Why the IPCC’s Carbon Budget Won’t Balance

fighter jet

This is the third of four articles on the IPCC’s AR6 WG1 report. –CCD ed

Mark Carney, United Nations Special Envoy on Climate Action and Finance, stated in his book Value(s) that the world needs to learn to live on a carbon budget.

He also contends that if we exceed this budget the worst-case scenarios of global warming will transpire, which Carney refers to as the “tragedy of the horizon.”

As the former governor of both the Bank of England and the Bank of Canada, Carney undoubtedly knows a lot about budgets. He should know that a financial budget based on incorrect financial principles is incorrect.

Mark Carney’s expertise is not in physics, but he should likewise realize that a carbon dioxide emissions budget based on incorrect global warming physics is, well, incorrect.

In Value(s) (p. 265) Carney states, “…scientists have concluded that the pace of global warming is roughly proportional to the amount of carbon dioxide in the atmosphere.”

That is a linear relationship that the Intergovernmental Panel on Climate Change (IPCC) would like all of us to believe, and how they draw us to that conclusion was discussed in my article IPCC: Programmed To Deceive The Media, Policymakers, And You – Climate Change Dispatch. But it is false.

The relationship between global warming to carbon dioxide in the atmosphere is not linear, it is logarithmic. The governing equation of that logarithmic relationship was written in 1896 by Svante Arrhenius, a Swedish Nobel Laureate. If you’re interested, you can read about it here. (scroll down to Greenhouse effect).

And if you’d like an explanation of why the Arrhenius carbon dioxide equation functions the way it does, I invite you to go to visit this author’s website and view Presentations.

Most people have difficulty imagining what a logarithmic function looks like. We are going to accomplish that with a thought experiment in three steps.

Imagine you are standing on the ground and directly in front of you but some distance away you see these scenarios:

  • A soldier fires a tracer bullet up at a 45-degree angle. The bullet travels in a straight line (we will disregard wind and gravity). If you viewed the bullet’s path from the side some distance away, it would look like a graph of a linear relationship: for every distance measured on the ground it travels away from the rifleman, it gains an equal distance in altitude. It’s an unchanging straight line.
  • A fighter jet takes off from a runway. At first, the jet travels over a lot of ground horizontally while gaining very little altitude. The pilot then pulls the nose high and the fighter curves into a steep climb until it is pointing almost straight up. The jet now covers very little ground distance while gaining tremendous altitude. If the jet’s path were a graph, it would draw an exponential function, an almost horizontal line transitioning smoothly into an almost vertical line.
  • A rocket is launched to put a satellite in orbit. At first, it gains tremendous altitude while traveling on a mostly vertical path. Then the rocket begins to curve off the nearly vertical and smoothly transitions to a flight path almost a constant distance from the surface of the Earth. It now travels a great distance on a mostly horizontal path with very little altitude gain. This graph would be a logarithmic function, an almost vertical line transitioning smoothly into an almost horizontal line.

If the logarithmic function (the rocket) seems similar to an exponential function (the fighter jet), it is. In mathematical terms, they are both geometric functions, but the logarithmic function is the inverse of the exponential function, just as division is the inverse of multiplication. One is the opposite of the other.

A generic exponential graph looks like this:

And a generic logarithmic graph looks like this:

The IPCC wants us to conclude that the relationship between global warming and CO2 is linear, forever. Similar to the graph traced by the bullet, global warming temperature would go up the same amount for the same amount of CO2 added, indefinitely.

This is not correct.

The logarithmic relationship has been accepted by the IPCC in the public domain and is the foundation of the carbon dioxide greenhouse gas theory. Another confirmation is buried deep in the almost 4,000 pages of the IPCC report, reference 5.5.1.2.1 line 42.

Similar to the graph made by the rocket launch, in a logarithmic relationship the first temperature gains are significant (corresponding to the y-axis on the graph immediately above) despite the relatively small increases in CO2 concentrations in the atmosphere (shown as the x-axis).

