The copyright line for this article was changed on 23 MAR 2015 after original online publication.
 The driving mechanism for the wintertime (December–March) Aleutian Low–Icelandic Low (AL-IL) seesaw is investigated with National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis data for 1948–2009. It is shown that the AL and the IL are dynamically linked through the eastern Pacific wave train (EPW) and that both the EPWs and the stratospheric polar vortex are found to work cooperatively to produce a significant AL-IL seesaw. In general, it is found that wave reflection by the polar vortex is crucial for the formation of the AL-IL seesaw. However, when the EPWs are extremely strong, the AL-IL seesaw appears to be caused primarily by horizontal wave propagation. It is further shown that the Pacific center of the traditional Arctic Oscillation pattern is present when the AL-IL seesaw is active, but it disappears when the AL-IL seesaw is absent.
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 It is now widely accepted that the so-called Arctic Oscillation (AO), or the Northern Annular Mode, is the dominant mode of climate variability during the Northern Hemisphere winter [Thompson and Wallace, 1998, 2000; Thompson et al., 2000]. Since Thompson and Wallace , however, there has been an ongoing debate over the question of whether the AO pattern is a real physical mode or if it is just a consequence of the empirical orthogonal function (EOF) methodology used in its definition [Deser, 2000; Ambaum et al., 2001; Wallace and Thompson, 2002]. Thompson and Wallace [1998, 2000] and Thompson et al.  proposed that the AO is a fundamental mode of climate variability which describes the seesaw of mass between the Arctic and midlatitudes. If this was the case, the three centers of action of the AO, namely, the Arctic center, the Atlantic center, and the Pacific center, should be closely correlated. Deser , however, found that among the three centers, only the Arctic and Atlantic centers are strongly correlated, exhibiting a negative value, which is indicative of the well-known North Atlantic Oscillation, while the Pacific center is only weakly correlated with the other two centers. In a later study, Wallace and Thompson  found that the Pacific and Atlantic centers are more strongly correlated when the Pacific/North American (PNA) pattern is inactive. In other words, the PNA pattern may have suppressed the Pacific-Atlantic linkage.
 The Arctic-Pacific linkage is generally weak, though some studies have shown that the Aleutian Low (AL) and the Icelandic Low (IL) do not fluctuate independently; rather, the two lows exhibit seesaw-like behavior from one winter to the next [Kutzbach, 1970; van Loon and Rogers, 1978; Wallace and Gutzler, 1981; van Loon and Madden, 1983]. Recently, Honda et al.  found that the AL-IL seesaw shows seasonal dependence, with the most significant seesaw being observed in late winter (February to mid-March) during the years 1973–1994. They further demonstrated that the AL-IL seesaw may be excited by a PNA-like wave train propagating across the North Pacific and North America then to the North Atlantic. Castanheira and Graf  presented another interesting finding that the AL-IL seesaw may be impacted by the stratospheric polar vortex. For a strong (weak) polar vortex, the seesaw is remarkably strong (weak). Castanheira and Graf  attributed the AL-IL seesaw formation to the upward propagation of stationary waves from troposphere and their subsequent reflection by the polar vortex.
 The above discussion shows that although much progress in the study of the AL-IL seesaw has been achieved, our knowledge of the AL-IL seesaw and its causes is still incomplete. Some questions remain unresolved. For example, is the AL-IL seesaw still statistically significant in late winter for other time periods different from that considered by Honda et al. ? More importantly, what physical process is responsible for the seesaw formation? Is it a consequence of the horizontal propagation of PNA-like stationary wave trains, as proposed by Honda et al. ? Or, is it caused by the reflection of upward propagating stationary wave trains by the polar vortex, as proposed by Castanheira and Graf ? If it is the latter, then an important question is, where is the wave source? The present paper attempts to address these fundamental questions by examining the wintertime AL-IL relation and diagnosing the three-dimensional propagation of stationary waves in the observations.
