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Jan 15, 2004 - 1971; Labitzke 1982). Recently, the influence .... say, 30- and 500-hPa levels, where real modes means we carefully check ... center is slightly located east of the Aleutian high, this ...... dependence and life cycle. J. Climate, 14 ... Zhou, S., A. J. Miller, J. Wang, and J. K. Angell, 2002: Downward- propagating ...
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Coupling between Tropospheric and Stratospheric Leading Modes HISANORI ITOH

AND

KEN-ICHI HARADA

Department of Earth and Planetary Sciences, Kyushu University, Fukuoka, Japan (Manuscript received 3 September 2002, in final form 24 March 2003) ABSTRACT Coupling between tropospheric and stratospheric leading modes in anomaly fields is investigated. By using daily data at many levels in addition to monthly mean data, the transition of spatial patterns and the direction and speed of the vertical propagation are examined in detail. Results show that the North Atlantic Oscillation mode (NAO) and the Pacific–North American mode (PNA) dominating in the troposphere couple with the annular mode (AM) and a wavenumber-1 mode (W1) dominating in the stratosphere, respectively, with significant temporal correlations. The transition of the patterns occur at about 150 hPa. The couple of NAO–AM (first mode) amplifies almost simultaneously from the surface to the 10-hPa level. Sometimes amplifications are repeated a few times, in which maxima of the amplification move to the lower atmosphere. Viewing these sequences from a relatively long time scale, the first mode slowly propagates to the lower atmosphere. The coupling of PNA–W1 (second mode) propagates from the troposphere into the stratosphere in about 1 week. There is some relationship between the first and second modes. After the second mode propagates from the troposphere into the stratosphere, the first mode develops with a lag of 10–15 days. However, this relationship has different characteristics between positive and negative phases. Since large-amplitude AM with one phase corresponds to the stratospheric sudden warming, the sudden warming is caused by the following sequence. The PNA with a negative anomaly over the Pacific amplifies in the troposphere, exciting the W1 with a positive anomaly over North America in the stratosphere, which causes the sudden warming. Thus, amplification of the PNA leads to the sudden warming.

1. Introduction It is well known that the stratospheric circulation is strongly affected by the tropospheric circulation. The influence ranges from short to long time scales. In a long time scale, stationary waves in the stratosphere have the excitation source in the troposphere (Charney and Drazin 1961). In a short time scale, it has been well studied theoretically and observationally that the stratospheric sudden warming is caused by the amplification of planetary waves in the troposphere (e.g., Matsuno 1971; Labitzke 1982). Recently, the influence of the stratospheric circulation on the troposphere has been extensively studied. There may be three mechanisms by which the stratosphere affects the tropospheric circulation, although it is impossible to strictly distinguish them. One mechanism is that the stratosphere acts as the boundary of the troposphere, in which the tropospheric circulation can alter mainly by the change of characteristics of planetary wave propagation (e.g., Boville 1984). The second is Corresponding author address: Prof. Hisanori Itoh, Dept. of Earth and Planetary Sciences, Kyushu University, 6-10-1 Hakozaki, Fukuoka 812-8581, Japan. E-mail: [email protected]

q 2004 American Meteorological Society

that the stratospheric circulation directly influences the tropospheric circulation. Namely, potential vorticity anomalies in the lower stratosphere induce height and wind perturbations extending downward to the troposphere (Hartley et al. 1998; Black 2002; Ambaum and Hoskins 2002). The third is the interaction between the tropospheric and stratospheric circulations. A typical example is the downward penetration of the zonal mean flow into the troposphere, resulting from the interaction of upward propagating planetary waves with the mean flow. There have been many studies about this phenomenon (e.g., Kodera et al. 1990; Kuroda and Kodera 1999; Christiansen 2001). Moreover, it has been found that, after the sudden warming, the tropospheric circulation considerably changes on a long time scale (order of month; e.g., Yoden et al. 1999; Kodera et al. 2000; Zhou et al. 2002). Thus, the tropospheric circulation and the stratospheric one are closely related to each other so that anomaly patterns in the troposphere and the stratosphere may also couple with each other. Following a pioneering work of Nigam (1990), treating troposphere–stratosphere zonal flow coupling, Baldwin et al. (1994) are the first to examine the mode coupling between the troposphere and the stratosphere. They showed that the

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North Atlantic Oscillation mode (NAO) dominating in the troposphere and a seesaw pattern between the midlatitude and the polar region, that is, the annular mode (AM) dominating in the stratosphere are a temporal covarying mode, using singular value decomposition (SVD) analysis. Following them, Perlwitz and Graf (1995), using canonical correlation analysis, and Cheng and Dunkerton (1995), using rotated SVD analysis, discovered that the Pacific–North American mode (PNA), which is another dominant mode in the troposphere, and a wavenumber-1 or -2 mode (hereafter referred to as W1, because wavenumber 1 is more dominant) in the stratosphere vary as a pair, in addition to the pair of NAO– AM. Kitoh et al. (1996) and Kodera et al. (1996) also gave the two pairs, and found that PNA–W1 is strongly affected by El Nin˜o events. Recently, the Arctic Oscillation (AO)1 proposed by Thompson and Wallace (1998) has been receiving much attention. The AO is originally defined as the first empirical orthogonal function (EOF) mode of the sea level pressure north of 208N. The horizontal pattern is a seesaw between the midlatitude and the Arctic region. Regressed patterns by time coefficients of this mode have an equivalent barotropic structure ranging to the stratosphere. From this nature, they propose that the AO is a basic mode common in the troposphere and the stratosphere. Baldwin and Dunkerton (1999) investigate the vertical propagation of this mode, though their definition is different from Thompson and Wallace’s, by applying a low-pass filter to daily data. They showed that the AO propagates downward from the stratosphere to the troposphere with a propagation time of about 20 days. Furthermore, using unfiltered daily data, Baldwin and Dunkerton (2001) present composite results in which large variations of the stratospheric circulation are followed by anomalous tropospheric circulations. During 60 days after the onset of these events, anomalous circulations persist, and average patterns resemble closely the AO pattern. Gillett et al. (2001) reconfirmed the apparent downward propagation of anomalies with statistical significance. However, it has been criticized that the AO is the same phenomenon as the NAO (e.g., Deser 2000). Ambaum et al. (2001) considered an idealized three-component system representing the three centers of action, that is, the Arctic, Atlantic, and Pacific regions, questioning that the NAO and PNA make an apparent AO. Itoh (2002) suspected a physical reality of the AO by a clearer method. The idea is that EOF analysis is made only in the midlatitudes. Then, independent variations 1 The AO is regarded as a surface (or at least lower tropospheric) pattern today. Instead, the Northern Hemisphere annular mode (NAM) is used for expressing the deep coupled mode. However, the AO will be preferentially used even for the deep mode in this study, to avoid confusion with the AM in the stratosphere frequently used in this paper.

