Perpetual winter simulations using the NCAR Whole Atmosphere Community Climate Model (WACCM) are conducted to document the differences of the initial transient response of the boreal winter Northern Hemisphere stratospheric polar vortex to central (CPW) and eastern Pacific warming (EPW) events. Idealized patches of positive sea surface temperature (SST) anomalies are superimposed onto a climatological SST field to mimic canonical CPW and EPW forcings. A 20-member ensemble was created by varying initial atmospheric conditions for both CPW and EPW cases. In the ensemble average, the vortex weakens under both CPW and EPW forcing, indicated by a negative zonal mean zonal wind tendency. This tendency is mainly tied to changes in the eddy-driven mean meridional circulation (MMC). A negative anomaly in the eddy momentum flux convergence also plays a secondary role in the weakening. The vortex response, however, differs dramatically among individual ensemble members. A few ensemble members exhibit initial vortex strengthening although weaker in magnitude and shorter in duration than the initial weakening in the ensemble average. The initial state and the subsequent internal variation of the extratropical atmosphere is at least as important as the type of SST forcing in determining the transient response of the stratospheric polar vortex. Interactions between the internal variability of the vortex and SST-driven wave anomalies ultimately determine the nature of the initial transient response of the vortex to EPW and CPW forcing. This sensitivity to the initial atmospheric state has implications for understanding medium-range forecasts of the extratropical atmospheric response to emerging tropical SST anomalies, particularly over high-latitude regions.
The stratospheric polar vortex is an important element of the Northern Hemisphere wintertime climate. Changes in the strength of the vortex often project onto tropospheric variability, and thus impact surface climate over high latitudes (Baldwin and Dunkerton 1999; Black 2002) and Europe (Bell et al. 2009; Ineson and Scaife 2009). The El Niño–Southern Oscillation (ENSO) is among several different climate phenomena that affect the strength of the polar vortex. The association between canonical El Niño events [i.e., eastern Pacific warming (EPW)] and a weak polar vortex has been well established via (i) perpetual winter modeling experiments (e.g., Taguchi and Hartmann 2006) employing prescribed El Niño–like SST anomalies, in models such as the Whole Atmosphere Community Climate Model (WACCM), (ii) Atmospheric Model Intercomparison Project (AMIP) experiments with selected significant ENSO events (e.g., Manzini et al. 2006), and (iii) through analysis of reanalysis data (Camp and Tung 2007; Garfinkel and Hartmann 2007; Hegyi and Deng 2011). The mechanism that drives the weakening of the vortex, as suggested by these studies, is established first through the propagation of tropospheric Rossby waves from the tropical Pacific to higher latitudes in the Northern Hemisphere in response to the Pacific SST anomalies and the associated convective heating anomalies (e.g., Hoskins and Karoly 1981). This is followed by anomalous upward propagation of wave activity from the extratropical troposphere to the stratosphere serving to decrease the strength of the stratospheric polar vortex.
The magnitude of the anomalous upward propagation of wave activity is especially sensitive to the phase of the forced anomalous Rossby waves in relation to the phase of the climatological planetary wave in the high latitudes of the Northern Hemisphere (i.e., via linear interference; e.g., Fletcher and Kushner 2011; Nishii et al. 2009). When the wave anomaly is in phase with the climatological wave (constructive interference), the upward wave propagation from the troposphere to the stratosphere is enhanced. Linear interference has been shown to be an important concept in understanding the interaction among several tropospheric phenomena and the stratosphere, including the interaction between stratospheric variability and blocking highs (Nishii et al. 2011). It also has been shown to be important in describing the link between stratospheric variability and autumnal Eurasian snow cover (Smith et al. 2010). In the case of the interaction between ENSO and the polar stratosphere, the constructive interference of the El Niño–forced tropospheric geopotential height anomalies (primarily over the North Pacific) with wavenumber-1 and -2 components of the climatological planetary waves leads to a net increase in the upward wave propagation and a weakened polar vortex (Garfinkel and Hartmann 2008; Garfinkel et al. 2010), through the effect of enhanced wave forcing on the stratospheric zonal mean zonal wind.
