Dynamical Feedback between Synoptic Eddy and Low-Frequency Flow as Simulated by BCC_CSM1.1(m)

There is pronounced and significant low-frequency (LF) climate variability in the midlatitude troposphere on a timescale greater than 10 days——for example, as manifested in the North Atlantic Oscillation (NAO), Pacific-North American pattern (PNA), Arctic Oscillation (AO), and Antarctic Oscillation (AAO) (Wallace and Gutzler, 1981; Thompson and Wallace, 1998, 2000; Gong and Wang, 1999). Synoptic eddies (SEs) with a lifetime of 2-8 days positively feedback onto the LF variability, which has been proposed as the major growth mechanism for LF variability (e.g., Lau, 1988; Nakamura and Wallace, 1993; Branstator, 1995; Jin et al., 2006a, 2006b; Luo et al., 2007; Jin, 2010; Kug et al., 2010a; Ren et al., 2011; Zhang et al., 2012; Tan et al., 2014). SE and LF (SELF) flow interaction plays a crucial role in the generation and maintenance of the major LF modes (e.g., Cai and Mak, 1990; Lau and Nath, 1991; Robinson, 1991a; Branstator, 1992; Limpasuvan and Hartmann, 1999; Lorenz and Hartmann, 2003; Jin et al., 2006a; Ren et al., 2009, 2012; Kug et al., 2010b; Tan et al., 2015). On the one hand, statistically anomalous SE activity acts to maintain monthly/ seasonal mean extratropical climatic variability through upscaled energy transport (e.g., Kok et al., 1987; Vautard et al., 1988); while on the other hand, LF flow can in return partly modulate the statistically anomalous SE activity, where ambient anomalous mean flow works to systematically organize high-frequency (HF) SEs and harvest eddy vorticity (EV) forcing (Nakamura and Wallace, 1993; Branstator, 1995).

In addition to theoretical and observational analyses, numerical models can be powerful tools for understanding the dynamics and processes of the two-way interactions between LF variability and transient SEs. Many studies have used climate models to show that LF flow is largely maintained by the positive feedback of HF eddies (Cai and Mak, 1990; Robinson, 1991a, 1991b, 2000; Branstator, 1995; Feldstein, 1998; Chang, 2006). For example, (Feldstein, 1998) used a simplified general circulation model (GCM) to demonstrate that HF transient eddy flux plays an essential role in maintaining anomalous LF flow. Based on a two-level primitive equation model, Robinson (1991a, 1991b) found that barotropic transient eddy feedback can slow the eastward propagation of LF flow and, similarly, that the eddy-momentum flux can be induced by LF flow. (Robinson, 2000) further emphasized the importance of surface friction in closing the dynamical feedback loop. Quasi-geostrophic models and linear models have also been widely employed to explore the feedbacks among the climatological mean state, LF variability, and transient eddies (e.g., Jin et al., 2006a, 2006b; Pan et al., 2006; Zhang et al., 2012; Nie et al., 2013). In particular, (Jin et al., 2006a) proposed a theoretical framework for dynamical closure of the two-way SELF feedback based on a stochastic dynamics hypothesis in which SE forcing can be empirically parameterized by LF flow. Their numerical experiments using a linear GCM showed that the extratropical atmospheric responses of tropical external forcing can be significantly enhanced with the eddy feedback operator introduced in the model.

Climate models are widely recognized as indispensable tools for climate simulation, climate prediction, and climate change projection (e.g., Zhou et al., 2007). However, it is important to evaluate a model's ability before application (Schuenemann and Cassano, 2009; Jiang et al., 2012). Since SE feedback is very important for the maintenance of LF variability, it is clear that the performance of models in simulating such SE feedback is crucial to reasonably reproducing the major types of climate variability and modes (e.g., PNA, AO, NAO, and AAO). (Kang et al., 2011) noted the remarkable impact of transient SEs on extratropical seasonal-mean predictability using DEMETER hindcasts. Similarly, it is important to comprehensively evaluate the dynamical feedback between SEs and LF flow in models, which can be accomplished with the diagnostics established in previous studies (Lau, 1988; Kug et al., 2010a; Ren et al., 2011, 2014).

