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    (top) Zonal mean meridional structures of the leading EOFs of the barotropic circulation and of the 500-hPa geopotential height (Z500). (bottom) Zonal mean meridional structures of the leading EOFs of the Z500 variability and of the Z500 variability regressed onto the 70-hPa NAM. U500 and Z500 (U500R and Z500R) denote the velocity and the 500-hPa geopotential height (regressed on the 70-hPa NAM). U00 and Z00 denote the velocity and geopotential height of the barotropic circulation. The structures are normalized to one std dev of the respective PCs. The geopotential height unities are gpm, and the velocity units are 10−1 × m s−1.

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    (top) First three EOF patterns of the 500-hPa geopotential height variability. (middle) Regression pattern of the Z500 field onto the 70-hPa NAM. (bottom) Same as top, but for the residual variability, i.e., the variability that remained after subtraction of Z500 regressed on the 70-hPa NAM. The patterns are normalized to one std dev of the respective PCs. The values in the right top of each row are the percentages of variance represented by each (EOF, PC) pair. Contour interval is 10 gpm, except in the regression pattern where the contour interval is 7.5 gpm.

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    Lagged correlations between the daily data projections onto the first EOF of the barotropic mode and the NAM indices. Solid curves are for stratospheric NAMs from 10 (black) to 150 hPa (light gray). The dashed black curve is for 1000-hPa NAM and the dashed gray curve is for 500-hPa NAM. Positive lags mean that NAM indices are leading.

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    Correlation between the zonal wind means in the longitude sectors of (90°–255°E) and (90°W–30°E). The solid black curve corresponds to daily anomalies. The dashed and the solid gray lines correspond to daily anomalies smoothed by 11- and 31-day running means, respectively.

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    (top) Zonal mean meridional structures of the first EOFs of the total and residual Z500 variabilities. (bottom) Zonal mean meridional structures of the first EOFs of the total and the second EOF of the residual variability. U500R and Z500R denote the meridional profiles of the velocity and geopotential height associated with the EOFs of the residual variability, respectively.

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    (top) Correlation maps between Z500 residual anomalies and the four time series defined over the Pac, Sib, Ice, and Ber centers. Contour interval is 0.15. The solid thick lines represent the zero contours.

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    Same as Fig. 2, but for the 1000-hPa geopotential height field (Z1000). Contour interval is 5 gpm.

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    Same as Fig. 6, but for Z1000 residual anomalies and the three 1000-hPa anomaly time series.

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    (top) Regression maps of the Z1000 residual anomalies on the three normalized 1000-hPa anomaly time series defined over the Atl, Pac, and Ice centers. (bottom) As in the top, but regressing out the variability associated with the PC2. Contour interval is 5 gpm. The solid thick lines represent the zero contours.

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Annular versus Nonannular Variability of the Northern Hemisphere Atmospheric Circulation

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  • 1 CESAM, Department of Physics, University of Aveiro, Aveiro, Portugal
  • | 2 Department of Physics, Universidade de Trás-os-Montes e Alto Douro, Vila Real, and Physics Department, University of Lisbon, Lisbon, Portugal
  • | 3 CESAM, Department of Physics, University of Aveiro, Aveiro, Portugal, and University of Vigo at Ourense, Ourense, Spain
  • | 4 Centre for Atmospheric Science, Geography Department, University of Cambridge, Cambridge, United Kingdom
  • | 5 CESAM, Department of Physics, University of Aveiro, Aveiro, Portugal
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Abstract

The annular variability of the northern winter extratropical circulation is reassessed based on reanalysis data that are dynamically filtered by normal modes. One-half of the variability of the monthly averaged barotropic zonally symmetric circulation of the Northern Hemisphere is statistically distinct from the remaining variability and is represented by its leading empirical orthogonal function (EOF) alone. The daily time series of the circulation anomalies projected onto the leading EOF is highly correlated (r ≥ 0.7) with the lower-stratospheric northern annular mode (NAM) indices showing that annular variability extends from the stratosphere deep into the troposphere. However, the geopotential and wind anomalies associated with the leading principal component (PC1) of the barotropic zonally symmetric circulation are displaced northward relative to the zonal mean anomalies associated with the PC1 of the geopotential height variability at single-isobaric tropospheric levels. The regression pattern of the 500-hPa geopotential height (Z500) onto the lower-stratospheric NAM also shows zonally symmetric components displaced northward with respect to those of the leading EOF of the Z500 field.

