Implementation of the SemiLagrangian Method in the Primitiveequations Model

The basic concept of the SemiLagrangian method was simply introduced,and then its concrete implementation in the primitiveequations model,especially in IFS model was presented.The idea of the Lagrangian advection is that an observer watches the world evolve around him as he travels with a fluid particle,and the key to its implementation is the calculation of the trajectory.Taking advantage of the spherical trigonometry and a higherorder approximation,the horizontal coordinates of the position for the midpoint and the departure point of the trajectory can be calculated directly in the spherical polar coordinates.To obtain the advantages of a semiLagrangian integration scheme,it was necessary to choose the order of the interpolation higher than fourthorder for the terms evaluated at the departure point.However,in order to avoid expensive cubic interpolation in three dimension,it was better to choose 3D "quasicubic" interpolation.

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