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Mar 15, 2002 - pattern has peaks over the eastern part of the Pacific and the Atlantic with ..... the order of operation is not important since the AO and the SOI are not ..... storm track, as well as the entrance and exit regions of the Atlantic storm ...
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VOLUME 15

Interdecadal Variations in Northern Hemisphere Winter Storm Track Intensity EDMUND K. M. CHANG*

AND

YUNFEI FU1

Department of Meteorology, The Florida State University, Tallahassee, Florida (Manuscript received 19 October 2000, in final form 15 August 2001) ABSTRACT In this paper, the interannual variations in the Northern Hemisphere winter storm tracks have been examined based on 51 winters (December–January–February) of NCEP–NCAR reanalysis data. The leading empirical orthogonal function (EOF) corresponds to the simultaneous strengthening/weakening of both the Pacific and Atlantic storm tracks. Interannual and month-to-month variations in the Pacific and Atlantic storm tracks are found to be significantly correlated. The principal component associated with the leading hemispheric EOF exhibits pronounced interdecadal variability. There appears to be a transition during the early 1970s from a weak storm track state prior to 1972/73 to a strong storm track state subsequently. Decadal mean storm track intensity during the 1990s is about 30% stronger than that during the late 1960s and early 1970s. The relationship between variations in storm track intensity and low-frequency (seasonal mean) flow anomalies has also been examined. It is shown that storm track variations and their associated seasonal mean flow anomalies are highly correlated. Relations to several other modes of interdecadal variability have also been explored. It is shown that part of the storm track variations may be related to the Arctic oscillation and part to the interdecadal ENSO-like variability. However, even when storm track variations that are linearly dependent on these other modes have been removed, substantial interdecadal variations still remain. In order to ascertain that the interdecadal variations have not been introduced into the reanalysis data by changes in the observation network, radiosonde observations along the storm track have been examined. Preliminary analyses suggest that the radiosonde observations are largely consistent with the reanalysis data, except for the possibility that biases in the reanalysis data may have led to an overestimation of the interdecadal variability. Unfortunately, since the peaks of the storm tracks lie over the oceans where no radiosonde stations with continuous record can be found, the variations over the storm track peaks cannot be verified.

1. Introduction From a synoptic perspective, storm tracks are regions over which midlatitude cyclones are prevalent. Hence to a large extent, midlatitude weather and climate during the cool season are closely related to changes in the location and intensity of the storm tracks. Blackmon (1976) showed that bandpass-filtered (2.5–6 days) rms 500-hPa geopotential height fields for the Northern Hemisphere (NH) display two peaks over the midlatitude oceanic regions, which correspond closely with the locations of maximum synoptic-scale cyclone activity. Wallace et al. (1988) showed that baroclinic waves tend to propagate along a track that is parallel to the maxima * Current affiliation: ITPA/MSRC, State University of New York at Stony Brook, Stony Brook, New York. 1 Permanent affiliation: Department of Earth and Space Sciences, University of Science and Technology, Hefei, Anhui, People’s Republic of China. Corresponding author address: Dr. Edmund K. M. Chang, ITPA/ MSRC, State University of New York at Stony Brook, Stony Brook, NY 11794-5000. E-mail: [email protected]

q 2002 American Meteorological Society

in the rms geopotential height fields (see also Chang and Yu 1999), hence we can identify the storm tracks as regions where the rms geopotential height fields are large. In this paper, we will investigate the interannual variability of the Northern Hemisphere winter storm track, using 51 yr of data produced by the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis project (Kalnay et al. 1996; Kistler et al. 2001). Lau (1988) first examined month-to-month storm track variations, and showed that these variations are closely related to changes in the low-frequency (i.e., monthly mean) component of the circulation. It is now well known that the low-frequency component of the flow exhibits significant interdecadal variability (e.g., Hurrell 1995; Mantua et al. 1997; Thompson et al. 2000; Zhang et al. 1997; and many others). Recently, Nakamura and Izumi (1999) suggested that there may be interdecadal variability in the Pacific storm track activity; midwinter storm track activity during the late 1980s and early 1990s is significantly stronger than that during the early to mid-1980s. Furthermore, based on decadal mean com-

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posites, Ebisuzaki and Chelliah (1998) suggested that there may be interdecadal variability in storm track intensity over the Atlantic; the Atlantic storm track is significantly weaker during the 1960s than in the other decades. In this paper, we will show, using the NCEP–NCAR reanalysis data, that storm track intensity indeed exhibits substantial interdecadal (and even multidecadal) variation. We will also explore briefly the relationship between storm track anomalies and several well-known ‘‘modes’’ of low-frequency variability. In section 2, we describe the data used in our analyses. The main results are discussed in section 3. In section 4, the mean flow changes associated with variations in storm track intensity are examined, and in section 5, we discuss the relationship between the storm track variations and several modes of low-frequency variability. We summarize with some discussions in section 6. In appendix A, we present a preliminary analysis of radiosonde observations along the storm track to see whether it is possible to see the storm track variations based on unassimilated observations. In appendix B, we summarize the similarities and differences between analyses based on storm tracks defined using different variables, and the correlation between the Pacific and Atlantic storm tracks (discussed in section 3a) is explored further in appendix C. 2. Data The main data source examined in this study is that produced by the NCEP–NCAR reanalysis project. As shown in previous studies (e.g., Blackmon et al. 1977; Trenberth 1991), the storm tracks can be highlighted using many different eddy variance and covariance quantities. In this paper, we have chosen to denote storm track intensity primarily using high-pass-filtered 300hPa meridional velocity (henceforth referred to as y 9) variance. Fifty one winters of data taken from December–January–February (DJF) of 1948/49 to 1998/99 have been examined. Most of the results to be discussed in this paper are based on a 24-hour difference filter (Wallace et al. 1988). This simple filter was chosen in order to facilitate direct comparison of the reanalysis data with radiosonde observations (see discussions in appendix A). We have also compared storm track variations as seen from other variables as well as from other time filters, and the results are very similar. Further discussion concerning this issue is provided in section 3, and a summary of the similarities and differences between storm track variations as defined by different variables is presented in appendix B. Storm track variations have been examined using an empirical orthogonal function (EOF) analysis of the 24h difference–filtered 300-hPa y 9 variance. For the EOF analysis, the 2.58 3 2.58 pressure level data obtained from the NCAR archives were transformed onto a T31 (64 3 32) Gaussian grid using the SPHEREPACK pro-

