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Manuscript Title: Program to calculate the least-squares estimates of the spherical harmonic expansion coefficients of equally angular gridded scalar field.
Authors: Z. Martinec
Program title: SPHAN
Catalogue identifier: ABTU_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 64(1991)140
Programming language: Fortran.
Computer: SIEMENS.
Operating system: BS2000.
Keywords: General purpose, Fit, Associated Legendre function, Truncated spherical Harmonic expansion, Method of least squares Adjustment, Fast fourier transform Of mix-radix.
Classification: 4.9.

Nature of problem:
There is a wide range of applications of spherical harmonic analysis of regularly spaced data in reduction of global data set to spherical harmonic coefficients.

Solution method:
The spherical harmonic coefficients of a scalar field are estimated by the method of least squares adjustment of data values measured on the globe in an equal angular grid. For such a regular grid the normal matrix is sparse, and thus the system of the normal equations can be reordered into a series of sub-systems according to the angular order m. The solution of each sub-system is sought by NAG subroutines FO4ABF based on Cholesky's decomposition. The fast Fourier transform of mix- radix is implemented in setting up the right-hand sides of the normal equations as well as in spherical harmonic synthesis at which series of spherical harmonic is summed.

Running time:
For the number of the latitude circles NTH=90, the CPU-time is roughly 102 s for the cutoff degree JMAX=30, is about 260 s for JMAX=50, is about 522 s for JMAX=70, and is about 1100 s for JMAX=90.