Over recent and deep geological time, when temperature and carbon dioxide are correlated, temperature is the ‘control knob’ of CO2, not vice-versa. Otherwise there is almost no correlation
By Paul MacRae, Climate Realists of British Columbia, Jan. 31, 2024
The basic theory underlying orthodox climate science is that the global temperature is highly sensitive to changes in carbon-dioxide levels. This is sometimes called the “control-knob” theory.1 If CO2 increases, so does temperature. If CO2 falls, so does temperature, more or less in lock-step—CO2 is the “control knob” of temperature.
And since we are in a “warming” world, and because CO2 levels are also going up—in other words, because temperature and CO2 levels appear to be correlated—orthodox climate science accepts that they are correlated—in fact, strongly correlated, as we’ll see. To stop this apparently dangerous warming, then, the climate scientist’s solution is to turn the “control knob” of carbon dioxide down by restricting carbon emissions in various ways, including phasing out CO2-emitting fossil fuels, thereby stifling economic growth and activity.
It’s not quite that simple, of course. A basic tenet of science is that evidence of correlation is not evidence of causation; put another way, just because it’s warming doesn’t mean carbon dioxide is causing it. The apparent correlation may be just a coincidence. So let’s take a deeper dive into the relationship of temperature and CO2: correlation or coincidence?
The degree of correlation between two factors is represented by the co-efficient of correlation, called “R”. “R” can be between 1 and minus-1, or R can equal zero.
An “R” co-efficient of “1” means the two values are perfectly correlated (when A is high, so is B, and vice-versa). An “R” co-efficient of “minus-1” means the two values are inversely correlated (if A is high, B is low, and vice-versa).
If “R” is between 0.0 and 0.5 on the plus scale, or between -0.5 and 0.0 on the minus scale, the correlation is considered weak. If “R” = “O” then there is no correlation at all (e.g., comparing pizza sales and tornado frequency, which have no relationship) 2 Figure 1 shows what various coefficients of correlation look like as scatter plots:
The rising average line in the left graph shows a high correlation (R = 1 or close to 1); a falling line means a negative or inverse correlation (R = -1 or close); a horizontal straight line shows no correlation at all (R = 0). In the case of climate science, to find the coefficient of correlation for CO2 and temperature, a scientist would compare a range of temperatures (vertical axis) against level of CO2 (the horizontal axis). Again, an “R” of less than 0.5 or less than -0.5 is considered a weak correlation.
Orthodox climate scientists have convinced themselves that the co-efficient of correlation between temperature and CO2 is close to “1”, and this belief is reflected in the climate-science computer models, which aim to predict future warming based on increased CO2 levels. In general, the model conclusions are alarming (i.e., CO2 rise is highly correlated with temperature rise), and we, the public, media and politicians, are therefore expected to also be alarmed.
In this article, we’ll look at actual evidence, not theory or what computer models tell us, to determine whether orthodox climate science is justified in believing the co-efficient of correlation between temperature and CO2 is quite high, and that we therefore face a “climate crisis” if the planet warms much more (a commonly cited figure is warming of 1.5 degrees Celsius higher than the “pre-industrial” era, roughly 1850).
Further, we’re going to assume that the laws of physics don’t change from day to day, century to century, millennium to millennium, geological era to geological era. If CO2 is the “control knob” of temperature today (i.e., highly correlated), then it must have been the “control knob” not just in the past few centuries or millennia but in the deep geological past as well. Let’s see if this is the case!
The Keeling Curve
The first controlled measurement of carbon-dioxide levels was undertaken by oceanographer Charles Keeling. He set up a laboratory on Mauna Loa in Hawaii in 1958 to measure CO2 in the atmosphere and created the “Keeling Curve” (see Figure 2).
The Keeling Curve leaves no doubt that carbon-dioxide levels have been rising in recent decades, with humans as at least a partial contributor through fossil-fuel emissions but also cities and farming. Temperatures have also risen, so on the surface at least, there appears to be a high coefficient of correlation between temperature and CO2!
