1. Introduction
While day-to-day weather changes are generally represented in terms of sequences of synoptic charts, climate variability on time scales of months and longer is often represented in terms of changes in the polarity and amplitude of a set of prescribed spatial patterns. Such climate variability patterns1 have been identified in numerous studies using a variety of linear statistical analysis techniques applied to a number of different atmospheric variables, most often based on monthly averaged data over extratropical Northern or Southern Hemisphere domains. With few exceptions, there seems to be a relatively good correspondence between the most prominent of the patterns identified in these studies. Regardless of the method and the variable used, analyzing the wintertime variability in the North Atlantic sector, for example, almost always yields a pattern similar to the North Atlantic Oscillation (NAO). Hence, it is accepted that there exist only a small number of independent patterns, which are simply viewed through different lenses so that as defined by each method they appear a little different. The NAO, for instance, may have been defined differently in Wallace and Gutzler (1981), Horel (1981), and Ambaum et al. (2001), yet it is viewed as the same entity. Recently, a different dynamical interpretation of the NAO was offered by Woollings et al. (2008), who defined the pattern in terms of the distinction between two states of the atmospheric circulation (North Atlantic atmospheric blocking versus an “unblocked” flow regime).
A number of well-established methods for defining climate variability patterns can be found in the literature. In assessing the utility of the variant of a given pattern as defined on the basis of a given analysis scheme, the following criteria are worthy of consideration:
the robustness of the pattern with respect to the choice of low-pass filter (if any) used in preprocessing the data, as well as with respect to the spatial domain of the analysis,
the strength and consistency of the associated climatic impacts,
the nature of the relation between the pattern and the background climatology,
the relevance of the suggested method of analysis to the dynamical processes considered in the study, and
the value of prescribed metrics, such as the fraction of explained variance or squared covariance, or the skewness and autocorrelation of the expansion coefficient time series.
In section 2 we describe the dataset and the data processing methodology. In section 3 we examine the statistics (mean and variance) of the 250-hPa zonal wind field and compare the teleconnectivity maps for the latter field and the 500-hPa geopotential height field. In section 4 we introduce and discuss the jet variability patterns derived from the EOF analysis. In section 5 we examine more closely the relation between the jet variability patterns and the storm tracks. We demonstrate the similarity between the sectoral zonal wind EOFs and the coupled patterns obtained by performing maximum covariance analysis (MCA) on the zonal wind field paired with an indicator of baroclinic wave activity. We also illustrate how baroclinic waves tend to maintain the jet anomalies upon which they are superimposed. In section 6 we provide a summary and discussion of our findings.
2. Data and analysis procedures
This study is based on the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40; Uppala et al. 2005), in particular the daily fields (1200 UTC) of the zonal and meridional wind components at 250 hPa (U250 and V250, respectively), geopotential height at 500 hPa (Z500), and potential temperature on the dynamical tropopause defined here as the 2–potential vorticity unit (PVU) surface (ΘPV2). The spatial resolution of the dataset is 2.5° × 2.5°. Our study focuses on the season December–March (DJFM; referred to as “wintertime”) through the years 1957–2002. The precipitation composites shown below (in Fig. 10) are based on the global daily precipitation analyses [from the Global Precipitation Climatology Project (GPCP)] provided by the National Aeronautics and Space Administration, which overlap with the rest of our data in the period 1997–2002 and have a spatial resolution of 1° × 1°.
EOF analysis of zonal wind is performed in two separate sectors of the Northern Hemisphere: 105°W–30°E, referred to as the Atlantic sector, and 120°E–105°W, referred to as the Pacific sector. The leading EOF in the Eurasian sector (20°–130°E) is also considered. In calculating the eigenvectors and the associated principal component (PC) time series we have area weighted the data to account for the uneven resolution of the spherical coordinate grid (North et al. 1982; Baldwin et al. 2009). Hemispheric patterns are produced by regressing the hemispheric zonal wind field onto the sectoral PCs. Within the respective sectors, these patterns define the corresponding EOFs and have the same units as the data (m s−1). Hereafter we refer to these hemispheric patterns as the zonal wind EOFs or jet variability patterns even though, in strict terms, they are extensions of them. The EOFs shown in the following sections have been tested for sampling errors using the “rule of thumb” suggested by North et al. (1982). In the related calculation of the standard error of each eigenvalue we have assumed that the effective number (Neff) of degrees of freedom in the daily data is equal to N/(2td), where N is the total number of days in the data and td is the e-folding decorrelation time of the respective PC. Leith (1973) shows this to be a conservative estimate based on a first-order Markov process fitted to the data time series. All the EOFs shown here qualify as statistically significant in terms of the abovementioned criterion.
For separating the synoptic-scale variability associated with baroclinic waves, a bandpass Fourier filter is used that retains all transients with periods of 2–10 days. A more detailed description of the filtering method used can be found in Athanasiadis and Ambaum (2009). These high-frequency transients are also referred to as synoptic eddies.
