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• Introduction
• Observed downward propagation of zonal wind variations
• Possible Mechanism
• Analysis I: Downward propagation in the stratosphere
• Analysis II: Downward propagation from the lower stratosphere to the lower troposphere
• Conclusions
• References

FIGURES

• Figure 1
• Figure 2
• Figure 3
• Figure 4
• Figure 5
• Figure 6
• Figure 7
• Figure 8
• Figure 9

1. Introduction

A mechanism for the downward propagation of polar cap mean zonal wind (u_pcm) variations, hypothesized by Thompson and Wallace (1998) and Baldwin and Dunkerton (1999), has been verified using ECMWF circulation data for NH winter 1988-89.

2. Observed downward propagation of zonal wind variations

Daily ECMWF Re-Analyses (ERA-15) from October 1988 to April 1989 (horizontal resolution 2.5Ž with pressure up to 10 hPa) are used to investigate the vertical propagation of variations of the zonal wind averaged over the polar cap north of 60Ž N.

Figure 1: The low-pass (91-day running mean) filtered u_pcm time series and second order polynomial fits for the winter (DJF) of 1988-89 at different levels. t_fitmax is the time at which the polynomial maximizes. The difference between the values of t_fitmax at different levels is a measure for the time lag for variations in u_pcm between these levels.

Figure 2: Correlation coefficient between the low-pass filtered u_pcm time series at 10 hPa and the low-pass filtered time series at all levels, with different time lags.

Figure 1 and 2 show that ultra-low frequency variations (described by the polynomial fits) of u_pcm propagate downward from 10 hPa to 200 hPa in about 20 days and then to the surface in about 5 days.

3. Possible Mechanism

I. Downward propagation in the stratosphere

A positive zonal-mean zonal wind anomaly (hereafter [u]', where the accent denotes the anomaly) in the stratosphere can propagate downward as follows. Planetary waves from the troposphere are refracted anomalously equatorward by anomalously large vertical [u] gradients, resulting in a positive anomaly of convergence of meridional momentum flux (hereafter F_m^' ) at high latitudes just below the original [u]'. The F_m' causes an acceleration of [u], so that the original [u]' is followed by a similar anomaly at the level below. This process is then repeated for lower and lower levels, resulting in a downward propagation of the [u] anomalies. Also the F_m anomalies are expected to propagate downward.

II. Downward propagation from the lower stratosphere to the lower troposphere

The u_pcm variations can then propagate further down to the lower troposphere in the following 4 steps (see Fig. 3):

1. F_m' in layer 1 drives, through the positive [u]' and associated meridional Coriolis force (F_c,u), a polar cap mean meridional wind (v_pcm), which associated zonal Coriolis force (F_c) counteracts the original F_m'. The v_pcm implies an equatorward v at 60Ž N in the stratosphere (v₁) and upper troposphere (v₂).
2. v₁ and v₂ at 60Ž N induce a lower tropospheric poleward flow (v₃), which slightly lags the upper equatorward flow. The difference between v₁+v₂ (denoted as v₁₊₂) and v₃ determines the tendency of the polar cap mean surface pressure ('p_0,pcm/'t).
3. The anomalous meridional surface pressure gradient around 60Ž N implies an anomalous [u] around 60Ž N and thus an anomalous u_pcm near the surface.
4. The Coriolis force F_c due to v₃ maintains the anomalous zonal flow against friction.

Figure 3: Illustration of the hypothesized mechanism for the downward propagation of zonal wind variations from the lower stratosphere to the lower troposphere.

4. Analysis I: Downward propagation in the stratosphere

The downward propagation of u_pcm variations in the stratosphere is analyzed by considering the temporal dependence of the different terms of the polar cap mean quasigeostrophic zonal momentum equation (Peixoto and Oort, 1992), neglecting friction:

The u_pcm tendency directly calculated from u_pcm [hereafter ('u_pcm/'t)_d] closely resembles the residual u_pcm tendency [hereafter ('u_pcm/'t)_r], which is the sum of the computed F_m and F_c, giving confidence in the accuracy of the computed F_m and F_c (see Figure 6).

Figure 4: The low-pass filtered time series of F_m at different levels.

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Figure 5: Correlation coefficient between the low-pass filtered F_m time series at 10 hPa and the low-pass filtered time series at all levels, with different time lags.

Figure 4 and 5 show that ultra-low frequency variations of F_m propagate downward from 10 hPa to 200 hPa in about 20 days, like the u_pcm variations in Figures 1 and 2, and consistent with the hypothesized mechanism.

5. Analysis II: Downward propagation from the lower stratosphere to the lower troposphere

STEP 1:

Figure 6: The low-pass filtered time series of ('u_pcm/'t)_r, ('u_pcm/'t)_d, F_m and -F_c averaged over layer 1 (as defined in Fig. 3). Ultra-low frequent variations in F_m are followed by similar variations in -F_c after one week, leading to a positive 'u_pcm/'t in the first part of the winter when F_m and -F_c increase and a negative 'u_pcm/'t in the second part of the winter when F_m and -F_c decrease. F_m seems to induce an equatorward flow in the stratosphere after one week, which associated zonal Coriolis force counteracts F_m.

STEP 2:

Figure 7: The low-pass filtered time series of the meridional wind at 60Ž N integrated over different layers (as defined in Fig. 3). The largest fluctuations in the equatorward flow occur in the stratosphere (layer 1). 'p_0,pcm/'t is proportional to (vdp)₁₊₂₊₃. v₁ and v₂ induce a lower tropospheric poleward flow (v₃), which slightly lags the upper equatorward flow, leading to a negative 'p_0,pcm/'t when -v₁₊₂ and v₃ increase and a positive 'p_0,pcm /'t when -v₁₊₂ and v₃ decrease.

STEP 3:

Figure 8: The low-pass filtered time series of u_pcm and u between 50-70ƒ N, both at 1000 hPa, and the difference between p_0,pcm and p₀ averaged between 40-60ƒ N. Variations in the meridional pressure gradient around 60ƒ N coincide with variations in the surface zonal wind around 60ƒ N and thus in u_pcm near the surface.

STEP 4:

Figure 9: The low-pass filtered time series of v and u², both averaged between 50-70ƒ N, at 1000 hPa. Since the Coriolis force F_c and the zonal frictional force F_w are proportional to v and u², respectively, the almost constant ratio between v and u² indicates a balance between F_w and F_c .

6. Conclusions:

This study has given evidence for the following aspects of the hypothesized mechanism:

- Downward propagation of low-frequent u and F_m variations in the stratosphere.

- All four steps of the downward propagation from the lower stratosphere to the lower troposphere.

The hypothesis therefore seems to be valid, at least for NH winter 1988-89.

7. References:

Baldwin, M. P. and Dunkerton, T. J. 1999. Propagation of the Arctic Oscillation from the stratosphere to the troposphere. J. of Geophys. Res. 104, 30937-30946.

Peixoto, J. P. and Oort, A. H. 1992, Physics of climate, AIP Press, 520pp.

Thompson, D. W. J., and Wallace, J. M. 1998. The Arctic Oscillation signature in the wintertime geopotential height and temperature fields. Geophys. Res. Lett. 25, 1297-1300.

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