Variability in the monthly mean flow and storm track in the North Atlantic basin is examined with a focus on the near-surface baroclinicity, B = Bxi + Byj. Dominant patterns of anomalous B found from empirical orthogonal function (EOF) analyses generally show patterns of shift and changes in the strength of B. Composited anomalies in the monthly mean wind at various pressure levels based on the signals in the EOFs display robust accompanying anomalies in the mean flow up to 50 hPa in the winter and up to 100 hPa in other seasons. Anomalous eddy fields accompanying the anomalous Bx patterns exhibit, broadly speaking, structures anticipated from linear theories of baroclinic instabilities and suggest a tendency for anomalous wave fluxes to accelerate/decelerate the surface westerly accordingly. Atmospheric anomalies accompanying By anomalies have patterns different from those that accompany Bx anomalies but are as large as those found for Bx. Anomalies in the sea surface temperature (SST) found for the anomalous patterns of Bx often show large values of small spatial scales along the Gulf Stream (GS), indicating that a meridional shift in the position of the GS and/or changes in the heat transport by the GS may be responsible for the anomalous Bx and concomitant tropospheric and lower-stratospheric anomalies. Anomalies in the net surface heat flux, SST in preceding months, and meridional eddy heat flux in the lower troposphere support this interpretation.
Baroclinicity in the lower atmosphere in classic theories of atmospheric stability is defined by the effect of the horizontal temperature gradient, in combination with the Coriolis force, on the vertical shear of the horizontal velocity and the vertical stability of the atmosphere (Charney 1947; Eady 1949). In its original form, the Eady maximum growth rate for baroclinic instability BGRMax is defined by
in a zonally homogeneous steady mean state, where U is the mean zonal flow, f is the Coriolis parameter, and N is the Brunt–Väisälä frequency. Charney’s formula is slightly different from the Eady’s but still incorporates the same effects. Lindzen and Farrell (1980) first applied the Eady parameter to atmospheric data to successfully estimate the maximum growth rate of baroclinic instability in the troposphere. Hoskins and Valdes (1990) used its localized version (i.e., U, N, and f are all local Eulerian mean values) as the central parameter in their study of the Northern Hemispheric storm tracks. This local version, or its simplified version, has been used successfully as an indicator of baroclinic wave generation in diagnostic studies of storm tracks in recent years as well (Nakamura and Sampe 2002, 2004; Nakamura et al. 2004). In our study, we define the baroclinic vector, B = Bxi + Byj, where
in which θ is the monthly mean potential temperature, and use it as the central quantity of the diagnoses. Unless stated otherwise, “anomalies” refer to deviations from the climatology hereafter. Though its meridional component does not appear in any classic theory of baroclinic instability, a theory that does incorporate the effect of By shows its important role in enhancing baroclinic wave generation locally to the east of the mean trough (Niehaus 1980). In the North Atlantic storm track region, where the surface temperature gradient has a substantial zonal component due to the northward-flowing downstream branch of the Gulf Stream (GS), By may play a significant role in the atmospheric variability.
Although B is an indicator of baroclinic wave generation, it is also a parameter of upper-level flow steering induced by the horizontal temperature structure in the underlying layers. In simple theories of general circulation with a zonally homogeneous basic state, the available potential energy generated by Bx is essentially the driving force of the middle latitude mean flow and synoptic-scale waves (e.g., Lorenz 1955). Anomalous B and ∇θ are anticipated to accompany anomalous V through the thermal wind balance. If there is a 1000-m-thick layer in which anomalous ∂U / ∂z = 10 ms−1 km−1, for instance, the upper atmosphere would have a 10 m s−1 anomaly in U if other layers have zero anomalies in ∂U/∂z One may anticipate anomalous baroclinic wave generation arising from anomalous B to efficiently suppress the effect of the B anomaly in the interior of the atmosphere, thereby minimizing the impact of the B anomaly on the upper atmosphere. On the other hand, if the anomalous baroclinic wave generation is not sufficient to suppress the effect of anomalous B and/or anomalous B triggers an atmospheric response that yields an equivalent-barotropic structure, like that of blocking, then the effect of B anomaly on the upper atmosphere can be significant. Furthermore, anomalous B may result in anomalous wave generation/dissipation that, in turn, acts on the larger-scale flow. Therefore, B anomalies may well be directly or indirectly involved in the upper-atmospheric anomalies in various ways.
The sea surface temperature (SST) is an important factor in determining B in the storm-track regions (e.g., Hoskins and Valdes 1990; Nakamura et al. 2004). SST anomalies (SSTAs) around the front of the GS or Kuroshio/Oyashio can have a profound impact on B along the storm tracks. A subtle point that has to be considered carefully in this regard is the spatial scale and the location of SSTAs with respect to the climatology since it is the anomalous surface temperature gradient of the atmospheric forcing scale that matters. For example, a small patch of warm SSTA with a diameter of 50 km embedded in the subpolar gyre is likely to be ignored by the large-scale atmospheric dynamics. On the other hand, a 50-km-wide patch of warm SSTA that extends along a sharp frontal current, such as the GS, over several hundred kilometers or more may have a significant impact on the large-scale atmospheric dynamics through its modification of B. The high sensitivity of B to changes in the temperature contrast across the front and changes in the width of the front, and the uncertainty in the impact of small SSTAs on B make assessing the effective B anomalies that are attributable to the SSTAs from the available data very difficult. Moreover, exactly how the SSTAs in the presence or absence of the land surface temperature anomalies may or may not produce B anomalies that are significant to the atmosphere is uncertain. For example, anomalously warm or cold land along the east coast of North America can alter B in the storm track without any SSTA. Or, large SSTAs along the east coast of North America can have no impact on B if the large-scale land surface temperature along the east coast of North America has the same anomaly. This complicating role played by the land surface in assessing the impact of SSTAs in the vicinity of a large landmass on the overlying atmosphere must be taken into account when studying potential roles of extratropical SSTAs in the extratropical atmospheric anomalies.
