CO2 Velocity

As I mentioned in an earlier post, I recently modified my smoothing program so that it would record not only the estimated smoothed value, but the estimated smooothed velocity (rate of change) as well. I’m always a little leery of a new analysis method, there could be some unanticipated quirk of its behavior, but let’s apply it anyway to estimate the momentary rate of change (the velocity) of CO2 on about a 5-year time scale.


Here’s the latest CO2 data from Mauna Loa:

I removed the seasonal cycle, then smoothed it to get this:

This smooth is pretty “fast” in order to pick some of the fine detail in CO2 changes. I also smoothed it with a slightly “slower” smooth, to get the velocity estimate on a 5-year time scale. That gives this for the smoothed rate of change of CO2:

To check how good the estimate is, I also computed the rate of change with another method of known reliability. I took the data, and for each 5-year time span I fit a combination of a linear trend (to estimate the growth rate) and a 4th-order Fourier series (to account for the seasonal cycle). Here are the growth rate estimates (in red) from that analysis, compared to those from the smoothing program:

The match is outstanding. Clearly the smoothing method gives good velocity estimates, at least in this case.

That’s not such a surprise. A lowess smooth estimates the smoothed value at a given time by taking the data near (in time) to the given moment and fitting a low-order polynomial (usually 1st or 2nd degree). The value of the fit at the given moment is the smoothed estimate. If the local polynomial fit is a good representation of the data, then its time derivative should be a good representation of the smoothed rate of change of the data. This particular data set bears that out.

It also shows, quite convincingly, that the velocity of CO2 has increased in recent decades. In fact it has increased consistently, but with large fluctuations superimposed on that increase. Those fluctuations are part of the complex carbon cycle. Some of the fluctuations are due to changes in the growth of land plants, which are related to other phenomena like ocean cycles such as the el Nino southern oscillation (ENSO) which affect not only temperature, but patterns of rainfall — and hence impact the biosphere and how much CO2 it sequesters.

There is one major fluctuation whose cause I don’t know: the large decrease in CO2 growth rate around 1992. The ENSO doesn’t explain it. I have heard it suggested that it’s related to the collapse of the former Soviet Union, and the decline in economic activity associated with that event. But CO2 emissions estimates (from CDIAC) don’t support that idea:

In any case, the fluctuations make it impossible to know how the trend is changing on short time scales. Hence when we do start to reduce our CO2 emissions, unless the reduction is dramatic (to the point of remarkable!) it will be years before we can see its influence in CO2 concentration with confidence.

That’s why there isn’t yet any reliable sign of a slowdown in the rate of increase of CO2 growth. Some might want to claim that the CO2 growth rate hasn’t increased in about 10 years or so — but considering the large and ubiquitous fluctuations, that’s just as nonsensical as the mistaken claim that the temperature trend has slowed. The evidence indicates that CO2 continues to grow at an ever-increasing rate, together with fluctuations, but the rate of increase of its growth has not yet slowed down.

And that’s cause for great concern. Climate is changing and we know the cause. It’s the changes we have wrought in the very air we breathe, the increase of greenhouse gases in our atmosphere. Chief among them is carbon dioxide (CO2), a byproduct of burning carbon-based fuels like oil, gas, and coal, which we pour into the air at the rate of billions of tonnes every year.

To avoid the worst case, we have to slow, then stop, dumping all that CO2 into the air. Yes it will help to reduce other greenhouse gases (like methane and nitrous oxide and chloroflourocarbons), and yes, to reduce CO2 emissions we must switch to a non-carbon-based energy infrastructure. All discussions of how to do so are important. But let’s not forget that the reason we must do so, and so soon, is that carbon dioxide is the root of the problem. It’s the elephant in the room. It’s the billion-ton whale. At the moment, it’s what it’s all about.

Perhaps the greatest danger is that natural responses to climate change will alter the carbon cycle itself in dramatic ways. About half the CO2 we presently emit is sequestered in other reservoirs, including the oceans (which are, unfortunately, acidifying as a result) and the biosphere. But we can’t count on those reservoirs to continue soaking up half of our excess CO2. They may even become sources rather than sinks for atmospheric CO2, making things a lot worse. And with the rapid disappearance of the cryosphere, things like melting permafrost may unleash a CO2 monster.

If that happens, then the one thing we know we could safely do to mitigate climate change — to stop dumping CO2 into the air so its growth slows or even stops — may no longer be an option. We could see incredibly rapid CO2 increase even if we bring our own emissions to zero. The CO2 train is already moving much too fast, and if it takes on a life of its own, unspeakable disaster will be the inevitable result.

So when it comes to doing the one thing we know we can safely do — I suggest we start immediately.

