Economical Determination of Departure Points for Semi-Lagrangian Models

An Eulerian procedure that avoids both interpolation and iteration is proposed for determining the departure points of trajectories. It is applicable to semi-Lagrangian models formulated either on the plane or on the sphere. The technique can achieve a high degree of accuracy; it is also simpler and more economical than other schemes, especially when applied on the sphere. The technique is applied to the cone advection test on the plane, as well as to a “Gaussian hill” problem on a rotating sphere.