{"id":303995,"date":"2024-02-24T10:46:40","date_gmt":"2024-02-24T09:46:40","guid":{"rendered":"https:\/\/climatescience.press\/?p=303995"},"modified":"2024-02-24T10:46:44","modified_gmt":"2024-02-24T09:46:44","slug":"a-curious-paleo-puzzle","status":"publish","type":"post","link":"https:\/\/climatescience.press\/?p=303995","title":{"rendered":"A Curious Paleo Puzzle"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

From Watts Up With That?<\/a><\/p>\n\n\n\n

Guest Post by Willis Eschenbach<\/em><\/strong><\/p>\n\n\n\n

I was wandering through the fabled land of X yesterday and came across the following\u00a0post<\/a>:<\/p>\n\n\n

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Figure 1. Post on X showing a shortened version of the original Figure 6 from the paper linked below.<\/em><\/figcaption><\/figure>\n<\/div>\n\n\n

Hmmm, sez I \u2026 looks like an interesting study. Paleo CO2<\/sub> levels back to about 65 million years ago, which peaked at about 2000 ppmv.<\/p>\n\n\n\n

I was reminded of an earlier graphic I\u2019d done, showing paleo CO2<\/sub>\u00a0levels over a much longer time span. Figure 1 above only covers the Tertiary and Quaternary ages, the far right two boxes on Figure 2 below.<\/p>\n\n\n

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Figure2. Full history of CO2 since the Cambrian Explosion of life.<\/em><\/figcaption><\/figure>\n<\/div>\n\n\n

So I went to the source listed in Figure 1, a study yclept \u201cAtmospheric\u00a0<\/a>CO2<\/a>\u00a0over the Past 66 Million Years from Marine Archives<\/a>\u201d by Rae et al. The graphic below is a shortened version of Figure 6 of the Rae et al. study.<\/p>\n\n\n

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FIgure 3. Panels a) and c) of Rae et al., Figure 6<\/em><\/figcaption><\/figure>\n<\/div>\n\n\n

The authors have fully bought into the \u201cCO2<\/sub> Roolz Climate\u201d theory, saying inter alia:<\/p>\n\n\n\n

\n

Changing levels of atmospheric CO2<\/sub> have long been implicated in the well-documented cooling of the climate through the Cenozoic; however, outside of a handful of well-studied climate transitions, it has been hard to make a close link between CO2<\/sub> and climate. Our new combined marine-based CO2<\/sub> compilation shows, more clearly than in previous studies, a close correlation between CO2<\/sub> and records of global temperature (based on either geochemical reconstructions and\/or the state of the cryosphere) through the entire Cenozoic (Figure 6).<\/p>\n\n\n\n

\u2026<\/p>\n\n\n\n

Nonetheless, it is clear, even with these caveats, that atmospheric CO2<\/sub> and temperature are closely coupled, both across the data set as a whole and within shorter time windows. While the data set as a whole suggests a relatively high climate sensitivity, much of this temperature change is apparently accomplished by jumps between different climate states.<\/p>\n<\/blockquote>\n\n\n\n

Hmmm, sez I \u2026 I wondered why they didn\u2019t mention the value of what they claim is \u201ca relatively high climate sensitivity\u201d<\/em> for the data set as a whole. So I figured I\u2019d take a look at their data.<\/p>\n\n\n\n

For the CO2<\/sub> data, that was easy. They provide it in an Excel file in their Supplemental Material<\/a>.<\/p>\n\n\n\n

For the temperature data, the total opposite. They say \u201cSurface temperature estimated from the benthic \u03b418O stack of Westerhold <\/a>et al. (2020), using the algorithm of Hansen<\/a> et al. (2013)\u201d \u2026 except they don\u2019t give you the relevant links to the data or the algorithm.<\/p>\n\n\n\n

Grrr. I did that, dug out Westerhold\u2019s data, found and applied the Hansen algorithm, links above, and dang, it took a while.<\/p>\n\n\n\n

In any case, here\u2019s their CO2<\/sub>\u00a0data.<\/p>\n\n\n

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Figure 4. Paleo CO2 levels to 66 million years ago<\/figcaption><\/figure>\n<\/div>\n\n\n

Our current levels are far from the highest even in just the last 5 million years, let alone 60 million years. (Note that I haven\u2019t added a LOWESS smooth of the data as they did, because that effectively invents tens of millions of years of data.)<\/p>\n\n\n\n

So my next question, of course, was how well the temperature corresponds with the log of the CO2<\/sub>\u00a0levels. Figure 5 shows that relationship.<\/p>\n\n\n

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Figure 5. Paleo temperatures, and linear fit of the base 2 log of the CO2<\/sub>\u00a0levels.<\/em><\/figcaption><\/figure>\n<\/div>\n\n\n

I have to say that is a very good agreement by climate and paleo standards, where measurements are always uncertain.<\/p>\n\n\n\n

Next I looked in detail at the cluttered area at the lower right. That\u2019s the time of the \u201cice ages\u201d, periods of glaciation followed by periods of warmth. Figure 6 shows the ice ages.<\/p>\n\n\n

