the model world, you can take the values from the initial state and the end state and compute an ECS”.
And in the real world there is no initial nor end state..outside of a lab.
It is all.. flux. No zero point of departure.
There has been a dramatic departure between Net radiation in the SH and OHC in the SH since they were aligned in 2015 for AR6. At December 2025, the departure had reached 140ZJ.
Also the OHC in the SH has been decelerating since 2015. On present trend, the accumulation will be negative by 2030.
It will be very difficult to maintain the ECS BS once the OHC in the SH goes negative. They will have to invent more BS why the hemispheres behave differently.
CO2 does next to nothing. It is all a sad hoax perpetuated by academics and other useful idiots who put salary above morals.
I couldn’t agree more. The Southern Hemisphere is not following the climatariat’s orders! More on that in my next post. The Southern Ocean is definitely a rebel.
It is not just the Southern Ocean. The OHC in the entire SH is trending toward falling by 2030. The deceleration has been close to 1ZJ per year for the past decade.
The cooling of the Southern Ocean has been spun as the isolation of Antarctica. It will be much harder to spin loss of ocean heat in all the oceans of the SH.
Especially the rebellious eastern Pacific off the coast of South America!
The attached shows the departure using the OHC and Net Radiation accumulation at December each year.
OHC in the SH is not far off going negative.
This departure will be very difficult to explain in AR7. Particularly without USA money and the inevitable collapse of the UNIPCC through lack of funding.
I have doubts that AR7 will materialise.
“CO2 does next to nothing.”
______________________________________________
“You can go outside and spit and have the
same effect as doubling carbon dioxide.”
Reid Bryson
My best estimate for doubling is 0.006C. That is based on the increase in atmospheric mass due to the added carbon altering the thermo-regulation of the ocean surface temperature.
Your estimate works a lot better when examining historical temperature data. The data shows no discernible effects from CO2.
Forcing is caloric redux.
Since its inception, the ECS concept has been characterised by poor science (including wishful thinking presented as gospel) and flawed estimates of measurement and overall uncertainty.
I am not critical of attempts to understand earth energy components. I have been publicly critical of poor climate science since I got involved with the bumbling efforts of Phil Jones at East Anglia in 1992.
If the personal income of climate scientists depended on creation of products wanted by the public and even saleable, the standard should improve. While there are huge pools of money taken as taxes and handed over to these poor scientists to feed each other, the standard will stay low.
Of course, such criticism will draw outcry from perps who benefit. Better to spend time understanding the difference between science fiction and science fact. Geoff S (hard scientist).
I could quibble on a few words, but nah, your post is just fine as written.
Harold The Organic Chemist Says:
ATTN: Andy May And Everyone!
RE: CO2 Does Not Cause Warming of Air!
RE: ECS is Zero!
Shown the chart (See below) is a plot of the annual mean temperature in Adelaide from 1857 to 1999. In 1857 the concentration of CO2 was ca. 280 ppmv (0.55 g CO2/cu. m. of air) and by 1997 it had increased to ca. 367 ppmv (0.72 g CO2/cu. m. of air) but there no was corresponding increase in the annual mean temperature. Instead there was a cooling which began in ca. 1940. Brisbane had a similar cooling. In 1857 the annual mean temperature was 17.2° C and by 1999 it had deceased slightly to 16.7° C.
To obtain more recent Adelaide temperature data, I went to:
https://www.extremeweatherwatch.com/cities/adelaide/average-temperature-by-year. The Thi and Tlo temperature data from 1887 to 2025 are displayed in a long table. The computed Tav for 2025 was 17.4° C. In 2025 the concentration of CO2 in dry air at the Mauna Loa Obs. in Hawaii was 427 ppmv (0.84 g CO2/cu. m. of air.). After 168 years the annual mean temperature in Adelaide has remained unchanged.
The reason there was no increase in the annual mean temperature in Adelaide is quite simple: There is just too little CO2 in the air to absorbed out-going long wave IR light to heat up the air. Please do forget how little CO2 there is currently in the air.
The above empirical data falsifies the claims by the IPCC that CO2 causes “global warming” and is the “control knob” of “climate change”. The data also show that the ECS is zero.
The chart was obtained from the late John L. Daly’s website:
“Still Waiting For Greenhouse” available at http://www.john-daly.com.
