1. Introduction
The annular mode, which is also called the Arctic Oscillation (AO) in the Northern Hemisphere (NH) and the zonal index in the Southern Hemisphere (SH), is the leading mode of extratropical atmospheric circulation in both the NH (Thompson and Wallace 1998, 2000) and the SH (Karoly 1990; Kidson 1988; Kidson and Sinclair 1995; Hartmann and Lo 1998; Gong and Wang 1999; Thompson and Wallace 2000). In the SH, Kidson (1988) highlighted the first two empirical orthogonal functions (EOFs) of the zonal-mean 500-hPa zonal wind with respect to the annular variability, and EOF1 has been known as the high-latitude mode (HLM; e.g., Karoly 1990) while EOF2 as the low-latitude mode (LLM: Watterson 2007). Several studies have examined seasonal variations of the AO, as well as the North Atlantic Oscillation (NAO; Portis et al. 2001; Ogi et al. 2004). These studies found that the seasonal variations of the AO/NAO are consistent with the seasonal variations of the climatological basic flow and storm-track activity. More recently, Pan and Jin (2005) investigated the seasonality of synoptic eddy feedback and the AO/NAO. They found that the synoptic eddy and low-frequency flow feedback is of significant importance for the formation of the AO/NAO in both winter and summer and the seasonal shifts in the spatial patterns of the AO/NAO are the result of the seasonal changes in climatological basic state and synoptic eddies. However, the seasonal variations of the annular mode in the SH and the seasonality of the feedback between synoptic eddies and low-frequency flow associated with the annular mode have not yet been well understood.
Seasonal variations of storm-track activity in the SH have been documented by Trenberth (1991). Nakamura and Shimpo (2004) have examined seasonal variations of storm tracks and jet streams in the SH based on the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP– NCAR) reanalysis dataset, and they emphasized the distinct difference of storm-track activity and jet flows between summer and winter because of the presence of the split jet structure in the SH winter. Several GCM studies have shown the seasonal variation of the zonal index and the eddy–mean flow feedback in the SH (Codron 2005; Watterson 2002, 2007). These studies suggested that seasonal variations of the annular mode and the eddy–low frequency feedback may also exist in the SH.
On the study of the variability of the zonal-mean zonal wind in the SH, Lorenz and Hartmann (2001, hereafter LH01) found that the leading EOF of the zonal-mean zonal wind represents the north–south movement of the midlatitude jet, and the second EOF corresponds to the strengthening (weakening) and sharpening (broadening) of the time mean midlatitude jet. They demonstrated that a positive eddy–zonal flow feedback accounts for the greater persistence of EOF1 zonal wind variability compared to EOF2 variability. LH01 also demonstrated the value of time-lagged regressions rather than simultaneous regression for diagnosing the effect of the changes in the zonal-mean wind on the eddies because only a small fraction of the eddy momentum flux anomalies at zero time lag can be attributable to the zonal wind anomalies; that is, most of the eddy forcing at zero lag is random and independent of the zonal wind anomalies (Feldstein and Lee 1996, 1998; Robinson 1996; Watterson 2002). LH01 applied the time-lagged regression diagnostics to show the following positive feedback mechanism: anomalous baroclinic wave activity is generated at the latitude of the anomalous zonal jet, and the net propagation of baroclinic wave activity away from the jet gives rise to momentum fluxes into the jet. This mechanism is only applicable for EOF1 variability, while there is no positive feedback for EOF2. For EOF2, LH01 hypothesized that the increased barotropic shear associated with EOF2 suppresses baroclinic wave growth by the barotropic governor mechanism (James 1987) and thus weakens the positive eddy feedback because the horizontal shear of EOF2 is coincident with the horizontal shear of the time-mean midlatitude jet.
One assumption in LH01 is that the seasonal cycle in the midlatitude of the SH is small compared to the NH, so they used the 20-yr (1978–97) daily data for their diagnostics. However, the presence of the split jet in the SH winter makes the midlatitude flow more zonally asymmetric (Taljaard 1972; Hurrell et al. 1998; Hartmann and Lo 1998; Bals-Elsholz et al. 2001; Yang and Chang 2006). Nakamura and Shimpo (2004) presented seasonal variations of the SH storm tracks and jet streams, especially between summer and winter. Furthermore, Lorenz and Hartmann (2003) showed that there is a positive eddy–zonal flow feedback for both EOF1 and EOF2 in the NH winter, even though the feedback associated with EOF1 is stronger than that of EOF2. Those studies suggest that the eddy–zonal flow feedback associated with the zonal indices in the SH may also have seasonal variations; hence further investigation for the different seasons is needed.
In the real atmosphere, the fully nonlinear interaction between high-frequency eddies and low-frequency flow makes it difficult to understand the feedback between them. As discussed in LH01, to isolate the part of the eddy forcing that is responding to the zonal wind anomalies, they have to diagnose a lag regression of 12 days. From the diagnostic point of view, storm-track modeling provides another way to separate out the two-way interaction into two distinct components: the response of transient eddies to changes in the low-frequency flow and the consequent eddy feedback onto that low-frequency flow itself (Chang et al. 2002). Based on the storm-track modeling approach, with the combination of a stationary wave model and a linear storm-track model, Yang and Chang (2006) demonstrated a two-way feedback between eddies and the monthly mean flow associated with the variability of the split/nonsplit jet in SH winter. It would be of interest to apply the storm-track modeling approach to investigate the seasonal variations of the eddy–zonal flow feedback associated with EOF1 and EOF2.