In this study, we focus on an evaluation of the dynamical SE feedback (SE to LF pathway) to examine how well it is simulated by BCC_CSM1.1(m), which has served operationally for seasonal prediction at the Beijing Climate Center since 2015. We focus on the key role that the dynamical SE feedback plays in maintaining the major climate modes as reproduced by this model. We expect our results to help in identifying model biases in simulating SELF feedback and to serve as a reference for model development and application.

The paper is organized as follows: The model, data and methodology are introduced in section 2. Features of climatological mean EV forcing are presented in section 3. We evaluate the eddy-induced growth rate in section 4, and examine climate modes and associated SE feedback patterns in section 5. Finally, in section 6, we provide a summary and discussion.

The model used in this study is BCC_CSM1.1(m)——specifically, its historical run in phase 5 of the Coupled Model Intercomparison Project (CMIP5). The atmospheric component in this model is version 2 of the BCC Atmospheric General Model, with a T106 horizontal resolution and 26 hybrid sigma/pressure layers in the vertical direction (Wu et al., 2010). The oceanic component is version 4 of the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model, with a tripolar grid in the horizontal direction and 40 levels in the vertical direction, and the sea-ice component is the GFDL Sea Ice Simulator. The land model is version 1.0 of the BCC Atmosphere and Vegetation Interaction Model. The different components are coupled without any flux correction.

The observational dataset used for model evaluation is ERA-Interim (Dee et al., 2011), with a horizontal resolution of 2.5^°× 2.5^°. For convenience of comparison, the model simulations are interpolated onto grid points with a 2.5^°× 2.5^° horizontal resolution using bilinear interpolation, and the period covered is from January 1979 to December 2012.

Based on the theoretical framework of atmospheric climate dynamics proposed by Jin et al. (2006a, 2006b), a dynamical closure was realized for the SELF interaction through introducing a linear operator into the "parameterization" of eddy forcing by LF flow itself (see Appendix A for details). Zonal and meridional winds are used to calculate streamfunction and relative vorticity fields for both the reanalysis and model historical simulation. The SE component on the timescale of 2-8 days is extracted by a Lanczos bandpass filter (Duchon, 1979) onto the daily data with 41 weights. To avoid boundary effects, a slightly extended period is used for filtering the daily data. LF variability is defined as the monthly mean anomaly (see details in section 2.3).

The streamfunction tendency (ψ_t) induced by anomalous EV fluxes can be expressed in terms of EV forcing to measure the dynamical SE feedback (see Appendix B for details). The monthly mean horizontal EV forcing (χ _vort) and EV flux (F _vort) are represented, respectively, as \begin{equation} \chi_{\rm vort}=\left(\dfrac{\partial\overline{\psi}_{\rm a}}{\partial t}\right)_{\rm ed}=-\Delta^{-1}\overline{J(\psi',\Delta\psi')}_{\rm a} =-\Delta^{-1}\nabla\cdot {F}_{vort} , \ \ (1)\end{equation} and \begin{equation} {F}_{\rm vort}=(\overline{u'\zeta'_{\rm a}},\overline{v'\zeta'_{\rm a}})=F_{\rm r}+F_{\rm i} , \ \ (2)\end{equation} where u', v', ψ' and ζ' denote the SE-scale (2-8 days) zonal wind, meridional wind, streamfunction and vorticity; \(\overline{( )}_a\) denotes the monthly mean anomaly derived by subtracting the climatology of the reanalysis or model simulations from the original data; ▽•( ) and ∆^-1( ) are the horizontal divergence and the Laplacian inversion operators, respectively; and ( ) _ed indicates the tendency induced by SE. The subscripts r and i in Eq. (2) represent the rotational and irrotational (divergent) components of the EV flux, respectively. The divergence (convergence) of EV fluxes give rise to a positive (negative) streamfunction tendency, which in turn lead to anticyclonic (cyclonic) tendencies in the LF vorticity. Here, the EV fluxes are taken as F _i=-▽∆^-1▽• F _vort (where ▽ is the horizontal gradient operator) because only the divergent component of EV fluxes contribute to variations in the LF flow.