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in the Atlantic region and the Pacific region are extracted. Including the Arctic region in the analysis, in-phase and out-of-phase modes between the Atlantic and Pacific regions simultaneously emerge, then the former changes to the AO. This arises because the Arctic region is a common center of action in the two variations. The independent variations in the Atlantic and Pacific regions are the NAO and PNA, respectively. Thus, the AO is almost apparent, which originates in independent variations of the NAO and PNA. Deser (2000) and Ambaum and Hoskins (2002) clearly showed that the regression from the AM in the stratosphere leads not to the AO in the troposphere but to the NAO. Thus, we may have a consensus that the couplings of NAO–AM and PNA–W1 are also pursued, along with investigations of troposphere–stratosphere coupling based on the AO view. In this paper, we carefully reconfirm that these significantly couple with each other at first. The method of determining coupling modes will be described in sections 2 and 4. Data used by all the studies investigating the coupling of NAO–AM and PNA–W1 were only two levels or so. Furthermore, many of them used monthly or seasonalmean data. Hence, it has never been clarified how pattern transitions occur between the troposphere and the stratosphere and what direction and phase speed of the propagation these modes have. The second purpose of this study is to make clear these characteristics. In order to do so, we will analyze data with many levels in both the troposphere and the stratosphere, and daily data together with monthly mean data. We also use 60-day low-pass-filtered data to interpret previous results using monthly mean data. The stratospheric patterns in the coupling modes are the AM and W1. Large-amplitude AM of one phase corresponds to the stratospheric sudden warming. It is known that many warmings arise from the amplification of wavenumber-1 patterns,2 although wavenumber-1 patterns may have different spatial phases from the W1 pattern. Thus, the interaction between the two coupling modes, NAO–AM and PNA–W1, sheds new light on the study of the sudden warming. Since interactions of coupling modes with the opposite phase lead to cooling, it is also interesting to see contrasts with the warming. This is the third purpose of the present paper. 2. Data and the method to determine coupling modes Daily mean and monthly mean geopotential height of the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data are used. The former covers 43 yr from 2 Wavenumber 1 here is usually defined as deviations from the zonal mean, while the W1 pattern is defined as anomalies from the time mean. However, as later shown, the W1 intensifies or weakens wavenumber-1 patterns as deviations from the zonal mean.

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1958 through 2000, while the latter includes 53 yr from 1948 through 2000. They are available on 2.58 latitude 3 2.58 longitude grids at 17 levels from 1000 to 10 hPa. Only winter (November–April) data are employed. The total number of months is 318, while the number of days is 7602 (42 winters), because January–April in 1958, November–December in 2000, and 29 February for leap years are excluded. Monthly anomaly data are made as deviations from the 53-yr mean of each calendar month. Daily anomaly data are constructed as follows. First, climate daily data are made by adopting the 43-yr mean of each calendar day and, then, the running mean of 31 days. Anomalies are calculated as deviations from the climate daily data. After that, the sixth-order Butterworth low-pass filter with a cutoff period of 60 days is applied. These monthly and daily anomaly data as well as daily low-pass filtered data are analyzed in this study. Since these anomalies have long-term trends, detrended anomalies may be more suitable for the present purpose. Then, we checked differences between two anomalies, and found that the two results are essentially the same, therefore we will show results from anomalies with trends only. EOF analyses are carried out over 58 latitude 3 108 longitude grids north of 208N, employing a covariance matrix. In this study, the spatial pattern of the nth mode in EOF analysis is called EOFn, while the time coefficient is named PCn. For a significance test, it is necessary to estimate the effective number of degrees of freedom. Correlation with a lag of 1 month, r1 , of leading modes for the monthly mean data is at most 0.4. Hence, the effective number of degrees of freedom can be estimated as 318(1 2 r1 )/(1 1 r1 ) 5 136. We conservatively set it to 120, for which 95% (99%) significant correlation is 0.179 (0.234). For the daily data, since the lag-1 autocorrelation is large, we use an estimation by Metz (1991). The effective number of degrees of freedom is estimated as 800 conservatively, for which 99% significant correlation is 0.091. It is important how coupling modes are determined. EOF analysis has a serious defect in that if there are two independent modes with spatial correlation, they are necessarily recognized as one mode (Itoh 2002). We must always check whether EOF modes are real or not. Thus, we should avoid the method whose patterns at each level is predetermined by simple EOF analysis only and whose correlations are taken between these amplitudes. Also, for the same reason, EOF analysis using multiple-layer data is not a good tool for this purpose. The same thing may be said for SVD analysis. Then, we adopt the following method. First, ‘‘real modes’’ are extracted at each stratospheric and tropospheric level, say, 30- and 500-hPa levels, where real modes means we carefully check that extracted modes are not artificially produced by EOF analysis. Then, regression method is employed to determine coupling modes at