I’ll close by saying that my request for donations was answered beyond my expectations, and (as my wife reminds me) I would be an ingrate not to express my sincere, in fact heartfelt, thanks to you all. I would also like to thank all loyal readers, including those unable to donate — I know how hard it can be in tough economic times. To everyone: your gifts, your attention, and your help in spreading the word (which is a mighty force!) are noticed — and not just here. Your collective efforts are far more potent than my poor power to add or detract. Fáinne óir ort!

35 responses to “CO2 Velocity

  1. Oh look you can make out all the economic recessions

  2. The big drop around 1992 is caused by the Pinatubo that made the Earth temperature fall, which increased the carbon capture. In theory, you could use exactly the same magic as the one you used for the temperature to extract each component,

    • You’d think so, but there is also El Chichon in 1982 which does not show up in the same graph.. could be a geographical effect, of course.

      It would be interesting to see the ENSO index on the same scale.

      • I’ve heard it said that El Chichon was a bit of an oddball volcanic eruption, climatically speaking, because of its timing in relation to an El-Nino at around the same time.

        A multivariate regression would unpick that if the signal is there.

  3. For the early 1990’s reduction in CO2 growth, I too had heard the explanation regarding the collapse of the Soviet Union. Another explanation is Pinatubo, cooling the Earth’s surface, perhaps allowing more absorption of CO2 by the ocean?

    [Response: I think it’s probably Pinatubo. For some reason I had it in my head that Pinatubo exploded in 1992 … but it was actually 1991.]

    • There was a [NASA?] report that the type of Pinatubo output caused an extended diffuse light period, which plants loved… more CO2 uptake [no mention of temperature!].

      The sobering on “[more] CO2 is good for plants” (depends if cultivar, no, or weed, yes e.,g.), this article discusses that plant uptake is less than thought of before: http://www.scientificamerican.com/article.cfm?id=plants-carbon-sinking-capacity-is-much-lower-than-thought

    • As Tamino responded, Pinatubo is the likely culprit. Sarmiento, 1993 is an early look at this, and there is interesting literature evaluating the carbon cycle’s response to large volcanic eruptions. The biogeochemical response to the eruptions is a bit more complicated than just cooling -> enhanced absorption; the carbon cycle responds indirectly to the eruptions via forced modes of climate variability which impact precipitation and temperature differently in different parts of the globe. The response over land has been shown to be either quite strong (Jones and Cox, 2001), quite weak (Rothenberg et al, 2012), or somewhere in between (Frolicher et al, 2011).

    • err forgot to mention that changes in the fraction of diffuse radiation due to scattering by volcanic aerosols deposited in the stratosphere also play a role in impacting the biosphere’s uptake of carbon following the eruptions (Krakauer and Randerson, 2003)

  4. David B. Benson

    Wonderful, but for the choice of term ‘velocity’. All how take physics learn that velocity is a vecotr quantity, expressible in terms of angles and a radial component, called speed.

    Now somehow economists never learned this, coning ‘velocity of money’ for what is simply the first time derivative of a scalar quantity. All too many have been infected by the idea that a three syllable word is somehow more scientific, or more authoritative, than a humble (and correct) one syllable word.

    After all, the traffic cop doesn’t give you a ticket for ‘velocitating’.

    /rant

    [Response: LOL]

    • Well, don’t you agree that Tamino makes up for this by coining the wonderful new word “smooothed”?

    • Yes. If caught speeding, try and convince the policeman that since you were doing a round trip, your average velocity would be zero.

      Of course, that means you’d get arrested for parking on the highway..

    • As an officially Math-Challenged Bear, I’d like to ask for an expansion, as this is a topic that does have some implications.

      Can a “scalar quantity” also be a “radial component?” I’d have said “sure, it can”–but then, I’m a MCB. It’s a bit (potentially) confusing, though, because on the one hand speed is always associated with a directionality in the real world; the quantity in effect ‘becomes’ scalar when we abstract the magnitude of displacement from the direction of displacement. Right?

      This bears–no pun intended–on some denialist argumentation, which I would at present call ‘bafflegab.’ For one example, see:

      http://johnosullivan.wordpress.com/2012/10/07/the-greenhouse-gas-warming-number-of-33-degrees-is-a-fatal-error/

      I’ve argued that there can’t be ‘scalar degrees K’ and ‘vector degrees K’–and moreover, while radiation may be *related* to temperature, it is not the same thing.

      That seems to me to be the conflation of which the ‘slayers’ are guilty. Their claim that TOA temperature is a vector quantity is a pure confusion, I think, comparable to failing to recognize the difference between ‘real-world’ examples of speed, and the notion of speed proper, which involves the ‘abstracting-out’ of directionality, as I discussed in my second paragraph.

      OK, how confused am I? Not much, I hope?

      • Much less confused than the slayers…

      • Thanks, Chris, but I’d hoped for something that would narrow it down a bit more than that!