Recently, a second type of El Niño has been identified [the central Pacific El Niño (Kao and Yu 2009; Yu and Kao 2007) or El Niño Modoki (Ashok et al. 2007)], which is characterized by warm sea surface temperature (SST) anomalies in the central Pacific and a relative lack of warm anomalies across the eastern Pacific. Several studies have attempted to quantify the effects of central Pacific warming on the polar vortex, through both reanalysis and general circulation model (GCM) studies. Analyzing reanalysis data, Hegyi and Deng (2011) discovered that central Pacific warming (CPW) events are associated with a strengthened polar vortex, in contrast to the impact of EPW events. In a WACCM model study, Xie et al. (2012) found a similar relationship that is dependent on the phase of quasi-biennial oscillation (QBO). In contrast, when analyzing reanalysis data, Graf and Zanchettin (2012) link CPW events to a weakened vortex.
Several characteristics of the reanalysis data studies may affect the conclusions reached by individual studies. A key difference between Hegyi and Deng (2011) and Graf and Zanchettin (2012) is the selection of CPW events to be included in the composite analysis. Using a small composite of events and different CPW indices as the basis of event selection and compositing can lead to oppositely signed vortex responses (Garfinkel et al. 2013). In addition, each individual year considered may contain additional contemporaneous climate features that impact the polar vortex and interfere with the response of the vortex to CPW and EPW. Characteristics of the internal variability of the polar vortex may also be different between individual years. Furthermore, the SST patterns of the years chosen in the composite analyses by various authors are rarely pure CPW or EPW, but they encompass a spectrum instead.
To address these ambiguities and to follow up the observational study of Hegyi and Deng (2011), we conduct a series of numerical experiments using the National Center for Atmospheric Research (NCAR) WACCM in which idealized SST anomaly patches are superimposed upon a climatological December–February (DJF)-mean distribution of SSTs. The patches are designed to represent canonical CPW and EPW patterns, respectively, thereby isolating the effects of each type of warming on the polar vortex. The purpose of our model experiments is to document the similarities and differences of the initial transient response (i.e., the response within the first 40 days) of the stratospheric polar vortex to CPW and EPW events. We investigate the initial and transient response of the vortex, in contrast to the equilibrium state response that was the main target of previous studies, to facilitating the understanding of the vortex response that in reality also occurs within a short, subseasonal time period. Specifically, these idealized experiments allow us to assess the relative significance of the SST forcing patterns versus the initial state of the extratropical circulation in determining the vortex responses across subseasonal time scales. Following the introduction, section 2 describes the model experiment design and the analysis tools employed. Key results from the model experiments are presented in section 3 while concluding remarks are given in section 4.
2. Data and methods
a. Model experiment setup
We employ the NCAR WACCM, version 4 (WACCM4), in this study (Garcia et al. 2007). WACCM4 is run as a component set within the NCAR Community Earth System Model, version 1.0.2 (CESM 1.0.2). The WACCM model is specifically designed to investigate the coupling between the stratosphere and the troposphere and is thus appropriate for experiments exploring the effects of tropical SSTs on the stratosphere. Versions of the WACCM model have been used in several previous studies of stratosphere–troposphere interaction (e.g., Calvo and Marsh 2011; Sassi et al. 2004; Taguchi 2010). Importantly, with 66 vertical levels and a model top at approximately 150 km, WACCM4 has a well-resolved stratosphere. It also includes an option to impose a realistic QBO on each model run. In our set of WACCM runs, perpetual 1 January conditions are selected in order to eliminate the impact of solar forcing and remove the seasonal cycle from each experiment. The imposed QBO was turned off, resulting in weak stratospheric easterly winds in the QBO region.
