Abstract

This study investigates linkages between the zonal asymmetry of the annular mode (AM) zonal pattern and the subtropical jet (STJ) over its downstream regions of the storm track by using an idealized model. Observational analyses show that the AM zonal patterns are more zonally asymmetric during days when the STJ downstream of the storm track is unusually strong, and vice versa. In the idealized model, the STJ downstream of the storm track is varied by introducing an additional zonally localized tropical heating. The model’s AM variability exhibits a nearly zonally uniform structure when there is no or only weak tropical heating. However, the signatures of the AM are locally strengthened in the heating sector; thus, the AM zonal pattern is zonally asymmetric when the tropical heating is large enough to create a strong STJ. The model results also show that the percentage of the variance explained by the AM, the persistence of the AM index, and the intensity of eddy feedback are also increased when the tropical heating becomes stronger. It is argued herein that the zonal asymmetry of the AM pattern is caused by the zonal asymmetry of the anomalous synoptic eddy forcing projecting on the AM, which is primarily due to the zonal asymmetry of the variations of the storm track between the nonheating and heating sectors.

1. Introduction

a. Motivation

The annular mode (AM; Limpasuvan and Hartmann 1999; Thompson and Wallace 2000) is the dominant pattern of internal variability in the extratropical atmosphere of the Northern Hemisphere (NH) and Southern Hemisphere (SH) on intraseasonal (10–100 days) time scales. Many studies have shown that the fundamental dynamical processes of the growth and maintenance of the AM are dominated by the transient eddy–mean flow interaction (e.g., Limpasuvan and Hartmann 2000). Some studies also offered a straightforward explanation for the origin of the AM, suggesting that the AM arises from the synoptic waves breaking (e.g., Benedict et al. 2004; Rivière and Orlanski 2007) or is a natural outcome of the interaction between synoptic-scale waves and planetary-scale waves (Luo et al. 2007). All of these explanations suggest that the zonal pattern of the AM closely relates to the storm track, and indeed the AM pattern is found to roughly follow the structure of the storm track in observations and in ideal model simulations (Vallis et al. 2004). In the zonal direction, a more zonally “annular” (localized) AM is associated with a more zonally uniform (localized) storm track. Recently, some studies have also revealed that the zonal pattern of the AM is strongly influenced by the boundary topography and land–sea contrast (Cash et al. 2005; Körnich et al. 2006; Gerber and Vallis 2009).

In this study, we highlight the importance of the strong subtropical jet (STJ) downstream of the storm track in setting the observed zonal asymmetry of the AM pattern. This is motivated by following observational analysis results [using 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) daily data]. Figure 1 shows the zonal patterns of the southern annular mode (SAM) during June–August (JJA) and December–February (DJF) and the North Atlantic Oscillation (NAO)1 during DJF (see section 2c for the definition of the AM pattern).

Fig. 1.

(a) The SH 300-hPa geopotential height anomalies (contours) regressed onto the daily southern annular mode (SAM) index during the austral winter (JJA). (b) The NH 300-hPa geopotential height anomalies (contours) regressed onto the daily NAO index during DJF. (c) As in (a), but during the boreal winter (DJF). Zero contours are omitted and the contour interval is 20 m. The shading denotes the corresponding climatological mean storm tracks (m): maximum regions are highlighted by the thick white lines.

Fig. 1.

(a) The SH 300-hPa geopotential height anomalies (contours) regressed onto the daily southern annular mode (SAM) index during the austral winter (JJA). (b) The NH 300-hPa geopotential height anomalies (contours) regressed onto the daily NAO index during DJF. (c) As in (a), but during the boreal winter (DJF). Zero contours are omitted and the contour interval is 20 m. The shading denotes the corresponding climatological mean storm tracks (m): maximum regions are highlighted by the thick white lines.

Let us first discuss the zonal patterns of the AM during the winter season of both hemispheres. In regions where the intensity of the storm track2 is relatively strong, it is not surprising that the zonal patterns of the SAM during JJA and NAO roughly follow the storm track, which reflects the close connection between the AM and the storm track (Vallis et al. 2004; Cash et al. 2005). However, the signatures of the AM tend to be strengthened in regions farther downstream of the maximum of the storm track. Thus, the zonal patterns of the AM are zonally asymmetric with a notable locally strengthened feature. Gerber and Vallis (2009) proposed a clear-cut relationship between the AM and the storm track. They considered that the AM is a large-scale response to the stirring of eddies (Vallis et al. 2004), and thus it tends to occur in regions downstream of the storm track maximum where the baroclinic waves begin to decay and significant eddy momentum fluxes are deposited due to the wave breaking. Therefore, the observed zonal patterns of the SAM during JJA and the NAO are well consistent with the relationship between the AM and the storm track proposed by Gerber and Vallis (2009).

However, the structure of the SAM during DJF exhibits somewhat different behavior.3 The zonal pattern of the SAM during DJF is roughly zonally symmetric/annular without an evident locally strengthened feature over the downstream regions of the maximum of the storm track (its maximum corresponds well to the maximum of the storm track).

The differences of the zonal patterns of the AM between the SAM during DJF and the SAM during JJA or the NAO are also seen in the zonal wind anomalies associated with the AM (Fig. 2). In Fig. 2, the corresponding climatological mean 850-hPa zonal wind roughly represents the structure and location of the eddy-driven midlatitude jet (MLJ). For the SAM during JJA (Fig. 2a) and the NAO (Fig. 2b), the regression patterns show that the zonal wind anomalies associated with the AM are emphasized to represent the south–north shift of the tail of the MLJ, which is consistent with the zonally asymmetric/locally strengthened characteristic of the AM. However, for the SAM during DJF (Fig. 2c), there is a good correspondence between the regression pattern and the location of climatological MLJ, which indicates that the SAM during DJF represents a latitudinal shift of the entire MLJ in the SH.

Fig. 2.

As in Fig. 1, but for the 300-hPa zonal wind anomalies. Zero contours are omitted and the contour interval is 2 m s−1; shading denotes the corresponding climatological mean 850-hPa zonal wind.

Fig. 2.

As in Fig. 1, but for the 300-hPa zonal wind anomalies. Zero contours are omitted and the contour interval is 2 m s−1; shading denotes the corresponding climatological mean 850-hPa zonal wind.

Since the AM in both hemispheres and during different seasons is considered to have the same dynamic mechanism, then the diversity in the zonal patterns of the AM we discussed above may be related to the different background flows. Figure 3 shows the climatological mean 300-hPa zonal wind and storm track for the SH during JJA (Fig. 3a), the NH during DJF (Fig. 3b), and the SH during DJF (Fig. 3c). During JJA, the SH has a strong STJ stretching from the west-central Indian Ocean across the Pacific Ocean located downstream and to the north of the SH storm track. In the NH, over the eastern Atlantic Ocean and North Africa, there is also a strong STJ locating downstream and to the south of the Atlantic storm track. During DJF, however, the SH only has an eddy-driven MLJ, which corresponds well to the storm track and no more evident STJ is found. According to Fig. 3, a common feature in the zonal wind distribution for the AM (the SAM during JJA and NAO), which has a zonally asymmetric characteristic, is noticed: both have a strong STJ over the downstream regions of the storm track. Therefore, we hypothesize that a strong STJ over the downstream regions of the storm track plays an important role in forming the zonal asymmetry of the AM pattern.

Fig. 3.

The climatological mean distribution of the 300-hPa zonal wind (shading, m s−1) and storm track (contours, interval is 20 m) during (a) austral winter (JJA) in the SH, (b) boreal winter (DJF) in the NH, and (c) boreal winter (DJF) in the SH.

Fig. 3.

The climatological mean distribution of the 300-hPa zonal wind (shading, m s−1) and storm track (contours, interval is 20 m) during (a) austral winter (JJA) in the SH, (b) boreal winter (DJF) in the NH, and (c) boreal winter (DJF) in the SH.

b. Objective and approach

According to the above hypothesis, the main objective of the present study focuses on this question: can the STJ over the downstream regions of the storm track cause the zonal asymmetry of the AM pattern?

To answer this question, observational analyses and ideal numerical experiments are both employed. Using reanalysis data, we pick up days when the STJ over the downstream regions of the storm track is uncharacteristically strong and weak and then analyze and compare the zonal patterns of the AM on those days. This analysis is motivated by a simple logical consequence: if, indeed, the STJ influences the zonal pattern of the AM, then the AM patterns on the strong and weak STJ days should be different. This analysis is also an observational basis for further ideal numerical experiments. For acquiring an unambiguous answer for the question that we addressed above, several numerical experiments with a different intensity of the STJ are performed by using a simplified atmosphere model. Also, the zonal patterns of the AM in these numerical experiments are analyzed and compared to investigate the influences of the STJ on the zonal pattern of AM.

