Selection of Momentum Variables for a Three-Dimensional Variational Analysis
Selection of Momentum Variables for a Three-Dimensional Variational Analysis
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DOI：
10.1007/s00024-011-0374-3
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发表时间：
2012-03
影响因子：
2
通讯作者：
Yuanfu Xie;A. MacDonald
中科院分区：
文献类型：
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作者：
Yuanfu Xie;A. MacDonald
气象变分分析的三个控制变量(3DVAR或4DVAR)与水平风有关：(1)流函数和速度势，(2)东向和北向速度，(3)涡度和散度。本文通过统计分析和数值试验，揭示了实际3DVAR资料同化中这些变量在理论和数值上的差异。本文证明：(A)流函数和速度势可能引入分析误差；(B)利用速度或涡度和散度的三维变分除协方差外，还提供一个自然尺度相关的影响半径；(C)对于区域分析，流函数和速度势是根据Neumann边界条件从背景速度场中提取的。不适当的边界条件可能导致进一步的分析误差；(D)使用导数作为控制变量的变分数据同化或反问题产生更平滑的分析，例如，使用涡度和散度作为控制变量的3DVAR得到的风分析比使用速度或流函数/速度势作为控制变量的3DVAR所获得的分析更平滑；(E)变量的高阶导数的统计误差更独立，例如，U和V之间的统计相关性小于流函数和速度势之间的统计相关性，因此，当变量之间的相互关系因效率或其他原因而被忽略时，高导数中的变量更适合于变分系统。综上所述，东向和北向速度或涡度和散度是变分系统较好的控制变量，前者因其数值效率而更具吸引力。利用解析函数和实际大气观测数据进行了数值实验。
Three choices of control variables for meteorological variational analysis (3DVAR or 4DVAR) are associated with horizontal wind: (1) streamfunction and velocity potential, (2) eastward and northward velocity, and (3) vorticity and divergence. This study shows theoretical and numerical differences of these variables in practical 3DVAR data assimilation through statistical analysis and numerical experiments. This paper demonstrates that (a) streamfunction and velocity potential could potentially introduce analysis errors; (b) A 3DVAR using velocity or vorticity and divergence provides a natural scale dependent influence radius in addition to the covariance; (c) for a regional analysis, streamfunction and velocity potential are retrieved from the background velocity field with Neumann boundary condition. Improper boundary conditions could result in further analysis errors; (d) a variational data assimilation or an inverse problem using derivatives as control variables yields smoother analyses, for example, a 3DVAR using vorticity and divergence as controls yields smoother wind analyses than those analyses obtained by a 3DVAR using either velocity or streamfunction/velocity potential as control variables; and (e) statistical errors of higher order derivatives of variables are more independent, e.g., the statistical correlation betweenUandVis smaller than the one between streamfunction and velocity potential, and thus the variables in higher derivatives are more appropriate for a variational system when a cross-correlation between variables is neglected for efficiency or other reasons. In summary, eastward and northward velocity, or vorticity and divergence are preferable control variables for variational systems and the former is more attractive because of its numerical efficiency. Numerical experiments are presented using analytic functions and real atmospheric observations.