Abstract
For the purpose of studying the atmospheric response (or sensitivity) to the seasonal forcing, we propose a time-space spectral general circulation model. In the present work we use a low-order equivalent Barotropic vorticity equation with forcing and dissipation terms. The original low-order equation consists of three-component in the space-spectral domain: one purely zonal component and two wave components with the same zonal wavenumber but different mode numbers. Further expanding this equation in the space-spectral domain into that in the time-spectral domain, we finally obtain a time-space spectral model, which is a simultaneous nonlinear algebraic equations system.
The model used in the present work consists of one steady and one periodic components in the time-domain. The nonlinear equations system is solved by using the "revised Marquardt method" (Levenberg-Marquardt-Morrison method) and a "Continuation method". Addition of the periodic forcing besides the steady forcing brings about a new stable solution together with the stable solutions corresponding to those under the steady forcing only. This multiplicity of solutions with the moderate intensity of steady and periodic forcings is very interesting for understanding climatic change, and suggests that we can expect to obtain useful results, by extending our model to a further larger timespace spectral general circulation model based on the above-mentioned numerical methods.
