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F-F. Jin
,
L-L. Pan
, and
M. Watanabe

Abstract

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.

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F-F. Jin
,
L-L. Pan
, and
M. Watanabe

Abstract

Amidst stormy atmospheric circulation, there are prominent recurrent patterns of variability in the planetary circulation, such as the Antarctic Oscillation (AAO), Arctic Oscillation (AO) or North Atlantic Oscillation (NAO), and the Pacific–North America (PNA) pattern. The role of the synoptic eddy and low-frequency flow (SELF) feedback in the formation of these dominant low-frequency modes is investigated in this paper using the linear barotropic model with the SELF feedback proposed in Part I. It is found that the AO-like and AAO-like leading singular modes of the linear dynamical system emerge from the stormy background flow as the result of a positive SELF feedback. This SELF feedback also prefers a PNA-like singular vector as well among other modes under the climatological conditions of northern winters.

A model with idealized conditions of basic mean flow and activity of synoptic eddy flow and a prototype model are also used to illustrate that there is a natural scale selection for the AAO- and AO-like modes through the positive SELF feedback. The zonal scale of the localized features in the Atlantic (southern Indian Ocean) for AO (AAO) is largely related to the zonal extent of the enhanced storm track activity in the region. The meridional dipole structures of AO- and AAO-like low-frequency modes are favored because of the scale-selective positive SELF feedback, which can be heuristically understood by the tilted-trough mechanism.

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L-L. Pan
,
F-F. Jin
, and
M. Watanabe

Abstract

In this three-part study, a linear closure has been developed for the synoptic eddy and low-frequency flow (SELF) interaction and demonstrated that internal dynamics plays an important role in generating the leading low-frequency modes in the extratropical circulation anomalies during cold seasons.

In Part III, a new linearized primitive equation system is first derived for time-mean flow anomalies. The dynamical operator of the system includes a traditional part depending on the observed climatological mean state and an additional part from the SELF feedback closure utilizing the observed climatological properties of synoptic eddy activity. The latter part relates nonlocally all the anomalous eddy-forcing terms in equations of momentum, temperature, and surface pressure to the time-mean flow anomalies. Using the observational data, the closure was validated with reasonable success, and it was found that terms of the SELF feedback in the momentum and pressure equations tend to reinforce the low-frequency modes, whereas those in the thermodynamic equation tends to damp the temperature anomalies to make the leading modes equivalent barotropic. Through singular vector analysis of the linear dynamical operator, it is highlighted that the leading modes of the system resemble the observed patterns of the Arctic Oscillation, Antarctic Oscillation, and Pacific–North American pattern, in which the SELF feedback plays an essential role, consistent with the finding of the barotropic model study in Part II.

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