中文摘要：

背景误差方差的集合估计值中带有大量采样噪声,在应用之前需进行降噪处理.区别于一般的高斯白噪声,采样噪声具有空间和尺度相关性,部分尺度上的噪声能级远大于平均能级.本文针对背景误差方差中采样噪声的特征,引入小波阈值去噪方法,并根据截断余项的小波系数分布特征发展了一种计算代价很小,能自动修正阈值的算法.一维理想试验结果表明,该方法能滤除大量采样噪声,提高背景误差方差估计值的精度.相对于原来的小波阈值方法,修正阈值后减少了因部分尺度上噪声能级过大导致的残差,去噪后的RMSE减少了13.28%.将该方法应用在实际的集合资料同化系统中,结果表明,小波阈值方法优于谱方法,阈值修正后能在不影响信号的前提下增大小波去噪强度.

英文摘要：

A large amount of sampling noise which exists in the ensemble-based background error variance need be reduced effectively before being applied to operational data assimilation system. Unlike the typical Gaussian white noise, the sampling noise is scaled and space-dependent, thus making its energy level on some scales much larger than the average.Although previous denoising methods such as spectral filtering or wavelet thresholding have been successfully used for denoising Gaussian white noise, they are no longer applicable for dealing with this kind of sampling noise. One can use a different threshold for each scale, but it will bring a big error especially on larger scales. Another modified method is to use a global multiplicative factor, α, to adjust the filtering strength based on the optimization of trade-off between removal of the noise and averaging of the useful signal. However, tuning α is not so easy, especially in real operational numerical weather prediction context. It motivates us to develop a new nearly cost-free filter whose threshold can be automatically calculated.According to the characteristics of sampling noise in background error variance, a heterogeneous filtering method similar to wavelet threshold technology is employed. The threshold, TA, determined by iterative algorithm is used to estimate the truncated remainder whose norm is smaller than TA. The standard deviation of truncated remainder term is regard as first guess of sampling noise. Non-Guassian term of sampling noise, whose coefficient modulus is above TA, is regarded as a small probability event. In order to incorporate such a coefficient into the domain of [-T, T ], a semi-empirical formula is used to calculate and approach the ideal threshold.Investigations are first conducted in a one-dimensional（1D） framework： several methods such as spectral filter,primal wavelet filter, optimal wavelet filter, and proposed filter are used to denoise the scale and space-dependent sampling noise in variance estimations. Their validity