Stable recurrent calculation of isotropic Gaussian filter coefficients

Abstract Filtering in the spherical harmonic domain has become a common practice for the post-processing of GRACE temporal gravity field solutions. The most frequently used filtering technique to suppress correlated errors in GRACE data is the isotropic Gaussian averaging filter. In this study, we revisit the methods for calculating isotropic Gaussian filter coefficients (i.e., forward recurrence relation and numerical integration) and address some open problems regarding their implementation. We focus on the instabilities of the forward recurrence relation and the limited accuracy of numerical integration. We also propose alternative expressions for the stable recurrent calculation of isotropic Gaussian filter coefficients. These expressions are also more accurate and more computationally efficient than numerical integration.