# Review of calculation of CO$_2$ contribution to warming

In a Swedish Facebook group for "climate change skeptics" Erik Larsen has shared his calculation of how big part of temperature change can be attributed to human emissions of carbon dioxide. His reasoning goes as follows:

1. Temperature has raised by 1 °C since 1850.
2. Carbon dioxide has raised by 30%.
3. Carbon dioxide only constitute 4% of the greenhouse gases (the main part consists of water vapor).
4. Carbon dioxide is only 1/4 as efficient as water vapor per molecule as a greenhouse gas.

From this he concludes that the temperature raise from carbon dioxide is only 1 °C × 0.30 × 0.04 × 1/4 = 0.003 °C.

I have tried to explain (in Swedish) that this calculation is not correct, but of course he refuses to accept that and writes that my objections are not logical. Today I wrote that it's lucky for him that his calculation is not peer-reviewed and suggested that I could share it in a physics and/or mathematics group for review. He complied. So here it is.

What do you think of his calculation?

• @a_donda. The site's name is "Earth Science (Beta)" not "Geo Science" and there are tags 'climate-change', 'co2' and 'human-influence', which is what the questioned calculation is about. Therefore I think that the question belongs here. What other site would be better for my question? – md2perpe Jul 27 '20 at 19:15
• @a_donda. I'm not looking for exchange of opinions. I'm asking for a review of his calculation. – md2perpe Jul 27 '20 at 19:18
• If he dismisses ipcc he'll dismiss science anyway. Your friend must proove he's right, not the rest of the world the he's wrong. The question has been posted and answered countless times, it's in many FAQs on climate related sites, Wiki has several articles, even in here a quick search shows several hits. If you'd be willing to show some basic search efforts yourself on anthropogenic contribution and how Co2 works, we'd have a ground to start from. – user20217 Jul 27 '20 at 20:14
• All of the arguments except for the first ('"temperature has risen by 1 °C since 1850") are completely spurious. Anti-scientists love to play numerological games, and that is all that this is. There is no winning in arguments with these kinds of people as they are fully immunized against logic and evidence. – David Hammen Jul 27 '20 at 20:30
• Where to even start... His most fundamental flaw is that he assumes Temperature will change immediately as a consequence of an increase in ghg levels. However, an increase in ghg levels changes radiation balance. It takes time for the earth system to adapt to those changes. So he should ask himself. What will the temperature be like when the system is in equilibrium (keyword ECS: equilibrium climate sensitivity). But then of course, his calculation is pure garbage. Ask him how he derives his spectacularly weird forumula. – J. Fregin Jul 28 '20 at 9:19

This reminds me of using Bjørn Lomborg's book in statistics, as examples how not to do statistics, his calculations never make any sense or just make unfounded leaps to conclusions.

Erik seems to have the same problem he just throws numbers together with no rhyme or reason.

Let's just break down his calculation.

1 °C × 0.30 × 0.04 × 1/4 = 0.003 °C.

Why are we multiplying by 0.25, he says CO$$_2$$ is only 25% as good as water, but water is nowhere in this calculation, there is no reason for this to even be here much less to be multiplied. Also why can't he solve 1/4?

1 °C × 0.30 × 0.04 = ??

This is just plain wrong, CO$$_2$$ comprises 0.04% of total gas and ~93% of trace gasses, even more of greenhouse gasses, unless he is arguing some undiscovered change in nitrogen or argon is acting as a greenhouse gas, this has no place in the calculation. Also again why is he multiplying by the increase in CO$$_2$$? Does he think ALL gasses in the atmosphere increased by 30% that the atmosphere got 30% heavier in 150 years?

1 °C × 0.30 = ??

What is this calculation meant to do? One times anything is always whatever you multiply it by, so all you are calculating is units, but units are ignored in the calculation, and what purpose does multiplying degrees of change times percentage of increase do?

There is no point arguing with Larsen, either he does not understand math (in which case you are wasting your time) or he is purposefully being misleading (and it just gives him attention). Either way there is no benefit to arguing with him. Your best case is he does not understand math otherwise he is just using a completely unjustified string of numbers to have something that looks scientific because it has a equation in it counting on the fact most people who read it don't know enough about math to see the problem.

• While there is no point in arguing with Larsen and his ilk in private, there is a point in arguing with those fraudsters in public. The problem is that some people will believe those fraudulent arguments if left unrefuted. – David Hammen Jul 28 '20 at 2:59
• Here I need to correct you: CO2 comprises 416 ppm, which is 0.0416 %. – md2perpe Jul 28 '20 at 6:45
• @md2perpe good catch total typo on my part. – John Jul 28 '20 at 17:30

From this he concludes that the temperature raise from carbon dioxide is only 1 °C × 0.30 × 0.04 × 1/4 = 0.003° C.

His number for the amount of CO2 is high. A better value is 0.027 rather than 0.04. That does not mean that the correct answer is 0.002° C. This argument is completely fallacious. The author of this calculation is playing numerological games. There is zero justification for multiplying these numbers.

Artificially adding carbon dioxide to the Earth's atmosphere is a forcing agent. Doing so increases the Earth's average temperature, which has a side effect of increasing evaporation. This forced feedback is a rather nasty side effect.

On the other hand, artificially adding water vapor to the Earth's atmosphere is not a forcing agent. Doing so would merely increase the local chance of precipitation. Excess water vapor very quickly rains itself out of the atmosphere. Excess carbon dioxide does not rain itself out of the atmosphere. Plants and rocks take a long time to absorb excess carbon dioxide.

As the internet gives these people influence that far exceed their numbers, it is important to rebut their arguments. As I already mentioned, there is zero justification for multiplying the numbers in the way the author of this argument did. This is what science deniers do: They create completely fallacious arguments.

tl;dr This sounds like silliness through-and-through. Addressing it as though it were a real scientific calculation would seem to be missing the forest for the trees.

1. Temperature has raised by 1 °C since 1850.
2. Carbon dioxide has raised by 30%.
3. Carbon dioxide only constitute 4% of the greenhouse gases (the main part consists of water vapor).
4. Carbon dioxide is only 1/4 as efficient as water vapor per molecule as a greenhouse gas.

From this he concludes that the temperature raise from carbon dioxide is only 1 °C × 0.30 × 0.04 × 1/4 = 0.003 °C.

This doesn't make any sense. Someone's just started with a number, stringing together random multiplication factors. Presumably they could just keep multiplying by other numbers, basically at random, if they wanted.

How do you fix this? You don't. There aren't any errors to be fixed.

By analogy, if someone rips a piece of paper, you might be able to tape it back together. But if someone incinerates a piece of paper, then it's not really productive to see it as "paper" anymore. Likewise, this isn't a "logical argument" to be fixed; you can't "fix" this because there's not enough of something there to be "fixed".

I'd speculate that you know this. Presumably it's just that someone's wrong on teh interwebz and you'd wanted to fix it. But I doubt that you'll manage to identify a subtle mistake in their logical analysis as I doubt that there was any logical analysis in the first place.

The "calculation" - 1 °C × 0.30 × 0.04 × 1/4 = 0.003 °C is meaningless. Rather than attempt to show that directly my response would be to ask "if the contribution of CO2 to 1 °C of warming really were only 0.003 °C then what caused the other 0.997 °C of warming?"

Seems clear that water vapour, even if having 4 times the greenhouse potential of CO2 does not - and if there are other factors at work what are they and why are those omitted?

Ultimately the question of how much CO2 contributed to 1 °C of surface air temperature rise that has taken place must be answered through understanding the climate processes that are at work, including the Greenhouse Effect as climate science understands it.