Chaos and ODEs Part 1c: The Numerical Methods
The numerical solution methods that will be used to check convergence are given in a file that I uploaded.
Let me know if you see any typos or if you want to see some results for a specific equation system.
I’m thinking that Part 1d will be some numerical results.
Chaos and ODEs Part 1b: The Equation Systems
The equation systems that will be used to check convergence are given in a file that I uploaded. I had tons o’ links and cross references and other good stuff but nothing worked out. Maybe later.
Let me know if you see any typos or if you want to see some results for a specific equation system.
I’m thinking that Part 1c will be the numerical methods.
UPDATE Nov 19, 2007: I have replaced the original uploaded file with a version that has some identification for me in it.
Chaos and ODEs Part 1a: The Literature Sources
I have way too much material for a single post. I have spent days trying to force a good fit for all the material into a single document. I have put that aside for a while. So these discussions will be broken into several parts. At some future time I might try to tie all the pieces together by use of HTML/PDF.
Mass and Energy Conservation
When the basis of the mathematical models used in AOLGCM models/codes are discussed it is almost always stated that the ‘fundamental laws of conservation and mass and energy’ are at the foundations of the models. This is an incomplete, and somewhat incorrect, statement on several levels.
Conservation of mass and energy is the focus of the following discussion.
Chaos Part 1: A Long Time Coming
This work is taking longer than I expected; my experience has been that research is like that.
Plus, writing documentation sufficient for independent verification is hard, because writing is hard. Writing lots of information takes lots of time.
Plus, the moto riding season is here.
Plus vacation time is here.
Editorial Policies of Scientific Journals
The recent results of an Independent Verification of a calculation at Climate Audit and discussed here brings me to mention the editorial policies of scientific journals relative to Verification, Validation, Software Quality Assurance, and Qualfications of models, methods, software, calculations, users, and applications. I have posted comments about the issues relative to publication of peer-reviewed papers on several blogs and given more detailed discussion here.
According to the results of a very unscientific survey by me, the scientific journals have no interest in these very important issues. Many engineering journals, however, have addressed the problems and developed editorial appropriate policies which must be met by authors.
A little over two years ago I wrote letters to the editors of several scientific journals in which the climate change community publishes papers. I have uploaded an example of the letter.
I think it’s time to followup on that letter, for a second time. Continue reading
Coding Guidelines and Inline Documentation: GISS ModelE
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.
Verify the Calculation: An Example
The calculation requires Independent Verification. The calculation includes the coding, the data provided to the code at run time, built in options chosen by the user at run time, and the qualifications of the user.
An excellent example has been provided by the work over on Climate Audit. The results of the excellent work by Climate Audit is being discussed at Climate Science.
The example started with this, which led to this, and leading finally to this.
An excellent piece of Independent Verification accomplished without the benefit of source coding, and actually without any publicly available equations whatsoever. Exactly why the equations and codes are kept secret from the people who paid for them is another very significant issue. Keeping models, methods, procedures, and associated source code secret is not a part of the accepted scientific method.
Verify the Coding: A Couple of Examples
A couple of interesting examples of real-world failures here and here. Verify the calculation, also, of course. Additional discussions of the latter are here.
Chaos and Butterflies yet again
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.
Models Methods Software 