中文摘要：

本文从理论和数值试验上讨论了两种常用的预报误差增长近似模型的偏差问题：累加近似模型和线性近似模型.理论结果表明初始误差、模式误差的累加近似的偏差在短期内随时间是线性增长,但其增长速度后者约为前者的一半.误差增长的线性近似的偏差与误差线性分量的模成正比.利用Lorenz-96系统数值模拟结果进一步验证了理论分析的结果,并进一步指出误差累加近似和线性近似的偏差对背景状态不敏感,模式误差源的性质对累加近似的平均偏差的影响较小.研究结果可为确定预报误差演变近似模型的适用范围、误差增长的阶段划分等研究提供理论依据.

英文摘要：

The deviations of accumulative approximate model and linear approximate model of errors＇ growth are discussed in theoretical and numerical experiments.Theoretical results show that the deviations of accumulative approximation for the initial errors,as well as for the model errors,grow linearly with time,but the growth rate of the deviations for model errors is about one half of that for initial errors.The deviations of linear approximation of initial or model errors are proportional to the norm of errors＇ linear part.The results are illustrated by experiments in Lorenz＇96 system.Experimental results also show that the deviations of accumulative approximation and linear approximation are both insensitive to background state,and the deviations of accumulative approximation of model errors are insensitive to model errors＇ sources.These results provide theoretical basis for understanding the applicable range of approximate models and the separation of error growth phases.