A principal component analysis (PCA) of the residual variability of the Z500 field remaining after the substraction of the Z500 regressed onto the lower-stratospheric NAM index also reveals a pattern with a zonally symmetric component at midlatitudes. However, this zonally symmetric component appears as the second EOF of the residual variability and is the imprint of two independent dipoles over the Pacific and Atlantic Oceans.

Results show that a zonally symmetric component of the middle- and lower-tropospheric circulation variability exists at high latitudes. At the middle latitudes, the zonally symmetric component, if any exists, is artificially overemphasized by the PCA on single-isobaric tropospheric levels.

Corresponding author address: J. M. Castanheira, Department of Physics, University of Aveiro, Aveiro 3810-193, Portugal. Email: jcast@ua.pt

Abstract

The annular variability of the northern winter extratropical circulation is reassessed based on reanalysis data that are dynamically filtered by normal modes. One-half of the variability of the monthly averaged barotropic zonally symmetric circulation of the Northern Hemisphere is statistically distinct from the remaining variability and is represented by its leading empirical orthogonal function (EOF) alone. The daily time series of the circulation anomalies projected onto the leading EOF is highly correlated (r ≥ 0.7) with the lower-stratospheric northern annular mode (NAM) indices showing that annular variability extends from the stratosphere deep into the troposphere. However, the geopotential and wind anomalies associated with the leading principal component (PC1) of the barotropic zonally symmetric circulation are displaced northward relative to the zonal mean anomalies associated with the PC1 of the geopotential height variability at single-isobaric tropospheric levels. The regression pattern of the 500-hPa geopotential height (Z500) onto the lower-stratospheric NAM also shows zonally symmetric components displaced northward with respect to those of the leading EOF of the Z500 field.

A principal component analysis (PCA) of the residual variability of the Z500 field remaining after the substraction of the Z500 regressed onto the lower-stratospheric NAM index also reveals a pattern with a zonally symmetric component at midlatitudes. However, this zonally symmetric component appears as the second EOF of the residual variability and is the imprint of two independent dipoles over the Pacific and Atlantic Oceans.

Results show that a zonally symmetric component of the middle- and lower-tropospheric circulation variability exists at high latitudes. At the middle latitudes, the zonally symmetric component, if any exists, is artificially overemphasized by the PCA on single-isobaric tropospheric levels.

Corresponding author address: J. M. Castanheira, Department of Physics, University of Aveiro, Aveiro 3810-193, Portugal. Email: jcast@ua.pt

1. Introduction

After some initial discussion (e.g., Deser 2000; Ambaum et al. 2001; Wallace and Thompson 2002) on the northern annular mode (NAM) and on the North Atlantic Oscillation (NAO) paradigms, the annular mode seems to be increasingly and implicitly assumed as a fundamental variability pattern whose manifestation over the Northern Atlantic is the NAO. In the NAM paradigm, the extratropical variability at the surface is dominated by an oscillation of atmospheric mass between the polar cap and the midlatitudes, a pattern named the Arctic Oscillation (AO). Given geostrophic balance, the NAM may be understood as the variability of the zonal mean zonal wind at middle and high latitudes, while the NAO may be understood as the variability of the westerlies over the North Atlantic basin. In spite of many works studying physical mechanisms for the NAM and/or the NAO and the widespread use of NAM and NAO indices, the dynamical nature of these variability structures remains unclear. Thompson and Wallace (1998, 2000), Baldwin and Dunkerton (2001), and Wallace and Thompson (2002) argued that a dynamical coupling between the stratosphere and troposphere is manifest as vertically coherent variations in the annular modes of extratropical variability, which are characterized by zonally symmetric fluctuations of the geopotential height and zonal wind fields. However, in the stratosphere the NAM is more readily interpreted as representing the variability of polar vortex strength. In the troposphere, the interpretation is much more difficult because of the entangled sources of tropospheric variability. In fact, empirical orthogonal function (EOF) analysis may produce zonally symmetric leading patterns even when the dynamics are not particularly zonally coherent on hemispheric length scales (Ambaum et al. 2001; Gerber and Vallis 2005). As shown by these authors, performing a principal component analysis (PCA) on a variability field dominated by independent dipolar structures, like the NAO or the North Pacific Oscillation (NPO)–west Pacific (WP) pattern, one may obtain leading EOF patterns with a high degree of zonal symmetry. Deser (2000) and Ambaum and Hoskins (2002) argued that the leading EOF of the extratropical circulation in the lower troposphere does not represent a teleconnection pattern and that the annular mode in the stratosphere is coupled with the NAO. Itoh and Harada (2004) also argued that the leading EOF (NAM) of the extratropical stratospheric circulation variability is coupled with the NAO in the troposphere, whereas the second EOF is coupled with the Pacific–North American (PNA) teleconnection pattern.