      • David B. Benson

        Kevin McKinney — A vector quantity requires specifying two or more scalars. one for each ‘direction’. [I leave out the trivial one-dimension vector space as simply confusing to begin with.]

        Speed is the rate of change over time (first time derivative) of the radial component of a velocity. Velocity is the time rate of change of a displacement. Strictly speaking, noting else has speed.

        The correct term for quantities other than displacements is ‘flux’. For quantity Q the time rate of change is ‘Q flux’. Examples include money flux or CO2 flux.

        However, ‘speed’ is often misused as is ‘velocity’.

    • Sceptical Wombat

      David a vector can be one dimensional. The rate of increase of CO2 concentration can certainly be regarded as a one dimensional vector. Speed would not be a good description of the rate of increase because speed can never be negative whereas CO2 concentrations could in theory decrease.

      If you want to experience true frustration try explaining to an economist that while a negative increase ( in GDP for instance) is perfectly meaningful, a negative change is impossible (you would have to get closer to where you started than you were when you started).

      • David B. Benson

        Of course; even zero dimensional. But it usually is most helpful to beginners to distinguish between scalar quantities, such as energy and its derivatives, and vector quantities, such as position and its derivatives.

        Yes, speed measures rate of change as opposed to rate of increase.

      • Thanks, gentlemen!

        till ruminating over all of this, but all that was helpful. (I think it’s confusing because I ‘think’ in natural language, not mathematically, so there’s ‘translation’ delays and ambiguities at every turn as I try to work through the various concepts.)

        Oh, speaking of ambiguity–DBB, your sentence, “Nothing else has speed,” confuses me a tad–to what does the “nothing else” refer? (Put alternatively, what *does* ‘have speed?’)

        Considering the last two comments, I conclude that since “speed measures rate of change, as opposed to rate of increase,” and “For quantity Q the time rate of change is ‘Q flux’,” then speaking of a ‘negative flux’ of CO2 (or anything else) would be a misnomer (albeit perhaps understandable, since *within the context* it would be trivial to construct a mathematically consistent definition consistent with the usage?)

    • David B. Benson

      Kevin McKinney | October 13, 2012 at 12:35 pm | — Rate of change of position is speed; strictly speaking nothing else is speed.

      I am sure I was not clear. For a scalar quantity Q the flux can certainly be negative, as when one flushes the toilet, for example.

  5. There was a significant La Nina commencing in 1988. That would account for the initial fall, which was picked up an increased by Pinatubo effects. I will note that what is absorbed by the ocean due to cool water will largely be restored to the atmosphere when the ocean warms again. Consequently, while the La Nina, and especially Pinatubo are probably responsible for the large dip around 1992, the slow down in emissions due to the collapse of the Soviet Union will be responsible for reduced acceleration in the 1990s as a whole.

  6. Why are you wishing gold rings on people?

    [Response: To congratulate them with an Irish expression meaning “well done.”]

  7. The 1992 drop is likely Pinatubo – specifically iron fertilization of the ocean

    http://www.nature.com/nature/journal/v385/n6617/pdf/385587b0.pdf

  8. Still can’t donate. Tried multiple times using various combinations of filling and not filling the amount and password boxes. Finally got: “We cannot process this transaction because there is a problem with the PayPal email address supplied by the seller.”

    Let us know when you get it fixed and I’ll try again.

  9. Tamino, confirming “… a problem with the PayPal email address supplied by the seller.” — Haven’t changed anything on my end other than the usual updates to everything, fiddled with blockers/tracker stuff etc. I suspect PayPal needs an authorization or confirmation for email, or hit a full mailbox, or something.

    Aside on charting – happened to look and noticed that
    http://www.woodfortrees.org/examples
    has added quite a bit since I last looked there.

    I haven’t compared this CO2 example there with Tamino’s yet but it might be worth a look (Links on the original page)

    “… Some deeper cleaning to find longer-term patterns:

    “CO2 with the long-term slope removed, and annually averaged
    Note the bowl curve in the detrended CO2 shows that the rate of increase has not been constant, and has increased over the period.”

  10. > early 1990′s reduction
    I recall that as the USSR began to fall apart they also had a big, big problem with natural gas (methane) leaks in the whole extensive transmission system because maintenance wasn’t being done. So they burned less fuel as the economy collapsed but — just guessing — the world might have seen a bounce in CO2 in following years as methane oxidized

  11. Seems to be a consensus that the early 1990s slowing in the rate of CO2 rise was due in some part to Pinatubo. This is a nice debunking of the myth that rising CO2 in the atmosphere is due to volcanoes rather than us.

  12. I have yet to see a proposal that would reduce CO2 levels in any substantial way. As you say the level is accelerating, and switching out lightbulbs in a few countries or driving smaller cars and taking the bus won’t change that when other countries are moving in the reverse direction.

    [Response: Cop-out.]