As you can see from Figure 2, the Keeling Curve rises at a fairly steep angle of almost 30 degrees in this image, although the degree of angle falls if the graph is “stretched” horizontally. That said, if orthodox climate science is correct in believing that CO2 and temperature are highly correlated, we’d expect temperatures, when graphed, to rise at about the same rate as the Keeling Curve—let’s say it’s 20 degrees or higher.
Not surprisingly, this 20-plus-degree angle of warming (or higher!) is pretty much exactly what most climate models predict, as Figure 3 shows.
Figure 3 displays a collection of 40 IPCC models that, with “hindcasting,” predicted what temperatures would be from 1975 to 2020, with the Keeling Curve inset for comparison. (“Hindcasting” means comparing the model predictions over previous decades with the actual measured temperatures for those decades.) The angles of the two curves are both quite high, although the model predictions are closer to 30 degrees, so even higher than the angle of the Keeling Curve.
In other words, for climate modelers, temperature is so sensitive to CO2 levels—the coefficient of correlation is so high!—that the angle of warming is even higher than the angle of CO2 increase! “Climate crisis” ahead, clearly!
Now look at Figure 4. It shows the “hindcasted” model predictions (red line) as well as the historical temperature readings from 1975-2020 (green line).
As you can see, the actual, historical warming is much lower than the warming predicted by the models. This means that the actual coefficient of correlation between temperature and CO2 is much lower than orthodox climate scientists believe (and present as “the settled science” to the public, media and politicians to scare us into believing there is a “climate crisis”).
Let’s have a look at some more historical data to see if the correlation between temperature and carbon dioxide is high (close to R=1) or low (R = -1), somewhere in between, or maybe just R = 0.
CO2 and temperature over 600 million years
Figure 5 is one of the most famous graphs in climate science. It shows the levels of carbon dioxide compared to the temperatures (both levels are, obviously, estimates) over 600 million years. What do we see?
There have been times when CO2 levels were very high (600-450 million years ago, for example) but temperatures were flat or falling (e.g., the ice-age dip of 450 million years ago when CO2 is very high, but temperature is very low. Zero correlation here!). CO2 and temperature seem highly correlated about 300 million years ago in one of Earth’s three recent ice ages (ours is the third), but from 250 million years ago to now, temperature and CO2 seem to be operating independently (e.g., CO2 falling, but temperatures up to 10°C higher than today’s). It’s also worth noting that today’s CO2 levels are the lowest in 600 million years, a fact that should concern us.
If CO2 and temperature are, as orthodox climate science believes, highly correlated—if CO2 is the “control knob” of climate—then assuming physical laws remain constant over time and don’t change just because orthodox climate scientists “want” them to, we should be seeing this tight correlation over this period of 600 million years. We don’t. Not even close.
Figure 6 is a scatter plot of temperature and CO2 over the past 450 million years.3 The almost horizontal, slightly descending line indicates a very weak inverse coefficient of correlation of R = -0.19.
CO2 and temperature from 65 million years ago
Let’s have a look at the claimed tight correlation of CO2 and temperature a bit nearer to our own time, over the past 65 million years (Figure 7).
Once again, we see very little correlation between temperature (the top orange line) and carbon dioxide (the black shaded line). And this particularly the case from 30 million to 15 million years ago (the Oligocene and half of the Miocene), when CO2 is falling, but temperatures are on the rise, then start to fall again and finally converge in our own time, giving the current impression of correlation.
If CO2 is falling, but temperature is rising, then some other factor or factors than CO2 must have been the “control knob” in the Oligocene and Miocene. Perhaps some other factor or factors than CO2 are the “control knob” of global warming today, as well…. Let’s see.
The two-million-year ice-age roller coaster
About two million years ago, our planet descended into an ice age, only the third ice age in the past 500 million years. In fact, our ice age is considered the coldest of the three ice ages in that time.4 And we are supposed to worry about “global warming”!