Here we present an analysis clearly showing that much of the tropospheric NAM variability, that is, the variability projected onto the leading EOF of geopotential height at single isobaric levels, is not coupled with the variations of the polar vortex strength. A large fraction of the midlatitude zonally symmetric component of the tropospheric NAM seems to result from two independent dipolar structures over the Pacific and Atlantic Oceans. A zonally symmetric component of the middle- and lower-tropospheric zonal wind variability seems to only exist at high latitudes. Section 2 describes the data and the methods of analysis. Section 3 presents the obtained results, and section 4 provides some final remarks.

2. Data and method

The data were obtained from the global reanalysis dataset of the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR). We have used November–March daily means of the horizontal wind components (u, υ) and of the geopotential height, available at 17 standard pressure levels from 1000 to 10 hPa, with a horizontal grid resolution of 2.5° latitude × 2.5° longitude, covering the period 1958–2005. The polar vortex strength is represented by the stratospheric NAM indexes (Baldwin and Dunkerton 2001).

The horizontal wind (u, υ) and the geopotential height (z) were expanded onto the normal modes of the NCEP–NCAR reference atmosphere (Castanheira et al. 2002),
i1520-0442-21-13-3180-e1
In this equation, Gm(p) represent the separable vertical structures, where p is the pressure, and m is a vertical index. Here, m = 0 refers to the barotropic vertical structure, and m > 0 refers to baroclinic vertical structures. The matrix 𝗖m = diag[(ghm)1/2, (ghm)1/2, ghm] is a diagonal matrix of scaling factors with g the earth’s gravity and hm the equivalent height. Each horizontal structure function is given by the product of a zonal wave with wavenumber s and a vector [U(θ), iV(θ), Z(θ)]Tmsl,α, which defines the meridional profile of the wave, and l is a meridional index. The index α = 1, 2, 3 refers to westward-traveling inertio-gravity waves, planetary Rossby waves, and eastward-traveling inertio-gravity waves, respectively. The expansion onto the 3D normal modes allows partitioning of the atmospheric circulation into planetary Rossby waves and inertio-gravity waves, with both types of waves possessing barotropic and baroclinic vertical structures (Castanheira et al. 2002). We replaced the Southern Hemisphere circulation with the specular image of the northern one before the projection onto the normal modes because we are interested in the variability of the northern extratropical circulation. The extratropical circulation is in very close geostrophic balance, and in the subsequent analysis we retained only the barotropic Rossby modes (α = 2).

The daily mean seasonal cycle of the circulation fields was estimated by the 48-yr means for each calendar day and then by smoothing the obtained time series of daily multiannual means using a 31-day running average. Daily anomalies of the circulation fields were obtained by subtracting the seasonal cycle from the original data. Principal component analyses were performed both on the phase space of the 3D normal mode projection coefficients wαmsl and on the extratropical 500- and 1000-hPa geopotential height fields north of 20°N. Before performing the PCA, the anomaly time series were smoothed using a 31-day running mean, leaving only the daily smoothed values between 16 November and 15 March for the November–March period. The 3D normal mode projection coefficients wαmsl were obtained by a horizontal-area integration (Castanheira et al. 2002). To use equal area–weighted data in the analyses of the 500- and 1000-hPa geopotential height fields, the grid point data were weighted with the square root of the cosine of the latitude before calculating the covariance matrixes.

3. Results

a. 500-hPa geopotential height field (Z500)

As shown by Ambaum et al. (2001), hemispheric EOF analyses of different lower-tropospheric parameter fields that one might expect to be dynamically related can yield very different results and patterns that are not obviously related. They found this to be the case for the 850-hPa geopotential height and the 850-hPa streamfunction. On the other hand, Thompson and Wallace (1998, 2000) and Wallace and Thompson (2002) argue that a dynamical coupling between the stratosphere and troposphere is manifest in the annular modes, which characterize deep, zonally symmetric fluctuations of the geopotential height and zonal wind fields. Having these results in mind, it seems useful to look for the joint variability of the zonal means of geopotential height and zonal wind at all isobaric levels.