He found over 200 weather stations that showed no warming up to 2002.
I’ll bet dollars to donuts that these investigators who do all these fancy and esoteric calculations do not how calculate the mass of CO2 in a cubic meter of air from the data from the MLO. They should stop wasting so much time, effort and energy on these useless calculations.
NB: If you click on the chart, it will expand and become clear. Click on the “X” in the circle to contract the chart and return to Comments.
Good thread, and John Clauser and Willie Soon discussed at the recent ICCC in Washington, DC the circular reasoning and intellectual fraudulence behind “adjusting” the CERES satellite data to match OHC.
One point of contention is your (which I view as dubious) assumption that even the recorded increase in temperatures since the 1960’s is primarily due to increases in atmospheric CO2, since via proxies there is evidence that the earth has been slowly gradually warming since the end of the LIA 300 years ago, well before CO2 increased, without acceleration. Likely because of the neutralizing effects of negative more than positive feedbacks, including clouds, oceanic cycles and atmospheric circulation changes, including of the polar vortex.
This was an assumption I made for the post. It is not my opinion, just proposed to make the post work. I actually have no idea what has caused the recent warming. I assume that additional CO2 played some role, solar variability had an influence, and natural internal variability also contributed. How much each contributed is unknown as far as I know. The cooling period from 1945 to 1975 suggests that CO2’s contribution is minor. Time will tell.
Good article, Andy, thanks.
Dear Sir,
I am (really) very, very bad at mathematics, so my understanding of this article is therefore almost nonexistent. However, it did not escape me that the question of ECS was somewhat “the crux of the matter” when it comes to climate research.
Earlier today, I was reminded of an article from WUWT dealing with the calibration of aerosols in models. From what I recall, it is a bit of a “magic card” that allows modelers to keep things afloat.
It is quite difficult to estimate very precisely the quantity of aerosols present in the atmosphere a few decades ago. But recent and very welcome pollution-control laws could, according to some mainstream climatologists (so, let’s be honest: relatively alarmist), “reveal” the “true warming” that was previously masked by atmospheric pollution. In other words, according to these people: “Get ready, we haven’t seen anything yet, and it’s going to heat up!”
I do understand that the question of estimating ECS is far from being resolved, and that the level of cooling caused by aerosols (very diverse) resulting from anthropogenic emissions is just as (if not more) difficult to clarify.
So, do you have an opinion on the statements made by the aforementioned mainstream scientists?
I am not, of course, asking you to settle the issue definitively, because as we all know: Science is not settled.
I’ve never looked into aerosols as a factor in climate, but I doubt they make much difference since they cannot last very long in the atmosphere before being destroyed.
You making the same mistake as everyone, and it is the only reason people wrongly believe feedbacks were positive. You must not use an OLS regression when there are errors in the x-values. It will cause “regression dilution” and produce a far to low slope.
A reasonable regression here would be TLS. I did a quick reanalysis of the first scatter plot and here is the correct result..
Interesting idea so I tried it. These are the results:
Using Total Least Squares:
> ECS_Myhre_TLS$ECS
[1] -18.68741
> ECS_Myhre_TLS$TCR
[1] 6.168215
> ECS_Myhre_TLS$alpha_feedback
[1] 0.1985294
Using Ordinary Least Squares:
> ECS_Myhre$ECS
2.255342
> ECS_Myhre$TCR
1.517393
> ECS_Myhre$alpha_feedback
-1.644983
I’m not sure TLS is the best choice here. As Ross McKitrick wrote in Climate Dynamics in 2023 (https://doi.org/10.1007/s00382-022-06315-z):
McKitrick’s explanation is complex and hard to summarize, but basically TLS coefficients are likely to be wrong unless the data are prepared very carefully and they are truly independent. In this case the two variables are not independent, and they have different means and standard deviations. The slope here is probably corrupted by the ratio of the error variances. The range of the SST anomaly (see figure 1) is ~.2 to ~0.8 and the range in N is 0 to 2 and N is tuned to match the derived OHC from SST. TLS is probably inappropriate.
I might be able to figure out a way to manipulate the data in such a way that TLS can be used. I’ll think about it.
“The range of the SST anomaly (see figure 1) is ~.2 to ~0.8 “
This is assuming the data used to create the baseline and the anomaly are 100% accurate, i.e. measurement uncertainty is zero.
