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6. Summary

We have demonstrated the programming technique and the programming style for improving readability and modifiability of the programs, which have been considered and implemented through the development of the SPMODEL, a series of hierarchical spectral models for geophysical fluid dynamics. It has been shown that the program source codes can be written in a form similar to the mathematical expressions of the original governing equations by intensively applying array-operation features and user-defined array-valued functions of the Fortran90 features. By adopting the systematic naming conventions for data arrays and functions like these,

(data space identifier)_(variable name)
(output data space identifier)_(action)_(input data space identifier)

program source codes may be written in a form resembling the contraction convention of the tensor calculus. Since the spaces on which the input and the output data of the function are defined can be recognized from the function name, we can expect that the procedure of functional operation will become more recognizable, and consequently reduce the possibility of programming errors. It is also a great advantage that the source codes of the time integration part of the program can be written down in a form similar to the governing mathematical expressions, since the setup for utilizing the spectral method is hidden underneath. Some typical examples of programs of geophysical fluid models and their numerical results have been presented.

In the SPMODEL, the spaces on which argument array and the output of array-valued functions exist are recognized by the naming convention. One might suppose that this kind of problem could be more unfailingly solved by utilizing the features of programming language, that is, object-oriented programming. Since structure constructor is provided in Fortran90, defining the structures and their functions for corresponding data types appears to be an attractive solution. However, the language specification of Fortran90 is unsatisfactory for object-oriented programming. In particular, the fatal point is that inheritance of operations from the subclass modules is not supported so that every operation must be re-defined in the upper class modules. Therefore, we recommend here that, in Fortran90 programming, only the features of array operation enhanced from FORTRAN77 should be utilized, and not the structures. Sufficient benefit may be reaped just by wrapping existing library subroutines written in FORTRAN77 with array-valued functions of Fortran90.

The programming technique and style proposed here by the SPMODEL project are not restricted to the spectral method. For example, they are also applicable to the finite difference method. The programs can be developed in a form similar to the governing equations by defining array-valued functions for finite difference calculations corresponding to the derivatives. We are now coordinating a unified programming coding rule applicable in various classes of numerical models by evolving the SPMODEL programming style ([13]).

We have so far proposed a solution for improving readability and modifiability of programs among the necessary elements for achieving understandings by numerical calculations instead of equations and their mathematical manipulations listed in Section 1. The third point, convenience of visualization and post-processing is even more important. To solve this problem, we are now proposing a convention of the output data format, placing special emphasis on the post-processing and visualization (gtool4 netCDF convention[14]), and are in the process of developing a library to accomplish the output with this format (Appendix 2). By using this library, one can attach supplementary information for the post-processing and visualization, such as information of grid points, titles, and parameters for numerical experiments, to the main output data. The output netCDF gtool4 data can be visualized with 'GPhys', 'gave' and other utilities developed by the GFD Dennou Club Ruby project (Appendix 3). The figures of numerical results shown in Section 5 were produced using the software.

In this article, we have described our attempt in promoting shared understandings in the era of numerical calculations. However, understandings of the more complicated realistic models for meteorology and climate of Earth and planets that have been presented in recent years are not easily achieved even when the results of their numerical calculations are available. In order to achieve some level of understanding of the numerical results, it is necessary to associate the results with various conceptual understandings which have been obtained by models having simpler frameworks.

However, the rapid progress and increase in the complexity of the models for meteorology and climate tend to prevent us from establishing such an association, resulting in the formation of a gap between simulation and understanding ([17]). We are working to construct a computing environment for thinking in order to fill this gap by extending the framework of the SPMODEL from simple and ideal models for geophysical fluid dynamics to more complex and realistic models. Reduction in time and labor involved in the creation of a program from the governing equations allows us to develop and maintain a wide variety of models. Thanks to the unified style of the program codes, comparative numerical experiments between models having different approximation levels can be performed more readily. We are currently developing a series of models for such comparative research. We have presented simple models in a one-dimensional domain, models in two-dimensional planar, channel and spherical domains, a three-dimensional primitive model on a sphere and a Boussinesq fluid model in a spherical shell ([13]).

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