李志锦,纪立人. 1995. 轨线不稳定与误差增长[J]. 气象学报, 53(2):138-147, doi:10.11676/qxxb1995.016
轨线不稳定与误差增长
INSTABILITY OF TRAJECTORY AND ERROR GROWTH
投稿时间:1993-05-29  修订日期:1993-08-10
DOI:10.11676/qxxb1995.016
中文关键词:  轨线  不稳定  误差增长率
英文关键词:Trajectory  Instability  Error growth rate
基金项目:中国科学院KY-85项目资助
作者单位
李志锦 中国科学院大气物理研究所, 北京, 100080 
纪立人 中国科学院大气物理研究所, 北京, 100080 
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中文摘要:
      从一般的谱展开方程出发,详细推导了误差增长方程。结果表明误差增长率主要由准确解的切线性方程所决定,扰动非线性平流作用不产生方差意义下的误差增长,而只起分配误差的作用。轨线不稳定是产生误差增长的根本原因。文中提出了计算轨线不稳定增长率的方法。这一方法也适合于时间演变状态不稳定问题的讨论,对Lorenz系统的轨线不稳定计算表明了理论分析的正确及其意义。
英文摘要:
      The objects of this study are to propose the dynamical mechanism of the growth of the initial error in numerical weather prediction.The equations of error growth are obtained from the spectral primitive equation model. The results have shown that the error growth rate is determined by the tangent linear equations along the orbit of exact solutions.The nonlinear advective process of error itself has no effect on the error growth rate in the mean square error sense a:d only redistributes error over the spectral space.The trajectory instability is the essential cause to error growth. A method to compute the instability growth rate is developed, which could be used to study the instability of the time dependent state. Then trajectory instability of the Lorenz system is analyzed and the theoretical results are verified.
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