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other levels with these real modes. When two regressed patterns, one from the tropospheric base and the other from the stratospheric base, are similar, we can judge that these modes are coupled. This method is very simple, but we believe it is most reliable. For daily data, we need to consider lag between tropospheric and stratospheric modes. This will be described in section 4. Two comments should be given for methods to determine coupling modes. First, in our method, base levels must be predetermined. This seems to be very subjective. However, results are not sensitive to this choice, unless base levels are set near the tropopause. Second, rotated SVD would give similar results to ours (see Cheng and Dunkerton 1995). However, we think that differences between two modes, that is, one from the tropospheric base and the other from the stratospheric base, are also important, because the differences tell us that two modes are not coupled one to one. We thus employ this method. If we adopted rotated SVD, resulting patterns would be mediates of two different patterns. 3. Results for monthly mean data Figure 1 shows EOF1 and EOF2 at 30 hPa for the monthly mean data. Percent variances explained by these two modes are 48.2% and 16.5%, respectively. EOF1 may be called the ‘‘Arctic Oscillation’’ pattern or an annular mode, while EOF2 exhibits a wavenumber-1 pattern with maxima over North America and Eurasia. Similar results using the NCEP–NCAR reanalysis have already been shown in previous studies (e.g., Perlwitz and Graf 2001a). Although the North American center is slightly located east of the Aleutian high, this mode basically intensifies or weakens the Aleutian high; the temporal correlation coefficient between PC2 and the amplitude of wavenumber 1 as deviations from the zonal mean, which compares well with the Aleutian high, is 20.596. The EOF1 and EOF2 modes are robust, in a sense that even midlatitude EOFs (excluding the Arctic region) obtained by the same procedure as in Itoh (2002) show similar patterns (not shown). Thus, we can say that these modes are real, and are not artificially produced by EOF analysis (see also Deser 2000). Using PC1 and PC2 at this level, regressed patterns are calculated for other levels. Figure 2 shows regressed patterns at 500 hPa. The NAO (PNA) pattern appears for PC1 (PC2). The NAO pattern in this case has a significant area in Siberia, as was pointed out by Baldwin et al. (1994). Furthermore, the reader may think that this NAO pattern over the polar cap looks more like the AO. However, almost all ‘‘NAO patterns’’ have this nature. See, for example, Wallace (2000) and Deser (2000). The PNA pattern is also shifted somewhat east, compared with that in Wallace and Gutzler (1981). On the other hand, the shift is not so conspicuous as the tropical–Northern Hemisphere pattern shown by Barnston and Livezey (1987). Note again that it is not the

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FIG. 1. Horizontal patterns of (a) EOF1 and (b) EOF2 of the monthly mean 30-hPa geopotential height anomaly north of 208N. Percent variance explained by each mode is shown at upper right. Positive values are shown by solid lines, while negative values by dashed lines. The EOF patterns are normalized such that the squared integral over the whole area is equal to the variance of each mode (i.e., factor loading), which are equivalent to regression patterns. Contour intervals are (a) 40 and (b) 30 m.

AO in the troposphere to couple with EOF1 in the stratosphere, as was already clarified by Deser (2000) and Ambaum and Hoskins (2002). These results coincide with the results before the AO was proposed (Baldwin et al. 1994; Cheng and Dunkerton 1995; Perlwitz and Graf 1995; Kitoh et al. 1996; Kodera et al. 1996).

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FIG. 2. Geopotential height patterns at 500 hPa regressed by (a) PC1 and (b) PC2 at the 30-hPa level. The contour interval is 5 m. Areas with correlations higher than 0.179 (95% significance) are shaded.

We hereafter call the couple of AM–NAO the first mode, and the couple of W1–PNA the second mode. Also, patterns shown in Figs. 1 and 2 are defined as the positive phase of each couple, while reversed patterns are called negative phase. Regressed patterns at levels lower than 500 hPa are similar to the 500-hPa patterns. Figure 3 shows patterns at 1000 hPa. Although overall features are the same as in Fig. 2, they also have different aspects. Since the NAO pattern has a well-known baroclinic structure, the

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FIG. 3. As in Fig. 2 except for 1000 hPa. Contour intervals are (a) 4 and (b) 2.5 m.

FIG. 4. As in Fig. 2 except for 150 hPa. Contour intervals are (a) 10 and (b) 8 m.

center over the Arctic at 1000 hPa is east of that at 500 hPa. Among the three centers in the second mode at 500 hPa, only one center over the Pacific is dominant at 1000 hPa. Also, note that it does not exist over the Aleutian low, but substantially east of it. Transition between these patterns occurs between the troposphere and the stratosphere. A typical level is 150 hPa. Figure 4 illustrates regressed patterns at this level. The first mode shows an almost annular pattern in the midlatitudes, although the center of action in the Arctic is located over Baffin Bay. In the second mode, one

center placed in the Pacific troposphere is considerably shifted to the west at this level, existing in Siberia. On the other hand, a center over North America nearly stands up from the troposphere to the lower stratosphere. The pattern rather changes to a wavenumber-1 pattern. Regression from PCs at one level does not tell us whether a base pattern and a regressed pattern are truly coupled or not. We therefore make regression from a tropospheric base. Hereafter, patterns having the base level in the stratosphere are called S modes, while patterns having the base level in the troposphere are named