A control run with climatological SSTs was performed first. The control run consists of a 1000-day simulation forced by 1870–2009 DJF-average SSTs taken from the Hadley Centre Sea Ice and Sea Surface Temperature (HadISST) dataset (Rayner et al. 2003). The control run was used to (i) provide a source of initial conditions and (ii) serve as a basis for comparisons with the two ensembles of CPW and EPW patch runs. In the second step, two 20-member ensembles of 90-day simulations forced by idealized tropical SST anomaly patterns were conducted. To create the prescribed SSTs for each set of forced runs, the idealized SST anomaly “patches” (Figs. 1a,b) were added to the DJF-average climatological SSTs used in the control run (thus these ensemble members are referred to as the “patch” runs). In the first ensemble, the patch is applied in the central Pacific mimicking the canonical pattern of CPW. In the second ensemble, the patch is applied in the eastern Pacific to represent EPW events. Each ensemble member is initialized using unique initial conditions drawn from the control run. The initial conditions were chosen to cover a variety of the strength of the stratospheric polar vortex that is typically measured by the zonal mean zonal wind at 10 hPa and 60°N. All the ensemble members have values of this intensity index in the initial conditions ranging between 22.5 and 27.5 m s−1, which are average November values of this index in reanalysis data. The effects of the patches are assessed by comparing the patch run results with the corresponding 90-day period in the control run (the first day of this period is identical to the day from which the initial condition of the patch run is drawn). As a consequence, the control state used for comparison is different for each ensemble member with different initial conditions. The same 20 initial conditions were used for the CPW and EPW ensemble, allowing also for direct comparisons across the two ensemble groups. Statistical significance of the ensemble average anomalies relative to the control run was calculated through a two-tailed Student’s t test.
The SST patches used in the patch ensembles were created using a cosine-squared function identical to the function used in Barsugli and Sardeshmukh (2002):
The SST patch equation is a function of latitude and longitude λ. The subscripts k and w represent the center point of the patch and the width parameter of the patch, respectively. The parameter B represents the maximum amplitude of the patch. The CPW (EPW) patch was centered at 0°, 165°W and (0°, 110°W). Each patch is an ellipse with a minor axis of 20° in length in the north–south direction and a major axis of 60° in length in the east–west direction, and a maximum amplitude of B = 3.0 K. The latitude and longitude width parameters were set to 40° and 27°, respectively, for each patch, to create a more gradual decrease of the SST anomaly values when moving away from the center of the patch. Outside of the patch areas, the SST anomalies are equal to the climatological SSTs used in the control run. With these parameters, the average SST anomaly over each patch is 1.383 K. The bounds of the EPW patch are designed to cover most of the Niño-3 and Niño-1+2 regions and to extend eastward to the South American coast. The bounds of the CPW patch are very similar to the central Pacific anomaly box used in the definition of the Modoki index in Ashok et al. (2007), with the only difference being that the CPW patch is extended 5° eastward to match the size of the EPW patch.
b. Analysis method
where overbars represent the zonal average and primes represent the deviation from the zonal average. According to Eq. (2), the net tendency of the zonal mean zonal wind is equal to the sum of the convergence of the eddy momentum flux , the Coriolis force exerted on zonal mean meridional wind , and the drag term . The zonal mean meridional wind and the vertical velocity are tied together through the continuity equation and represent the mean meridional circulation (MMC). We thus call the Coriolis force term in Eq. (2) the contribution to the zonal mean zonal wind tendency by the eddy-driven MMC forcing. In the results section, we thus focus our discussion on the roles of the two components of the eddy forcing—the eddy MMC forcing and eddy momentum forcing, in generating the simulated response of the vortex to the specified CPW and EPW events. Specifically, we investigate the contributions of anomalies in these two eddy forcing terms to the changes in the evolution of the stratospheric polar vortex during the first 40 days after the CPW or EPW heating is switched on.
