3-DIMENSIONAL MASS-CONSERVING SEMI-LAGRANGIAN SCHEME EMPLOYING FORWARD TRAJECTORIES

Through the use of the dimensional splitting ''cascade'' method of gri d-to-grid interpolation, it is shown that consistently high-order-accu rate semi-Lagrangian integration of a three-dimensional hydrostatic pr imitive equations model can be carried out using forward (downstream) trajectories instead of the backward (upstream) trajectory computation s that are more commonly employed in semi-Lagrangian models. Apart fro m the efficiency resulting directly from the adoption of the cascade m ethod, improved computational performance is achieved partly by the se lective implicit treatment of only the deepest vertical gravity modes and partly by obviating the need to iterate the estimation of each tra jectory's location. Perhaps the main distinction of our present semi-L agrangian method is its inherent exact conservation of mass and passiv e tracers. This is achieved by adopting a simple variant of the cascad e interpolation that incorporates mass (and tracer) conservation direc tly and at only a very modest additional cost. The conserving cascade, which is described in detail, is a generic algorithm that can be appl ied at arbitrary order of accuracy. Tests of the new mass-conserving s cheme in a regional forecast model show small but consistent improveme nts in accuracy at 48 h. It is suggested that the benefits to extended global forecasting and simulation should be much greater.