To estimate the efficiency of the dynamical SE feedback, we use the empirical diagnostics developed by Ren et al. (2011, 2014) to measure the eddy-induced growth rate of LF variability for the EV feedback, as follows: \begin{equation} \lambda=\dfrac{\iint_S\chi_{\rm vort}\overline{\psi}_{\rm a}dxdy}{\iint_S\overline{\psi}_{\rm a}\overline{\psi}_{\rm a}dxdy} , \ \ (3)\end{equation} where S is the horizontal integral domain over the annular extratropical regions [(30^°-70^°N, 0^°-360^°E) for the Northern Hemisphere and (30^°-70^°S, 0^°-360^°E) for the Southern Hemisphere]. Equation (3) expresses the relationship between the variance of LF variability and the covariance of eddy forcing and LF variability, and can be considered as \(\chi_\rm vort= -\Delta^-1\nabla\cdot F_\rm vort=\left(\dfrac\partial \psi\partial t\right)_\rm ed\approx \lambda\psi\) to show the intensity of SE feedback. Λ>0 (<0) expresses the positive (negative) feedback, and a larger Λ magnitude means stronger SE feedback. Also, Λ can be applied to each vertical level to examine the eddy-induced growth for the EV feedback.

Furthermore, because the eddy-induced growth rate has been shown to be geographically dependent (Ren et al., 2014), we examine the spatial features of the eddy-induced growth rate by defining a local growth rate (\(\tilde\lambda\)), with the horizontal integral domain S=S_f: \begin{equation} \tilde{\lambda}=S_f(\lambda) ,\ \ (4) \end{equation} where S_f represents a sliding window of 40^° longitude × 20^° latitude.

Previous studies have used various approaches to obtain the major climate modes, including the PNA, NAO, AO, and AAO. For example, (Barnston and Livezey, 1987) used a rotated principal component analysis to construct the PNA and NAO modes, which isolates the primary teleconnection patterns in all months and allows the construction of time series of the patterns. Thompson and Wallace (1998, 2000) identified the AO and AAO modes as the leading modes by applying an EOF to the monthly mean SLP anomalies expressed in terms of the equivalent 1000-hPa height poleward of 20^° latitude in both hemispheres. In this study, to evaluate the SE feedback on the anomalous LF modes in the model, we reconstruct the teleconnection indices in BCC_CSM1.1(m) and ERA-Interim. We calculate the monthly PNA and NAO indices by applying EOF analysis to the monthly mean 250-hPa geopotential heights over (30^°-80^°N, 150^°E-60^°W) and (30^°-80^°N, 100^°W-40^°E), respectively (see Table 1). We obtain the monthly AO and AAO indices by applying EOF analysis to the monthly mean 1000-hPa geopotential heights poleward of 20^° latitude in both hemispheres, following Thompson and Wallace (1998, 2000). All indices are obtained from the primary component of the corresponding EOF.

Many studies have used the association between EV forcing and LF flow patterns to show a positive SELF feedback (e.g., Lau, 1988). Before discussing the model's performance in simulating the SELF feedback, we first show a broad picture of the model's performance in simulating the basic dynamic fields, climatological annual mean streamfunction and zonal wind at 250 hPa, as shown in Fig. 1. We can see that, in general, BCC_CSM1.1(m) can capture the basic features of streamfunction and zonal wind well, including the two subtropical jets centered in the Northwest Pacific and Northwest Atlantic. The model biases show that, in both the Northern and Southern Hemisphere, the magnitude of streamfunction in BCC_CSM1.1(m) is slightly larger than observed. Jets in the North Pacific and North Atlantic shift northwards.

Figure 1.  Climatological annual mean streamfunction (shaded; units: 10⁶ m² s^-2) and zonal wind (contours, with intervals of 5 m s^-1 for the top and middle panels, and 3 m s^-1 for the bottom panel), calculated using BCC_CSM1.1(m) (a), ERA-Interim (b), and the difference between the two (c), at 250 hPa.

Figure 2.  Climatological mean EV forcing pattern in terms of streamfunction tendency (shaded; units: m² s^-2) and zonal wind (contours, with intervals of 10 m s^-1 for the left and middle panels, and 5 m s^-1 for the right), calculated using BCC_CSM1.1(m) (left), ERA-Interim (middle), and the difference between the two (right), in the Northern Hemisphere at the 250-hPa level for DJF, MAM, JJA, and SON.

