{"id":301114,"date":"2024-02-10T21:00:29","date_gmt":"2024-02-10T20:00:29","guid":{"rendered":"https:\/\/climatescience.press\/?p=301114"},"modified":"2024-02-10T21:00:32","modified_gmt":"2024-02-10T20:00:32","slug":"proof-that-the-spencer-christy-method-of-plotting-temperature-time-series-is-best","status":"publish","type":"post","link":"https:\/\/climatescience.press\/?p=301114","title":{"rendered":"Proof that the Spencer & Christy Method of Plotting Temperature Time Series is Best"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

From Roy Spencer, PhD.<\/a><\/p>\n\n\n\n

February 9th, 2024 by Roy W. Spencer, Ph. D.<\/small><\/p>\n\n\n\n

Since the blogosphere continues to amplify Gavin Schmidt\u2019s claim that the way John Christy and I plot temperature time series data is some form of \u201ctrickery\u201d, I have come up with a way to demonstrate its superiority. Following a suggestion by Heritage Foundation chief statistician Kevin Dayaratna, I will do this using only climate model data, and not comparing the models to observations. That way, no one can claim I am displaying the data in such a way to make the models \u201clook bad\u201d.<\/p>\n\n\n\n

The goal here is to plot multiple temperature time series on a single graph in such a way the their different rates of long-term warming (usually measured by linear warming trends) are best reflected by their placement on the graph, without hiding those differences.<\/em><\/strong><\/p>\n\n\n\n

A. Raw Temperatures<\/strong><\/p>\n\n\n\n

Let\u2019s start with 32 CMIP6 climate model projections of global annual average surface air temperature for the period 1979 through 2100 (Plot A) and for which we have equilibrium climate sensitivity (ECS) estimates (I\u2019ve omitted 2 of the 3 Canadian model simulations, which produce the most warming and are virtually the same).<\/p>\n\n\n\n

Here, I am using the raw temperatures out of the models (not anomalies). As can be seen in Plot A, there are rather large biases between models which tend to obscure which models warm the most and which warm the least.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

B. Temperature Anomalies Relative to the Full Period (1979-2100)<\/strong><\/p>\n\n\n\n

Next, if we plot the departures of each model\u2019s temperature from the full-period (1979-2100) average, we see in Plot B that the discrepancies between models warming rates are divided between the first and second half of the record, with the warmest models by 2100 having the coolest temperature anomalies in 1979, and the coolest models in 2100 having the warmest temperatures in 1979. Clearly, this isn\u2019t much of an improvement, especially if one wants to compare the models early in the record\u2026 right?<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

C. Temperature Anomalies Relative to the First 30 Years<\/strong><\/p>\n\n\n\n

The first level of real improvement we get is by plotting the temperatures relative to the average of the first part of the record, in this case I will use 1979-2008 (Plot C). This appears to be the method favored by Gavin Schmidt, and just looking at the graph might lead one to believe this is sufficient. (As we shall see, though, there is a way to quantify how well these plots convey information about the various models\u2019 rates of warming.)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

D. Temperature Departures from 1979<\/strong><\/p>\n\n\n\n

For purposes of demonstration (and since someone will ask anyway), let\u2019s look at the graph when the model data are plotted as departures from the 1st year, 1979 (Plot D). This also looks pretty good, but if you think about it the trouble one could run into is that in one model there might be a warm El Nino going on in 1979, while in another model a cool La Nina might be occurring. Using just the first year (1979) as a \u201cbaseline\u201d will then produce small model-dependent biases in all post-1979 years seen in Plot D. Nevertheless, Plots C and D \u201clook\u201d pretty good, right? Well, as I will soon show, there is a way to \u201cscore\u201d them.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

E. Temperature Departures from Linear Trends (relative to the trend Y-intercepts in 1979)<\/strong><\/p>\n\n\n\n

Finally, I show the method John Christy and I have been using for quite a few years now, which is to align the time series such that their linear trends all intersect in the first year, here 1979 (Plot E). I\u2019ve previously discussed why this \u2018seems\u2019 the most logical method, but clearly not everyone is convinced.<\/p>\n\n\n\n