The present paper is organized as follows: section 2 outlines the data, model, and experimental setup. The detailed descriptions of the zonal patterns of the AM on the weak and strong STJ days are presented in section 3. Section 4 presents and discusses the results of the numerical experiments. Possible mechanisms responsible for the variations of the zonal pattern of the AM in the model are discussed in section 5. Finally, section 6 provides conclusions and further discussion of this study.

2. Data, experiment setup, and method

a. Data

The reanalysis data used in this study are the ERA-40 daily data (Uppala et al. 2005). The data are archived on 23 pressure levels spanning from 1000 to 1 hPa with a 2.5° × 2.5° horizontal resolution. The data used in this study are confined to boreal winter (DJF) and austral winter (JJA). The ERA-40 daily data cover the time period from 1 September 1957 to 31 August 2002. Hence, we analyze data for 45 northern winters (4050 days in all; 29 February during each leap year has been removed) and 45 southern winters (4140 days in all).

b. Experiment setup

The Geophysical Fluid Dynamics Laboratory (GFDL) dynamical core model (Held and Suarez 1994, hereafter HS94) is used to perform our numerical experiments. This is a dry, sigma (σ = p/ps) coordinate spectral model of primitive equations on the sphere, which is widely used in ideal atmospheric dynamics studies. As a simplified model, only idealized physical parameterizations have been included in this model. Newtonian relaxation toward on an equilibrium temperature Teq profile is used to represent diabatic heating. We set the radiative damping parameter above the planetary boundary layer (above level σ = 0.7) to ka = 30 day−1; the radiative damping parameter within the planetary boundary layer (below σ = 0.7) ks = 2 day−1 everywhere. Rayleigh drag is applied to the three lowermost model levels to represent the frictional effects of the planetary boundary layer. The drag parameter at the surface is set by kf = 1 day−1 and linearly decreases to zero at σ = 0.7. The model also includes a horizontal eighth-order hyperdiffusion ∇8 and the parameter is with a dissipation time scale of day on the smallest resolved scale to remove enstrophy.4

In the present study, four integrations are carried out with a horizontal resolution of T42, using 10 evenly spaced sigma levels in the vertical. The zonal symmetry of Teq profile is broken by a cooling anomaly centered at roughly 60° latitude to generate localized baroclinic regions similar to observations. Downstream of the high-latitude cooling, an additional heating with a variable intensity centered at the equator for controlling the intensity of the STJ is introduced into the Teq profile as well. The form of the additional cooling and heating is taken from the sea surface temperature anomalies used in Brayshaw et al. (2008) with a little modification and is given by

 
formula
 
formula
 
formula

where θ denotes the longitude, φ is the latitude, φ0 is the latitudinal center of the cooling or heating, φw = 20° is the latitudinal width, and c and h are the maximum amplitude of cooling and heating, respectively. The parameter α, as used by Son and Lee (2005), is introduced in the cooling and heating both to make sure the strong meridional temperature gradients created by the cooling are concentrated in the lower troposphere and to increase heating in the tropical upper troposphere. The magnitude of the additional high-latitude cooling is fixed in the four ideal experiments to produce approximately unchanged high-latitude baroclinic regions. The only difference between these four experiments is the intensity of the additional tropical heating. One experiment is performed with no additional tropical heating (Exp_0k), and the other three experiments include weak (Exp_5k), medium (Exp_10k), and strong tropical heating (Exp_15k).

We use the Teq profile of HS94, which is contained in the model codes with a modification of the reference temperature from 315 to 305 K. This slight adjustment makes the tropical temperature closer to observations during DJF. Because in the present study the localized strong baroclinic regions are produced by adding the additional high-latitude cooling, we also alter the equator and polar temperature difference (ΔT)y from 60 to 30 K, which is more suitable to represent the situation of the weak baroclinic regions in the earth. The spatial distribution of Teq including the additional high-latitude cooling and tropical heating at the lowermost model level for the Exp_10k integration is shown in Fig. 4. Also, we define a nonheating sector between 0° and 180° and a heating sector between 180° and 360°.

Fig. 4.

The distribution of Teq on the lowermost model level for Exp_10k (K).

Fig. 4.

The distribution of Teq on the lowermost model level for Exp_10k (K).

These four experiments are outlined in Table 1. In this study, the model is run for 6200 days for each integration. The model output of the last 6000 days is analyzed. To make sure that the zonal pattern of the AM extracted from the model results is robust, we also analyze the ensemble mean zonal patterns of the AM by dividing the total 6000-day model output into four members (each member has a 1500-day output). Because the NH and SH in these experiments are symmetric in their statistics, for each experiment we can double the number of ensemble members by adopting the SH results, that is, eight members for each ensemble. It is found that the zonal patterns of the AM extracted from the 6000-day model output and the ensemble mean results are almost the same. Therefore, the 6000-day integration time is long enough to obtain a stable AM pattern. For sake of brevity, we do not show the ensemble results in this study.

Table 1.

Prescribed parameters for four experiments performed for our study.

Prescribed parameters for four experiments performed for our study.
Prescribed parameters for four experiments performed for our study.

c. The definition of the AM pattern

In this study, the AM pattern is defined as the 300-hPa geopotential height anomalies (defined as the deviation of a long-term mean) regressed onto the daily AM indices. In the observational analysis, the DJF (JJA) daily SAM index is defined as the first principal component (PC1) of the SH daily 700-hPa geopotential height anomalies (20°–90°S) during DJF (JJA). The daily NAO index is defined as the PC1 of the DJF daily sea level pressure (SLP) anomalies over the Atlantic region (20°–85°N, 90°W–50°E). In the model analysis, the daily AM index is defined as the PC1 of the NH daily SLP anomalies (20°–90°N). Before the performance of empirical orthogonal function (EOF) analysis, the data were weighted by the square root of the cosine of latitude to account for the decrease of grid area toward the pole.

d. The eddy feedback diagnostic procedure

In this study, we also use the vorticity budget and eddy feedback diagnostic procedure developed by Barnes and Hartmann (2010a,b) to quantitatively analyze the eddy feedback intensity of the AM. The intensity of the eddy feedback is derived from the lag cross correlation between the eddy forcing time series z and the index of the AM. The eddy forcing time series z is acquired by projecting the daily mass-weighted upper-level (σ = 0.1, 0.2, and 0.3) eddy forcing field − · (ζU′) onto the mass-weighted lower-level (σ = 0.9, 0.8, and 0.7) relative vorticity anomalies associated with the AM [for details of this procedure, see Barnes and Hartmann (2010a,b)]. In this study, the total and synoptic eddy forcing fields are defined as − · (ζU′) by using the unfiltered and 2–7-day bandpass-filtered (using a Lanczos filter with 31 weights) results of the anomalous horizontal wind U′ and the vorticity ζ′.

3. Observational analyses

To investigate the influences of the STJ on the zonal pattern of the AM by utilizing the reanalysis data, in this section we show and compare the AM patterns on the days when the downstream STJ is unusually strong and weak. An index describing the STJ intensity is defined as the zonal wind speeds averaged over a downstream box region of the storm track. The strong and weak STJ days are picked out according to the 1.0 standard deviation of this intensity index. In the SH (NH), the box region is located at subtropics of the southern Indian Ocean (North Atlantic Ocean) at 10°–30°S, 60°–120°E (10°–30°N, 60°W–0°), and there are 650 (619) strong STJ days and 678 (650) weak STJ days picked out from the 45 austral (boreal) winters.

Figure 5 shows the great differences between the days when the downstream STJ is unconventionally strong and weak in the SH. Clearly, over the subtropical regions of the southern Indian Ocean, the averaged STJ on the strong (weak) STJ days is stronger (weaker) than the climatological value. In the strong STJ days, the SAM midlatitude node5 over the southern Indian Ocean is significantly localized over the downstream of the maximum of the storm track (west of Australia; see Fig. 5c), and the zonal wind anomalies associated with the SAM over the southern Indian Ocean are concentrated at the tail of the MLJ (see Fig. 5e). In contrast, on the weak STJ days the SAM midlatitude node over the southern Indian Ocean is much broader in the zonal direction, following the structure of the storm track, and the maximum of this SAM node well corresponds to the maximum of the storm track (see Fig. 5d). The zonal wind anomalies associated with the SAM are also mainly located at the middle part of the MLJ (see Fig. 5f).

Fig. 5.

(a) The SH average 300-hPa zonal wind distribution, (c) the SH 300-hPa geopotential height anomalies (contours, interval is 20 m), and (e) 300-hPa zonal wind anomalies (contours; interval is 2 m s−1) regressed onto the daily SAM index on the strong subtropical jet (STJ) days. (b),(d),(f) As in (a),(c), and (e), respectively, but on the weak STJ days. The shading denotes the corresponding average 300-hPa storm track in (c) and (d) and the average 850-hPa zonal wind in (e) and (f). The maximum regions of storm track are highlighted by thick white lines.

Fig. 5.