2 Data and Methodology
 For this study, we use National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis data for the 1948–2009 winter seasons (December–March) [Kalnay et al., 1996]. Daily sea level pressure (SLP) is used to calculate the intensity of the Aleutian Low and the Icelandic Low. The seasonal cycle is removed from the daily SLP data by subtracting the long-term mean of each day. In order to reduce the influence of possible data inhomogeneities on time series analysis and exclude decadal variability that may be due to external forcing, we also detrend the SLP data by subtraction of the 5 year running mean, as in Castanheira and Graf , and the main results are not sensitive to different detrending methods. The results reported here are obtained with the linearly detrended SLP data. The intensities of the Aleutian Low and the Icelandic Low are represented by Aleutian and Icelandic Low indices, which are defined in a manner similar to that used by Castanheira and Graf : The Aleutian Low index is defined as the area average of the daily SLP over the North Pacific inside the 0.75 hPa per standard deviation contour of the AO pattern (the first EOF of SLP north of 20°N), and a 31-day running mean has been applied to the time series of the AL index. Similarly, the Icelandic Low index corresponds to the area average of the daily North Atlantic SLP within the −2.5 hPa per standard deviation contour of the AO pattern. The AL-IL correlation was calculated with both daily and monthly mean AL and IL indices. Since small differences are found, hereafter, we present only the results based on the monthly mean AL and IL indices.
 Monthly mean geopotential height fields and Plumb [1985, equation (5)] are used to calculate the three-dimensional stationary wave activity fluxes from sea level to the stratosphere. Figure 1 shows the climatology of the Northern Hemisphere wintertime stationary wave activity fluxes at 500 and 250 hPa for the 1949–2008 winter seasons. The arrows in Figure 1 indicate the horizontal component of the wave activity fluxes, and the contours illustrate the vertical component. The main feature revealed in Figure 1a is that there exist three distinct centers of wave activity over the eastern Asia–western Pacific, eastern Pacific–North America, and North Atlantic regions. (The vertical wave activity flux center over the eastern Pacific is much weaker compared with the other two centers, although its variance is actually as large as that for the other two.) The 250 hPa wave activity flux (Figure 1b) shows similar features, except that the downward vertical flux over the northern North America is stronger than at 500 hPa, which is thought to be a sign of wave reflection of the upward propagating waves from the East Asia–West Pacific by the polar vortex. We define the wave activity flux center over the eastern Pacific and North America as the eastern Pacific wave train (EPW), which originates over the central North Pacific and propagates horizontally over the eastern Pacific, through North America, and into the North Atlantic, as well as vertically from the troposphere well into the stratosphere [Zhou et al., 2012]. The relationship between the AL-IL seesaw and both the horizontal and vertical components of the wave activity propagation, including reflection by the stratospheric polar vortex, will be examined.
 To describe the intensity of the EPW, an EPW index (EPWI) is defined as the volume average of the monthly vertical wave activity flux in the domain (30°N–60°N; 170°W–120°W; 925–500 hPa). It turns out that the EPWI defined in this manner can describe not only the strength of the vertical wave activity fluxes of the EPW but also the strength of its horizontal fluxes. This is due to the fact that the strengths of the two components of the wave activity flux are usually highly correlated [Zhou et al., 2012].
 The propagation property of the stationary waves entering the stratosphere depends on the state of the polar vortex. When the zonal winds associated with the polar vortex are weak, the waves can propagate higher into the stratosphere. Waves will be refracted equatorward or even reflected downward back into the troposphere if the zonal winds associated with the polar vortex are sufficiently strong. As in Castanheira and Graf , the monthly and zonal mean zonal winds along 65°N at 50 hPa, i.e., U50, are chosen to represent the strength of the polar vortex. The polar vortex is labeled as strong when U50 > 18 m/s (122 months); otherwise, it is labeled as weak (126 months). Here a smaller value of 18 m/s, rather than 20 m/s as in Castanheira and Graf , is chosen to increase the sample size. The results to be presented are not very sensitive to this standard.
 Table 1 shows the AL-IL correlation for each winter month along with that for the entire winter for 1948–2009. It is seen that the AL-IL correlation shows seasonal dependence. The correlation coefficient (r) is −0.33 and −0.35 in December and January, respectively. It is slightly smaller in February (r = −0.26), while in March, the two lows show no statistically significant correlation. The correlation coefficient for the entire winter is −0.26, which is as large as that in February.
Table 1. Correlation Between the Aleutian Low and the Icelandic Low for Cold Season (December–March)a
aValues with one or two asterisks are significantly exceeding the 95% or 99% confidence level, respectively.
 Interdecadal variability in the AL-IL correlation is also apparent. In December, the two lows are significantly negatively correlated only for 1995–2009 (r = −0.55). In January, the AL and the IL are significantly correlated only for 1948–1972 (r = −0.41), while in February, the AL-IL correlation reaches its highest value of −0.73 for 1973–1994. For March, it still shows no statistically significant correlation for all the three subperiods. For the entire winter, the correlation is −0.29 for 1948–1972, it rises to −0.40 for 1973–1994, while no statistically significant correlation is found for 1995–2009.
