A semi-implicit semi-Lagrangian time integration schemes with a predictor and a corrector and their applications in CMA-GFS

A classical two-time level semi-implicit semi-Lagrange scheme (SISL) is used in CMA-GFS. Lagrange advection velocity and nonlinear terms are calculated by temporal extrapolation, which can cause computational instability and even integration interruption in large gradient areas such as the areas of jet. A SISL/P-C (predictor-corrector) algorithm is developed in CMA-GFS to reduce the impact of temporal extrapolation and construct a quasi-second order precision time discretization scheme by reducing the semi-implicit coefficients from 0.72 to 0.55. Results of idealized and real-data experiments show that this new scheme can effectively improve forecast accuracy, stability and conservation. The integration time step can be increased from 300 s to 450 s at 0.25° horizontal resolution, and the model calculation efficiency can be increased by 20%.