Maximum covariance analysis is performed in a hemispheric domain upon zonal wind and a measure of baroclinic wave activity at 250 hPa. For this purpose, baroclinic wave activity or “storminess” S is defined as the square root of the squared high-pass meridional wind anomaly, namely (υ′υ′)1/2. Wettstein and Wallace (2010, hereafter WW10) based their analysis on EOFs of υ′υ′ at 300 hPa, which they acknowledged as having a strongly skewed frequency distribution, and therefore not being ideally suited for EOF analysis. Using a power transform of the variable [i.e., (υ′υ′)1/2] partly eliminates this problem. WW10 showed that their results were largely insensitive to whether this transform is included or not, and the same is true of the results reported here.
3. Variance and teleconnectivity of the zonal wind field
This study examines the variability of the zonal wind field during December–March. Before decomposing this variability into spatial patterns, the climatological mean and the temporal variance of the U250 field are examined. Figure 1 shows the distributions of these quantities. The thick lines2 in this and subsequent figures represent the positions of the climatological-mean wintertime jets at 250 hPa. As evidenced by the almost perfect correspondence between these thick lines and the contours in the U250 climatological-mean distribution, the zonal component of the wind completely dominates the climatological-mean wind speed field. Two continuous jet streams stretch zonally and spiral slightly toward the pole. In the oceanic (Atlantic and Pacific) sectors, the exit region of the extratropical, eddy-driven jet coexists at some longitudes with the entrance region of the subtropical jet.
The distribution of the zonal wind variance in the abovementioned sectors relates differently to these jets: in the Pacific the variance is focused on the jet axis whereas in the Atlantic it is more meridionally dispersed, with hints of maxima north and south of the jet. Also, the region of high variability is located farther downstream of the jet in the Atlantic sector. At subtropical latitudes the variability is stronger at the longitudes of the jet entrance regions over the eastern Atlantic and Pacific oceans than at other longitudes. Relative to the oceanic sectors, in the Eurasian sector the zonal wind variance (jet variability) is much weaker.
Wallace and Gutzler (1981) defined the teleconnectivity of a specified field, such as 500-hPa height, at a specified grid point as the absolute value of the strongest negative correlation between that grid point and any other grid point. Teleconnectivity analysis is well suited for exploring patterns of variability in geophysical fields because of the straightforward and dynamically informative interpretation of the result—a teleconnectivity map and a set of preferred teleconnection patterns. In this section we examine the daily teleconnectivity of the 250-hPa zonal wind field and compare it with that of the 500-hPa geopotential height field. Results are shown in Fig. 2. Note the clear relationship between the position of the jets (indicated by the thick lines) and the locations of the strongest zonal wind teleconnectivity (centers of action).
The teleconnectivity field for zonal wind exhibits strong features in the Atlantic and Pacific jet exit regions. In the Atlantic, a tripole pattern of teleconnectivity maxima is found: the middle and poleward maxima, in which U250 is anticorrelated with a teleconnectivity value of 0.60, straddle the exit region of the North American/Atlantic eddy-driven jet, while the equatorward maximum, in which U250 is anticorrelated with U250 in the middle maximum with a teleconnectivity value of 0.58, stretches westward from the entrance region of the North African jet. A similar tripole pattern is found in the Pacific; however, in this case the strongest anticorrelation (−0.68) is between the middle and equatorward centers, and the middle center coincides with the exit region of the Asian/Pacific jet. In contrast, over Eurasia there is a pair of zonally elongated anticorrelated centers (−0.65) and a distinctive teleconnectivity minimum in between, centered just to the south of the jet axis. In general, the centers of strong teleconnectivity tend to be more prominent and more zonally elongated in the zonal wind field than in the geopotential height field, especially in the Atlantic and Eurasian sectors.
Teleconnectivity patterns for monthly mean data (not shown) are similar to those for the daily data, with the maxima being more pronounced, especially in the Atlantic and the Pacific sectors, as indicated in Table 1.
In the next section we show results of an EOF analysis of the zonal wind field in the Atlantic, Pacific, and Eurasian sectors (as defined in the previous section). This choice of sectors is consistent with the longitudinal separation of the strongly correlated centers in the zonal wind field (Fig. 2), as well as with the apparent separation between the distinct Atlantic and Pacific maxima in the zonal wind variance distribution (Fig. 1b; note the “notch” over the north-central United States).