 In conclusion, substantial seasonal and decadal variability in the AL-IL relation is detected. Furthermore, the conclusion of Honda et al.  that the AL-IL seesaw is most significant in later winter is only apparent for the 1973–1994 subperiod, not for the entire 1948–2009 period.
 Next, we explore the relationship between the AL-IL seesaw, the EPWs, and the polar vortex. Zhou et al.  found that the AL and the EPWs are closely related. For a weak (strong) AL, the vertical component of the stationary wave activity flux over the eastern Pacific is weak (strong), and the associated EPW is also weak (strong). Thus, it is to be expected that for weak (strong) EPWs, the AL-IL linkage may also be weak (strong), as a lesser (greater) amount of wave activity may propagate from the eastern Pacific to the North Atlantic. There are two possible routes through which the EPWs transfer their energy from the North Pacific to the North Atlantic. One is through horizontal propagation, as Honda et al.  suggested, and the other is through vertical propagation and wave reflection by the polar vortex, as Castanheira and Graf  proposed. Obviously, the second route is indirect—it works only when the polar vortex is strong: The EPW first propagates vertically into the stratosphere, and it is then reflected downward by the strong polar vortex into the troposphere over the North Atlantic.
 Before we examine how the polar vortex and the EPWs work cooperatively to produce a significant AL-IL seesaw, we first examine the polar vortex/EPW relation for 1948–2009. Calculation shows that the correlation coefficient is 0.014 and 0.116 for the winter mean and monthly mean indices, respectively, which indicates that the EPWs and the polar vortex behave independently. Then, we separately examine the AL-IL relation under different polar vortex and EPW states. Table 2 shows the AL-IL correlation for different polar vortex conditions (the first column in Table 2). As can be seen, the AL and the IL are significantly anticorrelated for strong polar vortices (r = −0.36), while for weak polar vortices, the two lows are not significantly correlated. Figure 2 shows the wave activity fluxes for strong polar vortices. As can be seen, in the upper troposphere (Figure 2a), there are strong downward wave activity flux anomalies over northeastern North America and Greenland, along with eastward and southeastward wave activity flux anomalies over much of North America and the North Atlantic, respectively. The wave activity flux anomalies are spread over a much wider region in the stratosphere than in the upper troposphere (Figures 2b and 2c). For weak polar vortices, the opposite is found (not shown). This result, combined with the absence of statistically significant wave activity flux anomalies over the eastern Pacific and western North America, supports the view that wave reflection by the polar vortex plays an important role for AL-IL seesaw formation.
Table 2. The AL and IL Correlation Under Different Strengths of the EPWs and Polar Vorticesa
EPWI > 1.0
EPWI > 0.5
EPWI > 0
EPWI < 0
EPWI < −0.5
EPWI < −1
aValues with one or two asterisks are significantly exceeding the 95% or 99% confidence level, respectively. Numbers in parentheses are the corresponding numbers of the months. SPV stands for the strong polar vortex, and WPV stands for the weak polar vortex. Mixed stands for no distinction of the polar vortex and/or EPW conditions.
 Table 2 also shows the AL-IL correlations for different EPW strengths (the first row in Table 2) without considering the strength of the polar vortex. As can be seen, the AL and the IL do not have a statistically significant correlation for weak EPWs (EPWIs < 0), while the AL-IL correlation reaches −0.42 for strong EPWs (EPWIs > 0). The correlation increases for larger EPWIs, and it even reaches a value as high as −0.65 for extremely strong EPWs (EPWIs > 1.0). This indicates that the AL-IL relation is influenced by EPWs, with the presence of strong EPWs being favorable for AL-IL seesaw formation. Figures 2e–2f show the wave activity fluxes for EPWIs > 0 at 250 hPa (Figure 2d), 100 hPa (Figure 2e), and along 65°N (Figure 2f), respectively. We see strong upward wave activity fluxes over the eastern Pacific and zonal wave activity fluxes across the eastern Pacific, North America, and the North Atlantic (much stronger than the climatology), with the strongest anomalies occurring in the upper troposphere. We also see significant downward wave activity flux anomalies in the upper troposphere over northeastern North America and Greenland and in the lower stratosphere over Greenland and the North Atlantic. So this means that both the horizontal propagation and the vertical reflection of the EPWs by the polar vortex may contribute to the AL-IL seesaw formation, although we are still unable to distinguish their relative contribution.