The barotropic 3D normal modes represent a mass-weighted vertical mean of the atmospheric circulation and, therefore, are very sensitive to the tropospheric circulation (Castanheira et al. 2002). A PCA on the joint variability of the geopotential and the zonal wind fields requires that the two fields are adequately weighted. The U and Z components of the zonally symmetric Rossby modes satisfy the geostrophic balance, and the projection onto the normal modes allows for an appropriate weighting of the two fields. On the other, an EOF analysis on the projection coefficients will retrieve dynamically consistent patterns for both fields. Hence, the analysis of the joint variability of the zonal means of the geopotential height and zonal wind at all isobaric levels was performed by a PCA of the coefficients of the barotropic zonally symmetric Rossby modes. Using these procedures, the ageostrophic motions were filtered away, and the geopotential height and wind were simultaneously weighted in a dynamical self-consistent way. The leading EOF (Fig. 1) represents one-half (50.4%) of the total variability and is statistically distinct according to North’s rule of thumb. The EOF meridional structures were retrieved retaining only the zonally symmetric barotropic Rossby modes (i.e., m = 0, s = 0, α = 2) in the expansion (1) and replacing the coefficients w200l with the respective EOF loadings (Castanheira et al. 2002). The meridional profile of the zonal mean geopotential height associated with the leading EOF of the Z500 field is also represented in the same figure. Before drawing the figure, the zonal mean amplitude of the leading EOF of Z500 was divided by the square root of the cosine of the latitude to retrieve the zonal mean meridional profile of the geopotential height. The meridional profile of the zonal mean zonal wind (U500) associated with the leading EOF of the Z500 field was obtained using the geostrophic relationship. The first three EOF patterns of the Z500 field are shown in the upper panel of Fig. 2 for reference purposes. The results are virtually the same when we use an 11-day running mean instead of a 31-day running mean, but the leading PCs of the 11-day smoothed data represent a smaller fraction of the respective variability.

The fact that the leading EOF of the zonally symmetric barotropic Rossby modes is representing annular variability over the whole vertical domain is demonstrated by Fig. 3. It shows the lagged correlations between the daily NAM indices and the projections of daily anomalies onto the first EOF of the barotropic mode. These projections are highly correlated with the NAM indices over the whole atmosphere, and a signal of delayed correlation with the high levels in the stratosphere is observed.

Comparing the zonal mean geopotential height profiles in Fig. 1, one observes that the leading EOF of Z500 has larger amplitudes at midlatitudes. At high latitudes, it shows amplitudes comparable to those of the leading EOF of the barotropic zonally symmetric Rossby modes. The differences of the geopotential height profiles lead to remarkable differences of the respective zonal mean zonal wind profiles. The leading EOF of Z500 represents a seesaw of zonal mean zonal wind between the subtropics and midlatitudes, whereas the seesaw is displaced northward in the zonally symmetric barotropic circulation, presenting stronger zonal wind anomalies at high latitudes. The leading EOF of the Z500 field captures much more zonally symmetric variability in the midlatitudes than the one represented by the leading EOF of the zonally symmetric barotropic circulation. This suggests that the leading EOF of the Z500 field pattern may include variability structures that are not part of the vertically coherent variations of the annular mode. Clearly the correlation of the tropospheric NAMs with the barotropic annular mode (Fig. 3) is reduced when compared with the stratospheric NAMs. This is especially the case when the tropospheric NAM leads by more than 5 days.

The lagged correlations in Fig. 3 are based on unfiltered daily time series, and a signal of delayed correlation is suggested by the asymmetry of correlation curves for NAM indices at levels above 50 hPa. At stratospheric levels below 50 hPa, the correlation curves are very close and nearly symmetric, suggesting a rapid progression of the circulation anomalies from the lower stratosphere to the troposphere. It is convenient to use a NAM index well inside the stratosphere, but close to the tropopause, for the study of the coupling of the stratospheric and tropospheric circulations and to avoid the necessity of consideration of lagged effects. Considering results of Fig. 3, we chose to represent the polar vortex strength by the 70-hPa NAM index. However, the results were shown to be qualitatively the same if we used the 50- or 100-hPa NAM indices.

The middle panel in Fig. 2 shows the regression pattern of the Z500 field on the 70-hPa NAM. To make the regression and the EOF patterns comparable, the Z500 field was also weighted by the square root of the cosine of the latitude before performing the regression. By visual inspection, one might say that the regression pattern shares the main annular features of the leading Z500 EOF, but with a weaker Pacific center. However, comparing the respective meridional structures, shown in the lower panel of Fig. 1, it becomes clear that they are different. The regression pattern shows a zonal mean meridional structure close to that of the leading EOF of the barotropic mode (U00 and Z00 in the upper panel of Fig. 1).

