Abstract. The stability properties as characterized by the fluctuations of finite-time Lyapunov exponents around their mean values are investigated in a three-level quasi-geostrophic atmospheric model with realistic mean state and variability. Firstly, the covariance structure of the fluctuation field is examined. In order to identify dominant patterns of collective excitation, an empirical orthogonal function (EOF) analysis of the fluctuation field of all of the finite-time Lyapunov exponents is performed. The three leading modes are patterns where the most unstable Lyapunov exponents fluctuate in phase. These modes are virtually independent of the integration time of the finite-time Lyapunov exponents. Secondly, large-deviation rate functions are estimated from time series of finite-time Lyapunov exponents based on the probability density functions and using the Legendre transform method. Serial correlation in the time series is properly accounted for. A large-deviation principle can be established for all of the Lyapunov exponents. Convergence is rather slow for the most unstable exponent, becomes faster when going further down in the Lyapunov spectrum, is very fast for the near-neutral and weakly dissipative modes, and becomes slow again for the strongly dissipative modes at the end of the Lyapunov spectrum. The curvature of the rate functions at the minimum is linked to the corresponding elements of the diffusion matrix. Also, the joint large-deviation rate function for the first and the second Lyapunov exponent is estimated.

中文翻译：

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中等复杂度大气模型中有限时间李雅普诺夫指数的波动：多元大偏差视角

摘要。在具有现实平均状态和可变性的三级准地转大气模型中研究了以有限时间李雅普诺夫指数围绕其平均值波动为特征的稳定性特性。首先，考察涨落场的协方差结构。为了识别集体激励的主导模式，对所有有限时间李雅普诺夫指数的波动场进行了经验正交函数 (EOF) 分析。三个领先模式是最不稳定的李雅普诺夫指数相位波动的模式。这些模式实际上与有限时间李雅普诺夫指数的积分时间无关。第二，基于概率密度函数并使用勒让德变换方法，从有限时间李雅普诺夫指数的时间序列估计大偏差率函数。时间序列中的序列相关性得到了适当的考虑。可以为所有 Lyapunov 指数建立大偏差原理。对于最不稳定的指数，收敛速度相当慢，在李雅普诺夫谱中进一步下降时会变得更快，对于近中性和弱耗散模式非常快，并且对于李雅普诺夫谱末端的强耗散模式再次变慢. 最小速率函数的曲率与扩散矩阵的相应元素相关联。此外，估计第一和第二李雅普诺夫指数的联合大偏差率函数。