4. EOFs of zonal wind by sector
First, we show the jet variability patterns separately for the Atlantic and the Pacific sectors. The top panels in Figs. 3 and 4 show hemispheric regressions of zonal wind onto the first two sectoral PCs of unfiltered daily U250. The zonal wind patterns, also referred to as EOFs, are labeled A1, A2, P1, and P2, where the letter indicates the respective sector (Atlantic or Pacific), and the number refers to the PC rank. The shapes and locations of these patterns are largely insensitive to the exact location of the sectoral longitudinal borders (±15°). Therefore, for symmetry we choose sectors that are adjacent to one another and have the same longitudinal span. The longitudinal borders of the sectors are highlighted for reference on all maps, while the jet axes—as defined in the previous section—are included to aid the interpretation of the EOFs.
In both the Atlantic (Fig. 3) and Pacific (Fig. 4) sectors the EOFs exhibit tripole patterns with anomalies elongated in the zonal direction. Bearing in mind that the dominant teleconnection patterns in the middle- and upper-tropospheric geopotential height field exhibit meridionally oriented dipole patterns, tripole patterns in the zonal wind field are to be expected on the basis of geostrophy. Also, given that zonal wind is the meridional gradient of the streamfunction field, it is expected that the features in its dominant modes of variability should be of smaller meridional scale and hence more zonally elongated than their counterparts in the dominant modes of streamfunction or geopotential. Finally, using wind in our analysis rather than geopotential avoids the “artificial” emphasis on high latitudes that geopotential gives. This results in higher EOF loadings at low and middle latitudes, emphasizing the anomalies in the subtropical jets.
The corresponding EOFs of monthly mean fields (not shown) are virtually identical to the patterns shown in Figs. 3 and 4. The fractions of the total variance explained by the EOFs of the monthly mean field (A1: 30%, A2: 17%, P1: 26%, P2: 17%) are considerably larger than the corresponding fractions explained by the EOFs of the unfiltered daily data. We have chosen to use the daily EOFs for two reasons: first, to demonstrate the robustness of the patterns and second, to have daily time series available (here the PCs) to use in the analysis that follows.
The middle panels of Figs. 3 and 4 show the daily 500-hPa geopotential height field regressed on the same PCs of U250. In the Atlantic sector, the patterns for A1 and A2 clearly resemble the NAO (Hurrell et al. 2003) and the eastern Atlantic pattern (Wallace and Gutzler 1981), respectively. The corresponding correlation coefficients for the monthly indices are 0.70 and 0.71 based on the definitions of the patterns defined in those papers. Relative to the patterns derived directly from the analysis of the geopotential field, published in previous studies, the features in the Z500 patterns tend to be slightly compressed in the meridional direction and more zonally elongated. In the Pacific sector, P1 is closely related to the Pacific–North America (PNA; monthly correlation with PNA index is 0.74) pattern. P2, on the other hand, does not seem to correspond to any previously defined teleconnection pattern. We will show that P2 plays an important role in determining the location of the jet over the eastern North Pacific, as well as the location of the storm track that impinges on the western coast of the United States and Canada.
It should be noted that one-point correlation maps of daily U250 (not shown) for the primary centers in A1, A2, P1, and P2 exhibit patterns very similar to the corresponding EOF. However, only the leading EOF in each sector has centers that coincide—approximately—with the maxima of the U250 teleconnectivity field in the respective sector. The centers of A2 and P2 are somewhere between these maxima; thus, the latter EOFs are associated with lower teleconnectivity.
Among other studies, Wallace and Gutzler (1981), Horel (1981), Esbensen (1984), and Barnston and Livezey (1987) have shown the PNA and the western Pacific (WP) pattern to be the two most prominent wintertime variability patterns in the Pacific sector. Our analysis, however, identifies P1 (counterpart of the PNA) and P2 as the dominant patterns. With regard to the prevalence of P2 over the WP pattern in our results, the following factors may be of some relevance:
Seasonality: P2 appears in the analysis of data for the entire winter (DJFM) but it is predominantly a late winter pattern. In late autumn and early winter the second EOF in the Pacific sector more closely resembles the WP pattern. Figure 5 contrasts the respective P2 patterns for November–December and February–March. This seasonal dependence may be related to the increasing prominence of the subtropical jet toward the later part of the winter. The corresponding P2 pattern for January (not shown) shares characteristics of both its November–December and February–March counterparts. Barnston and Livezey (1987) have also noted significant seasonal changes in the WP pattern.
The range of frequencies included in the analysis: The use of unfiltered daily data (as opposed to monthly means) in our analysis places greater emphasis on the eastern Pacific where the jet varies strongly on intermediate (10–30 days) time scales (e.g., see Blackmon et al. 1984a, their Figs. 2b,e). The daily U250 variance field in Fig. 1b exhibits a broader area of high variance over the eastern Pacific.
Inclusion of low latitudes: It was found that for monthly mean data, the latitudinal extent of the Pacific sector affects the shape of the U250 EOF 2. In particular, if the low-latitude zone from the equator to 20°N is excluded from the Pacific sector, the resulting U250 EOF 2 corresponds to the WP pattern rather than the P2 pattern.
