The Eulerian-and Lagrangian-Mean Meridional Circulations in the Stratosphere at the Time of a Sudden Warming

Abstract

The Eulerian-mean (usual zonal mean) and the Lagrangian-mean (an average in the zonal direction along a curved "material line," consisting of definite individual air particles) meridional circulations are investigated, given an upward propagating planetary wave incident on a critical level. The Eulerian-mean circulation is such that an upward motion appears at higher latitudes, a downward motion at lower latitudes, and an equatorward meridional flow near the critical level. The Lagrangian circulation is quite different from the Eulerian one. A strong poleward meridional flow appears concentrated at the critical level. In connection with this meridional flow, a Lagrangian-mean vertical motion occurs which diverges from this level at higher latitudes, i.e., it consists of a downward motion below the critical level and an upward motion above the level. At lower latitudes, vertical motions converge toward the critical level. The vertical motion field of this four-sector structure in the meridional section causes corresponding zonal mean temperature changes as observed in real sudden warnings. From a set of equations derived by Andrews and McIntyre (1978b), which govern the Lagrangian-mean quantities, we can obtain the above results directly. By interpreting the physical meaning of this system of equations, we interpret the strong meridional flow at the critical level as an Ekman-transport-like motion caused by a strong westward force at the critical level, which arises from a sharp gradient of the zonal component of the radiation stress associated with the wave. The mechanism of a sudden warming as viewed in terms of the Lagrangian-mean motion is discussed.