From the leading EOF and the regression patterns in Fig. 2, using the geostrophic relationship, we may conclude that the largest zonal wind anomalies must occur in the [90°W, 30°E] and the [90°E, 255°E] longitude sectors. Figure 4 shows the correlations between the zonal means of the 500-hPa zonal winds in each longitude sector. The correlations are small and negative at middle latitudes and higher and positive at high latitudes. The strong negative correlations near the pole are in agreement with the displacement of the vortex center over Greenland. This figure shows that positively correlated zonal wind anomalies corresponding to a true annular component occur only at high latitudes. The longitude sector over the Pacific, in which the zonal wind was averaged, is rather broad, and its east side is close to the west side of the Atlantic longitude sector. Considering a smaller [90°E, 225°E] longitude sector does not appreciably change the correlation curves. It may also be possible that the zonal winds are shifted in latitude between the two basins. We recomputed the correlations considering the zonal mean wind over the Pacific shifted by 2.5°, 5.0°, 7.5, ° and 10.0° to the north or south of the zonal mean wind over the Atlantic sector. Generally the correlations decrease as the latitudinal shift increases. Only for the subtropical (south of 35°N) latitudes and high latitudes (north of 80°N) do the correlation values increase slightly for some shifts.

By construction, both the regression pattern and the leading EOF of the barotropic mode represent tropospheric annular variability coupled with stratospheric annular variability. However, it may be possible that there is an annular component of the tropospheric variability decoupled from the stratosphere. To investigate this possibility, we performed a PCA on the residual Z500 field that remained after the subtraction of the Z500 data regressed linearly onto the 70-hPa NAM.

The first three EOFs of the residual Z500 field are shown in the bottom panel of Fig. 2. Comparing these EOFs with the corresponding EOFs of the total variability, in the top of the figure, one observes that the third EOF is quite insensitive to the stratospheric variability. The most pronounced differences are seen in the first two EOFs. The first EOF of the residual variability shows the PNA structure and a wave train over the Atlantic and Eurasia, like the augmented PNA pattern proposed by Wallace and Thompson (2002). These results suggest that the first two EOFs of the Z500 total variability represent mixed variability associated with both the PNA and the stratospheric vortex variability. The second EOF of the Z500 residual variability shows two dipoles over the Atlantic and Pacific oceans. As argued by Gerber and Vallis (2005), performing a PCA on a variability field dominated by independent dipolar structures, one may end up falsely with leading EOF patterns with a high degree of zonal symmetry. Figure 5 shows, again, the meridional structures of the first EOF of the total Z500 field and the meridional structures of the first two EOFs of the residual Z500 field. The meridional structure of the leading EOF of the residual variability shows a seesaw shifted equatorward relative to the leading EOF of the total variability. On the other hand, the meridional structures of the first EOF of the total field and of the second EOF of the residual field are very similar, except at high latitudes north of 65°N, where the residual EOF shows a flattened geopotential profile. The flattening of geopotential at high latitudes with a zonal mean zonal wind close to zero must be because of the absence of the annular variability regressed on the stratospheric variability. These results suggest that, at latitudes south of 65°N, the zonally symmetric component of the first EOF of the total field may largely be the imprint of the two dipolar structures revealed in the second EOF of the residual variability. Here the question remains whether the dipolar structures in the second EOF of the residual variability are independent.

Hence, we defined four anomaly time series of the residual field as follows:

  1. Pacific time series (Pac): the area–weighted average of the Z500 anomaly inside the minimum contour of EOF1 of the residual variability over the Pacific;

  2. Iceland time series (Ice): the area–weighted average of the Z500 anomaly inside the minimum contour of EOF2 of the residual variability over Iceland and Greenland;

  3. Bering Strait time series (Ber): the area–weighted average of the Z500 anomaly inside the dotted contour on the EOF2 of the residual variability over the Bering Strait; and

  4. Siberia time series (Sib): the area–weighted average of the Z500 anomaly inside the maximum contour of EOF3 of the residual variability over Siberia.

Figure 6 shows the correlation maps between the Z500 residual anomalies at each grid point and at the four time series defined above. The correlation with the Pacific time series shows the characteristic PNA pattern. The secondary wave train over the Atlantic and Eurasia observed in the EOF1 of the residual variability is only reminiscent in the correlation pattern. Wallace and Thompson (2002) argued that if we calculated the regression maps instead of the correlation maps, the secondary wave trains would be emphasized. We did that, but the secondary wave train remained reminiscent (not shown). These results suggest a regional (not hemispheric) character of the PNA. The correlation with the Siberia time series shows a pattern similar to the third EOFs of the residual and total variabilities, suggesting that both EOFs are capturing true teleconnectivity. These EOFs show a wave train that is nearly in quadrature with the wave train over the Atlantic and Eurasia observed in the EOF1 of the residual variability. Then it is possible that the PNA, through its Florida center, may influence the excitation of the Atlantic–Eurasian wave train represented in the third EOF (Reyers et al. 2006). In this case, the leading EOF of the residual variability would represent teleconnectivities implied by the both the Pacific–North American wave train and the Atlantic–Eurasian wave train.