Additionally, we also make an attempt to compare the relative importance of the initial atmospheric state, internal variability, and the CPW/EPW-forced variability in determining the transient response of the vortex. To do that, we first define the following nomenclature: variable from any model run is labeled as , where CTL denotes the control run, PCH denotes the patch run and indicates the time after the patch is introduced. Thus, the initial condition is . Given the design of the model experiment, this value is identical for a control run and the corresponding EPW and CPW patch run. Following these definitions, any variable in the patch run can be written as the following:
where , the initial condition, is denoted as IC, the difference between the patch run and control run (the term inside the first bracket) is referred to as forced variability (FV), and the difference between the variable value at and the initial value in the control experiment (the term inside the third bracket) is considered the internal variability (IV) of the system. Similarly, any variable in the control run can be written as the following:
Following Eqs. (3a) and (3b), we decompose the eddy zonal and meridional wind in the eddy momentum flux term . Taking the difference of this quantity between the patch and the corresponding control run yields the following:
The subscripts here represent the variable used to calculate each term, with the primes omitted in the notation (e.g., ). In our discussion, we consider the first term on the rhs of Eq. (4) the nonlinear heating component since it is purely a product of FV terms associated with the imposed CPW or EPW forcing. The second and third term on the rhs of Eq. (4) are considered linear components as they are both products of FV and IV or IC. The relative importance of the nonlinear and linear components in generating the CPW/EPW-forced vortex response will be discussed for the eddy momentum forcing.
Finally, to explicitly diagnose the transient difference of the stratospheric zonal mean zonal wind between the patch run and the control run, we integrate Eq. (2) from time 0 to τ, neglect the drag term , and take the difference of the integrated equation between the patch and control run to obtain the final diagnostic equation:
In Eq. (5), the left-hand side corresponds to the difference of the vortex strength between the patch run and the control run at any time , where the vortex strength is obtained by averaging the zonal mean zonal wind between two latitudes and (taken to be 50° and 80°N in our calculation). Equation (5) basically states that the instantaneous difference in the vortex strength between the patch and the control run can be attributed to two components of the eddy forcing: the eddy-driven MMC forcing [the first term on the rhs of Eq. (5)] and the eddy momentum forcing [the last term on the rhs of Eq. (5)], where the eddy momentum forcing can be further decomposed into nonlinear and linear components according to Eq. (4).
a. Ensemble average
The ensemble average of the EPW and CPW patch runs shows evidence of a weakened vortex in response to both CPW and EPW forcing (Fig. 2). What is plotted in Fig. 2 are the differences of the zonal mean zonal wind between the patch run and the corresponding control run averaged over 50°–80°N as a function of pressure and time (in terms of the number of days since the CPW/EPW heating is switched on). The 50°–80°N latitudinal range corresponds to where the winter stratospheric polar vortex resides in the Northern Hemisphere. There are negative anomalies present starting from day 22 in both the CPW and EPW case. The anomalies extend throughout the stratosphere in both cases, but extend lower into the upper troposphere in the CPW case than in the EPW case. The anomalies peak in intensity around day 35 in the CPW case, and day 37 in the EPW case. Despite these minor differences, the vortex weakens with a similar magnitude and timing when CPW or EPW forcing is imposed. The 10-hPa zonal mean zonal winds decrease by 8.8 (10.1) m s−1 in the CPW (EPW) ensemble average during the peak of the initial response. In addition, the ensemble spread is 11.0 (12.6) m s−1 in the CPW (EPW) ensemble average, as measured by the intermember standard deviation.
Figure 3 shows the corresponding ensemble averages of the anomalies in the eddy-driven MMC and eddy momentum flux forcing. For the CPW case (top panels), consistent with the initial vortex weakening starting from day 22, a large negative eddy-driven MMC anomaly emerges in the middle and upper stratosphere (Fig. 3a). A weaker negative anomaly of the eddy momentum forcing also appears in the stratosphere a couple of days earlier, relative to the negative MMC forcing anomaly (Fig. 3b). Thus, both components of the eddy forcing act to weaken the vortex in the CPW case with the eddy-driven MMC forcing being greater in magnitude when compared to the eddy momentum forcing. In the EPW case, the negative anomaly of the eddy-driven MMC forcing occurs at a much later time (around day 30; Fig. 3c). The negative anomaly of the eddy momentum forcing therefore plays a more important role in the initial weakening of the vortex in EPW (Fig. 3d), while the negative eddy-driven MMC forcing anomaly dominates during the peak of the vortex weakening. The slight timing differences in the occurrences of the eddy forcing anomalies may explain the slight differences in timing of the vortex weakening between the CPW and EPW case. In the ensemble average, although both the eddy momentum and eddy-driven MMC forcing contribute to the initial and transient weakening of the vortex, the eddy-driven MMC forcing has a larger magnitude and clearly dominates the process.