Lau (1988) investigated patterns of anomalous storm track activity and associated low-frequency flows by computing empirical orthogonal functions (EOF) for high-frequency 500-hPa geopotential heights for the Northern Hemisphere winters. He found that both North Atlantic and North Pacific storm tracks have a pattern of meridional shift and a pattern of increased or decreased eddy activity in the first two EOFs. He also found that these changes in the storm tracks have symbiotic relationships with the background flows and have substantial impacts on the mean flow. We have attempted to examine this issue of variability in the mean flow and storm tracks from a perspective that focuses on B, in hopes of finding a clear link between the extratropical atmospheric anomalies and underlying oceanic anomalies along the fronts. In this regard, we have chosen not to project our results onto the two major modes of variability that involve the North Atlantic basin, the North Atlantic Oscillation and Arctic Oscillation, so that our presentation and discussion are mostly confined to the wave–mean flow dynamics on a monthly or shorter time scale.
Our approach to the search for a link between anomalies in the GS and the overlying atmosphere is as follows: 1) identify dominant patterns in anomalous B in the storm track for each month and identify years in which the anomaly fits the pattern well, 2) composite anomalies in the monthly mean circulation and high-frequency transients in the atmosphere to obtain a typical atmospheric state that accompanies the patterns of anomalous B, 3) composite SSTA to obtain a typical oceanic state that accompanies and precedes the patterns of anomalous B, and 4) composite anomalous net surface heat flux that accompanies and precedes the pattern of anomalous B. With this approach, we obtain typical pictures of anomalous states in the atmosphere and oceans with anomalous B as their connecting interface.
Section 2 describes the data and procedure to compute B. Section 3 describes the climatology and variance of B. Dominant patterns of B are shown in section 4, followed by composited anomalies in various atmospheric fields and SST in section 5. Finally, we present some discussions on the results, examining a potential cause–effect relationship between anomalies in the SST and atmosphere, and offer some suggestions for future model experiments in section 6.
2. Data and calculation procedures
The data used to calculate B are the monthly mean temperature at 2 m above the surface (T 2m) and temperature at pressure levels available from the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40) (Uppala et al. 2005). We chose the ERA-40 T 2m data over the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis products for its explicit inclusion of the observed near-surface temperature in producing the T 2m data. The monthly mean surface pressure data from the NCEP–NCAR reanalyses (Kalnay et al. 1996) were used to determine the pressure levels to be used for B calculation, and to calculate θ at 2 m above the surface from T 2m. We used the NCEP–NCAR surface pressure data for convenience since we had already compiled the dataset for calculating transient eddy fluxes to be mentioned later and the ERA-40 surface pressure data are not readily available. We later compared the NCEP–NCAR monthly mean sea level pressure with that of ERA-40 and found the difference between the two products to be immaterial for the purpose of the current study. We also used ERA-40 monthly mean horizontal wind and geopotential height at pressure levels, net surface heat flux (the sum of latent heat flux, sensible heat flux, solar radiation, and the thermal radiation), Fh, and Hadley Centre sea surface temperature data (Rayner et al. 2003) to compile anomaly composites accompanying anomalous patterns in B. In addition, we used 6-hourly temperature and wind data from the NCEP–NCAR reanalyses to compute various eddy fields.
We computed B near the surface by calculating the horizontal gradient in θ2m, using centered finite differencing, and calculating N also by the centered finite differencing, using the lowest 3 vertical pressure levels. Both ∇θ2m and N were calculated locally as in Hoskins and Valdes (1990) and Nakamura and Shimpo (2004). The entire 45 years, from September 1957 to August 2002, were used for the Northern Hemisphere.
The 6-hourly bandpassed (period of 2–7 days) eddy fields and ultralow-frequency (period of 30 days and longer) background fields were computed from the NCEP–NCAR reanalyses, using simple time filters (Lau and Lau 1984) first. The filtered time series were then visually examined against the raw time series and, then, used to calculate the slowly evolving bandpassed meridional velocity variance (), meridional temperature flux (), and the three-dimensional transient wave activity flux defined on a zonally varying basic state by Plumb (1986). The wave activity flux consists of the zonal and meridional advective fluxes (MU and MV), the zonal and meridional radiative fluxes (MRx and MRy), and the radiative vertical flux (MRz). The flux is essentially the Eliassen–Palm flux (Eliassen and Palm 1961) in a zonally inhomogeneous mean flow (Plumb 1986). The wave activity flux is calculated from February 1948 to November 2004 only for the extratropics poleward of 20° latitude. Also, it is calculated only from 850 to 30 hPa owing to the double vertical derivatives required for the calculation. The flux of particular interest in this study is the vertical component. Here, MRz is defined by
where q is quasigeostrophic potential vorticity, p is the pressure, p0 is the reference surface pressure set to 1000 hPa here, θ0 is the area-weighted ultralow-frequency hemispheric mean potential temperature at each height, θ′ is the bandpassed potential temperature, and z is the geopotential height. An overbar denotes an ultralow-frequency component and a prime denotes bandpassed component. The 6-hourly time series of wave fluxes was computed by using the time series of ultralow-frequency fields as the basic state and high-frequency fields as eddies. In short, the time series is calculated by changing the meaning of an overbar from the time mean state to an ultralow-frequency state and changing the meaning of a prime from a departure from the mean to a high-frequency state. The 6-hourly eddy fields are averaged over each month to produce monthly mean time series. This dataset allows us to examine anomalous eddy fields accompanying anomalous B in specific months. The climatology for the eddy fields was computed from 47 years: January 1958 to December 2003.
We performed the diagnoses on the entire globe with the emphasis on storm tracks, but report results for the North Atlantic storm track region in the present paper.
3. Climatology and variance
The climatology and variance of Bx and By were computed for each month and examined closely for their spatial and temporal structures. We have used the monthly climatology as the reference in our study since we found that the climatology for two successive months differs only slightly, in general, but differs to the extent that it contaminates the results of EOF analyses when the seasonal mean is used as the climatology.
