Comparing hybrid data assimilation methods on the Lorenz 1963 model with increasing non-linearity
Comparing hybrid data assimilation methods on the Lorenz 1963 model with increasing non-linearity
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DOI：
10.3402/tellusa.v67.26928
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发表时间：
2015-05
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影响因子：
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通讯作者：
M. Goodliff;Javier Amezcua;P. V. van Leeuwen
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作者：
M. Goodliff;Javier Amezcua;P. V. van Leeuwen
我们系统地比较了ETKF-4DVAR、4DVAR- ben和4DENVAR在Lorenz 1963模型上与两种传统方法（4DVAR和ETKF）和集成变换卡尔曼平滑（ETKS）的性能。我们特别研究了增加非线性和使用准静态变分同化算法作为比较的这种性能。以分析均方根误差（RMSE）为度量标准，考虑(1)同化窗口长度和观测区间大小以及(2)集合大小，对这些方法进行比较，研究混合背景误差协方差矩阵和非线性对方法性能的影响。对于接近线性动力学的短同化窗，所有混合方法的均方根误差都比传统方法有所提高。对于较长的同化窗长度，其中非线性动力学是重要的，变分框架可能难以找到成本函数的全局最小值，因此我们探索了一种准静态变分同化（QSVA）框架。在混合方法中，可以看到，在一定的参数下，不使用气候背景误差协方差的混合方法不需要QSVA来准确执行。总体而言，结果表明，由于背景误差协方差矩阵完全依赖于流量，因此不使用带有QSVA的气候背景误差协方差矩阵的ETKS和混合方法优于所有其他方法，这也允许最大的非线性。
We systematically compare the performance of ETKF-4DVAR, 4DVAR-BEN and 4DENVAR with respect to two traditional methods (4DVAR and ETKF) and an ensemble transform Kalman smoother (ETKS) on the Lorenz 1963 model. We specifically investigated this performance with increasing non-linearity and using a quasi-static variational assimilation algorithm as a comparison. Using the analysis root mean square error (RMSE) as a metric, these methods have been compared considering (1) assimilation window length and observation interval size and (2) ensemble size to investigate the influence of hybrid background error covariance matrices and non-linearity on the performance of the methods. For short assimilation windows with close to linear dynamics, it has been shown that all hybrid methods show an improvement in RMSE compared to the traditional methods. For long assimilation window lengths in which non-linear dynamics are substantial, the variational framework can have difficulties finding the global minimum of the cost function, so we explore a quasi-static variational assimilation (QSVA) framework. Of the hybrid methods, it is seen that under certain parameters, hybrid methods which do not use a climatological background error covariance do not need QSVA to perform accurately. Generally, results show that the ETKS and hybrid methods that do not use a climatological background error covariance matrix with QSVA outperform all other methods due to the full flow dependency of the background error covariance matrix which also allows for the most non-linearity.