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T modes. Also, the first and second S (T) modes are called S1 (T1) and S2 (T2), respectively. The base level is taken at 500 hPa. There is no doubt that the NAO and PNA are real at this level. Then, the problem is how the NAO and PNA are objectively obtained. Among several methods, we adopt rotated EOF. It is calculated by 19 EOFs whose percent variances are larger than 1.0%. The first mode is identified as the PNA, while the second mode is the NAO. Both explain 13.5% of the total variance. The patterns obtained here are similar to those regressed from the 30-hPa PCs, but with somewhat different configurations and phases (not shown). Pattern correlations are 0.84 for the NAO (i.e., between S1 and T1) and 0.80 for the PNA (i.e., between S2 and T2). Based on the PCs of the 500-hPa NAO and PNA, regressions are made for other levels. Results at 30 hPa are shown in Fig. 5. For the NAO, the AM is well reproduced, though the pattern is elongated in Eurasia. For the PNA, the center over Eurasia splits into two, which locate over the western Pacific and Europe. This pattern does not seem to correspond to the W1 based on 30 hPa. However, the center over North America is the same as that for the W1, and the center over the western Pacific disappears at higher levels than 30 hPa, resulting in the one positive center over Eurasia. In short, the pattern transition occurs at upper levels than that in S2. Hence, it can be said that the W1 pattern basically appears for the tropospheric base. Pattern correlations between S1 and T1, and between S2 and T2 are indicators of pattern similarity. Those for the first mode are over 0.8 at all the levels except 10 hPa (not shown; see also temporal correlations in Fig. 6) so that the similarity is clear. Correlations for the second mode are generally worse than those for the first mode. In particular, the correlation at 100 hPa is only 0.64. However, correlations at higher or lower levels become large, for example, 0.87 at 10 hPa and 0.82 at 300 hPa. In other words, the lowest correlation at 100 hPa is a reflection of the difference in the transition level between S2 and T2. Thus, we can safely say that patterns regressing from the stratosphere and from the troposphere are basically the same for both of the first and second modes. Next, time coefficients TC (p, t) (p: pressure, t: time) for regressed patterns R(l, f, p) (l: longitude, f: latitude) at each level are calculated as follows:

TC( p, t) 5

EE

z(l, f, p, t)R(l, f, p) cosf dl df

1EE R(l, f, p)

2

1/2

2

cosf dl df

, (1)

where z(l, f, p, t) represents the monthly mean height anomaly data. The denominator is a normalization factor. This expression is different from that of Baldwin

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FIG. 5. Geopotential height patterns at 30 hPa regressed by the time coefficients of (a) the NAO and (b) PNA at the 500-hPa level. The contour interval is 15 m. Areas with 95% significance are shaded.

and Dunkerton (1999), but is essentially the same. We thus obtain 4 (S1, S2, T1, and T2) 3 17 (levels) time coefficient data. Using these time coefficient data, temporal correlations between a base level and other levels are calculated for both of the first and second modes. The base levels are 30 hPa for the S mode and 500 hPa for the T mode. Also, correlations between S1 and T1 and between S2 and T2 are computed at each level. Figure 6 shows the results.

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troposphere, respectively, and are connected loosely (see also Kodera and Kuroda 2000). Near 150 hPa, correlations from lower levels and from upper levels are equally high. In fact, when correlations are taken at the 150-hPa base level, they exceed 0.6 at all levels for both S1 and T1 (not shown). We consider that the AM and the NAO connect because both have high correlations near the 150-hPa level. The second mode has similar characteristics. One large difference is that temporal correlations between S2 and T2 near 100 hPa are small compared with the first mode. This reflects the fact that both patterns are considerably different near this level, as earlier stated. However, the other levels have large correlations. The second difference is that sudden changes in correlations occur at higher levels (near 100 hPa) than in the first mode. Near this level, both correlations are high, which seems to make the connection of the W1 and PNA. 4. Results for daily data

FIG. 6. (a) Vertical profiles of correlations of regressed time coefficients for S1 (solid) and T1 (dashed) whose base levels are at 30 and 500 hPa (indicated by V), respectively. The dotted line shows correlations between S1 and T1. (b) As in (a) except for the second mode.

Let us see characteristics of the first mode. The first to be noted is that temporal correlations between S1 and T1 are high at all levels, which is consistent with high spatial correlations. The second is that, although high correlations are obtained in the stratosphere (troposphere) for S1 (T1), the ‘‘other sphere’’ also has large correlations to some extent. It is clear that correlations are significant at all levels. However, since they suddenly become small near the tropopause, it should not be regarded that the first mode is a unified mode in the stratosphere and the troposphere. Instead, the AM and NAO are independent modes in the stratosphere and the

In this section, we try to clarify mainly the propagation direction and speed of the first and second modes, using the daily data. The 60-day low-pass-filtered data are also used in addition to the anomaly data. The former roughly corresponds to monthly mean or 30-day running mean data, which have been used for many previous studies. We will use the same base patterns at all the levels as in section 3. This is because time lag due to vertical propagation makes it difficult to extract base patterns by the regression from daily data. Also, this can offer more consistent discussion with the results for the monthly mean data than the employment of different base patterns. The use of the same base patterns will be verified by later results (see Fig. 8). We have confirmed in advance that the same dominant modes for the daily data are obtained as those for the monthly mean data, performing EOF (rotated EOF) analysis at 30 hPa (500 hPa). Time coefficients are calculated for both S and T modes. The method is the same as for the monthly mean data. Results analyzing these data will be shown in the following. Lag correlations of the S and T modes are calculated. The base levels are 30 hPa for the S mode and 500 hPa for the T mode, as before. The result is shown in Fig. 7. Correlations of S1 are similar to those of the monthly mean data, that is, those are large above near the 200hPa level, then decreasing below. Even though, correlations are larger than 0.35 at all the levels in the troposphere. The most conspicuous feature is that maxima appear at nearly lag 0 at all levels. To our knowledge, this feature has not been reported explicitly, although some figures and notes suggest this feature (Baldwin and Dunkerton 2001; Gillett et al. 2001); maximum amplitudes in Fig. 2 in Baldwin and Dunkerton (2001) show almost straight phase in vertical. Ambaum and

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FIG. 7. Vertical profiles of lag correlations of regressed time coefficients for (a) S1 and (b) T1 whose base levels are at 30 and 500 hPa, respectively. (c), (d) The same as in (a), (b), respectively, except for the second mode. Positive values are shown by solid lines, while negative values by thin dashed lines. Thick dashed lines connect maximum correlations.

