More gumf from the Grauniad. Supposedly based on something in PNAS: anyone seen it? The usual suspects: the Potsdam folk and Tim Lenton and so on. Sadly (?) the online version doesn’t have the appalling map that the print edition has, featuring highly implausible timescales for those bits I know anything about (Greenland and W Ant gone in 300 years). One of the dangerous tipping points was the greening of the Sahara, errrrm, because that could lead to dangerously low food prices? Shurely shom mishtake. I’m being unfair: that gets a mention (in print) as a rare beneficial example.

Anyway, I await the PNAS version to see if there really is anything new.

Update: for those who haven’t lost the will to live, the proof is at http://researchpages.net/media/resources/2008/02/05/final_proof.pdf

And the search for a meaningful definition of tipping point continues.

As before, the first step is to rename tipping points into tipping elements. Then we try to define it:

*A system S is a tipping element if the following condition is met: The parameters controlling the system can be transparently combined into a single control P, and there exists a critical control value Pcrit from which any significant variation by dP > 0 leads to a qualitative change (Fˆ ) in a crucial system feature F, after some observation time T > 0, measured with respect to a reference feature at the critical value, i.e.,*

[1] | F(P > Pcrit + dP|T) – F(Pcrit|T) | >= F^ > 0

*This inequality applies to forcing trajectories for which a slight deviation above a critical value that continues for some time inevitably induces a qualitative change. This change may occur immediately after the cause or much later.*

Hmm, makes you long for the clarity of Aristotle, no? What to make of it?

First to note, that later on 3 extra conditions and tacked on to make “policy relevant tipping points”, but they are a bit dull so I’ll ignore them.

F^ is a “qualitative change” but clearly also a quantitative one, since it needs to have a numerical value. So already we are in arbitrary land: anyone can define anything as qualitative, since it appears to mean “something we care about”. But also, I can’t see any discussion of what values F^ might take (can you?). I looked at the sea ice and Greenalnd sections, and don’t see what values might be being proposed. If you don’t know F^, the definition becomes meaningless.

The formala bears a resemblance to limits stuff from analysis, but sadly you can’t use it like that, of course, because of natural variability. So dP cannot be infinitesimal, and L et al decide that we can all agree that dP ~ 0.2 oC is reasonable (in the cases they consider P is a temperature-like variable). So what it reduces to, in the absence of any idea of what they mean by F^, is that if you perturb the temperature by an amount bigger than natural variabilty, then the system will change.

Which is the bleedin’ obvious.

Oh, and timescales. There is nothing new. The paper says that Gr or WAnt disintegration will take >300 years. Predicatably, the Grauniad removed the “>” sign. And the 300 years lower estimate? Its from Hansen. At least they didn’t take his with-a-century stuff seriously.