An Efficient Semi-Lagrangian Scheme Using Third-Order Semi-Implicit Time Integration and Forward Trajectories

Abstract A new method of implementing the semi-Lagrangian technique is presented in the context of a limited-area, barotropic primitive equation model. The most notable feature of the new method is the way in which the semi-Lagrangian advection is treated. Instead of the commonly used backward-trajectory approach, forward trajectories are computed to the next time level using a method formally equivalent to the application of the third-order in time Adams-Bashforth method and incorporating a robust semi-implicit treatment of fast gravity modes. Extensive comparisons between the new third-order in time forward-trajectory model, a second order forward-trajectory model, and two backward-trajectory schemes are made using the Australian Bureau of Meteorology Research Centre's regional barotropic model. A total of 100 cases is used to compare the methods, and they confirm in practice the theoretical superiority of the third-order method.