Abstract:The quality of atmosphere de-aliasing models significantly impact the precision of GRACE temporal gravity field models. Improvement of atmosphere de-aliasing models will benefit the exact signal extraction of Earth mass changes from GRACE satellites. As spherical harmonic analysis is the main process to convert atmosphere pressure into atmosphere de-aliasing models, this paper deduces five kinds of spherical harmonic analysis formulae that can be adapted to the computation of atmosphere de-aliasing models based on the analytic integral formulae. Simulated data,with or without white noise,are used to verify the validity and effectiveness of five spherical harmonic analysis methods by closed loop processes. Five atmosphere de-aliasing models are calculated based on the combination of ERA-interim surface pressure data and five spherical harmonic analysis approaches. Using the comparison of inter-satellite range rate residuals and cumulative geoid height errors, we verify that different spherical harmonic analysis methods can lead to variability of range rate residuals up to 0.6 nm/s and that the first Neumann method has the highest precision. It can be recognized that the impact of five spherical harmonic analysis methods on the state-of-the-art GRACE satellite gravity field recovery could be negligible, while the first Neumann method is recommended to compute atmosphere de-aliasing models for future satellite gravity missions with laser ranging measurements.