RE: Environment

Allan Harvey (
Mon, 24 Jun 1996 17:09:11 -0600

At 03:14 PM 6/24/96 EDT, James Turner wrote:
> I would like to raise a concern I have on the topic of predictions. When
>I was an undergraduate I took a course in dynamical systems (from the pure
>math side) and much later read James Glieck's book _Chaos_. One thing I came
>away with from both of them was that if one is using a computer to make
>predictions of a system, based upon some mathematical model, the difference
>between the predicted and actual value can be quite large the farther in the
>future one is trying to predict to.
>Unfortunately, a computer has the same problem. No matter how sophisticated,
>it still must approximate irrational numbers and so it seems to me that any
>computer models that attempt to make long term predications could have
>unreliable results. But I am also not an expert and I would like to know if
>this is a legitimate concern of mine or can it be easily dealt with in theory
>and/or practice.

While this seems to be a common misconception (that's too strong a word - it
is technically correct in a sense), it isn't an issue in practice, or at
least not a significant one in the grand context of the uncertainty of
predictions. One can always reduce roundoff errors and their propagation by
making the numerical algorithms better, and good scientific work will always
take steps to ensure that these errors are not significant to the work.

The problem with predictions of some dynamical systems is their extreme
sensitivity to initial conditions and parameters. If we don't know a
parameter (like maybe the IR absorption behavior for a given atmospheric
species) or an initial condition (like maybe the current distribution of
that species in the atmosphere) precisely enough, those factors (not the
computing precision) will limit the ability to make predictions. Good
scientific work will also recognize these limitations.

In general, you are not going to find any real-world situation where the
uncertainty in the parameters and initial conditions is not many orders of
magnitude more than the roundoff errors in modern computers.

| Dr. Allan H. Harvey | |
| Physical and Chemical Properties Division | Phone: (303)497-3555 |
| National Institute of Standards & Technology | Fax: (303)497-5224 |
| 325 Broadway, Boulder, CO 80303 | |
| "Don't blame the government for what I say, or vice versa." |