As part of our current ice age, massive two-mile-high glaciers grew to cover much of the northern parts of North America, Europe and Asia, then retreated, then returned, at least ten times over the past million years on a hundred-thousand-year cycle. In this cycle, the glaciers dominated on average for 80,000-90,000 years, with warm interglacials of 10,000-20,000 years. Our interglacial, the Holocene, began about 12,000 years ago, to humanity’s very great good fortune! The roller-coaster operation of our ice age for the past 350,000 years is shown in Figure 8.
Several features are interesting here. One, temperature and CO2 do seem to be rising and falling together during this time, so apparently highly correlated! Two, the warming of our current Holocene interglacial is still not as high as the three previous interglacials shown, which strongly suggests that our interglacial’s current “warming” is due to natural variation, not human-caused CO2. Finally, CO2 levels are the lowest in Earth’s history. This should give us pause when we are told that CO2 levels are “too high.”
Getting back to the first feature, the apparent correlation of temperature and carbon dioxide over this time: you’ve probably seen Al Gore’s 2006 film An Inconvenient Truth, with its huge wall chart of temperature and CO2 over the past 650,000 years (Figure 9), with CO2 rising so high Gore has to stand on a lift to point to it!
In his narration, Gore strongly implies, without saying so directly, that it is rising and falling CO2 levels that are causing these rather drastic rises and falls of temperatures, glacials and interglacials. He describes this relationship as “complicated,”5 but viewers are clearly supposed to get the message that CO2 is the “control knob” here.
In reality, the relationship isn’t that “complicated”, but it is a problem for Gore because the actual relationship of CO2 and temperature is the opposite of his interpretation. Throughout this long stretch of time, temperature change has preceded CO2 level change by about a thousand years, more or less, as Figure 10 shows.6
In other words, over the past 650,000 years, the temperature has gone up or down, and centuries later, the CO2 level has gone up or down. So there is a correlation, but it’s not the correlation Gore and orthodox climate science wishes us to believe. It would appear, then, that temperature is the “control knob” of climate during this time, but we also have to ask: what made the temperature go up and down so drastically during this long period of geological time?
The answer is that an astronomical process called the Milankovitch Cycles seems to be one of the “control knobs” here. When the Earth’s surface is farther from the Sun due to slight changes in orbit and the Earth’s “tilt”, glaciers form and expand. When the Earth’s surface is closer to the Sun, the glaciers recede and we get a warm interglacial. Once again, changes in CO2 levels are not the correlative “control knob” of temperature during this long period of time nor, ultimately, is temperature.
It’s worth remembering that CO2 levels have been very low for hundreds of thousands of years: a graph from the National Aeronautic and Space Administration (NASA) shows CO2 levels over this time7 (Figure 11).
The white arrow in Figure 11 points to the lowest CO2 level in 800,000 years, 180 parts per million, about 650,000 years ago. And if you refer back to Figure 5, you will see that CO2 levels are also the lowest in 600 million years!
A little-publicized fact in orthodox climate science is that carbon dioxide is an essential plant fertilizer. Below 150 ppm, plants can no longer live, which means other forms of higher life (like animals and people) can also no longer live.8 Although CO2 levels over this time have usually been in the mid-200 ppm range, this level still seems a bit too close to 150 ppm for comfort.
Curiously, NASA offers this graph as proof that we are experiencing too much CO2 these days. Puzzling. You’d think we’d want to get as far above the 150 ppm mark as possible, that current CO2 levels aren’t too high but too low!
The last 10,000 years
How about the last 12,000 years or so, when Earth emerged from its glacial prison and we got a very welcome interglacial warming? Has CO2 been the “control knob” during this period of time? Once again, the answer is no, as Figure 12 shows.