Choice with respect to standardization: For the same data, EOF analysis based on the covariance matrix yields patterns that explain large fractions of the variance, whereas an analysis based on the correlation matrix (i.e., on standardized data) yields patterns that explain larger fractions of the squared correlation between time series of the field at different grid points. Consequently, compared to the teleconnectivity analysis of Wallace and Gutzler (1981), which was based on standardized data, our EOF analysis gives more weight to patterns over the central and eastern Pacific, where the variability is stronger. EOF analysis based on the correlation matrix (not shown) yields a second EOF that corresponds more closely to the WP pattern.
To provide a potential vorticity–potential temperature (PV-Θ) view of the same jet variability patterns, regressions of ΘPV2 onto the PCs are shown in the bottom panels of Figs. 3 and 4. In these it can be seen that the potential temperature anomalies at the 2-PVU surface coincide with the locations of maximum meridional shear of the zonal wind, indicating that the latter defines corresponding PV anomalies reflected in the ΘPV2 distribution. This interpretation is supported by our analysis of PV teleconnectivity and EOFs at upper levels (results not shown). It also provides a link between the jet variability patterns shown here and the potential vorticity analysis of Athanasiadis and Ambaum (2010).
Figures 6 –9 show maps of wind speed [(u2 + υ2)1/2] and baroclinic wave activity (υ′υ′) for the opposing polarities of these patterns. These composites are formed by averaging for all days, during positive or negative polarity, on which the absolute value of a given PC exceeds 1 standard deviation.
For the Atlantic sector, for A1 in Fig. 6 the jet configuration is strikingly different between the two polarities. In particular, in the positive polarity a split jet occurs within the Atlantic sector, with the eddy-driven jet stream near the North American coast displaced poleward of its climatological position and the entrance of the North African jet shifted westward over the subtropical North Atlantic. Over the Azores (near 35°N, 30°W), which lie midway between the two jets, the zonal flow almost vanishes. In the positive polarity of A1, the North Atlantic storm track is intensified and shifted poleward of its climatological-mean position, stretching from Newfoundland to the British Isles and northern Europe. In contrast, in the negative polarity of A1, the subtropical and the polar-front jets merge into a single midlatitude jet, while the storm track is abnormally weak and shifted equatorward toward southern Europe and the Mediterranean. These findings are very much in agreement with the results of WW10 and at the same time demonstrate the NAO-like character of the A1 pattern.
The corresponding patterns for A2, shown in Fig. 7, exhibit differences in the position and intensity of both the subtropical and the polar-front jets. During positive A2 the westerly flow appears to be completely blocked over the midlatitude eastern Atlantic (near 45°N, 25°W), leading to a broken tail-shaped storm track, in which disturbances approaching Europe are deflected poleward.
In the Pacific sector, the P1 composites in Fig. 8 show that in the positive polarity the jet stream is intensified over the central Pacific, whereas it is weakened and shifted poleward in the negative polarity. The Pacific storm track is stronger and shifted poleward in the negative polarity. The orientation of the storm track along the western coast of North America is also quite different in the two composites: west-southwest–east-northeast in P1+ and west-northwest–east-southeast in P1−, consistent with composites for the PNA pattern. Also, during P1− the entrance region of the North American jet is shifted westward from the Baja Peninsula toward Hawaii.
P2 affects the jet stream configuration and the latitude and intensity of the storm track over the eastern Pacific and western North America (Fig. 9). During P2+ the Asian/Pacific and North American/Atlantic jets merge to form a continuous but rather weak and diffuse band of westerlies, and the storm track is also weak and diffuse. In contrast, during P2− the two jets are distinct and the storm track over this sector is much more active and more clearly defined.
An interesting point in this discussion is the contrast between North Atlantic and North Pacific wintertime jet stream climatologies—both are characterized by extratropical (eddy driven) and subtropical jets but the latitudinal separation between these jets is twice as large in the Atlantic as in the Pacific (Fig. 1a). Hence, it is understandable that the relationships between extratropical and subtropical jets are quite different in the Atlantic and Pacific EOFs. Eichelberger and Hartmann (2007, hereafter EH07) found that the differences between the meridional structures of the climatological-mean jet streams in the Atlantic and Pacific sectors is instrumental in shaping the leading mode of zonal wind variability in the two sectors. Their EOF analysis of the zonal wind field, zonally averaged over the respective sectors, yielded patterns that correspond closely to our A1 and P1 at the jet stream level. The zonal wind composites for contrasting polarities of their PCs, shown in their Fig. 4, concisely illustrate the meridional structure of the contrasting jet stream configurations.