Interestingly, as shown in Fig. 4, if the eddy momentum forcing is further broken down into the nonlinear and linear parts as defined in section 2b following Eq. (4), the linear part shows a negative contribution to the zonal mean zonal wind tendency. This is consistent with the overall influence of the eddy momentum forcing on the vortex strength (Figs. 4b,d). The nonlinear part actually has a positive contribution that tends to strengthen the vortex (Figs. 4a,c). The nonlinear part is slightly weaker in magnitude compared to the linear part and this is the main reason why the overall eddy momentum forcing is weakly negative. For both the CPW and EPW cases, it is clear that the linear part of the eddy forcing, which represents the interactions between the CPW/EPW-forced variability and the initial condition/internal variability of the extratropical atmosphere, contributes to a significant weakening of the vortex.
Figure 5 shows the ensemble-averaged anomalies of the two components of the linear part of the eddy momentum forcing, namely, FV–IC (interaction between SST-forced variability and the initial atmospheric condition) and FV–IV (interaction between SST-forced variability and the internal variability of the atmosphere). FV–IC results in a positive anomaly in the stratosphere starting from day 14 and extending to day 25 (Figs. 5a,c). The positive anomaly is slightly stronger initially in response to CPW than in response to EPW. FV–IV, on the other hand, produces negative anomalies in both the CPW and EPW cases (Figs. 5b,d). These anomalies appear at a similar time as the FV–IC anomalies, but have a much larger magnitude and are consistently negative, ultimately making the total linear part of the eddy momentum forcing negative. This result, together with the overall significance of the linear component of the eddy momentum forcing as demonstrated in Fig. 4, lends support, from a transient response perspective, to the linear interference mechanism proposed by earlier studies in an attempt to explain the connection between the tropical Pacific warm SST events and the weakening of the stratospheric polar vortex. It suggests that the interaction between the extratropical wave response to the tropical Pacific warming and the initial state/internal variability of the extratropical atmosphere largely determines the tendency of the zonal mean zonal winds in the polar stratosphere, and thus the anomalous transient evolution of the stratospheric polar vortex.
b. Diverse vortex responses in individual ensemble members
Despite the consistency in the ensemble average, there is much variability in the initial, transient vortex response to CPW and EPW forcing in the individual ensemble members. This diverse response is a reflection of the importance of the initial atmospheric state and the subsequent internal variation of the extratropical atmosphere in determining the overall response of the vortex to a tropical SST anomaly. For example, although the vortex initially weakens in response to CPW and EPW in most individual ensemble members (marked by blue squares and asterisks in Fig. 6), the vortex initially strengthens in response to CPW or EPW in a few of the individual ensemble members (marked by red squares and asterisks in Fig. 6). This is consistent with the distribution of vortex responses in Garfinkel et al. (2013), where a few of the ensemble members show a strengthened vortex in response to CPW and EPW. The vortex initially strengthens in response to both CPW and EPW in case 4, and the vortex initially weakens in response to CPW and strengthens in response to EPW in case 20. We also document the longitudinal position of the zonal wavenumber-1 and -2 wave in Fig. 6. These planetary waves are most likely to propagate up from the troposphere to the stratosphere and affect the strength of the polar vortex. In these cases, the longitudes where peak values of the initial wavenumber-1 and -2 components of the tropospheric planetary waves are found to deviate significantly from the corresponding ensemble-averaged values (denoted by the black asterisk in Fig. 6). Specifically, the cases where the vortex response is not consistently weakening tend to have a wavenumber-1 wave in the initial state whose peak value is found at a longitude far away from the longitude of approximately 165°E in the ensemble average. Given the importance of the linear part of the eddy momentum forcing in determining the vortex response, it is plausible that the observed diverse vortex response arises from the differences in the way how the CPW/EPW-forced waves interact with the initial and the subsequent internal variation of the extratropical planetary waves. We therefore conduct a more detailed investigation of two anomalous cases: case 4 and case 20.
