Coding Standards Finally Appear
Steve Easterbrook has provided a list of coding standards that are associated with some of the climate models. The first one is for the NASA / GISS ModelE model and code.
Professor Easterbrook states,
Two followup tasks I hope to get to soon – (1) analyze how much these different standards overlap/differ, and (2) measure how much the model codes adhere to the standards.
Here are a few leads relative to Task (2):
The first of these posts was written almost four years ago. The date on the NASA / GISS ModelE document is February 2010. I’m not hopeful that Better late than never will work out in this case. It’s very difficult to retro-fit coding standards to code that is several decades old.
Internal Variability=Weather and Numerical Artifacts
This post is based on some notes related to verification and numerical artifacts that I made back in early July.
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Validation is a Process
AOLBGCM validation is an ongoing process.
Can’t ever do too much of it.
Averaging Planet Earths or Averaging Planet Xs
Update January 23, 2011. I fixed the broken links.
There are several discussions floating around on the subject of comparing GCM-calculated numbers with experimental data. Climate Audit and Lucia both have several threads. There are too many threads to give links; let me know if you need a specific thread. One focus of these discussions is the ensemble-average approach that is considered to be necessary for the comparisons. The ensemble is made up of the results from the various different versions of GCMs that calculate the results. Not only are GCMs different from each other, but the suggested approach is to make perturbations in the initial conditions between the runs.
I have mentioned that the results do not reflect the effects of perturbations in only the initial conditions. Everything about the approach is different between the runs. The GCMs are based on different continuous-equation models, numerical solution methods, application procedures, run-time options, and users, and maybe other aspects. How can we be sure that the results are all appropriate for Earth?
Pattern Matching in GISS/NASA ModelE Coding
In a previous post I gave an illustration of how GISS/NASA employees have implemented new and innovative ways to produce inactive code using the capabilities provided by F90/95. I had run across the following statements in routine DIAG.f:
EWATER(J)=EWATER(J)+EL !+W*(SHV*T(I,J,L)*PK(L,I,J)+GRAV
! * *HSCALE*LOG(P(I,J)/PMID(L,I,J)))
The ‘!’ in the first line is going to be very difficult to remember it exists and correctly maintain. Someone might come along and say, “I wonder what that’s doing in the middle of an executable statement.” and promptly un-do the comment. Or un-do the comment of the second line while overlooking the comment in the first line. That would make a screw up on several levels.
Today I have found many more examples of innovative coding by employees of GISS/NASA. It is clear that the NASA Software Quality Assurance procedures are ignored by GISS/NASA. It is equally clear that there are no Software Quality Assurance procedures being applied to the GISS/NASA ModelE code. None.
Update November 2, 2008 down near the end.
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.
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.
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.
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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.
Models Methods Software 