The real strength of methane

Methane, (CH₄) as everyone knows is a more powerful green house gas than CO₂.  It is often quoted as being 20 times as powerful as carbon dioxide and often there is a further phrase in the sentence; namely "on a one hundred year basis".  What does this mean.

When methane is released into the atmosphere, it begins to react with oxygen (as OH) and turn into carbon dioxide.  The half life of methane has been variously estimated.  I will use the often quoted 7 years for illustration.  Put a kilogram of methane into the atmosphere today and in 7 years half of it will be left,  in 14 years a quarter.  In 21 years an eighth, in 28 years a sixteenth and so forth.  Over a hundred years, the warming that this kilogram of methane will contribute to the earth is a certain amount.  The exact amount is not important for this example since we just want to be able to compare methane and Carbon dioxide.

When Carbon dioxide is released into the atmosphere it is stable.  It is not broken down or combined with anything.  However, photosynthesis takes it up.  A figure I have heard quoted for the half life of a quantity of carbon dioxide released into the atmosphere is 100 years.  If you release a kg of Carbon dioxide into the atmosphere today, in 100 years, half of it will still be there.*

*If you have better figures for the half life of these two gases, plug them into the formula below and see what result you come up with.


If you are fluent in calculus you can do a better calculation than I will do below but the following calculation, while not exact, will be easier to follow.  It is a pretty good first approximation.

First off we need the formula for the amount of a gas left in the atmosphere.  It is:

A_t = A₀ x 1/2^t/h

Where:
A_t = the amount at time t
A₀ = the amount at time 0 (when you released the gas)
t is the time in years that has elapsed since the release
h is the half life of the gas in the air in years
     note that t/h is the number of half lives that have passed.

Looking at methane first:
After the first 7 years, half a kg of methane is left from a kg released.  You start with 1, end with a half.  The average is (1 + 1/2)/2 = 3/4.  Do the second 7 year period.  It is (1/2 + 1/4)/2 = 3/8.  You see the way this is going.  The next few are 3/16, 3/32, 3/64 etc.  If I add up 14 of these which nearly makes up 100 years you come up with a number very close to 1.5.

Note I could have done one year intervals to find the total effect over 100 years when compared with the effect in the first year but as long as I use the same interval for Carbon dioxide, the relationship between the numbers remains almost the same. 

Make a graph


The pink shaded area is a graphic representation of the amount of methane which causes global warming over a hundred year period following an initial release.

Now for Carbon dioxide
Using h as 100 years and t as seven years, for the first 7 year period, you start with 1kg and end with 0.9256kg.  Average 0.9763.  Continue for each 7 year period and add them up and you come to 9.621.


Create a graph

The pink shading represents the amount of Carbon dioxide remaining after an initial release.  That large amount of Carbon dioxide has only 1/20th the green house gas effect as the small amount of Methane in the first graph


In numbers, despite a relative 6.414 (9.621/1.5) times as much Carbon dioxide in the atmosphere over the 100 year period as methane, from an initial release of a kg of each, methane still caused 20 times as much warming as the Carbon dioxide.

Since 6.414 X 20 = 128,  Methane,  is 128 times as potent a green house gas as carbon dioxide.  Note that I am simply reverse engineering what the scientist worked out for the relative effectiveness of these two gasses  They then calculated the true value based on the difference in their half lives.  I can't find the original work that says how effective a greenhouse gas each gas is.  Does anyone out there know where the original work is to be found.

So what does all this mean.  As long as methane is being released at a more or less constant rate, the X20 figure makes sense.  It reaches an equilibrium between  release into the atmosphere and oxidation and indeed the times 20 figure expresses the long term effect of the same amount of each gas released over a hundred year period.  Where this nice scenario breaks down is if the amount of methane being released is accelerating and it seems to be doing just that.

Massive methane seeps have been observed, especially over the vast Russian Arctic continental shelf where areas of bubbling of a km in diameter have been observed.  Methane is also coming out of the thawing permafrost.  Worse still, the amount of methane stored in these two locations plus deep sea methane is of the same order of magnitude with respect to the quantity of carbon contained, as all the carbon we have burnt so far plus all the reserves we know about.

I can't even imagine the implications of releasing just the Arctic methane over, say a decade,  with a potency kilogram for kilogram of more than 100 times that of carbon dioxide.  It would almost certainly cause enough warming to release a lot of the rest of the stored clathrates on, for instance, the ocean bottom.