The black curve in Figure 12 is a global temperature reconstruction; the red curve is CO2 levels, as measured on the left vertical scale. The graph shows that carbon dioxide began increasing 8,200 years ago, but temperatures went down. This could not happen if temperature was closely correlated with CO2 levels.
In other words, despite CO2 levels lower than today’s during this 11,000 years (CO2 only rose to 290 ppm at the start of the 20th century), the planet several times somehow managed to warm to levels equal to or higher than today’s (e.g., Holocene Optimum/ Minoan/ Roman/ Medieval Warm Periods), although temperatures still trended downward.
Since these Warm Periods were at least as warm as today, and mostly warmer, while CO2 levels remained lower than today’s (under 300 ppm for tens of thousands of years; today it’s 425 ppm), it’s clear that CO2 couldn’t have been the climate “control knob” during this time, either. Something else (solar fluctuations as part of the Milankovitch Cycles? Sun spots?) caused these earlier rises and falls of warming, and the same is almost certainly true today.
‘Global warming’ in the last 2,000 years
Zeroing in closer to the present day, what’s the climate been doing over the last 2,000 years? Figure 13 shows the ups and downs of warming over this time. What do we see?
We know that during the last 2,000 years, carbon-dioxide levels were relatively stable, in the 280 ppm range9, and yet there is a wide variation in temperature during these two millennia, at least some of it caused by fluctuations in solar energy. For example, the cooling of the Little Ice Age and subsequent warming to today’s levels are highly correlated with changes in the frequency of sunspots (see Figure 14): when sunspots are scarce, the planet cools, when plentiful, we get warming.10 Again, CO2 need not apply.
‘Warming’ over the past 70 years
When we look at “global warming” over the last 70 years or so, and particularly in the last few decades, we see a curious thing: whole decades with little or no warming, followed by jumps in warming during El Niño events that bring up the average and create the illusion of continuous, CO2-caused warming. Since CO2 has been increasing continuously, we’d expect the increase of “global warming” to be continuous as well. This isn’t the case, as we’ll see.
What follows may seem controversial, given all the scare-mongering around “rising temperatures”, but you can check the temperature data for yourselves using a website called woodfortrees.org.
Woodfortrees.org collects the temperature data from five climate-monitoring agencies (explained in the endnote11) and makes them available in graphic form. Note that the charts show temperature anomalies—variations—from a previous 30-year baseline, not the actual temperatures.
Getting the data into graph form is a bit complicated but the process is explained at the Climate Realists of B.C. website, at https://climaterealists.ca/climate101/#using-woodfortrees.
First, let’s look at the temperatures from 2000 to 2023 in Figure 15, when global-warming alarmism has been at its height. Not surprisingly, when we graph the temperatures for these years there is an upward trend. Global warming due to increased CO2 confirmed!
What we see in this time is that the four agencies vary in the warming increase between +0.25°C and +0.5° Celsius for two decades, depending on the agency, or roughly .18°C per decade. If this continued to 2100, warming would be 1.8°C.
No warming between 2000-2014
The problem is, when we break 2000-2023 down into parts, the increased “global warming” due to CO2 disappears. For example, look at Figure 16, which shows the “warming” between 2000 and 2014.
Incredibly, the four agencies show virtually no warming from 2000-2014: GISS (top set) is up about 0.2°C; Hadcrut (second set) is flat; RSS (third set) is slightly rising; UAH (bottom set) is actually falling a tiny bit. That’s 14 years without appreciable warming! If CO2 was highly correlated to temperature, we’d expect to see temperatures also rising in this time in lock-step. They didn’t. Odd.
As further evidence, Figure 17 is a scatter plot of temperature and CO2 from 1999-2014,3 Although CO2 continues to steadily increase, the “R” is horizontal (meaning zero correlation between temperature and CO2 during this time). If CO2 is the “control knob” of temperature, this total lack of correlation is simply not possible.
No warming between 2017-2023
Let’s look at temperatures between 2017-2023 (Figure 18).