(a) The SH average 300-hPa zonal wind distribution, (c) the SH 300-hPa geopotential height anomalies (contours, interval is 20 m), and (e) 300-hPa zonal wind anomalies (contours; interval is 2 m s−1) regressed onto the daily SAM index on the strong subtropical jet (STJ) days. (b),(d),(f) As in (a),(c), and (e), respectively, but on the weak STJ days. The shading denotes the corresponding average 300-hPa storm track in (c) and (d) and the average 850-hPa zonal wind in (e) and (f). The maximum regions of storm track are highlighted by thick white lines.

The analogous analysis results for the NAO are shown in Fig. 6. The results show that the NAO patterns and the associated zonal wind anomalies on the strong and weak STJ days differ greatly from each other, too. On the weak STJ days, the maximum of the NAO pattern and its associated zonal wind anomalies are located in the east-central Atlantic Ocean. In contrast, on the strong STJ days the NAO has a significant downstream displacement shifting to the coastlines of Europe. From Figs. 5 and 6, it can be inferred that, indeed, the zonal patterns of the AM are different on the strong and weak downstream STJ days. Signatures of the AM become more prominent over the downstream regions of the maximum of the storm track when the downstream STJ is strong. Thus, the AM patterns are zonally asymmetric. In contrast, the maximum of the signatures of the AM overlaps with that of the storm track and the zonal patterns of the AM are relatively zonally symmetric (annular) when the downstream STJ is weak.

Fig. 6.

As in Fig. 5, but for the NH and regressing onto the daily NAO index on (a),(c),(e) strong and (b),(d),(f) weak STJ days.

Fig. 6.

As in Fig. 5, but for the NH and regressing onto the daily NAO index on (a),(c),(e) strong and (b),(d),(f) weak STJ days.

One might argue that the STJ may not be considered as an independent factor in observations. During the positive phase of the AM, the MLJ and STJ are well separated, whereas in the negative AM phase they are merged together. Thus, observed variations of the AM patterns on the strong and weak STJ days may relate to the different phases of the AM and reflect the variability between the positive and negative phases of the AM rather than the influences of the downstream STJ. We calculate the average AM index during the high and low STJ index states. The results show that the average NAO index is about −0.346 (0.151) and the average SAM index is −0.232 (0.137) during the high (low) STJ index state, which indicates that the high (low) STJ index state is linked to the negative (positive) phase of the AM. However, we still insist that the variations of the AM patterns between the strong and weak STJ days reflect the influence of the STJ on the zonal pattern of the AM. This is for two main reasons. 1) Indeed, the variations of the NAO pattern during the positive and negative phases are evident (Cassou et al. 2004). However, it should be pointed out that the action centers of the NAO have a significant eastward displacement for the positive NAO phase compared to the negative NAO phase (Cassou et al. 2004). Our observational results show that the action centers of the NAO have an eastward (westward) shift in the high (low) STJ index state, which corresponds to the negative (positive) NAO phase. 2) Furthermore, no evidence supports the idea that the zonal patterns of the SAM are different during the positive and negative SAM phases.

The results given in this section showing that AM patterns are different between the strong and weak STJ days are robust. We also repeat these analyses based on half of the available data, or based on STJ indices’ 1.5 or 0.5 standard deviations. These results are similar to the results of 1.0 standard deviation of the STJ intensity index. We also calculate the composites of the AM patterns based on the standard AM index on strong and weak STJ days and the variations of the AM patterns are also similar to the results shown here.

4. Experimental results

In this section, we present the results of four ideal numerical experiments that differ only in the intensity of downstream STJ to investigate the influences of the STJ on the zonal patterns of the AM.

a. Variations of the zonal patterns of the AM

The climatological mean 300-hPa zonal wind distributions and the meridional gradients of the 850-hPa temperature of the four experiments are collectively shown in Fig. 7. The strong meridional gradients of the 850-hPa temperature above the center of the panels produced by the high-latitude cooling denote the strong baroclinic regions. Eddies grow intensely by extracting mean flow available potential energy in strong baroclinic regions and begin to develop downstream (Chang and Orlanski 1993). In the Exp_0k integration, there is no additional tropical heating. In the other three integrations, to control the intensity of the downstream STJ, an additional localized tropical heating with a different intensity downstream of the strong baroclinic regions (thus downstream of the storm track) is introduced into the model. The strong meridional temperature gradients located at lower latitudes roughly represent the longitudes of the tropical heating. In the Exp_0k integration, there is only one eddy-driven MLJ, while in the Exp_5k and Exp_10k integrations, downstream of the strong baroclinic regions, there is an additional STJ produced by the tropical heating through enhancing the Hadley cell located downstream and to the south of the MLJ. The STJ and the MLJ are well separated, and clearly there is a double jet structure. In the Exp_15k integration, the STJ is so strong that the double jet structure disappears and there is only one single strong jet downstream of the strong baroclinic regions (see Fig. 7d). This is in agreement with Lee and Kim (2003), who investigated the relationship between the latitudinal positions of the eddy-driven MLJ and the strength of the STJ and found that the MLJ and STJ merge together and a single jet structure is seen in the troposphere when the STJ is sufficient strong.

Fig. 7.

The climatological mean 300-hPa zonal wind distributions (shading; m s−1) and the meridional gradients of the 850-hPa temperature (contours) for (a) Exp_0k, (b) Exp_5k, (c) Exp_10k, and (d) Exp_15k. Solid (dashed) contours are positive (negative) and zero contours are omitted. The contour interval is 2 × 10−6 K m−1.

Fig. 7.

The climatological mean 300-hPa zonal wind distributions (shading; m s−1) and the meridional gradients of the 850-hPa temperature (contours) for (a) Exp_0k, (b) Exp_5k, (c) Exp_10k, and (d) Exp_15k. Solid (dashed) contours are positive (negative) and zero contours are omitted. The contour interval is 2 × 10−6 K m−1.

The AM patterns and the corresponding climatological mean storm track of the four integrations are shown in Fig. 8. In the Exp_0k integration, the storm track is roughly annular and the maximum of the storm track is located just downstream of the strong baroclinic regions. Compared to the storm track in the Exp_0k integration, in the other three integrations the maximum of the storm track is located farther downstream. We also notice that in the integrations with additional tropical heating, the storm tracks become a little stronger and have an equatorward shift relative to the Exp_0k integration. This is consistent with the results of previous studies indicating that a Hadley cell that is enhanced due to tropical heating would cause the MLJ and storm track to become stronger and shift equatorward (Chang 1995; Lee and Kim 2003; Brayshaw et al. 2008).

Fig. 8.

The 300-hPa geopotential height anomalies (m) regressed onto the daily AM index (contours; interval is 20 m) for (a) Exp_0k, (b) Exp_5k, (c) Exp_10k, and (d) Exp_15k. The shading denotes the corresponding average 300-hPa storm track.

Fig. 8.

The 300-hPa geopotential height anomalies (m) regressed onto the daily AM index (contours; interval is 20 m) for (a) Exp_0k, (b) Exp_5k, (c) Exp_10k, and (d) Exp_15k. The shading denotes the corresponding average 300-hPa storm track.

Besides the changes of the storm track, the point that we try to highlight is the great changes of the AM patterns when the localized tropical heating is introduced into the model. Although the midlatitude lobe of the AM in the Exp_0k integration has two action centers downstream of the storm track, nevertheless, generally speaking, the entire zonal pattern of the AM is zonally symmetric (annular) without an evident locally strengthened characteristic downstream of the storm track. In the Exp_5k integration, the AM pattern is similar to that of the Exp_0k integration except that amplitude of the AM polar lobe and the action centers of the AM midlatitude lobe become stronger, and the AM polar lobe has a slight downstream displacement, but the AM pattern is still relatively zonally symmetric. However, in the Exp_10k and Exp_15k integrations, the midlatitude lobe of the AM becomes significantly prominent downstream of the storm track and the polar lobe of AM also shifts away from the pole, concentrating over the downstream regions of the storm track. Once the model has a strong enough STJ downstream of the storm track, the signatures of the AM are strengthened over the downstream regions of the maximum of the storm track; thus, the AM pattern becomes zonally asymmetric with no more annular features. This conclusion is also confirmed by zonal wind anomalies associated with the AM shown in Fig. 9. In the Exp_0k integration, the 300-hPa zonal wind anomalies associated with the AM indicate that the AM represents the south–north shift of the entire MLJ. In contrast, in Exp_10k and Exp_15k the zonal wind anomalies associated with the AM emphasize a latitudinal displacement of the tail of the MLJ.

Fig. 9.

The 300-hPa zonal wind anomalies (m s−1) regressed onto the daily AM index (contours; interval is 2 m s−1) for (a) Exp_0k, (b) Exp_5k, (c) Exp_10k, and (d) Exp_15k. The shading denotes the corresponding average 850-hPa zonal wind.

Fig. 9.

