{"id":280254,"date":"2023-09-24T21:20:54","date_gmt":"2023-09-24T19:20:54","guid":{"rendered":"https:\/\/climatescience.press\/?p=280254"},"modified":"2023-09-24T21:20:56","modified_gmt":"2023-09-24T19:20:56","slug":"comment-and-reply-to-grl-on-evaluation-of-cmip6-simulations","status":"publish","type":"post","link":"https:\/\/climatescience.press\/?p=280254","title":{"rendered":"Comment and Reply to GRL on evaluation of CMIP6 simulations"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"407\" data-attachment-id=\"210489\" data-permalink=\"https:\/\/climatescience.press\/?attachment_id=210489\" data-orig-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?fit=1275%2C717&amp;ssl=1\" data-orig-size=\"1275,717\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"00IMAGE-numerical-weather-modeling-050216-1120&amp;#215;534-landscape\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?fit=723%2C407&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?resize=723%2C407&#038;ssl=1\" alt=\"\" class=\"wp-image-210489\" srcset=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?resize=1024%2C576&amp;ssl=1 1024w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?resize=300%2C169&amp;ssl=1 300w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?resize=768%2C432&amp;ssl=1 768w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?resize=1200%2C675&amp;ssl=1 1200w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?w=1275&amp;ssl=1 1275w\" sizes=\"auto, (max-width: 723px) 100vw, 723px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">From <a href=\"https:\/\/judithcurry.com\/\">Climate Etc.<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">by Nicola Scafetta<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Outcome of an exchange of Comments at Geophysical Research Letters (GRL)&nbsp; on my paper regarding ECS of CMIP6 climate models<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Back in March 2022 Gavin Schmidt on&nbsp;<a href=\"https:\/\/www.realclimate.org\/index.php\/archives\/2022\/03\/issues-and-errors-in-a-new-scafetta-paper\/\">RealClimate.org<\/a>&nbsp;critiqued&nbsp;one of my papers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Scafetta, N., Advanced testing of low, medium, and high ECS CMIP6 GCM simulations versus ERA5-T2m, Geophysical Research Letters, 49, e2022GL097716, 2022,&nbsp;<a href=\"https:\/\/doi.org\/10.1029\/2022GL097716\">https:\/\/doi.org\/10.1029\/2022GL097716<\/a>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">My GRL paper compared the warming of the global surface temperature data from 1980\u20131990 to 2011\u20132021 against the CMIP6 GCM hindcasts and found that only the GCM macro-ensemble made with the models with an Equilibrium Climate Sensitivity (ECS) \u2264 3 \u00b0C well agrees with the global surface temperature observations. The result is rather important because the GCMs with a low ECS are also those that project a moderate and nonalarming warming for the 21st century, in particular when the SSP2-4.5 scenario, which is the only SSP that seems to be realistic, is used for the climate projections.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Schmidt disliked my paper and claimed that it contains \u201cnumerous conceptual and statistical errors that undermine all of the conclusions\u201d. Together with Gareth Jones and John Kennedy, he wrote a letter to the Editorial Board of GRL asking them to retract my paper. They claimed that (1) my GRL 2022 paper overlooked the error of the mean of the temperature data from 2011 to 2021, which they claimed to be 0.10 \u00b0C, and (2) they insisted that \u201cthe full ensemble for each model must be used\u201d to test the models.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Their retraction request was rejected. GRL decided that a Comment-Reply exchange was more appropriate to clarify the subtle statistical issues that were being raised by their critiques and my rebuttals. Thus, Schmidt, Jones and Kennedy submitted their formal Comment, which essentially repeated the claims previously published on Real Climate. After their Comment was accepted on the 28th of January 2023, GRL asked me to write a formal Reply, which I submitted on the 21st of February 2023. My Reply was accepted on the 22nd of July 2023 and, finally, on the 21st of September both papers were published by GRL:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Schmidt, G.A., Jones, G.S., &amp; Kennedy, J.J. (2023). Comment on \u201cAdvanced testing of low, medium, and high ECS CMIP6 GCM simulations versus ERA5-T2m\u201d by N. Scafetta (2022).&nbsp;<em>Geophysical Research Letters<\/em>, 50, e2022GL102530.