Using the NCAR/NCEP reanalysis, we here present evidence suggesting that the out-of-phase relationships of temperature anomalies both between the low and high latitudes and between the stratosphere and troposphere are intimately related to the meridional and downward propagation of anomalies of both signs. The temperature anomalies propagate poleward and downward above the tropopause and propagate equatorward below the tropopause. The characteristic time scale for anomalies of one polarity to propagate from the equator to the pole (or the half period of the complete cycle) is about 55 days. The relatively slow meridional propagation helps to explain the well-known seesaw oscillatory pattern between low and high latitudes found in monthly data. The equatorward propagation in the troposphere is synchronized with the poleward propagation of the stratospheric temperature anomalies of the opposite sign in both low and high latitudes, responsible for the out-of-phase relation between the stratospheric and tropospheric temperature anomalies in the polar region. Since it takes about 55 days for anomalies of one polarity to propagate from the tropics to the pole, such an intimate linkage between the anomalies in the deep tropics and high latitudes would imply a longer lead time for intra-seasonal climate prediction in the extratropics.
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 The Northern Annular Mode (NAM) is known as a meridional seesaw oscillatory pattern between the subtropics and the polar region [Thompson and Wallace, 1998]. It is characterized by a deep and equivalent barotropic structure of geopotential height and zonal wind from the stratosphere to the surface in the polar region. Evidence also shows that there exists a downward propagation of stratospheric disturbances of zonal-mean zonal wind [Kodera and Kuroda, 1990] and geopotential height [Baldwin and Dunkerton, 1999] into the troposphere in the extratropics. The lead time of a few weeks between the stratospheric and the surface anomalies due to the downward propagation has an immediate implication for weather regime prediction in the troposphere [Baldwin and Dunkerton, 2001].
 There are a number of observational studies showing a poleward propagation of zonal-mean zonal wind anomalies associated with the NAM [Kodera and Kuroda., 2000; Dunkerton, 2000; Kuroda, 2002]. In a series of recent publications [Ren and Cai, 2006; Cai and Ren, 2006, 2007] (hereinafter referred to as CR), we showed that temperature anomalies propagate poleward and downward simultaneously along the upper isentropic surfaces (400 ∼ 650K) whereas along the lower isentropic surfaces in the extratropics (290K and below) they propagate equatorward. CR proposed that the simultaneous poleward and downward propagation in the stratosphere and the equatorward propagation in the troposphere are associated with the variation of the global mass circulation. The poleward propagating positive (negative) stratospheric temperature anomalies are associated with a stronger (weaker) warm air branch of the global mass circulation whereas the variability of the compensating cold air branch is synchronized with the warm air branch, responsible for the equatorward propagating negative (positive) tropospheric temperature anomalies.
 The analysis reported in CR is done in the θ-PVLAT coordinate (isentropic coordinate in the vertical and equivalent latitude represented by potential vorticity contours). Because the isentropic surfaces in the lower troposphere do not extend from the pole to the tropics without intersecting with the ground, it is difficult to clearly display a continuous equatorward propagation signal along the lower isentropic surfaces outside the extratropics. In this paper, we provide evidence on the equatorward propagation of the tropospheric anomalies and their temporal phase relation with the simultaneous poleward and downward propagation of anomalies in the stratosphere in the isobaric coordinate. The goal of this paper is to show how the co-existence of the simultaneous poleward and downward propagating temperature anomalies in the stratosphere and the equatorward propagation of temperature anomalies of the opposite sign in the troposphere results in the out-of-phase relationships of temperature anomalies both between low and high latitudes and between the polar stratosphere and troposphere.
2. Data and Analysis Procedure
 The data used in this study are temperature field on 2.5° × 2.5° grids at 17 standard pressure levels from 1000 to 10 hPa derived from the daily NCEP-NCAR reanalysis II covering the period of 1 January 1979 to 31 December 2003 [Kalnay et al., 1996; Kistler et al., 2001; Kanamitsu et al., 2002]. The daily climatological annual cycle is obtained by first averaging the daily data on Julian day across all years from 1979 to 2003. Then a 31-day running mean operator is applied to obtain a smoothly varying annual cycle. The daily anomalies are obtained straightforwardly by taking out the annual cycle from the total fields.