The most prominent structures in the correlation maps with the Icelandic and the Bering Strait time series are two meridional dipolar structures over the respective ocean basins. The correlations of both time series with gridpoint anomalies over the opposite ocean basin are very small, explaining less than 4% of their variabilities. The correlation map with the Icelandic time series depicts the NAO pattern. It is worth remarking that similar correlation maps are obtained if we consider the total Z500 variability, or if we use an 11-day running mean instead of a 31-day running mean.

Table 1 shows the correlations between the four time series defined above. The statistical significance of the correlation values was assessed by performing 10 000 random permutations of the years. Permuting only the years, one conserves the serial autocorrelation of the smoothed daily time series. Using a one-sided statistical test at the level p = 0.15, the weak correlation between the Icelandic and Bering indices (r = 0.07) does not reject the null hypothesis that they are uncorrelated. The results of Fig. 6 and Table 1 together show that, at least, a very large fraction of the zonally symmetric component of the leading EOF of the Z500 total variability is due to the independent variability of dipolar structures over the Pacific and Atlantic basins. This result is completely consistent with the theoretical findings of Gerber and Vallis (2005).

b. 1000-hPa geopotential height field (Z1000)

Much of the discussion about the teleconnectivity represented in the NAM–AO structure was based on the analysis of the variability of the mean sea level pressure field (PSL) and the 1000-hPa geopotential height field (Z1000) (e.g., Thompson and Wallace 1998; Deser 2000; Ambaum et al. 2001; Wallace and Thompson 2002). Figure 7 shows an analysis similar to the one in Fig. 2, but for the 1000-hPa geopotential height field. The regression of the Z1000 anomalies on the 70-hPa NAM reveals a pattern very close to that of the first EOF of Z1000 (the Arctic Oscillation). The spatial correlation between the two patterns is r = 0.97. The bottom panel of Fig. 7 shows the three EOFs of the residual Z1000 field that remained after regressing out the 70-hPa NAM. The second and third EOFs seem to be very insensitive to the stratospheric variability. The first EOF of the residual field is similar to the first EOF of the total field (their spatial correlation is r = 0.94), but with the relative magnitudes of the Atlantic and Pacific centers changed. This is because of the regression of Z1000 on the 70-hPa NAM is stronger over the Atlantic area than over the Pacific area.

Because the leading EOFs of the total and residual Z1000 fields are similar, one may, again, question if there is a tropospheric annular component independent from the stratospheric annular variability. To check this possibility in the Z1000 residual field, we defined the following three time series:

  1. Pacific time series (Pac): the area weighted average of Z1000 anomaly inside the maximum contour of the EOF1 of the residual variability over the Pacific;

  2. Iceland time series (Ice): the area weighted average of Z1000 anomaly inside the minimum contour of EOF1 of the residual variability over Iceland and Greenland; and

  3. Atlantic time series (Atl): the area weighted average of Z1000 anomaly inside the maximum contour of the EOF1 of the residual variability over the Atlantic.

Figure 8 shows the correlation maps between the Z1000 residual time series anomalies at each grid point and the three time series defined above. Similar correlation maps (not shown) were obtained when we considered the Z1000 total anomalies instead of residual anomalies. The correlation maps reproduce the NAO dipole and a surface imprint of the PNA pattern. However, the correlations between the Atlantic center and Z1000 anomalies over the Pacific are near zero and even negative over the northern Pacific. It may be argued, as in Wallace and Thompson (2002), that the positive correlation between the Atlantic and Pacific centers is “destroyed” by the anticorrelation associated with the EOF2 pattern. They suggested that the structure of the EOF2 represents an augmented PNA teleconnection pattern. Using their same argument, we must expect that such a teleconnection pattern would reinforce the anticorrelations between the Icelandic center and the Z1000 anomalies over the Pacific. However, the anticorrelation between the Icelandic center and the Z1000 anomalies over the Pacific is small, and it seems not be different from the anticorrelation implied by the EOF2 itself. In fact, following the procedure of Wallace and Thompson (2002), one obtains contradicting results. The top panel in Fig. 9 shows the regression maps of the Z1000 residual anomalies on the three normalized 1000-hPa anomaly time series defined above. The regression map on the Atlantic time series depicts the NAO pattern. On the other hand, the regression map on the Icelandic time series is similar to the leading EOF. Their spatial correlation is r = −0.83. The bottom maps in Fig. 9 also show the same regression maps, but after removing the variability represented by PC2. Now the regression map with the Atlantic center shows a center with equal polarity over the Pacific. However, the regression on the Icelandic time series lost its center over the Pacific and depicts the NAO pattern. Very similar results were obtained when the same analysis is performed on the total variability instead of the residual variability. Therefore, the above correlation and regression maps suggest that the Pacific center of the leading Z1000 EOF does not belong to the teleconnection pattern represented by the NAO dipole.