&nbsp;<a href=\"https:\/\/doi.org\/10.1029\/2022GL102530\">https:\/\/doi.org\/10.1029\/2022GL102530<\/a><\/li>\n\n\n\n<li>Scafetta, N. (2023). Reply to \u201cComment on \u2018Advanced testing of low, medium, and high ECS CMIP6 GCM simulations versus ERA5-T2m\u2019 by N. Scafetta (2022)\u201d by Schmidt et al. (2023).&nbsp;<em>Geophysical Research Letters<\/em>, 50, e2023GL104960.&nbsp;<a href=\"https:\/\/doi.org\/10.1029\/2023GL104960\">https:\/\/doi.org\/10.1029\/2023GL104960<\/a><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">My Reply demonstrates that Schmidt et al. made gross statistical and physical errors and that, in any case, their critiques do not change the conclusions of my 2022 GRL paper.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The Plain Language Summary of my Reply reads:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Schmidt, Jones, and Kennedy\u2019s (SJK) (2023, GRL,&nbsp;<a href=\"https:\/\/doi.org\/10.1029\/2022GL102530\">link<\/a>) assessment of the error of the ERA-T2m 2011\u20132021 mean (\u03c3<sub>\u03bc,<\/sub><sub>95%<\/sub>&nbsp;= 0.10 \u00b0C) incorrectly assumes that, during such a period, the global surface temperature was constant (T(t) = M) and that its interannual variability (\u0394T&nbsp;<sub>i<\/sub>&nbsp;= T&nbsp;<sub>i&nbsp;<\/sub>\u2013 T (t<sub>i<\/sub>) = T&nbsp;<sub>i&nbsp;<\/sub>\u2013 M) was random noise. This is a nonphysical interpretation of the climate system that inflates the real error of the temperature mean by 5\u201310 times. In fact, the analysis of the ensemble of the global surface temperature members yields a decadal-scale error of about 0.01\u20130.02 \u00b0C, as reported in published records and deduced from the Gaussian error propagation formula (GEPF) of a function of several variables (such as the mean of a temperature sequence of 11 different years). Instead, SJK assessed such error using the standard deviation of the mean (SDOM), which is an equation that can only be used when there exists a distribution of repeated measurements of the same variable, which is not the present case. Furthermore, SJK misinterpreted Scafetta (2022, GRL,&nbsp;<a href=\"https:\/\/doi.org\/10.1029\/2022GL097716\">link<\/a>) and ignored published literature such as Scafetta (2023, Climate Dynamics,&nbsp;<a href=\"https:\/\/doi.org\/10.1007\/s00382-022-06493-w\">link<\/a>) that already contradicted their main claim about the role of the internal variability of the models and confirmed the results of Scafetta (2022, GRL,[<a href=\"https:\/\/doi.org\/10.1029\/2022GL097716\">link<\/a>].<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Both publications are open access, so interested readers can judge the scientific merits of both points of view for themselves.&nbsp; See also Schmidt\u2019s latest post at RealClimate [<a href=\"https:\/\/www.realclimate.org\/index.php\/archives\/2023\/09\/the-scafetta-saga\/\">link<\/a>].<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">I found the Comment by Schmidt, Jones and Kennedy to be outdated and paradoxical because their main arguments had already been fully rebutted in another and much more extended paper of mine (Scafetta, N., CMIP6 GCM ensemble members versus global surface temperatures, Climate Dynamics 60, 3091\u20133120, 2023, [<a href=\"https:\/\/doi.org\/10.1007\/s00382-022-06493-w\">link<\/a>], which they did not even cite. They also ignored other works (e.g. Lewis, N., Objectively combining climate sensitivity evidence, Climate Dynamics 60, 3139\u20133165, 2023 [<a href=\"https:\/\/doi.org\/10.1007\/s00382-022-06468-x\">link<\/a>], first published on 18 September 2022) which essentially confirmed my main result that the actual ECS had to be \u2264 3 \u00b0C. The same result is now also confirmed by a third work (Spencer, R.W., Christy, J.R., Effective climate sensitivity distributions from a 1D model of global ocean and land temperature trends, 1970\u20132021, Theoretical and Applied Climatology, 2023 [<a href=\"https:\/\/doi.org\/10.1007\/s00704-023-04634-7\">link<\/a>]. My GRL Reply performs the calculations using the same data as in my GRL 2022 study, also considering Schmidt et al.\u2019s main critiques outlined above, and once again validates the original finding in my &nbsp;2022 GRL paper.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Herein, I would like to address only a major statistical and simple topic discussed in my Reply that might be of general interest: how to calculate the error of the mean of a temperature record.