Semi-Implicit and Semi-Lagrangian integration scheme

The semi-implicit and semi-Lagrangian (SI-SL) algorithm is a computational algorithm that is widely used in numerical weather prediction models for the discretization of the equations governing atmospheric system. A Lagrangian description of a system (such as the atmosphere) focuses on following individual air parcels along their trajectories as opposed to the Eulerian description, which considers the range of change of system variables fixed at a particular point in space. A semi-implicit and semi-Lagrangian integration scheme uses Eulerian framework but the discrete equations come from the Lagrangian perspective.