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

Abstract

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.