THE INSTABILITY OF TRAJECTORY AND ERROR GROWTH^*

The purpose of this paper is to study the dynamical mechanism of error growth in the numerical weather prediction.The error is defined in the sense of generalized energy,simply called energy error.From the spectral form of the primitive equations,we have derived the evolution equations of error in detail.The analyses of these equations have shown that the error growth rate is determined by the tangent linear equations.The nonlinear advection caused by the error perturbation itself contributes nothing to the error growth rate,and only redistributes the error.Furthermore,an approach to calculation of the error growth rate has been developed,which can also be used to study the local instability of time-independent basic state as well as time-dependence basic state.This approach is applied to well-known Lorenz's system,and the results are indicative of the correctness and significance of the theoretical analyses.