Category: mathemagick


Regarding climate models, physician and science fiction writer Michael Crichton had this to say:

“Since climate may be a chaotic system—no one is sure—these predictions are inherently doubtful, to be polite.” (Aliens Cause Global Warming)

What does he mean when he says that climate may be chaotic, and what impact does this have on climate modelling?

Flash back to the early 1960s. Meteorologist Edward Lorenz was studying a bare-bones weather model, consisting of three differential equations. Give the model an initial state and the differential equations would describe how the state changes over time, in much the same way that you can predict where Johnny will be in three hours’ time, given that he starts in Chicago and is driving west at 60 miles per hour. The hope was that with a big enough computer, a powerful enough model, and an accurately measured state of the atmosphere, the weather could one day be predicted far in advance.

Lorenz, the story goes, found a run of the model which interested him, and sat down to replay the simulation. He entered the initial conditions and set the model in motion, only to watch in bewilderment as the replay rapidly diverged from the original simulation.

"From nearly the same starting point, Edward Lorenz saw his computer weather produce patterns that grew farther and farther apart until all resemblance disappeared" (Image and caption from Chaos: Making a New Science, by James Gleick, 1987, p.17)

Lorenz tore his code apart looking for the error, only to realise that the error had been in his assumptions. In a distinctly Crichtonesque twist, the computer worked with numbers to six decimal places (0.123456) but only printed out values to three decimal places (0.123) in order to save space. It was these shortened number which Lorenz entered as the initial conditions for his model. Surely those last digits were inconsequential; after all, they were but a few hundred parts per million, comparable to the atmospheric concentration of the trace gas carbon dioxide.

Oh, but the consequences! Its roots stretched back to earlier anomalies and the term ‘chaos’ would not be introduced for another decade, but it was Lorenz’s observation which heralded the beginnings of chaos theory.

Lorenz had discovered that even very small changes in the state of a chaotic system can quickly and radically change the way that the system develops over time. This property is known as extreme sensitivity to initial conditions, also called the ‘Butterfly Effect’ because it suggested neglecting an event as small as the flapping of a butterfly’s wings could be enough to derail a weather forecast. There is more to chaotic systems than the Butterfly Effect, but this characteristic is one of their best know properties. Lorenz’s work put and end to hopes of long-term weather forecasting. The state of the atmosphere could only be known so well, and even the smallest of imprecisions would lead the simulations to catastrophic failure.

‘Nobody believes a weather prediction twelve hours ahead. Now we’re asked to believe a prediction that goes out 100 years into the future? And make financial investments based on that prediction? Has everybody lost their minds?’ – Crichton

But does chaos theory signal doom for climate modelling? Stay tuned for part II….

A part of my John Everett series – read more: 0/I – II.0 – II.5 – II.75 –  III.0 – III.3 – IV.0 – IV.4 – IV.8 – V – VII – VIII – Full Report 

People who minimize or deny the threat of climate change (or ocean acidification, as in part IV of Dr. Everett’s testimony) will often demand that the change be “unprecedented” – that nothing like it has ever happened before in Earth history. (eg, here) The reasoning seems to be that if there have been ecological events like anthropogenic climate change in the past, then current events must not be alarming, since life on earth has each time survived and recovered:

“We know that the Earth has seen these conditions before, and that all the same types of animals and plants of the oceans successfully made it through far more extreme conditions. ” – Everertt (part V)

 

This has always seemed to me like it’s setting the bar a bit low: Do we only become alarmed when faced with the possibility of sterilizing the planet? And considering the amount of violence which earth life has withstood over the ages, it doesn’t seem a very strong statement that human impact is unlikely to wipe it out.

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A part of my John Everett series – read more: 0/I – II.0 – II.5 – II.75 –  III.0 – III.3 – IV.0 – IV.4 – IV.8 – V – VII – VIII – Full Report 

The last couple posts looked at Dr. Everett’s discussion of the growth rate of carbon dioxide. There’s one other claim in this section which warrants inspection: that a constant airborne fraction is a challenge to projected acidification.

I got the bright idea to sudo rm -rf in my /etc/ and now GIMP is broken. So none of my sweet graphics this episode. Instead here's a diagram of the carbon cycle, courtesy of NASA (click for sauce.) It's just as well. The coolest thing I could think to draw was some pictures of pie. Mmmm pie.