The purpose of this study is to further clarify how the eddy–zonal flow feedback associated with EOF1 and EOF2 changes in SH winter and summer. We will use storm-track modeling to diagnose the mechanism governing the eddy–zonal flow feedback. In this study, we will try to understand the following questions: Is the eddy–zonal flow feedback different in the different seasons? Or, does the persistence time scale for EOF1 and EOF2 have seasonal difference? If it does, can we explain the difference? In particular, why do eddies feed back onto wind anomalies associated with north–south displacements of the midlatitude jet and not onto the strengthening (weakening) of the midlatitude jet?
The paper is organized as follows. The data, methodology, and models are described in section 2, and the seasonal variations of the persistence time scale of EOF1 and EOF2 are discussed in section 3. The simulations of the eddy responses to the zonal flow change during EOF1 and EOF2 episodes based on the linear storm-track model are shown in section 4a, and the consequent eddy feedback onto the zonal flow is diagnosed by a wave-response model in section 4b. In section 5, the dynamics involved in the eddy–zonal flow feedback is presented, and the difference of EOF2 between summer and winter is discussed. The paper ends with the conclusions and discussions in section 6.
2. Data, methodology, and models
a. Data and methodology
For this study, we used the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) 6-hourly wind and temperature data at constant pressure levels. We used data for the SH from 1979 to 2001 on a 2.5° × 2.5° latitude–longitude grid and 13 vertical levels (1000, 925, 850, 775, 700, 600, 500, 400, 300, 250, 200, 150, and 100 hPa).
To analyze variability of the zonal-mean zonal wind, we first found daily anomaly data by removing the mean seasonal cycle. The mean seasonal cycle is obtained by applying a 31-day moving average over the 23-yr daily climatology. We then performed an EOF analysis for the zonal-mean zonal wind using the 23 years of daily anomaly data, and the same EOF analysis is also applied for each season. For the EOF analysis, the data fields were properly weighted by the square root of the cosine of latitude and the square root of the pressure interval to account for the decrease of area toward the pole and the uneven spacing of the pressure levels. We present the EOFs in meters per second and not in normalized form, which is done by a regression of the anomaly data on the normalized principle component (PC) time series, so that the magnitude of the structures can easily be seen.
All composite fields shown in this paper refer to the average of the fields for days when the PC index exceeded +1.0 standard deviation from the mean. We have also computed the composites for the negative phase, but the results are quite linear and will not be shown here. For all eddy statistics, all variables are first filtered by a high-pass filter, which is a spatial filter with total wavenumber-7 cutoff (Anderson et al. 2003).
b. A linear storm-track model
A linear storm-track model is constructed based on an initial condition approach pioneered by Branstator (1995, hereafter B95). Here, the initial value technique employed by B95 is briefly described. Starting from a spatially white random distribution of perturbations superimposed on a 3D basic state, a linear model is integrated for several days to determine how disturbances would tend to evolve under the influence of the background flow. With the effects of local regions of enhanced baroclinicity and the steering effect of the background winds, there is a tendency for perturbations with certain structures in certain regions to grow and be focused into preferred sectors while other perturbations decay. From a sufficient number of such integrations, what amounts to a climatology of the dominant, fast time-scale disturbances of the model can be formed. Using this technique, one can find the storm tracks for a given background state. Details of this method can be found in B95.
The eddy heat and momentum fluxes are of essential importance in the maintenance of climate and its low- frequency anomalies. How well the linear model can reproduce these flux terms will serve as an important indicator of the model’s performance. Using parameters used by B95, the momentum fluxes simulated by the linear storm-track model have good agreement with those from GCM output; however, the model generates stronger heat fluxes compared with those of GCM climate (B95). Zhang and Held (1999, hereafter ZH99) have successfully simulated the midlatitude storm-tracks produced by an atmospheric GCM using a linear stochastic model, and the model presents good agreement of both heat and momentum fluxes with those of GCM climate. They found that the model results are sensitive to the manner in which the model is stirred, and best results for eddy variances and fluxes are obtained by stirring the temperature and vorticity at low levels. Though we use the initial value approach to construct a linear model, ZH99’s results are also relevant here. We found that best results for eddy fluxes could be obtained by setting a vertical distribution of perturbation magnitude of white-noise initial condition, rather than perturbing all levels with the same magnitude (see below).
The length of each integration to collect the storm-track statistics is another important factor for this model. As discussed by B95, day 5 is a good cutoff for representing the storm-growing stage. Here, since we put most initial perturbations in lower levels, we found that collecting statistics during days 3–7 gives a good agreement of storm-track statistics. One possible reason is that waves may take longer time to grow and propagate upward if most perturbations are put in the lower levels, compared with the case of perturbing all levels. After tuning, we decided to only perturb the vorticity field. The white noise is seeded between 65° and 25°S.
Our model has been explicitly tuned to determine the parameters α, β, and the vertical distribution factor of the perturbation amplitude. In this tuning process, we choose the June–August (JJA) climatology from ERA-40 as the target system. The second-moment statistics of the JJA climatology is obtained from the high-pass field of the ERA-40 dataset. After tuning, we have found a reasonably good fit to the eddy heat and momentum fluxes with α = 0.8 day, β = 1.6 day, and the vertical distribution factor of perturbation amplitude from the bottom to the upper boundary in 14 levels (1.0 for 0.997–0.777, 0.8 for 0.675, 0.6 for 0.568, 0.4 for 0.460, 0.2 for 0.355, and 0.0 for 0.257–0.015).
