Additional methods for the stable calculation of isotropic Gaussian filter coefficients: The case of a truncated filter kernel
The isotropic Gaussian filter is frequently used as a post-processing method for mitigating errors in Gravity Recovery and Climate Experiment (GRACE) time-variable gravity field solutions. It is known that the recurrent calculation of isotropic Gaussian filter coefficients in the spherical harmonic domain results in numerical instabilities. This issue has been recently resolved by Piretzidis & Sideris (Computers & Geosciences 133:104303) for the case of a global Gaussian filter. In this paper, we extend this work for the case of a regional Gaussian filter (i.e., a Gaussian filter with a truncated kernel). We show that instabilities also occur when the coefficients of a regional Gaussian filter are calculated using a conventional recurrence relation, and we provide methods for their proper treatment. We also briefly present some theoretical preliminaries related to recurrence relations and examine algorithms (i.e., initial value and boundary value algorithms) for their stable evaluation. Our analysis indicates that the initial value algorithms are ineffective for the calculation of regional Gaussian filter coefficients, contrary to the global Gaussian filter. The comparison of the boundary value algorithms shows that the Thomas and lower-upper (LU) decomposition algorithms are the most suitable for this case. Their main advantage is their insusceptibility to numerical limitations, such as overflow errors. The Thomas algorithm is also the most efficient in terms of computational speed.