Abstract:  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. T he 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.