The real issue is that the measurement uncertainty of the SST is at least +/- 0.5C to +/- 1.0C and is probably even greater. If you make two anomaly plots assuming a +/-1.0C, one for the positive maximum range and one for the negative maximum range one will have a positive slope and one will have a negative slope regardless of the method of regression used.
In other words, the data being used isn’t fit for the purpose of determining what is actually happening. By throwing away the measurement uncertainty of the data, climate science is just fooling itself – and we all know what Feynman said about that.
Tim,
True, the SST data is inaccurate, I have a post soon that discusses that more, you can also see some of my thinking here:
https://andymaypetrophysicist.com/2026/03/31/toa-eei-versus-surface-net-flux/
However, the key point is that the CERES data are adjusted to match ocean heat content, thus Figures 1 and 3 (d(N)/d(SST) are not independent but intimately linked. The regression, regardless of the method used, is contaminated by that. The problem with figure 3 (the Gregory plot) is deeper, it is conceptually flawed.
I’ve read much of what you have written. Here is one quote:
“They then go on to explain that to avoid this problem they adjust the SW and LW fluxes within their ranges of uncertainty to force the satellite measurements to reflect the imbalance calculated using ocean heat content. As mentioned above, in CERES EBAF (“Energy Balanced and Filled”) version 4, the global annual mean values are adjusted such that the July 2005– June 2015 mean net TOA flux is 0.71 ± 0.10 W/m2, which is from Johnson et al. (2016) and an update from the previous value of 0.58 W/m2.”
What range of uncertainty?
The issue here is the +/- 0.1 W/m^2 value. I will guarantee you that is the standard deviation of the sample means, the SDOM, (aka the standard error) which is *NOT* the measurement uncertainty. It is a metric for how precisely the mean of the population can be located. The measurement uncertainty is far more related to the variance of the measurement data than it is to the SDOM. The variance of the global annual TOA flux is far more than +/- 0.10 W/m^2. The outgoing flux at any point on the globe at any point in time is a complex function of the atmospheric makeup, the surface conditions (e.g. sand vs water vs soybeans vs etc) as well as the latitude of the point on the globe and the axial tilt of the earth. That outgoing flux will have a wide variance and, therefore, a large measurement uncertainty. That variance just can’t be ignored using the meme of “all measurement uncertainty is random, Gaussian, and cancels”. The variance will propagate onto any higher level average, be it a daily, a monthly, or an annual average.
Think about it for a minute. The outgoing flux is at best an exponential decay driven by a sinusoidal input during part of the day. That means the heat loss at any point on the globe is quite variable during the diurnal cycle, i.e. a large variance so a large measurement uncertainty, which propagates onto the diurnal cycle mean value. It doesn’t matter which satellite system you use, the system doesn’t collect enough data to be fit for the purpose of finding a “net annual outgoing flux” from the earth to the tenths digit, let alone at the TOA. I would be absolutely amazed if the measurement uncertainty is better than 10% or +/- 14 W/m^2.
“What range of uncertainty?”
This is explained in Loeb, 2009:
https://journals.ametsoc.org/view/journals/clim/22/3/2008jcli2637.1.xml
For the overall uncertainty in the CERES EBAF data see Loeb, 2018:
https://journals.ametsoc.org/view/journals/clim/31/2/jcli-d-17-0208.1.xml
Andy,
“The actual uncertainty for CERES resulting from calibration alone is 1% SW and 0.75% LW radiation [one standard deviation (1σ)], which corresponds to 2 W m−2, or 0.6% of the total TOA outgoing radiation.”
I said: “The issue here is the +/- 0.1 W/m^2 value. I will guarantee you that is the standard deviation of the sample means, the SDOM, (aka the standard error) which is *NOT* the measurement uncertainty.”
I see nothing here which invalidates my assertion. As usual with climate science, “adjusted” values are used to minimize the difference between actual and expected results.
“They then go on to explain that to avoid this problem they adjust the SW and LW fluxes within their ranges of uncertainty to force the satellite measurements to reflect the imbalance calculated using ocean heat content.”
OHC has its own measurement uncertainty. Using OHC to adjust flux values ADDS to the measurement uncertainty associated with the flux values, it doesn’t decrease the measurement uncertainty of the flux values. It’s like saying the OHC *calculated* results are “true values” with no measurement uncertainty. If that is actually the case then why bother with the CERES satellite system at all?
