自适应分辨率全球正压准地转小波谱模式之研究

Abstract The goal of this term is to construct a barotropic spectrum.model applying the wavelet technique. First we investigated the properties of several wavelet bases,Daubechies wavelet,symmetric wavelet, Coifman wavelet and biorthogonal wavelet, and found that the biorthogonal wavelet is superior than the others in data compression and reconstruction. It can significantly attenuate the Gibbs phenomenon.Second, the wavelet bases were applied in building the interpolation.6 interpolation methods, including Fourier, cubic spline,.linear,Shanonn and cubic spline wavelet interpolation, were numerically studied for frequency-limited and general signals. It turned out that the cubic spline and wavelet interpolation are better than the rest among the six methods. Their interpolation accuracy is about the same within the interval or domain considered, while the.cubic spline’s is much better than the wavelet’s in the boundaries. It.shows the defect of the wavelet interpolation for bounded signal or.function, which implies the request of the wavelet basis defined on an.interval or an area with complex bounds.Finally, we employed the wavelet basis in the development of.numerical spectrum model for barotropic atmosphere. The periodic wavelet basis is our choice for constructing the spectrum model. Based on the Daubechies scale basis we made a low-order wavelet spectrum model and simulated the propogation of Rossby wave in a β-plane channel.Furthermore we developed Charney barotropic model with diserpation,diabetic heating and topography into a wavelet-based spectrum model with several new techniques we made. A series of numerical experiments were performed and the results were compared with Charney’s resolution in 1981..Besides, the Sideways heat equation is regularized and completely proved by wavelet method. This work indicates the defect in Reginska’s article and modified her results.

设计具有自适应分辨率的b平面和球坐标系的准地转小波谱模式,需要研究小波基的选取,地文夂系募妓瓜窒?负地形问题,边界问题,格谱转换问题,球小波--加辽金方法,时空分辨率的协调及南北极点的处理等内容.这些问题的解决将为设计全球初始方程小波谱模式,有限区域中小尺度小波谱模式,乃至大洋环流小波谱模式奠定了基础.