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gram obtained from NCAR, and the variance from each winter was then smoothed to T12 resolution before the EOF computations were performed.1 However, results using data without any smoothing were very similar. Only data for the NH have been used in the computations since Southern Hemisphere data are expected to be strongly influenced by changes in satellite coverage over the years (see discussions in appendix A). Before the EOF computations were performed, the y 9 variances were weighted by the square root of the cosine of the latitude to account for differences in area represented by each grid point (e.g., Thompson and Wallace 2000). The EOFs and principal components (PCs) were computed using singular value decomposition (SVD) of the weighted data matrix. It will be shown in the following section that the maxima in the spatial patterns corresponding to the leading mode of storm track variability are located over the oceans (Fig. 1), and that the corresponding PC exhibits a transition during the early 1970s (Fig. 2). Although the reanalysis was performed with a consistent numerical model and analysis scheme for the entire period, spurious variations could still be introduced due to changes in the observing system (Kistler et al. 2001). Consequently, in appendix A we discuss some results from preliminary analyses of radiosonde observations from selected stations along the storm track. The radiosonde data have been archived as part of the reanalysis project and were obtained from the NCAR archives. In section 4, storm track variations are related to anomalies in the seasonal mean flow fields. The DJF mean zonal wind (U ) and geopotential height (z ) fields were taken from the NCEP–NCAR reanalysis. The mean sea level pressure (MSLP) data were provided courtesy of the Data Support Section at NCAR (Trenberth and Paolino 1980), but results based on NCEP– NCAR reanalysis data are very similar. The sea surface temperature (SST) data come from a concatenated EOF and optimal interpolation (OI) SST dataset (Reynolds and Smith 1994; Smith et al. 1996) for the period 1950– 99, provided courtesy of T. Mitchell (available online at http://tao.atmos.washington.edu/data/sstpeofoi). 3. Leading EOF of storm track variations The leading EOF of the interannual storm track variations accounts for 29% of the total variance. The spatial pattern of this mode is plotted in Fig. 1a, and its principal component (PC1-NH) is plotted in Fig. 2 (top curve). The PC has been normalized to unit standard deviation. In Fig. 1a, instead of plotting the eigenvector, which involves latitudinal weighting, we 1 The grid transformation and smoothing were performed to suppress small-scale features and to facilitate comparisons with results of earlier studies (e.g., Whitaker and Sardeshmukh 1998) as well as with data from our own model studies (not discussed here).

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FIG. 1. (a) Regression of DJF mean 300-hPa y 9 2 (24-h filtered) on PC1-NH. Contour interval 10 m 2 s 22 . (b) Climatological mean 300-hPa y 9 2 plus Fig. 1a. (c) Climatological mean minus Fig. 1a. Contour interval 100 m 2 s 22 . (a)–(c) have been smoothed to T12 resolution.

have plotted the regression of PC1-NH with the 300hPa y 9 variance, which is equivalent to the eigenvector divided by the square root of the cosine of the latitude. Hence, the pattern shows the storm track anomaly corresponding to one standard deviation of the PC. The pattern has peaks over the eastern part of the Pacific and the Atlantic with roughly equal amplitudes. In the Pacific, the peak occurs slightly to the south of the position of the climatological peak in the Pacific storm track, and the peak in the Atlantic occurs slightly downstream of the climatological Atlantic storm track maximum. This mode clearly represents variations in the intensity of the storm track. To demonstrate the significance of the anomaly shown in Fig. 1a, in Fig. 1b we have plotted the sum of the climatological storm track and this anomaly, and in Fig. 1c, the difference between the climatological storm track and this anom-

aly. It is apparent that the difference between Figs. 1b and 1c corresponds to more than 30% in the storm track amplitude. Note that during much of the 1960s, the value of PC1-NH is approximately 21 (Fig. 2), and during much of the late 1980s and 1990s, the value of PC1-NH is approximately 11. Examining the PC1-NH time series in Fig. 2, we can identify a clear transition during the early 1970s, from an earlier period when the NH storm track is generally weak, to the more recent era when the storm track is significantly stronger. Prior to 1971/72, the value of the PC never exceeds zero, and after 1972/73, its value never falls below 20.1. In section b of appendix A, it is shown that radiosonde observations also suggest a significant increase in storm track amplitude during the early 1970s. In the following subsections, two other interesting observations are highlighted.

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FIG. 2. (top curve) PC time series of the leading storm track EOF (PC1-NH). The dotted horizontal lines represent 61s. (middle and bottom curves) Same as above, but for leading PC for EOF analysis of the Atlantic and Pacific sector, respectively. Note that the year identifying the winter corresponds to the year for Jan and Feb, so that ‘‘50’’ corresponds to the winter of 1949/50.

a. Correlation between the Pacific and Atlantic storm tracks In Fig. 1a, we can see two peaks in the spatial pattern, one over the eastern Pacific, and the other over the Atlantic. Since EOFs are designed to maximize the amount of explained variances, the appearance of two peaks in the pattern does not necessarily imply that the two peaks vary together in a coherent manner. To examine this, we have performed two EOF analyses, one over each ocean basin, taking the sector from 1208E to 1008W to represent the Pacific storm track, and the sector from 908W to 508E to represent the Atlantic storm track. Note that these two sectors do not overlap. The spatial pattern of the leading EOF in each sector resembles the spatial pattern in the respective sector plotted in Fig. 1a, and the two EOFs account for 43% and 35% of the total variance in each sector, respectively. Their PCs (PC1PAC, and PC1-ATL) are also shown in Fig. 2. The correlation between the Pacific and Atlantic leading PC is 0.47, which is statistically significant at the 99% level even after accounting for serial correlation (e.g., Trenberth 1984). In Fig. 2, we see that while some of the peaks and troughs do not match exactly, the low-frequency behavior of the three time series appears to be much closer. Both PC1-ATL and PC1-PAC display mainly negative values prior to the early 1970s, and mainly positive values after that time, similar to what we observed earlier for PC1-NH. To explore the relationship between the Pacific and Atlantic storm tracks even further, an EOF analysis of storm track variations, based on monthly instead of winter mean data (a total of 153 winter months), has been performed. The leading EOF in this case has a spatial pattern very similar to that shown in Fig. 1a (the anomaly correlation between the two patterns is 0.93), and accounts for 22% of the total month-to-month variance. The leading PC based on Atlantic sector–only data (the corresponding EOF accounts for 29% of the variance)

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is again significantly correlated (correlation equals 0.43) with the leading PC based on Pacific sector–only data (the corresponding EOF accounts for 35% of the variance). We have also examined monthly data from the European Centre for Medium-Range Weather Forecasting (ECMWF) reanalysis project from the period 1979– 93, and the results are very similar. The correlations between the two storm tracks have also been studied using SVD analyses (see Bretherton et al. 1992) of the covariance between the Pacific and Atlantic storm tracks, based on 300-hPa y 9 2 and other storm track variables. The SVD pairs, which have structures very similar to the leading individual basin EOFs, have time series that show even higher correlations than those between the leading EOF pairs (e.g., the correlation between Pacific and Atlantic time series from the SVD analyses equals 0.67 for DJF mean data, and 0.55 for monthly mean data), and the results are summarized in appendix C. All these results demonstrate that the high correlation between the two storm tracks is robust. b. Decadal variations in storm track intensity As pointed out above, the PC time series shown in Fig. 2 display significant low-frequency, decadal-scale variability. To highlight this, in Fig. 3 we show difference maps corresponding to periods with highest and lowest average index values. These periods have been identified from the PC1-NH time series. Figure 3a shows the difference between the 10-yr periods, 1989/90 to 1998/99, when the 10-yr average PC value is highest, and 1961/62 to 1970/71, when this average is lowest. Areas where the difference is larger than 20% of the mean of the two periods have been shaded. We can see that during the 1990s, the storm track is significantly stronger than it was during the 1960s, with large parts of the Pacific and Atlantic storm tracks being 20% or more stronger during the more recent period. To this point, we have mainly discussed results based on the 24-h difference filter. As pointed out above, we have also examined storm track variability using different filters, and the results are very similar. In Fig. 3b, we show results based on unfiltered data, except for the removal of the monthly mean for each month. It should be noted that to directly compare the values of the variances shown in Figs. 3a and 3b, the values shown in Fig. 3a should be divided by 4, since waves with a 2-day period will have their amplitude doubled after the application of the 24-h difference filter. The periods chosen for the composite shown in Fig. 3b are based on an EOF analysis of the unfiltered data. The leading EOF for the unfiltered data again corresponds to intensification/weakening of the entire NH storm track, and the temporal correlation of the PCs based on unfiltered and 24-h-difference filtered data is 0.87. Comparing Figs. 3a and 3b, we see that even in the unfiltered variances, the storm track is significantly stronger in the more recent decade than in the 1960s. Nevertheless, the dif-