Hoskins (2002) state that the NAO leads to the AM by 4 days. There is a minor discrepancy between our and their results, but we do not understand the reason of this discrepancy. Concerning T1, correlations are large below 70 hPa. Therefore, both S1 and T1 show large correlations between 200 and 70 hPa. The phase of T1 is similar to that of S1, showing almost a straight vertical line. The most reliable method to determine coupling modes with predetermined modes at one level for daily data is to calculate lag-regression at other levels, and to extract modes with the largest variance. From the lag with the largest variance, the propagation direction and speed are also determined. We carry out this calculation to reconfirm the earlier result. Thick lines in Fig. 8 show normalized variances. The largest variance appears at lag 0 (2 days) at the 500-hPa (30 hPa) level for the 30hPa S1 (500-hPa T1) time coefficient. This result is

consistent with the previous result. A regressed pattern at 500 hPa by the 30-hPa S1 time coefficient clearly shows the NAO pattern (Fig. 9a; cf. Fig. 2a) and vice versa (not shown, but almost the same as Fig. 5a). In contrast, the second mode shows the propagation from the troposphere to the stratosphere. It takes about 1 week from the troposphere to the stratosphere for both of S2 and T2. It is interesting that correlations are comparable to those of the monthly mean data, though the sample size of the daily data is much larger than that of the monthly mean data. Since correlations of this mode are larger than those of the first mode, this mode has stronger coupling than the first mode. Here, S2 has large values even at the lowest level (1000 hPa), while T2 shows high correlations until 50 hPa. Furthermore, S2 shows higher correlations than T2. This implies that, although the PNA excited in the troposphere does not always penetrate to the stratosphere, the W1 in the

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FIG. 8. Normalized variances as a function of lag. The normalization factor is the maximum of each variance. The thick solid (dashed) line represents variances of the 500-hPa (30-hPa) pattern regressed by the 30-hPa S1 (500-hPa T1) time coefficient. Positive lag means that 500-hPa (30-hPa) data lead to the 30-hPa S1 (500hPa T1) time coefficient. The thin solid (dashed) line expresses variances of the 500-hPa (30-hPa) pattern regressed by the 30-hPa S2 (500-hPa T2) time coefficient.

stratosphere is not self-exciting, but basically excited by the tropospheric PNA mode. Thin lines in Fig. 8 show normalized variances for the second mode. The largest variance appears at lag 26 (5) days for the 500-hPa (30 hPa) level to the 30hPa S2 (500-hPa T2) time coefficient. This result is

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again consistent with the earlier result. A regressed pattern at 500 hPa by the 30-hPa S2 time coefficient clearly shows the PNA pattern (Fig. 9b; cf. Fig. 2b) and vice versa (not shown, but almost the same as Fig. 5b). Figure 7 gives us other important information. It is the time scale of each mode. The AM has the longest time scale, while the W1 shows the shortest one. The NAO and PNA have similar, intermediate scales. These can be confirmed by spectral analysis (not shown). We conjecture that it is related to the short time scale of the W1 that the coupling of the second mode in the daily data is comparable to that in the monthly mean data. Since lag correlations are statistical results, the straight phase in vertical seen in the first mode might be an artifact arising from the coexistence of upward and downward propagations. We must then examine individual couplings. For this purpose, time–height sections of the amplitude, TC (p, t), of each mode are constructed for all years. Among these results, six typical winters (1959/60, 1968/69, 1980/81, 1983/84, 1988/ 89, and 1990/91) for S1 and S2 are shown in Fig. 10. Amplitudes are normalized at each level, and only absolute values larger than one standard deviation are plotted. Cases when the first mode with negative phase has large amplitudes almost coincide with stratospheric sudden warmings. There are many cases for both the first and second modes connecting between the troposphere and the stratosphere. Most cases for the first mode exhibit almost straight phase in vertical, although some propagating cases are also seen. The second mode shows clearer coupling than the first mode, generally propagating from the troposphere to the stratosphere. From the earlier results, it can be concluded that the char-

FIG. 9. (a) Regressed pattern at 500 hPa at lag 0 by the S1 time coefficient at 30 hPa. (b) Regressed pattern at 500 hPa at lag 26 days by the S2 time coefficient at 30 hPa. Contour intervals are (a) 6 and (b) 10 m. Shading indicate 99% significant regions.

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FIG. 10. Time–height sections of normalized time coefficients for six winters (1959/60, 1968/69, 1980/81, 1983/84, 1988/89, and 1990/ 91 from left to right) for (a) S1 and (b) S2. Areas where absolute values are less than 1 are not colored. The color bar is shown at the lowerright corner. The abscissa indicates day from 1 Nov for each winter.

acteristics of the coupling seen in Fig. 7 are not artifacts resulting from a statistical process, but reflect individual cases. Next, results from the 60-day low-pass-filtered data will be given. Figure 11 illustrates lag correlations for the four modes, corresponding to Fig. 7. The propagation direction of S1 is downward in both the stratosphere and the troposphere, but the phase slightly leads at the tropospheric side in the transition layer. Here, T1 has similar features to S1 in the stratosphere, while the phase line is almost vertical in the troposphere. Correlations are large below 100 hPa, therefore the 200– 100-hPa layer shows large values equally from the troposphere and from the stratosphere. In order to clarify the reason of the ‘‘contradiction’’ of the almost straight vertical phase in the raw anomaly data and downward phase propagation in the filtered data, time–height sections of normalized amplitudes for S1 are shown in Fig. 12. The same winters as in Fig. 10 are selected. Comparing Figs. 10 and 12, the following relation can be found. Although individual events in Fig. 10 show almost straight vertical phase, maxima of amplitudes move to lower levels in a series of events. This can be seen as phase delay in lower levels in Fig. 12. Thus, the slow downward propagation in Fig. 12 occurs as gatherings of in-phase events seen

in Fig. 10. Zhou et al. (2002) point out that the downward propagation of the zonal flow associated with sudden warmings has a similar feature. The second mode shows the propagation from the troposphere to the stratosphere even in Fig. 11, which is the same as in the raw anomaly data. It has an almost constant phase velocity overall, though a slightly straight phase in vertical showing in the troposphere. It takes about 15 days from the troposphere to the 10-hPa level. This is considerably slow, compared with that of the raw data. The difference may be explained by the same reason as the first mode, that is, the difference between individual events and gatherings. Perlwitz and Graf (2001b) show that the strength of the polar winter vortex strongly affects propagation characteristics of zonal wavenumber 1. Then, it is interesting to see how coupling characteristics are changed by the strength of the polar vortex. We define strong (weak) polar vortex as positive (negative) values of the 60-day low-pass filtered anomaly. Figure 13 shows 500hPa variances regressed by the 30-hPa S1 and S2 time coefficients, as a function of lag. Since amplitudes of S1 are much larger than those of S2, normalized variances for S2 are generally larger those for S1. Of course, we see that coupling is stronger in the stronger vortex case than in the weak one. Maxima appear at lag 26

