An Analysis of the Spectral Transform Operations in Climate and Weather Models

The spectral transform method used in climate and weather models is known to be computationally intensive. Typically accounting for more than 90% of the execution time of a serial model, it is poised to benefit from computational parallelism. Since dimensionally global transforms impact parallel performance, it is important to establish the realizable parallel efficiency of the spectral transform. To this end, this paper quantitatively characterizes the parallel characteristics of the spectral transform within an atmospheric modeling context. It comprehensively characterizes and catalogs a baseline of operations required for the spectral transform. While previous investigations of the spectral transform method have offered highly idealized analyses that are abstract and simplified in terms of orders of computational magnitude, this research provides a detailed model of the computational complexity of the spectral transform, validated by empirical results. From this validated quantitative analysis, an operational closed-form expression characterizes spectral transform performance in terms of general processor parameters and atmospheric data dimensions. These generalized statements of the computational requirements for the spectral transform can serve as a basis for exploiting parallelism.