作为非线性动力系统问题的资料同化：预报同化系统的稳定性和收敛
Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system
摘要：
我们研究预测同化系统，这已经成为常规的气象学和海洋学，并迅速蔓延到地球科学和连续物理学的其他领域。这样一个系统的长期，非线性稳定性导致其顺序估计的解决方案的唯一性，并需要这些解决方案的收敛到系统的真实，混沌演化。我们的方法的关键思想说明了一个线性化的洛伦兹系统。两个非线性预报同化系统的稳定性动力气象学研究下，通过完整的频谱的李雅普诺夫指数，这两个系统是由一个大的一组普通和偏微分方程，分别。数据诱导稳定的程度对于这样的系统的性能至关重要。这一程度又取决于两个关键因素：（i）观测网络，无论是固定的还是数据自适应的;（ii）同化方法。
英文摘要：
We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive; and (ii) the assimilation method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