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FIG. 11. As in Fig. 7 except for the 60-day low-pass-filtered data.

to 25 days for S2 and 21 to 2 days for S1. Patterns at 500 hPa are identified as the PNA and NAO for S2 and S1, respectively. Thus, our results are not sensitive to the strength of the polar vortex. Figure 12 exhibits an interesting feature. Namely, after the second mode propagates from the troposphere to the stratosphere, the first mode with the same sign is formed. Typical examples are seen around days 40–65 in 1980/81 and days 50–80 in 1988/89 for positive phase, and around days 50–80 in 1959/60 and days 20– 50 in 1968/69 for negative phase. In cases of negative phase, this sequence corresponds to the amplification of planetary wave 1 and the stratospheric sudden warming. Figure 12 moreover shows that the same sequence occurs even for positive phase. In order to ascertain these sequences statistically, keyday analysis is performed, based on time coefficients of S2 at 10 hPa. Key days are defined as maxima or minima exceeding one standard deviation of the time coefficients. Numbers of selected key days are 42 for positive phase and 41 for negative phase. Composites of time coefficients are shown in Fig. 14. It is clear that, about 15 days after the second mode propagates from the troposphere, the first mode becomes dominant. The previous feature is not only seen in the 60-day low-pass-filtered data, but also in the daily data (see Fig. 10). Figure 15 represents composites for time co-

efficients. Key days are defined as maxima or minima exceeding 1.5 times the standard deviation. Numbers of key days are 95 for positive phase and 98 for negative phase. Overall features are similar to Fig. 14. The difference is seen in time scales of the propagation and the conversion from the second mode to the first mode. The time scales generally shift to the short side. The propagation time of the second mode is about 1 week, and the conversion time is about 10 days. Figure 15 shows a distinct difference between positive and negative phases, although Fig. 14 also exhibits this difference; in cases of negative phase, before negative events start, the first mode with positive phase is dominant. On the other hand, in positive phase, there is no such indication. The transition from positive to negative phase in the first mode is fast. This may reflect the following sequence: intensification of the polar vortex in the lower stratosphere, that is, formation of socalled ‘‘preconditioned’’ state → amplification of planetary wave 1 → sudden warming (e.g., Yoden et al. 1999). There is another difference between positive and negative phases. In positive phase, the first mode significantly penetrates into the troposphere. On the other hand, in negative phase, the influence stays in the stratosphere for lag 0–15 days. Consequently, in positive phase, the NAO appears after the PNA in the tropo-

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FIG. 12. As in Fig. 10 except for the 60-day low-pass-filtered data.

FIG. 13. As in Fig. 8 except for dividing into the strong and weak jet cases. The thick solid (dashed) line represents variances of the 500-hPa pattern regressed by the 30-hPa S1 (S2) time coefficient for the strong jet case. Thin lines expresses variances for the weak jet case.

sphere, while there is no such relation in negative phase. This characteristic does not seem consistent with previous studies, where negative phase, that is, warmings can penetrate more into the troposphere. This contradiction may be understood from the fact that warmings following the wave-2 amplification are not treated in this study. It has been reported that this type of warming can penetrate more into the troposphere (e.g., Yoden et al. 1999). After lag 20 days, the NAO pattern is established even in the lower troposphere for both positive and negative phases. Thus, the NAO pattern emerges after the PNA pattern in the troposphere. Figure 15 was composited, based on the 10-hPa S2 time coefficient. It is then interesting to examine similar composites by a tropospheric criterion. If the PNA with amplitudes over this criterion is followed by the amplification of the AM, we can use it as a predictor of the weakening or strengthening of the stratospheric vortex, that is, stratospheric warmings or coolings. We define the criterion as the 500-hPa S2 time coefficient exceeding 1.8 times the standard deviation. Factor 1.8 is chosen because selected key days are almost the same as Fig. 15. Figure 16 shows the result. Although amplification is marked at the 500-hPa level, amplitudes in the stratosphere are not so conspicuous. As a result, subsequent

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FIG. 14. Composited time coefficients for (a) positive and (b) negative phases for the 60-day low-pass-filtered data. Values are normalized at each level. Key days are defined as (a) maxima and (b) minima of 10-hPa S2 exceeding one std dev. Selected key days for (a) and (b) are 42 and 41, respectively. The contour interval is 0.2, with shading indicating 99% significant regions.

amplification of the first mode is weak, especially for the negative phase, though it is significant. This result is natural, because variations in the troposphere do not necessarily reflect those in the stratosphere, as earlier stated. We can guess that the W1 with the opposite phase to the PNA prevents the second mode from propagating. Then, one condition is added for the selection of key days; that is, the 10-hPa S2 time coefficient is larger than minus one standard deviation for positive phase and smaller than one standard deviation for negative phase. Since this is a weak condition, excluded key days are only 12 for positive phase and 11 for negative phase. Though only about 10 cases are excluded, the result is greatly altered (Fig. 17). Both positive and negative phases present marked amplification of the first mode. Thus, we can say that when the PNA pattern is strengthened in the troposphere on the condition that the W1 pattern is not in opposite phase with large amplitudes in the stratosphere, warmings or coolings occur subsequently in the stratosphere, though in a statistical sense. 5. Discussion The first discussion is devoted to differences in the wavenumber between the troposphere and the stratosphere in coupling modes. The NAO is characterized

