小波抽样与气象要素场插值

Wavelet Sampling and Meteorological Record Interpolation

首先用6种插值方法对一个带限与非带限一维信号分别进行等距插值计算检验.6种方法是基于Shannon抽样定理的插值法、两种基于小波抽样的插值法、三次样条插值法、三次卷积插值法和快速Fourier变换插值法.结果显示小波和三次样条插值法最好,其中小波插值误差的局域性最好.最差的是快速Fourier变换法.其次,剔除快速Fourier变换插值法,将其它5种插值公式推广到二维的情形,对大气层中层500hPa高度场、海平面气压场和降水量场也进行了插值计算.误差分析表明对于降水量场三次样条小波插值最好,对高度场和海平面气压场三次样条插值法仍然是最好的.在此基础上,提出了既保证降水量场插值精度又能避免插出"负降水"的插值处理方法并进行了计算检验.最后指出了小波插值法有待改进的问题.

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'Gibbs phenomena' by the boundary although it is smaller and more localized than Shannon interpolation.This difficulty remains to solve.