论文

Lorenz模型中外源强迫强弱对初值可预报性的影响研究

  • 李一伟 ,
  • 范广洲 ,
  • 赖欣
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  • 成都信息工程大学大气科学学院/高原大气与环境四川省重点实验室/气候与环境变化联合实验室,四川 成都 610225

收稿日期: 2019-03-25

  网络出版日期: 2020-02-28

基金资助

国家自然科学基金项目(91537214);国家重点研发计划项目(2018YFC1505702);公益性(气象)行业科研专项(GYHY201506001);成都信息工程大学中青年学术带头人科研基金(J201516);成都信息工程大学校引进人才启动基金(KYTZ201639)

Study on the Influence of External Forcing Weakness on the Predictability of Initial Value in Lorenz Model

  • Yiwei LI ,
  • Guangzhou FAN ,
  • Xin LAI
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  • School of Atmospheric Sciences /Plateau Atmosphere and Environment Key Laboratory of Sichuan Province /Joint Laboratory of Climate and Environment Change,Chengdu University of Information Technology,Chengdu 610225,Sichuan,China

Received date: 2019-03-25

  Online published: 2020-02-28

摘要

通过调整Lorenz模型中表征外源强迫强弱的参数值r, 采用显式四阶龙格-库塔(Runge-Kutta)方法, 以探究不同外源强迫下所构建Lorenz系统的初值可预报性。得出了外源强迫增大, 初值的可预报性降低, 误差增长增大, 可预报期限缩短, 预报效果变差, 系统对初值敏感依赖性增大的结论。初始值与其叠加微小偏差的相关系数随外源强迫增大出现三次骤减, 在模拟出的Lorenz系统运动轨迹图中, Lorenz系统的奇异吸引子由一个变为两个, 奇异吸引子周围的曲面也由一片演变成两片, 混沌效应显现。XYZ值的方差; X值、 Y值超出一个标准差的步数随外源强迫增大表现出振荡上升趋势。外源强迫的增大也使得Lorenz系统分异与第一次出现反向所用的积分步数减小, 两组数据的并行时间越来越短。统计XYZ值的误差在5%, 10%和20%范围内的积分步数发现, 系统的误差增长随外源强迫增大而增大, 不再处于合理范围内, 因此初值可预报性降低, 可预报期限也大大缩短。

本文引用格式

李一伟 , 范广洲 , 赖欣 . Lorenz模型中外源强迫强弱对初值可预报性的影响研究[J]. 高原气象, 2020 , 39(1) : 153 -161 . DOI: 10.7522/j.issn.1000-0534.2019.00061

Abstract

To explore the predictability of the initial value of the Lorenz system constructed under different external forcings by adjusting the parameter value r that characterizes the external forcing in the Lorenz model, and using the explicit fourth-order Runge-Kutta method.It is concluded that the predictability of the initial value decreases and the error growth increases, so the forecast period is shortened, the forecast effect is worse, and the system is more sensitive to the initial value with the increase of external forcing.The correlation coefficient between the initial value and its superimposed small deviation has three sudden decrease with the increase of external forcing.In the picture of simulated Lorenz system motion trajectory, the strange attractor of the Lorenz system changes from one to two, and the surface around the strange attractor also evolves from one to two, and Chaos phenomenon appears.The variance of the XY, and Z values; the number of steps in which the X value and the Y value exceed one standard deviation show an upward trend with the increase of external forcing.The increase in external forcing also reduces the number of integration steps of differentiation and the first reversal used in the Lorenz system, and the parallel time of the two sets of data is shorter and shorter.By counting the number of integration steps in the error range in 5%、 10%、 20% of XY, and Z values, it is found that the error growth of the system increases with the increase of external forcing.It is no longer within a reasonable range, so the predictability of the initial value is reduced and the forecast period is greatly shortened.

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