A Relationship between Local Error Growth and Quasi-stationary States: Case Study in the Lorenz System
A Relationship between Local Error Growth and Quasi-stationary States: Case Study in the Lorenz System
复制标题
局部误差增长与准稳态之间的关系：洛伦兹系统的案例研究
DOI：
10.1175/1520-0469(1991)048
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发表时间：
1991
影响因子：
3.1
通讯作者：
S. Yoden
中科院分区：
文献类型：
--
作者：
H. Mukougawa;M. Kimoto;S. Yoden
本文首先研究了三变量Lorenz系统的局地可预报性，提出了一种替代传统的统计和经验方法的数值天气预报技能预报的动力方法。作为局部可预测性的度量，我们采用洛伦兹指数，它给出了在规定时间间隔内均方根误差的扩大率。特别是，我们努力理解准定态在决定洛伦兹指数变化中的作用。在间歇混沌区域中，Poincare截面中一次返回的时间间隔所确定的Lorenz指数在层流阶段开始时有一个最小值，在层流阶段中逐渐增加，在层流阶段结束时突然达到一个较大的值。如果我们把层流相看作是由一维庞加莱映射中的局部极小点产生的准定态，那么这一特征是不存在的。
Abstract Properties of the local predictability in the Lorenz system of three variables are investigated as a first step to develop a dynamical method for the skill prediction in the numerical weather forecasts instead of conventional statistical and empirical methods. As a measure of the local predictability, we adopt Lorenz's index which gives the amplification rate of the root-mean-square error during a prescribed time interval. In particular, we exert ourselves to understand a role of the quasi-stationary state in determining the variation of the Lorenz index. In an intermittent chaos regime, the Lorenz index determined for a time interval of the one return in the Poincare section has a minimum value at the onset of the laminar phase, gradually increases during the laminar phase, and abruptly attains a large value at the break of the laminar phase. If we consider the laminar phase as a quasi-stationary state generated by a local minimum point in the one-dimensional Poincare map, this characteristic ev...