Figure 1 shows the eddy heat flux at 850 hPa and the eddy momentum flux at 300 hPa from the linear model (Figs. 1a and 1b) and the ERA-40 dataset (Figs. 1c and 1d). The vertical structure of the zonal-mean heat flux and momentum flux from the linear model and ERA-40 is depicted in Fig. 2. It can be seen that the overall distribution and the magnitude of eddy heat and momentum fluxes are reproduced very well by the linear model.
To be noted here, tuning of the storm-track model for December–February (DJF) is a little bit different from that for JJA. We found that the linear model simulates weaker heat flux compared with ERA-40 DJF climatology, so we also perturb temperature field at the lowest five levels as extra forcing (figures not shown here). One possible reason is that the model here is a dry model. While dry dynamics is a good approximation for the relatively dry SH winter, it is not as good for the relatively moist SH summer. The condensational heating in the moist atmosphere acts as a source of eddy available potential energy, and baroclinic conversion is strongly enhanced in the presence of diabatic heating (Chang et al. 2002); thus, eddies in a moist atmosphere are stronger than that in a dry atmosphere. Because of this difference in the model tuning, in our discussions below, we will mainly focus on applying our model to interpret differences between the two EOFs within a single season and avoid direct quantitative comparisons between the two seasons.
Lag-regression maps of high-pass filtered data can be used to illustrate the spatial structure and propagation characteristics of baroclinic eddies (Chang 1993). Figure 3 shows the lag-regression maps of meridional wind on the longitude–pressure plane at 50°S from the stormtrack model and ERA-40 for lags of −1, 0, and +1 days. The reference point is located at (60°E, 300 hPa). The wave train and the downstream development are clearly present in the linear model, as well as in ERA40. Note that the temporal evolution of the wave train agrees better with observations than that obtained in the stochastic storm-track model developed by ZH99.
It seems that the storm-track model is capable of reproducing the climatological horizontal and vertical distribution of eddy heat and momentum fluxes, as well as the propagation properties of eddies. In section 4a, we will examine the eddy response to the basic-state changes associated with PC1 and PC2 zonal flow variations using this model.
c. A wave-response model
The model used in section 4b is a stationary wave model, which has been employed to diagnose the stationary wave anomalies associated with the variability of the split jet in the SH winter (Yang and Chang 2006). Here, the model is only integrated for several days to examine the response of the mean flow to the eddy anomalies, so it is called a wave-response model. The model description can be found in Yang and Chang (2006). The model is very similar to the storm-track model described above except that stronger damping is imposed to damp the development of baroclinic waves. Instead of seeding with white noise, the model integration starts with the basic flow as the initial condition, and the model response to the imposed forcing is then computed. The forcings are anomalous eddy heat and vorticity fluxes obtained from the storm-track model simulations with the basic-state change in section 4a. To hold the linear constraint, we only integrate the model for several days and then examine the tendency of the zonal flow change with the prescribed forcings. The model solution shown below is the model output at day 5.
3. The zonal indices and their persistence time scale
Before examining the variability of the zonal-mean zonal wind, it is useful to describe the climatological jet structure. The climatological jets in the SH include a subtropical jet at 30°S and a midlatitude jet at 50°S (LH01). Figure 4 shows the zonal wind at 300 hPa and the vertical structure of zonal-mean zonal wind in SH winter and summer. The upper-tropospheric flow in the SH shows seasonal variations, for example, a single jet in summer and a split jet in winter (Figs. 4a and 4b). The mean jet flow in summer is relatively zonally symmetrical while it is asymmetrical in winter. The subtropical jet is absent in the SH summer and is stronger than the polar front jet in the SH winter.
We performed an EOF analysis on the 23-yr daily data. The leading EOF of the daily zonal-mean zonal wind is an equivalent barotropic dipole with maximum anomalies at 40° and 60°S (Fig. 5a), and it explains 35% of the total variance. The second EOF also captures an equivalent barotropic pattern with a stronger positive anomaly at 50°S and two weaker negative anomalies at 30° and 65°S (Fig. 5d); this mode explains 19% of the total variance. To see the seasonal contribution from these two EOFs to the total variance, we project the EOFs onto the daily data of each season and calculate the percentage of variance explained by the corresponding EOF. Table 1 shows that the percentage of the explained variance by EOF1 and EOF2 changes with season. In DJF, the ratio between the variance explained by EOF1 and EOF2 is about 2, while it is about 1.5 in JJA. This difference suggests that we should diagnose the mechanism associated with zonal-mean wind variations by each season, so we performed EOF analysis on the daily data of each season separately. The percentage of variance explained by EOF1 and EOF2 in each season is also listed in Table 1; it shows similar seasonal change as found in the annual EOF analysis. To be noted here, the positive center of EOF1 has a slight poleward shift from SH summer to SH winter (Figs. 5b and 5c), and the positive center of EOF2 in winter extends over a broader latitude range than that of EOF2 in summer (Figs. 5e and 5f).
LH01 suggested that persistence of each EOF is an important factor contributing to the explained variance of the corresponding EOF. The autocorrelation of the principal component (PC) time series is applied here to estimate the persistence of the corresponding EOF. Figure 6 shows the autocorrelation of PC1 and PC2 in 23 JJA seasons, 23 DJF seasons, and 23 yr. Consistent with LH01, PC1 has greater persistence than PC2 from the data time series over the whole 23 yr, and the e-folding time scale of PC1 is about 4 days longer that of PC2 (Fig. 6a). Meanwhile, in JJA, PC1 has slightly greater persistence than PC2, and the difference of e-folding time scale between two PCs is only about 1 day. In DJF, the persistence of PC1 is significantly greater than that of PC2, and there is an 8-day difference between the corresponding e-folding time scales.