The 300-hPa zonal wind anomalies (m s−1) regressed onto the daily AM index (contours; interval is 2 m s−1) for (a) Exp_0k, (b) Exp_5k, (c) Exp_10k, and (d) Exp_15k. The shading denotes the corresponding average 850-hPa zonal wind.

b. Persistence of the AM and eddy feedback intensity

In the Exp_0k, Exp_5k, Exp_10k, and Exp_15k experiments, the explanation variances of the AM are 10.73%, 14.78%, 24.27%, and 30.85%, respectively. It seems that the changes in the intensity of the downstream STJ in the model not only remodel the AM pattern but also greatly increase the percentage of the variance explained by the AM in the EOF analysis. The autocorrelation functions of the AM index for these four experiments are shown in Fig. 10. Consistent with the increasing explanation variances of the AM, the persistence of the AM index become much longer as well from Exp_0k to Exp_15k. These results are consistent with the viewpoint that the persistence of each EOF is an important factor contributing to the explained variance of the corresponding EOF (Lorenz and Hartmann 2001). The longer persistence of the AM index also suggests that the positive eddy feedback becomes much stronger. To support this argument, we perform a quantitative analysis about the eddy feedback intensity in the four ideal experiments by using the vorticity budget and eddy feedback diagnostic procedure developed by Barnes and Hartmann (2010a,b).

Fig. 10.

The autocorrelations of the AM index in the four ideal experiments.

Fig. 10.

The autocorrelations of the AM index in the four ideal experiments.

The cross correlations between the z time series of eddy forcing and the AM index for the total (Fig. 11a) and synoptic eddy (Fig. 11b) in the four ideal experiments are shown in Fig. 11. The negative (positive) lag days denote that the eddy forcing leads (lags) the AM index. Generally speaking, the shapes of the cross correlations of the four experiments are well consistent with many other previous studies (e.g., Lorenz and Hartmann 2001). The cross correlations are always maximal when the eddy forcing leads the AM by a few days, suggesting that the AM is “driven” by the eddy forcing. Because of the negative correlation of the low-frequency eddy forcing (not shown), the cross correlations between the total eddy forcing and AM index have a sharp drop when the eddy forcing immediately lags the AM. The positive cross correlations from 0 to 30 days indicate that there is a positive feedback between the eddy forcing and the circulation anomalies associated with the AM. Larger positive cross correlations would help increase the persistence of the AM pattern. From Fig. 11, we observe great differences in the cross correlations among the four experiments. With the increase in intensity of the downstream STJ, the cross correlations become higher, indicating that the positive eddy feedback is stronger.

Fig. 11.

Cross correlations between the z time series and AM index for (a) total eddy forcing and (b) synoptic eddy forcing in the four ideal experiments. (c),(d) As in (b), but for synoptic eddy forcing over the nonheating and heating sectors in the four ideal experiments, respectively.

Fig. 11.

Cross correlations between the z time series and AM index for (a) total eddy forcing and (b) synoptic eddy forcing in the four ideal experiments. (c),(d) As in (b), but for synoptic eddy forcing over the nonheating and heating sectors in the four ideal experiments, respectively.

We also analyze the eddy feedback intensity over the nonheating (0°–180°; in this sector there is no additional tropical heating/STJ) and heating sectors (180°–360°; the additional tropical heating/STJ is confined in this sector), respectively. The cross correlations between the z time series of synoptic eddy forcing and the AM index for the nonheating (Fig. 11c) and heating sectors (Fig. 11d) in the four experiments are also shown in Fig. 11. Compared to the experiment Exp_0k, although the positive eddy feedback over the nonheating sector in the other three experiments also becomes stronger, it is clear that the eddy feedback intensity over the heating sector has a rapid increase, which indicates that the increasing intensity of the eddy feedback mainly occurs over the heating sector.

5. Mechanisms

In section 4, the model results show that the signatures of the AM tend to be strengthened over the heating sector when a sufficiently strong STJ over the downstream region of the storm track is introduced into the model. Thus, the AM pattern becomes zonally asymmetric. In this section, we examine the physical mechanisms that might determine the zonal asymmetry of the AM pattern in our ideal experiments. We place the emphasis on the results of the experiments Exp_0k and Exp_15k.

a. Zonal asymmetry of the anomalous synoptic eddy forcing

Figure 12 shows the regression patterns of 300-hPa vorticity (shading) and synoptic eddy forcing (contours) anomalies on the AM index at day 0 to represent the amplitude of the AM signals and the synoptic eddy forcing anomalies projecting onto the AM pattern. From Exp_0k to Exp_15k, all anomalous synoptic eddy forcing fields overlay well with the vorticity anomalies associated with the AM, which is consistent with the viewpoint that the AM structure is driven/maintained by the eddy forcing. From Fig. 12, we notice that unlike the nearly zonally symmetric pattern in Exp_0k and Exp_5k, the regressed anomalous synoptic eddy forcing patterns in Exp_10k and Exp_15k tend to have the highest amplitude in the longitudinal sectors where the signatures of the AM are strongest (i.e., the heating sector). It should be pointed out that, although the regression results shown in Fig. 12 are the results at day 0, the zonally symmetric (asymmetric) feature of the anomalous synoptic eddy forcing associated with the AM in Exp_0k and Exp_5k (Exp_10k and Exp_15k) is robust when we regress the synoptic eddy forcing anomalies against the AM index at the leading or lagging days (not shown). To highlight the zonal symmetry or asymmetry of the AM pattern and the anomalous synoptic eddy forcing projecting onto the AM, we show the zonal mean results of the regressed vorticity anomalies at 0 days and the synoptic eddy forcing anomalies at 0 days and at +20 days over the heating and nonheating sectors of Exp_0k and Exp_15k (Fig. 13). In Exp_0k, nearly identical curves of the heating and nonheating sectors indicate that the anomalous synoptic eddy forcing projecting on the AM is zonally symmetric, and so is the AM pattern. However, in Exp_15k, consistent with stronger AM signatures, the amplitude of the anomalous synoptic eddy forcing curves of the heating sector is stronger than that of the nonheating sector, indicating a strong zonal asymmetry of the anomalous synoptic eddy forcing. We also notice that the amplitude of the anomalous synoptic eddy forcing projecting on the AM in the experiment Exp_15k is still remarkable even at +20 days, which is consistent with the longer persistence of the AM index and stronger positive eddy feedback intensity of Exp_15k, shown in Figs. 10 and 11.

Fig. 12.

The synoptic eddy forcing (contours; interval is 1 × 10−11 s−2) and vorticity (shading; 1 × 10−6 s−1) anomalies at 300 hPa regressed onto the daily AM index for (a) Exp_0k, (b) Exp_5k, (c) Exp_10k, and (d) Exp_15k.

Fig. 12.

The synoptic eddy forcing (contours; interval is 1 × 10−11 s−2) and vorticity (shading; 1 × 10−6 s−1) anomalies at 300 hPa regressed onto the daily AM index for (a) Exp_0k, (b) Exp_5k, (c) Exp_10k, and (d) Exp_15k.

Fig. 13.

Sectoral zonal mean results of (a),(b) regressed vorticity and (c),(d) synoptic eddy forcing anomalies shown in Fig. 12 in the heating (solid) and nonheating (dashed) sectors for (a),(c) Exp_0k and (b),(d) Exp_15k. The gray solid and dashed lines in (c) and (d) denote the regressed 20-day-lag synoptic eddy forcing anomalies.

Fig. 13.

Sectoral zonal mean results of (a),(b) regressed vorticity and (c),(d) synoptic eddy forcing anomalies shown in Fig. 12 in the heating (solid) and nonheating (dashed) sectors for (a),(c) Exp_0k and (b),(d) Exp_15k. The gray solid and dashed lines in (c) and (d) denote the regressed 20-day-lag synoptic eddy forcing anomalies.

Given that the flow anomalies of the AM are considered to be mainly forced and maintained by the synoptic eddy forcing anomalies (see section 4b), the zonal asymmetry of the AM pattern can be considered as resulting from the zonal asymmetry of the synoptic eddy forcing anomalies. In our understanding, the synoptic eddy forcing anomalies come from three sources: 1) deformations of eddy structures, 2) variations of the eddy position (i.e., variations of the storm track), and 3) changes of the eddy intensity. Therefore, the zonal asymmetry of the anomalous synoptic eddy forcing must arise from the zonal asymmetry of the aforementioned three aspects, since in the model setting, factors such as baroclinicity, surface friction, and damping terms that influence the eddy intensity are not changed in the four experiments. Therefore, here we attempt to explain the zonal asymmetry of the synoptic eddy forcing anomalies from the zonal asymmetry of these two perspectives: (a) alterations of the synoptic eddy structures and (b) variations of the storm track.

