Azimuthal averaging -- Reconstruction filtering techniques for finite-difference general circulation models in spherical geometry

Numerical experiments have shown that the ring average technique introduces minimal artifacts in the polar region of general circulation model (GCM) solutions, which is a significant improvement compared to commonly used low-pass filtering techniques such as the fast Fourier transform method. Since the finite-difference adaption of the ring average technique is a post-solver type of algorithm, which requires no changes to the original computational grid and numerical algorithms, it has also been implemented in much more complicated models with extended physical-chemical modules such as the Coupled Magnetosphere-Ionosphere-Thermosphere (CMIT) model and the Whole Atmosphere Community Climate Model with thermosphere and ionosphere eXtension (WACCM-X).

The implementation of ring average techniques in both models enables CMIT and WACCM-X to perform global simulations with a much higher resolution than that used in the community versions. The new technique is not only a significant improvement in space weather modeling capability, but it can also be adapted to more general finite-difference solvers for hyperbolic equations in spherical and polar geometries.