To study the feasibility of goestatistical method on time series forecast, we use a section of Lorenz system for extrapolation and try to give a theoretic explanation. Numerical investigation points out that though Ordinary Kriging's(OK) solution resembles that of AR model. OK is better for forecast whether the series is stable or not. Universal Kriging's (UK) results present a drift which deviates from the real value obviously. Three experimental schemes were designed. In a comparison calculation of the ideal datum and meteorological datum, it indicates that the schemes is possible to improve the extrapolation accuracy. It lies on the characteristics of the series and needs further study.

Several interpolation methods and their applications are focused on on one and two dimension fields.There are six interpolation methods:Shannon,cubic spline,cubic convolution,linear,FFT and cubic spline wavelet interpolations.The last one is based on wavelet sampling without frequency bandlimits.Two one-dimensional signals,i.e.,Shannon interpolation basis function and single pulse,are interpolated by the six methods.It is indicated that the cubic spline is the best interpolation for the frequency-bounded signal(Shannon basis), while the cubic convolution interpolation is the most accurate one among them for the single pulse signal.;Numerical interpolations are carried out for three reanalysis data sets produced by NCEP,National Center for Environmnet Prediction of the United States.Numerical results show that the cubic spline wavelet interpolation is of the highest accuracy for the monthly rainfall field,where the cubic spline interpolation is the best one for the monthly geopotential height field and the sea surface pressure field.The linear and the cubic spline wavelet interpolations are combined to avoid the negative rainfall produced by almost all the interpolations except for the linear one.This method can raise the rainfall interpolation accuracy too.One problem left is that the wavelet interpolation could produce"quot;Gibbs phenomena" by the boundary although it is smaller and more localized than Shannon interpolation.This difficulty remains to solve.

A single pulse and peak signals are decomposed and reconstructed with four types of wavelet bases in different orders. Results demonstrate that the biorthogonal wavelet is of a best fitting to the signals, and the Coifman wavelet is at the last in the four bases. After truncating the expansion series of the wavelets and the Fourier transform, the reconstruction shows that the wavelet reconstruction got higher precision with less number of non-zero coefficients and the local error distribution compared with the Fast Fourier transform we calculated. Thus the wavelet reconstruction can greatly attenuate "Gibbs phenomenon" and limit the errors in a narrow domain around the singularities of the signals.Besides, we also make expansions for the topography of Tibetan plateau in wavelets and Fourier transform. Its reconstruction with or without truncation shows the similar features as the one-dimensional signal reconstruction above.