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FIG. 3. The 300-hPa y 9 2 difference between the decade with largest PC and the decade with smallest PC. (a) 24-h difference filter (contour interval 50 m 2 s 22 ). (b) Unfiltered data (apart from removal of monthly mean, contour interval 20 m 2 s 22 ). Shadings represent difference greater than 20%, 40%, and 60% of the mean, respectively.

ferences are not as large (in terms of percentage) as those shown in Fig. 3a. However, results based on a 1– 8-day Lanczos filter (not shown) display similar percentage changes as those computed using the narrower 24-h difference filter, suggesting that changes computed using the 24-h difference filter do adequately represent changes in the synoptic-scale waves. More details in this regard are presented in appendix B. As discussed in the Introduction, Nakamura and Izumi (1999) suggested that the Pacific storm track is significantly stronger during the late 1980s and early 1990s compared to the early 1980s. Our results (Fig. 2, bottom curve) are consistent with their suggestions, but from Fig. 2, we can see even more significant variations with the longer time series shown here; the Pacific storm track is even weaker during the 1960s than during the late 1970s and early 1980s. Our results are also consistent with those of Ebisuzaki and Chelliah (1998) indicating that the Atlantic storm track is weak during the 1960s. Here, we see that the interdecadal variations of both storm tracks are well captured by the leading EOF of NH storm track variations. 4. Relationship to mean flow variations To examine how the storm track variations are related to those of the mean state, PC1-NH was regressed with the DJF mean 300-hPa U , 500-hPa z , MSLP, and SST, and the results are shown in Fig. 4. In the figure, areas

over which the correlation between PC1-NH and the corresponding field is larger than 0.4 are depicted by shading. To see how well these mean state variations relate to the storm track variations, the patterns shown in Fig. 4 were projected back onto the observed seasonal anomalies for that variable, and the resultant time series, shown in Fig. 5, were then correlated with PC1-NH. The correlations (r) are 0.80 for 300-hPa U and 500hPa z , showing that the storm track pattern shown in Fig. 1a and the patterns shown in Figs. 4a and 4b do vary together closely. In fact, we have also performed an SVD analysis on the cross-covariance matrix between storm track and 500-hPa z anomalies, and in this case the leading SVD pair (which accounts for 42% of the squared covariance fraction) have structures very similar to the patterns shown in Figs. 1a and 4b. In comparison, the MSLP and SST variations shown in Figs. 4c and 4d are not as tightly connected to the storm track variations, with r equaling 0.70 and 0.64, respectively. Nevertheless, all of the time series shown in Fig. 5 clearly show very similar low-frequency variability, with the values being mainly positive during late 1980s and early 1990s, and negative during the 1960s and early 1970s. The 300-hPa U and 500-hPa z patterns shown in Figs. 4a and 4b are clearly consistent geostrophically. The main centers in the 300-hPa U pattern are dipoles straddling the Pacific and Atlantic jets, just downstream of the respective jet maximum. When this pattern is added

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FIG. 4. (contours) Regression of PC1-NH on DJF mean (a) 300-hPa U (contour interval 0.5 m s 21 ); (b) 500-hPa z (contour interval 5 m); (c) MSLP (contour interval 0.5 hPa); and (d) SST (contour interval 0.18C). (Shades) Correlation of PC1 with the respective fields. Correlation values with magnitude larger than 0.4 and 0.6 are shaded.

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TABLE 1. Correlations between PC1 and various indices. PC1-NH PC1-ATL PC1-PAC PC1-ATL PC1-PAC -SOI AO PDO

0.80 0.90 — 0.40 0.53

0.47 — 0.72 —

(0.31) — 0.59

-SOI

AO

— 0.48

—

In Fig. 2, we saw that the leading PC of interannual storm track variability displays a sharp transition during the early 1970s, and indicates a generally upward trend during the past few decades. Several ‘‘modes’’2 of lowfrequency variability in the atmosphere as well as the coupled atmosphere–ocean system have been reported in the literature that also show either a trend or a transition during the 1970s (or both), among them are the Arctic oscillation (AO; Thompson and Wallace 2000; Thompson et al. 2000), which is highly correlated with the North Atlantic oscillation (e.g., Hurrell 1995); and the ENSO-like interdecadal variability (Zhang et al.

1997), which is significantly correlated with the Pacific decadal oscillation (PDO; e.g., Mantua et al. 1997). It is thus of interest to examine whether the decadal storm track variations discussed above are simply a manifestation of one (or a combination) of these oscillations. In Table 1, the correlation between PC1-NH and various other indices are shown. The indices shown are PC1-ATL and PC1-PAC, which correspond to the PCs of the leading interannual storm track EOF for the Atlantic and Pacific basin, respectively (shown in Fig. 2). The Southern Oscillation index (SOI) is based on the Comprehensive Ocean–Atmosphere Dataset (COADS) data,3 the negative sign adopted here is for ease of comparison, since the SOI correlates negatively with the other indices. The AO and the PDO indices are based on the references cited above. For all indices, the DJF values have been averaged to form a NH winter seasonal mean value, and then correlated with PC1-NH. All six time series are plotted in Fig. 6 (dashed lines). All of the time series have been normalized to unit standard deviation, and the mean for the period has been removed. In Table 1, all correlations shown are statistically significant at the 95% level after accounting for serial correlation (see Trenberth 1984), except for the correlation between -SOI and PC1-PAC, which is only significant at the 90% level. From Table 1, we can see that PC1-NH is correlated with the AO and the PDO at moderate levels. Upon further inspection, it is clear that the AO correlates well with storm track intensity over the Atlantic (PC1-ATL) but not over the Pacific (PC1-PAC). This is consistent with Deser (2000) who showed that the coherence between the Arctic and midlatitudes is strongest over the Atlantic sector. However, unlike MSLP (and 500-hPa z ) anomalies, which are not well correlated between the Atlantic and Pacific midlatitudes, the Pacific and Atlantic storm tracks are significantly correlated (section 3a). What contributes to such a difference between the behavior of the mean flow and storm track anomalies remains to be resolved. The PDO is well correlated with the storm track intensity over the Pacific but not over the Atlantic. The SOI is only weakly correlated with Pacific storm track intensity, and is moderately correlated with the PDO. Table 1 suggests that PC1-NH is not significantly correlated with the SOI. Nevertheless, Zhang et al. (1997)

2 Here ‘‘modes’’ is used in a loose sense, without any implication that these are normal modes of the system.

3 The index is prepared by T. Mitchell and available online at http: //tao.atmos.washington.edu/data/soicoads2/soicoads2.dat.