Figure 3.  As in Fig. 2, but for the Southern Hemisphere. The sign of EV forcing has been flipped to maintain a consistent cyclonic/anticyclonic notation with the Northern Hemisphere.

Figure 4.  Local growth rate derived from EV forcing, calculated using BCC_CSM1.1(m) (left), ERA-Interim (middle), and the difference between the two (right), in the Northern Hemisphere at the 250-hPa level for MAM, JJA, SON, and DJF.

Next, we examine the climatological mean EV forcing patterns at 250 hPa during different Northern Hemisphere seasons; we examine model simulations, observational data and model biases, as shown in Fig. 2. The results demonstrate that BCC_CSM1.1(m) can capture the major spatial features of the observed EV forcing. The greatest EV forcing magnitude appears in December-January-February (DJF), and the smallest in June-July-August (JJA), indicating that the strongest SE feedback occurs during boreal winter, and the weakest during boreal summer. We use boreal winter (i.e., DJF) to illustrate the spatial distribution of EV forcing in both the model results and observations. The EV forcing is almost entirely negative over the North Pacific region and shows a dipolar distribution in the meridional direction over the North Atlantic region. This spatial pattern is likely associated with the PNA and the NAO——the two dominant climate modes in the North Pacific and North Atlantic regions, respectively——and contributes to the climatological mean patterns (see Appendix A). These two regions are still within the active storm track areas, where the strongest SE feedback appears (Lau and Nath, 1991; Branstator, 1995; Rivi\`ere and Orlanski, 2007). The EV forcing patterns in March-April-May (MAM) and September-October-November (SON) are similar to those in DJF, although they have slightly different magnitudes. Unlike in the other three seasons, the EV forcing in JJA is negative almost everywhere in the Northern Hemisphere.

Figure 5.  As in Fig. 4, but for the Southern Hemisphere.

We note that systematic biases exist in the BCC_CSM1.1 (m) results, showing positive EV forcing anomalies over the North Pacific region and negative anomalies over the North Atlantic region during boreal winter. These results suggest that, compared with observations, the intensity of SE feedback in BCC_CSM1.1(m) is smaller over the North Pacific and the midlatitude North Atlantic area, and bigger over the high-latitude North Atlantic area——a feature that is also true in other seasons. The reason for a weak EV forcing in the model over the North Pacific region is probably because the eddy-driven jet in the midlatitudes becomes weaker, which decreases the baroclinicity and eddy activity, which in turn gives rise to a weak EV forcing. Jets in the North Atlantic area show a similar change in intensity as in the North Pacific and may also experience a northward shift, leading to a stronger EV forcing at high latitudes and a weaker EV forcing at midlatitudes, which can be clearly seen by the climatological mean zonal wind in Fig. 2.

Figure 3 shows the climatological mean EV forcing patterns in the Southern Hemisphere. Compared with the Northern Hemisphere, the EV forcing patterns have a more zonally annular structure in all seasons, which may be due to the annular mode in the Southern Hemisphere (i.e., the AAO). Compared with observations, the simulations show a smaller magnitude over the mid-to-high latitude South Atlantic area and a greater magnitude over the mid-to-high latitude South Pacific area during all seasons. This is probably associated with the model's weaker subtropical jets over the midlatitude South Atlantic area and stronger jets over the midlatitude South Pacific area.

Figure 6.  Vertical profiles of the climatological eddy-induced growth rates, calculated using BCC_CSM1.1(m) (left) and ERA-Interim (right), in the Northern Hemisphere (top) and Southern Hemisphere (bottom), for MAM (green), JJA (red), SON (yellow), and DJF (blue).

Figure 7.  PNA-regressed 250-hPa anomalous streamfunction (contours, with an interval of 1× 10⁶ m² s^-1), EV forcing in terms of streamfunction tendency (shading; units: m² s^-2), and the irrotational (divergent) component of EV fluxes (vectors; units: m s^-2), calculated using BCC_CSM1.1(m) (left), ERA-Interim (middle), and the difference between the two (right), for MAM, JJA, SON, and DJF. The latitude and longitude range for the regions shown is (30^°-80^°N, 150^°E-60^°W).

