The interaction between synoptic eddy and low-frequency flow (SELF) has been recognized for decades to play an important role in the dynamics of the low-frequency variability of the atmospheric circulation. In this three-part study a linear framework with a stochastic basic flow capturing both the climatological mean flow and climatological measures of the synoptic eddy flow is proposed. Based on this linear framework, a set of linear dynamic equations is derived for the ensemble-mean eddy forcing that is generated by anomalous time-mean flows. By assuming that such dynamically determined eddy-forcing anomalies approximately represent the time-mean anomalies of the synoptic eddy forcing and by using a quasi-equilibrium approximation, an analytical nonlocal dynamical closure is obtained for the two-way SELF feedback. This linear closure, directly relating time-mean anomalies of the synoptic eddy forcing to the anomalous time–mean flow, becomes an internal part of a new linear dynamic system for anomalous time–mean flow that is referred to as the low-frequency variability of the atmospheric circulation in this paper.;
In Part I, the basic approach for the SELF closure is illustrated using a barotropic model. The SELF closure is tested through the comparison of the observed eddy-forcing patterns associated with the leading low-frequency modes with those derived using the SELF feedback closure. Examples are also given to illustrate an important role played by the SELF feedback in regulating the atmospheric responses to remote forcing. Further applications of the closure for understanding the dynamics of low-frequency modes as well as the extension of the closure to a multilevel primitive equation model will be given in Parts II and III, respectively.