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Figure 6. Paleo temperatures, and linear fit of the base 2 log of the CO2<\/sub>\u00a0levels. I\u2019ve added lines between the temperature and fitted CO2<\/sub>\u00a0values for each measurement time.<\/em><\/figcaption><\/figure>\n<\/div>\n\n\n

Once again, by the standards of paleo and climate, these are good fits.<\/p>\n\n\n\n

So \u2026 what\u2019s not to like? Does this actually show that CO2<\/sub> at 0.04% of the atmosphere is really the secret global temperature control knob as the authors claim?<\/p>\n\n\n\n

Perhaps not.<\/p>\n\n\n\n

Let\u2019s start by looking at the math. I\u2019ll divide the math off so as not to bother folks who are math-averse \u2026 for you, just jump over this section. Here is the summary of the linear fit of log2(CO2<\/sub>) and temperature.<\/p>\n\n\n\n

\n\n\n\n
Coefficients:<\/strong>\n\n             Estimate   Std. Error   t value    P-value\n(Intercept)    7.4810     0.1954       38.3      <2e-16\nlog2_CO2       6.3137<\/strong>     0.1087       58.1      <2e-16\n\nResidual standard error: 2.468 on 644 degrees of freedom\nMultiple R-squared: 0.8398, Adjusted R-squared: 0.8395\nF-statistic: 3375 on 1 and 644 DF, p-value: < 2.2e-16\n<\/code><\/pre>\n\n\n\n
\n\n\n\n
\u201clog2_CO2\u201d is the base 2 logarithm of the change in CO2<\/sub>. The \u201cEstimate\u201d of 6.3<\/strong> in bold above is the climate sensitivity<\/strong>, the estimate of the temperature change corresponding to a doubling of CO2<\/sub>.<\/p>\n\n\n\n
So yes, as the authors say above, this does show a \u201crelatively high climate sensitivity\u201d. The climate sensitivity of 6.3 is the third highest of 172 various past estimates of climate sensitivity. Here\u2019s a look at previous estimates.<\/p>\n\n\n
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Figure 7. Estimates of climate sensitivity from theory and reviews, observations, paleoclimate, climatology, and GCMs.<\/em><\/figcaption><\/figure>\n<\/div>\n\n\n
Another problem, beyond the climate sensitivity being one of the highest of the 173 estimates, is the much higher CO2<\/sub> values earlier in the past shown in Figure 2. If climate sensitivity is 6.3\u00b0C per doubling, that would put the global average surface temperature at around 40\u00b0C in the Cambrian and around 36\u00b0C in the Devonian \u2026 seems unlikely.<\/p>\n\n\n\n
However, there\u2019s a larger problem. The CO2<\/sub> theory is that a rise in CO2<\/sub> absorbs more upwelling longwave radiation. This causes an imbalance in the net radiation at the top of the atmosphere by redirecting some of the upwelling longwave back to the surface. The amount of this increased downwelling radiation is called the CO2<\/sub> forcing.<\/p>\n\n\n\n
The surface temperature then warms, increasing the upwelling surface longwave radiation to restore the balance.<\/p>\n\n\n\n
Figure 8 below shows the difficulty factor. When the earth\u2019s surface warms, it emits more radiation following something called the Stefan-Boltzmann equation. Figure 8 below shows the increased forcing due to increased CO2<\/sub>\u00a0levels in the past, along with the corresponding increase in surface upwelling longwave radiation from the temperature increases.<\/p>\n\n\n
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Figure 8. Changes in upwelling surface longwave radiation, and downwelling atmospheric longwave radiation due to CO2<\/sub>.<\/em><\/figcaption><\/figure>\n<\/div>\n\n\n
Yikes. So there\u2019s the perplexitude\u2014we\u2019re told to believe that a change in CO2<\/sub> forcing of 13 W\/m2<\/strong> causes a corresponding 128 W\/m2<\/strong> in upwelling surface longwave radiation.<\/p>\n\n\n\n
But where does the extra energy come from? Seems like the tail is wagging the dog. After allowing for the 13 W\/m2 of CO2<\/sub> forcing, there\u2019s another 115 W\/m2 of extra energy leaving the surface \u2026 but where did it all come from?<\/p>\n\n\n\n
By comparison, solar energy absorbed by the surface is 164 W\/m2. So the surface needs to be getting another three-quarters of a sun\u2019s worth of energy from \u2026 somewhere \u2026<\/p>\n\n\n\n
It would have to be some extraordinarily large feedback to the warming if that\u2019s what caused more warming. The feedback factor would have to be ~ 0.9 \u2026 and if the feedback factor is greater than 1.0, it grows without end. And that would suggest that at some point in the past, the natural fluctuations in this feedback would have led to endless growth.<\/p>\n\n\n\n
And it\u2019s difficult to think of a physical process that would supply that 115 W\/m2 to the surface. For example, total cloud albedo reflects about 75 W\/m2 back to space. So if the positive cloud feedback led to the complete disappearance of the clouds, that would only increase the surface absorbed solar by 66 W\/m2 after adjusting for increased surface reflection \u2026 and we\u2019re looking for 115 W\/m2.<\/p>\n\n\n\n
