Improvement of the semi-Lagrangian advection scheme in the GRAPES model: Theoretical analysis and idealized tests

Abstract

The Global/Regional Assimilation and PrEdiction System (GRAPES) is the new-generation numerical weather prediction (NWP) system developed by the China Meteorological Administration. It is a fully compressible non-hydrostatical global/regional unified model that uses a traditional semi-Lagrangian advection scheme with cubic Lagrangian interpolation (referred to as the SL_CL scheme). The SL_CL scheme has been used in many operational NWP models, but there are still some deficiencies, such as the damping effects due to the interpolation and the relatively low accuracy. Based on Reich’s semi-Lagrangian advection scheme (referred to as the R2007 scheme), the Re_R2007 scheme that uses the low- and high-order B-spline function for interpolation at the departure point, is developed in this paper. One- and two-dimensional idealized tests in the rectangular coordinate system with uniform grid cells were conducted to compare the Re_R2007 scheme and the SL_CL scheme. The numerical results showed that: (1) the damping effects were remarkably reduced with the Re_R2007 scheme; and (2) the normalized errors of the Re_R2007 scheme were about 7.5 and 3 times smaller than those of the SL_CL scheme in one- and two-dimensional tests, respectively, indicating the higher accuracy of the Re_R2007 scheme. Furthermore, two solid-body rotation tests were conducted in the latitude-longitude spherical coordinate system with nonuniform grid cells, which also verified the Re_R2007 scheme’s advantages. Finally, in comparison with other global advection schemes, the Re_R2007 scheme was competitive in terms of accuracy and flow independence. An encouraging possibility for the application of the Re_R2007 scheme to the GRAPES model is provided.