A forward-trajectory global semi-Lagrangian transport scheme

A forward-trajectory semi-Lagrangian scheme for advection on the surface of the sphere is proposed. The advection scheme utilizes the forward (downstream) trajectory originating at Eulerian grid points and cascade interpolation, a sequence of 1D interpolations, to transfer data from the downstream Lagrangian points to the Eulerian points. A new and more accurate algorithm determines pole values. The resulting forward-trajectory semi-Lagrangian scheme can easily incorporate high-order trajectory integration methods. This avoids the standard iterative process in a typical backward-trajectory scheme. Two third-order accurate schemes and a second-order accurate scheme are presented. A mass-conservative version of the forward-trajectory semi-Lagrangian scheme is also derived within the cascade interpolation framework. Mass from a Lagrangian cell is transferred to the corresponding Eulerian cell with two 1D remappings through an intermediate cell system. Mass in the polar region is redistributed by way of an efficient local approximation. The resulting scheme is globally conservative, but restricted to meridional Courant number, Cθ⩽1.