b. Altering the synoptic eddy structures

To examine the spatial structures of the synoptic eddy, we calculate one-point correlation maps of 2–7-day bandpass-filtered 300-hPa geopotential height at every grid point of a middle-latitude band (30°–60°N) where the eddy activity is strongest. We depict the typical synoptic eddy structures of the heating and nonheating sectors by averaging all the one-point correlation maps in the heating and nonheating sectors6 to investigate the possible zonal asymmetry of the altering of the eddy structures. In such an analysis, the one-point correlation maps are shifted in longitude and latitude before averaging so that the base points of the one-point correlation maps will coincide. For acquiring the typical eddy structures of a normal condition (i.e., climatology or undisturbed), the composite processes are performed for all 6000 days. For the typical eddy structures of positive (negative) AM phase condition, the composite processes are performed on the days that the AM index is equal to or greater (less) than 1.0 (−1.0).7

Figure 14 shows the typical eddy structures of (top) the normal condition and the (middle) positive and (bottom) negative AM phase conditions in the heating and nonheating sectors of Exp_15k.8 Under normal conditions, the eddy structures in the heating and nonheating sectors are zonally asymmetric. Compared to the nonheating sector, the eddy structures in the heating sector have a significant tilt in the northeast–southwest direction, indicating that the synoptic wave trains in the heating sector have an evident equatorward propagation characteristic, which obviously reflects the influences of the STJ on the propagation of the synoptic wave train. Previous studies have shown that an STJ located downstream and equatorward of the MLJ may act like a waveguide (Hoskins and Ambrizzi 1993), affecting wave propagation. Chang (1999) had shown that, in observations, the upstream baroclinic wave train propagating along the upstream MLJ splits into two branches, with a stronger tendency to propagate toward the subtropical latitudes than toward the higher latitudes (see Figs. 10 and 11 in Chang 1999). Seager et al. (2003, 2010) also showed in their numerical model that the tropical heating alters the upper-level background flows in the subtropics, so that transient eddies propagate farther equatorward.

Fig. 14.

Composites of the one-point correlation maps (contours, interval is 0.1) of 2–7-day bandpass-filtered geopotential height at 300 hPa during the (top) normal, (middle) positive, and (bottom) negative AM phase conditions that depict the synoptic eddy structures of Exp_15, showing results for the (left) heating and (right) nonheating sector. Shading denotes vorticity anomalies (s−1) aroused by the altering of eddy structures. Black contours denote the results in the normal condition; red and blue contours denote the results in the positive and negative AM phase conditions, respectively.

Fig. 14.

Composites of the one-point correlation maps (contours, interval is 0.1) of 2–7-day bandpass-filtered geopotential height at 300 hPa during the (top) normal, (middle) positive, and (bottom) negative AM phase conditions that depict the synoptic eddy structures of Exp_15, showing results for the (left) heating and (right) nonheating sector. Shading denotes vorticity anomalies (s−1) aroused by the altering of eddy structures. Black contours denote the results in the normal condition; red and blue contours denote the results in the positive and negative AM phase conditions, respectively.

Under the AM positive (negative) phase condition, the eddy structures in the heating and nonheating sectors both systematically tilt in the northeast–southwest (northwest–southeast) direction compared to the normal condition. We argue that the tilts of the eddy structures result from the interaction between synoptic-scale eddies and the large-scale flow anomalies associated with the AM. There are two possible explanations. 1) The tilts of the eddy structures can be explained as a result of the large-scale flow anomalies associated with the AM stirring and deforming the synoptic eddy. The positive (negative) AM phase corresponds to the poleward (equatorward) shift of the MLJ and thus is associated with a dipole structure of the zonal wind anomalies—that is, westerly (easterly) wind anomalies in the high latitudes and easterly (westerly) wind anomalies in the midlatitudes. Therefore, under the flow anomalies associated with the positive (negative) AM phase, the synoptic eddy structures are systematically deformed into the northeast–southwest (northwest–southeast) tilt. 2) The tilts of the eddy structures can also be explained by the different wave breaking types resulting from the meridional shift of the MLJ. It is well known that the wave breaking can be divided into anticyclonic and cyclonic types, which, in the NH, correspond to the northeast–southwest and northwest–southeast tilts of the eddy structures, respectively (Thorncroft et al. 1993). Rivière (2009) proved that a baroclinic wave tends to break in the anticyclonic (cyclonic) manner when it develops and propagates at higher (lower) latitudes. Therefore, for the positive (negative) AM phase, which corresponds to a higher (lower)-latitude MLJ, the synoptic waves tend to break in the anticyclonic (cyclonic) way; thus, the eddy structures appear with a northeast–southwest (northwest–southeast) tilt.

Because of the systematic tilts of the synoptic eddy structures, compared to the eddy structures of the normal condition (or undisturbed eddy), anomalous vorticity patterns of the synoptic eddies (shaded areas in Fig. 14) are generated. It is noted that the anomalous vorticity patterns of the synoptic eddies shown here are similar to the results of Ren et al. (2009, see their Figs. 3 and 4) and of Jin (2010, see his Fig. 2). As illustrated by Jin (2010), the anomalous vorticity patterns associated with the northeast–southwest (northwest–southeast)-tilted synoptic eddies led to an anomalous divergence (convergence) of eddy vorticity flux into the center of the eddies. Therefore, the deformations of the synoptic eddy structures serve to maintain the existence of the anomalous circulation associated with the AM (Ren et al. 2009).

To highlight the zonal asymmetry of the anomalous synoptic eddy forcing due to the altering of the eddy structures in the heating and nonheating sectors, Fig. 15 shows the zonal mean results of the eddy forcing associated with the typical synoptic eddy in the heating and nonheating sectors under normal and AM conditions (Fig. 15a). The anomalous synoptic eddy forcing defined as the differences of the eddy forcing between the AM conditions and normal condition is also shown (Fig. 15b). For the calculation of − · (ζU′) associated with the typical synoptic eddy, first, as in the calculation of the one-point correlation maps, we use the normalized 2–7-day bandpass-filtered 300-hPa geopotential height at every base point as a time series to regress the 2–7-day bandpass-filtered 300-hPa vorticity and wind fields to obtain the vorticity and wind fields associated with the synoptic eddy. Then, we calculate − · (ζU′). Thus, every base point has an eddy forcing field. Also, the synoptic eddy forcing associated with the typical synoptic eddy in the heating (nonheating) sector is acquired by averaging all the eddy forcing fields in the heating (nonheating) sector (not shown). It should be pointed out that the longitude range for the zonal mean calculation is confined in a narrow sector (−20° to 20°) since the eddy forcing is mainly located in that narrow longitude band (not shown).

Fig. 15.

(a) Sectoral zonal mean results of composites of the synoptic eddy forcing associated with the synoptic eddy in the heating and nonheating sectors during normal (black), positive (red), and negative (blue) AM phase conditions in Exp_15k. The solid (dashed) lines represent the results in the heating (nonheating) sector. (b) As in (a), but for the synoptic eddy forcing anomalies under the positive and negative AM phase conditions.

Fig. 15.

(a) Sectoral zonal mean results of composites of the synoptic eddy forcing associated with the synoptic eddy in the heating and nonheating sectors during normal (black), positive (red), and negative (blue) AM phase conditions in Exp_15k. The solid (dashed) lines represent the results in the heating (nonheating) sector. (b) As in (a), but for the synoptic eddy forcing anomalies under the positive and negative AM phase conditions.

From Fig. 15 we see that the zonal mean eddy forcing associated with the synoptic eddy is characterized by a south–north dipole structure (positive at higher latitudes and negative at lower latitudes), indicating that the synoptic eddies transport positive (negative) vorticity into higher (lower) latitudes (see Fig. 15a). Under the positive (negative) AM phase condition, the eddy forcing anomalies correspond to a divergence (convergence) of eddy vorticity in the center of the eddy (see Fig. 15b), as illustrated by Jin (2010).

Relative to the normal condition, the zonal mean results also show that the intensity of the eddy forcing in the positive (negative) AM phase condition becomes stronger (weaker) with a poleward (equatorward) displacement. Clearly, this is due to the anomalous northeast–southwest (northwest–southeast) tilt of the synoptic eddy (see Fig. 14). We also notice that there is a notable zonal asymmetry between the eddy forcing associated with the synoptic eddy in the heating and nonheating sectors whether under the normal or the AM conditions. Generally speaking, the intensity of the eddy forcing in the heating sector is stronger than that in the nonheating sector. However, for the eddy forcing anomalies, it should be underscored that the zonal asymmetry between the heating and nonheating sectors is relatively weak, which suggests that the zonal asymmetry of the altering of the eddy structure is not the primary reason for the zonal asymmetry of the anomalous synoptic eddy forcing projecting onto the AM, even though the eddy structures and the intensity of the eddy forcing do have a significant zonal asymmetry between the heating and nonheating sectors.

c. Variations of the storm track

In this subsection, we investigate the zonal asymmetry of the variations of the storm track. Figure 16 shows the spatial distributions of the climatological storm track (the normal condition) and the storm track in the positive and negative AM phase conditions in Exp_0k and Exp_15k. The red lines in Fig. 16 correspond to the latitudes of the maximum of the climatological storm track (i.e., the axis or core of the storm track). It is clear that the climatological storm track of Exp_0k primarily extends in the zonal direction without evident displacements in the meridional direction. In contrast, the climatological storm track of Exp_15k has a notable equatorward deflection in the heating sector, which is consistent with the equatorward propagation characteristic of the synoptic wave train in that sector (see Fig. 14).

