Exponential Trouble

I was researching one of the graphs in the IPCC report for policy makers when I came across two terrifying graphs with a terrifying relationship.

The first graph shows the estimated annual emissions of carbon dioxide as a result of human activity versus the year of emission. The data runs from 1750 until 2010.

Annual human emissions of carbon (mainly in carbon dioxide) versus year of emission. Notice the nature of the catastrophic events which cause a deviation from the rising trend.

Annual human emissions of carbon (mainly in carbon dioxide) versus year of emission. Notice the nature of the catastrophic events which cause a deviation from the rising trend.

The terrifying feature of this graph is that the only events to interrupt the rise are catastrophic events such as world wars, depressions, and the oil crisis of the mid-1970s.

The second graph shows the cumulative total of annual emissions of carbon dioxide as a result of human activity versus the year to date.

Cumulative human emissions of carbon (mainly in carbon dioxide) versus year of emission. Notice that not even catastrophic events slow the inexorable rising trend.

Cumulative human emissions of carbon (mainly in carbon dioxide) versus year of emission. Notice that not even catastrophic events slow the inexorable rising trend.

The terrifying feature of this graph is its inexorable rise. Even the wars and depressions which are visible in the annual emissions graph are barely detectable.

And the terrifying relationship between the two graphs can be seen if they both plotted together.

Annual Emissions and Cumulative emissions plotted on the same graph but with different vertical scales

Annual Emissions and Cumulative Emissions plotted on the same graph but with different vertical scales. The curves overlap tolerably well indicating that the rise is exponential.

This third graph merely confirms that the rate of emission of carbon dioxide is not just increasing, but the rate at which it is increasing is increasing. A curve of this form in which the rate of rise of a quantity increases as the quantity itself rises is called exponential.

It is of course physically impossible for these graphs to continue rising indefinitely: eventually we run out carbon! But we are still hundreds of years away from the limit. What strikes me is that for all our concern about carbon emissions, there is not even a detectable blip on either curve resulting from our goodwill.

And given the scale of events which have affected global emissions in the last 100 years, I really don’t know which terrifies me more: the prospect that we will fail to agree to cut emissions; or the prospect that we will succeed.

Data

6 Responses to “Exponential Trouble”

  1. rogerthesurf Says:

    The data you are reading is sensationalism.

    Although the numbers are impressive, they mean nothing unless they are compared against the background. For example the number of tonnes of nitrogen in the atmosphere, or the number of tonnes of all other gases in the atmosphere excluding CO2.

    As I explained in another comment on your blog, CO2 is a friendly gas and we are not any where close to it being a nuisance.

    I also notice you seemed unable to answer my final comment on your other post. I suspect it is because you could not find any peer reviewed academic papers that contradicted my statements.

    I thoroughly suggest that you visit my blog at http://www.rogerfromnewzealand.wordpress.com and check out some of the unsensationalized FACTS there.

    Cheers

    Roger

  2. protonsforbreakfast Says:

    The data are not ‘sensationalism’ they are facts.

    Regarding their scaling against the mass of gases in the atmosphere, they key gases to scale against are not nitrogen and oxygen because those gases have very weak infrared activity. The key gases are carbon dioxide and water vapour.

    At the start of the 18th Century we estimate there was around 2200 billion tonnes of CO2 in the atmosphere (roughly 280 ppmV).

    We have emitted roughly 350 billion tonnes of C in CO2 or about 1300 billion tonnes of CO2. Some of this is absorbed in the oceans leading to increasing acidity. Some goes to improved growth in plants on Earth, and the rest (around 800 billion tonnes) is still in the atmosphere and will stay there for a period on the order of a few hundred years. The current amount of CO2 in the atmosphere is around 3000 billion tonnes. So human emissions (1300 billion tonnes) are a significant fraction of CO2 in the atmosphere.

    The amount of water vapour in the atmosphere is much larger and much more significant (by a factor of roughly 20) from an infra red point of view. However the residence time of water in the atmosphere is only 11 days – so the amount of water in the atmosphere equilibrates rapidly to the prevailing average temperature. In contrast the CO2 will add a small but continuous warming contribution.

    I have looked through your web site and marvelled. YOu seem to be perfectly aware that CO2 is an infra red active gas but ignore the possible harm this could cause and instead say (and I paraphrase) that plants love CO2. Great. But that doesn’t answer the basic concern:

    >Anthropogenic emissions of CO2 appear to be warming our planet roughly in line with what we would expect.<

    Should we do something about it? You are perfectly entitled to say 'No, I prefer the benefits of using of carbon'. Fair enough. But don't deny the facts or belittle other people's concerns.

  3. rogerthesurf Says:

    Suggest you read my blog more carefully. Especially the links to peer reviewed research.
    I never said your figures were incorrect, although you may do well by stating your sources. I am saying that you are quoting huge numbers out of context.
    390 ppmv is an infinitesimal proportion.
    Why don’t you calculate how much CO2 is in your room? Try multiplying the internal volume of your room by .000390 or you could try calculating the amount of CO2 in a vertical beam that hits the earth. You could look up the thickness of the atmosphere and give it a radius of 500mm. This would give you an idea of how much CO2 the sun has to shine through to reach the earth.
    And then you could look on my blog for the relationship between H20 and CO2 because it is this relationship that models rely on when they attempt to forecast global warming.

    Then try thinking what would happen to our food supply if we carry out all the prescriptions given by the IPCC.
    If you can’t figure it out I may take the time to tell you, and I assure you its not pretty.

    I don’t care what you believe, but when you start supporting a process that could starve every normal family on earth, including mine, I feel I really need to encourage people to look at the truth.

    You see unless you look at this thing rationally in this fashion, you will be overtaken by the propaganda as you have already demonstrated.

    Cheers

    Roger

    http://www.rogerfromnewzealand.wordpress.com

  4. Do we really want lower energy prices? | Protons for Breakfast Blog Says:

    […] and gas and is associated with emissions of carbon dioxide into the atmosphere. As I mentioned in a previous post, the amount of carbon dioxide emitted is phenomenal and rising year on year. To the best of our […]

  5. Terence Says:

    Well put. The graphs you chose illustrate a very complex situation in a nutshell.

    The greenhouse effect was previously managed by natural Earth systems. Now a species of exponentially-reproducing ape has gained the knowledge and the power to exercise a significant influence upon it.

    As you say, that’s terrifying.

    I remember as a kid being amazed to learn that burning fossil fuels was releasing into the atmosphere the energy stored over millions of years in a matter of decades. I’m even more amazed as an old man that we’re still doing it. At an exponentially-increasing rate.

    Good to know that there are people like you out there making sense of science, in the face of arrogance and ignorance that would be laughable if they weren’t so dangerous.

    Best wishes
    Terence

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