 We use the unsmoothed raw daily polar vortex oscillation (PVO) index reported by CR as the time series for the regression analysis. The PVO index is the time series of the leading EOF mode of the daily potential vorticity (PV) anomalies in the θ-PVLAT coordinate, which explains about 69% of the total variance of daily PV anomalies over the entire Northern Hemisphere. According to CR, the PVO index is highly correlated with upper stratosphere NAM indices. Because the θ-PVLAT coordinate servers as a dynamical filter that naturally filters out day-to-day variability due to advective processes, there is no need to apply a mathematical filter for isolating the low frequency variability in the θ-PVLAT coordinate. Furthermore, the low frequency variability captured in the θ-PVLAT coordinate retains the “sharpness” of natural events or the high frequency component of natural events is preserved.
 In this paper, the temporal and spatial evolution of the circulation anomalies in the isobaric coordinate is obtained by regressing the daily anomaly fields against the daily PVO index in winter seasons (December to March). Since the dominant intraseasonal timescale of the PVO index in winter is about 110 days [Ren and Cai, 2006], we have carried out the regression calculation by varying the lead time of the PVO index from −60 to 60 days in order to get a complete cycle of the evolution. The meridional and temporal evolution of anomalies is obtained by zonally averaging the 3-D regressed anomaly fields.
Figure 1 shows the regressed temperature anomalies against the PVO index at the zero lead time, corresponding to the situation of the positive phase of a NAM event. One of the dominant features is the meridional dipole pattern of temperature anomalies in the stratosphere with the node at around 50°N. The temperature anomalies in the lower troposphere also exhibit a meridional dipole pattern that is nearly out of phase with the stratospheric counterpart except that the tropospheric node point is at 70°N. These two features together result in a vertical dipole pattern over the polar region and an opposite vertical dipole pattern in low latitudes, sandwiched by a vertical monopole structure between 50°N and 70°N.
 We next show how such a dipole structure in both the meridional and vertical directions is related to the poleward propagation in the stratosphere and the equatorward propagation in the troposphere. Displayed in Figure 2 are the lead/lag regression diagrams of the zonally averaged temperature anomalies layer by layer. The poleward propagation of temperature anomalies of both signs is very evident in the upper 4 pressure levels that lie entirely in the stratosphere throughout the hemisphere (Figures 2a–2d). The poleward propagation is relatively faster in tropics and high latitudes and slower in mid-latitudes. Over the polar region, the poleward propagation of temperature anomalies of both signs results in the oscillation between a cold/strong and a warm/weak polar vortex. It takes about 55 days for the cold temperature anomalies to propagate from the tropics to the pole and another 55 days for the warm temperature anomalies to reach the pole. Therefore, the period of the complete cycle of the phenomenon is about 110 days, which is consistent with the power spectral analysis of the PVO index reported by CR. The slow poleward propagation of daily temperature anomalies of both signs results in a meridional out-of-phase pattern at any given instance, or a seesaw oscillatory pattern between low and high latitudes when averaging anomalies over a month. Another noticeable feature in Figures 2a–2d is that the poleward propagation signal at a higher level always leads the signal at a lower level, as reported by CR. For example, the arrival of the poleward propagating anomalies in the polar region at 100 hPa lags that at 20 hPa by about 20 days.
Figures 2e–2h are for those pressure levels that intersect with the tropopause in different latitudes, reflecting the fact that the tropopause level generally decreases with increasing latitude. Clearly, the latitude band where the poleward propagation signal is evident shrinks poleward as the altitude of isobaric surfaces decreases. Replacing the poleward propagation in low latitudes (as isobaric surface height decreases) is the equatorward propagation. For example, the poleward propagation signal at 150 hPa is evident throughout the extratropics, but becomes diluted in the deep tropics by an equatorward propagation signal at the latitudes south of 20°N where the 150 hPa surface insects with the tropopause. At 300 hPa level, the poleward propagation signal is limited to the latitude band 40°N poleward whereas the equatorward propagation signal prevails over the latitude south of 40°N. The region of the equatorward propagation expands poleward as pressure increases and eventually prevails over the entire hemisphere at the pressure level below 500 hPa. This clearly suggests that the tropopause serves as the interface that separates the poleward propagation of temperature anomalies above from the equatorward propagation below. Such a hemispheric scale of the equatorward propagation cannot be easily identified in the isentropic coordinate as shown by CR because few isentropic surfaces can remain entirely in the troposphere without intersecting with either the tropopause or the surface [Hoskins et al., 1985].