It’s statistics, baby! It is not per se “right” or “wrong”. That is just like an opinion poll will not give the election result. But if done well, it will give us an idea, and if not, it may be totally off. OLS here is totally off.
Also McKitrick is a bit off here. TLS assumes equal errors in both x- and y-values, and that may of course be questionable. Ideally you would know the respective errors in both instances and build an almost perfect regression then. However, we do not know, and therefore TLS is yet the best fit.
The problem with OLS is twofold. First we have a massive error in the x-values, which makes it illicit. The second problem is with the numerical slope of the plot. The steeper the slope, the more nonsensical the OLS result becomes. Remember, it minimizes the vertical(!!) residuals. That makes zero sense when the plot itself is vertical. Just invert the OLS regression to see it will not fit. Greg Goodman has written a more consistent article on the problem on J. Curry’s blog.
Another issue we owe to software. When making a chart of the plot, the software automatically fits the intervals so that the data nicely spread out. However, that will distort the shape of the plot. As a side effect a non fitting OLS slope may look appropriate, while it is not. That is why I always use symmetric intervals.
Also your AI ECS result is hallucination. It should be..
3.7/5.03 = 0.74K
https://greenhousedefect.com/the-holy-grail-of-ecs/regrettable-regressions-a-reanalysis
OK, I’ve spent way too much time on this TLS nonsense. The ECS value you refer to is not from AI, it is from R. The data we are dealing with is:
> N
[1] 0.5363030 0.1273197 0.4789832 0.6874660 0.4068113 0.8056902 0.1894508 1.1911202 0.8954363
[10] 0.0134505 0.7186961 1.3744631 0.5780136 0.8480457 1.0848583 0.9399038 0.9392878 1.3575622
[19] 1.3446951 0.7255915 1.5038711 1.4929610 1.8330392 0.8090864 1.4716599
> T
[1] 0.2793897 0.3134376 0.3404527 0.3328818 0.3312851 0.3325346 0.2594107 0.2444300 0.3682510
[10] 0.3784038 0.2728918 0.3392096 0.3611463 0.4525990 0.5708395 0.6106063 0.5496695 0.5064159
[19] 0.5815551 0.5645211 0.4653958 0.5072142 0.7382775 0.7909708 0.7068914
>
In order to get lambda, we need d(N)/d(T). TLS chokes because it is very sensitive to variance.
I was using svd and the line is nearly horizontal because the variance in N is ~1.5 W/m2 and the variance in T is ~0.15 degC.
Thus the cloud is very elongated in the N direction and TLS chokes on that. It gives a beta of -0.1985, which is absurd. TLS is totally inappropriate here.
I then tried ODR (orthogonal distance regression), but it failed for the same reason and would not give bootstrap CIs.
As a last resort I tried Deming, it would not give me CIs on the fit, but it did give me CIs on the ECS, as follows:
> alpha
[1] 5.037037
> ECS
[1] 0.7365441
> ECS_LCI
[1] 2.139368
> ECS_UCI
[1] 0.4448485
All the values are nonsense. The only thing that works with this data is OLS. I think McKitrick is right. He writes, and this is very true:
“In the absence of specific evidence supporting use of TLS it should not be a default option.”
OLS is a much better option, especially in this case where N and T are not independent and they have very different variances, by a factor of ten. I’m with McKitrick on this.
Happy to see you have done the dirty work involved in verifying assumptions that are necessary for proper statistical analysis. That is something climate science is woefully short on.
Some additional thoughts on TLS and ODR. Both fail here for the same reasons.
McKitrick identified the reasons using theory, But this problem is a poster child example of the theoretical failings he identified:
My data does not lie on a line and it should not!
This is because my SSTs have a very small variance.
TLS interprets all residual structure as “measurement error in T,” which forces the slope upward or downward depending on geometry. This is why the TLS slope was nonsensical.
TLS/ODR/Deming require assumptions about error variances, identifiability, and deterministic structure that this data does not satisfy.
When those assumptions fail, the methods become unstable, biased, or undefined.
One needs to remember what relates OLR to Ts – it is the SB law after all. Within terrestrial temperatures this ratio is naturally somewhere between 3 to 6.
