Application of Backward Nonlinear Local Lyapunov Exponent Method to Assessing the Relative Impacts of Initial Condition and Model Errors on Local Backward Predictability

Abstract

Initial condition and model errors both contribute to the loss of atmospheric predictability. However, it remains debatable which type of error has the larger impact on the prediction lead time of specific states. In this study, we perform a theoretical study to investigate the relative effects of initial condition and model errors on local prediction lead time of given states in the Lorenz model. Using the backward nonlinear local Lyapunov exponent method, the prediction lead time, also called local backward predictability limit (LBPL), of given states induced by the two types of errors can be quantitatively estimated. Results show that the structure of the Lorenz attractor leads to a layered distribution of LBPLs of states. On an individual circular orbit, the LBPLs are roughly the same, whereas they are different on different orbits. The spatial distributions of LBPLs show that the relative effects of initial condition and model errors on local backward predictability depend on the locations of given states on the dynamical trajectory and the error magnitudes. When the error magnitude is fixed, the differences between the LBPLs vary with the locations of given states. The larger differences are mainly located on the inner trajectories of regimes. When the error magnitudes are different, the dissimilarities in LBPLs are diverse for the same given state.

摘要

初始状态误差和参数误差对于大气可预报性的丧失具有重要的影响. 哪一类误差对于特定状态可预报性具有更大的影响依然存在着争议. 在本工作中, 我们选择Lorenz模型, 评估了两类误差对于给定状态可预报性的相对影响. 模型中存在初始状态误差 (模式误差)时, 利用向后非线性局部Lyapunov指数 (BNLLE) 方法, 给定状态的理论最长提前预报时间, 即向后可预报性, 可以被定量确定. 研究结果显示, Lorenz吸引子特定结构导致了给定状态的向后可预报性呈现层状分布. 即, 在单个环形轨圈上, 给定状态的向后可预报期限基本一致, 在不同的环形轨圈上, 向后可预报期限则不同. 向后可预报性期限的空间分布显示, 初始状态误差和模式误差对于局部向后可预报性的相对影响取决于给定状态所在的空间位置以及误差量级大小. 当误差量级大小固定时, 两类误差导致的向后可预报期限差值随着给定状态空间位置的变化而变化. 较大差值主要分布在冷暖位相的内圈. 当误差量级不同时, 对于相同的给定状态, 两类误差导致的向后可预报期限差值也是不同的.