Abstract: Based on spherical wavelet, a new model of background error covariance （B） in global variational data assimilation system is designed and implemented. The frame theory is introduced, which is used to construct the basis functions of spherical wavelet. A model of B-matrix is designed based on spherical wavelet transform. The validity of the new method to model global B-matrix with spherical wavelet is demonstrated by numerical and simple experiments. The results of experiments show that the method has the ability to filter the sample noise from limited number of background error member effectively and to estimate the background error correlation functions correctly.

Key words: background error covariance, spherical wavelet, variational data assimilation, numerical weather prediction

摘要： 在全球变分资料同化系统中设计和实现了基于球面小波的背景误差协方差（B）模型。引入框架理论构造了球面小波函数；设计了一个基于球面小波变换的全球B矩阵模型；分别通过理想数值试验和在全球变分同化系统中的实现对新模型的有效性进行了验证。试验结果表明：基于球面小波的背景误差协方差模拟方法能够克服由有限背景误差样本引入的取样噪声，能估计出真实的背景误差相关函数；在全球变分同化系统中新模型能够模拟出在物理和动力上正确和有效的背景误差结构函数。

关键词: 背景误差协方差, 球面小波, 变分资料同化, 数值天气预报