Re: [asa] The Mathematics of Global Warming

Hi John

I'm not a mathematician, but I spent 33 years developing computer models of
various systems. Most of the systems I modeled were pretty well-behaved, but
in the mid 70's I developed a radar bomb-scoring system (RBS) for the Navy.
The Navy uses huge quantities of ordnance in training. Not only is this
costly it leaves tons of unexploded ordnance around that eventually has to
be cleaned up. And the noise annoys civilians, making it necessary to do
training in remote locations. They wanted me to write a program that would
track an aircraft making a practice bomb run and simulate the bomb
ballistics to determine whare the bomb would land. In addition to being able
to detect the moment when the bomb was released, we had to determine or
estimate the bomb's initial velocity with respect to the aircraft and
correctly model the bomb's aerodynamics, which were highly nonlinear. There
was an additional complication: some bombs, known as cluster bombs,
consisted of a shell containing a number of smaller "bomblets". At a
specified altitude the shell would open and the bomblets would be released.
Of course the bomblets had completely different aerodynamics from the shell,
so the solution had to be stopped an restarted with new initial conditions.

We tested the RBS system by having aircraft drop real practice bombs (bombs
without explosives but with the correct mass and aerodynamics) and comparing
the real impact point with the predicted. As I remember the results were
close enough to be usable, but had the bombing been from any higher altitude
or had the aircraft been taking evasive action they wouldn't have been.
Variations in barometric pressure and humidity affected the results too.

But trying to predict climate years in advance is a great deal more
difficult than trying to predict a bomb trajectory from an aircraft flying a
few hundred to a few thousand feet above the deck.

I've spent some time looking at computer models of climate. Most of them are
too complicated to be easily analyzed. Even a retiree has limited time :-).
And most of them are too big to be run on the equipment available to me: a
macbook pro. But the complexity of the models argues for careful assessment
by people not having a vested interest in the accuracy of the models. I
don't know whether this has been done.

However there is one paper by Tobias and Weiss: Resonant Interactions
between Solar Activity and Climate that you can get at
http://ams.allenpress.com/perlserv/?request=get-document&doi=10.1175%2F1520-0442%282000%29013%3C3745%3ARIBSAA%3E2.0.CO%3B2
that uses the Lorenz equations to model the earth's climate. They find a
stochastic resonance phenomenon that can result in warming of the earth's
climate with very small variation in solar activity. Now one might rightly
question the simplification of using the Lorenz Differential equations to
model the earth's climate, but still the model points out a possible
connection between solar activity and earth's climate. I made a fairly
extensive study of the CCSM climate model, one of the models commonly used
by the GW community, and solar input is just a constant, so that model
doesn't model solar variation at all. The GISS model is somewhat more
difficult to analyze, and I haven't yet determined how or whether they model
solar variation.

Another approach to studying climate dynamics is that used by Scafetta. His
web site is http://www.fel.duke.edu/~scafetta/ on which he has reprinted
many of his papers. In addition there is a video of a talk he gave at the
EPA back in February that is worth watching. Among other things Scafetta has
done extensive analysis of the statistics of climate data and solar output
and found "echoes" of the solar input in the climate data, leading him to
conclude that solar variation is exciting global warming. (I'm not doing
justice to Scafett' research, which is extensive)

So, while I admit the possibility that the various climate models used by
IPCC could be correct, I am very leery of basing policy decision on them
until more analysis of the models and their input data and results is done
by an impartial party.

On Mon, Nov 30, 2009 at 6:34 AM, 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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-- 
William E (Bill) Hamilton Jr., Ph.D.
Member American Scientific Affiliation
Austin, TX
248 821 8156
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