The percentage of explained variance and the persistence time scale of each EOF are summarized in Table 1. Table 1 provides us with a consistent seasonal variation between the explained variance and the persistence time scale of each EOF. In DJF and September–November (SON), PC1 has a significantly longer time scale than PC2, and the ratio of explained variance between PC1 and PC2 is larger (about 2). In March–May (MAM) and JJA, the persistence time scale of PC1 is only about 1 day longer than that of PC2, and the ratio of explained variance between PC1 and PC2 is smaller (about 1.5). Similar seasonality in the persistence time scale of PC1 was also documented by Feldstein (2000) using the NCEP–NCAR analysis data, and examination of a long time series (100 yr) of GCM simulation by Watterson (2002) has also shown that PC1 in the model simulation has longest time scale in DJF and much shorter time scales in MAM and JJA. It is well known that there is a positive eddy–zonal-mean wind feedback for PC1 and this feedback increases the persistence of PC1 (Karoly 1990; Kidson and Sinclair 1995; Hartmann and Lo 1998; LH01; Watterson 2002, 2007; Codron 2005). The remaining question here is why the persistence time scale of PC2 in DJF is significantly shorter than that of PC1, while in JJA it is comparable with that of PC1.
One relevant question is whether these low-frequency anomalies can sustain themselves without eddy forcing. To address this question, the stationary wave model with the seasonal climatological basic state, initialized with the low-frequency anomalies without any forcing, have been run for cases of PC1 and PC2 in DJF, and PC1 and PC2 in JJA, respectively. The model results show that the anomalies for all cases dissipate with time and the modeled dissipation time scales are quite similar (figures not shown). Thus, the observed seasonal variations of the persistence time scale of each PC cannot be explained by self-maintenance of low-frequency anomalies without eddy feedback.
This suggests that the eddy–zonal flow feedback for PC2 may be significantly different in JJA and DJF, with the strength of the feedback affecting the time scale of persistence. In the next section, we will apply a storm- track model to simulate the response of eddies associated with the zonal-mean wind change, and then use a wave-response model to diagnose the consequent eddy feedback onto that zonal-mean wind itself.
In this study, we only focus on the eddy–zonal flow feedback in SH winter (JJA) and summer (DJF) because JJA (DJF) is, respectively, a good case of a season with zonally asymmetric (symmetric) background flow in the SH.
4. Storm-track modeling and a wave-response model diagnostic
In this section, the linear storm-track model is applied to simulate the response of eddies to changes in zonal-mean wind for PC1 and PC2 in JJA and DJF, and then the wave-response model is run to diagnose the eddy–zonal flow feedback.
a. Modeling the eddy response during PC1 and PC2 episodes
We use the storm-track model, which has been tuned so that eddy heat and momentum fluxes are consistent with observations, to simulate the eddy anomalies associated with PC1 and PC2 zonal flow variations in JJA and DJF. For each season, we have a seasonal climatology of eddies, which is reproduced by the storm-track model with the seasonal climatological 3D basic state of ERA-40. Then, also for each season, we computed composite 3D flows based on the PC1 and PC2 index, respectively, to use as the basic state of the linear model to simulate eddies during PC1 and PC2 episodes.
Figure 7 shows the anomalous heat flux at 700 hPa and the anomalous momentum flux at 300 hPa from the storm-track model and the composite zonal wind at 300 hPa for PC1 and PC2 episodes during JJA.1 For PC1 of JJA, in the latitudes of positive (negative) westerly wind anomalies, the poleward (equatorward) heat fluxes increase, and the poleward (equatorward) momentum fluxes also increase at a latitude that is slightly equatorward of the region of wind anomalies, and the pattern of anomalies is almost annular (Figs. 7a–c). The wind anomalies for PC2 are mainly in the South Pacific Ocean (Fig. 7f). Consequently, the response of heat and momentum flux to the wind anomalies for PC2 is mainly in the South Pacific Ocean, downstream and less zonally symmetric than that of PC1 (Figs. 7d and 7e).
Figure 8 depicts the anomalous heat flux at 700 hPa and the anomalous momentum flux at 300 hPa for PC1 and PC2 episodes during DJF. The anomalous heat and momentum fluxes for PC1 present a similar picture as those for PC1 in JJA: enhanced poleward (equatorward) heat fluxes in the latitudes of positive (negative) anomalous zonal winds (Figs. 8a,c) and enhanced poleward (equatorward) momentum fluxes at a latitude that is slightly equatorward of that (Fig. 8b). However, for PC2, the changes in eddy fluxes are much weaker and show a different relationship with the zonal flow anomalies compared to the other cases (Figs. 8d–f).
The storm-track model simulations give the eddy response to zonal wind flow changes during PC1 and PC2 episodes in JJA and DJF. To investigate the feedback between eddies and the zonal flow, we should examine the basic-state response to eddies, which were themselves induced by the basic-state change. In section 4b, we will apply a wave-response model to diagnose this feedback.
b. Diagnostics using a wave-response model
Figure 9a shows the model response of the zonal-mean zonal wind to model-generated eddy anomalies associated with PC1 in JJA. To be noted here, the model response is 3D in nature, and the zonal-mean zonal wind response is shown here because it is the component of main interest. Compared with the zonal flow anomalies (Fig. 9b), the eddy fluxes can be seen to reinforce the zonal flow anomalies except that there is about a 5° phase shift equatorward around 60°S and a 2.5° phase shift poleward around 40°S (Fig. 9c). This suggests a positive feedback between eddies and the zonal flow for PC1 in JJA.
