The Stability And Application Of Semi-Implicit Time Integration Scheme In Numerical Weather Prediction Model

Global atmospheric hydrostatic spectral model is one of the heatedly discussed topics in most numerical forecast centers, for it's high forecasting accuracy for global Macro-scale general circulation, and it is also the basis and of new generation global non-hydrostatic spectral model. The dynamical framework for the global spectral model is one of most key issues to exploit the model, including the selection of model equations, the discretization in space and the time integration scheme. Semi-implicit time integration scheme is being widely employed by many forecasting models for its better stability and longer time steps, but the topic on its stability is remaining a hot spot, because the improvement of its stability can improve the accuracy of the prediction, increase the time step and then improve the computing efficiency. Therefore, stability analysis is a vital phase during the design of a semi-implicit time integration scheme for global spectral models and it also provides meaningful references to the design of a model dynamical framework.Semi-implicit time integration scheme is a time integration scheme with implicit treatment for linear terms and explicit treatment for nonlinear residual terms. Before the application of semi-implicit scheme, the model equations should be linearized around an ideal reference atmosphere to separate linear terms and nonlinear residual terms. The Helmholtz equations related to model prediction variables can be obtained after the application of semi-implicit scheme, then the prediction model systems can be integrated and resolved.The implicit formulation is unconditional stable and the explicit formulation is conditional stable. From the design principle of the semi-implicit time integration scheme, it is known that the stability is determined mainly by the design of the explicit formulation for the nonlinear residual terms, in which the reference temperature is the most important parameters. The stability analyses model for time integration scheme based on harmonic wave analysis also shows that the stability is related to the selection of model prediction variables, the design of explicit formulation, the horizontal and vertical resolutions, reference atmosphere and time step. So the reference temperature is the most important factor for the stability of semi-implicit scheme.With the constant reference temperature replaced by a new one which varies vertically but remains constant horizontally and is warmer than actual atmosphere in the present model, there derive obvious improvement to the hydrostatic global spectral model, GSM T511. The numerical experiments show that, both of the modified model and original model have good performance on the prediction of global Macro-scale general circulation and global temperature, but the modified model is better on the prediction of circumpolar latitude circulation and top-layer temperature at the 10 th days, it also have a obvious promotion on the prediction accuracy of Height under 200 h Pa. And the modified model rectifies the diffuse tendency of total energy which exists in the original model and have better performance on stability, especially for longer time step to 1800s.