As you can see, the “climate” didn’t budge between 2017 and 2023. Dead flat. Six years without warming. How can this be, given that we’re told warming is out of control?
The temperature plot for 2000-2023 (Figure 15) shows warming of up to 2.5°C/decade, but only because the average temperature was brought up by a very large El Niño event in 2015-2016 (the El Niño warming peak is very clear in Figure 15). Without an El Niño, temperatures remain flat. This means that CO2 is not the “control knob” of temperature, at least in the period 2000-2023, but El Niños may be.
Is it possible that El Niños are being influenced by rising CO2 levels? The answer is no (although orthodox climate scientists may beg to differ)—El Niños have been occurring for thousands of years, long before CO2 increases due to industrial civilization. 13
No warming between 1979-1994
If we go back a few decades in time, we find the same pattern. For example, Figure 19 shows temperature anomalies from 1979 to 1994.
Once again, almost dead flat for all for agencies—that’s 15 years without appreciable warming. Why did I make the end date 1994? Because in 1995 the planet did start to warm a bit leading up to the huge 1998 El Nino, which raised the “trend” temperature for the whole time between 1979 and 1998, creating the illusion of considerable “warming” (see Figure 20).
In other words, while CO2 is steadily increasing, temperature remains pretty much flat except during an El Niño event, which “ratchets” up the average temperature and creates the illusion of a steadily increasing warming caused by steadily increasing CO2. Figure 21 shows what is really happening to our “warming” planet—a “hiatus” from 1979 to 1997, and from 2000-2012 (actually 2014).
Figure 22 offers a scatter plot of CO2 and temperature between 1959 and 2014, clearly showing the two “hiatuses,” one between 1959-1975 and the other between 1999-2014. 14 I
Incredibly, this means there has been a virtually zero coefficient of correlation (R = O, or very close, meaning no relationship at all) between temperature and carbon dioxide for 35 of the 56 years between 1959 and 2014. In the real world of physics, this total lack of correlation would be impossible if steadily rising CO2 really was the “control knob” of temperature. Similarly, it’s hard to believe that CO2 is the reason why the coefficient of correlation suddenly leaps up to near-“1” in the middle 21 years—some other causal factor must be involved.
CO2 is not the ‘control knob’ of temperature
So, is carbon dioxide the “control knob” of “global warming,” as orthodox climate science claims?
As we’ve seen, CO2 hasn’t been the “control knob” of climate in the past, over centuries, millennia and the deep geological past, and if you examine the actual temperature data from the last 45 years, carbon dioxide is clearly not driving “global warming” today. How do we know? Because the modern temperature is pretty much flat except when ratcheted up to a new level by an El Niño event. And, ironically, this is the time period when global-warming alarmism has been at its height!
When temperature and CO2 do appear to be correlated, as over the past million years during the glacial/interglacial cycles, temperature change, not CO2, is the “control knob.” But temperature was in turn being influenced by factors other than CO2, including fluctuating astronomical events (the Milankovitch Cycles) and other mostly natural influences, particularly fluctuations in solar radiance. There is no reason to believe the much deeper geological past and the present would be any different—the laws of physics don’t change over time.
The coefficient of correlation (“R”) between temperature and CO2 is not constant, as orthodox climate science would have us believe; it fluctuates over historical and prehistorical times but when there is an apparent correlation, once again, temperature, not CO2, is the “control knob.”
If this is so, then it is clear that drastically limiting CO2 emissions, as the Trudeau Liberals and many other governments (including the United Nations) wish to do, will have almost no effect on temperatures.
However, this anti-carbon crusade, based in part on a scientific error in calculating the coefficient of correlation between temperature and CO2, is causing immense damage to the Western economies, and could ultimately destroy Western civilization itself.
This is a summary of Chapters 1-4, which deal with CO2 and temperature over time, from Paul MacRae’s book Through the Looking Glass: A Citizen’s Do-It-Yourself Guide to Climate Science, available at Amazon in Kindle print and e-editions, and at other outlets such as Apple Books in e-edition format.