Fig. 16.

Composites of the storm track at 300 hPa during the (top) normal (climatology), (middle) positive, and (bottom) negative AM phase conditions for (left) Exp_0k and (right) Exp_15k. The interval of the contours is 10 m and the minimum value of the contours is 40 m. Red lines denote the axis of the climatological storm track.

Fig. 16.

Composites of the storm track at 300 hPa during the (top) normal (climatology), (middle) positive, and (bottom) negative AM phase conditions for (left) Exp_0k and (right) Exp_15k. The interval of the contours is 10 m and the minimum value of the contours is 40 m. Red lines denote the axis of the climatological storm track.

Under the positive (negative) AM phase condition, the entire storm track of Exp_0k is symmetrically shifted poleward (equatorward) compared to the climatology. Thus, the variations of the storm track in Exp_0k are zonally symmetric. The variations of the storm track in the nonheating sector of Exp_15k also share a similar characteristic. However, the variations of the storm track in the heating sector of Exp_15k are strikingly different. Under the positive AM phase condition, the storm track in the heating sector has a remarkable poleward shift relative to its climatological position. However, we notice that during the positive AM phase the storm track in the heating sector is not located in latitudes higher than that of the storm track in the nonheating sector. Therefore, the stronger poleward shifting of the storm track in the heating sector is primarily due to the fact that the climatological storm track in the heating sector has an evident equatorward deflection. The storm track in the heating sector is basically confined in the subtropical regions and becomes very narrow with a slight equatorward displacement when the AM phase is negative. These results indicate that for Exp_15k there is a remarkable zonal asymmetry of the variations of storm track between the nonheating and heating sectors.

To clearly demonstrate the zonal asymmetry of the variations of the storm track in Exp_15k, the sectoral zonal mean results of the storm track in the heating and nonheating sectors under the normal and AM conditions are shown in Figs. 17a and 17b. As stated above, under the positive AM phase condition the storm track in the heating sector has stronger poleward shifting. Under the negative AM phase condition, the width of the storm track in the heating sector is very narrow. We also notice that for the storm track in the heating sector, under the positive (negative) AM phase condition, its intensity is obviously stronger (weaker) than its climatological value. We will briefly discuss the possible physical mechanism responsible for that later. The key conclusion from Figs. 16 and 17 is that there is an evident zonal asymmetry of the variations of the storm track between the nonheating and heating sectors in Exp_15k.

Fig. 17.

Sectoral zonal mean results of composites of the (a),(b) storm track and (c),(d) synoptic eddy forcing at 300 hPa in the (a),(c) heating and (b),(d) nonheating sectors under the normal (solid), positive (dashed), and negative (dotted) AM phase conditions for Exp_15k.

Fig. 17.

Sectoral zonal mean results of composites of the (a),(b) storm track and (c),(d) synoptic eddy forcing at 300 hPa in the (a),(c) heating and (b),(d) nonheating sectors under the normal (solid), positive (dashed), and negative (dotted) AM phase conditions for Exp_15k.

We argue that the zonal asymmetry of the synoptic eddy forcing anomalies that we discussed in section 5a results from the zonal asymmetry of the variations of the storm track. To support this argument, the sectoral zonal mean results of the synoptic eddy forcing in the heating and nonheating sectors under the normal and AM conditions are also shown in Figs. 17c and 17d. It is clear that the differences of the synoptic eddy forcing between the normal and AM conditions (i.e., the anomalous synoptic eddy forcing) in the heating sector are greater than that in the nonheating sector, which is consistent with the zonal asymmetry of the anomalous synoptic eddy forcing. Under the positive AM phase condition, the greater synoptic eddy forcing anomalies in the heating sector are primarily due to (a) the stronger storm track and (b) the stronger poleward shifting of the storm track. Because the poleward shifting of the storm track in the heating sector is more pronounced, the difference of the synoptic eddy forcing between the normal and positive AM phase condition is also greater than that in the nonheating sector. Thus, even if the intensity of the storm track does not become stronger, the anomalous synoptic eddy forcing in the heating sector is still stronger than that in the nonheating sector. Under the negative AM phase condition, although the intensity and the equatorward shifting of the storm track are relatively weak, the intensity of the synoptic eddy forcing is still much stronger than that of the climatology, especially in the midlatitude band (see Fig. 17c). We argue that the stronger synoptic eddy forcing is primarily due to the narrower width of the storm track. This can be explained as follows: the composites in the preceding section showed that a synoptic eddy transports positive (negative) vorticity in higher (lower) latitudes, forming a meridional dipolar structure. Its typical meridional scale is about 20–30° latitude (see Fig. 15). If we divide the climatological storm track in the heating sector using its axis, we find that the width of the northern portion is much wider than that of the southern portion. For example, if we take 40 m as the boundary of the storm track, then the width of the southern (northern) portion of the climatological storm track is about 15° (25°) latitude (see Fig. 17a). The northern portion of the storm track has sufficient space to allow the presence of the dipolar structure of vorticity forcing. Therefore, as illustrated in Fig. 18a, in the normal condition (climatology), the positive vorticity transported by the synoptic eddy propagating along the axis of the storm track is partly canceled out by the negative vorticity transported by the synoptic eddy propagating in the northern portion of the storm track. However, during the negative AM phase, the width of the storm track significantly shrinks, especially for the northern portion of the storm track. The width of the southern (northern) portion is about 13° (17°) latitude (taking 40 m as the storm track boundary; see Fig. 17a). Thus, the width of the storm track only roughly allows the existence of one dipolar structure of vorticity forcing. Therefore, the cancellation effect between the positive and negative vorticity forcing existing in the normal condition is very weak (see Fig. 18b). Therefore, during the negative AM phase when the storm track width is very narrow, we observe that the synoptic forcing is stronger than that of the normal condition, especially for the positive vorticity forcing in the midlatitude band.

Fig. 18.

Schematic for the dipolar structure of the synoptic eddy forcing under the (a) normal (climatology) and (b) negative AM phase conditions. The meridionally elongated solid (dashed) ellipses indicate the synoptic eddy propagating along the axis (at the north portion) of the storm track.

Fig. 18.

Schematic for the dipolar structure of the synoptic eddy forcing under the (a) normal (climatology) and (b) negative AM phase conditions. The meridionally elongated solid (dashed) ellipses indicate the synoptic eddy propagating along the axis (at the north portion) of the storm track.

d. “Released” and “enhanced” influences of the STJ

Why does the storm track in the heating sector have a more pronounced poleward shift with a stronger intensity during the positive AM phase, while it becomes narrower and weaker during the negative AM phase? We argue that this is due to the released and enhanced influences of the STJ on the propagation of the synoptic eddy train. To demonstrate this argument, we show one-point correlation maps of 2–7-day bandpass-filtered meridional wind at 300 hPa under the normal and AM conditions in Fig. 19. The base points for the calculation of the one-point correlation maps are located in the axis of the storm track at 120°W.

Fig. 19.

One-point correlation maps of the 2–7-day bandpass-filtered 300-hPa meridional wind (contours; interval is 0.1), the composites of 300-hPa zonal wind (shading; m s−1), and the axis of the storm track (red line) under the (top) normal, (middle) positive, and (bottom) negative AM phase conditions. The base points for the calculations of the one-point correlation maps are chosen at the center of the storm track at 120°W.

Fig. 19.

One-point correlation maps of the 2–7-day bandpass-filtered 300-hPa meridional wind (contours; interval is 0.1), the composites of 300-hPa zonal wind (shading; m s−1), and the axis of the storm track (red line) under the (top) normal, (middle) positive, and (bottom) negative AM phase conditions. The base points for the calculations of the one-point correlation maps are chosen at the center of the storm track at 120°W.

Owing to the existence of the STJ, under the normal condition, the synoptic wave train has a notable equatorward propagation characteristic (see Fig. 19a). In contrast, under the positive AM phase condition it is found that the synoptic wave train primarily propagates along the MLJ and the equatorward propagation characteristic of the synoptic wave train that we observed under the normal condition is less evident (see Fig. 19b). This result suggests that under the positive AM phase condition, the STJ has weak influences on the synoptic wave train propagation. In other words, the influences of the STJ are released. Thus, relative to the climatological storm track, which is under the control of the STJ with an evident equatorward deflection feature, the released storm track under the positive AM condition has a pronounced poleward shifting. Furthermore, Son et al. (2009) indicated that the storm track becomes stronger when the synoptic wave train persistently propagates in the zonal direction because, in addition to the local baroclinicity, the storm track is also affected by the far-upstream disturbances via downstream development of the synoptic eddies. Therefore, we also observe that the intensity of the storm track in the heating sector is stronger when the AM phase is positive.

