David F. Parrish Abstract: A multigrid algorithm is adapted for direct computation of the product of a full correlation matrix with a vector. This is currently being tested at NCEP for initial application to generate 2-dimensional anisotropic correlations used by the NCEP RTMA (Real Time Mesoscale Analysis). The operational NCEP GSI (Gridpoint Statistical Interpolation) analysis program contains the RTMA application as an option. The recursive filter method is currently used in operations to generate anisotropic correlations for the RTMA. The recursive filter is very efficient, scaling linearly for arithmetic with the total number of grid points. However, a substantial amount of communication is required for MPI application. The next planned upgrade for the RTMA will no longer fit in the required time window, regardless of the number of processors used. One alternative is to evaluate the correlation on a coarser grid, interpolating the result back to the analysis grid. This is already done in the 3D NAM Hybrid Ensemble GSI, and works quite well. However, for the RTMA, there is interest in trying to reproduce fine details that might be lost by interpolation to a coarser grid.
The initial version of the multigrid algorithm has been coded for single processor use. However, it is very fast and there is no communication. It should be possible to use this in the next upgrade of RTMA, where many additional variables will be added. Even with the single processor version of multigrid, it can still take advantage of multiprocessing in this case by assigning each variable to its own processor. If the multigrid scheme proves to be an acceptable alternative for the RTMA, work will begin on a parallel version for future increases in resolution. Because this will be part of the GSI, it is expected that the multigrid scheme can also be used for static background and localization in 3D-4D applications.
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