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The issue was to determine the error of the mean of the global surface temperature record from 2011 to 2021, that is an 11-year period. Schmidt, Jones, and Kennedy claimed that such an error must be calculated with an equation known as the Standard Deviation of the Mean (SDOM) and adopted the following equation:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"83\" data-attachment-id=\"280255\" data-permalink=\"https:\/\/climatescience.press\/?attachment_id=280255\" data-orig-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-738.png?fit=768%2C88&amp;ssl=1\" data-orig-size=\"768,88\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"image-738\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-738.png?fit=723%2C83&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-738.png?resize=723%2C83&#038;ssl=1\" alt=\"\" class=\"wp-image-280255\" srcset=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-738.png?w=768&amp;ssl=1 768w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-738.png?resize=300%2C34&amp;ssl=1 300w\" sizes=\"auto, (max-width: 723px) 100vw, 723px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">where T\u00a0<sub>i<\/sub>\u00a0are the N = 11 annual temperature values from 2011 to 2021 and<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"76\" data-attachment-id=\"280257\" data-permalink=\"https:\/\/climatescience.press\/?attachment_id=280257\" data-orig-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-739.png?fit=768%2C81&amp;ssl=1\" data-orig-size=\"768,81\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"image-739\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-739.png?fit=723%2C76&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-739.png?resize=723%2C76&#038;ssl=1\" alt=\"\" class=\"wp-image-280257\" srcset=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-739.png?w=768&amp;ssl=1 768w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-739.png?resize=300%2C32&amp;ssl=1 300w\" sizes=\"auto, (max-width: 723px) 100vw, 723px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">is the mean over the 11-year period. As a result, they stated that the global surface temperature records from 2011 to 2021 are affected by a mean error of 0.10 \u00b0C.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">However, such a result is clearly incorrect because the decadal uncertainty associated with the global surface temperature record from 2011 to 2021 (or even since 1980) has never been calculated to be 0.10 \u00b0C in scientific literature. Even on an annual scale, the global surface temperature data error has been reported to be much smaller than 0.10 \u00b0C, as also GISTEM (authored by Schmidt) and HadCRUT (authored by Kennedy) clearly show. For example, the Berkeley Earth\u2019s global surface temperature record [<a href=\"https:\/\/berkeley-earth-temperature.s3.us-west-1.amazonaws.com\/Global\/Land_and_Ocean_complete.txt\">link<\/a>] reports a decadal scale error of about 0.02 \u00b0C (I reported the data version published in April 2023). Moreover, the claimed 0.10\u00b0C error is arbitrary calculated because Eq.&nbsp;<a href=\"https:\/\/judithcurry.com\/2023\/09\/24\/comment-and-reply-to-grl-on-evaluation-of-cmip6-simulations\/#x1-2r1\">1<\/a>&nbsp;with the monthly temperature record (which has N = 132) yields an error of about 0.03 \u00b0C. As a result, utilizing the SDOM makes no sense because by simply interpolating the data and raising N, one may obtain an error as small as desired.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In fact, Schmidt, Jones, and Kennedy did not realize that, in our specific case, Eq.\u00a0<a href=\"https:\/\/judithcurry.com\/2023\/09\/24\/comment-and-reply-to-grl-on-evaluation-of-cmip6-simulations\/#x1-3r2\">2<\/a>\u00a0is not the mean of a distribution of N repeated random measurements of one quantity, but a function of N different quantities. The 11 annual mean temperature data used for evaluating the mean from 2011 to 2021 are not 11 stochastic estimates of their 11-year mean and, therefore, they do not form a distribution of stochastic measurements of one quantity. When one just has a function of N different quantities, its error cannot be computed with the SDOM but only with a different equation known as the Gaussian Error Propagation Formula (GEPF) of a function of several quantities. In the case of the function called \u201cmean\u201d, the GEPF establishes that its error is given by the equation<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"110\" data-attachment-id=\"280258\" data-permalink=\"https:\/\/climatescience.press\/?attachment_id=280258\" data-orig-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-740.png?fit=768%2C117&amp;ssl=1\" data-orig-size=\"768,117\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"image-740\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-740.png?fit=723%2C110&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-740.png?resize=723%2C110&#038;ssl=1\" alt=\"\" class=\"wp-image-280258\" srcset=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-740.png?w=768&amp;ssl=1 768w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/image-740.png?resize=300%2C46&amp;ssl=1 300w\" sizes=\"auto, (max-width: 723px) 100vw, 723px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">where \u03c3<sub>z<\/sub><sub>i<\/sub><sup>2&nbsp;<\/sup>is the variance of the single measurements z<sub>i<\/sub>, that is the reported experimental error of z<sub>i<\/sub>, and \u03c3<sub>z<\/sub><sub>i<\/sub><sub>,z<\/sub><sub>j<\/sub>&nbsp;is the covariance of the individual measurement errors. When Eq.