The model solution of the zonal-mean zonal wind for PC2 in JJA is depicted in Fig. 9d. It shows that the eddy forcing forces the same tendency as the zonal flow anomalies, and the positive peak of the model solution is in phase with the zonal flow anomalies, though the negative peaks have phase shifts from the zonal flow anomalies (Figs. 9e and 9f). For PC2 in JJA, it is apparent that a positive eddy–zonal flow feedback still exists.
Figures 10a–c depict the model response and the zonal flow anomalies for PC1 in DJF. For this case, the eddy fluxes also reinforce the zonal flow anomalies except that there is a 2.5° phase shift equatorward around 60°S and a 5° phase shift poleward around 40°S. This also implies a positive eddy–zonal flow feedback for PC1 in DJF.
The model response of the zonal-mean zonal wind and the zonal flow anomalies for PC2 in DJF are shown in Figs. 10d–f. The model response to the eddy forcing is almost out of phase with zonal flow anomalies except there is a narrow positive region centered about 50°S. Compared with PC1 in JJA and DJF and PC2 in JJA, PC2 in DJF shows no positive feedback.
Here F is given by the wave-response model estimated by using the model response at day 5 divided by 5 days, so we can estimate the eddy feedback time scale τ for each case. The feedback is stronger if τ is shorter and vice versa. The results are summarized in Table 2. The persistence time scale of the PCs is also listed here for comparison. At this stage, we have a consistent picture between the persistence and the eddy–zonal flow feedback of each zonal index. In JJA, PC1 and PC2 both have the positive feedback, and the difference in their persistence time scale is only about 1 day. In DJF, PC1 has positive feedback while there is no positive feedback for PC2 (the feedback time scale is negative), and the persistence time scale of PC1 is about 8 days longer than that of PC2. This consistency confirms that the positive eddy–zonal flow feedback increases the persistence of the corresponding zonal index, and stronger (weaker) positive feedback contributes to longer (shorter) persistence time scale. In the next section, we will discuss the dynamics governing the strength of the feedback and especially why the eddy feedback time scale and persistence time scale of PC2 is so different between JJA and DJF.
5. Dynamics of the feedback
The Eliassen–Palm (EP) flux vectors (Edmon et al. 1980) are employed here to diagnose the mechanism governing the feedback. Figure 11 depicts the model-generated anomalous EP flux vectors for PC1 and PC2 in JJA and DJF. For the cases of PC1 in JJA and DJF and PC2 in JJA, the EP flux vectors all show the following mechanism for the zonal wind–eddy feedback: enhanced (reduced) baroclinic wave source (heat fluxes) at a low level in the region of positive (negative) zonal wind anomalies and waves propagate upward and then equatorward from the wave source, thus giving momentum fluxes that reinforce the wind anomalies. However, for PC2 in DJF, the above mechanism is not present, and the dominant feature is inhibited baroclinic waves around 40°S. To be noted here, for PC1 in JJA and DJF, as well as PC2 in JJA, the maxima in the reduced baroclinic wave source (heat fluxes), as well as the convergence of the horizontal EP flux vectors, are not exactly in phase with the zonal wind anomalies, while they shift to the poleward side of the region of negative zonal wind anomalies. This shift is also obvious in the wave-response model solutions (Figs. 9c and 10c). A possible reason for this shift will be discussed later in this section.
Figure 12 shows the climatological zonal wind, PC2 composite zonal wind anomalies, and PC2 composite zonal wind at 300 hPa for DJF and JJA. The DJF climatology is close to zonally symmetric while the JJA climatology is zonally asymmetric because of the presence of the split jet (Figs. 12a and 12d). For PC2 in DJF, the barotropic part of the wind anomalies reinforces the horizontal shear of the climatological jet (Figs. 12a and 12b), and the baroclinic part of the wind anomalies is also close to zonally symmetric (Fig. 12c). For PC2 in JJA, both the barotropic and baroclinic part of the wind anomalies are mainly in the Pacific Ocean where the climatological jet is weak, so wind anomalies broaden the climatological jet rather than reinforce the climatological jet (Figs. 12d–f). In the Indian Ocean, the barotropic shear of the wind anomalies is coincident with the horizontal shear of the climatological jet, while the baroclinic part is much weaker than that in the Pacific Ocean.
LH01 hypothesized that the barotropic shear associated with EOF2 suppresses the baroclinic wave growth (James 1987) and thus weakens the baroclinic positive feedback since the horizontal shear of EOF2 is coincident with the horizontal shear of the time mean midlatitude jet. They argued that they found no positive feedback for EOF2 due to this “barotropic governor” hypothesis. Based on Fig. 12, we expect the hypothesis to be valid in the SH summer with zonally symmetric background flow, and it may also play a role in the Indian Ocean in the SH winter. Next, we will use the linear storm-track model to test the barotropic governor hypothesis for EOF2 in DJF and JJA.
We set up a new run for PC2 using the storm-track model. The anomalous surface winds of PC2, which represents the anomalous barotropic part of PC2, are removed from all levels to construct a new basic state, and the baroclinic part is unchanged. We use this “new” basic state associated with PC2 to run the storm-track model for the SH summer and winter, respectively. This new run is called the baroclinic run and the run for PC2 in section 4 the control run. Figures 13a and 13b show the anomalous heat flux at 700 hPa and the anomalous momentum flux at 300 hPa for the baroclinic run, and the difference between the baroclinic run and the control run is shown in Figs. 13c and 13d. For the baroclinic run, the poleward (equatorward) heat fluxes increase in the latitudes of positive (negative) westerly wind anomalies, and the poleward (equatorward) momentum fluxes also increase at a location slightly equatorward of the wind anomalies. The pattern of anomalies for the baroclinic run is almost annular; it is similar to that of PC1 in DJF.
