Re: [asa] Creation Care

David,

Concerning computer modelling - the problem with numerical imprecision is
pretty hard. Chaotic behaviour can be shown to happen even with something
as small as a third order non-linear differential equation - a noted example
being the "Lorenz strange attractor" which I believe is a simplistic model
for atmospheric convection. As a simple test I did two runs of the model
once with the smallest possible numerical change to one of the initial
conditions (a relative change of 10^(-16) is the smallest possible at double
precision). Within a few hundred steps the results were about as different
as they could possibly be.

I believe this can be a big problem in short term weather forecasting -
there are times when the system enters an ergodic region and it's just not
possible to predict in the short term with any accuracy. Other times it is
more predictable.

However, what does NOT change is the general behaviour. The appearance of a
plot of results of the Lorenz attractor looks the same whatever the starting
conditions. I imagine, therefore that long term computer models of
something like global warming would certainly be able to predict the general
trend.

Very large software systems are usually designed in modules that can each be
unit-tested, but it's clear that you won't track down all the bugs.
However, testing against historical data is probably a pretty good test of
the correctness of the algorithm - most bugs would cause the system to give
nonsensical results.

Regards,
Iain

On 1/20/07, Dave Wallace <wdwllace@sympatico.ca> wrote:
>
> David Opderbeck wrote:
>
> > It
> > would be interesting to see how many authors and academic institutions
> > are represented in those 900 articles, how many of those articles
> > present truly new models or approaches to modeling, how extensively the
> > models have been cross-checked through work in other disciplines, etc.
> > It's not a trivial amount, I'm sure, but it doesn't approach the volume
> > of work that's been done, say, on biological evolution.
> >
> I took a couple of undergraduate courses in numerical methods and a
> graduate course. As best I can tell, as an outsider, the climate
> models, at least the better ones involve solving differential equations
> numerically (ie programs on computers) using the techniques of numerical
> methods. One thing I learned is that for these computationally
> intensive numerical modeling programs that one needs a really good
> numerical analyst who can perform a very though error analysis, much
> more knowledgeable and experiences than I ever was. My experience
> working at a university for a while after graduation is that very few
> scientists approached the numerical experts for help.
>
> Climate and weather modeling also tends to be chaotic where small errors
> in initial and boundary conditions can effect the result dramatically.
> A frequently overlooked point however, is that each floating
> point computation is only an approximations and introduce the same
> kinds of effects that imprecision in constants... does.
>
> As a programmer for 40 years I also learned that in any large complex
> program there is no such thing as finding all the bugs. These models
> likely have to run on a massively parallel processor complex, one more
> source of error/bugs. Typically the models are validated against
> historical data and when they match then people stop looking for bugs.
> On the space shuttle NASA runs control programs on different hardware
> and with programs independently produced.
>
> Given the large economic impacts of many of the proposals, have any of
> the models been totally independently programmed and validated during
> development by experts in numerical analysis?
>
> I was involved with some modeling of systems for a couple of years off
> and on. In one case we were using a commercially available package to
> get most of the results. If we got the results wrong then the down
> stream result would have been for a fighter pilot to fly into a hill.
> Thus I was concerned enough about the validity of our results that I
> wrote a brute force program to check the results, at least for a few
> tiny samples of the data.
>
> > Where warming
> > is different from ID/evolutionary science, I think, is in the extent of
> > the conclusions that legitimately can be drawn from the science to date
> > and in the breadth of the consensus. The volume of work done, the
> > cross-disciplinarity, the correlation with predictions and observations,
> > all are far more extensive in evolutionary science than in the science
> > of climate change at this point in the respective research programs.
>
>
> The other big difference is that, as far as I know, results in
> evolutionary science do not depend so heavily upon computer modeling, at
> least not to any where near the same extent as do studies of climate.
> Researchers studying evolution can do physical modeling on small
> populations and see what happens under various stimuli. Also of course
> if the science backing evolution is wrong only a very few people are
> affected, unlike with climate studies.
>
> Am I saying that the scientists who do the modeling are incompetent? By
> no means, my point is that numeric computer modeling is hard, very hard,
> to get right. An example from another programming area, do you think
> that Micro Soft likes to keep developers developing fixes rather than
> working on new development?
>
>
> It appears that the results could be very bad if nothing is done about
> global warming however, doing something in the wrong way could also
> impact people very negatively. My take is that most actions related to
> global warming should also take Glenn's discussion on peak oil flow
> seriously and attempt to do something about both problems. Improving
> transportion systems has already been mentioned, but considerable energy
> also goes into heating, cooling and lighting at least up here north of
> the 49th parallel.
>
> Dave Wallace
>
>
>
>
>
>
>
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