It may be too late.  The only solution I can come up with is to sit on a chair, put your head between your knees and kiss your nether regions  good by.  I hope I am just being an alarmist and I have this all wrong.

Incidentally, as counter intuitive as it seems, if we could find a way to light most of the methane seeps and turn them into carbon dioxide, that would be a great help.


Three days later
I wish I could say I had got out my calculus books and worked out the integral but I didn't.  I found this most amazing site on the web.  You put in your formula and it does the integration for you.  I can't seem to get my blog to do mathematical notation.  If anyone knows how to do this, please let me know. The notation in the following paragraph is messy.
  Check it out.

The integral of A times (1/2)^(t/h) is minus A times h times 2^(-t/h) divided by log2.  Doing the calculation over 100 years for both Methane, using a half life of 7 years and Carbon dioxide, using a half life of 100 years, there is 7.14 as much CO₂ in the air over that period, from the same initial release, as there is CH₄.  In other words, with only 1/7.14 as much CH₄ as carbon dioxide, the warming effect is 20 times as much.  The instantaneous heating effect is therefore 7.14 times 20 equals 143 and not 128 which I calculated using the interval method.

If you look at this site, the situation seems even more dire.  If you scroll down to the chart on radiative forcing you will see that for 2019, the radiative forcing of the amount of Carbon dioxide that was in the atmosphere then was 2.076W/m2.  Go the next column to the right and you will see that the radiative forcing of methane in 2019 was 0.516W/m2.  Now go to this site and you will see that in 2019, the concentration of CO2 was 409ppm while CH4 was 1860ppb (1.86ppm).

 

In other words, even though methane was only 409/1.86 = 1/220 (0.0045) as much as CO2. it has 2.076/.516 = 1/4 (0.25) as much radiative forcing as CO2.  Doing a crude calculation, if Methane was 4 times as concentrated; In other words 7.44ppm it would have the same radiative forcing as the 409ppm of CO2.  It would appear then that the relative strength of Methane is 409/7.44 = 55 times as strong as Carbon dioxide.    Whatever figure you take, the prospect of a sudden evolution of methane from any source is not something to be ignored.

 

ie.  If we had a serious evolution of methane from the bottom of the Russian Arctic continental shelf or from the permafrost of the northern regions, the warming in that year would be spectacular.*  If no more methane was released, the effect would half each 7 years but the likelihood is that a big increase of methane would trigger off more and more deposits to release their methane.  Since the methane deposits are said to be greater than all the fossil fuel we have used so far and since, in the short term, methane is so much more powerful than Carbon dioxide, we may just possibly be in a spot of bother fairly soon.

There is another possibility, unfortunately.  With the present rate of release of methane, the OH system seems to be able to keep up with oxidizing it and turning it into Carbon dioxide.  If, somehow, OH generation increased, presumably  the half life of methane would decrease.  I don't know how the chemistry works in this case but it seems possible that a huge evolution of methane might overcome the OH generation system and the half life of methane would increase. 

*  Note that the West Antarctic ice sheet is said to be in the process of disintegrating and there are some indications that methane may be trapped under the Antarctic Ice sheets.

Incidentally, this may be an explanation for the end of glacials such as occurred 11,500 years ago and periodically during this present ice age which is 2.5 million years old so far.  If methane clathrate collected under the continental ice sheets, from buried swamps and seeps from fossil fuel deposits, it would sit there ready to be released if the ice started to melt.  Since methane is so powerful, an amount only a hundredth as much as would be needed than if it was Carbon dioxide to start a run away green house melting.  We wouldn't see the methane in ice bubbles since it is rapidly oxidized to carbon dioxide   This may also be part of the explanation for the sudden rise in Carbon dioxide seen in ice bubbles during the end of the glacial.  Note that a top so called Firn layer of an ice sheet doesn't yet have closed bubbles and has some exchange of gas with the Atmosphere.  It is about 70 years deep.

There is another little wrinkle to this story.  Clathrates are a sort of permafrost.  The clathrate ice holds sediments together on the Continental shelves and slopes.  As the clathrate disintegrates, not only does this "glue" disappear but the evolving bubbles expand and make the sediment into sort of a fluidized bed.  Have a wee tremor and this porridge can start to collapse and flow down hill.  There are indications that land slides on other continental shelves have caused localized but very severe tsunamis.  One would suspect that the first place we might see such tsunamis would be in the Arctic where methane evolution from the bottom is accelerating.

As Pat Condell would say, raising two fingers.  "Peace"