To examine more closely the climatic impacts of the jet variability patterns, in Fig. 10 we show composite differences of daily precipitation for contrasting polarities of the PCs. These are calculated using the GPCP dataset for the DJFM season in the period 1997–2002. The effect of orography on precipitation is apparent, for example, in British Columbia, southwest Greenland, and the northwest region of the Iberian Peninsula. The precipitation anomalies associated with each jet variability pattern are consistent with the respective changes in baroclinic wave activity, as seen in Figs. 6 –9. The precipitation patterns for A1, A2, and P1 project positively onto the corresponding precipitation patterns of the NAO, the eastern Atlantic pattern, and the PNA, respectively. The precipitation anomalies associated with P2 are comparable in strength to those associated with P1 and they have a pronounced influence on precipitation along the western coast of North America. Precipitation composites for contrasting polarities of P2, shown in the bottom panels of Fig. 10, indicate a meridional shifting of the belt of heavy coastal precipitation between northern California (P2+) and British Columbia (P2−).
The precipitation anomalies associated with the El Niño–Southern Oscillation (ENSO) project positively onto the respective P2 precipitation anomalies over the western coast of North America: the belt of heavy coastal precipitation tends to be shifted southward in El Niño years. Between El Niño and La Niña years,3 a difference of 0.6 standard deviations was found in the P2 PC mean. Also, it was found that the shape of P2 varies with the polarity of the ENSO cycle, with the main centers being closer to the North American coast during El Niño years.
To examine the temporal characteristics of the jet variability patterns, first we show the autocorrelation functions of their PC time series (Fig. 11). These plots show that the EOFs are slowly varying patterns. A1 and P1 in particular have e-folding decorrelation times of approximately 11.5 and 8.5 days, respectively, slightly longer than the NAO and the PNA decorrelation times found by Feldstein (2000). The enhanced persistence of A1 and P1 relative to the conventional NAO and the PNA pattern can be understood by noting that for patterns with a specified two-dimensional wavenumber, those that are zonally elongated tend to have redder frequency spectra (see, e.g., Wallace and Lau 1983). It is worth noting also that the autocorrelations remain positive at all lags, suggestive of variability of these modes on climatic time scales, in agreement with the findings of Blackmon et al. (1984b). It is notable that A2 and P2 exhibit shorter decorrelation times of approximately 7 and 6.5 days, respectively. Also, after projecting the U250 fields for the whole DJFM season onto the November–December P2 pattern (Fig. 5), it was found that the derived time series exhibits a decorrelation time comparable to the P1 pattern. The autocorrelation functions for all four patterns remain positive out to lags of 30 days and beyond; this is thought to be partly due to the forcing of the planetary waves by slowly varying sea surface temperature anomalies.
Particularly for the NAO, the negatively skewed distribution of its time-varying index has recently received special attention (e.g., Woollings et al. 2010; Rennert and Wallace 2009) as a reflection of the dynamical processes that govern the NAO variability. As noted in the former study, defining an NAO-like pattern on the basis of zonal wind yields a stronger negative skewness than defining it on the basis of Z500 or sea level pressure. The PC time series of our leading Atlantic pattern (A1), which is based on unfiltered daily data, also exhibits a strong negative skewness (−0.30). Based on the estimator (6/Neff)1/2 for the standard error of the skewness, the respective standard error is 0.16. For Neff = N/td, which is a less conservative estimate, the standard error is equal to 0.11.
Figure 12 shows lag-regressions onto the same PCs. It demonstrates how the evolution of these patterns exhibits an apparent poleward group velocity while the individual centers in the patterns remain fixed. The poleward group velocity, which is common to all four patterns, suggests that some part of the jet stream variability is forced from the tropics, or that on average it is the eddy-driven jet that responds to the subtropical jet rather than vice versa.
Figure 13 shows the U250 leading EOF of the Eurasian sector. This EOF is considerably weaker than the Atlantic and Pacific leading EOFs, and it produces only a minor distortion of the very strong jet stream upon which it is superimposed. Hence, this mode is much less influential in shaping the hemispheric jet stream configuration than the modes considered earlier in this section. Note that the Eurasian sector as defined here overlaps slightly with the Atlantic and Pacific sectors, but it has the same longitudinal span (135°) as those sectors.
5. Coupling between zonal wind variability and storm-track variability
Here we present a more detailed analysis of the coupling between the zonal wind and storm-track variability, closely paralleling analyses in previous studies of Lau (1988) and WW10, but rather than keying the analysis on the modes of storm-track variability we base it on the EOFs and PCs of 250-hPa zonal wind. Our analysis also parallels some of the steps in Lorenz and Hartmann (2003), but in this case the analysis is based on the leading EOFs of the zonally varying distribution of zonal wind, whereas theirs is based on the zonally and vertically averaged distribution. For a review on the interaction between jets and storm tracks, the interested reader is referred to Chang et al. (2002).