FIG. 5. PC1-NH (top curve) and time series obtained by projecting the patterns shown in Fig. 4 onto their respective seasonal mean anomalies.

onto (or subtracted from) the climatological 300-hPa U pattern (not shown), there is no significant change in the jet strength, but the jet tilts slightly toward the north (south) downstream of both jet maxima. The MSLP can be easily transformed into 1000-hPa z (in m) by multiplication of the MSLP values (in hPa) by a factor of 8. When we multiply Fig. 4c by 8 and compare that to Fig. 4b, we see that the lows over the Aleutian Islands, near the southern tip of Greenland, and over northwestern Russia, have strong barotropic components, but the ridge over western Canada at 500 hPa is not present at the surface. The SST pattern shown in Fig. 4d will be discussed further in section 5. Since seasonal mean wind and height fields are expected to be much more strongly constrained by observations as compared to variances (see Ebizusaki and Kistler 1999), the tight relationship between storm track and monthly mean flow variations give us more confidence that the storm track variations are probably realistic. The dynamical link between storm track and mean flow variations is beyond the scope of this paper. 5. Relationship to other low-frequency variations

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FIG. 6. (dashed lines; top to bottom): Time series for PC1, PC1ATL, PC1-PAC, the AO index, negative of the SOI index, and the PDO index. (solid lines) Their respective 5-yr running mean.

suggested that there may be two distinct modes of variability associated with SST variations in the tropical Pacific; a higher-frequency, interannual timescale ENSO cycle, and a lower-frequency, ENSO-like interdecadal variability. The lower-frequency mode can be obtained as the leading EOF based on an EOF analysis of 6-yr low-pass-filtered Pacific basin sea surface temperature anomaly (SSTA) data, but Zhang et al. also showed that the PC time series can be retrieved simply by low-pass filtering of the SOI. Using the second approach, we have defined a low-frequency component of the SOI simply by applying a 5-yr running mean to the interannual time series (thick solid line in Fig. 6). We have regressed this time series with SSTA, and the resulting pattern (not shown) is very similar to the pattern shown in Zhang et al. This result is interesting because the SSTA pattern associated with this low-frequency variability, with a broad SSTA maximum straddling the equatorial Pacific and SSTA of opposite sign centered around 408N with about the same magnitude, looks somewhat similar to the regression of SSTA with PC1-NH shown in Fig. 4d, suggesting that part of the storm track variability may be associated with this mode of variability. The above discussions suggest that part of the lowfrequency storm track variability may be associated with these other low-frequency variability. In order to see how much of the storm track variations are unrelated to these other modes, the following analysis was performed. The storm track data were regressed against both the high- (original SOI minus 5-yr running mean) and low-frequency (5-yr running mean) components of the SOI separately, and the part that is linearly dependent upon these two indices (referred to as SOI2 in Figs. 7–8 and the discussions below) was removed. This was done under the assumption that the high- and low-frequency components of SOI might be physically distinct (see Zhang et al. 1997; K. Kim 2001, personal communication). Had we not separated the SOI into high-

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and low-frequency components before removing the SOI signal, the low-frequency variability in the residual data would have been even more pronounced than that shown below. The residual data were then linearly regressed against the AO index, and the part that is linearly dependent upon the AO was then also removed. Although we removed the SOI signal before the AO signal, the order of operation is not important since the AO and the SOI are not significantly correlated. Unlike the SOI, we chose not to separate the AO into high- and low-frequency components, since at the present moment we do not have any reason to believe that the dynamics of the AO is different between the two different timescales. This procedure removes 23% of the year-to-year storm track variability. Table 1 suggests that over the Pacific basin, PC1 is better correlated with the PDO than with the SOI. We have chosen to remove the part of storm track variations that is linearly dependent upon the SOI instead of that linearly dependent on the PDO, because the SOI is defined based on tropical Pacific SSTA and presumably represents forcing away from the midlatitude storm track region. Meanwhile, the PDO is defined by midlatitude SSTA, part of which could be a response to changes in atmospheric circulation associated with storm track variations (e.g., Deser et al. 1999; Seager et al. 2000). Since currently it is not exactly clear what are the physical mechanisms that cause the low-frequency variations and trends in the AO and the SOI, we have operated here under the assumption that they are distinct mechanisms, and we have removed the maximum amount of storm track variations that are linearly dependent on both of them just to see how much of the variations remain in the residual. An EOF analysis was performed on the residual data. The pattern corresponding to the leading EOF (EOF1b), which again accounts for 29% of the residual variance, is shown in Fig. 7a. Its corresponding PC time series (PC1b) is shown in Fig. 8. Figure 8 clearly shows that even after the SOI and the AO signals have been removed, there is still substantial interdecadal variability in the storm track data, with the residual storm track generally weak during the 1960s and strong during the late 1970s and late 1980s. In Fig. 7, we also show the regression of PC1b against 500-hPa z , MSLP, and SST (all with SOI2 and AO removed). The 500-hPa z and MSLP patterns again show a strong barotropic component, with the amplitude at the surface being about 70% of that at the 500-hPa level. The cyclone over the North Atlantic is now shifted eastward compared to Fig. 4, and the low over northern Russia is no longer present. When we project the patterns shown in Figs. 7b and 7c back onto the original data to obtain two time series, the correlations between PC1b and the time series so obtained are 0.82 and 0.81, respectively, indicating that the patterns shown in Figs. 7a–c are indeed closely related. The most significant change in the SST pattern (Fig. 7d) is the near disappearance of the positive SSTA

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FIG. 7. (a) Same as Fig. 1a, except that EOF analysis is performed after removal of parts linearly dependent on the SOI and the AO from the data. (b)–(d) Same as Fig. 4b–d, except that the SOI and the AO signals have been removed.