Because of it, and the errors in the x-values, OLS is TOTALLY ILLICIT here, while TLS is perfectly fine. And it shows how feedbacks are negative.
And there are physical reasons for it. The negative lapse rate feedback dominates a relatively weak WV feedback. “Consensus science” believes the opposite because in the regional and seasonal proxies they confused a positive LR component, as opposed to a negative one they expected, to be evidence of a strong WV feedback.
And although they learned about their mistakes..
(Dessler et al 2008)
(Inamdar, Ramanathan 1998)
..they still make the same unsubstanted claim of a positive total WV Feedback.
btw.. what do you not like about an ECS of 0.74?
I think I have made my point. As McKitrick says, and for the reasons he gives, TLS is inappropriate in most climate science applications – in particular this one. I spent hours trying to get it to work with the dataset shown in figure 1 and demonstrated to my satisfaction that TLS is useless with this dataset. I also demonstrated that ODR and Deming do not work. McKitrick is clear from a theoretical standpoint why it should not work with this data.
The data, in its entirety is above in a previous comment. Knock yourself out trying, I do not think you will get it to work.
If you still believe OLS was valid, why not simply invert it? I mean that is the basic procedure even taught in school.
iOLS: 5.44
This is not an exercise in statistics. The value I was after was dN/dT, I have no interest in dT/dN. Besides, from a purely statistical exercise point of view, the regression is not valid. N is tuned to T, they are not independent. Let’s not forget the objective.
I did not post any regression statistics, right? Why? Because they are invalid. The main reason that TLS is invalid here is that the points do not necessarily fall on a line and the variance of T is very small. TLS assumes the points are supposed to fall on a line and that the variances are about equal. Anyway, I wasted way too much time on this, but at least I learned something.
Remember, TLS is very delicate and breakable, OLS is more robust.
Most importantly, McKitrick discusses something completely different. There it is about climate attribution, ie. the plotting of modelled temperature against measured temperature. In this instance “consensus science” prefers TLS over OLS, because it suggests a larger anthropogenic factor. That is why McKitrick opposes TLS in this instance.
I do not even know what the better regression might be in this case, because it really depends on the nature and structure of the data. However, his judgement must not be generalized and is by no means applicable to the dOLR/dTs relation we are discussing here.
Here OLS is, again, totally illicit, while TLS is opportune. If you’d ask McKitrick, or any statistician, they would tell you just the same. Strangely enough you are flipping KcKitricks intent, which is antagonizing “consensus science”, while you act (though unknowingly) pro “consensus science” in an instance where it is totally wrong.
I’ll let mr Dibbell comment on that..
the world is heating up wayy to fast
Only socially.
Good post, Andy.
In addition to the several (perhaps inadequate) EBM observational estimates of ECS at about 1.6-1.7C, over the past years I developed a number of ‘independent’ estimates (including one from Moncton’s ‘irreducible’ equation) all of which are in the same range. For example, Guy Callendar’s famous 1935 curve predicts 1.68C. Interestingly, the only CMIP6 model that does not produce a spurious tropical troposphere hotspot—INM CM5— produces 1.8C.
Thanks Rud, good points. I just spent way too long looking into a variety of orthogonal best fitting methods only to find what I already knew that ordinary least squares is best. Oh well, at least I learned about them. Be very careful with total least squares, orthogonal distance regression, and the Deming method, they can all spit out crap.
I wanted to show something many people miss when reviewing a regression with a confidence interval. A confidence interval defines where values may be. The graph must be interpreted as to what it could possibly show. I have added lines that are possible, however, one can draw many more inside the the confidence interval which indicates the likely values that should be considered.
In other words, the best fit line does not have a 100% possibility of being correct. The correct line is unknown.
Correct and a good point.
In term of uncertainty of the fit, it can be argued that the prediction interval (PI) is more appropriate than the confidence interval because the PI typically spans all the data points.
It also gives a wider uncertainty interval.
If you are rolling two six-sided dice the confidence interval for the next roll is 7 +/- 0.1. The prediction interval is 2,12.
It raises an interesting question about climate science. Why is climate science so focused on estimating the next mean value rather than estimating the actual interval in which the next value might lie?
It seems like it falls into the old way of forecasting where all past data is weighted equally with the most recent data. How many shovels I sold ten years ago is weighted equally with how many I sold last year and the year before that. I wind up tracking the long term mean instead of the predicting how many shovels to order for next year.
