This research has been funded by 1) NOAA’s THORPEX program and 2) the NOAA Hurricane Forecast Improvement Program. We are grateful for the work of Dave Parrish (NCEP) for leading the implementation of the hybrid software in GSI, John Derber (NCEP) for optimization of the EnKF, and Xuguang Wang (University of Oklahoma) for contributions to the hybrid development.
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The computation of the equivalent grid spacing for a given triangular truncation can be somewhat ambiguous. A nominal equivalent grid spacing depends on whether the model forecast is transformed from its spectral basis to a linear or to a Gaussian grid. A truncation at wavenumber M on a linear grid (ECMWF’s approach) uses 2M + 1 grid points around a latitude circle; a Gaussian grid (NCEP’s approach) uses 3M + 1 grid points. Use of the Gaussian grid eliminates aliasing errors during the computation of the products of two or more truncated spectral harmonic expansions but otherwise does not provide a finer discretization and more resolution. For more information, see Durran (1998, section 4.4.3). The equivalent grid spacing calculations here assume 111 kilometers per degree × cos(latitude) for the number of kilometers per degree at a given latitude.