| Abstract: | The Asselin-Robert time filter used in the leapfrog scheme does degrade the accuracy of calculations. As an attractive alternative to leapfrog time differencing, the second-order Adams-Bashforth method is not subject to time splitting instability and keeps excellent calculation accuracy. A second-order Adams-Bashforth model has been developed, which represents better stability, excellent convergence and improved simulation of prognostic variables. Based on these results, the higher-order Adams-Bashforth methods are developed on the basis of NCAR (National Center for Atmospheric Research) CAM 3.1 (Community Atmosphere Model 3.1) and the characteristics of dynamical cores are analyzed in this paper. By using Lorenz nonlinear convective equations, the filtered leapfrog scheme shows an excellent pattern for eliminating 2Δt wave solutions after 20 steps but represents less computational solution accuracy. The fourth-order Adams-Bashforth method is closely converged to the exact solution and provides a reference against which other methods may be compared. Thus, the Adams-Bashforth methods produce more accurate and convergent solution with differencing order increasing. The Held-Suarez idealized test is carried out to demonstrate that all methods have similar climate states to the results of many other global models for long-term integration. Besides, higher-order methods perform better in mass conservation and exhibit improvement in simulating tropospheric westerly jets, which is likely equivalent to the advantages of increasing horizontal resolutions. Based on the idealized baroclinic wave test, a better capability of the higher-order method in maintaining simulation stability is convinced. Furthermore, after the baroclinic wave is triggered through overlaying the steady-state initial conditions with the zonal perturbation, the higher-order method has a better ability in the simulation of baroclinic wave perturbation. |