Figure 13e depicts the anomalous EP flux vectors of the baroclinic run. The positive feedback type of wave flux pattern similar to those for PC2 in JJA, and PC1 in DJF and JJA, is present here. Enhanced wave activity is generated in the region of positive wind anomalies, and waves are inhibited in the region of negative wind anomalies. The dominant feature of the difference between the baroclinic run and the control run is the enhanced wave activity in the region of positive wind anomalies (Figs. 13c and 13f). The baroclinic run demonstrates that the barotropic governor plays an important role in the suppression of the eddy–zonal flow feedback for PC2 in DJF.
The anomalous heat flux at 700 hPa and the anomalous momentum flux at 300 hPa for the baroclinic run for PC2 in JJA, and the difference between the baroclinic run and the control run, are shown in Figs. 14a–d. The difference between the baroclinic run and the control run shows that the anomalous barotropic shear inhibits the wave sources within the entire band between 55° and 35°S. However, the upper-level momentum fluxes do not correspond in phase with the low-level wave activity everywhere. In the Atlantic and Indian Oceans, where the mean flow presents a single jet structure (Fig. 12e), enhanced (reduced) poleward momentum fluxes can be found located equatorward of the enhanced wave source region. In the Pacific Ocean, with the presence of the double jet, the pattern of the upper-level momentum fluxes is almost out of phase with that in the Atlantic and Indian Ocean. It is of interest to note that over this split jet region, the behavior of the differences in eddy momentum flux anomalies between the baroclinic and control runs shown in Fig. 14d resembles the behavior of the interjet disturbances discussed in Lee (1997). Why this structure only shows up in the difference (Fig. 14d) but not in the baroclinic run (Fig. 14b) is not clear. One speculation is that the barotropic shear may act to selectively damp the interjet disturbances more than other disturbances over the split jet region, but further studies are needed to clarify this point.
The anomalous EP flux vectors of the baroclinic run for PC2 in JJA is depicted in Fig. 14e. The wave activity in the baroclinic run is more consistent with the wind anomalies than that in the control run (Figs. 14e and 11b); that is, enhanced wave activity is generated in the region of positive wind anomalies and propagates equatorward at the upper troposphere, and waves are inhibited in the region of negative wind anomalies. The difference plot (Fig. 14f) shows that the barotropic shear strongly suppresses the wave source between 35° and 55°S. However, while the divergence of EP flux at the upper troposphere is also suppressed, the suppression of this EP divergence is not complete because of partial cancellation over the Pacific sector (Fig. 14d), such that, even though the upward flux anomaly around 45°S becomes negative in the control run (Fig. 11b), there is still equatorward propagation diverging out from the positive wind anomaly. It is this residual divergence that gives rise to the positive feedback for PC2 in JJA. As discussed above, the opposite phase of the momentum flux anomalies in the Pacific sector (Fig. 14d) is likely connected to the split jet over that region. Hence, we conclude that the difference of PC2 between DJF and JJA is due to the zonal asymmetry of the climatological flow in JJA.
The barotropic governor also has modification to the eddy feedback associated with PC1 in DJF and JJA. In the latitudes centered around 50°S, the wind anomalies are close to zero; that is, the anomalous baroclinic shear is zero, while the reduced eddy activity is remarkable for both seasons (Figs. 11a and 11c). One possible reason is due to the anomalous barotropic shear, which is not zero at these latitudes. Baroclinic runs for PC1 in DJF and JJA have also been conducted. Figures 15a and 15c show the anomalous EP flux vectors for PC1 in DJF and JJA, respectively. The baroclinic runs present a more consistent relationship between the wave activity and the wind anomalies than the control runs, that is, enhanced (reduced) wave activity in the latitudes of the positive (negative) wind anomalies. In the baroclinic runs, the anomalies of the wave activity in the latitudes around 50°S are much weaker than those in the latitudes of positive/negative wind anomalies. The difference between the baroclinic runs and the control runs demonstrates that the barotropic governor suppresses the eddy generation mostly in the region of strong anomalous meridional shear around 50°S. Based on these storm-track model experiments, the phase shift between the mean flow response to anomalous eddy fluxes and the zonal-mean flow anomalies for PC1 in JJA and DJF is due to the barotropic governor. Note that the poleward displacement of the negative peak in eddy feedback relative to the peak in negative wind anomaly (Figs. 9c and 10c), as well as the pattern of the EP flux anomalies seen in Figs. 11a and 11c, are consistent with the eddy feedback diagnosed by LH01 based on reanalysis data (see their Fig. 8).
6. Conclusions and discussion
The persistence time scale of the zonal indices shows seasonal variations. In SH summer, the persistence time scale of PC1 is significantly longer than that of PC2, while the persistence time scale of PC1 is only 1 day longer than that of PC2 in SH winter. Correspondingly, the variance explained by PC1 exceeds that explained by PC2 by a factor of 2 in the SH summer, while the factor is only 1.5 in SH winter. A storm-track modeling approach is applied to demonstrate that seasonal variations of eddy–zonal flow feedback for PC1 and PC2 may at least partly account for the seasonal variations of persistence time scale. The eddy feedback time scale estimated from a storm-track model simulation and a wave-response model diagnostic shows that PC1 in JJA and DJF, and PC2 in JJA, have a positive eddy–mean flow feedback, while PC2 in DJF has no positive feedback. The consistency between the persistence and eddy feedback time scale for each PC suggests that positive eddy–zonal flow feedback increases the persistence of the corresponding zonal index, and stronger (weaker) positive feedback results in a longer (shorter) persistence time scale.