But at some point, there are negligible temperature gains (y-axis) with relatively large increases in CO2 (x-axis).

Note the logarithmic example graph above is not a representation of the Arrhenius CO2 global warming equation, it is shown only as a generic representation of the shape of a logarithmic equation.

Now let’s look at the actual IPCC CO2 budget that Mr. Carney insists is critical to adhere to, found in the Summary for Policymakers section of the IPCC report Climate Change 2021: The Physical Sciences Basis (Table SPM.2).

It is the very last table presented in that section and therefore could be viewed as the final recommendation from the IPCC plan to save the planet from an existential global warming threat.

We will not contest the data, but we’ll use it to demonstrate the budget does not match the theory accepted by the IPCC. Note the preamble to the table states, “They refer to CO2 emissions while accounting for the global warming effect of non-CO2 emissions.”

This means the budget includes all non-CO2 global warming drivers.

The red arrows and red circles added by this author.

The red arrow on the left points out that in the last 120 years or so we have likely experienced 1.07°C of global warming, and the red arrow on the right points out during that time humans likely emitted 2,390 gigatonnes of CO2. (The IPCC defines likely as a 66 to 100 percent probability.)

If global warming by CO2 was a linear relationship, then the next 1.07°C increase in temperature should take about another 2,390 gigatonnes of CO2. Think of a graph like a bullet trajectory, where vertical is temperature and horizontal is CO2 additions.

The red circle on the left indicates on the budget a forecast increase of 0.93°C and the red circle on the right indicates it corresponds to further emissions of only 1,150 gigatonnes, slightly less than one-half of the historical emissions.

That’s only 28 years at today’s emission rates. The 67% likelihood column was chosen to be consistent with the IPCC definition of likely.

The carbon budget as published by the IPCC is far worse than a linear relationship. It is trending toward an exponential relationship as the next 0.93°C of global warming takes less than one-half of the CO2 emissions of the first 1.07°C of global warming.

Think of a graph that looks like the fighter jet, again where vertical is temperature and horizontal is CO2 additions.

Those who looked up the Arrhenius CO2 global warming equation will know that its logarithmic solution, as agreed to by the IPCC on the website link included above, dictates the next 1.07°C of global warming will take double the CO2 as the first 1.07°C.

That’s 4,780 gigatonnes—four times the IPCC budget—for only 0.93°C. That would take about 117 years of emissions at today’s levels, and therefore four times longer than the IPCC carbon budget.

Think of a graph that looks like the rocket going into orbit: the temperature increase is slowing dramatically.

The IPCC carbon budget is wrong because it contradicts the IPCC acknowledged foundational physics equation of global warming by the greenhouse gas effect of CO2.

The carbon budget implies an exponential relationship, where it takes less CO2 additions to gain the same global warming.

Even a near-linear relationship between global warming and CO2 additions, as claimed by the text of the IPCC report, would require almost 60 years for the next 1.07°C of global warming. But that is not correct either.

Global warming by the greenhouse-gas effect is a well-established and accepted logarithmic relationship, which means even at today’s emission rates, the next 117 years of global warming should be a repeat of the last 120 years.

And that’s assuming, which has not been established, that greenhouse gases caused all the warming in the last century and there are no other natural cycles to consider.

Mr. Carney: The global warming effect of CO2 emissions is no longer a tragedy when the horizon is pushed back another 90 years. The IPCC carbon budget does not balance with what the IPCC accepted.


Ron Barmby is a Professional Engineer with a Bachelor’s and Master’s degree, whose 40+ year career in the energy sector has taken him to over 40 countries on five continents. His book “Sunlight on Climate Change: A Heretic’s Guide to Global Climate Hysteria” (AmazonBarnes & Noble) explains in understandable terms the science of how both natural and human-caused global warming work. Over two dozen other articles and presentations can be found at www.ronaldbarmby.ca.

Permission to use all or parts of this article is allowed freely to all, provided that any such use is accompanied by author attribution and a link to the original article.

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