Figure 1 shows the climatology of Bx, U200, By, V200, 850,200, MRz850, and U1000 for February as an example of the winter reference state. The numeric superscript indicates the pressure level in hectopascals. The winter mean, December–February for example, is noticeably more diffused in structure, particularly for Bx and By, than those shown in Fig. 1. There are no surprises in the overall picture of Bx. The region of large land–sea temperature contrast and the GS shows very large Bx, peaking in February and weakening toward the summer. The position of Bx maximum associated with the GS remains more or less the same throughout the year, most likely due to the presence of the ocean front, while its magnitude changes visibly. The magnitude of Bx decreases throughout the spring, reaching the minimum in July. As the insolation starts decreasing, Bx begins increasing with a month or two of delay. Through the fall, Bx continues to increase, reaching the maximum in February. As reported by Nakamura et al. (2004), the U200 maximum is displaced from the Bx maximum visibly in winter months, although U200 is generally large over the area of large Bx in the core of the storm track. The displacement is less pronounced in warm months. The seasonal variation of U200 along the storm track follows that of Bx very closely.
The magnitude of By is smaller than that of Bx, in general, but can be greater than that of Bx where By is large. Large By is generally seen along the boundary between a large landmass and ocean, and over continents. Around the North Atlantic basin, large positive By is seen along the eastern shore of North America, over the Labrador Sea, in the vicinity of the western shore of Greenland, and off of the eastern edge of Greenland, in cool months. Also, By is large where the downstream branch of the GS, the North Atlantic Current, flows northward in the mid North Atlantic. In warm months, By along the eastern shore of North America and Greenland turns negative as the land heats up, whereas By in the Labrador region becomes very small. Also, positive By to the east of the North Atlantic Current becomes significantly smaller in warm months. The spatial relationship between large By and V200 in the extratropics suggests that V200 reflects very broad structures of By in the sense of the thermal wind balance.
We note that the structures of the climatological Bx and By generally reflect those of ∂θ2m/∂y and ∂θ2m/∂x, respectively, with some exceptions where the surface slope contributes significantly to Bx and By in isolated areas over the land, most clearly over Greenland.
The position and structure of the storm track as indicated by 850 and 200 are, at least for the winter, essentially the same as those reported in earlier studies on the storm tracks (e.g., Chang et al. 2002). The maxima in 850 and 200 are located very close to the band of large Bx along the GS in cold months. In warm months, however, they are displaced to the north of the band. We also note that the maximum is located downstream of the U maximum in the winter, whereas it is located close to the U maximum in warm months. The difference is attributed to the difference in the strength of the upper-tropospheric flow that advects synoptic-scale disturbances as they enter and grow in the storm track. The characteristics of MRz850 whose divergence out of and convergence into the planetary boundary layer are related to, respectively, acceleration and deceleration of the surface pseudowesterly, when the horizontal flux convergence is negligible (Plumb 1986), are roughly in accord with those of 850, which is a primary component of MRz850. The sense of the surface momentum forcing by MRz850 along the storm track is pseudoeastward (with a weak northward component in this case) since the potential vorticity gradient at 850 hPa is predominantly meridional and positive and MRz850 is almost entirely upward along the storm track. The near-surface climatological U along the storm track is generally positive, which may be attributed to this wave forcing.
The variance of Bx is large over land and in the vicinity of land–ocean boundaries. Values along the storm track are only moderately large and are roughly half of those in areas of large variance over the land and land–sea boundaries. These patterns arise from large fluctuations in the near-surface temperature over the land due to a much smaller heat capacity of the land surface as compared to that of oceans. Also, the large values to the north of the storm track may reflect the effect of sea ice in the ocean. The variance of By is large along boundaries of the land and oceans in areas where the climatological values are large. Note that fluctuations in N can be a significant contributor to the Bx and By variances where the surface slope is large.
4. Dominant anomalous patterns of Bx and By
To identify dominant anomalous patterns of Bx and By in the vicinity of the storm track, we applied EOF analyses to Bx and By for each month in the domain with the boundary set by 80°W, 20°W, 25°N, and 60°N. This area of EOF application is indicated by red boxes in Fig. 1 and in many of the figures to be introduced later. This area has been chosen to include a part of the North American continent so that anomalies in Bx and By arising from the land–sea temperature contrast are included in the diagnosis. We note, however, that the horizontal resolution of the data may not be sufficient to capture the anomalies at the land–sea boundaries accurately. Even if the full resolution reanalyses were available, this still remains a potential problem. One must remain cautious in this regard.
a. Modes of Bx
The percentages of Bx variance explained by its first four EOFs are given for each month in Table 1. The first EOF (EOF1) of Bx explains 20% or more of Bx variance for winter months December–March and 15%–20% for other months. The values are generally greater for cooler months. This is also the case for the second EOF (EOF2) of Bx. The EOF2 of Bx explains 10%–20% of Bx variance for each month, with larger values seen in the cooler months. The third and fourth EOFs of Bx each explain only about 10% or less of the variance. The autumn shows the least clear separation among the first four modes. The percentage explained by the first two modes varies from roughly 45% in December, January, and February to about 28% in September, October, and November. These differences suggest that the stronger air–sea interactions during the cold months and relatively stable heat transport by the GS may constrain the modes of variability during the winter more than they do during summer and fall. When the time series of EOF1 and EOF2 are examined, they generally show different evolutions even for warmer months. Nevertheless, the small difference in the percentage of variance explained by the first two modes found for May–November is suggestive of unclean separation between EOF1 and EOF2. In the following, we focus on the first two modes of Bx in the cold months, December–April, for further examination.
The top half of Fig. 2 shows the regression values of Bx with the first two EOFs for February, superimposed on the corresponding climatological values, the correlation values of Bx with the EOFs, and the correlation and regression values of U200 with the EOFs. When viewed with respect to the climatological structure, the first two EOFs of Bx show two similar patterns for most of the cooler months, November through April. One of the two patterns is indicative of a tendency for meridional shift of the band of large Bx and is visible in most months to varying degrees. The first mode for February shown is an example of this pattern. This pattern typically shows an area of large Bx anomalies whose center is displaced by 500 to 1000 km from the climatological Bx maximum in the storm track. We note that this pattern also has a tendency to accentuate the structure of Bx around the storm track. It is associated with a meridional shift in the position of the zonal flow, with some tendency to accentuate the jet (Fig. 2e). For those months that exhibit a clear shifting tendency in one of the first two modes, the other mode shows a fairly clean pattern of tendency to increase or decrease Bx in the band of large climatological Bx along the storm track. An example of this can be seen in the second mode for February. This pattern typically has an area of large Bx anomalies whose center is more or less collocated with the climatological maximum in Bx. It is also accompanied by an enhanced or suppressed zonal flow (Fig. 2f). These two anomaly patterns are qualitatively the same as two of the most prominent patterns found by Lau (1988). For the majority of the 12 months, however, the anomalous patterns of the first two modes exhibit both of the two tendencies simultaneously. The EOFs for warm months are not as well organized as those in the cooler months.
