Research On Basic Dynamical Framework Of Spectral Model

At present, spectral model is one of the widest applied numerical model in the research of numerical forecast and climatic variation simulation. To improve the precision and efficiency of spectral method can great contribute to developing numerical forecast. Furthermore, the most two key numerical algorithms for spectral model is consistent of numerical calculation method of nonlinear terms and semi-implicit time integration algorithm, which all are included in the spectral model dynamical framework. Study on the two aspects, however, is few in the late thirty years. In this study, one basic spectral model dynamical framework is designed on the basis of some important globe integral relations such as energy conservation and vorticity etc. Using the spectral dynamical framework, the research especially focuses on the most two key numerical algorithms mentioned above in an attempt to advance the spectral model. By theoretical analyses and contrasting experiments the comparing investigation also has been conducted between the new-designed spectral dynamical framework and the common framework used internationally. The following is the main results achieved:(1).Either on the physics or on numerical algorithm aspect, the new-designed spectral dynamical framework can satisfy a series of important physical variables' integral relations, such as energy, vorticity etc. Also, its numerical algorithms can be easily introduced into any one spectral model.(2).According to the principle of the nonlinear term calculation through degradation of demensionality, perfect spectral latitudinally and pseudo-spectral longitudinally methods, one new nonlinear terms calculating scheme suitable for any one spectral model is designed. The new scheme carries on degradation of demensionlity in zonal direction by exponential function, and spectral coefficient of each nonlinear term is calculated in Fourier space. Gauss grid also is used in mediation in order to realize high-algebra-precision Gauss numerical integration. In additional, using this new method the spectral coefficient of nonlinear term can work out without transform between the Fourier space and the gird space. So it can entirely avoid aliasing errors, and eliminate truncated errors introduced by the Fourier transform, these errors always exit in the transform method. Hence, by the new method these source of small errors in calculating nonlinear terms(for example,advection terms) of spectral model can be eliminated, and the calculating precision of nonlinear terms such as advection terms is improved. Besides, in the new spectral dynamical framework the calculation amount firstly is decreased to half by properly using the complex conjugate relation of spectral coefficients and the symmetric and anti-symmetric character of spherical function. Then in the new designed nonlinear calculation method considering the trait that the addition numerical calculation need more time than the multiplication, terms of the same kind probably existed is combined to enhance numerical calculation efficiency. The new designed spectral dynamical framework can be easily applied to either globe or hemi-spherical spectral model. So far as the spectral dynamical framework is concerned, its calculating amount has no significant difference with the transform method, but in numerical weather forecast and the simulating of climate, its calculating precision can be improved to some extent.(3). The new designed calculating scheme of nonlinear terms adopts perfect spectral method to represent meteorological variables. This is helpful to simulate the important nature of prevailing zonal movement in general circulation, and favor of more precisely modeling the nonlinear interaction between all weather scale systems. Contrasted with the transform method, it can simulate the distribution of westerly jets better.(4).For the new designed nonlinear term calculation, spectral model's total zonal grid design directly depends on the need of variable's zonal spectral evolution, not depends on whether or not it could resolute analytically the wavenumber of interaction between two nonlinear terms. Under the same wavenumber truncation, the new designed nonlinear term calculating scheme only need meet the condition / > 2M + 1 to avoid the aliasing errors of interaction between two nonlinear terms; However,the transform method must meet the condition I >3M + 1 (Here, / is the total number of zonal spacing-equivalent grid, and M is the zonal maximum truncation wavenumber). The nature is very important for both theory and practical application, it can help to cut down the sharp increasing calculating amount of spectral model, especially in developing high-resolution diabetic spectral model or in perfecting all kinds of physical parameterizations.(5). Moisture prognostic results is very sensitive to these small errors caused by calculating nonlinear terms(such as advection term). The important affect of nonlinear term calculating precision and stability can be apparent after integrating a very short time. Because the new designed scheme can improve the precision and stability on calculating the spectral coefficients of nonlinear terms in spectral model as compared with transform method, The new scheme has very important influence for spectral model in enhancing the simulating and forecasting of moisture balance.(6). In fact, the popular semi-implicit integration scheme of spectral model still includes some important linear terms difference by time explicit scheme. Furthermore, these terms are directly related with fast gravity waves in the forecasting equation. According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation, one new semi-implicit integration scheme also is designed. By adopting a kind of revised time-explicit-difference scheme to these linear terms still included in spectral model governing equations, this defect of spectral model only partly used in semi-implicit integrating scheme, can be overcome to some degree. By properly introduce a adjust coefficient, the time-step (computation stability) can be enlarged (increased), besides that the spectral coefficient of each prognostic variable can be gotten without any iteration.(7). With several objective analysis data as initial field, numerical experiments have been carried out by utilizing the new designed spectral dynamical framework and the popular framework on a worldwide basis, respectively. Results indicate that: Under the popular dynamical framework, the south(north) westerly shift in early summer May is more stronger(weaker) than observations, and the westerlies center above Japan also is simulated southward. However, better simulating results can achieved by using the new designed spectral dynamical framework. Additionally, the new designed framework can improve the computation precision and stability according to the differences between their 500hpa anomaly correlation coefficients of prognostic variables and energy curls.