The same is true for the positive water feedback. The numbers aren\u2019t big enough. The IPCC AR6 WG1 Chapter 7 Section 7.4.2.2<\/a> estimates a combined water vapor and lapse rate feedback at 1.12 W\/m2 per \u00b0C of warming. The warming back to 60 million years ago is about 15\u00b0C. So water vapor+lapse rate feedback would be on the order of 15\u00b0C * 1.12 W\/m2 per \u00b0C = 17 W\/m2 \u2026 and we\u2019re looking for 115 W\/m2.<\/p>\n\n\n\n
What else \u2026 the paleo temperature or paleo CO2<\/sub> might be incorrectly calculated, in which case none of this shows anything.<\/p>\n\n\n\n
A final possibility, of course, is that the warming has little to do with CO2<\/sub> and that the CO2<\/sub> levels are a function of temperature and not the other way around \u2026<\/p>\n\n\n\n
I titled this post \u201cA Curious Paleo Puzzle\u201d. That\u2019s the puzzle. How can an increase of 13 W\/m2 in CO2<\/sub> forcing cause an increase of 115 W\/m2 of upwelling surface longwave radiation?<\/strong><\/p>\n\n\n\n
All suggestions welcome.<\/p>\n\n\n\n
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Here on our redwood forested northern California hillside, there\u2019s a small triangle of the Pacific Ocean visible between the far hills on a warm sunny day after a long string of storms. The wind brings us the sound of the surf gnashing and gnawing on the coast six miles (ten km) in the distance. The grandkids, two and four years old, play and laugh in the next room.<\/p>\n\n\n\n
With best wishes for sun, rain, and the joys of family in your life,<\/p>\n\n\n\n
w.<\/p>\n\n\n\n
You May Have Heard This Before:<\/strong> When you comment, I ask that you quote the exact words you are discussing. It avoids endless misunderstandings.<\/p>\n\n\n\n
Data: <\/strong>I\u2019ve made two CSV files containing the data used in this analysis so they can be used in Excel or the computer language of your choice. One contains the temperatures, 23,722 different paleo measurements.<\/p>\n\n\n\n
The other contains the paleo CO2<\/sub> data, 646 measurements. That one also contains the temperatures from the other dataset, interpolated at the dates of the CO2 measurements. This allows for the calculation and graphing of the relationship between the datasets.<\/p>\n\n\n\n
The datasets are \u201cRae CO2 and Interpolated Temps.csv<\/a>\u201d and \u201cRae Temperatures.csv<\/a>\u201c, available at the links from my Dropbox.<\/p>\n\n\n\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
Hmmm, sez I \u2026 looks like an interesting study. Paleo CO2\u00a0levels back to about 65 million years ago, which peaked at about 2000 ppmv.<\/p>\n","protected":false},"author":121246920,"featured_media":304011,"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":"Hmmm, sez I \u2026 looks like an interesting study. Paleo CO2\u00a0levels back to about 65 million years ago, which peaked at about 2000 ppmv.","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":[691823091,691819127,691818076,691819106,691827127],"class_list":{"0":"post-303995","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","6":"hentry","7":"category-uncategorized","8":"tag-atmospheric-co2","9":"tag-climate-sensitivity","10":"tag-co2","11":"tag-control-knob","12":"tag-paleo-co2-levels","14":"fallback-thumbnail"},"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2024\/02\/0-CO2-1.jpeg?fit=3072%2C2304&ssl=1","jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/paxLW1-1h59","jetpack-related-posts":[{"id":317245,"url":"https:\/\/climatescience.press\/?p=317245","url_meta":{"origin":303995,"position":0},"title":"Scientists Selectively Reject CO2 Measurements That Do Not Align With The Human-Caused Narrative","author":"uwe.roland.gross","date":"10\/04\/2024","format":false,"excerpt":"Reconstructions of paleo CO2 levels openly rely on data derived from plant stomata. 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During the\u00a0Cretaceous period, which ended 66 million years ago when that giant asteroid killed all the dinosaurs, CO2 levels were mostly above 1000ppm \u2013 over double today\u2019s CO2 level. Did all those T-Rex dinosaurs\u2026","rel":"","context":"In \"carbon dioxide (CO\u2082)\"","block_context":{"text":"carbon dioxide (CO\u2082)","link":"https:\/\/climatescience.press\/?tag=carbon-dioxide-co%e2%82%82"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2024\/12\/0Photosynthesis-Diagram-1024x759-2.jpg?fit=1024%2C759&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2024\/12\/0Photosynthesis-Diagram-1024x759-2.jpg?fit=1024%2C759&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2024\/12\/0Photosynthesis-Diagram-1024x759-2.jpg?fit=1024%2C759&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2024\/12\/0Photosynthesis-Diagram-1024x759-2.jpg?fit=1024%2C759&ssl=1&resize=700%2C400 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