The statistical significance of these modes is robust. The threshold values for the 95% and 99% confidence test by the Student’s t test are, respectively, 0.29 and 0.38. The correlation of Bx with the first two EOFs is high in areas of large regression values in the vicinity of the storm track for most months (Figs. 2c,d). It is statistically significant in some remote areas in cold months also. As found for the regression values, the correlation tends to be higher in cooler months and tends to be high in larger areas in the cooler months. However, the correlation is the weakest in May and June, not July and August.
The modes show significant relation with U200 as well. The correlation of the EOFs with U200 is statistically significant in large zonally elongated areas extending out from the domain of EOF analyses both upstream and downstream. The regression values of U200 with the EOFs with the maximum of 5–10 m s−1 are nonnegligible values compared to its climatology.
b. Modes of By
The percentages of variance of By explained by its first four EOFs are given for each month in Table 2. Values for By EOF1 are generally greater than those for Bx for each month. Also, their seasonal dependence appears somewhat different from that of Bx. The first mode explains 20% or more of the variance for January, February, March, April, June, October, November, and December. The value for February is conspicuously high at 47%. The second mode explains only 10%–15% of the variance and shows generally clearer separation from the first mode than its counterpart for Bx. The third and fourth modes explain only 10% or less of the variance. Because of the visibly weaker significance of the second mode and substantially smaller magnitude of By anomalies in comparison to those of Bx in the key region of the storm track, we consider only the first mode for further diagnoses.
Regression values of By for its EOF1, superimposed on its climatology, correlation coefficient between By and the EOF1, and correlation coefficient between V200 and the EOF1 for February and May are shown as examples in the lower half of Fig. 2. The patterns of anomaly often exhibit a dipole in the domain of EOF analysis, with one of the poles showing large values in the Labrador Sea and the other pole to its west in North America, including the ocean off its east coast, showing a rather broad structure. The longitudinal extent of the dipole is greater during winter than in other seasons. The areas of large anomalies shift southeastward during warmer months. As in the case of Bx, the warmer months exhibit less organized and smaller-scale structures compared to cooler months.
The correlation between By and its EOF1 is generally strong in the Labrador Basin in the cold months, November through April. In warm months, the area of strong correlation in Labrador shifts southeastward, as in the case of large regression values. Strong correlation of opposite polarity is usually seen to the west of Labrador over eastern North America from October through January. Again, the correlation is significant at 95% confidence level or higher in much of the areas of large regression values.
In relation to the climatological By, the patterns tend to accentuate the large By in Labrador or the mid North Atlantic by increasing By in Labrador or the mid North Atlantic and decreasing By in eastern North America, including the ocean off its east coast, in the positive phase. In the negative phase, they tend to flatten the By structure.
As in the case of U200 and Bx, the correlation between V200 and the EOF1 is strong with substantial regression values. The accompanying anomalous V200 exhibits wave-train-like patterns that emanate from the western North Atlantic both eastward and westward.
5. Anomaly composites
In an attempt to identify typical anomalous states that accompany the aforementioned anomalous patterns in Bx and By, we produced sets of anomaly composites for Bx, By, T 2m, U, V, , , MRz, and SST. For this purpose, we first examined the time series of each EOF for each month and picked those years that reach or exceed the threshold absolute value, 0.5, for the positive and negative phases separately. We then simply averaged anomalies of these years to create pictures that represent the positive and negative anomalous conditions found by the EOF analyses. This approach may show us some of the nonlinear response of the atmosphere in strongly anomalous cases that may remain hidden in simple linear correlation analyses. The years selected for the composites are listed for each month in Tables 3 –8. Note that some particular months of particular years are used in composites for both EOF1 and EOF2 of Bx. Most of these months show very large values in one of the two modes and marginal values in the other mode. This is a manifestation of incomplete separation between the first two modes of Bx. We chose to use all months whose EOF time series reach or exceed 0.5 in the absolute value to avoid subjective manipulation of the data. Anomaly composites of U and V were made at 50, 100, 200, 500, 700, and 1000 hPa to examine the vertical structure of the anomalies. For the eddy quantities, at 850 hPa, at 200 hPa, and MRz at various pressure levels were examined. The former two were chosen as the standard measures of storm track variation, whereas the third was chosen as a measure of wave forcing variation that originates from the anomalous B. The composites for cool months generally show structures that are defined more clearly than those for warm months, especially for the modes of Bx.
a. Anomalous conditions associated with the first two modes of Bx
Composited anomalous Bx and other atmospheric fields show interesting structures with substantial anomaly values mostly in cold months, December–April. We focus on these months in the following, showing some examples. Figures 3a,b show composites of anomalous U200, superimposed on those of anomalous Bx for both positive and negative phases of the EOF1 for February. These U200 composites exhibit large anomalies with their maximum absolute values ranging from 7 to 15 m s−1. These anomaly values are of significant magnitude with respect to the climatology and standard deviation of U200 for each month. The absolute values of composited anomalies are generally comparable to or somewhat greater than the standard deviation. The positions of the composited anomaly maxima are near or slightly downstream of the anomalous Bx maxima. Obviously, these anomalies are manifestation of shifts in the latitudinal position and/or changes in the magnitude of the jet. Most of the anomalies are in thermal wind balance, especially in the vicinity of the storm track entrance, as one may anticipate from the geostrophic balance as the valid first approximation to the planetary- and synoptic-scale atmospheric motions. Anomalous U generally shows equivalent-barotropic structures with the maximum U anomalies found near the tropopause, extending up to 50 hPa in cold months and up to 100 hPa in the warmer months (Fig. 4), showing that the anomalous Bx identified by the EOF is often associated with planetary-scale anomalies of the external mode (Panetta et al. 1987; Held et al. 2002).
