Semi-implicit time-integrators for a scalable spectral element atmospheric model

The Naval Research Laboratory's spectral element atmospheric model (NSEAM) for scalable computer architectures is presented. This new dynamical core is based on a high-order spectral element (SE) method in space and uses semi-implicit methods in time based on either the traditional second-order leapfrog (LF2) or second-order backward difference formulas (BDF2). The novelties of NSEAM are: it is geometrically flexible and thereby can accommodate any type of grid; LF2 or BDF2 are used to construct the semi-implicit method; and the horizontal operators are written, discretized, and solved in three-dimensional Cartesian space. The semi-implicit NSEAM is validated using: five baroclinic test cases; direct comparisons to the explicit version of NSEAM which has been extensively tested and the results previously reported in the literature; and comparisons with operational weather prediction and well-established climate models. A comparison with the US Navy's spectral transform global forecast model illustrates that NSEAM is 60% faster on an IBM SP4 using 96 processors for the current operational resolution of T239 L30. However, NSEAM can accommodate many more processors while continuing to scale efficiently even at higher grid resolutions. In fact, we show that at T498 L60, NSEAM scales linearly up to 384 processors.