Hann-Ming Henry Juang
Environmental Modeling Center, NCEP, Washington, DC
There are two kinds of forcing terms in numerical atmospheric and oceanic modeling which limit numerical time step for model integrations; one is the advection term, the other is the high-frequency forcing term. The method of semi-Lagrangian advection has been used in atmospheric numerical modeling for decades to avoid the numerical instability with large time step. And the semi-implicit time scheme has been used to handle the high-frequency mode with large time step as well. For global spectral model and some other global/regional models, these two methods are using together. However, these two methods target to two different forcing terms. Since semi-implicit time scheme partitions forcing into past time and future time, there is nothing related to location. Nonetheless, while applying semi-Lagrangian advection scheme, the locations of Lagrangian forcing determine the locations to formulate semi-implicit scheme. And it is more convenient to use departure and arrival points to partition the semi-implicit scheme together with semi-Lagrangian advection.
Since semi-Lagrangian and semi-implicit schemes target two different forcing terms, as mentioned, it may not necessary to formulate them together. An idea of treating semi-Lagrangian scheme as numerical method to compute advection forcing then apply semi-implicit scheme at model grid without considering departure and arrival points have been developed. In this method, the advection is computed as Eulerian forcing using semi-Lagrangain advection method to avoid the numerical instability, and semi-implicit time scheme as original configuration (at model grid) to avoid high frequent modes. This configuration has been implemented into NCEP global spectral model and whole atmospheric model with success. The results show very reasonable prediction with larger time step as compared to Eulerian scheme. Further comparison to traditional semi-Lagrangian semi-implicit scheme is under way. The advantage of this method is to provide easy implementation of semi-Lagrangian advection to any existed models without a complicated recoding.