混沌系统模型误差平均绝对误差增长过程研究

Study on the mean absolute growth of model error for chaos system

混沌系统的平均绝对误差增长最初是用来刻画初始值误差增长的,本文依照平均绝对误差增长的定义来研究模型误差的增长过程,获得了一些很有意义的结论.研究发现,在初期模型误差的平均绝对误差增长呈指数级增长,增长指数同模型的扰动相关,与真实系统最大Lyapunov指数没有直接关系.其后模型误差进入非线性增长过程,误差增长放缓,最终达到饱和.误差饱和值恒定,当真实系统和模型系统吸引子差别较小时,模型误差饱和值基本上同真实系统的初始值误差饱和值相等.利用上述研究结论可以求出模型的可预报期限,这在数值天气预报中具有重要的意义.进而利用模型的可预报期限可以对同一真实系统的不同模型进行评价,相对真实系统越精确的模型拥有更高的可预报期限.这对新模型的开发具有很强的指导作用.

Mean absolute growth of model error which is used to describe the initial error growth for chaos system, is employed in this paper to investigate the model error growth, and some meaningful conclusions are drew from it. It is found that the mean absolute growth of model error is initially exponential with a growth rate which has no direct relationship with the largest Lyapunov exponent. Afterwards model error growth enters into a nonlinear phase with a decreasing growth rate, and finally reaches a saturation value. If the difference between the attractor of real system and that of the model system is very small, the model error saturation level is consistent with the initial error saturation level of real system. With these conclusions one can obtain the predictability limit of a model easily, which is meaningful for weather prediction models. Also the predictability limit of model can be used for model comparison. The exacter model has a higher predictability limit which is useful for new model development.