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There is a great description from @civiltalker of "why cows are like closed power stations". Its an imperfect but interesting example of the important differences between CO2 and CH4. Lets take a look.

A twitter story: 1/17
Lets assume there is a rancher named Jane. Her family has had a herd of 1,000 cows for the past 30 years. Each day these cows happily graze, eating grass and burping out methane that mixes with the atmosphere. 2/17
However, the methane in the atmosphere is constantly oxidizing and breaking down. The average lifetime of the methane emitted from her cows is around 10 years. 3/17
This means that while Jane's herd produces around 100 tons of methane per year (0.1 tons per cow), a similar amount of methane emitted by their predecessors is breaking down, and the amount of atmospheric methane remains unchanged as long as the herd size stays constant. 4/17
The total amount of atmospheric methane from Jane's cows over the long term depends on how much is emitted each year – not the sum of emissions over time. 5/17
If Jane adds a new cow to the herd atmospheric methane will increase by one ton (each cow's annual emissions of 0.1 tons remains in the atmosphere for ~10 years, so 0.1 tons / year * 10 years = 1 ton). If Jane removes a cow atmospheric methane will decrease by 1 ton. 6/17
Jane's town has a very small 1MW coal powerplant that powers the 500 or so homes. This coal powerplant generates 10,000 MWh of electricity and emits around 10,000 tons of CO2 each year. 7/17
It turns out that 10,000 tons of CO2 has the same warming effect as 100 tons of methane – if both remain in the atmosphere (as methane is ~100x strong than CO2 while its in the atmosphere). So are Jane's cows as bad for the climate as the coal fired powerplant?

Nope. 8/17
As long as Jane's herd isn't growing, the methane the emitted is perfectly balanced out by previously emitted methane breaking down in the atmosphere.

The same is not true for the CO2 emitted from the coal powerplant, however! 9/17
Each year about half the CO2 emitted by the coal powerplant remains in the atmosphere – with about half being absorbed by land and ocean sinks. So while Jane's cows add 0 additional methane to the atmosphere, the coal plant adds 5,000 tons of CO2 every year. 10/17
The warming effect of the coal powerplant is the same as if Jane were adding an additional 50 cows to her herd each year (50 cows increase atmospheric methane by 50 tons, methane is 100x stronger than CO2, so its the same as 5,000 tons of CO2). 11/17
The next year the town decides that it would cheaper to generate their electricity with zero-carbon solar + storage. They close down the old coal powerplant. However, the carbon that was previously emitted by the coal fired powerplant remains in the atmosphere. 12/17
While it will slowly decline over the next few centuries, for the time being the closed coal powerplant is warming the planet just as much as Jane's 1,000-cow herd – even though its no longer emitting any CO2! 13/17
If Jane were to decide to get out of the ranching business (and her herd all became hamburgers), their methane emissions would fall to zero and all the methane they had ever emitted would be gone from the atmosphere in a decade or two. 14/17
This story highlights the critical distinction between CO2 and methane: CO2 accumulates in the atmosphere, and once we emit it we are stuck with it (barring actively sucking it out of the atmosphere). 15/17
Methane does not accumulate over the long term; the amount of methane in the atmosphere depends on the rate of emissions rather than the total amount that has ever been emitted. 16/17
Both are important greenhouse gases (methane is ~25% of warming since preindustrial, CO2 is responsible for ~50%). But they behave in very different ways that we need to account for when planning how to mitigate each! 17/17
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