| Summary: | A simple theoretical model is proposed to clarify how synoptic-scale waves drive the life cycle of the North Atlantic Oscillation (NAO) with a period of nearly two weeks. This model is able to elucidate what determines the phase of the NAO and an analytical solution is presented to indicate a high similarity between the dynamical processes of the NAO and zonal index, which is not derived analytically in previous theoretical studies. It is suggested theoretically that the NAO is indeed a nonlinear initial-value problem, which is forced by both preexisting planetary-scale and synoptic-scale waves. The eddy forcing arising from the preexisting synoptic-scale waves is shown to be crucial for the growth and decay of the NAO, but the preexisting low-over-high (high-over-low) dipole planetary-scale wave must be required to match the preexisting positive-over-negative (negative-over-positive) dipole eddy forcing so as to excite a positive (negative) phase NAO event. The positive and negative feedbacks of the preexisting dipole eddy forcing depending upon the background westerly wind seem to dominate the life cycle of the NAO and its life period. An important finding in the theoretical model is that negative-phase NAO events could be excited repeatedly after the first event has decayed, but for the positive phase downstream isolated dipole blocks could be produced after the first event has decayed. This is supported by observed cases of the NAO events presented in this paper. In addition, a statistical study of the relationship between the phase of the NAO and blocking activity over Europe in terms of the seasonal mean NAO index shows that blocking events over Europe are more frequent and long-lived for strong positive-phase NAO years, indicating that the positivephase NAO favors the occurrence of European blocking events.
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