4. Concluding remarks

A PCA on the variability of the 31-day running averages of the barotropic zonally symmetric circulation of the Northern Hemisphere was performed for the cold season (November–March). The leading EOF represents one-half (50.4%) of the total variance and is statistically distinct from the remaining variability. The second EOF represents 23.3% of the total variance. The daily time series of the circulation anomalies projected onto the leading EOF is highly correlated (r ≥ 0.7) with the lower-stratospheric annular mode indices, showing that the annular variability extends from the stratosphere deep into the troposphere. However, the analysis also reveals differences between the zonally symmetric components of the annular modes defined at single isobaric tropospheric levels (EOF1) and the meridional profile of the EOF1 of the barotropic zonally symmetric circulation. It is shown that the annular modes defined at single isobaric tropospheric levels (EOF1) represent a much larger fraction of zonally symmetric variability at midlatitudes than that represented by the EOF1 of barotropic zonally symmetric circulation. The zonally symmetric component of the 500-hPa geopotential height regressed onto the lower-stratospheric (70-hPa) NAM also reveals the same differences with the zonally symmetric components of the annular modes defined at single isobaric tropospheric levels (EOF1). Therefore, it is concluded that a large fraction of the midlatitude zonally symmetric variability represented by the leading EOF at single isobaric tropospheric levels is not linearly associated with the stratospheric variability.

A PCA was performed on the residual variability of 500-hPa geopotential that remained after regressing out the 70-hPa NAM index. The leading EOF of this variability reveals the PNA teleconnection pattern associated with a secondary wave train over the Atlantic and Eurasia. The second EOF has a zonally symmetric component similar to that of the leading EOF of the total variability, and it is the imprint of two meridional dipoles over the Pacific and Atlantic Oceans. Only a very small fraction (less than 4%, |r| < 0.2) of the variability over each ocean basin is correlated with the variability of the northern center of the meridional dipole in the opposite ocean basin. The analysis of the 1000-hPa geopotential height field gave results consistent with the analysis of the 500-hPa geopotential height field. The Pacific and Atlantic centers of the leading EOF of the Z1000 residual field do not belong to a common three-center teleconnection pattern. These results show that the midlatitude annular imprint on the leading EOFs of the Z500 and Z1000 total fields is strongly exaggerated by the PCA method, whose criterion is the maximization of the represented variance integrated over the analyzed domain. In fact, the zonal mean zonal wind anomalies over each northern ocean are positively correlated only at high latitudes.

No zonally symmetric coherent variability was found in the residual tropospheric circulation. Hence, the zonally symmetric coherent variability of the extratropical tropospheric circulation appears to be always coupled with the stratospheric annular variability. By construction, the leading EOF of the barotropic zonally symmetric circulation takes this coupling into account explicitly. However, because the barotropic component is approximately the vertical mass-weighted average of the atmospheric circulation, it is much more sensitive to the tropospheric variability. On the other hand, the leading EOFs of the total geopotential fields at single isobaric levels show midlatitude zonally symmetric components that are strongly exaggerated by variability due to local dynamics. This does not seem to be the case of the leading EOF of the barotropic zonally symmetric circulation, which represents a weaker annular component in the middle latitudes. Together these results suggest that the projections onto the leading EOF of the barotropic zonally symmetric circulation may provide a better index for the annular behavior in the troposphere than the projections onto the leading EOFs of geopotential fields at single isobaric levels (NAM indices).

Finally, we remark that the tropospheric NAM indices do not seem to be appropriate for representing the zonally symmetric circulation response to climate changes. In fact, as already stressed, the zonally symmetric component of the leading EOF of the isobaric geopotential height field in the troposphere is, at least to a great part, the imprint of independent dipolar structures over the ocean basins. These results are particularly important for studies of the tropospheric response to changes originating in the stratosphere, for example, changes in stratospheric chemical composition. The use of indices based on the leading EOF of tropospheric geopotential height field may imply some artificial impact at midlatitudes.

