The four-dimensional variational data assimilation (4D-Var) method has been widely employed as an operational scheme in mainstream numerical weather prediction (NWP) centers. In addition to the ensemble data assimilation method, the randomization technique is still used to diagnose the standard deviations of background error in variational data assimilation (VAR) systems; however, such randomization techniques induce sampling noise, which may contaminate the quality of the standard deviations. First, this paper studies the properties of the sampling noise induced by the randomization technique. The results show that the sampling noise is on a small scale displaying high-frequency oscillations around the estimate compared with the estimate and this difference motivates the use of filtering techniques to eliminate the sampling noise effects. The characteristics of the standard deviation field of the control variables are also investigated, and the standard deviation fields of different model parameters have different scales and vary with the vertical model levels. To eliminate such sampling noise, the spectral filtering method used widely in the operational system and a modified spatial averaging approach are investigated. Although both methods have splendid performance in eliminating sampling noise, the spatial averaging approach is more efficient and easier to implement in operational systems. In addition, the optimal filtered results from the spatial averaging approach are dependent on model parameters and vertical levels, which is consistent with the variation in the standard deviation field. Finally, the spatial averaging approach is tested on the operational system at the global scale based on the YH4DVAR and the global NWP system, and the results indicate that the spatial averaging approach has positive effects on both analysis and forecast quality.

中文翻译：

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长度刻度变化在诊断4D变量系统中背景误差的标准偏差时的影响和滤波方法研究

四维变异数据同化（4D-Var）方法已被广泛用作主流数值天气预报（NWP）中心的操作方案。除了集成数据同化方法外，随机技术仍用于诊断变异数据同化（VAR）系统中背景误差的标准偏差。但是，这种随机化技术会引起采样噪声，这可能会污染标准偏差的质量。首先，本文研究了随机技术引起的采样噪声的特性。结果表明，与估计值相比，采样噪声在小范围内显示出围绕估计值的高频振荡，并且这种差异促使使用滤波技术来消除采样噪声影响。还研究了控制变量的标准偏差场的特性，不同模型参数的标准偏差场具有不同的尺度，并随垂直模型水平的变化而变化。为了消除这种采样噪声，研究了在操作系统中广泛使用的频谱滤波方法和改进的空间平均方法。尽管这两种方法在消除采样噪声方面均具有出色的性能，但空间平均方法更有效且更易于在操作系统中实现。此外，空间平均方法的最佳滤波结果取决于模型参数和垂直水平，这与标准偏差字段中的变化一致。最后，