 In order to investigate how the polar vortex and the EPWs work cooperatively to produce a significant AL-IL seesaw, we next examine the AL-IL relation under different polar vortex and EPW conditions. As can be seen from Table 2 (the second and third rows), the AL-IL relation undergoes large changes when the polar vortex regimes are taken into consideration. For weak EPWs, the AL and the IL fluctuate independently for weak polar vortices, while the two lows are significantly anticorrelated (r = −0.34) when the polar vortex is strong, which indicates that wave reflection by the polar vortex plays a key role to the AL-IL seesaw formation. Even for strong EPWs (EPWI > 0), as a whole, the role of the wave reflection still appears to be crucial to the AL-IL seesaw formation. When the polar vortex is weak, the AL-IL seesaw is also weak (r = −0.21, not passing the statistical significance test), while when the polar vortex is strong, the AL and the IL are highly anticorrelated (r = −0.50). However, when the EPWs are extremely strong (EPWI > 0.5 or above), the relationships change. For this case, the AL and the IL become highly anticorrelated even for a weak polar vortex, and the AL-IL correlation remains unchanged for EPWI > 0.5 or only slightly increases for EPWI > 1.0. This implies that for extremely strong EPWs, the AL-IL seesaw is most likely caused by the horizontal propagation of the EPWs, and the influence of wave reflection by the polar vortex is very weak. An examination of the upper tropospheric wave activity flux for EPWI > 0.5 with a weak polar vortex shows that there exist strong upward wave activity flux anomalies over the eastern Pacific and strong horizontal wave activity flux anomalies over the eastern Pacific and North America, which provides evidence of strong EPWs, without significant wave reflection over northeast North America and the North Atlantic (Figure 2g).
 After suggesting mechanisms for the formation of the AL-IL seesaw, we next investigate whether the Pacific center of the traditional AO pattern may hint at the presence of the AL-IL seesaw [e.g., see Honda et al., 2001]. Table 2 shows that the AL-IL seesaw is strong for EPWI > 0.5, but it becomes very weak for EPWI < 0.5. If the above argument is correct, it would be expected that the first SLP EOF for EPWI > 0.5 (EPWI < 0.5) would show a stronger (weaker) Pacific center. Figures 3a and 3b show that this is indeed the case. As expected, the first EOF shows a stronger Pacific center for EPWI > 0.5 than the traditional AO pattern (Figure 3a), while the Pacific center almost disappears from the EOF pattern when EPWI < 0.5 (Figure 3b).
4 Concluding Remarks
 This study shows with NCEP/NCAR reanalysis data for 1948–2009 that the wintertime AL-IL seesaw exhibits seasonal variability. December and January show a higher negative AL-IL correlation (r = −0.33) than February (r = −0.26), and there is no statistically significant correlation detected in March. The AL-IL seesaw also assumes apparent interdecadal variability, being most significant in February 1973–1994 (r = −0.73).
 It is found that the AL and the IL are dynamically linked through EPWs. The results suggest that both the EPWs and the polar vortex work cooperatively to produce a significant AL-IL seesaw. Generally, wave reflection by the polar vortex appears to be crucial for the formation of the AL-IL seesaw. However, for extremely strong EPWs, the AL-IL seesaw is most likely caused by the horizontal propagation of the EPWs, with the contribution by wave reflection being weak.
 It is further shown that the Pacific center of the traditional AO pattern has an imprint left by the AL-IL seesaw, as it appears that this center depends upon the presence of an active AL-IL seesaw.
 Our work extends the work of Castanheira and Graf . First, we found that the tropospheric source of the reflected waves is from the eastern Pacific. Second, we show that in addition to wave reflection by the polar vortex, horizontal propagation associated with the EPWs also contributes to the AL-IL seesaw formation.
 It is also interesting to examine the relation between the EPWs and the PNA pattern. Zhou et al.  suggested that the EPWs and the PNA are the same phenomenon as revealed in different variables. The EPWs correspond to wave activity fluxes, while the PNA is in the form of a wave train of geopotential height anomalies. There exists a strong linkage between the EPWs and the PNA. Strong (weak) EPWs correspond to the positive (negative) PNA phase. Keeping this in mind, it is now clear why Honda et al.  could come to their conclusion by considering only the horizontal propagation of a PNA-like wave train. It turns out that for the month of February, for the 1973–1994 period considered by Honda et al. , the PNA is dominated by its positive phase (strong EPW events, not shown), which leads to a highly significant AL-IL seesaw (r = −0.73).
 We are very grateful to Steven B. Feldstein and Sukyoung Lee for their scientific comments and language polish which improved the manuscript. We also thank H.-F. Graf and an anonymous reviewer for their helpful comments. This research was supported by the Chinese NSF Key Project under grant 41130962 and by the National Basic Research Program of China under grant 2010CB428606.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.