Re: [asa] The Mathematics of Global Warming

With respect to climate vs weather, a simple analogy may be made with
chaotic non-linear differential equations. Essentially there are several
different outcomes to the solution of a non-linear differential equation:

. A stable point (attractor)
. An unstable, divergent solution.
. A regular limit-cycle (predictable)
. A "strange attractor"

The last of these is "chaotic" in the sense that you can't predict its
precise value because arbitrarily small changes in initial conditions make
for large differences in the solution after increasing amounts of time.

However, the "strange attractor" isn't just random chaos. For example the
"Lorenz Attractor" (a third order system) has a distinctive shape in phase
space that is recognisable, and one can predict at least that at any given
time it will be somewhere on that surface (which is a fractal-dimensional
subspace of the 3-d space). Given that this constrains highly where it will
end up, one could say that the general properties are well-defined; they are
defined by the strange attractor.

By the same token, climate would be the general properties of the weather,
without the details of the day-to-day behaviour of the weather.

Randy wrote:

Everyone I know in the field desperately wishes it weren't true and would be
delighted to hear of any data or any analysis saying it ain't so. If anyone
has such info, please pass it along. This one isn't it.

I'll second that. By the tone of some of the posts on this topic one would
think that folks actually WANT climate change to be true. What absolute
nonsense!

Iain

On Mon, Nov 30, 2009 at 7:20 PM, Randy Isaac <randyisaac@comcast.net> wrote:

> Though there are similarities, there are some significant differences in
> modeling climate vs weather. One of those differences is that weather is
> critically sensitive to initial conditions and the solution depends on the
> very sensitive dynamic response to those initial conditions. Climate, on the
> other hand, depends on a long term steady state solution that is relatively
> insensitive to initial conditions. Solutions to the latter are much easier
> to obtain than the former. Heuristically, one can predict the climate for
> July 4 twenty years from now but you can't predict the weather ten days from
> now, let alone next July 4.
>
> As I've mentioned previously, global warming predictions do not depend
> solely on models. It is noteworthy that all diverse lines of investigation
> point in the same direction. Paleoclimatology, current trends, future
> models, are all consistent, having a range of solutions for the specifics at
> 2100 but all with the same message. Everyone I know in the field desperately
> wishes it weren't true and would be delighted to hear of any data or any
> analysis saying it ain't so. If anyone has such info, please pass it along.
> This one isn't it.
>
> The statement that no valid scientific conclusions can be made concerning
> global warming is not supported by any logical reasoning that I know of.
>
> Randy
>
> --------------------------------------------------
> From: "John Walley" <john_walley@yahoo.com>
>
>
>
>> 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.
>>
>
>
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