## 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.

## A Short Summary of Future Discussions

The chaotic phenomenology of small systems of non-linear ODEs is entirely numerical ODE chaos. And, the original Lorenz system of 1963 contains no physical phenomena or processes of interest in NWP and AOLGCM applications.

## A Start on a V&V and SQA Bibliography

Here is a start on a bibliography for V&V and SQA books and articles.

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## Lack of Convergence, Under-Resolution, and Numerical Errors

**The Basic Hypotheses**

The following is well known but because it is the focus of this discussion I list it for handy reference.

**Convergence is Paramount; Nothing else Counts**

The fundamental objective of numerical solution of systems of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs) is to ensure that the approximations made in order to solve the equations do not in fact influence the solutions. In the case of systems of algebraic equations, it must be shown that the stopping criteria applied to iterative solution methods does not influence the accepted solutions. The solutions are independent, to an acceptable level, of the stopping criteria, and the calculated numbers satisfy the equations.

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