&nbsp;<a href=\"https:\/\/judithcurry.com\/2023\/09\/24\/comment-and-reply-to-grl-on-evaluation-of-cmip6-simulations\/#x1-4r3\">3<\/a>&nbsp;is applied to the global surface temperature data from 2011 to 2021, it yields an error that varies between 0.01 and 0.02 \u00b0C according to whether the covariance of the errors is used or not.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The difference between the SDOM and the GEPF is covered in any 101 course of Statistics and Error Analysis in Physics and are detailed in popular textbooks (e.g. see Chapter 3 and Chapter 4 in Taylor, J.R., An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements (second edition), University Science Books, 1997; see also Chapter 4 and 5 in Evaluation of measurement data \u2014 Guide to the expression of uncertainty in measurement, JCGM 100:2008. [<a href=\"https:\/\/www.bipm.org\/documents\/20126\/2071204\/%20JCGM_100_2008_E.pdf\/cb0ef43f-baa5-11cf-3f85-4dcd86f77bd6\">link<\/a>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In a nutshell, the GEPF must be used to assess the error of the mean weight between Mary and John (two different quantities) when using the same scale; the SDOM must be used to estimate the error of the weight of John (one quantity) when using two measurements from two separate scales. For example, every child knows that the mean between 10 and 20 (two different quantities) is 15. However, the SDOM adopted by Schmidt, Jones and Kennedy (Eq.&nbsp;<a href=\"https:\/\/judithcurry.com\/2023\/09\/24\/comment-and-reply-to-grl-on-evaluation-of-cmip6-simulations\/#x1-2r1\">1<\/a>) calculates 15\u00b15 even when 10 and 20 indicate two different quantities and are error-free, which is clearly wrong because, for example, 11 or 17 are not be the mean of 10 and 20. The SDOM can be used only if 10 and 20 are two stochastic measures of the&nbsp;<strong><u>same thing<\/u><\/strong>&nbsp;of which one would like to estimate the best estimate.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Even more paradoxically, the erroneous adoption of the SDOM physically implies that Schmidt, Jones, and Kennedy assumed that the climate temperature of the Earth from 2011 to 2021 was constant, and that natural fluctuations such as ENSO and (natural and anthropogenic) trends are just errors of measure. To justify such a claim, Schmidt, Jones, and Kennedy even invented a new concept in climatology, the concept of \u201c<em>random nature<\/em>\u201d (perhaps derived from a parallel universe theory?). However, their interpretation of the temperature data is clearly nonphysical. Natural variability does not contribute to the error of measure of the data, but at most only to the error of a model regression coefficient of the data. However, here the issue was not to test an isothermal climate model of the type T (t) = M.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Then, Schmidt, Jones and Kennedy used their erroneous and inflated 0.10 \u00b0C error of the mean of the global surface temperature record from 2011 to 2021 to qualitatively claim that the conclusion of my GRL 2022 paper was wrong just because a very few GCM member simulations obtained with a very few GCM models with an ECS &gt; 3 \u00b0C agree with the data within such erroneous interval, as Figure&nbsp;<a href=\"https:\/\/judithcurry.com\/2023\/09\/24\/comment-and-reply-to-grl-on-evaluation-of-cmip6-simulations\/#x1-51\">1<\/a>a shows. However, their own figure clearly shows that all the GCMs with ECS &gt; 3 \u00b0C produce hindcasts that are statistically skewed toward temperature values larger than the warming reported by the data: see the green dots indicating the GCM average simulations. Thus, statistically speaking, such models run too hot. In fact, as my Figure&nbsp;<a href=\"https:\/\/judithcurry.com\/2023\/09\/24\/comment-and-reply-to-grl-on-evaluation-of-cmip6-simulations\/#x1-62\">2<\/a>&nbsp;shows, when the right error of the mean is considered and the climate models are ensembled into three macro-GCM indicating the three ECS ranges (1.5\u20133.0 \u00b0C; 3.0\u20134.5 \u00b0C; and 4.5\u20136.0 \u00b0C) as did in my 2022 GRL paper and the proper statistics is evaluated also assuming some statistical dispersion due to their internal variability, the warm bias of the GCM groups with an ECS &gt; 3.0 becomes evident. My figures are reported below.