非线性误差增长理论在大气可预报性中的应用

Application of nonlinear error growth dynamics in studies of atmospheric predictability

中文关键词:  非线性， Lyapunov指数， 可预报性， 位势高度场

英文关键词:Nonlinearity, Lyapunov exponent, Predictability, Geopotential height field

中文摘要:

      为了能从非线性误差增长动力学的角度来研究大气的可预报性问题，在非线性动力系统的理论和方法基础上，文中引入了可预报性研究的新方法——非线性局部Lyapunov指数。非线性局部Lyapunov指数及其相关统计量能够用来定量地确定混沌系统可预报性的大小，真正地实现了对可预报性的定量化研究。首先给出了利用大气单个变量的实际观测资料获得其可预报期限估计的计算方法，因而解决了将非线性误差增长理论应用到大气实际的可预报性研究中的问题。然后，以位势高度场为例，详细讨论了逐日时间尺度上全球可预报性的时空分布，得到的主要结论为：（1）在水平方向上，全球位势高度场可预报性表现为一定的南北纬向带状分布，赤道地区和南极地区的可预报期限最长，可以达到两周左右；北极地区次之，可预报期限大约为9—12 d；北半球中高纬度地区可预报期限相对较短，可预报期限大约为6—9 d；而在南半球的中纬度地区最短，可预报期限仅为4—6 d。此外，500 hPa位势高度场可预报性分布随季节有明显变化，季节不同一些可预报期限的高值区和低值区所在的纬度和经度也会不同，总体来说，全球大部分地区的可预报性冬季都大于夏季，尤其在南极地区、热带印度洋以及北太平洋地区。（2）在垂直方向上，位势高度场可预报期限随高度升高而增加，可预报期限从对流层下层的两周以下增加到平流层下层的1个月左右，对流层和平流层天气尺度运动的可预报期限与其时间尺度是十分一致的。

英文摘要:

      This paper provides an algorithm that computes the predictability limit of atmospheric variables by use of observational data, based on the concept of the nonlinear local Lyapunov exponent (NLLE) and related nonlinear error growth dynamics developed by the authors in the recent years. The NLLE and its derivatives can be used to quantify the predictability of chaotic dynamical systems. The algorithm introduced here is practical in the sense that it applies the nonlinear error growth theory to the estimate of actual atmospheric predictability through using observations. As an example, the temporal spatial distributions of the predictability limit of geopotential height fields are calculated and discussed. It is found that for the 500 hPa height fields, the annual mean predictability limit (AMPL) appears a zonal distribution with the maximum of around two weeks in the tropics and Antarctic. The AMPL is about 9-12 days in the Arctic, 6-9 days in the middle-high latitudes of the Northern Hemisphere, and 4-6 days in the middle latitudes of the Southern Hemisphere. Moreover, the atmospheric predictability limit varies with season. For most regions of the two hemispheres, especially for the Antarctic, the tropical Indian Ocean, the North Pacific and North Atlantic, the predictability limit in winter is much longer than that in summer. Vertically, the predictability limit increases with height. It changes from below two weeks in the lower troposphere to about one month in the lower stratosphere. This is consistent with the fact that weather patterns in the troposphere tend to alter on a time scale of a few days, and circulation regimes in the stratosphere tend to persist for several weeks or more.