Generalized Adams–Bashforth time integration schemes for a semi‐Lagrangian model employing the second‐derivative form of the horizontal momentum equations

We present a generic class of semi-implicit time-integration methods, the ‘Generalized Adams–Bashforth’ schemes, for the simultaneous treatment in a semi-Lagrangian model of the equations of horizontal momentum and kinematics in a rotating environment. The salient feature of the approach is that it deals directly with Lagrangian parcel momentum in terms of the parcel's second time-derivative of position. The classical Adams–Bashforth methods can be generalized to accommodate equations of second-derivative form and, as we demonstrate, can be formulated in such a way that the further important refinement of a semi-implicit handling of the fastest gravity modes follows in a natural way. The principal advantages expected of this unified approach over the more conventional separate semi-Lagrangian treatment of kinematics and momentum are: (i) greater economy of storage at a given order of accuracy, (ii) smaller truncation errors at a given order of accuracy. Tests were run with a full-physics three-dimensional regional semi-Lagrangian forecast model applied on a daily basis to archived operational data over a period of three months. Verifications based on the 48 hour forecasts confirm that the expected benefits of the new schemes are also realized in practice.

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