We now turn our attention to the accompanying anomalies in the storm track. Figures 3c,d also show composited anomalies in 200, 850, and MRz850 for both phases of the EOF1 for February. In a linear framework, locally enhanced 850, 200, and MRz850 for positive Bx anomalies, and vice versa, are anticipated. Broadly speaking, this is indeed the case, suggesting the diffusive role of transient eddies (e.g., Kushner and Held 1998). On the other hand, however, the winter months, January and February in particular, do show some signs of the eddy fields locally changing in a way opposite to that expected from linear theories. In fact, there is a general tendency for anomalous 200 to be displaced far downstream of the area of large Bx anomaly and the maximum anomaly in U200 in the winter. This tendency is weak or nonexistent from spring to autumn. This counterintuitive relationship between the eddy activity and Bx is akin to that found for the winter North Pacific storm track by Nakamura (1992). It is probably a manifestation of the stronger upper-tropospheric mean flow advection of synoptic-scale transients in the winter. In a paradigm of baroclinic wave growth through interactions of waves at the low level and tropopause (Hoskins et al. 1985), some time is needed for the waves to interact with each other and grow. When insufficient time is allowed for them to interact, growth of the waves is likely to be suppressed locally. On the other hand, the stronger advection of upper-level waves in the entrance region of the storm track may advect more energy downstream undissipated into the exit region where waves grow with help from the barotropic deformation field or grow via processes demonstrated by Chang (1993) and Chang and Orlanski (1994). Anomalous 850 shows a similar, albeit weaker, tendency as that displayed by 200 in the winter also. The modification of the waves by the altered jet may contribute to these changes to some extent also. The displacement of the upper-level jet from the area of strong Bx as the cause of suppressed eddy activity over the North Pacific in mid winter (Nakamura and Sampe 2002) does not explain the locally suppressed eddy activity in areas of enhanced Bx here since the upper-level jet and Bx have a positive linear relationship in our cases. The reader is referred to Chang et al. (2002) for a comprehensive review of the current state of storm track research. Of course, significant heating anomalies anticipated to accompany the anomalous 850 are bound to modify the stationary waves and, thus, the mean flow throughout the troposphere and lower stratosphere (Held et al. 2002). Note that the magnitudes of composited anomalies are nonnegligible with respect to those of the climatology.
Anomalous wave forcing arising from the Bx anomalies can be qualitatively deduced from composited anomalous MRz at the lowest level of its computation, 850 hPa in our case. Also, the sense of anomalous momentum forcing of the underlying ocean by the anomalies in the synoptic-scale transients may be deduced from MRz near the surface. As examples, composited anomalies in MRz850 for February are shown in Figs. 3e,f, along with the accompanying anomalous U at 1000 hPa. The magnitude of composited anomalous MRz850 is generally nonnegligible compared to its climatology. Positive and negative MRz850 anomalies (i.e., anomalous divergence and convergence of the wave flux in the planetary boundary layer, assuming negligible horizontal flux divergence) tend to generate positive and negative U anomalies below, respectively. Note that the anomalous U1000 shown is not necessarily the product of the accompanying MRz850 anomalies since there are other factors at upper levels that can affect U1000. The anomalies in MRz850 only contribute to the anomalous U1000. In a linear framework, positive and negative MRz850 anomalies are anticipated from, respectively, enhanced and reduced Bx. We find this to be true in a broad sense for most of the composites. As discussed above for and , however, some sign of the opposite association is seen in the winter. Such a nonlinear relationship makes straightforward correlation studies undesirable for investigating this kind of processes. We note that significant anomalies in MRz with the horizontal structures similar to those of MRz850 are present throughout the troposphere. Although the horizontal structures become visibly larger and different up above the tropopause, organized large anomalies in MRz are found at 100 hPa throughout the year and at 50 hPa in the winter. The Bx anomalies along the storm track appear to have a strong impact on the wave forcing penetrating into the midstratosphere, not to mention the troposphere. We also attempted to examine anomalies in the divergence of the total wave fluxes in the troposphere and stratosphere, but could not obtain clear pictures owing to the noisiness of the contribution from the advective fluxes.
Composited U anomaly for the Bx EOF2 for each month is also fairly large. Figures 5a,b show the composited U200 anomaly, superimposed on the composited Bx anomalies for both phases of the EOF2 for February, as examples. Despite its smaller contribution to the total variance of Bx, as compared to the contribution from the first mode, the maximum values of Bx and U200 anomaly composites for the second mode are fully comparable to those for the first mode. (Of course, this may be partly due to the smaller sample sizes used for making the composites.) These patterns are manifestation of latitudinal shifts and changes in the magnitude of the jet that are different from the patterns found in the first mode. In the case of February, the anomalies tend to enhance or suppress the jet in its core. As found for the first mode, the anomalies have a vertically coherent structure from 700 hPa to 100 or 50 hPa, with a downstream displacement in the area of large anomalies at 1000 hPa, in a manner similar to that found for the first mode. Also as was the case for the first mode, the anomaly structures are defined more clearly in cooler months.
The accompanying anomalies in the eddy fields have qualitatively the same characteristics as those found for the first mode, as far as their relations to the anomalies in Bx and U200 are concerned. The magnitudes of the anomalous eddy fields for the second mode are also nonnegligible. Examples are shown in Figs. 5e,f that show V ′θ′850 with 200 and MRz850 with U1000 for February.