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FIG. 8. The PC time series corresponding to the pattern shown in Fig. 7a.

over the tropical Pacific, and this change is clearly associated with the removal of the SOI signal. The remaining SSTA signal is probably consistent with the SST being forced by changes in surface circulation (Fig. 7c). The amplitude of the SST changes (20.48C maximum over the northern Pacific) is probably too small to be able to force an atmospheric response as large as those shown in Figs. 7a–c (e.g., Peng and Whitaker 1999; Peng et al. 1997; Ferranti et al. 1994), although the atmospheric response to SSTA obtained by Latif and Barnett (1994, 1996) could come close. 6. Summary and discussion In this paper, variations in the NH winter storm tracks as depicted by the NCEP–NCAR reanalysis data have been examined using an EOF analysis. The leading EOF represents the intensification/weakening of the entire storm track. The interesting result herein is that the PC corresponding to this EOF exhibits strong interdecadal variability, with a strengthening trend from the 1960s to the present, and a sharp transition around 1972/73. The storm track during the 1980s and 1990s is about 30% stronger than the storm track during the 1950s and 1960s (Fig. 3). By examining EOFs performed on the individual basins (using seasonal as well as monthly mean data), and SVD analyses performed on the covariance matrices between the two basins (appendix C), we have shown that the Pacific and Atlantic storm track variations are significantly correlated. What is the dynamical link between the two storm tracks? One possibility could arise from the fact that the eddies in the Atlantic storm track are seeded by the Pacific storm track (see Chang and Yu 1999), hence a stronger Pacific storm track could conceivably lead to a stronger Atlantic storm track. Alternatively, one could imagine that the low-frequency flow patterns shown in Fig. 4 represent an internal mode of low-frequency variability of the atmosphere (or atmosphere–ocean coupled system), and the correlation between the two basins arise from the link between the two regions in the low-frequency flow, rather than due to the effect of synoptic-scale eddy propagation and seeding. Careful data analyses and modeling studies will

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have to be performed to examine these (and other) possibilities. In section 4, we have shown that the storm track variations are closely linked with the monthly mean flow variations. Since objective analyses of the low-frequency flow are much less affected by changes in the observing network (Ebisuzaki and Kistler 1999) than are analyses of variances, the close correspondence between the storm track and mean flow variations has given us more confidence that the storm track changes are realistic. However, one could argue that part of the analysed storm track changes could have been due to the model’s response to mean flow changes. Thus, it is important to examine storm track variability based directly on observations. In appendix A, we have presented findings from a preliminary analysis of radiosonde observations based on 21 stations along the storm track, and found that the radiosonde data largely confirm the EOF pattern shown in Fig. 1a, except over Japan where radiosonde observations do not appear to be consistent with the reanalysis data. Moreover, radiosonde data also support a significant increase in the storm track intensity during the early 1970s. However, our results also suggest that there may be systematic biases in the reanalysis data, such that the storm track variances are biased low prior to the early 1970s, with the implication that the actual interdecadal storm track variability may be less than that suggested by the reanalysis. Unfortunately, there are no radiosonde stations with continuous record over the peak of either storm track to allow examination of this issue. Currently we are examining aircraft observations to see whether storm track variations over the peaks of the storm tracks are captured in the aircraft data. The relationships between the decadal storm track variations and other modes of low-frequency variability were explored in section 5. In order to assess whether most of the storm track variability can be explained by the AO or the ENSO-like interdecadal variability, we removed from the data the part that is linearly dependent on the SOI (both high- and low-frequency components) and on the AO. The residual data still show significant interdecadal variability in storm track intensity (Fig. 8), suggesting that much of the storm track variations are not linearly related to either the AO or tropical SSTA. Obviously, the results do not exclude the possibility that much of the storm track changes could be nonlinearly related to the AO or tropical SSTA. What, then, can be the cause of the storm track variations? Could it be a midlatitude atmosphere–ocean coupled mode, with dynamics analogous to those suggested by Latif and Barnett (1994, 1996) and others? The observed atmospheric anomalies (Figs. 4c, 7c) are certainly capable of driving midlatitude SSTA with amplitudes like those shown in Figs. 4d and 7d (e.g., Deser et al. 1999; Seager et al. 2000). The SST anomalies associated with the storm track variations (Figs. 4d, 7d), however, appear to be relatively modest, and the at-

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mosphere must be much more sensitive to midlatitude SSTA than most GCM experiments indicate for the SSTA feedback onto the atmosphere to have a magnitude comparable to what is observed. Regardless of the causes for the storm track variations, we have demonstrated here that the amplitude of the Northern Hemisphere storm tracks have undergone significant interdecadal variations during the last half century. Since the baroclinic waves that make up the storm tracks transport the momentum, heat, and moisture that help to maintain the large-scale circulation, there must have been significant changes in the momentum, heat, and hydrological budgets over the midlatitudes associated with these storm track variations. We are currently working on diagnosing those changes. Acknowledgments. The authors would like to thank Dr. Mike Wallace and an anonymous reviewer for useful comments, and Dr. Phil Cunningham for reading the manuscript and making many useful suggestions. The NCEP–NCAR reanalysis data and radiosonde observations used in this paper were obtained through NCAR, and assistance from the Scientific Computing Division is appreciated. The figures in this paper were produced using GrADs, first developed by Brian Doty of COLA. Part of this work was done when the authors were at MIT, where they were supported by NOAA Grant NA86GP0210 and NSF Grant ATM-9731393. The authors were supported by NOAA Grant NA06GP0023 and NSF Grant ATM-0003136 at FSU.

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APPENDIX A Validation of Storm Track EOF Pattern Using Radiosonde Observations We saw earlier that the peaks in the pattern of storm track variability lie over the oceans (Fig. 1a). The amount of data over the ocean is obviously much less than that over land, and it is not clear that over data sparse regions (e.g., eastern Pacific) the analysis faithfully reflects the correct storm track amplitude. As an example, Chang (2000) pointed out that the storm track amplitude over the Southern Hemisphere oceans differs by more than 20% between the NCEP–NCAR reanalysis and the ECMWF reanalysis, suggesting that storm track amplitudes may not be strongly constrained by observations over data-sparse areas. One of the major changes between the 1960s and more recent decades is the availability of satellite observations since the late 1970s. The number of aircraft observations had also increased, but a significant number of those were already available in the late 1960s. Mo et al. (1995) compared analyses with and without satellite observations for August 1985 and concluded that satellite observations strongly affect SH analyses, but the impacts on NH analyses are small. However, that was done on NH summer instead of winter data. As part of the NCEP–NCAR reanalysis project, an analysis was performed for the entire year of 1979 without making use of satellite observations (NOSAT), which

TABLE A1. Comparison between radiosonde observations and NCEP–NCAR reanalysis at selected stations. (* in column 1 defined in text.) Low-index years

(1)

(2) Lat/lon of nearest grid

(3) Station id(s)

1 *2 *3 *4 *5 *6 *7 *8 *9 *10 *11

37.58N, 127.58E 358N, 1408E 37.58N, 1408E 42.58N, 1458E 508N, 1458W 508N, 127.58W 47.58N, 1258W 37.58N 122.58W 47.58N 107.58W 458N, 87.58W 42.58N, 708W

47122, 43201 47646 47590 47420 4YP 71109, 25223 72797, 24240 72493, 23230 72768, 94008 72645, 14898 74494, 72606, 14764 72712, 14607 78016, 13601 4YJ 03953 03920, 03917 03808 06447, 06476 06181, 10184 26038, 02974 22550

*12 47.58N, 67.58W 13 32.58N, 658W *14 52.58N, 208W 15 52.58N, 12.58W *16 558N, 58W 17 508N, 58W *18 508N, 58E *19 558N, 12.58E *20 608N, 258E 21 658N, 408E Average of all

High-index years

High–Low

(7) (4) (5) (6) Varncep Nobs Varobs Varncep (all 890)