Here’s what he has to say:

The meaning of this information [the supposed leveling off of CO2 growth rate] (and the future of all climate models[)] became VERY cloudy on 31 December 2009 with the ScienceDaily acknowledgment of a paper published by American Geophysical Union and authored by Wolfgang Knorr that shows “No Rise of Atmospheric Carbon Dioxide Fraction in Past 160 Years”, despite the predictions of carbon cycle/climate models3. The implications of this have yet to be assimilated by the modeling community. This does not mean that CO2 proportion is not rising but rather that the proportion not being assimilated has not changed since 1850. Importantly, it means that the rate of CO2 cycling increases as it becomes more concentrated, and does not decrease as assumed in climate models. The rate of projected growth in CO2 appears to be greatly exaggerated.

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A part of my John Everett series – read more: 0/I – II.0 – II.5 – II.75 –  III.0 – III.3 – IV.0 – IV.4 – IV.8 – V – VII – VIII – Full Report 

The CO2 scenarios are literally falling flat and need revision. The observational trend line shows monotonic growth – pretty much a straight line as in the chart below of global marine CO2 measurements (NOAA data)4, while the IPCC scenarios used in most research rely on an accelerating growth. Certainly the predicted rapid acceleration of the IS92a model (see solid black line in middle of the figure on the right) is missing from the NOAA data plotted below. In fact, if the last 8 or 12 years are representative of the future, we might imagine a downward slope in the growth rate.

Last time, we looked at one claim Dr. Everett makes in this paragraph: that the measured rate of change in atmospheric carbon dioxide is inconsistent with the emissions scenarios used to predict future ocean acidification. To do this, he plays fast and loose with quantities and their derivatives (the rates at which they change.) The imprecision extends even to his quoted numbers: in pidginthe previous paragraph, he gives a growth rate as “3.05 ppm”. That’s a not a growth rate; it’s a concentration. He means 3.05 ppm per year. His projection is an extrapolation of “the average rate of increase for the past 10 years (1.87/year)…” 1.87 WHAT per year? I know that he means 1.87 ppm/year, but a lot of people wouldn’t, and I shouldn’t have to make assumptions. If Everett is being sloppy with his units, he’s being sloppy with his science.

The other claim that Dr. Everett draws from the rate of change in CO2 is that “the growth rate seems to be leveling off, if not declining […] In fact, if the last 8 or 12 years are representative of the future, we might imagine a downward slope in the growth rate. ” Look at the graph of the growth rate again. It goes up and down- a lot.

The record of changes in atmospheric carbon dioxide since 1980. It's got it's ups and downs. Click to see the full record back to 1959.

A part of my John Everett series – read more: 0/I – II.0 – II.5 – II.75 –  III.0 – III.3 – IV.0 – IV.4 – IV.8 – V – VII – VIII – Full Report 

The last post covered Dr. Everett’s introductions; now we’re going to move on to part II of his testimony, titled “The Physics”. In this section he questions estimates of future acidification.

Dr. Everett never seriously challenges the 0.1 pH of acidification which has already occurred, or that human CO2 emissions are the cause (though he will in later sections challenge its impact). His purpose in this section is to challenge projections for future acidification, on the basis that less carbon dioxide will be emitted than is projected in the models used:

…if the projections we are concerned with today are based on the IPCC IS92a model, […] we should give the information on its impacts a second look.

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A part of my John Everett series – read more: 0/I – II.0 – II.5 – II.75 –  III.0 – III.3 – IV.0 – IV.4 – IV.8 – V – VII – VIII – Full Report 

The front matter Everett provides (0) is as good a place to start as any. He gives a bit of biographic information, highlighting his experience with NOAA and the IPCC; his expertise is in fisheries, not geochemistry. This itself doesn’t invalidate what he has to say: A non-expert can have a valid opinion, even a contrary one (his opinion is much more relevant than that of Sigorney Weaver, who also testified). But when a non-expert disagrees with the opinions of most experts, we should at least take a more critical look at the basis for their opinion. Everett also cites his website, ClimateChangeFacts, which he tries “to keep unbiased in its treatment of conflicting science”. One of the first lines on his site is a reference to ClimateGate, the conspiracy-that-wasn’t to falsify climate data; ClimateGate itself has been widely debunked (“ClimateGate is a hoax”: 10 google hits.) Already, I have to be skeptical of his expertise.

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