张蕾,邱崇践,张述文. 2009. 在四维变分同化中运用集合协方差的试验[J]. 气象学报, 67(6):1124-1132, doi:10.11676/qxxb2009.108
在四维变分同化中运用集合协方差的试验
Experiments on the 4D variation wi th ensemble convariances
  修订日期:2008-11-13
DOI:10.11676/qxxb2009.108
中文关键词:  资料同化,背景误差协方差,四维变分,预报集合,奇异值分解
英文关键词:Data assimilation, Background error covariance, 4D variation , Ensemble forecasts, Singular value decomposition
基金项目:国家高技术研究计划(863计划)(2007AA12Z140),国家自然科学基金项 目(40875063、40775065)和科技部公益性行业(气象)科研专项(GYHY200806029)
作者单位
张蕾 半干旱气候变化教育部重点实验室兰州大学大气科学学院兰州730000 
邱崇践 半干旱气候变化教育部重点实验室兰州大学大气科学学院兰州730000 
张述文 半干旱气候变化教育部重点实验室兰州大学大气科学学院兰州730000 
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中文摘要:
      利用浅水方程模式和模式模拟资料进行数值试验比较3种不同的背景误差协方差矩阵 处理方法对四维变分(4DVAR)资料同化的影响。3种背景误差协方差矩阵分别是:(1)对单 一变量将背景误差协方差矩阵简化为对角矩阵;(2)将背景误差协方差矩阵的作用简化为 高斯过滤;(3)由预报集合生成背景误差协方差矩阵并利用奇异值分解技术解决矩阵的求 逆。 通过一系列数值试验,比较不同观测密度、不同观测误差下3种背景误差协方差处理方 法对4DVAR同化效果的影响。 结果表明,背景误差协方差的结构对4DVAR有重大影响。当观 测资料的空间密度不够高时,采用对角矩阵得不到满意的结果。 高斯过滤方案可以明显改 善同化结果,但是对背景误差特征长度比较敏感。 第3种方法采用的背景误差协方差矩阵是 流型依赖的,而且并不以显式的方式出现在目标函数中, 避免了对它求逆的复杂运算。 由于做了降维处理,在观测点的密度较低和观测误差较大时可望取得较好的同化结果, 同化效果较为稳定。
英文摘要:
      Using the two dimensional shallow water equation model and model simulated dat a, a set of numerical experiments were conducted to evaluate the im pacts of three different specification schemes of the background error covarianc e matrix on the four dimensional variational (4DVAR) data assimilation in the c a se of different observation densities and observation errors. The three schemes are as follows: (1)for a single control variable, the background error covarian ce is assumed to be a diagonal matrix; (2) the background error covariance is si mplified to a Gaussian form with the homogeneous and isotropic assumptions; (3) the background error covariance is restructured through using the ensemble forec asts and the solving of the inverse of the background error covariance matrix is carried out by using the singular value decomposition (SVD) technique. The resu lts show that the background error covariance plays an important role in 4DVAR d ata assimilation. When the observational spatial density is not high enough, the re is no satisfied analysis available if the background error covariance matrix is simply reduced to a diagonal matrix. The Gaussian filter scheme has the abili ty to improve the analysis accuracy, but this it is sensitive to the length scal e of background error correlations. The third method shows a stable performance. In this method, the background error covariance matrix is calculated implicitly so the computation of the inverse of background error covariance matrix is avoi ded. When observations are sparse or large errors exist in the observations, the third method will behave better compared to the other two methods.
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