Spherical harmonic analysis and synthesis using FFT: Application to temporal gravity variation

FFT and complex algebra-based methods of spherical harmonic analysis and synthesis are presented. Two computer programs in FORTRAN are developed based on the methods. Both general and special cases are discussed. Special cases involve the analyses of gravity changes of the hydrological origin and the atmospheric origin. Functionals of the Earth's gravity field such as gravity anomaly and geoidal height can also be computed via synthesis. Thermal-corrected sea level anomaly from TOPEX/Poseidon and atmospheric pressure from ECMWF are used to compute changes of geopotential coefficients due to oceanic and atmospheric mass redistributions. Interesting phenomena in the changes of geopotential coefficients have been identified. The two computer programs can facilitate analyses and syntheses of gravity products from satellite missions such as GRACE.