Figures 14 and 15 show the leading EOFs of Atlantic and Pacific sector 250-hPa zonal wind repeated from Figs. 3 and 4, together with the corresponding anomalies in storm-track variability, obtained by regressing the distribution of high-pass filtered υ′υ′ upon the respective PC time series. In all four modes shown here, baroclinic wave activity tends to be enhanced in regions of westerly wind anomalies, except for the subtropical centers of action. In the case of A1 the enhancement is much larger over the northern center—hence the correspondence between this pattern and WW10’s “pulsing mode” of storm-track variability. In the case of A2 and P1 the patterns of storm-track variability are shifted somewhat equatorward of the corresponding features in the zonal wind, but they still project positively on them. In these modes, the patterns of storm-track variability appear to be no less anchored to the climatological-mean jet streams than the zonal wind EOFs themselves.
As a measure of the impact of the synoptic-scale eddies on the jet variability, the bottom panels of Figs. 14 and 15 show regressions of the pseudovector (υ′2 − u′2, −υ′u′) divergence onto the PCs, where the primes denote high-frequency components (synoptic transients). Since the time averaging and spatial differentiation operators are commutative, it follows that the time mean of this divergence corresponds to ∇ · E, where E represents the horizontal components of the so-called E vector. Hoskins et al. (1983) have shown that under certain approximations the E vector divergence relates directly to the local zonal wind tendency—see Eq. (A8) in their appendix:
To examine the temporal relationship between the jet variability and the anomalies in baroclinic wave activity that—as shown above—tend to maintain the jet anomalies, we show the cross-correlation functions between the PC time series of the jet variability patterns and the time series obtained by projecting the baroclinic wave activity (υ′υ′) fields onto the standardized patterns of the associated variations (as from Figs. 14 and 15). The resulting cross correlations, shown in Fig. 16, indicate that at negative lags (anomalies in baroclinic wave activity leading the jet anomalies) the correlations are slightly stronger. Significant cross correlations extend out to longer lags for A1 than for any of the other patterns.
Finally, it is instructive to compare the jet and storm-track variability patterns in the above analysis to those obtained as coupled patterns via maximum covariance analysis, shown in Fig. 17. Interestingly, despite the fact that the MCA was performed in the full hemispheric domain, the resulting patterns are remarkably similar to the coupled patterns based on the sectoral zonal wind EOFs. This correspondence not only reinforces the credibility of the coupled jet–storm-track patterns but also signifies that the dynamically interactive components of the storm-track and jet variability are confined within the Atlantic and Pacific sectors.
6. Summary and discussion
In this study we explored the characteristics of zonal wind EOFs computed separately in the Atlantic and the Pacific sectors. The patterns were derived from unfiltered daily data; performing the analysis on monthly mean fields yields almost identical patterns but with considerably higher percentages of explained variance. These patterns are referred to as jet variability patterns and according to sector and rank they are named A1, A2, P1, and P2. The leading Atlantic (A1) and Pacific (P1) patterns correspond quite well to the NAO and the PNA, respectively. A2 is seen as a representation of the eastern Atlantic pattern. P2 has no counterpart in the literature as far as we are aware, yet it was found to have a pronounced influence on the jet configuration and precipitation distribution over the western coast of North America.
A1 is characterized by a north–south shifting of the eddy-driven jet in the Atlantic sector and primarily by a pulsing of the storm track, consistent with the results of WW10. It is also characterized by an extension/retraction of the subtropical jet at its entrance over the eastern Atlantic. In A1+ the exit region of the eddy-driven jet is displaced poleward of its climatological-mean position and the entrance region of the subtropical jet is extended westward, so that the two jets overlap over a substantial range of longitudes, with weak westerlies at latitudes in between the jets. The storm track is anomalously strong and displaced poleward of its climatological-mean position. In A1− the eddy-driven and subtropical jets are less distinct: the exit region of the former merges with the entrance region of the latter. The storm track is anomalously weak and displaced equatorward of its climatological-mean position. Anomalously heavy rainfall is observed over Portugal, Spain, France, Italy, and Greece. A1 projects strongly upon the North Atlantic Oscillation as defined in Hurrell (1995).
A2 is characterized by an extension/retraction of the eddy-driven jet in the Atlantic sector. In A2− the exit region of the eddy-driven jet extends eastward of its climatological-mean position and stretches zonally all the way across the Atlantic such that storms approaching the coast are aimed toward France. Precipitation over northern Europe tends to be above normal. In A2+ the storm track is shifted poleward of its climatological-mean position over the eastern Atlantic such that storms pass north of the British Isles and progress eastward toward the coast of Norway. A center of very weak flow to the west of France (45°N, 25°W) indicates frequent occurrence of blocking in this region. The subtropical jet is anomalously strong and displaced northward toward the Mediterranean. A2 projects strongly upon the eastern Atlantic pattern as defined in Wallace and Gutzler (1981).