(11) (8) (9) (10) Varncep Nobs Varobs Varncep (all 890)

(14) (12) (13) Varncep Varobs Varncep (all 890)

629 628 612 480 634 535 651 768 627 590 770

297 291 300 320 560 537 507 387 446 519 523

188 191 231 274 427 423 455 301 400 485 501

152 174 197 154 392 422 427 289 364 433 476

801 881 866 874 — 836 684 711 791 736 847

256 244 297 381 592 645 697 579 556 557 654

223 29 45 84

77 57 68 107

156 178 232 193 52 95

241 202 296 192 109 166

770 790 787 549 634 654 — 496 405 762 11096

504 247 503 410 489 468

442 218 409 306 382 346

584 275 740 724 696 676 561 528 455 299 506

140 93

421 233 251

465 319 338

353 312 203 337

645 381 — 772 846 853 816 882 764 508 13932

136 128

379 401 238 406

427 216 399 351 350 319 308 311 257 204 307

154 170 134 144

187 192 123 187

274 282 345 404

265 248 299 381

693 685 620 638 571 619

655 657 597 591 594 667

640 375

582 311

831 722 720 601 532 572 372 550

772 702 684 593 540 504 326 524

104 69 99 227 200 224 270 290 193 124 178 156 59 341 373 346 357 253 217 198 95 199

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653

FIG. A1. (contours) The 24-h filtered 300-hPa y 9 2 (DJF mean), high-index years minus lowindex years, contour interval 100 m 2 s 22 . (circles) Location of stations used to verify EOF pattern. (Crosses) Location of stations used to verify storm track trend during the early 1970s.

can be compared to the control analysis that contains satellite observations (SAT). We computed the storm track statistics using these two sets of data, and arrived at a similar conclusion that for NH winter analyses, the impacts of satellite observations are minimal (however, the impact of satellite observations on SH storm tracks is very large). In fact, the NH winter storm track in the SAT analysis is slightly weaker than that in the NOSAT analysis, opposite to the sense that is needed to explain the weaker storm track in the earlier decades. In the 1950s and early 1960s, apart from the lack of satellite observations, the number of aircraft observations were also significantly less. Ebisuzaki and Kistler (1999) compared two sets of analyses for 1998, one with all the available data, and the other without using satellite, aircraft, and SH bogus surface pressure data. Their results show that there may be significant biases in the analyses over the NH oceans when satellite and aircraft data are not available. However, the real situation may not be as bad as that implied by their results, since during the 1950s, although there were very few aircraft observations, there were several weather ships over the eastern Pacific and Atlantic that made 12-hourly radiosonde observations. These weather ships were no longer present in 1998, thus the impact of aircraft data might have been larger for 1998 than for the 1950s. a. Differences between high- and low-index years In order to assess how much changes in the observing system could have affected the EOF analysis discussed in section 3, we examined radiosonde observations taken along the storm track, especially over regions where the amplitude is large in Fig. 1a. We chose the five winters with the largest PC value (high-index years: 1993/94, 1998/99, 1997/98, 1988/89, and 1987/88), and the five with the lowest PC value (low-index years: 1955/56, 1968/69, 1956/57, 1962/63, and 1964/65). Note that all five high-index years occur after 1985, while the low-index years all come before 1970. The composite difference between the five high- and lowindex years, based on the NCEP–NCAR reanalysis data,

is shown in Fig. A1. For this figure, unlike Fig. 1a, the data are shown based on a 2.58 3 2.58 resolution and have not been smoothed to T12. In order to directly compare radiosonde observations and reanalysis grids, we searched the NCEP–NCAR reanalysis observation archives to find radiosonde stations along the NH storm track that reported most of the time during the high- and low-index winters. The stations that we chose are plotted as open circles in Fig. A1, and a complete list can be found in the third column of Table A1. Four stations were chosen around 1208E (#1– 4 in Table A1), over the far western end of the pattern. Seven stations were selected over the United States and Canada (#6–12), and six over Europe (#15–17 and 19– 21). Several weather ships reported during the low-index years (e.g., #5 and #14 in Table A1) but have been decommissioned during the high-index years, and they were not included in this comparison. The radiosonde observations (300-hPa meridional wind) were taken as is—no quality control was performed except that data were dropped for the few instances when the reports appeared to be erroneous.4 The radiosonde stations chosen all reported regularly once every 12 h. Nevertheless, there were times when reports were missing. No attempts were made to fill in the missing reports. Instead, variances were computed using the 24-h-difference filter, taking all the times when two observations separated by 24 h were available (varobs: columns 5 and 9). To compare the reanalysis data directly to observations, the gridpoint values of the grid closest to each station (taken from the 2.58 3 2.58 NCEP reanalysis data) were taken only during the times when radiosonde observations were available from that station, and the variance based only on those times was computed (varncep: columns 6 and 10) in exactly the same way. This was the main reason why the 24-h difference filter was chosen over other filters in this 4 For this study, data were dropped when the difference between reanalysis grid and observation was larger than 50 m s 21 . We have tried different cutoff values and found that the results were not sensitive to that.

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study—no interpolation was needed for missing data. The number of 24-h differences used to compute the variances for the high- and low-index years for each station is listed in Table A1 (nobs: columns 4 and 8). Note that the maximum number possible for each winter is 178, hence 890 is the maximum possible for each period. To limit the impact of missing data (see Kidson and Trenberth 1988), we only included stations at which reports were available during over 40% of the time. The variances computed from all 890 data pairs using the NCEP–NCAR reanalysis grid (the values displayed in Fig. 7) are also shown in Table 1 in italics (columns 7 and 11) for reference. The differences between the highand low-index years are shown in columns 12–14. Since reanalysis gridpoint data are available at all times, errors and biases introduced due to missing data can be assessed by comparing columns 6–7, 10–11, and 13–14. In general, these appear to be less than the differences between radiosonde observations and reanalysis grids taken only at times when observations are available (columns 5 and 6, 9 and 10, and 12 and 13). If we examine the variances computed directly using the radiosonde observations (columns 5 and 9), we see that the observed variances are clearly stronger during the high-index years than during the low-index years over all stations, except for stations #1 and 2, which are located over the far western end of the pattern. The differences between the high- and low-index years (column 12) are in general less than those computed from the reanalysis data (column 13). Comparing columns 5– 6 and 9–10, we see that the reanalysis data seem to contain less variance than radiosonde data, which is reasonable since analyses generally provide some smoothing due to the presumed existence of observational errors. However, the differences are clearly larger during the low-index years, possibly giving rise to underestimation of the storm track intensity during the low-index years, leading to a possible overestimation of the differences between the high- and low-index years. While the preceding paragraphs suggest that the reanalysis data may contain some biases introduced by changes in the observing system, results from Table A1 clearly show that the storm track is significantly stronger during the high-index years over North America and northern Europe, over the exit regions of the Pacific storm track, as well as the entrance and exit regions of the Atlantic storm track. Unfortunately there are no radiosonde stations to directly support the changes near the peaks of both storm tracks. Hence we can only conclude that at least part of the storm track EOF pattern that show up in the reanalysis data (Fig. 1a) is supported by radiosonde observations. b. The ‘‘transition’’ during the early 1970s The PC time series shown in Fig. 2 suggests that there is a transition during the early 1970s, when the storm track intensity ‘‘jumps’’ from around 21s during 1970/

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FIG. A2. Time series of 24-h filtered 300-hPa y 9 2 (DJF mean) during the early 1970s. (thick solid line) Radiosonde observations from 16 stations. (thin solid line) NCEP–NCAR reanalysis at grid points closest to the stations, only at times when observations are available. (dashed line) NCEP–NCAR reanalysis at all analysis times. (Dotted line in lower panel) NCEP–NCAR reanalysis, all analysis times, area averaged over 358–608N, 1208–608E.