 Despite the fact that the tropospheric temperature anomalies are about 5–10 times smaller than their stratospheric counterparts, it is very evident that there exists a robust temporal phase relation between the stratospheric and tropospheric temperature anomalies. For example, the equatorward propagation of cold (warm) temperature anomalies at 500 hPa starts at about day 25 (−30), which is nearly synchronized with the arrival of the warm (cold) temperature anomalies into the polar circle at 300 hPa. The arrival of the warm (cold) temperature anomalies at 300 hPa in turns is about 25 days after the arrival of the warm (cold) temperature anomalies into the polar circle at 20 hPa. Such a synchronized timing between the stratospheric poleward propagation and the equatorward propagation of tropospheric temperature anomalies of the opposite sign results in an out-of-phase relation of temperature anomalies between the lower stratosphere and troposphere over the polar region. This is consistent with the fact that a warmer/weaker polar vortex tends to be followed by more frequent and severe cold outbreaks near the surface [Thompson et al., 2002; Cai, 2003]. It is equally of importance to point out that the timing of the arrival of the equatorward propagating tropospheric temperature anomalies in low latitudes is also a few days after the beginning of the poleward propagating temperature anomalies of the opposite sign from the lower stratosphere in the tropics.
 The temporal delay of the poleward propagation from upper to lower levels would immediately imply a downward propagation in the stratosphere. The reversed meridional propagation from the stratosphere to the troposphere suggests that the tropopause serves as the lower boundary of the downward propagation of temperature anomalies. According to Figure 3, temperature anomalies of both signs appear first at the highest level (10 hPa), and then propagate downward. The downward propagation is evident in all latitudes from the tropics to the pole. The downward propagation of the stratospheric temperature anomalies ends at the tropopause level in both low (Figures 3a and 3b) and high latitudes (Figures 3g–3h) where stratospheric temperature anomalies are negatively correlated with tropospheric anomalies. Because the tropopause height decreases poleward, the vertical extent of the downward propagation would increase with latitudes.
 Following Cai and Ren , this paper presents evidence suggesting that the out-of-phase relationships of the temperature anomalies both between low and high latitude and between the stratosphere and troposphere are intimately related to the coupling of the poleward propagation in the stratosphere and the equatorward propagation of the tropospheric anomalies of the opposite sign. The meridional propagation time scale for anomalies of one polarity to reach the pole from the equator or the half period of the complete cycle for anomalies of both signs is about 55 days. The slow meridional propagation of daily temperature anomalies of both signs results in a meridional out-of-phase pattern at any given instance, or a seesaw oscillatory pattern between low and high latitudes in both the troposphere and troposphere for monthly averaging anomalies.
 The upper stratospheric poleward propagation leads the poleward propagation in the lower stratosphere. As a result, there appears a simultaneous downward propagation in the stratosphere. The stratospheric downward propagation terminates at the tropopause as a result of the reversing of the meridional propagation direction in the troposphere. Because the tropopause height decreases with latitudes, the vertical span of the downward propagation is deeper in high latitudes than in low latitudes. This also helps to explain why the tropospheric equatorward propagation appears first in low latitudes and gradually expands to the entire hemisphere in the lower troposphere.
 The coupling of the stratospheric poleward and tropospheric equatorward propagation spanning over the entire hemisphere not only helps to explain the out-of-phase relation between the stratospheric and tropospheric temperature anomalies in the polar region, but also relates the tropospheric temperature anomalies in the extratropics to the temperature anomalies in the upper level atmosphere in the tropics. Since it takes about 55 days on average for the signal to propagate from the tropics to the pole, such an intimate linkage between the circulation anomalies in the deep tropics and the tropospheric anomalies in high latitudes would imply a longer lead time for intra-seasonal climate prediction in the extratropics.
 During the course of this study, RRC was supported by National Basic Research Program of China (2006CB403600), the Chinese NSF grants 40575041 and 40523001 and MC supported by grants from the NOAA Office of Global Programs (GC04-163 and GC06-038). The authors are grateful for the valuable suggestions and comments from two anonymous reviewers. We also thank Vinette Burns for editorial suggestions on the first draft of the paper.