Notes
- Andrew A. Lacis et al., “Atmospheric CO2: Principal Control Knob Governing Earth’s Temperature.” Science, Oct. 15, 2010, pp. 356-359. Available online but often behind a pay wall, although there are repostings on some public websites. For a summary of Lacis’s paper see https://pielkeclimatesci.wordpress.com/2010/11/03/guest-post-co2-the-thermostat-that-controls-earth%e2%80%99s-temperature-by-andy-lacis/. ↩
- For a more detailed discussion of the coefficient of correlation, see Patrick Hunt’s There is a random correlation between CO2 and global warming on the climate realist website. ↩
- Danley Wolfe, “A look at carbon dioxide vs. global temperature.” Watts Up With That, Sept. 12, 2014. Available online. ↩
- National Oceanographic and Atmospheric Administration (NOAA), “What’s the coldest the Earth’s ever been?” Climate.gov, Feb. 18, 2021. ↩
- Al Gore, An Inconvenient Truth: The Planetary Emergency of Global Warming and What We Can Do About It. Emmaus, Penn., Rodale Press, 2006, p. 67. His exact words are: “It’s a complicated relationship (between CO2 and temperature), but the most important part is this: When there is more CO2 in the atmosphere, the temperature increases because more heat from the Sun is trapped inside.” ↩
- For example, see Kneev Sharma & Dimitre Karamanov, “Investigating the historical correlation between atmospheric carbon dioxide concentration and global temperature change.” Ecological Engineering and Environmental Protection, No. 1, 2021, pp. 5-16. The Executive Summary ends: “It was found that historically CO2 concentration in the last 650 000 years lags global temperature rise by 1,020-1,080 years with a maximum correlation coefficient of 0.8371-0.8372.” Available online. ↩
- NASA, “How do we know climate change is real?” July 4, 1996. Website: climate.nasa.gov. ↩
- Ministry of Agriculture, Government of Manitoba, “Greenhouse CO2 supplement.” The site offers advice to greenhouse gardeners and notes: “At 100 PPM of CO2 the rate of photosynthesis would be stopped completely. At 150 PPM the plants begin to respire, and photosynthesis is stopped. At this low level the plant will no longer be able to obtain CO2 from the atmosphere and photosynthesis is restricted. The plant will eventually use all of the CO2 present, photosynthesis will stop and the plant will die.” And so will most other forms of life on the planet. ↩
- NASA, “Graphic: The relentless rise of carbon dioxide.” The text notes: “During ice ages, CO2 levels were around 200 parts per million (ppm), and during the warmer interglacial periods, they hovered around 280 ppm.” ↩
- Eigil Friis-Christensen & K. Lassen, “Length of the solar cycle: An indicator of solar activity closely associated with climate.” Science, Nov. 1, 1991, pp. 698-700. ↩
- The five climate-monitoring agencies are the U.S.-based Goddard Institute for Space Studies (GISS); the England-based Hadley Institute (HadCrut), both taking land-and-sea temperatures; two agencies that use satellites for atmospheric readings, University of Albama at Huntsville (UAH) and Remote Sensing Systems (RSS); and a relatively new agency, Berkeley Earth Surface Temperatures (BEST), that adds texture but not much light to the picture so I will be ignoring it. ↩
- Danley Wolfe, “A look at carbon dioxide vs. global temperature.” Watts Up With That, Sept. 12, 2014. Available online. ↩
- See Andrew Davies, et al., “Tropical ocean-atmosphere controls on inter-annual climate variability in the Cretaceous Arctic.” Geophysical Research Letters 38. Also, found at Watts Up With That?, “New paper: Unlikely that man-made global warming would cause a permanent El Niño state.” Feb. 11, 2011. ↩
- Danley Wolfe, Ibid. ↩