The EP flux diagnostics demonstrate the dynamics governing the positive feedback between eddies and anomalous zonal flow for PC1 in JJA and DJF and PC2 in JJA. The mechanism of the positive feedback is as follows: enhanced baroclinic waves (heat fluxes) at a low level in the region of positive wind anomalies propagate upward and then equatorward from the wave source, thus giving rise to momentum fluxes that reinforce the wind anomalies. This mechanism was also shown by a 12-day lag-regression diagnostics using the reanalysis data by LH01. For PC2 in DJF, the baroclinic waves are inhibited in the region of positive wind anomalies.
The difference of PC2 between DJF and JJA is because of the zonal asymmetry of the climatological flow in JJA. For PC2 in DJF, wind anomalies reinforce the climatological jet. For PC2 in JJA, wind anomalies are mainly in the Pacific Ocean where the climatological jet is weak, so wind anomalies broaden the climatological jet rather than reinforce the climatological jet. A “baroclinic” simulation for PC2 in DJF by the storm-track model, with anomalous barotropic component removed, shows increased baroclinic wave activity in the region of positive zonal wind anomalies. The baroclinic run and the “control” run directly show that the “barotropic governor” plays an important role in suppressing the eddy generations for PC2 in DJF, thus inhibiting the positive eddy–zonal flow feedback. For PC2 in JJA, the barotropic governor effect still appears to be active over the Atlantic/Indian Ocean sector where the basic flow consists of a single jet. Over that region, reduction in wave source (in the form of reduced lower-tropospheric poleward eddy heat flux) results in reduction in the convergence of the upper-level momentum flux. However, over the Pacific sector, where the climatological jet is split, suppression of the wave source leads to enhanced convergence of eddy momentum flux. This opposite relationship between heat and momentum flux over the Pacific is similar to that of the interjet disturbances found by Lee (1997). Due to the zonal asymmetry in the effect of the barotropic suppression, the reduction in eddy momentum flux convergence is much less than that for PC2 in DJF, and the barotropic governor effect does not completely suppress the positive eddy feedback.
Lorenz and Hartmann (2003) showed that EOF2 in the NH winter also has a positive feedback. In NH winter, EOF2 in part represents meridional shifts in the midlatitude jet because in the Pacific and Atlantic sectors the time-mean jet lies at different latitudes. LH01 postulate that the positive eddy–zonal flow feedback occurs for meridional shifts in the midlatitude jet. Our modeling results also support this mechanism. However, EOF2 in SH winter is different from that in NH winter. EOF2 in SH winter basically represents the zonal extension of the polar front jet mainly in the Southern Pacific Ocean because of the unique split jet feature in the SH winter season.
The storm-track modeling approach used in this study provides a new tool to diagnose eddy–zonal flow feedback. Causality between eddies and zonal-mean flow change becomes clear in the storm-track modeling framework because the two-way interaction is separated into two distinct pieces: the response of transient eddies to changes in zonal flow and the consequent eddy feedback onto that zonal flow itself. A storm-track model and a wave-response model, from the diagnostic view, establish a direct link between those two parts and thus demonstrate the feedback between them. The results from the model simulation are very encouraging: for instance, the model reproduces an anomalous positive feedback type of wave activity pattern associated with PC1 in JJA and DJF, which is consistent with that diagnosed from reanalysis data by LH01.
Since the tuning of the storm-track model is different for the two seasons, we have avoided direct quantitative comparison between the two seasons, and only focus on quantitative differences between PC1 and PC2 within the same season and qualitative differences between the results in the different seasons. In this study, we explained the difference of the persistence time scale between PC1 and PC2 in the SH summer and winter, respectively, due to differences in the eddy–zonal flow feedback. However, we did not answer why the persistence time scale of PC1 in summer is longer than that of PC1 in winter. One possible reason is the contribution from the low-frequency eddies. As shown by Lorenz and Hartmann (2001, 2003), the low-frequency eddies act to damp the zonal wind anomalies. However, it is not clear whether this damping effect is the same in different seasons. In addition, in this study, effects of frictional damping have been assumed to be independent of the season. However, based on examination of GCM simulations, Watterson (2007) has provided some evidence that the effects of damping may be different between the different seasons. Whether low-frequency eddies and surface friction play a role in the seasonal difference in the persistence of the zonal indices in the real atmosphere needs further investigation.
Acknowledgments
This research is supported by NSF Grant ATM0354616 and NOAA Grant NA06OAR4310084.
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Distribution of eddy heat fluxes at 850 hPa from (a) the linear storm-track model and (c) ERA-40, and eddy momentum fluxes at 300 hPa from (b) the linear storm-track model and (d) ERA-40 in JJA. Contour intervals are 4 m s−1 K in (a) and (c) and 20 m2 s−2 in (b) and (d). Shaded regions denote values less than −12 in (a) and (c) and less than −40 in (b) and (d).
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
Vertical distribution of zonal-mean eddy heat fluxes for (a) the linear model and (c) ERA-40 and zonal-mean eddy momentum fluxes for (b) the linear model and (d) ERA-40 in JJA. Contour intervals are 2 m s−1 K in (a) and (c) and 5 m2 s−2 in (b) and (d). Shaded regions denote values less than −12 in (a) and (c) and values less than −30 in (b) and (d).
