Recursive Filters as Covariance Operators on the Gnomonic Cubed Sphere

This paper investigates application of sequential spatial-recursive filters as the covariance operators on the equiangular cubed-sphere, the future grid framework for NCEP’s Global Statistical Interpolation (GSI) data assimilation system, which will accommodate the new dynamical core, FV3, developed at NASA/GSFC and NOAA/GFDL. At present, the recursive filters are used to generate global GSI covariances on overlapping orthogonal grids (two polar stereographic, sandwiching one nonpolar cylindrical). The equiangular gnomonic cubed-sphere offers a convenient modeling configuration with six faces of the cube that can naturally extend over each other, circumventing in that way edge and vertex singularities through grid interpolation and blending. The nonorthogonality of the grid can be addressed by using both normal and diagonal directions of the one-dimensional smoothers, similarly as it is already done in the NCEPS’s operational Real Time Mesoscale Analysis. Two main issues with this design are infinite impulse-response of the quasi-Gaussian smoothing with the recursive filters, and related to that, the scalability on the massively parallel computers. Several methods, including replacement of recursive filters with B-splines, are considered for a quasi-Gaussian smoother with the finite impulse-response, which should localize spatial covariance influence and reduce amount of data movement among processors. Another related feature under development is application of a “multigrid” strategy, which should improve scalability of the parallel computation keeping the sequential recursions local to processors through preconditioning at lower scales and blending between neighboring processing elements at higher scales.