In case 4, the vortex initially strengthens slightly starting from about day 22 in response to both CPW and EPW (Figs. 7a and 8a). The strengthening is quite brief in the sense that it lasts only approximately 3–4 days and is weaker in magnitude than the initial strengthening in the ensemble CPW and EPW response. In this case, the initial strengthening response [days 22–26 zonal mean zonal wind anomaly at 10 mb] has a magnitude of 3.8 and 4.4 m s−1 for CPW and EPW, respectively. The magnitude of these strengthening responses is about 40% of the ensemble average response, and within 1.15 standard deviations from the mean, based on the ensemble spread. The strengthening is largely related to a positive anomaly of the eddy-driven MMC forcing in the stratosphere (Figs. 7c and 8c). Following the initial strengthening, the vortex weakens starting from about day 28, as a pronounced negative anomaly of the eddy momentum forcing emerges (Figs. 7b and 8b). In the EPW case, the eddy-driven MMC forcing also switches to a strong negative anomaly around day 34, contributing to the subsequent weakening of the vortex (Fig. 8c). Just like in the ensemble average, the interactions between the CPW/EPW-forced variability and the initial state and internal variability of the extratropical atmosphere (i.e., the linear part of the forcing; Figs. 7e and 8e) largely contribute to the negative anomaly of the eddy momentum forcing. The nonlinear part of the forcing resulting from CPW/EPW-forced variability alone tends to be positive and leads to strengthening of the vortex (Figs. 7d and 8d). Thus the main difference between case 4 and the ensemble average is that in case 4 the initial positive anomaly of the eddy-driven MMC forcing lasts much longer, particularly under CPW forcing (Fig. 7c).
In case 20, the vortex initially strengthens slightly at about day 20 in response to EPW and CPW (Figs. 9a and 10a). However, the initial strengthening in the CPW case is much weaker than that in the EPW case. The initial strengthening response (days 18–24 zonal mean zonal wind anomaly at 10 mb) has a magnitude of 2.7 and 10.1 m s−1 for CPW and EPW, respectively. The magnitude of these strengthening responses is about 30% (100%) of the CPW (EPW) ensemble average response, and within 1.06 (1.61) standard deviations from the CPW (EPW) mean, based on the ensemble spread. Since we define the sign of the transient response in this study using the anomalous 10-mb zonal mean zonal winds averaged over the period days 20–30 (see the caption of Fig. 5), the transient response of the vortex to CPW in case 20 is denoted as a weakening in Fig. 6, due to the weakening that occurred a few days after the initial minor strengthening (Fig. 9a). Figures 9c and 10c indicate that positive anomalies of the eddy-driven MMC forcing in the stratosphere are responsible for the strengthening of the vortex in both CPW and EPW cases that start at day 20. The positive anomaly of the eddy-driven MMC forcing is much larger in magnitude in the EPW case (Fig. 10c) compared to that in the CPW case (Fig. 9c). This is the primary reason why the eddy-driven MMC forcing can overcome the negative anomaly associated with the eddy momentum forcing (Fig. 10b) and lead to the overall transient strengthening of the vortex in response to EPW. In the CPW case, the weak positive anomaly of the eddy-driven MMC forcing (Fig. 9c) is eventually dominated by the negative eddy momentum forcing anomaly (Fig. 9b), resulting in the vortex weakening following the initial minor strengthening (Fig. 9a). Consistent with case 4 and the ensemble average, the negative anomaly of the eddy momentum forcing found in case 20 is largely associated with its linear part, and the nonlinear part of the forcing resulting from CPW/EPW-forced variability produces a positive anomaly (Figs. 9d,e and 10d,e). Additionally, in both cases 4 and 20, the negative anomaly in the linear part of the eddy-momentum forcing is primarily driven by the interaction between SST-forced variability and the internal variability of the extratropical atmosphere (i.e., the FV–IV term), while the interaction between SST-forced variability and the initial condition of the atmosphere (i.e., the FV–IC term) remains largely positive, especially in the lower stratosphere (figures not shown).
