Stable recurrent calculation of isotropic Gaussian filter coefficients

Filtering in the spherical harmonic domain has become a common practice for the post-processing of temporal gravity field solutions derived from the Gravity Recovery and Climate Experiment (GRACE) satellite mission. The most frequently used filtering technique to suppress high-frequency noise in GRACE data is the isotropic Gaussian averaging filter. The implementation of the isotropic Gaussian filter in the spherical harmonic domain requires the calculation of filter coefficients, which is performed using either a forward recurrence relation, or numerical integration. Both methods show limitations, namely, the forward recurrence relation is numerically unstable and the numerical integration suffers from low accuracy. The objective of this study is to investigate these open problems more thoroughly and to provide alternative expressions for the calculation of isotropic Gaussian filter coefficients. We test three methods (i.e., backward recurrence, continued fraction and sweep algorithms) for the stable evaluation of three-term recurrence relations and examine their properties. All methods successfully solve the instability issues of the forward recurrence relation. They are also more accurate and more computationally efficient than numerical integration.