Models Methods Software

Dan Hughes

Journal of Computational Physics Special Issue

The journal of Computational Physics has a special issue that might be of interest to many here, Predicting weather, climate and extreme events.

This is a review article.

And Elsevier, aka Big Science Publishing, has kindly provided links to 8244 related articles.

July 16, 2008 Posted by | Uncategorized | , , | Leave a comment

GCMs are Consistent With Chaotic Response …

of equation systems that do not possess chaotic response.

Executive Summary
The original PDEs that describe the Rayleigh-Benard convection problem do not posses chaotic behavior. The chaotic response observed with Lorenz-like low-order models (LOM) obtained via mode expansions disappears whenever sufficient resolution is used in the numerical solution methods applied to the original PDEs.

The low order model of the Lorenz equations omits the terms that are responsible for interaction between smaller scales and the large scales. The very interactions that form the basis for invoking the turbulence analogy.

GCMs are consistent with the chaotic response obtained from incorrect low-order models (LOM) expansions of PDEs.

GCMs are consistent with the chaotic response obtained from incorrect solutions to ODEs and PDEs.

GCMs are consistent with the chaotic response observed whenever insufficient resolution is used with numerical solution methods.

Continue reading

July 5, 2008 Posted by | Uncategorized | , , , | 3 Comments

An Important Peer-Reviewed Paper: Part 1

We’ll now look at some of the results presented in the paper.

Introduction and Background
The authors have introduced the subject of convergence of numerical methods into the field of chaotic dynamical systems. This field is very important in many areas of current intense study and investigation. Numerical models and solution methods exhibit chaotic dynamical-system characteristics in weather and climate modeling, direct numerical and large eddy simulations of turbulent flows, as well as the classical studies of chaotic systems through nonlinear ODEs as introduced by Lorenz and others. The author’s paper seems to be the first in the literature to present results of systematic investigations of convergence into this important field of research and applications.
Continue reading

March 22, 2007 Posted by | Chaos and Lorenz, Verification | , , , , , | 1 Comment

An Important Peer-Reviewed Paper: Part 0

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.

Continue reading

March 9, 2007 Posted by | Uncategorized | , , , , , | Leave a comment