Understanding and application of the decay theory of initial condition effect in numerical climate simulation studies

The complete dynamical equations of the atmospheric motion and the qualitative theory of nonlinear atmosphere with dissipation and external forcing in Hilbert space suggest that the initial condition will not affect the status of a long-time numerical simulation with AGCMs. In this research, we first introduce the key points for understanding the decay of initial condition effect, and then employ two atmospheric general circulation models (AGCM),SAMIL and ECHAM, to investigate the effect of initial condition on the simulation results in an actual computing environment with round -off errors. The round-off error mean ensemble (REME) experiments are conducted to reduce the uncertainty caused by round-off errors. The results indicate that in the actual computing environment, a big initial condition error/spread will lead to a small fluctuating final error. But for a tiny initial condition error/spread, it will lead to the same-magnitude final fluctuating error. This is against the theoretical analysis. However, the discrepancy can be explained by the existence of the round-off errors which are not considered in the theoretical analysis. The final error balance is consistent with the error saturation property indicated by the nonlinear error growth theory.The initial error decay curves of SAMIL and ECHAM are obtained, from which we find that the initial condition error in the two AGCMs decays to the final error within about 40-60 days of integration. At last, we used the initial error decay theory to conclude that the initial mean ensemble (IME) is capable of reducing the error in climate simulation studies.