As mentioned above, the eddy-induced growth rate can be used to quantitatively estimate the efficiency of the dynamical SE feedback. We compute the climatological mean of the local growth rate in the Northern Hemisphere at the 250-hPa level, where the maximum growth rate occurs in the vertical direction. Figure 4 shows that, in the Northern Hemisphere, the eddy-induced growth rate appears to be positive over all extratropical areas, indicating a positive SE feedback onto the LF variability and major atmospheric modes. Both the model simulations and observations show a zonal annular structure, with two centers over the North Pacific and North Atlantic regions where the SE activity is strongest. This distribution is reminiscent of the midlatitude storm tracks (Chang et al., 2002) and suggests a strong SELF feedback that maintains some major climate modes, such as the PNA and NAO (Limpasuvan and Hartmann, 1999; Lorenz and Hartmann, 2003). In contrast, the growth rate over Eurasia is relatively weak. Although the local growth rate has a similar distribution in MAM, JJA, SON and DJF, the amplitude is different among the four seasons. In observations, the maximum amplitude occurs in DJF and the minimum amplitude in JJA, suggesting a stronger eddy-induced growth rate of LF variability and a more efficient SE feedback that maintains some major atmospheric modes during cold seasons than during warm seasons.

Relative to observations, the growth rate in BCC_CSM1.1 (m) has a slightly eastward and poleward shift, which is most obvious during boreal spring. BCC_CSM1.1(m) can roughly reproduce this seasonality, showing a maximum growth rate in MAM and a minimum in JJA in the Northern Hemisphere.

The annular patterns of local growth rate are more zonally symmetric in the Southern Hemisphere than in the Northern Hemisphere (Fig. 5), which further confirms the importance of the EV forcing on the dominant hemispheric annular modes, such as the AAO. Both the model and observations show a maximum growth rate during austral winter (i.e., JJA) and a minimum during austral summer (i.e., DJF), both with an annular distribution. However, BCC_CSM1.1(m) is unable to capture the geophysical positions of the observed centers of growth rate in either the Southern or Northern Hemisphere.

To compare the growth rate at different pressure levels, Fig. 6 shows vertical profiles of the climatological eddy-induced growth rate, calculated by Eq. (3), over the two hemispheres. The values are positive at levels up to 50 hPa in all seasons, indicating a generally positive SE feedback onto the LF variability throughout the extratropical troposphere in both the Northern and Southern Hemisphere. This observed feature is reproduced well in BCC_CSM1.1(m). In the Northern Hemisphere, the maximum growth rate occurs during boreal autumn (i.e., SON) and spring (i.e., MAM) in both the model simulations and observations, and the minimum growth rate occurs during boreal summer (i.e., JJA). In the Southern Hemisphere, both the model and observations show that the maximum growth rate occurs during austral winter (i.e., JJA) and the minimum during austral summer (i.e., DJF).

The model realistically captures the observed seasonal dependence of growth rate, showing a greater growth rate during the cold season and a smaller growth rate during the warm season. The magnitude of the growth rate is only slightly smaller in BCC_CSM1.1(m) than in the ERA-Interim data. These results indicate that the model can simulate the observed climatological-mean vertical profiles of the eddy-induced growth rate well in the two hemispheres.

Note that the eddy-induced growth rate peaks at the 250-hPa level, where the strongest EV forcing exists. The model captures the amplitude of the growth rate well compared with observations. The value of the growth rate reaches approximately 0.10-0.15 during cold seasons, which corresponds to an e-folding timescale of 6.7-10 days——similar to the eddy lifecycle.

Figure 8.  Climatological mean precipitation rate (shaded; units: mm d^-1), calculated using BCC_CSM1.1(m) (left), CMAP (middle), and the difference between the two (right), for DJF, MAM, JJA, and SON.

Figure 9.  As in Fig. 7, but for the NAO. The latitude and longitude range for the regions shown is (30^°-80^°N, 100^°W-40^°E).

Figure 10.  As in Fig. 7, but for the AO.

Figure 11.  As in Fig. 7, but for the AAO.

