投影阴影法数据同化
Projected Shadowing-based Data Assimilation
AI总结：
本文提出基于计算时间依赖稳定/不稳定分裂的数据同化算法，结合阴影细化与同步技术，通过Lyapunov指数/向量计算投影非稳定子空间，扩展参数估计并适应观测不全的情况，利用 Lorenz 63 和 96 模型验证方法有效性。
摘要：
本文开发了基于计算时间依赖稳定/不稳定分裂的数据同化算法。我们的方法基于阴影细化和同步技术，受不稳定子空间同化（AUS）和伪轨道数据同化（PDA）工作启发。算法利用时间依赖投影到由Lyapunov指数/向量确定的非稳定子空间。方法扩展到参数估计而不改变问题动态，并讨论在观测不全时的适应技术。通过Lorenz 63和Lorenz 96模型的分析和数值实验，展示技术的有效性，并表明结果优于其他变分技术。
英文摘要：
In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by work on Assimilation in the Unstable Subspace (AUS) and Pseudo-orbit Data Assimilation (PDA). The algorithm utilizes time dependent projections onto the non-stable subspace determined by employing computational techniques for Lyapunov exponents/vectors. The method is extended to parameter estimation without changing the problem dynamics and we address techniques for adapting the method when (as is commonly the case) observations are not available in the full model state space. We use a combination of analysis and numerical experiments (with the Lorenz 63 and Lorenz 96 models) to illustrate the efficacy of the techniques and show that the results compare favorably with other variational techniques.
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