We argue that the released influences of the STJ are due to the fact that the MLJ is located in higher latitudes and the MLJ and the STJ are well separated when the AM phase is positive. This simple argument is based on the possible physical mechanisms responsible for the equatorward displacement of the synoptic wave train propagation (or storm track) associated with the STJ/tropical heating. According to the authors’ knowledge, at least, there are two possible distinct explanations. 1) The equatorward shift of the synoptic wave propagation can be understood in terms of the refraction of synoptic waves due to the enhanced STJ (Seager et al. 2003, 2010). 2) The more southward storm track is closely related to the enhanced baroclinicity caused by the tropical heating (Orlanski 2005). Clearly, the mechanism for the equatorward displacement of the storm track associated with the STJ/tropical heating is controversial, and full discussions are beyond the scope of this study. However, both explanations suggest that the influences of the STJ/tropical heating on the propagation of the synoptic wave train will become weaker when the MLJ where the activity of the synoptic eddies is strongest is farther away from the STJ/tropical heating.

Under the negative AM phase condition, the STJ and MLJ are merged together, forming a very strong and narrow jet in the heating sector (see Fig. 19c). In such a situation, the influences of the STJ on the synoptic wave train propagation are enhanced. First, a strong waveguide effect due to the sharp potential vorticity (PV) meridional gradients flanking at the northern and southern sides of the strong jet confines the meridional radiation of the synoptic eddies (Hoskins and Ambrizzi 1993).9 Thus, the width of the storm track in the heating sector becomes very narrow. Second, as suggested by Harnik and Chang (2004), who investigated the effect of jet width on the intensity of a storm track, a narrow jet makes the intensity of the storm track weaker. Thus, because of the enhanced influences of the STJ, we observe that the storm track in the heating sector is narrower and weaker when the AM phase is negative.

6. Conclusions and discussion

a. Conclusions

In this study, motivated by observations, we argue that a strong STJ over the downstream regions of the storm track can make the AM pattern become zonally asymmetric. To support this argument, the reanalysis data and the numerical model are both used. Our main conclusions are as follows:

  1. We analyze and compare the zonal pattern of the SAM (NAO) during the days that the STJ over the downstream regions of the SH storm track (the Atlantic storm track) is uncharacteristically strong and weak by using ERA-40 daily data. The results show that the signatures of the SAM and NAO are locally strengthened over the downstream region of the storm track, and thus the zonal patterns of the SAM and NAO become more zonally asymmetric during the strong STJ days and vice versa, which suggests that the downstream STJ plays an important role in determining the zonal patterns of the SAM and NAO.

  2. Four numerical experiments that differ only in the intensity of the STJ downstream of the storm track (the STJ is produced by introducing a localized additional tropical heating with different intensities over the downstream region of the storm track) with a zonally uniform boundary, using the GFDL dynamical core model, are conducted. The model results show that the AM patterns are zonally symmetric (annular) without an evident locally strengthened characteristic when there is no additional tropical heating or weak tropical heating in the model, whereas the signatures of the AM become prominent over the downstream region of the storm track (i.e., the heating sector); thus, the zonal patterns of the AM are zonally asymmetric when the tropical heating is sufficiently large to create a strong STJ downstream of the storm track. We also find that the percentage of the variance explained by the AM, the persistence of the AM index, and the eddy feedback intensity are also increased when the downstream STJ becomes stronger. The results of the idealized experiments strongly indicate that a strong STJ over the downstream regions of the storm track can indeed make the zonal pattern of the AM zonally asymmetric.

  3. We consider that the zonal asymmetry of the AM pattern in the model is ultimately caused by the zonal asymmetry of the anomalous synoptic eddy forcing projecting on the AM. We also find that it is primarily due to the zonal asymmetry of the variations of the storm track between the nonheating and heating sectors during the positive and negative AM phases. Generally speaking, the entire storm track shifts poleward (equatorward) during the positive (negative) AM phase. However, compared to the climatological storm track, during the positive AM phase the storm track in the heating sector has a more pronounced poleward shifting with a stronger intensity, and during the negative AM phase the storm track in the heating sector becomes narrower and weaker and is confined to the subtropics. These variations of the storm track in the heating sector induce the anomalous synoptic eddy forcing in the heating sector that is much stronger than that in the nonheating sector, which drives and maintains the zonal asymmetry of the AM pattern. The zonal asymmetry of the variations of the storm track is considered as the result of the released (enhanced) influences of the STJ on the propagation of the synoptic wave train during the positive (negative) AM phase. We also find that the altering of the synoptic eddy structures is less important for the zonal asymmetry of the synoptic eddy forcing anomalies because the differences of the anomalous eddy forcing due to the altering of the eddy structures between the nonheating and heating sectors can be neglected despite the fact that the synoptic eddy structures in the nonheating and heating sectors are indeed different.

b. Discussion

In observations, the zonal pattern of the NAO is greatly localized, concentrating over the North Atlantic region. Gerber and Vallis (2009) found that the AM patterns in their integrations are zonally asymmetric and much closer to the observed NAO pattern when a proper combination of both topography and thermal forcing at mid–high latitudes are used in their model (see their Fig. 2). Therefore, their results suggest that the localized NAO-like patterns arise from the confluence of topographic and diabatic forcing. The results reported in this study deliver a new viewpoint that a strong downstream STJ can also make the AM pattern become zonally asymmetric. Thus, this study suggests that the strong STJ over the downstream regions of the Atlantic storm track also plays an important role in forming the observed localized NAO pattern.

In the model results, we find that the variations of the storm track in the heating sector where the STJ presents during the positive and negative AM phases are amplified by the STJ through the so-called “released and enhanced influences of the STJ” mechanism. Actually, the enhancement of the variations of the storm track due to the STJ is essential for the zonal asymmetry of the AM pattern that we discuss in this study. We find that the amplification of the variations of the storm track due to the STJ can also be seen for the observed NAO. Similar to Fig. 17, but for the observed NAO, Fig. 20 shows the sectoral zonal mean results of the composites of storm track and the synoptic eddy forcing in the North Atlantic sector (60°W–0°) during the positive and negative NAO phases on the days when the STJ over the downstream regions of the Atlantic storm track is normal (Figs. 20a,c) or unusually weak (Figs. 20b,d). It is clear that the storm track only has a slight poleward (equatorward) shifting during the positive (negative) NAO phase when the STJ is unusually weak (see Fig. 20b), which strongly resembles the variations of the storm track in the nonheating sector (see Fig. 17b). Conversely, the variations of the storm track are much stronger when the STJ has a normal intensity (see Fig. 20a). These results clearly manifest the amplification of the variations of the storm track due to the STJ in observations.

Fig. 20.

As in Fig. 17, but for the sectoral zonal mean results of the observed NAO over the Atlantic sector (60°W–0°) when its downstream STJ is (a),(c) normal or (b),(d) weak.

Fig. 20.

As in Fig. 17, but for the sectoral zonal mean results of the observed NAO over the Atlantic sector (60°W–0°) when its downstream STJ is (a),(c) normal or (b),(d) weak.

It is interesting to notice that for the observed NAO on the days that the STJ is normal, the intensity of the storm track becomes stronger during the positive NAO phase and the storm track is narrower and weaker during the negative NAO phase. These results are similar to the results of the heating sector in Exp_15k that we show in Fig. 17a except that we do not observe the greater poleward shifting of the storm track during the positive NAO phase. The evident poleward shifting of the storm track during the positive NAO phase cannot be observed, which might be due to the fact that, unlike the climatological storm track in the heating sector of Exp_15k, which has a notable equatorward deflection, the climatological Atlantic storm track has a notable poleward deflection (Orlanski 1998). Thus, the variations of the Atlantic storm track during the positive and negative NAO phases are consistent with the results of Wettstein and Wallace (2010), namely that the NAO is associated with a pulsing of the Atlantic storm track. However, from the spatial distribution of the composites of the Atlantic storm track during the positive and negative NAO phases, we do observe that the Atlantic storm track shifts greatly to the north during the positive NAO phase, whereas it is confined in the subtropics over the intersection region between the MLJ and STJ [see Fig. 15 of Wettstein and Wallace (2010), Fig. 2 of Rivière and Orlanski. (2007), or Fig. 6 of Athanasiadis et al. (2010)], which, as we suggest, reflects the “released and enhanced” influences of the STJ on the storm track. From the sectoral zonal mean results of the synoptic eddy forcing shown in Figs. 20c and 20d, it is also clear that when the STJ has a normal intensity, the meridional displacement distance of the storm track between the positive and negative NAO phases is greater than when the STJ is unusually weak.10