4. Summary and conclusions
The purpose of this study is to identify the similarities and differences in terms of the initial, transient response of the stratospheric polar vortex to the central and eastern Pacific warming events. In our idealized modeling experiments, we introduce an elliptic patch of positive SST anomalies in the tropical Pacific to roughly mimic the mean structure and amplitude of a canonical CPW or EPW event. Two 20-member ensembles of 90-day simulations forced by these idealized tropical SST anomalies are conducted. The transient responses of the stratospheric polar vortex (defined in terms of the 10-hPa zonal mean zonal winds averaged over 50°–80°N for the period days 20–30) in the patch runs where SST anomalies have been applied are compared against those in the control run where climatological SSTs have been used. The differences in the transient response between the patch and the control runs are interpreted in a framework based on the quasigeostrophic zonal mean zonal momentum equation on a beta plane.
Two important results arise from this analysis. First, we find that in the ensemble average, both the CPW and EPW forcing result in a transient weakening of the vortex. This response is the same sign as what has been shown in studies investigating the equilibrium response to CPW and EPW (e.g., Garfinkel et al. 2013). Both the eddy momentum forcing and the eddy-driven MMC forcing contribute to this weakening. Despite a few minor differences between the CPW and EPW ensemble average, the weakening occurs at a similar time (starting approximately 22 days after the SST anomaly is imposed) and location (throughout the stratosphere and the upper troposphere) under both types of warming events. Thus, in an ensemble average sense, the transient response of the vortex to the CPW and EPW is very similar. Negative anomalies in the eddy momentum and eddy-driven MMC forcing jointly contribute to the initial weakening of the vortex. The eddy-driven MMC forcing is higher in magnitude and thus plays a more significant role. Separating the eddy momentum forcing into a linear and a nonlinear component reveals that in the ensemble average, the nonlinear part, which involves only the extratropical wave response to the CPW/EPW forcing, contributes positively to the zonal mean zonal wind tendency. The linear part, which quantifies the interaction between the extratropical wave response to the CPW/EPW forcing and the initial state/internal variation of the extratropical atmosphere, is responsible for producing negative anomalies in the eddy momentum forcing. This contrast is consistent under both CPW and EPW forcing and the presence of two terms of similar magnitude but opposite signs leads to the total eddy momentum forcing being weakly negative. It is further shown that the negative anomaly associated with the linear part is primarily a result of the interaction between the SST-forced variability and the internal variability of the vortex. These facts lend further support (from the perspective of the initial transient response) to the linear interference mechanism that has been proposed to explain the connection between the stratospheric polar vortex variability and the tropical Pacific warming.
Second, although consistent initial weakening of the vortex is identified in the ensemble average of the CPW and EPW cases, not all of the individual ensemble members show this weakening. There are a few cases where the vortex initially strengthens in response to both the CPW and EPW forcing. The magnitude of this strengthening is equal to or less than the ensemble average [e.g., 20–30-day average anomaly in 10-hPa zonal mean zonal winds is 2.7 (10.1) m s−1 for the CPW (EPW) case 20 versus 8.8 (10.1) m s−1 in the CPW (EPW) ensemble average during the peak initial decrease], and approximately 1–1.6 standard deviations from the ensemble mean. The time scale of these strengthening events, 6–8 days, is shorter than the initial weakening in the ensemble average, which is more than 15 days. In cases 4 and 20 where the vortex initially strengthens slightly, a positive anomaly in the eddy-driven MMC forcing plays a critical role in driving this strengthening, in contrast to the largely negative anomaly found in the ensemble average. Since the only differences between different individual ensemble members is the initial state of the atmospheric flow, the diverse response exhibited by individual members suggests that when initial transient response is considered (cf. the equilibrium response), the initial atmospheric state when the SST anomalies start emerging and the subsequent intrinsic evolution (internal variability) of the atmospheric flow also plays a nontrivial role in determining the time-dependent response of the vortex. In some cases (e.g., case 4) the importance of the initial state could outweigh the effect of a tropical Pacific SST anomaly.
