何光鑫,李刚,张华. 2011. GRAPES-3DVar高阶递归滤波方案及其初步试验[J]. 气象学报, 69(6):1001-1008, doi:10.11676/qxxb2011.087
GRAPES-3DVar高阶递归滤波方案及其初步试验
The scheme of high-order recursive filter for the GRAPES 3DVar with its initial experiments
投稿时间:2009-04-17  修订日期:2011-09-05
DOI:10.11676/qxxb2011.087
中文关键词:  变分同化, 各向同性, 特征尺度, 高阶递归滤波
英文关键词:Variational assimilation, Isotropy, Intrinsic scale, High order recursive filters
基金项目:公益性行业(气象)科研专项(GYHY200806003)、国家高技术研究发展计划863项目(2007AA12Z140)、国家重点基础研究发展计划973项目(2009CB421502),风云气象卫星遥感开发与应用示范项目(0806FiDAF106)
作者单位
何光鑫 南京信息工程大学数理学院南京210044 
李刚 南京信息工程大学数理学院南京210044 
张华 国家气象中心北京100081 
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中文摘要:
      背景误差协方差矩阵 B及其逆的求解是三维变分同化研究的核心问题之一。在GRAPES区域三维变分同化系统(GRAPES-3Dvar)中背景误差协方差矩阵的水平变换部分,假定各向同性并进行递归滤波运算。原有方案中采用一阶递归滤波器,但收敛不够迅速,每次循环同化时需滤波10次才能使目标函数收敛。根据Purser等2003年的研究思路,研究发展了针对GRAPES区域三维变分同化系统的高阶递归滤波方案;理想试验结果表明,使用四阶递归滤波仅需运行一次就能使目标函数收敛,滤波后的输出场呈现高斯型分布,达到计算精度要求,并且,滤波效果明显好于一阶递归滤波运行4次的结果。另外,为了使高斯型函数的功率谱接近大气实际的谱衰减,对3种不同特征尺度的四阶递归滤波器进行线性组合。通过实验表明,拟合后的多尺度四阶递归滤波在保持原有大尺度信息的基础上,更清晰地显示出了一些中小尺度的信息。
英文摘要:
      The background error covariance (B) and the calculation of the inverse of B are one of the core problems in the 3D variational assimilation. The recursive filter with the isotropic Gaussian covariance is applied to the horizontal transformation of the background error covariance in the GRAPES-3DVar system. In the original scheme, the one-order recursive filter does not converge fast enough, i.e. it should be utilized 10 times in order to make the objective function convergence. Using the method of Purser and Wu (2003a), this paper develops a high-order recursive filter suitable for the GRAPES 3DVar system. The results from the ideal experiments show that the objective function can ensure a quick convergence by using the fourth-order recursive filter only once. The resulting output field adheres better to the Gaussian distribution than the one developed by a continuous four times application of the simple first-order filter. Also, in order to make the power spectrum of Gaussian type function adhere closer to the spectrum attenuation of the actual atmospheric, a linear combination of three sequential four-order recursive filters with different intrinsic scales is carried out. The preliminary experimental results indicate that the new four-order recursive filter can show some mesoscale information clearly with the original largescale information retained.
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