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In conclusion, the Comment by Schmidt, Jones, and Kennedy is flawed, both statistically and physically. Its publication, together with my Reply, is important only because pointing out such errors is also useful for educational purposes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">I need to add that this is not the first time that Schmidt has critiqued one of my works using severely flawed mathematics and logic. Some readers may remember that in 2009 Benestad and Schmidt published a paper in JGR (Benestad, R.E., and G.A. Schmidt, Solar trends and global warming, J. Geophys. Res. 114, D14101, 2009, [<a href=\"https:\/\/doi.org\/10.1029\/2008JD011639\">link<\/a>], which was actually a kind of comment on some of my works. Here Schmidt made severe and na\u00efve errors in the wavelet analysis and multilinear regression model, as I first demonstrated here [<a href=\"https:\/\/pielkeclimatesci.wordpress.com\/2009\/08\/03\/nicola-scafetta-comments-on-solar-trends-and-global-warming-by-benestad-and-schmidt\/\">link<\/a>]. Such errors obscured the empirically evident and significant solar contribution to climate change and might have misled the scientific community on this topic. For the interested readers, the detailed rebuttal of Benestad and Schmidt\u2019s paper was later published here: Scafetta, N., Discussion on common errors in analyzing sea level accelerations, solar trends and global warming, Pattern Recognition in Physics 1, 37\u201357 [<a href=\"http:\/\/www.pattern-recogn-phys.net\/1\/37\/2013\/prp-1-37-2013.html\">link<\/a>]. Schmidt recently wrote other Real Climate flawed articles that critique papers that I have coauthored with Dr. Connolly, Dr. Soon, and many other colleagues which show the possibility that the sun can significantly contribute to climate change of the last century. The rebuttals of his critiques are found on [<a href=\"https:\/\/www.ceres-science.com\/news\">link<\/a>].<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In conclusion, these are cases that clearly demonstrate the necessity of having formal Comments and Replies published together to let the readers to properly evaluate both viewpoints. Thus, I am surprised that on\u00a0<a href=\"https:\/\/www.realclimate.org\/index.php\/archives\/2023\/09\/the-scafetta-saga\/\">RealClimate<\/a>, Schmidt appears to complain that his Comment was not published by alone, before or even without my Reply. However, it is critical that professionally written Comments and Replies are published concurrently. Furthermore,\u00a0\u00a0for the sake of science, any form of political manipulation of journals behind the scenes (as the ClimateGate emails revealed\u00a0<a href=\"https:\/\/tallbloke.wordpress.com\/2014\/02\/07\/anti-scientic-intimidation-of-journal-editors-and-publishers-by-ipcc-authors\/\">link<\/a>) must be abhorred. This must be done mostly for ethical reasons, notably to avoid potentially occurring instances of scientific disinformation campaigns promoted by the authors of the Comments and by various activist scientists.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"636\" height=\"800\" data-attachment-id=\"280260\" data-permalink=\"https:\/\/climatescience.press\/?attachment_id=280260\" data-orig-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/0Screen-Shot-2023-09-24-at-9.09.59-AM.webp?fit=636%2C800&amp;ssl=1\" data-orig-size=\"636,800\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"0Screen-Shot-2023-09-24-at-9.09.59-AM\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/0Screen-Shot-2023-09-24-at-9.09.59-AM.webp?fit=636%2C800&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/0Screen-Shot-2023-09-24-at-9.09.59-AM.webp?resize=636%2C800&#038;ssl=1\" alt=\"\" class=\"wp-image-280260\" style=\"width:760px;height:auto\" srcset=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/0Screen-Shot-2023-09-24-at-9.09.59-AM.webp?w=636&amp;ssl=1 636w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/0Screen-Shot-2023-09-24-at-9.09.59-AM.webp?resize=239%2C300&amp;ssl=1 239w\" sizes=\"auto, (max-width: 636px) 100vw, 