Abstract The analysis error covariance is not readily available from four-dimensional variational (4dvar) data assimilation methods, not because of the complexity of mathematical derivation, but rather its computational expense. A number of techniques have been explored for more readily obtaining the analysis error covariance such as using Monte–Carlo methods, an ensemble of analyses, or the adjoint of the assimilation method; but each of these methods retain the issue of computational inefficiency. This study proposes a novel and less computationally costly, approach to estimating the 4dvar analysis error covariance. It consists of generating an ensemble of pseudo analyses by perturbing the optimal adjoint solution. An application with a nonlinear model is shown.

中文翻译：

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一组扰动分析来近似 4dvar 中的分析误差协方差

摘要 四维变分（4dvar）数据同化方法中的分析误差协方差并不容易获得，不是因为数学推导的复杂性，而是其计算成本。为了更容易地获得分析误差协方差，已经探索了许多技术，例如使用蒙特卡罗方法、分析集合或同化方法的伴随；但是这些方法中的每一种都存在计算效率低下的问题。这项研究提出了一种新颖且计算成本较低的方法来估计 4dvar 分析误差协方差。它包括通过扰动最优伴随解来生成一组伪分析。显示了具有非线性模型的应用程序。