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
One-point lag-regression map of high-pass filtered meridional wind on the longitude–pressure plane at 50°S for the linear model on lag day (a) −1, (b) 0, and (c) +1 and for ERA-40 on lag day (d) −1, (e) 0, and (f) +1. The reference point is located at 60°E and 300 hPa. Contour interval is 2 m s−1. Shaded regions denote values greater than 2.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
The 300-hPa climatological zonal wind for (a) DJF and (b) JJA and the vertical structure of climatological zonal-mean zonal wind for (c) DJF and (d) JJA. Contour interval is 5 m s−1. The shaded region in (a) and (b) denotes zonal wind greater than 20 m s−1.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
EOF1 of the zonal-mean zonal wind for (a) 23 yr, (b) 23 DJF seasons, and (c) 23 JJA seasons. EOF2 of the zonal-mean zonal wind for (d) 23 yr, (e) 23 DJF seasons, and (f) 23 JJA seasons. Contour interval is 1 m s−1 in (a)–(c) and 0.5 m s−1 in (d)–(f).
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
Autocorrelation as a function of time (days) of PC1 andPC2 during (a) 23 yr, (b) 23 JJA seasons, and (c) 23 DJF seasons.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
For JJA, the distribution of eddy heat fluxes at 700 hPa from the linear storm-track model for (a) PC1 and (d) PC2, eddy momentum fluxes at 300 hPa from the linear storm-track model for (b) PC1 and (e) PC2, and composite zonal-mean zonal wind anomalies at 300 hPa for (c) PC1 and (f) PC2. Contour intervals are 2 m s−1 K in (a) and (d), 10 m2 s−2 in (b) and (e), and 2 m s−1 in (c) and (f); shaded region denotes values less than −0.5 in (a) and (d), values less than −5 in (b) and (e), and values larger than 2 m s−1 in (c) and (f).
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
As in Fig. 7 but for DJF.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
For JJA, the wave-response model solution of the zonal-mean zonal wind from 1000 to 100 hPa for (a) PC1 and (d) PC2, composite of the zonal-mean zonal wind anomalies from 1000 to 100 hPa for (b) PC1 and (e) PC2, and the vertical mean of the wave-response model solution and composite anomalies for (c) PC1 and (f) PC2. Units are m s−1 and contour interval is 1 m s−1. Shaded regions denote values larger than 2 in (a) and (d) and values larger than 4 in (b) and (e).
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
As in Fig. 9 but for DJF. Note that contour interval is 0.5 m s−1 in (d), and shaded regions in (d) represent values larger than 0.5.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
Anomalous EP flux vectors from 1000 to 100 hPa for (a) PC1 and (b) PC2 in JJA and (c) PC1 and (d) PC2 in DJF. The contour shows the composite zonal-mean zonal wind anomalies; contour interval is 2 m s−1.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
PC2 composite 300-hPa zonal wind anomalies for (a) DJF and (d) JJA with the 300-hPa climatological zonal wind shaded, PC2 composite zonal wind at 300 hPa for (b) DJF and (e) JJA, and the difference between PC2 composite 300- and 1000-hPa zonal wind for (c) DJF and (f) JJA. Contour intervals are 2 m s−1 in (a), (c), (d), and (f), and 5 m s−1 in (b) and (e). Shaded region denotes values larger than 20 in (a), (b), (d), and (e), and values larger than 2 in (c) and (f).
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
For PC2 in DJF, the distribution of (a) eddy heat fluxes at 700 hPa and (b) eddy momentum fluxes at 300 hPa for the baroclinic run from the linear storm-track model and the difference of (c) eddy heat fluxes at 700 hPa and (d) eddy momentum fluxes at 300 hPa between the baroclinic run and the control run; (e) anomalous EP flux vectors from 1000 to 100 hPa for the baroclinic run and (f) the difference of EP flux vectors between baroclinic run and control run. Contour intervals are 1 m s−1 K in (a) and (c), 5 m2 s−2 in (b) and (d), and 1 m s−1 in (e). Shaded region denotes values less than −0.5 in (a) and (b); and values less than −5 in (c) and (d).
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
As in Fig. 13 but for PC2 in JJA. Contour interval is 2 m s−1 K in (a) and (c).
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
Anomalous EP flux vectors from 1000 to 100 hPa for the baroclinic run of PC1 in (a) DJF and (c) JJA; the difference in the anomalous EP flux vectors from 1000 to 100 hPa between the baroclinic run and the control run for PC1 in (b) DJF and (d) JJA. The contour shows the composite zonal-mean zonal wind anomalies; contour interval is 1 m s−1.
Citation: Journal of the Atmospheric Sciences 64, 9; 10.1175/JAS4005.1
The explained variance (%) of seasonal and annual first two EOFs in each season and the e-folding time scale (in days) of PC1 and PC2.
The eddy feedback time scale and persistence time scale of PC1 and PC2 in JJA and DJF.
Note that no observed counterpart is shown for the eddy anomalies. As discussed in section 1, it is difficult to diagnose the eddy feedback from observations since the zero-lag eddy anomalies are mostly due to random eddy fluctuations rather than the eddy response to the mean flow changes. LH01 diagnosed the eddy response by examining the lag-12 eddy distribution. However, as discussed above, the e-folding time scales of the EOFs are generally less than 12 days, hence it is doubtful whether the lag-12 eddy distribution captures the entire eddy feedback.