636px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"517\" data-attachment-id=\"280261\" data-permalink=\"https:\/\/climatescience.press\/?attachment_id=280261\" data-orig-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/00Screen-Shot-2023-09-24-at-9.10.09-AM.webp?fit=768%2C549&amp;ssl=1\" data-orig-size=\"768,549\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"00Screen-Shot-2023-09-24-at-9.10.09-AM\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/00Screen-Shot-2023-09-24-at-9.10.09-AM.webp?fit=723%2C517&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/00Screen-Shot-2023-09-24-at-9.10.09-AM.webp?resize=723%2C517&#038;ssl=1\" alt=\"\" class=\"wp-image-280261\" srcset=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/00Screen-Shot-2023-09-24-at-9.10.09-AM.webp?w=768&amp;ssl=1 768w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/00Screen-Shot-2023-09-24-at-9.10.09-AM.webp?resize=300%2C214&amp;ssl=1 300w\" sizes=\"auto, (max-width: 723px) 100vw, 723px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Outcome of an exchange of Comments at Geophysical Research Letters (GRL)\u00a0 on my paper regarding ECS of CMIP6 climate models<\/p>\n","protected":false},"author":121246920,"featured_media":210489,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_crdt_document":"","advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[691822924,691822920,691822921,691822923,691822922],"class_list":{"0":"post-280254","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","6":"hentry","7":"category-uncategorized","8":"tag-activist-scientists","9":"tag-cmip6-climate-models","10":"tag-equilibrium-climate-sensitivity-ecs-2","11":"tag-gaussian-error-propagation-formula-gepf","12":"tag-standard-deviation-of-the-mean-sdom","14":"fallback-thumbnail"},"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?fit=1275%2C717&ssl=1","jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/paxLW1-1aUe","jetpack-related-posts":[{"id":280164,"url":"https:\/\/climatescience.press\/?p=280164","url_meta":{"origin":280254,"position":0},"title":"More on the statistical dispute between Scafetta and Schmidt","author":"uwe.roland.gross","date":"24\/09\/2023","format":false,"excerpt":"The argument about the proper way to estimate error in the European Centre for Medium-Range Weather Forecast (ECMWF)\u00a0ERA5\u00a0weather reanalysis dataset between Nicola Scafetta and Gavin Schmidt has finally been published by\u00a0Geophysical Research Letters. Schmidt, Jones, and Kennedy\u2019s comment is\u00a0here\u00a0(Schmidt, Jones, & Kennedy, 2023), and Scafetta\u2019s response is\u00a0here\u00a0(Scafetta N., 2023a).","rel":"","context":"In \"AR6 ECS\"","block_context":{"text":"AR6 ECS","link":"https:\/\/climatescience.press\/?tag=ar6-ecs"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?fit=1200%2C675&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?fit=1200%2C675&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?fit=1200%2C675&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?fit=1200%2C675&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/07\/00IMAGE-numerical-weather-modeling-050216-1120x534-landscape.jpg?fit=1200%2C675&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":220716,"url":"https:\/\/climatescience.press\/?p=220716","url_meta":{"origin":280254,"position":1},"title":"CMIP6 GCMs versus global surface temperatures: ECS discussion","author":"uwe.roland.gross","date":"26\/09\/2022","format":false,"excerpt":"Two publications examining the equilibrium climate sensitivity (ECS) have recently been published in\u00a0Climate Dynamics","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/09\/image-1237.png?fit=768%2C556&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/09\/image-1237.png?fit=768%2C556&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/09\/image-1237.png?fit=768%2C556&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2022\/09\/image-1237.png?fit=768%2C556&ssl=1&resize=700%2C400 2x"},"classes":[]},{"id":385343,"url":"https:\/\/climatescience.press\/?p=385343","url_meta":{"origin":280254,"position":2},"title":"Scafetta: Climate Models Have\u00a0Issues","author":"uwe.roland.gross","date":"27\/06\/2025","format":false,"excerpt":"The Coupled Model Intercomparison Project (CMIP) global climate models\u00a0(GCMs) assess\u00a0that nearly\u00a0100% of global surface warming\u00a0observed\u00a0between 1850\u20131900 and 2011\u20132020 is attributable to\u00a0anthropogenic drivers like\u00a0greenhouse gas emissions.