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:

----
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<http://en.wikipedia.org/wiki/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<http://en.wikipedia.org/wiki/Reynolds-averaged_Navier-Stokes_equations>
(RANS),
supplemented with turbulence models (such as the k-ε model), are used in
practical computational fluid
dynamics<http://en.wikipedia.org/wiki/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
On Mon, Nov 30, 2009 at 12:34 PM, John Walley <john_walley@yahoo.com> wrote:
> I found this to be very interesting. I wonder if any of the mathematicians
> on the list have any comment?
>
> John
>
> November 30, 2009
> The Mathematics of Global Warming
> By Peter Landesman
> http://www.americanthinker.com/2009/11/the_mathematics_of_global_warm.html
>
> The forecasts of global warming are based on the mathematical solutions of
> equations in models of the weather.  But all of these solutions are
> inaccurate. Therefore no valid scientific conclusions can be made concerning
> global warming. The false claim for the effectiveness of mathematics is an
> unreported scandal at least as important as the recent climate data fraud.
> Why is the math important? And why don't the climatologists use it
> correctly?
>
> Mathematics has a fundamental role in the development of all physical
> sciences. First the researchers strive to understand the laws of nature
> determining the behavior of what they are studying. Then they build a model
> and express these laws in the mathematics of differential and difference
> equations. Next the mathematicians analyze the solutions to these equations
> to improve the understanding of the scientist. Often the mathematicians can
> describe the evolution through time of the scientist's model.
>
> The most famous successful use of mathematics in this way was Isaac
> Newton's demonstration that the planets travel in elliptical paths around
> the sun.  He formulated the law of gravity (that the rate of change of the
> velocity between two masses is inversely proportional to the square of the
> distance between them) and then developed the mathematics of differential
> calculus to demonstrate his result.
>
> Every college physics student studies many of the simple models and their
> successful solutions that have been found over the 300 years after Newton.
> Engineers constantly use models and mathematics to gain insight into the
> physics of their field.
>
> However, for many situations of interest, the mathematics may become too
> difficult. The mathematicians are unable to answer the scientist's important
> questions because a complete understanding of the differential equations is
> beyond human knowledge.  A famous longstanding such unsolved problem is the
> n-body problem:  if more than two planets are revolving around one another,
> according to the law of gravity, will the planets ram each other or will
> they drift out to infinity?
>
> Fortunately, in the last fifty years computers have been able to help
> mathematicians solve complex models over short time periods. Numerical
> analystshave developed techniques to graph solutions to differential
> equations and thus to yield new information about the model under
> consideration.  All college calculus students use calculators to find
> solutions to simple differential equations called integrals.  Space-travel
> is possible because computers can solve the n-body problem for short times
> and small n.  The design of the stealth jet fighter could not have been
> accomplished without the computing speed of parallel processors.  These
> successes have unrealistically raised the expectations for the application
> of mathematics to scientific problems.
>
> Unfortunately, even assuming the model of the physics is correct, computers
> and mathematicians cannot solve more difficult problems such as the weather
> equations for several reasons.  First, the solution may require more
> computations than computers can make.  Faster and faster computers push back
> the speed barrier every year.  Second, it may be too difficult to collect
> enough data to accurately determine the initial conditions of the model.
> Third, the equations of the model may be non-linear. This means that no
> simplification of the equations can accurately predict the properties of the
> solutions of the differential equations. The solutions are often unstable.
> That is a small variation in initial conditions lead to large variations
> some time later. This property makes it impossible to compute solutions over
> long time periods.
>
> As an expertin the solutions of non-linear differential equations, I can
> attest to the fact that the more than two-dozen non-linear differential
> equations in the models of the weather are too difficult for humans to have
> any idea how to solve accurately.  No approximation over long time periods
> has any chance of accurately predicting global warming.  Yet approximation
> is exactly what the global warming advocates are doing.  Each of the more
> than 30 modelsbeing used around the world to predict the weather is just a
> different inaccurate approximation of the weather equations.  (Of course
> this is only an issue if the model of the weather is correct. It is probably
> not because the climatologists probably do not understand all of the
> physical processes determining the weather.)
>
> Therefore, logically one cannot conclude that any of the predictions are
> correct. To base economic policy on the wishful thinking of these so-called
> scientists is just foolhardy from a mathematical point of view. The leaders
> of the mathematical community, ensconced in universities flush with global
> warming dollars, have not adequately explained to the public the above
> facts.
>
> President Obama should appoint a Mathematics Czar to consult before he goes
> to Copenhagen.
>
> Peter Landesman mathmaze@yahoo.comis the author of the 3D-maze
> bookSpacemazes for children to have fun while learning mathematics.
>
>
>
>
>
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