Composited SSTAs accompanying the composited anomalous Bx for its first and second modes are very interesting. Figures 6 and 7 show, respectively, composites of anomalous SST and T 2m for both positive and negative phases of EOF1 and EOF2 for January, February, March, April, and December. In many of the composites, including those for warmer months not shown here, small-scale structures in the vicinity of the GS are clearly visible. Close examination of these composites reveals that the substantial SSTAs in the vicinity of the GS are located almost exactly along the climatological position of the core of the GS. Note that the spatial scale of these anomalies is considerably smaller than that of the corresponding T 2m anomalies. Also, there are small areas in which the anomalous SST and T 2m have opposite signs, which indicates that the anomalous T 2m is strongly influenced by the large-scale motions of the atmosphere and is not necessarily dictated by the SSTA. It is also possible that the inaccuracy of the SST and/or T 2m data is responsible for the mismatch in the sign of SSTA and T 2m anomaly locally. An important point to note is that a slight difference in the latitudinal position of the SSTA can make a large difference in the concomitant Bx anomaly. In fact, a 100-km difference in the latitude of an SSTA along the GS can mean a difference in the sign of the resulting large Bx anomaly. We could have plotted composited anomalies in the meridional gradient of SST for its direct connection with Bx. However, it turned out that plots of composited SSTAs themselves provide pictures that are more physically intuitive, while allowing us to deduce the associated anomalous gradient.
Given the small spatial scale of the SSTAs along the GS, it is tempting to speculate that anomalies in the path of and/or heat transport by the GS are forcing the atmosphere in such a way that it generates large-scale anomalies in various atmospheric fields shown above. Anomalies in 850 are generally found to have a tendency to suppress the accompanying anomalous meridional T 2m gradient that appears to have a direct association with SSTAs. Thus, the atmospheric eddies are working to destroy the effect of SSTAs on the lower atmosphere. Of course, the cause–effect relation between the SSTAs and anomalous atmospheric state cannot be ascertained in the current study. Nevertheless, we argue that latitudinal shifts in the GS and/or variations in the heat transport by the GS help produce Bx anomalies near the surface and further alter circulations in the troposphere and lower stratosphere. In the light of major climatological impact of the GS up to the upper troposphere found recently (Minobe et al. 2008), it would not be surprising if anomalies in the GS produce significant anomalies in the upper troposphere or lower stratosphere. We emphasize, at the same time, that major Bx anomalies along the GS does not necessarily produce major anomalies in the atmosphere. The strong response of the atmosphere is expected only when anomalous Bx along the GS is the dominant one in the large region surrounding the storm track and the jet is flowing over the area of the Bx anomalies.
For the anomaly composites discussed above, we performed significance tests on the difference in the mean of the anomalies between the positive and negative phases, using the Student’s t test. Examples of the tests are shown for February composites in Fig. 8. As expected from the high correlation of U with Bx, the composited anomalous U is significant at 95% in very large areas. The simpler eddy fields, 850 and 200, show fairly high significance, 90% and higher in areas of large absolute values in the composited anomalies in general. However, the areas in which composited anomalies of these eddy fields are significant are scattered and small in February compared to other cold months, indicating stronger nonlinearity in the atmospheric response to Bx anomalies. Even worse is the significance of the composited anomalous MRz850. Except for March, areas of high significance of the anomalous MRz850 are scattered and small. Finally, the difference between SSTAs in the positive and negative phases is significant at 90% confidence level in small patches along the GS or in the vicinity of the GS in most of the composites shown above. Considering that there is really no physical reason to expect a linear relationship between anomalies in Bx and SST, while one may expect a linear relationship between anomalies in Bx and smoothed anomalous meridional SST gradient, we find the significance of the SSTAs along the GS intriguing.
b. Anomalous conditions associated with the first mode of By
Composites of anomalous V made for the first mode of By show substantial values with respect to its climatology and standard deviation throughout the year. Figure 9 shows anomalous By, V200, 850, 200, MRz850, and U1000 composited for both positive and negative phases of the By EOF1 for February and May. Again, the absolute values of composited anomalies are comparable or slightly larger than the standard deviation for each month.
Reflecting the characteristics of By EOF1 patterns, the wavenumber of V200 anomalies in cold months tends to be smaller than in warm months. On the other hand, the geometrical horizontal extent of the anomalous structures is more or less the same for the winter and other seasons. We also find the anomalous V patterns in the winter defined at higher latitudes than those in warmer months. We hypothesize that this difference in the latitudinal position, and perhaps the difference in the wavenumber also, arises from the different role of the stratosphere played in these anomalous conditions. Interestingly, however, the magnitude of the composited anomalous V200 for cold months and warm months is about the same. Furthermore, the total zonal extent of a wave-train-like structure in warm months is generally greater than that in cold months, often spanning 180° or more in longitude, although the plots in Fig. 9 do not show the total zonal extent of the anomalies. Comparing with the climatology, the patterns in cold months tend to shift the location of the V200 maximum near Greenland zonally, simultaneously enhancing or suppressing the V200 maximum. The patterns in warm months show less of the tendency to shift zonally the location of the V200 maximum near Greenland. We also note that the phase of anomalous V200 in the positive phase of EOF1 is visibly shifted eastward compared to that in the negative phase in the winter.
The vertical structure of the composited anomalous V is very similar to that of the composited anomalous U discussed above. It generally shows anomalous V of the same sign from 1000 hPa up to 100 or 50 hPa, with the largest absolute value found near the tropopause or in the lower stratosphere. Summer anomalies penetrate up to only l00 hPa in our diagnoses, which is consistent with the lack of westerlies above the lower stratosphere in the summer. Also, the phase of anomalous V is visibly displaced eastward with respect to that of By at all pressure levels examined, to the extent that the maxima in V and By are clearly out of phase. This is a major difference from the relationship between anomalous Bx and U presented above. This pattern, along with the equivalent-barotropic structure of the V anomalies, suggests a possibility that the By anomalies are products of anomalous heat transport by the anomalous V.
Anomalous eddy fields that accompany By anomalies in different seasons show the same traits. Examples are shown in Fig. 9. The traits shared by almost all composites are manifested by the areas of increased/decreased 850 and 200 along the storm track where the anomalous V is positive/negative. It is a manifestation of enhanced/suppressed synoptic-scale wave generation to the east of an anomalous trough/ridge. The maxima in 200 anomalies are nearly collocated with those in 850, with some tendency for the former to be slightly downstream of the latter in the winter. These spatial relationships among anomalies in V, V ′θ′850, and 200 hold true in other seasons as well. The localized enhancement of baroclinic wave generation along the eastern flank of a mean trough is in a broad agreement with a linear theory of Niehaus (1980). Structures of composited MRz850 anomalies reflect those of 850 reasonably well, albeit some differences in details that arise from other factors that determine MRz. The accompanying anomalies in U1000 are in the sense expected from the pattern of MRz850 anomalies over all, with some exceptions such as the area just to the south of the Greenland.