There are several LF climate modes, such as the PNA, NAO, AO and AAO, that dominate in the extratropical atmosphere. The dynamical feedback of SE onto the LF modes plays an essential role in maintaining these climate modes. In this section, we examine the four major climate modes (the PNA, NAO, AO and AAO), in different seasons, to examine the model's performance in simulating the observed anomalous EV forcing patterns in the upper troposphere.

Figure 7 shows the primary EOF-related EV forcing pattern over the North Pacific, which denotes the seasonally varying PNA pattern. Figure 7 demonstrates that the simulated streamfunction patterns are relatively weaker than observed during the winter, but stronger during the other seasons, which is similar to the intensities of the EV forcing patterns in different seasons. The anomalous EV fluxes generally converge into the northeastern Pacific cyclonic center of the PNA. This follows the "left-hand" rule, i.e., that the EV fluxes tend to be directed to the left-hand side of the PNA flow (Kug and Jin, 2009; Ren et al., 2009, 2011; Kug et al., 2010a, 2010b, 2010c), which suggests a positive SE feedback during all four seasons. These results indicate that the model can reproduce the relationship between the EV fluxes and LF flow. Furthermore, the model also captures the seasonality in the EV forcing and EV fluxes; boreal winter is characterized by a relatively large magnitude of EV forcing and EV fluxes, whereas boreal summer has smaller-magnitude fluxes. Thus, the coldest season has a much stronger SE feedback onto the LF flow than warmer seasons.

Comparing the SE feedback pattern in the model with observations shows that the simulated convergent center of EV fluxes has a westward shift relative to observations during all seasons. This is related to the westward shift in the simulated PNA patterns and may be associated with a westward shift in the tropical Pacific heating center in the model, as represented by the precipitation rate shown in Fig. 8. In Fig. 8, we can see that, compared with observations, for each season, the tropical Pacific heating center in the model always features a westward shift and has a relatively small magnitude, which can be seen both in the tropical Pacific and Atlantic areas. This may be a reason why the simulated EV forcing pattern has a westward shift relative to observations during all seasons.

Figure 9 shows the NAO-related LF flow and eddy feedback patterns. The model reproduces the NAO patterns in different seasons relatively well, albeit showing some differences in intensity and position. The model also captures the positive SE feedback onto the NAO flow during all seasons, and shows the maximum EV forcing during boreal winter and the minimum during summer. The observed evolution of the NAO from JJA to DJF shows changes in intensity for the northern action center and changes in both position and intensity for the southern action center. The southern action center of the NAO is divided into two parts during the warm seasons, and the EV forcing pattern has a smaller magnitude. During winter, the two action centers emerge and have an upstream feedback onto the NAO, as shown by Ren et al. (2009, 2012). The model successfully mimics the observed changes in intensity for the northern action center; however, the simulated southern NAO lobe has two action centers during both the warm and the cold seasons that change only in intensity. The model simulations show, as observed, that the EV fluxes tend to diverge from the NAO anticyclonic centers and converge into the cyclonic centers, suggesting a positive eddy feedback. However, due to the model biases in reproducing the NAO's southern action center, the divergence of EV fluxes features two split centers during all seasons. Additionally, the western center is west of the non-split action center in the observation, with a larger magnitude relative to the observation, which is most obvious during boreal winter. This is probably due to the combination of the shifts in position and intensity of the subtropical jets (as seen in Fig. 2) and the westward shift in the tropical Atlantic heating center (as seen in Fig. 8 ) in the model. These features may give rise to a reduced baroclinicity and eddy activity in the North Atlantic storm track area, resulting in a westward shift and a relatively small EV forcing magnitude.

Figures 10 and 11 show the seasonal mean flows and EV forcing patterns for the AO and AAO, respectively. In observations, the AO flow pattern represents a zonally annular structure, with some action centers over the East Asia, North Pacific and North Atlantic regions. The strongest EV forcing pattern occurs during boreal winter, with EV fluxes converging into the cyclonic center and diverging from the anticyclonic center; the weakest EV forcing pattern appears during boreal summer. It is clear that the model can simulate the in-phase relationship between the EV forcing and AO patterns, but shows the strongest EV forcing patterns during boreal spring and autumn, which is different from observed. Furthermore, the simulated AO-related flow and accompanying EV forcing patterns are stronger in the model than observed during boreal spring, summer and autumn, but become weaker during boreal winter. Given the similar results for the PNA and NAO patterns, these features may be evidence of a model bias in the dynamical eddy feedback in BCC_CSM1.1(m).