with wavenumber 1 in the troposphere, which couples with the AM of wavenumber 0 in the stratosphere. The PNA cannot be said to be a wavenumber-1 pattern, but it couples with the wavenumber-1 pattern in the stratosphere. How can such wavenumber changes be understood? Different discussions seem to be needed between NAO–AM and PNA–W1. Since both the NAO and AM have straight phase in vertical in the time domain, they are not propagating modes excited in the troposphere. One candidate is a tropospheric reflection of stratospheric vortex changes, that is, geostrophic and hydrostatic adjustment to potential vorticity changes in the stratosphere (Black 2002; Ambaum and Hoskins 2002). Also, they may be grasped as resonant modes, since they are dominant modes without phase delay in vertical. Whether the AM is a resonant mode in the stratosphere can be relatively easily checked; setting observed time-mean fields in a global numerical model, linear resonant modes can be obtained (e.g., Itoh and Kimoto 1999). In this calculation, it is important that the AM is a global mode. The NAO, however, does not have global extent. For this case, ‘‘local resonance’’ must be calculated. In addition to the validity of the notion, local resonance, results may strongly depend on the lateral boundary, which is a rather arbitrary condition. There are several problems to overcome these difficulties.

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FIG. 15. As in Fig. 14 except for the daily anomaly data. Selected key days are (a) 95 and (b) 98, where peaks are extracted over 1.5 3 the std dev.

The PNA may also be a resonant mode, since this mode alone shows straight vertical phase. When the PNA couples with the W1, this mode clearly reveals a propagating nature. In this case, a question is why wavenumbers are changed between the troposphere and the stratosphere. Although there are several possibilities, the most promising mechanism is that wavenumbers are changed interacting nonzonal basic fields. It is interesting to see whether the W1 dominates in the stratosphere, setting the PNA in the troposphere under observed zonally varying fields. Furthermore, there are nonpropagating cases as well as propagating ones so that what brings the difference must also be investigated. It is believed that the stratospheric sudden warming is caused by the amplification of planetary waves in the troposphere (Matsuno 1971). In particular, the relation to blocking has been pointed out. However, its evidence is not clear (e.g., Quiroz 1986). This may be involved in the earlier-stated situation; wavenumbers dominating in the troposphere do not necessarily reflect those dominating in the stratosphere. Indeed, we have shown here that the PNA pattern with negative phase causes the sudden warming mediating the wavenumber-1 pattern in the stratosphere. It is noteworthy discussing the cooling corresponding to positive phase. The warming is brought about by the deposition of the easterly momentum associated with planetary wave breaking in the stratosphere and result-

ing downward motion near the polar region. The reverse of breaking is impossible. Then, how can the cooling occur? One possibility is the relaxation toward the radiative equilibrium, that is, the so-called radiative limit (Gillett et al. 2001). This may be possible if the time scale of phenomena in question is long enough, but it is hard to apply this possibility to phenomena with short time scales like this. In cases of short time scales, we conjecture that stationary waves mediate between the PNA with positive phase and cooling. As stated earlier, the W1 with positive phase weaken the Aleutian high. When positive W1 intensifies, waves (stationary waves 1 transient waves) weaken below some level, while waves above that level keep their amplitudes. This situation is the opposite of breaking, thus causing the cooling via the Eliassen–Palm flux divergence and the upward motion near the polar region. In this case, the cooling must have an upper limit; even if the amplitude of the W1 exceeds that of stationary waves, no more cooling can be produced. When composites of the height and the temperature are made, based on the amplitude of the W1 at 10 hPa, the height shows almost the same amplitude for positive and negative phases, while the temperature indicates that negative phase has larger amplitudes (not shown). We claimed that the mode change from the PNA to the NAO in the troposphere occurs. The relation between this mechanism and the Aleutian–Iceland (AL–

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FIG. 16. As in Fig. 15 except for selected key days, which are defined as (a) maxima and (b) minima of 500-hPa S2 exceeding 1.8 3 std dev. Selected key days are (a) 98 and (b) 88.

IL) seesaw is notable. Honda et al. (2001) presented that, in the AL–IL seesaw, the AL amplifies first, then wave trains propagate downstream, and the IL grows. This is a similar result to the mode change of the PNA to the NAO. Also, Honda and Nakamura (2001) and Nakamura and Honda (2002) showed that the AL–IL seesaw gives influences on the stratospheric circulation. This also coincides with the vertical propagation of the PNA. In this frame, an issue is whether the mode change of the PNA to the NAO is a phenomenon confined in the troposphere or under the participation of the stratosphere. This study may imply the latter because the NAO pattern seems to emerge as the downward propagation of the first mode. However, since details of three-dimensional variations are not analyzed, this also remains as a future problem. 6. Conclusions Coupling between tropospheric and stratospheric leading modes in anomaly fields is investigated. Daily mean and monthly mean geopotential height of the NCEP–NCAR reanalysis are used. The monthly mean (daily) data cover from 1948 (1958) through 2000. By using data at 17 levels, the transition of spatial patterns and the direction and speed of the vertical propagation are examined in detail. The result shows that the North Atlantic Oscillation

mode (NAO) and the Pacific–North American mode (PNA) dominating in the troposphere couple with the annular mode (AM) and a wavenumber-1 mode (W1) dominating in the stratosphere, respectively, with significant temporal correlations. The two modes in the stratosphere are the first and second EOF modes. Hereafter, couples of NAO–AM and PNA–W1 are called the first and second modes, respectively. The transition of the patterns occur at 200–100 hPa for the first mode and 150–70 hPa for the second mode, and temporal correlations have some gaps there. This implies that these dominant modes exist separately in the troposphere or in the stratosphere, and have a loose connection. Correlations from the troposphere and from the stratosphere are both high in the transition layers, through which tropospheric and stratospheric modes couple. The first mode amplifies almost simultaneously from the surface to the 10-hPa level. Sometimes amplifications are repeated a few times, in which maxima of the amplification move to the lower atmosphere. Viewing these sequences from a long time scale, the first mode slowly propagates to the lower atmosphere. The second mode propagates from the troposphere into the stratosphere in about 1 week. There is some relationship between the first and second modes. After the second mode propagates from the troposphere into the stratosphere, the first mode with