And therefore we are presented with proof positivie the science is “settled” and the models are “robust.”
I reject many of the terminology definitions created by the Trans-Reality Activists.
feedback
forcing function
Both of those have concise scientific and engineering definitions that do not apply as the models, etc., choose to hijack and redefine them.
But in the case of this article, most objectionable is Equilibrium Climate Sensitivity.
The Earths’ coupled energy systems are never in equilibrium, so ECS is a fabrication that has no applicability to reality.
Until the optimum climate is defined in metrics are are testable and measurable by anyone, how can we know if we have departed the optimum or are approaching it?
This is the number 1 flaw in all of the climate nonscience.
Do not misconstrue. I do applaud the analysis and effort put into this study.
Hooray for you. The very basic, most underlying theological truth of CAGW is that any warming since the LIA dooms the world. The optimum temperature has already been passed because of CO2 and we need to stop fossil fuels in order to return to past temperatures.
There is no evidence and no proof of what the optimum earth global temperature should be. Wouldn’t one think that should have been the very first thing considered 50 years ago? Instead it was traipsing off assuming temperature rise would never stop.
2025 earths energy budget consists of absorbed solar, reflected solar, emitted longwave and stratosphere solar heating.
Mostly stratospheric solar thermal heating (just above 100 watts) and reflected solar (above 120 watts) is highest between December and April.
When divided by 4 reflected is actually the difference (108 – 128 watts (winter and) summer 103 watts – 87 watts) 4 watts reflected.
Lowest reflected solar (below 100 watts) between May and September.
Mostly tropospheric thermal heat in the atmosphere which is emitted surface heat is highest (above 240 watts per square meter) between May and October.
This article admits the data isn’t based on satellite data.
The average reflected solar is 108 watts and solar input 235.8 watts.
The average thermal heat between surface and space is (232.38w-m2 absorbed heat (mostly troposphere)+104.95 watt (mostly absorbed stratosphere) 337.33w-m2 emitted by the
surface.
The stacked bar chart shows when land snow cover gives higher reflected heat in spring.
Reason this studies model ignored land.
16% radiation (54.3 watts) , 85% (283) convection (60%) 198 watts and latent heat (25%) 84.3 watts. 84.3 -54.3 = 34 from clouds.
From the above article:
“Myhre et al. specifies α = 5.35 and C/C0 = 2 (a doubling of the CO2 concentration), so ΔF2xCO2 is a fixed value of 3.71 W/m2.”
followed by
“Van Wijngaarden and Happer derive 3.0 W/m2 for ΔF2xCO2 in the midlatitudes at the TOA and pointed out that the forcing changes with altitude (Wijngaarden & Happer, 2020, Table 3).”
followed by
“AR6 ‘assessed’ a value of 3.93 (IPCC, 2021, p. 993) for the period from 1750-2019 and they call it “ERF” or effective radiative forcing.”
So, is “ΔF2xCO2” 3.71 W/m2, 3.0 W/m2, 3.93 W/m2, or some other value du jour? Note those three cited values have a variance of +/- 13% about the mean.
And, separately, certain “scientists” want to assert that the value of EEI can be calculated to an accuracy of 0.7 W/m2 compared to the largest independent input parameter of 341 W/m2 from TOA solar insolation as averaged over Earth’s surface, or to a comparitive accuracy of 0.2%?
Good grief!
Believe me, I share your frustration. They didn’t have a good handle on F, so they made it a variable! Just shows how little they know about CO2 and its effect on the global climate.
Just a reminder, the CERES measurement error envelopes the 0.7 W/m2 meaning we could have an energy deficit.
Just a nit. 341 W/m^2 is: the total power density in the planetary cross section area divided by the total planetary surface. The solar irradiance at the equator is not the same as the north or south pole.
Too many averages for any of this “settled science” to be valid.
One can not evaluate anything using average insolation at a point for 24 hours.
One can’t even make a correct argument that incoming insolation balances over anything less than a long, long time.
The sun heats the land and oceans. Those are heat sinks with their own thermodynamic quirks. Those quirks control what is radiated and when.
To arrive at a small 0.7 value over a decade worth of radiation is beyond my imagination.
“One can not evaluate anything using average insolation at a point for 24 hours.”