In addition to the initial state affecting the wave forcing in the troposphere, which we highlighted in this manuscript, the initial state also affects the vertical propagation of tropospheric wave activity into the stratosphere. The distribution of potential vorticity in the basic flow, an important term in the squared wave refractive index (Andrews et al. 1987; Matsuno 1970) is crucial in determining the pathways of the vertical propagation of Rossby waves and the wave (eddy) forcing of the zonal mean flow in the stratosphere. Differences in the distribution of potential vorticity in the initial basic flow, and thus the favored pathways for vertical propagation of Rossby waves, between ensemble members could also explain the different vortex responses.
An immediate implication of this result is that in any individual year, knowledge about the tropical Pacific SST alone is not enough to make a skillful medium-range forecast for the state of the polar stratosphere. The initial state of the extratropical atmosphere must also be considered in order to understand the subseasonal evolution of the polar stratosphere. Therefore medium-range forecasts of the stratospheric response to tropical SST anomalies are likely to be sensitive to the initial atmospheric state in the model, along with other factors such as the QBO phase (Garfinkel and Hartmann 2007). The response is much more complicated than a simple consistent weakening effect across all CPW and EPW events. This may partly explain the contradictory results in the literature for the effects of CPW and EPW (e.g., Graf and Zanchettin 2012; Hegyi and Deng 2011; Xie et al. 2012), especially in reanalysis studies where only a limited sample size of CPW and EPW events are available. The initial state of the extratropical flow and wave structure in a given cool season when CPW or EPW occurs differs from year to year, and this difference likely translates into differences in how CPW or EPW modulates the strength of the stratospheric polar vortex in an individual season. Only when a large number of seasons are considered or long-term model integrations are used we may be able to identify an averaged weakening effect of CPW and EPW on the vortex strength, as shown in the ensemble average here.
Finally, we emphasize that the analysis conducted here only serves as a first step to understand how the polar atmosphere responds to the emerging tropical SST anomalies. There are a variety of related questions that cannot be addressed without a substantial amount of additional modeling and diagnosis work. These include questions related to the method that we used to isolate the effects of CPW and EPW, such as the sensitivity of the results to the slight changes in the magnitude and structure of the prescribed SST anomalies, the impact of Pacific cold events on the polar atmosphere, the sensitivity of the choice of the date from which the perpetual conditions of the model experiments are taken, and the potential complications when we incorporate into the analysis additional factors such as EPW events being stronger in amplitude compared to CPW events. There are also still some questions unanswered related to the dynamical mechanism that we propose here to explain the initial, transient vortex response to CPW and EPW. Although we present here the relative importance of the contributions of the eddy-driven MMC and eddy momentum flux to the initial vortex response, along with the contributions of the initial condition (IC), internal variability (IV), and forced variability (FV) components of the eddy momentum flux term, how exactly these components interact to produce the differences in response between ensemble members is a subject for further study. Also, the relative importance of the effect of the initial state on the tropospheric wave forcing (e.g., Fig. 6) and the vertical wave propagation from the troposphere to the stratosphere is another important consideration left to be explored in future work.
The HadISST dataset is provided by the Met Office (www.metoffice.gov.uk/hadobs). Bradley M. Hegyi is supported by the NASA Earth and Space Science Fellowship under Grant NNX10AO64H, and Yi Deng is supported by the NSF Grant AGS-1147601 and by the DOE Office of Science Regional and Global Climate Modeling (RGCM) program under Grant DE-SC0005596.