the wave number‐ 1 and wave number‐ 2 are predominant waves that can propagate from the troposphere into the stratosphere (Charney & Drazin, 1961),
一致时加强 不一致时减弱
the wavenumber-1 height anomaly is mostly in phase with climatology at 500 hPa (Fig. 8a), whereas the wavenumber 2 is generally out of phase with climatology (Fig. 8g), indicating an enhancement of planetary wavenumber 1 and a reduction of wavenumber 2 in the mid-troposphere. In the lower stratosphere at 50 hPa, the wavenumber-1 anomaly is highly in phase with the climatological component (Fig. 8d), but the wavenumber 2 is out of phase with the climatological component (Fig. 8j). The amplitudes of wavenumber 1 are larger than that of wavenumber 2 at both 500 hPa and 50 hPa.
Correspondingly, there is an anomalously upward propagation of the wavenumber-1 EP flux anomalies from extratropical troposphere to stratosphere (Fig. 9d). Significant convergences of wavenumber-1 EP flux are observed in the extratropical stratosphere. Meanwhile, downward propagation of the wavenumber-2 EP flux anomalies are observed but with much weaker magnitude (Fig. 9g).
The anomalous EP fluxes of the planetary waves (wavenumbers 1–3) are quite parallel to those of wavenumber 1 indicating the prevalent planetary wavenumber-1 activities and EP flux convergences in the stratosphere (Fig. 9a), and thus a significantly weakened polar vortex (Fig. 3b).
在500百帕，波数1高度异常与气候学基本同相（图8a），而波数2与气候学基本异相（图8 g），这表明在对流层中层，行星波数1增强，波数2减弱。 在50 hPa平流层低层，波数-1异常与气候分量高度同相（图8d），但波数2与气候分量异相（图8 j）。 在500 hPa和50 hPa上，波数1的振幅均大于波数2的振幅。
相应地，波数为1的EP通量异常从温带对流层到平流层有异常向上的传播（图9d）。 在温带平流层中观测到了1波EP通量的显著辐合。 同时，观测到波数为2的EP通量异常向下传播，但幅度要小得多（图9 g）。
行星波（波数1 3）的异常EP通量与波数1的异常EP通量相当平行，这表明行星波数-1的活动和EP通量在平流层中的普遍收敛（图9a），因此极涡明显减弱（图3b）。
Figure 8 shows the anomalies in the wavenumber-1 and -2 components of the detrended 200 hPa geopotential height obtained by regressions on the PC1NA index on decadal timescales. The anomalies in the zonal wavenumber-1 component of the 200 hPa geopotential height at high-latitudes related to the North Atlantic SSTAs are in phase with its climatology, whereas its anomalies at mid-latitudes are in the opposite phase to its positive climatology (Fig. 8a). This means that the positive North Atlantic SSTAs tend to reinforce the climatological wavenumber-1 wave at high latitudes in the troposphere, but cancel the climatological wavenumber-1 waves at mid-latitudes, which implies the strengthened wavenumber-1 waves at high latitudes but weakened wavenumber-1 waves at mid-latitudes in the troposphere. By contrast, the anomalies in the wavenumber-2 component in the geopotential height related to the North Atlantic SSTAs are in the opposite phase to its climatology at high-latitudes, but in phase with its climatology at mid-latitudes (Fig. 8b). These features in the wavenumber-1 and -2 components of geopotential height in associated with North Atlantic SSTAs still exist after removing the PDO signals, but with smaller magnitudes of the anomalies in the wavenumber-1 component of geopotential height at high-latitudes (figure not shown). This implies that PC1NA-related SSTAs may result in a ridge in the Atlantic sector and a trough in the Pacific, but the SSTAs over the North Pacific may strengthen the ridge in the Atlantic sector and the trough in the Pacific, especially over the mid-latitudes.
图8显示了通过对年代际时间尺度上的PC 1 NA指数进行回归而获得的去除趋势的200 hPa位势高度的波数-1和-2分量的异常。 与北大西洋海温异常相关的高纬度200 hPa位势高度纬向波数-1分量的异常与其气候学正位相，而中纬度的异常与其正气候学正位相相反（图8a）。 这意味着正的北大西洋海温在对流层高纬度地区加强了气候学波数-1波，而在中纬度地区抵消了气候学波数-1波，这意味着在对流层高纬度地区加强了气候学波数-1波，而在中纬度地区减弱了气候学波数-1波。 相比之下，与北大西洋海温异常区相关的位势高度中的波数-2分量的异常，在高纬度与其气候学处于相反的相位，但在中纬度与其气候学处于相同的相位（图8b）。 在去除PDO信号后，与北大西洋SSTA相关的位势高度的波数-1和-2分量中的这些特征仍然存在，但在高纬度位势高度的波数-1分量中的异常幅度较小（图中未显示）。 这意味着与PC 1 NA相关的海温异常可能导致大西洋脊和太平洋槽的形成，而北太平洋海温异常可能会加强大西洋脊和太平洋槽，尤其是在中纬度地区。
波在大气中是向上传播还是向下传播是由波结构的垂直倾斜决定的。当槽/脊随高度向西倾斜时，EPz通量向上，而当槽/脊随高度向东倾斜时，EPz通量向下。由于平流层急流的过滤效应，只有小波数的波（波1和2）才能传播到平流层，而其他高阶波数（较小尺度）分量则被困在对流层中。
波数为1（PW1）的行星波可以到达平流层上部，并在该区域具有最大的振幅（图3 a）;然而，波数为2（PW2）的行星波的振幅在平流层中下具有最大值（图3b）。在平流层中，PW1模式表现为北大西洋上的一个海槽和北太平洋上的一个海脊，而在对流层中，PW2结构占主导地位，在东亚和东北美洲沿海地区有两个槽，在北太平洋和西欧上有两个海脊。因此，结合PW1和PW2的结构，对流层东亚槽向上和向西延伸，并整合到平流层北大西洋槽中（图3c）。相比之下，对流层的美洲东北部槽向上和向东延伸，直到它合并到平流层北大西洋槽（图3c）。因此，平流层中的波数1和对流层中的波数2的组合有利于欧亚大陆上的向上波通量和美洲东北部和北大西洋上的向下波通量。
Harnik, N., Lindzen, R.S., 2001. The Effect of Reflecting Surfaces on the Vertical Structure and Variability of Stratospheric Planetary Waves. J Atmos Sci 58, 2872–2894.. doi:10.1175/1520-0469(2001)058<2872:teorso>2.0.co;2
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一般认为，较强的极涡是由较弱的行星波活动引起的。