Optimization of Spherical Harmonic Transform Computations

Spherical Harmonic Transforms (SHTs) which are essentially Fourier transforms on the sphere are critical in global geopotential and related applications. Discrete SHTs are more complex to optimize computationally than Fourier transforms in the sense of the well-known Fast Fourier Transforms (FFTs). Furthermore, for analysis purposes, discrete SHTs are difficult to formulate for an optimal discretization of the sphere, especially for applications with requirements in terms of near-isometric grids and special considerations in the polar regions. With the enormous global datasets becoming available from satellite systems, very high degrees and orders are required and the implied computational efforts are very challenging. The computational aspects of SHTs and their inverses to very high degrees and orders (over 3600) are discussed with special emphasis on information conservation and numerical stability. Parallel and grid computations are imperative for a number of geodetic, geophysical and related applications, and these are currently under investigation.