According to the thermal wind relationship, the vertical gradients of the zonal wind of the STJ must be accompanied by horizontal gradients of temperature. Thus, generally speaking, a strong STJ is also accompanied by tropical heating.11 In fact, some studies have already suggested that tropical heating such as the warm phase of ENSO affects the midlatitude circulation by strengthening the STJ (Seager et al. 2003, 2005). Thus, from this viewpoint, the results of this study also have a potential value for understanding the influences of tropical heating on the AM. Here, we would like to briefly discuss the changes in the zonal pattern of the NAO and SAM during the warm and cold ENSO boreal winters (DJF). Figure 21 shows the NAO and SAM patterns and the zonal wind at 300 hPa for the warm and cold ENSO boreal winters.12 In the NH, besides the well-known zonal wind changes over the North Pacific (such as the eastward extension or westward retreat of the Pacific jet), a warm (cold)-phase ENSO also reduces (enhances) the intensity of the Atlantic Hadley circulation through the anomalous Walker circulation (e.g., Wang 2005). Therefore, we observe that the STJ over the North Atlantic is weakened (strengthened) during the warm (cold) phase of ENSO (see the zonal wind fields in Figs. 21a,b). Consistent with our argument, we find that the NAO pattern has a slight eastward displacement during the cold ENSO winters. In the SH, the zonal patterns of the SAM also have differences between the warm and cold ENSO winters. During the warm ENSO winters, the signatures of the SAM are slightly enhanced (reduced) over Pacific (Atlantic) where the STJ is strengthened (weakened), which is consistent with the results of this study. However, it should be noted that the zonal wind anomalies over the subtropics aroused by ENSO are very weak, especially for the SH (see Figs. 21c,d); thus, the changes in the zonal patterns of the NAO and SAM during the warm and cold ENSO winters are also small.

Fig. 21.

(a),(b) NH and (c),(d) SH mean zonal wind at 300 hPa (shaded; m s−1) and the NAO and SAM pattern (contour; interval is 20 m) during (a),(c) warm and (b),(d) cold ENSO boreal winters (DJF).

Fig. 21.

(a),(b) NH and (c),(d) SH mean zonal wind at 300 hPa (shaded; m s−1) and the NAO and SAM pattern (contour; interval is 20 m) during (a),(c) warm and (b),(d) cold ENSO boreal winters (DJF).

Quadrelli and Wallace (2002) discussed the changes of the structure of the NAM on the different phases of ENSO. They found that during the warm ENSO boreal winters, the structure of the NAM is dominated by its action center in the North Atlantic (i.e., the NAO), whereas the signature of the NAM is much more pronounced over the North Pacific sector (see their Fig. 2). Because the intensity of the Pacific STJ is enhanced (reduced) during the warm (cold) ENSO winters, the more (less) pronounced signatures of the NAM over the North Pacific during the cold (warm) ENSO phase are difficult to explain by changes of the Pacific STJ intensity associated with the different phases of ENSO. Song and Li (2010, manuscript submitted to J. Climate) argued that NAOs can be grouped into reflective and nonreflective types. Furthermore, they found the nonreflective NAO can impact the circulation over the North Pacific through the Asian jet via trapping quasi-stationary Rossby waves excited by the NAO, while the reflective NAO mainly impacts the circulation over the high latitudes of Eurasia. Also, they found that the NAO tends to be reflective (nonreflective) during warm (cold) ENSO winters. Thus, they suggested that the different structures of the NAM during warm and cold ENSO winters result from the distinct characteristics of the NAO’s reflection (reflective or nonreflective) during warm and cold ENSO winters.

In this study, in addition to the variations of the zonal pattern of the AM, we find that the eddy feedback intensity is increased when the downstream STJ becomes stronger. The increased eddy feedback intensity may partly be related to changes in the latitude of the jet. From Fig. 7, we notice that the jet gradually shifts equatorward when the tropical heating/STJ becomes stronger. This is evident in the climatological zonal mean 300-hPa zonal wind (not shown). To test the effect of latitudinal displacements of the jet on the eddy feedback intensity, another experiment is performed. The model design of this experiment is the same as Exp_0k except that the additional high-latitude cooling is latitudinally shifted 10° more equatorward. This adjustment is to force the MLJ in the model to have an equatorward displacement. The climatological zonal mean 300-hPa zonal wind of this experiment shows that the core of the MLJ is at 45°, which is about 5° farther equatorward than the MLJ in Exp_0k. We calculate the autocorrelations of the AM index and the cross correlations between the z time series of the total/synoptic eddy forcing and the AM index of this experiment (not shown). The results indicate that the AM index in this experiment has a longer persistence and the eddy feedback intensity is stronger compared to Exp_0k, which suggests that a decrease in the latitudinal position of the MLJ is associated with an enhancement in the eddy feedback intensity and a corresponding increase in the persistence of the AM index.

The linkage between the equatorward shift of the jet and the increase in the persistence of the AM index is already noted by Gerber and Vallis (2007) and Son et al. (2008). However, Gerber et al. (2008) found that this linkage does not hold for another set of simulations with different spatial resolution. Thus, Gerber et al. (2008) suggested that this linkage is an artifact of T42 resolution. However, in observations Codron (2005) also found that the eddy feedback is stronger when the mean jet is displaced toward the equator. Clearly, this still is an open question. Detailed discussions are beyond the scope of this study.

Recently, some studies have noted an important observed fact that the action centers of the NAO were located farther eastward during winters of the period 1978–97 compared to the period 1958–77, which has a profound influence on the relationship between the NAO and Arctic sea ice export through the Fram Strait during the boreal winter (Hilmer and Jung 2000; Jung and Hilmer 2001; Jung et al. 2003). Several studies have suggested that the eastward shifts of the NAO action centers are possibly related to the higher NAO index during the last several decades of the twentieth century (Peterson et al. 2003), the enhanced background westerly (Luo and Gong 2006), the eastward shift of the Atlantic storm track (Luo et al. 2010), global warming (Ulbrich and Christoph 1999; Hu and Wu 2004), or changes in the frequency distribution within the NAO continuum (Johnson et al. 2008). We notice that the STJ over the North Atlantic sector is slightly strengthened during winters of the period 1978–97 compared to the period 1958–77 (not shown). Also, our observational results show that the action centers of the NAO have an eastward shift when its downstream STJ is stronger (see Fig. 6). Therefore, we may connect the decadal eastward shift of the NAO action centers to the variations of the intensity of the downstream STJ. This is a further potential value of the present study.

Acknowledgments

A part of the work described here was done while the first author was a visitor at the City University of Hong Kong. This work is sponsored by National Nature Science Foundation of China (Grants 40805023 and U0833602) and the LASG Free Exploration Fund. JS and CYL are supported by the 973 program (Grant 2010CB950401). Works of WZ are partly supported by the City University of Hong Kong research grant (Grant 7002231).

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Footnotes

1

Strictly speaking, the AM in the NH is known as the northern annular mode (NAM). Some studies suggest that the NAO is indistinguishable from the NAM (Feldstein and Franzke 2006). In this study, however, we prefer to use the NAO rather than the NAM. This is because the NH has two separated storm tracks, while in the SH and in our model there is only one storm track. Thus, the use of the NAO is more convenient to link the model results to the real world. In observational analyses, the use of the NAM does not change our conclusions.

2

The storm track in this paper is defined as the root-mean-square of daily bandpass-filtered (2–7-day periods) geopotential height at 300 hPa.

3

Codron (2007) also discussed the variations of the SAM pattern with seasons.

4

We also conduct several parameters sensitive experiments using the Exp_15k model setting by slightly varying parameters ka and kf. The results show that the zonally asymmetric feature of the AM pattern is not very sensitive to the variations of the model parameters.

5

In section 3, the SAM (NAO) index on the strong and weak STJ days is defined as the PC1 of the SH 700-hPa geopotential height anomalies (SLP anomalies over the Atlantic region) on the strong and weak STJ days, respectively.

6

There are 768 base points in each of the heating and nonheating sectors.

7

There are 1030 (1092) positive (negative) AM phase days in Exp_15k.

8

The typical synoptic eddy structures of Exp_0k have a good zonally symmetric characteristic and are thus not shown.

9

See Fig. 19c; the one-point correlation coefficients spread in a whole latitude circle indicate the strong waveguide effect of the strong jet.

10

We also notice that the intensity of the storm track and the synoptic eddy forcing is stronger when the STJ is unusually weak. This may occur because the synoptic wave train has less ability to propagate equatorward when the STJ is unusually weak. Thus, the storm track is strengthened by the far-upstream disturbances via downstream development of the synoptic eddies (Son et al. 2009).

11

In the idealized experiments of this study, the STJ is introduced into the model by adding an additional localized tropical heating. It should be noticed that we try to keep the baroclinicity in the middle latitude unchanged. Therefore, it seems that the only way to produce a STJ in the model is to add heating in the tropics.

12

The warm and cold boreal winters of ENSO are selected based on 0.5 standard deviations of winter averaged values of the Niño-3.4 index from 45 boreal winters (1957/58–2001/02). There are 14 warm winters and 15 cold winters. The monthly Niño-3.4 index is downloaded from the Web site of the Climate Analysis Section (CAS) within Climate and Global Dynamics Division (CGD) of the National Center for Atmospheric Research (NCAR) Earth System Laboratory (NESL).