Composited SSTAs for the By EOF1 generally exhibit patterns that have spatial scales somewhat greater than those composited for the first two EOFs of Bx (not shown). There are some small-scale features along the GS, but do not necessarily contribute substantially to the anomalous By. The SSTAs that contribute to the By anomalies most are located north of 45°N for January and February and near Newfoundland for other months. The spatial scales of these anomalies are not quite those of the large-scale atmospheric anomalies, but not quite the scale of oceanic fronts either. Thus, we suspect that fluctuations in the path and/or strength of the GS are not directly involved in these patterns.
The composited anomalies for the first mode of By shown above were tested for their significance, as were the composites for the first two modes of Bx. Test examples are shown in Fig. 10 for February and May. The results are very similar to those described in the preceding subsection. The significance is very high for V over large areas and tends to fall off in the order of V, 200, and 850, SST, and MRz850.
6. Discussion and concluding remarks
We presented above the climatology and dominant anomalous patterns of Bx and By and accompanying anomalies in the atmosphere and SST. Perhaps the most interesting and also controversial among the results presented here are the SSTAs along the GS, associated with the major anomalies in the atmosphere. Because of the small spatial scale of the SSTAs and relatively short time scales of the processes represented in the data, we argue that the SSTAs produced by fluctuations in the path of and/or heat transport by the GS, possibly in combination with land surface temperature anomalies, are the cause of the anomalies in the overlying atmosphere, at least on the monthly time scale studied here. Needless to say, these SSTAs are forced, at least in part, by the atmosphere that drives the oceanic circulation, including the GS. Thus, we argue that there is a feedback loop that connects the atmosphere with the underlying ocean and land.
To investigate the cause–effect relationship between the SSTAs along the GS and the atmospheric anomalies, we compiled composites of anomalous net surface heat flux, Fh, for the corresponding months shown in Figs. 6 and 7, using the ERA-40 monthly mean surface flux products, despite the large uncertainty in the surface heat flux produced by various reanalyses. The results for EOF1 (corresponding to Fig. 6) are plotted along with the accompanying SSTAs in Fig. 11 as representative examples. Note that we have defined the upward flux as the positive flux here. We find no obvious connection between large SSTAs and Fh anomalies in all composites. When the composites are made for Fh anomalies leading the SSTAs by one and two months, no clear sign of the atmosphere forcing the SSTAs along the GS is found either. Generally, however, the areas of large SSTAs are found to be displaced visibly from the areas of large Fh anomalies. Also, the corresponding composited anomalous U1000 indicates no systematic relationships between anomalous Ekman heat transport and SSTA. Thus, the relationship between the composited anomalous SST and atmospheric forcing proves neither the case of the atmosphere forcing the large SSTAs along the GS nor the case of the SSTAs along the GS forcing the atmosphere. However, when the SSTAs are composited for the month preceding the months shown in Figs. 6 and 7, we observe the anomalies of slightly reduced (enhanced, in some cases) magnitudes with very similar structures. The composites corresponding to those shown in Fig. 6 are shown in Fig. 12 as representative examples. In fact, SSTAs composited for the one-month period preceding those shown in Figs. 6 and 7 by two months also show clear hints of the basic structures in the vicinity of the GS also (not shown). These findings suggest that the SSTAs are preexisting, though not necessarily causing large atmospheric anomalies in the preceding months. It thus suggests that the SSTAs are much more likely to be the cause of the atmospheric anomalies than otherwise in these cases. It is also consistent with the absence of direct association between anomalous SST and Fh in these composites. The composites made for the one-month periods following those shown in Figs. 6 and 7 also show SSTAs with similar patterns, indicating the persistence of the SSTAs near the GS (not shown).
When the large-scale Fh anomaly field is examined, its spatial pattern typically indicates positive and negative anomalies in areas of enhanced and suppressed Bx, respectively. It suggests that the anomalous Fh shown here is essentially due to changes in high-frequency transients since the synoptic-scale transients play major roles in the surface heat flux (e.g., Hazeleger et al. 2001). As mentioned earlier, anomalous 850 generally tends to suppress anomalous meridional T 2m gradient that clearly has a direct connection with the SSTAs, suggesting that it is more likely to be the SSTAs that are forcing the atmosphere in such a way that the net result is as shown above. Perhaps the most straightforward interpretation of the composited anomalous SST and Fh is that of preexisting SSTAs along the GS generating Bx anomalies, resulting in anomalous transient wave activity and concomitant Fh anomalies. In this scenario, the SSTA acts as a trigger for enhanced air–sea interaction and does not necessarily directly contribute to the anomalous Fh.
One interesting characteristic of the spatial relationship between the SSTA and Fh in these composites is the tendency for the larger Fh anomalies to be located to the south or southwest of the GS, to the east of its separation from the western boundary. This spatial relation is found between the SSTAs and Fh anomalies for the months preceding those shown above in many of the composites. If this relationship reflects reality, it raises an intriguing possibility of the GS collecting and transporting the heat anomalies produced by the atmospheric forcing in the subtropical gyre and along its path to force back to the atmosphere in the storm track. Given the typical flow speed of the GS, l–2 m s−1, it is not entirely inconceivable for the subtropical ocean to feed back onto the atmosphere along the storm track within a few to several months. Of course, it is also possible that the quality and spatial resolution of the surface heat flux products are just not adequate to be used for this type of diagnoses. We are cautious in this regard.
