From: Cameron Wybrow <wybrowc@sympatico.ca>

Date: Mon Nov 30 2009 - 16:38:35 EST

Date: Mon Nov 30 2009 - 16:38:35 EST

Iain:

I believe that the "wishful thinking" referred to in the article is "wishful thinking" about the adequacy of current mathematical models to handle complex and not-fully-understood climate systems, not a "wish" that the world should be subjected to catastrophic global warming.

Cameron.

----- Original Message -----

From: Iain Strachan

To: John Walley

Cc: AmericanScientificAffiliation

Sent: Monday, November 30, 2009 8:14 AM

Subject: Re: [asa] The Mathematics of Global Warming

OK I'm not an expert in the mathematical models used for climate modelling, but I am familiar with the problems related to solving non-linear differential equations - a non-linear equation of order as low as three can exhibit chaotic behaviour - which means that the solutions diverge with time due to arbitrarily small changes in initial conditions.

I think this is the substantive point that is being made, and it is correct in as far as it goes, were it not for the fact that other techniques can be applied to counter this problem. For example a related problem is the modelling of turbulent fluid flow in Computational Fluid Dynamics (CFD) which arises as a result of the Navier-Stokes equations. Again, I am not an expert in this, but my drinking partner is a world expert on this and author of some of the largest software packages in this field. This excerpt from Wikipedia (on Navier-Stokes equations) gives some idea of the type of techniques employed:

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The numerical solution of the Navier-Stokes equations for turbulent flow is extremely difficult, and due to the significantly different mixing-length scales that are involved in turbulent flow, the stable solution of this requires such a fine mesh resolution that the computational time becomes significantly infeasible for calculation (see Direct numerical simulation). Attempts to solve turbulent flow using a laminar solver typically result in a time-unsteady solution, which fails to converge appropriately. To counter this, time-averaged equations such as the Reynolds-averaged Navier-Stokes equations (RANS), supplemented with turbulence models (such as the k-å model), are used in practical computational fluid dynamics(CFD) applications when modeling turbulent flows. Another technique for solving numerically the Navier-Stokes equation is the Large-eddy simulation (LES). This approach is computationally more expensive than the RANS method (in time and computer memory), but produces better results since the larger turbulent scales are explicitly resolved.

----

As far as I'm aware, this kind of technique is very successful and my friend's code was famously involved in reconstructing the events following a famous UK railway station disaster where a front of flame shot up an escalator shaft (Kings Cross disaster). The results from the code were verified using a scale model.

Hence I don't think it's as simple as saying that if there are non-linear equations then you can't have any idea of the solution.

I would also add that the writer refers to "wishful thinking" as a basis for economic policy.

Would it not be more accurate to say that those who insist that climate change is NOT going to happen are indulging in wishful thinking?

I for one have no great desire to see global warming come true. I would love it if the whole thing was found to be a complete hoax, and to wake up one morning and find out it wasn't true, and that my grandchildren weren't going to inherit a world ravaged by flood, famine, disease and war. To suggest that those who believe this will happen are indulging in "wishful thinking" is absolutely preposterous.

Iain

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Received on Mon Nov 30 16:39:15 2009

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