Multispectrum Method and the Computation of Vapor Equation

In order to improve the practicality of spectral method and the efficiency of computation, the multi-spectrum method is proposed on the basis of multi-grid method. Coarse spectra are used to compute the slow nonlinear part (including physical process), while fine spectra are used to compute the fast linear part. This method not only can re-duce computation time, but also can obtain computational efficiency similar to that from only fine spectra. Thus, it is an economical numerical method. Both explicit complete-square-conservation scheme and multispectrum scheme are used to improve IAP L9 T42 spectral climate models, with and without physical forcings respectively, and the ad-vantage of reducing computation time is obtained satisfactorily. In order to overcome the difficulty that vapor equa?tion is very sensitive to the change of time step, the square-conservation semi-Lagrangian scheme is used to solve vapor equation. Because the semi-Lagrangian scheme has the property or square-conservation, computational in?stability can be avoided. When time step becomes longer with the semi-Lagrangian Scheme, through numerical ex?amples, the vapor transportation can be depicted objectively and the effect of precipitation simulation can be modi?fied.