One may wonder if the SSTAs shown in Figs. 6 and 7 are a product of cumulative anomalous Fh in the preceding months. We composited the change in the SSTA over three months (the months shown in Figs. 6 and 7 minus four months before) and the anomalous Fh integrated over the preceding three months to see if this may be the case. The composites corresponding to those shown in Fig. 6 are shown in Fig. 13 as representative examples. In general, small-scale structures in the SSTA changes and integrated anomalous Fh along the GS do not match at all, further reinforcing our argument for the SSTAs generated by the GS forcing the atmosphere. However, on the larger scale, when smoothed over 1000 km or so, the sense of the relationship between the changes in SSTA and integrated anomalous Fh in the vicinity of the GS is such that the atmosphere is producing the SSTA over the preceding three months. Given the relatively coarse resolution of and uncertainty in the Fh data, one may argue that the SSTA in the months identified by the EOF analyses is basically the product of anomalous atmospheric forcing accumulated during the preceding months. Even if so, on the small scale, we argue that the GS is redistributing the heat from the anomalous atmospheric forcing in such a way that it forces back the atmosphere more effectively. For example, the composites for both phases of January EOF1, positive phase of February EOF1, and both phases of December EOF1 show large anomalous integrated Fh displaced from large changes in SSTA in such a way that the advection by the GS and/or its southern recirculation help produce the large SSTA changes. In other words, some of these figures indicate a possibility of the oceanic advection playing a role of redistributing the anomalous heat provided by the atmosphere to force back the atmosphere in a more effective manner.
The results presented above strongly indicate the presence of complex feedbacks operating between the atmosphere and ocean, probably including the land. The following is our interpretation of the results found and presented here. Anomalies in the GS, in combination with the land surface temperature, may shift and/or strengthen or weaken the baroclinic forcing along the storm track. The mean flow in the troposphere and lower-stratosphere shifts and/or strengthens or weakens in response to the anomalous horizontal temperature gradient via the thermal wind balance. At the same time, the anomalies in B affect the activity of synoptic-scale transients in the storm track throughout the troposphere and lower stratosphere. The changes in the surface mean flow and Fh induced by the high-frequency transients, in turn, force the ocean in an anomalous way. Broadly speaking, if the ERA-40 surface flux products represent reality reasonably well, the effect of the anomalous Fh onto the ocean is, with the aid of strong advection by the GS, to enhance the existing SSTAs that appear to be responsible for the B anomalies in the storm track. The effect of the anomalous surface momentum forcing on the GS is, given the typical equivalent-barotropic wind anomalies in a linear framework, also to reinforce the existing anomalies in the latitudinal position and/or the strength of the GS.
In reality, however, such linear thinking has major limitations. First of all, because of the seasonal changes in the mean wind and B, the effect of the same SSTAs on the atmosphere via their effect on B changes from month to month. (Note that the land surface temperature comes into play here as well.) Thus, in an extreme case, an anomaly-reinforcing forcing from the atmosphere to the ocean may change its character to an anomaly-destroying one by the time when the ocean responds to the reinforcing effect from the atmosphere. Also, as demonstrated above, baroclinic wave generation does not necessarily increase when Bx increases in the winter. This type of nonlinear response of the atmosphere makes assessing the nature of the feedback even more difficult.
It has been known that response of the model atmosphere to extratropical SSTAs in various experiments is far from robust—some produce significant response while many others do not (e.g., Kushnir et al. 2002). We offer some possible explanations for the difficulty in obtaining clear-cut results in these experiments. The first issue is the spatial resolution of the model. A slight meridional shift in the position of the GS front and its impact on Bx simply cannot be resolved adequately by a grid spacing of 50 km or larger. To confidently resolve such anomalous Bx and a shift in the narrow band of latent heat release over the GS (R. J. Small 2007, personal communication) we suggest a grid spacing of 20 km or smaller. Also, such a high resolution is needed for the model to delineate the temperature front at the GS and that at the land–sea boundary where the GS flows fairly close to the continent after its separation from the boundary. The high spatial resolution is also required to correctly represent, in a nondiffusive fashion, how small blobs and filaments of potential vorticity produced by breaking large-amplitude synoptic-scale waves become embedded in the larger-scale field. This process is an essential part of the eddy–mean flow interaction that produces large response in the mean flow (e.g., Shutts 1983). If this process is represented in an unrealistically diffusive manner, the positive feedback of synoptic-scale eddies onto the planetary-scale flow that helps produce large amplitude anomalies with an equivalent-barotropic structure does not work effectively.
The second issue is the accuracy of the land temperature produced by the atmospheric simulation model. Even if the Bx anomalies at the oceanic fronts are resolved accurately by the model, the model may not respond to the Bx anomalies at the fronts if the Bx anomalies at the land–sea boundary are much greater than those at the oceanic front. Therefore, the accuracy of the land surface temperature representation in the model is critically important to perform clean experiments to study the effect of SSTAs in the vicinity of the GS on the large-scale atmospheric circulation. Critical assessment of the land surface representation in the models is a must before such experiments are conducted. One possible way to go around this problem is to somehow specify the land surface temperature as well as the SST.
We presented above a look at the extratropical atmospheric variability from a perspective of the surface forcing variability. We strongly believe that this is the way to examine the potential cause–effect relationships between the atmosphere and oceans in the extratropics, in a framework that takes the land temperature into account, since the atmosphere does not distinguish between land and sea. We have some reservation, however, on the validity of this particular study as a comprehensive treatment of baroclinic anomalies arising from the land, sea, and atmosphere, because of the coarse horizontal resolution of the data used in our study, although the data themselves have been produced with nudging toward the observation. To resolve the dominant modes in B arising from the land–sea temperature contrast, one may well need much higher horizontal resolution in the data. Also in question is the reliability of the Fh data used here. The apparent lack of systematic relationship between SSTA and Fh anomalies may be an artifact of poor quality and/or coarse resolution of the Fh data. We suggest that diagnoses of this kind be repeated when such datasets with very high horizontal resolution become available in the future.
We are grateful to Drs. Takeaki Sampe and Shang-Ping Xie for reading the original draft and providing helpful comments that led to improvement of the manuscript. We would also like to thank Dr. Shoshiro Minobe for a discussion that was helpful in improving the manuscript. Finally, we would like to acknowledge two anonymous reviewers and Dr. David Straus for their comments that were helpful in improving the manuscript.
* Current affiliation: Science and Engineering, Doshisha University, Kyotanabe, Kyoto, Japan
Corresponding author address: Mototaka Nakamura, Japan Agency for Marine-Earth Science and Technology, Yokohama, Kanagawa-Pref, 236-0001, Japan. Email: email@example.com