Since solar insolation (at TOA) is defined as a measured value and does NOT depend on the existent of planet Earth and since it is given in power flux units of watts/m^2 = joules/sec/m^2, it is not dependent on averaging over any specified duration of time nor on any amount of Earth’s surface area.
However, to obtain the total amount of solar energy impinging on an arbitrary surface in space vacuum at the fixed distance of 149597870700 m (one AU) from the Sun, one would need to double integrate the vector dot product of solar insolation over the defined surface area and over the defined time interval.
Finally, since geometric points by definition do not have any surface area, they cannot receive any solar insolation at all.
You are saying in essence that (1360 + 0) / 2 = average insolation. The number is meaningless to use in determining heat or temperature because it doesn’t reflect reality. It can’t even be used for energy out because radiation out is based on temperature, and 340 will not allow correct calculation of temperature during sunlite or the correct temperature during nighttime. Do you really think 340 will provide for tropical temperature.
Maybe you think 340 will give a correct Tmax and correct Tmin for a Global Average Temperature. It won’t. Temperature and radiation have a 4th power relation. Arithmetic averages don’t work.
Tell you what, go get some soil temperatures and see if you can justify them with 340 of insolation. So us what you find.
This is how it works:
340 – 79.8 (90N), 340 – 65.15 (80N), 340 – 38.61 (70N), 340 – 3.81 (60N), 340 + 21.28 (50N), 340 + 74.58 (40N), 340 + 98.52 (30N), 340 + 126.49 (20N), 340 + 119.02 (10N), 340 + 111.34 (0N), 340 – 102.49 (10S), 340 + 83.30 (20S), 340 + 67.05 (30S), 340 + 67.05, 340 + 33.19 (40S), 340 – 2.48 (50S), 340 – 34.57 (60S), 340 -98.24 (70S), 340 – 155.49 (80S), 340 – 169.97 (90S).
There is a reason Antarctic has huge ice sheets.
Sum all the positive and negatives except 90N and 90S then
add 50% of 90N -79.8 and 35% of 90S -169.97. Result 340.
340 is the insulation, negatives and positives are absorbing heat and outgoing heat. Sum them all they cancel each out and your left with atmospheric kinetic energy 189.6. Sum just negatives -648.09, sum the positives 837.65. 837.65 – 680 = 157.65 (-648.09 + 680) =31.91 157.65+31.91=189.56.
20N, 10N, 0N, 10S = 459.34. SH negatives -460.75
30N, 40N, 50N = 194.38 – 187.37.
459.32+194.38 + 7.01=660.71 (48%)
-460.75 – 187.37 – 1.41 = -649.53 (48%) (1310.24)
40 direct to space (2%).
The point you are missing is that different points on earth have different specific heats and different masses. You simply cannot assume that “a” point at 80N has the same radiative flux value all the way around the earth at that latitude. Even worse, since the makeup of the earth at every point at 80N is different there will be a different gradient downward into the earth and thus a different heat transfer over time. E.g. Point A at 80N that gets 1 joule of solar insolation may emit that 1 joule of heat over a day while Point B at 80N may emit that 1 joule of heat over a week. The flux values for Point A and Point B will be vastly different.
That different gradient also means that the temperatures at Point A and Point B will be different meaning they will radiate at a different intensity.
And since the outgoing flux is based on an exponential decay function, using an arithmetic average for all points at 80N will give a meaningless value.
The fact that you give no measurement uncertainty intervals for any of the flux values is a dead giveaway that your calculations are using non-physical values. It’s a common failing in climate science.
I see your numbers but no math to support them.
How are the ± numbers arrived at.
Something like explain why there is a change from + to – at 60°N.
Or why 40S is + and 50S is -.
Ooops . . . my incorrect terminology in my third-to-last sentence: the calculated population variance (not the range about the mean) is actually 0.1575 for the three values given and cannot be considered as a percentage of the mean. (So sue me, Suzy!)
“It suggests internal variability dominates the signal, at least over the period from 2001-2025, this is reinforced by known long-term ocean oscillations like the AMO. Such long-term internal variability, if not taken into account, may invalidate the AR6 pattern-effect methodology.”
Internal variability my foot! the AMO warmed because the solar wind weakened from 1995. The AMO is always warmer during centennial lows in solar activity.