Design and implementation of ultra-high-degree spherical harmonic model of earth topography

doi:10.11947/j.AGCS.2023.20220003

Abstract

Abstract: Aiming at solving the problems of calculation accuracy, stability and the large scale operations in the construction of 10 800 degree spherical harmonic of topography, the experiments were carried out. For the first part, Driscoll/Healy quadrature was proved to have higher computational accuracy by comparing and analyzing rectangular discrete quadrature, Gauss-Legendre quadrature and Driscoll/Healy quadrature. For the second part, a modified Belikov formula was given, which could make sure that fnALF is recursed to order 10 800 with better accuracy than 10^-12 in the full latitude range. Also, an optimization strategy was proposed for computing ultra-high-degree spherical harmonic coefficients by combining FFT and multi-core parallel technology based on OpenMP, which significantly improved the computational efficiency. For the last part, the 10 800 degree spherical harmonic model of topography, sph. 10 800_IEU, whose overall accuracy was similar to Earth2014_TBI2014.shc, was established by using the grid data of model Earth2014_TBI and model STO_IEU2020, however, its relative precision in the experimental areas was proved slightly better than that of model Earth2014_TBI2014.shc.

Key words: spherical harmonic model of topography, Gauss Legendre quadrature, Driscoll/Healy quadrature, rectangular discrete quadrature, FFT, OpenMP

CLC Number:

P223

SHAN Jianchen, LI Shanshan, FAN Diao, LI Xinxing, HUANG Yan, XING Zhibin. Design and implementation of ultra-high-degree spherical harmonic model of earth topography[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(5): 748-759.

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