71 to nearly 11s during 1972/73. In order to see whether there is any evidence of that, we composited radiosonde observations from stations along the storm track that reported more that 50% of the time every winter from 1968/69 to 1975/76. Data from 16 stations (marked by ‘‘X’’ in Fig. A1, and ‘‘*’’ in column 1 of Table A1) have been used, and the result is plotted as the thick solid line in Fig. A2. For comparison, NCEP–NCAR reanalysis data taken at the grid closest to the station and only during times when radiosonde observations are available are plotted as the thin solid line, and reanalysis data taken at these grids, but averaged over all analysis time (including times when observations are not available) are shown by the dashed line. The dotted line shown in the lower panel is the area average of storm track intensity between 358–608N, and 1208– 608E, taken from the reanalysis at all analysis time. To put this in context with respect to Fig. 2, the mean storm track intensity (dotted line averaged over 51 yr) is 360 m 2 s 22 , and the standard deviation is 45. Thus the dotted line shows that the storm track intensity changes from less than mean minus 1s during 1970/71 to over mean plus 1s during 1974/75, with most of the increase occurring between 1970/71 and 1972/73, similar to the change in PC1-NH seen in Fig. 2. Comparing the variance computed directly from the radiosonde observations (thick solid line) to that computed using the reanalysis grid (thin solid line), we see that both show an increase from 1969/70 to 1974/75, but the increase appears to be much more gradual than

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that implied by the area average of storm track intensity (dotted line, lower panel). Examining the difference between 1972/73 and 1970/71 in the reanalysis grids (not shown), the largest increase over those two years lie over the Pacific and Atlantic Oceans, over areas where we do not have any stations, thus it is not surprising that the sharp increase during those two years shown in the dotted line is not captured by the composites from the stations chosen. In addition, just like the differences between the high- and low-index years discussed above, the increase in storm track amplitude as seen in radiosonde observations is less than that in the reanalysis grid, again apparently due to a low bias in the reanalysis data during the earlier years. Thus while radiosonde data do support a significant increase in the storm track amplitude between 1969/70 and 1974/75, they also suggest that the increase is probably less than that suggested by the reanalysis. The apparent change in reanalysis bias during the early 1970s could in part be due to changes in the coding of radiosonde observations introduced during 1973 (J. Norris 2000, personal communication; see also Kistler et al. 2001). Extending the time series shown in Fig. A2 is not entirely straightforward since it is difficult to find stations with continuous reports over the years. Currently we are analyzing data from more radiosonde stations as well as aircraft observations in order to obtain a model-independent storm track intensity time series based on observations alone. APPENDIX B Summary of Storm Track Analyses Based on Different Time Filters, Variables, and Levels There are certainly many ways to define the storm tracks. A storm track is basically a region over which midlatitude synoptic-scale perturbations are prevalent, thus it is marked by maxima in eddy quantities such as geopotential height variances, eddy energy, heat fluxes, momentum fluxes, etc. (see Blackmon et al. 1977; Trenberth 1991). In addition, in order to highlight the synoptic timescale variances and covariances, different time

filters have been used (e.g., Wallace et al. 1988). Moreover, since midlatitude baroclinic perturbations have deep structures that extend from the surface to above the tropopause (e.g., Lim and Wallace 1991), one can examine storm track structures at different levels in the vertical (e.g., Lau 1978). In this paper, we have based our discussions mainly on 300-hPa y 9 variance, filtered using a 24-h difference filter. We have also analyzed storm track variations based on other variables, time filters, and at other vertical levels. In this appendix, we will briefly summarize some of these results. a. Different time filters Just like what we did using the 24-h difference filter, we have performed similar analyses using a 1–8-day Lanczos filter (Whitaker and Sardeshmukh 1998), which is a bit broader than the bandpass filter used by Blackmon (1976) and collaborators. The results using storm track defined based on 300-hPa y 9 2 filtered using the Lanczos filter are very similar to those using the 24-h difference filter, with the leading EOF pattern for that case displaying a structure very similar to Fig. 1a, and the correlation between the corresponding PC and PC1NH is 0.93. The results are summarized in Table B1. In the table, the rank, percentage variance, and correlation of the PC with PC1-NH, of the EOF whose PC correlates best with PC1-NH, are listed in columns 5, 6, and 7, respectively. Even if we had used unfiltered y 9 data (apart from the removal of monthly means—see row 3 in Table B1), the leading EOF still behaves very much like the one defined using the 24-h difference filter, except that it accounts for a smaller fraction of the total interannual variance–17% instead of 29%. Since there is no reason to expect that the variations in other storm track variables that are physically related to PC1-NH necessarily appear as an EOF, for each storm track variable we have also used a regression analysis to obtain the pattern that linearly correlates with PC1NH, and then projected that pattern back onto the interannual anomalies of that variable to obtain a time

TABLE B1. Correlations (r) between PC1-NH and PCs based on other filters, vertical levels, and storm track variables.

1 2 3 4 5 6 7 8 9 10 11

(2) Level (hPa)

(3) Variable

(4) Filter

(5) EOF No.

300 300 300 700 300 500 1000 400 400 700 300

y 92 y 92 y 92 y 92 z9 2 z9 2 z9 2 c9 2 c9 2 y 9T 9 u9y 9

24-h 1–8-day Unfiltered 24-h 24-h 24-h 24-h 24-h 1–8-day 24-h 24-h

1 1 1 1 1 2 2 1 1 1 —

(6) % var

(7) Correlation with PC1 (r)