P1 is characterized by an extension/retraction of the eddy driven jet in the Pacific sector and also by a north–south shifting of the Pacific storm track as it crosses the eastern Pacific sector, as noted by WW10. In P1+ the eddy-driven jet extends eastward to near 150°W while the entrance region of the subtropical jet west of Baja California is retracted. Rainfall is enhanced along the Pacific coast from Alaska to northern California, but the anomalies are weak and mainly offshore. In P1− the eddy-driven jet is retracted all the way to Japan, and in the mid-Pacific the westerlies are split into a northern branch that crosses the Gulf of Alaska, with the storm track embedded in it, and a southern branch that crosses Hawaii. P1 projects strongly upon the Pacific–North American pattern as defined in Wallace and Gutzler (1981).
The principal center of action of P2 is embedded in the gap between the eddy-driven and subtropical jets in the central and eastern Pacific (an area of high jet variability). When P2 is positive the zonal winds in that gap are anomalously strong, and the two jets merge into a single, continuous jet extending across the eastern Pacific and into North America, with an embedded storm track aimed at the California coast. Coastal precipitation is heavy to the south of the state of Washington and light over British Columbia and southeast Alaska, and the anomalies over land are larger than in the case of P1. P2− is characterized by a distinct separation between the eddy-driven and subtropical jet streams and an abnormally strong storm track embedded in the former and aimed at British Columbia, bringing anomalously heavy precipitation. To our knowledge, P2 has no counterpart in the climate dynamics literature, but it might be a useful diagnostic for weather forecasting applications, particularly for precipitation, over western North America.
In contrast to previous studies, our analysis did not yield a pattern in the Pacific sector resembling the western Pacific pattern. In section 4 we discussed four factors that contribute to this discrepancy: the seasonality of the EOF patterns, the sensitivity of the EOF patterns to the range of frequencies included in the analysis, the inclusion of the low-latitude (0°–20°N) zone in the Pacific sector, and the choice of whether or not to standardize the data before performing the analysis. The important thing is that our P2 pattern—irrespective of its relation to the western Pacific pattern—was shown to have significant climatic impacts.
It is of interest to compare the leading EOFs of the zonally varying zonal wind over the Atlantic and Pacific sectors at the jet stream level (A1 and P1) with the leading EOFs of the zonal wind zonally averaged over those same sectors4 as documented by EH07. The EOFs in EH07, displayed in the form of latitude–pressure cross sections, exhibit a nearly equivalent barotropic structure, and it is presumed that our jet variability modes share this characteristic. EH07 found that in the Atlantic sector, where the eddy-driven jet coexists with a subtropical jet, the leading EOF of jet stream variability consists of north–south displacements in the latitude of the eddy-driven jet. In contrast, over the Pacific sector there is on average a strong combined jet, and the leading EOF is characterized by variations in its strength rather than its position. Our leading patterns, A1 and P1, share these contrasting characteristics, and the latitudes of the secondary features also match up well with their counterparts in the EOFs found by EH07.
For A1 and P1, the autocorrelation functions of the PC time series exhibit an e-folding decorrelation time of approximately 10 days. From the same autocorrelations and the associated lag-regression maps it was found that these patterns tend to be stationary, which is another property of teleconnection patterns. The abovementioned lag-regression maps exhibit poleward propagation in the amplitude of the pattern anomalies (group velocity), suggesting that part of the jet stream variability is forced from the tropics.
It was found that the anomalies of the eddy forcing exhibit a pattern similar to the accompanying jet anomalies, thus indicating that the eddies play a maintenance role, as shown in previous studies. The associated time scale (jet anomaly divided by jet acceleration due to eddy forcing) was found to be approximately 5–6 days. As verified by the MCA results, these anomalies can be considered as coupled (jet and storm track) patterns.
Although clearly there are no “right” and “wrong” methods for defining a particular teleconnection pattern, such as the NAO, our study suggests the use of zonal wind variability at the jet level analyzed by sector as a candidate method with the following desired properties with respect to the “criteria” suggested in section 1:
It yields very robust patterns with respect to the range of frequencies included in the data (the patterns for unfiltered daily or monthly mean data have almost identical shapes) and the choice of sectors (jet variability patterns remain practically unchanged for slightly different sectors).
It yields patterns that have strong and clear climatic impacts and are broadly consistent with the climatic impacts of their traditionally defined counterparts. For example, A1 resembles the NAO and P1 the PNA pattern. We have not examined the signature of our jet variability patterns in the surface temperature field, but we have examined the associated precipitation anomalies (Fig. 10) and, of course, the jet configuration itself.
It yields patterns that relate transparently to the climatological-mean jets and, consequently, to the respective storm tracks. Therefore, for example, interpreting a mode of variability as the extension/retraction of the jet and pulsing of the respective storm track may be more meaningful from a dynamical perspective than representing the same teleconnection pattern only as a seesaw in pressure anomalies.
By placing emphasis on the jet stream variability, our method yields patterns that relate more directly to the dynamical aspect of jet–eddy interaction, which has received attention as an important driving mechanism for the NAO and annular mode variability.
