Models, Methods, Software

Introduction
I’ve decided to modify this post and put an example here. Examples have the potential to provide more understanding of the important technical issues.

So, let’s say it’s Saturday January 5, 2008, at 4:30 am and a Butterfly is sitting on the railing of the deck outside the house. Actually, the railing is snow-covered and the Butterfly is sitting on the snow. The air is still, the sky is crystal-clear, there is significant radiative cooling underway and the temperature is dropping like a rock; it’s well below zero in both C and F. The Butterfly uses one wing to stifle a yawn and that wing moves slowly toward its mouth and then back to its resting place; the Butterfly needs the cover for warmth.

Here’s the question. What effect will that flap of the Butterfly’s wing have on the potential for a hurricane to form in the Gulf of Mexico in July 2008.

Some of the technical issues behind this question are the subjects of this post and possibly one or two others in future.

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This paper Time-step Sensitivity of Nonlinear Atmospheric Models: Numerical Convergence, Truncation Error Growth and Ensemble Design addresses some of the important issues for which this blog was established. Extensive discussions will follow as I get the results of my work documented. I have used the 3D Lorenz equations for most of my work, but have looked at other ODEs for which chaotic response has been demonstrated.

One conclusion that I am almost certain about at this time is that standard numerical solution methods applied to ODEs that exhibit chaotic responses have never been shown to converge. Additionally, it is very likely that convergence can not be demonstrated. The calculated numbers are very likely noise that does not satisfy the continuous equations. Some parts of this conclusion will cary over to numerical solution methods for PDEs. Some of the issues were mentioned in this post. The chaotic responses calculated by AOLGCM models/codes are in fact purely numerical artifacts from a combination of the numerical solution methods, lack of convergence of the calculations, and the algebraic parameterizations used in the models.

These issues will be addressed in subsequent posts here. First we take a preliminary look at some of the issues brought to light by the subject paper.

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