(8) Regressed correlation

(9) Regressed pattern % var

29 26 17 20 22 16 13 23 25 22 —

— 0.93 0.87 0.86 0.82 0.80 0.63 0.95 0.87 0.59 —

— 0.94 0.94 0.94 0.95 0.94 0.81 0.96 0.90 0.89 0.84

— 26 16 19 21 17 16 23 24 18 11

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series for that pattern (similar to the technique that we used to relate the storm track EOF to seasonal mean flow discussed in section 4 above). The amount of variance associated with the regressed pattern is shown in column 9 of Table B1, and the correlation of its time series with PC1-NH is shown in column 8. The regressed patterns are by design more closely related to PC1-NH than the EOFs are (comparing columns 7 and 8). Nevertheless, the high correlations shown in column 8 show that the same type of variability displayed by PC1-NH is also present in the other variables as well. The relative insensitivity of the results to the different time filters is not restricted to 300-hPa y 9 2 alone, as we have also used both the 24-h difference filter and the 1–8-day Lanczos filter to analyze 400-hPa streamfunction variance and found very similar results (rows 8 and 9 in Table B1). In fact, the correlation between the two leading PCs in this case is 0.95 (not shown in the table), again showing that the results are not sensitive to the time filter. b. Different vertical levels The comparison with the analyses based on 700-hPa y 9 2 is shown in row 4. Again, the leading EOF behaves qualitatively like the one based on 300-hPa y 9 2 , except that it accounts for a smaller fraction of the variance. The maxima in the EOF pattern are also displaced about 308 longitude westward compared to the pattern shown in Fig. 1a. The insensitivity to vertical levels is somewhat dependent on the variable, though. If we analyze z9 2 instead of y 9 2 , the structure of the leading EOF changes, such that at 300 hPa, the leading EOF is the one most closely related to the one based on 300-hPa y 9 2 , but at 500- and 1000-hPa levels, it is the second EOF that corresponds most closely to that (see rows 5–7). Again, the relative amount of variance associated with PC1NH decreases as one moves closer to the surface. c. Different storm track variables In Table B1, we show comparisons with EOF analyses performed based on z9 2 at 300-, 500-, and 1000-hPa levels (rows 5–7), as well as 400-hPa streamfunction variance (rows 8 and 9), lower-troposphere heat flux (row 10), and upper-troposphere momentum flux (row 11). In most cases, either the leading or the second leading EOF corresponds closely to our storm track EOF, except for 300-hPa momentum flux, in which case none of the leading PCs correlate well with PC1-NH. Nevertheless, the regressed momentum flux correlates very well with our storm track PC, but the pattern only accounts for 11% of the momentum flux interannual variance. For z9 2 at 500 and 1000 hPa, the leading PC correlates very well with the AO index (correlation equals 0.70 and 0.86, respectively), with the spatial pattern showing a main maximum over the northern At-

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lantic and Europe centered around 658N, and only weak structures over the Pacific. The leading PC for 700-hPa heat flux also correlates better with the AO index (r 5 0.76) than with PC1-NH. Nevertheless, for all cases, the regressed time series correlate very well with PC1-NH (r . 0.80 for all cases, see column 8), showing that there are clearly variations present (accounting for significant portion of the variance: see column 9) in each of the variables analyzed that are closely linked to the storm track EOF discussed in this paper. Detailed threedimensional structure of the storm track variations, as well as implications of the anomalous eddy fluxes on forcing the seasonal mean flow, will be examined elsewhere. APPENDIX C Correlation between the Pacific and Atlantic Storm Tracks In section 3a, we showed that the Pacific and Atlantic storm track variations are significantly correlated, based on analysis of 24-h filtered 300-hPa y 9 2 . Here, we will briefly discuss how the correlation changes when different time filters and different variables are used to define the storm tracks. In section 3a, much of the discussions were based on the correlation between the leading PCs from EOF analyses performed separately on the two basins. However, there is no reason why the best correlated anomalies would naturally appear as EOFs in the data, hence to get structures that vary together in the two basins, we performed an SVD analysis (Bretherton et al. 1992) of the covariance matrix between the Pacific and Atlantic sectors. While SVD analyses act to find structures that have maximum covariance instead of maximum correlation, we are not interested in highly correlated structures that account for only a small part of the variance in either basin. Hence we have decided to base our discussions on SVD analyses instead of canonical correlation analyses which act to maximize the correlation. The results of SVD analyses based on the different variables discussed in appendix B are summarized in Table C1. For each of the variables, we sought the SVD pair which have time series that correlate best with PC1NH.5 For most variables, this turns out to be the leading SVD pair, but for 500 hPa z9 2 (row 6), it is the second leading SVD pair. The leading SVD pairs for 1000 hPa z9 2 (row 7) and 300 hPa u9y 9 (row 11) are not well correlated with PC1-NH, and the results for these variables are not shown here. In Table C1, the correlations between the Atlantic and Pacific time series are shown in column 5. In columns 6–8, the squared covariance fraction explained by the SVD pairs, and percentage variance explained by the 5 The average of the correlation between the two time series (ATL and PAC) and PC1-NH is shown in column 9.

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CHANG AND FU TABLE C1. SVD analysis of Pacific and Atlantic storm tracks covariance matrix.

1 2 3 4 5 6 7 8 9 10 11

(2) Level (hPa)

(3) Variable

(4) Filter

300 300 300 700 300 500 1000 400 400 700 300

y 92 y 92 y 92 y 92 z9 2 z9 2 z9 2 c9 2 c9 2 y 9T 9 u9y 9

24-h 1–8-day unfiltered 24-h 24-h 24-h 24-h 24-h 1–8-day 24-h 24-h

(5) ATL–PAC correlation

(6) Squared covariance fraction (%)

(7) PAC % variance

(8) ATL % variance

(9) Avg correlation with PC1-NH

0.67 0.63 0.69 0.60 0.57 0.51

78 70 50 52 47 29

41 36 22 31 32 22

29 28 16 17 20 19

0.91 0.83 0.82 0.76 0.83 0.73

0.59 0.59 0.50

57 66 44

32 32 20

24 29 26

0.84 0.79 0.69

Pacific and Atlantic patterns, respectively, are shown. For 24-h filtered 300-hPa y 9 2 (row 1), the leading SVD pair accounts for 78% of the squared covariance fraction, and the two patterns individually accounts for 41% and 29% of the variance in the respective basin, just slightly less than the variance accounted for by the leading EOFs in the respective basin (43% and 35%, respectively, refer to section 3a). The spatial patterns corresponding to the SVD pair are very similar to the structures of the EOFs. The correlation between the Pacific and Atlantic time series is 0.67, significantly higher than the correlation between the leading PCs in the individual basin (0.47). The two time series are also well correlated with PC1-NH (column 9). While it is difficult to directly compare the values of the correlation listed in column 5 of Table C1 since we have not tried to maximize the correlation for each variable, the results show that for most of the variables that we have examined, there are structures in the two basins that are well correlated with each other as well as with PC1-NH, and these structures account for a significant fraction of the variance in each basin. We have also performed similar analyses on monthly 24-h filtered 300-hPa y 9 2 data, using all 153 DJF months as well as only the 72 DJF months taken from 1975/76 to 1998/99 (including only data after the transition), and the results are very similar. The correlation between the time series for the leading SVD pair for both cases come out to be about 0.55, and the leading SVD pair accounts for over 70% of the squared covariance fraction. Hence our results in this appendix show that the significant correlation between the two storm tracks is robust. REFERENCES Blackmon, M. L., 1976: A climatological spectral study of the 500 mb geopotential height of the Northern Hemisphere. J. Atmos. Sci., 33, 1607–1623. ——, J. M. Wallace, N.-C. Lau, and S. L. Mullen, 1977: An observational study of the Northern Hemisphere wintertime circulations. J. Atmos. Sci., 34, 1040–1053. Bretherton, C. S., C. Smith, and J. M. Wallace, 1992: An intercom-

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