It yields patterns that (i) express significant parts of the total daily variance of the zonal wind field and (ii) exhibit greater persistence than their traditionally defined counterparts (as evidenced by the longer decorrelation times of the PC time series). With respect to skewness, which is a primary characteristic of the NAO, the PC time series of A1 exhibits stronger negative skewness (−0.30 for unfiltered daily data) than other daily NAO indices. Finally, wintertime teleconnectivity was found to be even stronger for zonal wind than for geopotential height.
Acknowledgments
This work was supported by the Joint Institute for the Study of the Atmosphere and Ocean (JISAO) under NOAA Cooperative Agreement NA17RJ1232. JMW was supported by the National Science Foundation under Grant ATM 0318675.
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Maps of U250 (a) mean and (b) daily variance for DJFM. The superimposed heavy lines indicate the position of the climatological-mean jet streams. The black segments of these lines indicate wind speed at the jet core exceeding 30 m s−1, and the white segments in the jet entrance regions indicate wind speeds between 25 and 30 m s−1. Contour intervals are (a) 10 m s−1 and (b) 50 m2 s−2.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
Maps of daily teleconnectivity for (a) U250 and (b) Z500. Contours are shown only for values above 0.50 for U250 and above 0.35 for Z500; contour interval is 0.05. The limits of the Atlantic and the Pacific sectors used in the subsequent EOF analysis are shown. Other details are as in Fig. 1.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
Regressions onto standardized Atlantic PC 1 and PC 2 for (top) U250 (contour interval = 2 m s−1), (middle) Z500 (contour interval = 12 m, and (bottom) ΘPV2 (contour interval = 1 K).
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
As in Fig. 3, but for Pacific PC 1 and PC 2.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
U250 regressions onto standardized Pacific PC 2 for (left) Nov–Dec and (right) Feb–Mar. Contour interval is 2 m s−1. The thick black lines represent the position of the climatological-mean jets for the corresponding period of the year.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
Composites for Atlantic PC 1. Fields are averaged separately for the positive and negative polarity for absolute PC values exceeding 1 std dev for (top) (u2 + υ2)1/2 at 250 hPa (contour interval = 10 m s−1) and (bottom) υ′υ′ at 250 hPa (contour interval = 50 m2 s−2).
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
As in Fig. 6, but for the Atlantic PC 2.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
As in Fig. 6, but for the Pacific PC 1.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
As in Fig. 6, but for the Pacific PC 2.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
(top), (middle) Daily precipitation composite differences—positive minus negative polarity—upon the Atlantic and Pacific PC 1 and PC 2, respectively. (bottom) Positive and negative polarity composites for Pacific PC 2. A threshold of 1.5 std dev is used for producing the composites. Units are mm day−1.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
Autocorrelation functions for the Atlantic and Pacific PC 1 and PC 2.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
Lag regressions onto standardized Atlantic and Pacific PC 1 and PC 2 for lags of (left) −6 days and (right) +6 days. Contour interval is 1.5 m s−1.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
Regression of U250 onto Eurasian PC 1. Other details are as in Fig. 3. The EOF analysis was performed in the highlighted domain (20°–130°E).
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
Regressions onto standardized Atlantic PC 1 and PC 2 for (top) U250 (contour interval = 2 m s−1), (center) υ′υ′ at 250 hPa (contour interval = 15 m2 s−2), and (bottom) ∇ · E (contour interval = 1 × 10−5 m s−2).
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
As in Fig. 14, but for the Pacific PC 1 and PC 2.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
Cross-correlation functions between Atlantic and Pacific PC 1 and PC 2 and the respective υ′υ′ 250-hPa time series obtained by regressing the υ′υ′ 250-hPa field onto the patterns in Figs. 14 and 15. At positive lags the PC (jet stream) anomaly leads the storm-track anomaly.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
MCA patterns of zonal wind (U) and (υ′υ′)1/2 (S) at 250 hPa. MCA is performed on daily hemispheric fields.
Citation: Journal of the Atmospheric Sciences 67, 5; 10.1175/2009JAS3270.1
Strongest daily and monthly anticorrelations in the Atlantic (ATL) and Pacific (PAC) sectors for U250 and Z500.
Also referred to as teleconnection patterns or modes of variability. The term “mode” implies a dynamical/deterministic behavior like that exhibited by well-defined mathematical solutions of the governing equations. This more rigorous definition does not necessarily apply to statistically deduced patterns of variability.
At each particular longitude in the NH, a simple algorithm searches for the grid point (latitude) with the strongest wind speed at 250 hPa. On a Cartesian grid, these points of maximum wind speed are smoothed by a high-order polynomial fit before being plotted in the polar stereographic maps.
Stratification of DJFM seasons based on terciles of the Cold Tongue index (Quadrelli and Wallace 2002).
