GENERALIZED ADAMS-BASHFORTH TIME INTEGRATION SCHEMES FOR A SEMI-LAGRANGIAN MODEL EMPLOYING THE 2ND-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 treatm ent 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 classica l 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 h andling of the fastest gravity modes follows in a natural way. The pri ncipal advantages expected of this unified approach over the more conv entional 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 r un with a full-physics three-dimensional regional semi-Lagrangian fore cast 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 realiz ed in practice.