\u00a0These models\u00a0also generate future climate projections based on shared socioeconomic pathways (SSPs), aiding in risk assessment and the development of costly \u201cNet-Zero\u201d climate mitigation strategies.","rel":"","context":"In \"Climate change\"","block_context":{"text":"Climate change","link":"https:\/\/climatescience.press\/?tag=climate-change"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/06\/0-CMIP6-climate-models.jpeg?fit=1200%2C900&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/06\/0-CMIP6-climate-models.jpeg?fit=1200%2C900&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/06\/0-CMIP6-climate-models.jpeg?fit=1200%2C900&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/06\/0-CMIP6-climate-models.jpeg?fit=1200%2C900&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/06\/0-CMIP6-climate-models.jpeg?fit=1200%2C900&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":252746,"url":"https:\/\/climatescience.press\/?p=252746","url_meta":{"origin":280254,"position":3},"title":"The error of the mean: a dispute between Gavin Schmidt and Nicola Scafetta","author":"uwe.roland.gross","date":"14\/04\/2023","format":false,"excerpt":"\u201cSeveral studies using CMIP6 models suggest that differences in climate sensitivity may be an important factor contributing to the discrepancy between the simulated and observed tropospheric temperature trends (McKitrick and Christy, 2020; Po-Chedley et al., 2021)\u201d(AR6, p. 443)","rel":"","context":"In \"ERA5-T2m\"","block_context":{"text":"ERA5-T2m","link":"https:\/\/climatescience.press\/?tag=era5-t2m"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/04\/0-modelling-climate-change.jpeg?fit=1024%2C682&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/04\/0-modelling-climate-change.jpeg?fit=1024%2C682&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/04\/0-modelling-climate-change.jpeg?fit=1024%2C682&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/04\/0-modelling-climate-change.jpeg?fit=1024%2C682&ssl=1&resize=700%2C400 2x"},"classes":[]},{"id":300205,"url":"https:\/\/climatescience.press\/?p=300205","url_meta":{"origin":280254,"position":4},"title":"What Period of Warming Best Correlates with Climate Sensitivity?","author":"uwe.roland.gross","date":"07\/02\/2024","format":false,"excerpt":"One way to investigate this problem is to look at climate model output across many models to see how their warming trends compare to those models\u2019 diagnosed equilibrium climate sensitivities (ECS). I realize climate models have their own problems, but at least they generate internal variability somewhat like the real\u2026","rel":"","context":"In \"CMIP6 models\"","block_context":{"text":"CMIP6 models","link":"https:\/\/climatescience.press\/?tag=cmip6-models"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2024\/02\/0Screenshot-2024-02-07-103854.png?fit=1198%2C784&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2024\/02\/0Screenshot-2024-02-07-103854.png?fit=1198%2C784&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2024\/02\/0Screenshot-2024-02-07-103854.png?fit=1198%2C784&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2024\/02\/0Screenshot-2024-02-07-103854.png?fit=1198%2C784&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2024\/02\/0Screenshot-2024-02-07-103854.png?fit=1198%2C784&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":266612,"url":"https:\/\/climatescience.press\/?p=266612","url_meta":{"origin":280254,"position":5},"title":"Understanding the role of the sun in climate change","author":"uwe.roland.gross","date":"10\/07\/2023","format":false,"excerpt":"Although the sun provides nearly all the energy needed to warm the planet, its contribution to climate change remains widely questioned. Many empirically based studies claim that it has a significant effect on climate, while others (often based on computer global climate simulations) claim that it has a small effect.","rel":"","context":"In \"Climate warming\"","block_context":{"text":"Climate warming","link":"https:\/\/climatescience.press\/?tag=climate-warming"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/07\/image-290.png?fit=1024%2C1024&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/07\/image-290.png?fit=1024%2C1024&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/07\/image-290.png?fit=1024%2C1024&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/07\/image-290.png?fit=1024%2C1024&ssl=1&resize=700%2C400 2x"},"classes":[]}],"_links":{"self":[{"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/posts\/280254","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/users\/121246920"}],"replies":[{"embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=280254"}],"version-history":[{"count":5,"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/posts\/280254\/revisions"}],"predecessor-version":[{"id":280264,"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/posts\/280254\/revisions\/280264"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/media\/210489"}],"wp:attachment":[{"href":"https:\/\/climatescience.press\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=280254"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=280254"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=280254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}