Models, Methods, Software

Using the NASA/GISS ModelE code browser I ran across the MODULE CONSTANT in which several constants are setup as parameters.

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Here’s an example of what a lack on coding guidelines (or ignoring them) can lead to. From the NASA/GISS ModelE online source code browser:

SUBROUTINE SURFCE 1,30
!@sum SURFCE calculates the surface fluxes which include
!@+ sensible heat, evaporation, thermal radiation, and momentum
!@+ drag. It also calculates instantaneous surface temperature,
!@+ surface specific humidity, and surface wind components.
!@auth Nobody will claim responsibilty

This is the entire header information for a 1228-line routine.

The last line says it all.

The NWP and GCM communities cannot think that a Butterfly will have any influence whatsoever on any physical phenomena or processes of interest. Instead the phenomenology of The Butterfly Effect as exhibited by the numerical calculations of some systems of ordinary differential equations is invoked by hypothesis into NWP and GCM models/methods/codes. I think we need to limit discussions to the Lorenz-like systems of ODEs, as these seem to be the basis for invoking the phenomenology into the NWP and GCM communities. Otherwise we will get side-tracked into discussions of the “chaotic response of complex dynamical systems” in general.

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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.
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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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All the contents of Tellus A, January 2007 - Vol. 59 Issue, 1 Page 1-154, are free online. The main page is here.

The article, “How reliable are climate models?” on pages 2 - 29 might be of interest to readers here. The abstract, the complete article in pdf and html.

The several Global Climate Model or General Circulation Model (GCM) codes around the world are the work horses for the ‘what-if’ studies relative to the Global Average Temperature (and many, many other things) that appear in the IPCC Assessment Reports. There are about 20 of these codes, more or less. The actual models in the codes vary considerably from code-to-code and as a function of time with a given code. The GISS ModelE code is the NASA versions of GCMs.

Some GISS/NASA information about the ModelE GCM code is available here. There you will find information about the documentation of the model and code along with access to download the source and and an online HTML-based code viewer.

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