In the last post I showed that not only is CO2 increasing, its growth rate is also increasing. So, the growth rate of CO2 is faster now than it was just a few decades ago. Significantly so.
There’s a generic term for growth rate: it’s called “velocity,” and is the time derivative of the quantity in question. Since the quantity in question is CO2 concentration, the velocity is the CO2 growth rate.
But indeed the growth rate hasn’t been constant. It has increased, as shown in this graph:
Clearly the growth rate (the velocity) is increasing over time, and yes, the increase is statistically significant. There’s a generic term for the rate of change of velocity: it’s called “acceleration.” Over the past several decades, the acceleration of CO2 is not zero, it’s positive. So, the long-term growth rate (the long-term velocity) is higher now than it was just a few decades ago.
Much to my surprise, I got an email from Tim Curtain, objecting to my post. He says:
Your Blog “Open (sic) Mind” today claims (wrongly) that there is an increasing rate of change of the rate of growth of atmospheric CO2, which in your Gospel must mean acceleration of the rate of change of the anomaly:
He also included this graph:
No, Tim. I didn’t say there was an increasing rate of change in the rate of growth of atmospheric CO2. I said there was an increase in the rate of growth of atmospheric CO2. I think you need to improve your reading comprehension skills.
All the evidence indicates that the increase in the growth rate is, as far as the data show, roughly constant over the long term. In other words, the acceleration of CO2, which is the rate of increase of velocity, is constant. That’s why a straight line fits the velocity data well in the above graph. Linearly increasing velocity means constant acceleration.
It does not mean an increasing rate of change in the growth rate. It means a constant non-zero change in the growth rate. Likewise, it does not mean an increase in the acceleration, it means a constant (non-zero) acceleration.
It’s possible that the long-term acceleration is itself changing, but the evidence doesn’t suggest that (yet).
There’s a generic term for the rate of change in acceleration: it’s called “jerk.” There’s no evidence of any jerk in CO2 concentration over the long haul — the long-term jerk can’t be shown to be different from zero. But the long-term acceleration can be shown different from zero. That’s what “increase in the growth rate” means.
What I actually said (referring to the above graph) is this:
Clearly the annual change in CO2 concentration fluctuates. A lot. But it’s consistently positive, CO2 is growing. And there’s a trend there as well as fluctuation, an upward trend, because the rate of increase is itself increasing. I’ve superimposed a trend line on the above graph.
Note: “it’s consistently positive” refers to the growth rate (velocity). That’s why “CO2 is growing.” But growth rate (velocity) is not constant so “there’s a trend there as well as fluctuation.” In other words, velocity is changing, i.e., CO2 is accelerating. And it’s “an upward trend, because the rate of increase is itself increasing.” In other words, the acceleration is positive, not zero, and not negative.
I never claimed, or even implied, that the acceleration was changing. I showed that the velocity (the growth rate) is changing. It’s increasing — so the acceleration is positive. As I said at the end:
Yet one fact remains, inexorable. CO2 continues to grow, significantly faster now than just a few decades ago.
Is that clear enough for you, Tim?
Also to my surprise, another email on the same topic appeared in my inbox, also from Tim Curtin, offering these pearls of wisdom:
tamino (aka Grant Foster) like Schmidt and his co-authors including Mike Hockeystick Mann, and Kevin Trenberth and their Australian cheerleaders JQ and hc cannot actually do calculus:
My calculus is fine, Tim. It’s your reading comprehension that needs work.
Feel free to object to what I say. Please don’t object to what I didn’t say, at least, not to me. I never said there was any “jerk” — in the CO2 concentration.