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FIG. 17. As in Fig. 16 except that one condition is added for the selection of key days. That is, the 10-hPa S2 time coefficient is (a) larger than minus one std dev and (b) smaller than one std dev. Selected key days are (a) 86 and (b) 77.

the same phase amplifies with a lag of 10–15 days. However, this relationship has different characteristics between positive and negative phases. Here, positive phase means that the first mode is negative in the polar region, and the second mode is positive (negative) in the Aleutian area (North America) in the troposphere and in Eurasia (North America) in the stratosphere. In positive phase, the first mode exerts an influence on the troposphere, while the influence is confined in the stratosphere in negative phase. Hence, the transition from the PNA to the NAO can be seen in positive phase, while there is no such indication in negative phase. Negative AM with large amplitudes coincides with the stratospheric sudden warming. Hence, rewording the previous statement, the PNA with a negative anomaly over the Aleutian area amplifies in the troposphere, exciting the W1 with a positive anomaly over North America in the stratosphere, which in turn causes the sudden warming. Thus, amplification of the PNA leads to the sudden warming. Conversely, when the PNA with positive phase is excited, the stratospheric cooling is produced. In a subsequent paper, dynamical analysis using wave activity flux diagnoses and so on will be performed to clarify the propagation characteristics from a dynamical point of view. Also, some problems raised in the discussion section will be pursued.

Acknowledgments. The authors would like to express their hearty appreciation to two anonymous reviewers for careful reading of and many appropriate comments on the original manuscript. This research is supported by the Grant-in-Aid for Scientific Research of the Japanese Ministry of Education, Science, Sports and Culture, and by the cooperative research project of Center for Climate System Research, University of Tokyo. The GFD-DENNOU Library of the Japanese meteorological community was used to draft the figures. REFERENCES Ambaum, M. H. P., and B. J. Hoskins, 2002: The NAO troposphere– stratosphere connection. J. Climate, 15, 1969–1978. ——, ——, and D. B. Stephenson, 2001: Arctic Oscillation or North Atlantic Oscillation? J. Climate, 14, 3495–3507. Baldwin, M. P., and T. J. Dunkerton, 1999: Propagation of the Arctic Oscillation from the stratosphere to the troposphere. J. Geophys. Res., 104, 30 937–30 946. ——, and ——, 2001: Stratospheric harbingers of anomalous weather regimes. Science, 294, 581–584. ——, X. Cheng, and T. J. Dunkerton, 1994: Observed correlations between winter-mean tropospheric and stratospheric circulation anomalies. Geophys. Res. Lett., 21, 1141–1144. Barnston, A. G., and R. E. Livezey, 1987: Classification, seasonality and persistence of low-frequency atmospheric circulation patterns. Mon. Wea. Rev., 115, 1083–1126.

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Black, R. X., 2002: Stratospheric forcing of surface climate in the Arctic Oscillation. J. Climate, 15, 268–277. Boville, B. A., 1984: The influence of the polar night jet on the tropospheric circulation in a GCM. J. Atmos. Sci., 41, 1132– 1142. Charney, J. G., and P. G. Drazin, 1961: Propagation of planetaryscale disturbances from the lower into the upper atmosphere. J. Geophys. Res., 66, 83–109. Cheng, X., and T. J. Dunkerton, 1995: Orthogonal rotation of spatial patterns derived from singular value decomposition analysis. J. Climate, 8, 2631–2643. Christiansen, B., 2001: Downward propagation of zonal mean zonal wind anomalies from the stratosphere to the troposphere. J. Geophys. Res., 106, 27 307–27 322. Deser, C., 2000: On the teleconnectivity of the ‘‘Arctic Oscillation.’’ Geophys. Res. Lett., 27, 779–782. Gillett, N. P., M. P. Baldwin, and M. R. Allen, 2001: Evidence for nonlinearity in observed stratospheric circulation changes. J. Geophys. Res., 106, 7891–7901. Hartley D. E., J. Villarin, R. X. Black, and C. A. Davis, 1998: A new perspective on the dynamical link between the stratosphere and troposphere. Nature, 391, 471–474. Honda, M., and H. Nakamura, 2001: Interannual seesaw between the Aleutian and Icelandic lows. Part II: Its significance in the interannual variability over the wintertime Northern Hemisphere. J. Climate, 14, 4512–4529. ——, ——, J. Ukita, I. Kousaka, and K. Takeuchi, 2001: Interannual seesaw between the Aleutian and Icelandic lows. Part I: Seasonal dependence and life cycle. J. Climate, 14, 1029–1042. Itoh, H., 2002: True versus apparent Arctic Oscillation. Geophys. Res. Lett., 29, 1268, doi:10.1029/2001GL013978. ——, and M. Kimoto, 1999: Weather regimes, low-frequency oscillations, and principal patterns of variability: A perspective of extratropical low-frequency variability. J. Atmos. Sci., 56, 2684– 2705. Kitoh, A., H. Koide, K. Kodera, S. Yukimoto, and A. Noda, 1996: Interannual variability in the stratospheric–tropospheric circulation in a coupled ocean–atmosphere GCM. Geophys. Res. Lett., 23, 543–546. Kodera, K., and Y. Kuroda, 2000: Tropospheric and stratospheric aspects of the Arctic Oscillation. Geophys. Res. Lett., 27, 3349– 3352. ——, K. Yamazaki, M. Chiba, and K. Shibata, 1990: Downward propagation of upper stratospheric mean zonal wind perturbation to the troposphere. Geophys. Res. Lett., 17, 1263–1266. ——, M. Chiba, H. Koide, A. Kitoh, and Y. Nikaido, 1996: Inter-

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