Admittedly, Plots C, D, and E all look quite similar\u2026 so how to know which (if any) is best?<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

How the Models\u2019 Temperature Metrics Compare to their Equilibrium Climate Sensitivities<\/strong><\/p>\n\n\n\n

What we want is a method of graphing where the model differences in long-term warming rates show up as early as possible in the record. For example, imagine you are looking at a specific year, say 1990\u2026 we want a way to display the model temperature differences in that year that have some relationship to the models\u2019 long-term rates of warming.<\/p>\n\n\n\n

Of course, each model already has a metric of how much warming it produces, through their diagnosed equilibrium (or effective) climate sensitivities, ECS. So, all we have to do is, in each separate year, correlate the model temperature metrics in Plots A, B, C, D, and E with the models\u2019 ECS values (see plot, below).<\/p>\n\n\n\n

When we do this \u2018scoring\u2019 we find that our method of plotting the data clearly has the highest correlations between temperature and ECS early in the record.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

I hope this is sufficient evidence of the superiority of our way of plotting different time series when the intent is to\u00a0reveal<\/em>\u00a0differences in long-term trends, rather than\u00a0hide<\/em>\u00a0those differences.<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

The goal here is to plot multiple temperature time series on a single graph in such a way the their different rates of long-term warming (usually measured by linear warming trends) are best reflected by their placement on the graph, without hiding those differences.<\/p>\n","protected":false},"author":121246920,"featured_media":301126,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","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_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"The goal here is to plot multiple temperature time series on a single graph in such a way the their different rates of long-term warming (usually measured by linear warming trends) are best reflected by their placement on the graph, without hiding those d","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"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":[691826847,691826848,691826683,691826569,691826849,691821361],"class_list":["post-301114","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized","tag-climate-model-data","tag-cmip6-climate-model","tag-linear-trends","tag-observations","tag-raw-temperatures","tag-temperature-anomalies","fallback-thumbnail"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2024\/02\/0Screenshot-2024-02-10-205706.png?fit=1128%2C897&ssl=1","jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/paxLW1-1gkG","jetpack-related-posts":[{"id":299413,"url":"https:\/\/climatescience.press\/?p=299413","url_meta":{"origin":301114,"position":0},"title":"Gavin\u2019s Plotting Trick: Hide the Incline","author":"uwe.roland.gross","date":"02\/02\/2024","format":false,"excerpt":"The only reason to object to the way we plot temperature time series is to Hide The Incline* in the long-term warming discrepancies between models and observations when showing the data on graphs.","rel":"","context":"In \"climate model\"","block_context":{"text":"climate model","link":"https:\/\/climatescience.press\/?tag=climate-model"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/08\/0climate-models-epic-fail.webp?fit=999%2C775&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/08\/0climate-models-epic-fail.webp?fit=999%2C775&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/08\/0climate-models-epic-fail.webp?fit=999%2C775&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/08\/0climate-models-epic-fail.webp?fit=999%2C775&ssl=1&resize=700%2C400 2x"},"classes":[]},{"id":281157,"url":"https:\/\/climatescience.press\/?p=281157","url_meta":{"origin":301114,"position":1},"title":"Climate model provides data-driven answer to major goal of climate research","author":"uwe.roland.gross","date":"09\/29\/2023","format":false,"excerpt":"UAH\u2019s Dr. John Christy reviews results from the one-dimensional climate model Dr. Roy W. Spencer developed. Credit: Liz Junod From Phys.org by Dr. Roy W. Spencer,\u00a0University of Alabama in Huntsville A\u00a0new research study\u00a0from The University of Alabama in Huntsville, a part of the University of Alabama System, addresses a central\u2026","rel":"","context":"In \"CO2\"","block_context":{"text":"CO2","link":"https:\/\/climatescience.press\/?tag=co2"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/00climate-model-provides.jpg?fit=1200%2C675&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/00climate-model-provides.jpg?fit=1200%2C675&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/00climate-model-provides.jpg?fit=1200%2C675&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/00climate-model-provides.jpg?fit=1200%2C675&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2023\/09\/00climate-model-provides.jpg?fit=1200%2C675&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":420929,"url":"https:\/\/climatescience.press\/?p=420929","url_meta":{"origin":301114,"position":2},"title":"Surface Air Temperature Trends, Climate Models vs Observations, 1979-2025","author":"uwe.roland.gross","date":"01\/11\/2026","format":false,"excerpt":"This is just a short update regarding how global surface air temperature (Tsfc) trends are tracking 34 CMIP6 climate models through 2025. The following plot shows the Tsfc trends, 1979-2025, ranked from the warmest to the coolest.","rel":"","context":"In \"(Tsfc) trends\"","block_context":{"text":"(Tsfc) trends","link":"https:\/\/climatescience.press\/?tag=tsfc-trends"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/01\/0Ranked-CMIP6-vs-Obs-Tsfc-warming-trends-1979-2025-1536x1283-1.jpg?fit=1200%2C1002&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/01\/0Ranked-CMIP6-vs-Obs-Tsfc-warming-trends-1979-2025-1536x1283-1.jpg?fit=1200%2C1002&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/01\/0Ranked-CMIP6-vs-Obs-Tsfc-warming-trends-1979-2025-1536x1283-1.jpg?fit=1200%2C1002&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/01\/0Ranked-CMIP6-vs-Obs-Tsfc-warming-trends-1979-2025-1536x1283-1.jpg?fit=1200%2C1002&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/01\/0Ranked-CMIP6-vs-Obs-Tsfc-warming-trends-1979-2025-1536x1283-1.jpg?fit=1200%2C1002&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":421404,"url":"https:\/\/climatescience.press\/?p=421404","url_meta":{"origin":301114,"position":3},"title":"Tropical Tropospheric Temperature Trends, 1979-2025: The Epic Climate Model Failure Continues","author":"uwe.roland.gross","date":"01\/15\/2026","format":false,"excerpt":"As a follow-on to my\u00a0recent post\u00a0regarding global surface air temperature trends (1979-2025) and how they compare to climate models, this is an update on a similar comparison for tropical tropospheric temperature trends, courtesy of tabulations made by John Christy. It also represents an update to my popular\u00a0\u201cepic fail\u201d blog post\u00a0from\u2026","rel":"","context":"In \"anthropogenic greenhouse gas (GHG)\"","block_context":{"text":"anthropogenic greenhouse gas (GHG)","link":"https:\/\/climatescience.press\/?tag=anthropogenic-greenhouse-gas-ghg"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/01\/0Screenshot-2026-01-15-101000.png?fit=1200%2C602&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/01\/0Screenshot-2026-01-15-101000.png?fit=1200%2C602&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/01\/0Screenshot-2026-01-15-101000.png?fit=1200%2C602&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/01\/0Screenshot-2026-01-15-101000.png?fit=1200%2C602&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/01\/0Screenshot-2026-01-15-101000.png?fit=1200%2C602&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":254196,"url":"https:\/\/climatescience.press\/?p=254196","url_meta":{"origin":301114,"position":4},"title":"40 years of expert failure: New NOAA STAR satellite temperatures only show half the warming that climate models do","author":"uwe.roland.gross","date":"04\/22\/2023","format":false,"excerpt":"An all new reanalysis of the STAR satellite data finds markedly lower temperature trends for the last 40 years. 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This is true, and in fact the temperature data from the region shows a\u2026","rel":"","context":"In \"Climate models\"","block_context":{"text":"Climate models","link":"https:\/\/climatescience.press\/?tag=climate-models"},"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":[]}],"_links":{"self":[{"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/posts\/301114","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=301114"}],"version-history":[{"count":7,"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/posts\/301114\/revisions"}],"predecessor-version":[{"id":301128,"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/posts\/301114\/revisions\/301128"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/media\/301126"}],"wp:attachment":[{"href":"https:\/\/climatescience.press\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=301114"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=301114"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=301114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}