Ensemble covariances adaptively localized with ECO-RAP. Part 2: a strategy for the atmosphere
Ensemble covariances adaptively localized with ECO-RAP. Part 2: a strategy for the atmosphere
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DOI：
10.1111/j.1600-0870.2007.00372.x
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发表时间：
2009-01
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影响因子：
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通讯作者：
C. Bishop;D. Hodyss
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文献类型：
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作者：
C. Bishop;D. Hodyss
摘要第1部分的定位方法，集合相关性提高到幂（ECO-RAP），被纳入局部集合变换卡尔曼滤波器（LETKF）中。由于蛮力合并将过于昂贵，我们证明了第1部分的协方差自适应本地化与ECO-RAP（CALECO）预测误差协方差矩阵的因式分解属性，连同其他简化，降低了成本。该属性廉价地提供了一个大的CALECO合奏，其协方差是CALECO矩阵。CALECO系综的每个成员是一个原始系综成员与ECO-RAP矩阵的平方根的一列之间的逐元素乘积。LETKF应用于CALECO系综而不是原始系综。该方法使大量的变量在每个观察体积内的更新，在很少的额外的计算成本。在合理的假设下，这使得CALECO和标准LETKF成本相似。CALECO LETKF不需要人为的观测误差膨胀或垂直限制的观测量，这两者都混淆了非本地观测，如卫星观测的同化。使用27个成员合奏从全球数值天气预报（NWP）系统，我们描绘了四维（4-D）流量自适应误差协方差定位和测试的能力，以减少分析误差的CALECO LETKF。
Abstract Part 1’s localization method, Ensemble COrrelations Raised to A Power (ECO-RAP), is incorporated into a Local Ensemble Transform Kalman Filter (LETKF). Because brute force incorporation would be too expensive, we demonstrate a factorization property for Part 1’s Covariances Adaptively Localized with ECO-rap (CALECO) forecast error covariance matrix that, together with other simplifications, reduces the cost. The property inexpensively provides a large CALECO ensemble whose covariance is the CALECO matrix. Each member of the CALECO ensemble is an element-wise product between one raw ensemble member and one column of the square root of the ECO-RAP matrix. The LETKF is applied to the CALECO ensemble rather than the raw ensemble. The approach enables the update of large numbers of variables within each observation volume at little additional computational cost. Under plausible assumptions, this makes the CALECO and standard LETKF costs similar. The CALECO LETKF does not require artificial observation error inflation or vertically confined observation volumes both of which confound the assimilation of non-local observations such as satellite observations. Using a 27 member ensemble from a global NumericalWeather Prediction (NWP) system, we depict four-dimensional (4-D) flow-adaptive error covariance localization and test the ability of the CALECO LETKF to reduce analysis error.