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An Iterative Ensemble Kalman Smoother in Presence of Additive Model Error
SIAM/ASA Journal on Uncertainty Quantification ( IF 2 ) Pub Date : 2020-02-04 , DOI: 10.1137/19m1244147 Anthony Fillion , Marc Bocquet , Serge Gratton , Selime Gürol , Pavel Sakov
SIAM/ASA Journal on Uncertainty Quantification ( IF 2 ) Pub Date : 2020-02-04 , DOI: 10.1137/19m1244147 Anthony Fillion , Marc Bocquet , Serge Gratton , Selime Gürol , Pavel Sakov
SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 1, Page 198-228, January 2020.
Ensemble variational methods are being increasingly used in the field of geophysical data assimilation. Their efficiency comes from the combined use of ensembles, which provide statistics estimates, and a variational analysis, which handles nonlinear operators through iterative optimization techniques. Taking model error into account in four-dimensional ensemble variational algorithms is challenging because the state trajectory over the data assimilation window (DAW) is no longer determined by its sole initial condition. In particular, the control variable dimension scales with the DAW length, which yields a high numerical complexity. This is unfortunate since accuracy improvement is expected with longer DAWs. Building upon the work of [P. Sakov and M. Bocquet, Tellus A, 70 (2018), 1414545], this paper discusses how to algorithmically construct and numerically test an iterative ensemble Kalman smoother with additive model error (IEnKS-Q) which is thought to be the natural weak constraint generalization of the IEnKS [M. Bocquet and P. Sakov, Quart. J. Roy. Meteorol. Soc., 140 (2014), pp. 1521--1535], as well as the generalization of IEnKF-Q [P. Sakov, J. Haussaire, and M. Bocquet, Quart. J. Roy. Meteorol. Soc., 144 (2018), pp. 1297--1309] to general DAWs. The number of model evaluations per cycle of the IEnKS-Q is also examined. Solutions based on perturbation decomposition are proposed to dissociate those numerically costly evaluations from the control variable dimension.
中文翻译：
存在加性模型误差的迭代集成卡尔曼平滑器
SIAM / ASA不确定性量化期刊，第8卷，第1期，第198-228页，2020年1月。
集合变分方法正在地球物理数据同化领域中越来越多地使用。它们的效率来自提供统计估计的合奏和通过迭代优化技术处理非线性算子的变分分析的组合使用。在四维整体变分算法中考虑模型误差是具有挑战性的，因为数据同化窗口（DAW）上的状态轨迹不再由其唯一的初始条件确定。特别地，控制变量尺寸随DAW长度成比例，这会产生很高的数值复杂性。这是不幸的，因为期望使用更长的DAW可以提高准确性。建立在[P. Sakov and M. Bocquet，Tellus A，70（2018），1414545]，本文讨论了如何在算法上构造和数值测试带有加性模型误差（IEnKS-Q）的迭代集成卡尔曼平滑器，这被认为是IEnKS的自然弱约束推广。Bocquet和P. Sakov，夸脱。罗伊 陨石 Soc。，140（2014），pp.1521--1535]，以及IEnKF-Q的推广[P. Sakov，J。Haussaire，和M. Bocquet，Quart。罗伊 陨石 144（2018），pp。1297--1309] 还检查了IEnKS-Q每个周期的模型评估次数。提出了基于扰动分解的解决方案，以将那些在数值上昂贵的评估与控制变量维度分离。
更新日期：2020-02-04
Ensemble variational methods are being increasingly used in the field of geophysical data assimilation. Their efficiency comes from the combined use of ensembles, which provide statistics estimates, and a variational analysis, which handles nonlinear operators through iterative optimization techniques. Taking model error into account in four-dimensional ensemble variational algorithms is challenging because the state trajectory over the data assimilation window (DAW) is no longer determined by its sole initial condition. In particular, the control variable dimension scales with the DAW length, which yields a high numerical complexity. This is unfortunate since accuracy improvement is expected with longer DAWs. Building upon the work of [P. Sakov and M. Bocquet, Tellus A, 70 (2018), 1414545], this paper discusses how to algorithmically construct and numerically test an iterative ensemble Kalman smoother with additive model error (IEnKS-Q) which is thought to be the natural weak constraint generalization of the IEnKS [M. Bocquet and P. Sakov, Quart. J. Roy. Meteorol. Soc., 140 (2014), pp. 1521--1535], as well as the generalization of IEnKF-Q [P. Sakov, J. Haussaire, and M. Bocquet, Quart. J. Roy. Meteorol. Soc., 144 (2018), pp. 1297--1309] to general DAWs. The number of model evaluations per cycle of the IEnKS-Q is also examined. Solutions based on perturbation decomposition are proposed to dissociate those numerically costly evaluations from the control variable dimension.
中文翻译：
存在加性模型误差的迭代集成卡尔曼平滑器
SIAM / ASA不确定性量化期刊，第8卷，第1期，第198-228页，2020年1月。
集合变分方法正在地球物理数据同化领域中越来越多地使用。它们的效率来自提供统计估计的合奏和通过迭代优化技术处理非线性算子的变分分析的组合使用。在四维整体变分算法中考虑模型误差是具有挑战性的，因为数据同化窗口（DAW）上的状态轨迹不再由其唯一的初始条件确定。特别地，控制变量尺寸随DAW长度成比例，这会产生很高的数值复杂性。这是不幸的，因为期望使用更长的DAW可以提高准确性。建立在[P. Sakov and M. Bocquet，Tellus A，70（2018），1414545]，本文讨论了如何在算法上构造和数值测试带有加性模型误差（IEnKS-Q）的迭代集成卡尔曼平滑器，这被认为是IEnKS的自然弱约束推广。Bocquet和P. Sakov，夸脱。罗伊 陨石 Soc。，140（2014），pp.1521--1535]，以及IEnKF-Q的推广[P. Sakov，J。Haussaire，和M. Bocquet，Quart。罗伊 陨石 144（2018），pp。1297--1309] 还检查了IEnKS-Q每个周期的模型评估次数。提出了基于扰动分解的解决方案，以将那些在数值上昂贵的评估与控制变量维度分离。
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