Acknowledgments

In this research, Dr. Laura de La Torre and M. L. R. Liberato have been supported by Grants SFRH/BPD/26474/2005 and SFRH/BD/32640/2006 of the FCT (Fundação para a Ciência e a Tecnologia, Portugal), respectively.

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Fig. 1.
Fig. 1.

(top) Zonal mean meridional structures of the leading EOFs of the barotropic circulation and of the 500-hPa geopotential height (Z500). (bottom) Zonal mean meridional structures of the leading EOFs of the Z500 variability and of the Z500 variability regressed onto the 70-hPa NAM. U500 and Z500 (U500R and Z500R) denote the velocity and the 500-hPa geopotential height (regressed on the 70-hPa NAM). U00 and Z00 denote the velocity and geopotential height of the barotropic circulation. The structures are normalized to one std dev of the respective PCs. The geopotential height unities are gpm, and the velocity units are 10−1 × m s−1.

Citation: Journal of Climate 21, 13; 10.1175/2007JCLI1960.1

Fig. 2.
Fig. 2.

(top) First three EOF patterns of the 500-hPa geopotential height variability. (middle) Regression pattern of the Z500 field onto the 70-hPa NAM. (bottom) Same as top, but for the residual variability, i.e., the variability that remained after subtraction of Z500 regressed on the 70-hPa NAM. The patterns are normalized to one std dev of the respective PCs. The values in the right top of each row are the percentages of variance represented by each (EOF, PC) pair. Contour interval is 10 gpm, except in the regression pattern where the contour interval is 7.5 gpm.

Citation: Journal of Climate 21, 13; 10.1175/2007JCLI1960.1

Fig. 3.
Fig. 3.

Lagged correlations between the daily data projections onto the first EOF of the barotropic mode and the NAM indices. Solid curves are for stratospheric NAMs from 10 (black) to 150 hPa (light gray). The dashed black curve is for 1000-hPa NAM and the dashed gray curve is for 500-hPa NAM. Positive lags mean that NAM indices are leading.

Citation: Journal of Climate 21, 13; 10.1175/2007JCLI1960.1

Fig. 4.
Fig. 4.

Correlation between the zonal wind means in the longitude sectors of (90°–255°E) and (90°W–30°E). The solid black curve corresponds to daily anomalies. The dashed and the solid gray lines correspond to daily anomalies smoothed by 11- and 31-day running means, respectively.

Citation: Journal of Climate 21, 13; 10.1175/2007JCLI1960.1

Fig. 5.
Fig. 5.

(top) Zonal mean meridional structures of the first EOFs of the total and residual Z500 variabilities. (bottom) Zonal mean meridional structures of the first EOFs of the total and the second EOF of the residual variability. U500R and Z500R denote the meridional profiles of the velocity and geopotential height associated with the EOFs of the residual variability, respectively.

Citation: Journal of Climate 21, 13; 10.1175/2007JCLI1960.1

Fig. 6.
Fig. 6.

(top) Correlation maps between Z500 residual anomalies and the four time series defined over the Pac, Sib, Ice, and Ber centers. Contour interval is 0.15. The solid thick lines represent the zero contours.

Citation: Journal of Climate 21, 13; 10.1175/2007JCLI1960.1

Fig. 7.
Fig. 7.

Same as Fig. 2, but for the 1000-hPa geopotential height field (Z1000). Contour interval is 5 gpm.

Citation: Journal of Climate 21, 13; 10.1175/2007JCLI1960.1

Fig. 8.
Fig. 8.

Same as Fig. 6, but for Z1000 residual anomalies and the three 1000-hPa anomaly time series.

Citation: Journal of Climate 21, 13; 10.1175/2007JCLI1960.1

Fig. 9.
Fig. 9.

(top) Regression maps of the Z1000 residual anomalies on the three normalized 1000-hPa anomaly time series defined over the Atl, Pac, and Ice centers. (bottom) As in the top, but regressing out the variability associated with the PC2. Contour interval is 5 gpm. The solid thick lines represent the zero contours.

Citation: Journal of Climate 21, 13; 10.1175/2007JCLI1960.1

Table 1.

Correlations between the time series of the area–weighted averages of the Z500 residual anomalies over the Pac, Sib, Ice, and Ber centers. The time series were smoothed by a 31-day running mean. The asterisk denotes values statistically different from 0 at the level p = 0.05, using a one-sided test.

Table 1.
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