标题： 集合动力学和 bred 向量 显示英文标题

标题： Ensemble Dynamics and Bred Vectors

摘要： 我们引入了新的概念EBV，以评估天气预报中模型输出对初始条件变化的敏感性。 新算法，我们称之为“集合繁殖向量”或EBV，在本质上基于集体动力学。 从构造上讲，EBV算法生成一个或多个主导向量。 我们研究了EBV的性能，将其与BV算法以及有限时间Lyapunov向量进行比较。 我们给出了理论上的理由来解释观察到的事实，即对于小振幅，BV、EBV和有限时间Lyapunov向量是相似的。 对三个方程的Lorenz模型以及一个在模拟热盐环流中出现的强制性、耗散性的Cahn-Hilliard型偏微分方程的数值比较表明，EBV能够对扰动场进行大小排序描述，并且在更高非线性区域比BV更稳健。 EBV揭示了Lorenz吸引子以及Cahn-Hilliard型偏微分方程的惯性流形的分形结构。 显示英文摘要

摘要： We introduce the new concept of an EBV to assess the sensitivity of model outputs to changes in initial conditions for weather forecasting. The new algorithm, which we call the "Ensemble Bred Vector" or EBV, is based on collective dynamics in essential ways. By construction, the EBV algorithm produces one or more dominant vectors. We investigate the performance of EBV, comparing it to the BV algorithm as well as the finite-time Lyapunov Vectors. We give a theoretical justification to the observed fact that the vectors produced by BV, EBV, and the finite-time Lyapunov vectors are similar for small amplitudes. Numerical comparisons of BV and EBV for the 3-equation Lorenz model and for a forced, dissipative partial differential equation of Cahn-Hilliard type that arises in modeling the thermohaline circulation, demonstrate that the EBV yields a size-ordered description of the perturbation field, and is more robust than the BV in the higher nonlinear regime. The EBV yields insight into the fractal structure of the Lorenz attractor, and of the inertial manifold for the Cahn-Hilliard-type partial differential equation.