The AAO-related patterns have a more annular structure than the AO patterns throughout the midlatitude regions, with centers in the Southwest Pacific, South Atlantic and South Indian oceans, in both the model simulations and observations. The simulated patterns feature an eastward shift over the midlatitude regions compared with the observed patterns, especially in MAM and JJA. Meanwhile, in the polar region, the simulated patterns show weaker magnitude than observed. However, the model simulates the in-phase relationship between the circulation and EV forcing patterns, and the prevailing directions of the EV fluxes relative to the AAO flow follow the left-hand rule. Observations show that the strongest EV forcing pattern occurs during austral winter and the weakest during austral summer; in the model, the patterns are similar in all four seasons.

This study uses the historical simulation of BCC_CSM1.1 (m) from CMIP5 to evaluate its performance in simulating the dynamical SE feedback onto LF flow. We examine the climatological EV forcing patterns both for the Northern and Southern Hemisphere. To estimate the efficiency of the SE feedback, we calculate the eddy-induced growth rate using the empirical definition of Ren et al. (2011, 2014). Additionally, we apply EOF analysis to obtain the climate modes and then examine the anomalous EV forcing and EV fluxes patterns for the PNA, NAO, AO and AAO. We systematically compare the model results with observations. Our main conclusions are as follows:

The model, BCC_CSM1.1(m), captures the basic features of the climatological EV forcing, showing a large magnitude during the cold seasons and a small magnitude during the warm seasons. But, compared with observations, the model still has some biases; it shows a smaller EV forcing magnitude over the North Pacific and midlatitude North Atlantic areas, and a larger EV forcing magnitude over the high-latitude North Atlantic area. These patterns probably result from the changes in intensity and position of the subtropical jets in the model, which alter the baroclinicity and eddy activity at mid-to-high latitudes.

The model reproduces the eddy-induced growth rate well, showing positive values throughout the extratropical areas at all pressure levels. There is a larger growth rate during the cold seasons and a smaller growth rate during the warm seasons. The local growth rate appears to be larger where the synoptic-scale storm track is highly active and the vertical profiles peak at the 250-hPa level, which are all consistent with observations.

For the dominant climate modes (the PNA, NAO, AO, and AAO), BCC_CSM1.1(m) can capture the basic features of dynamical feedback. However, due to deficiencies in the model, the four dominant modes are slightly shifted in the simulations relative to observations. For both the PNA and NAO, the EV forcing and EV flux patterns in the model have a westward shift, which may be associated with the westward shift of the simulated climate modes in the model and the interactions between SEs and the LF modes. However, the model can simulate the in-phase relationship between the EV forcing pattern and the AO and AAO patterns, although it still shows some biases with respect to the seasonality and amplitude of the dynamical feedback.

The present study provides a reference for the ability of BCC_CSM1.1(m) to simulate the dynamical feedback between SE and LF flow in the extratropics. The model has several deficiencies related to simulating the dynamical SE feedback, although it reproduces both the climatological and the anomalous aspects of the dynamical feedback relatively well. In addition to the biases regarding the climate modes, for the PNA, NAO and AO patterns, the simulated LF flow and accompanying EV forcing patterns are generally weaker during boreal winter and stronger in the other seasons. We suggest that these systematic biases in BCC_CSM1.1(m) are mainly associated with the model's biases with respect to the mean flow, baroclinicity, and storm track activity. There is also a bias in intensity in the climatological mean EV forcing and the eddy-induced growth rate. Attributions of these biases in the model need further study. Our evaluation has implications for improving the performance of BCC_CSM1.1(m) in simulating the eddy-induced growth of LF variability and predicting LF variability. For example, the positions and intensities of subtropical jets and tropical heating centers are not that precisely simulated in the model. It is worth mentioning that this study only gives the statistical diagnostics and model biases of dynamical SE feedback. Further examination in this model system of the relative importance of internal dynamical processes and extratropical forcings, such as tropical heating, in generating the dynamical feedback between SEs and LF variability, is an open question in need of further study.