1. Introduction
Teleconnections from the ENSO heating region into midlatitudes are largely barotropic (Horel and Wallace 1981; Hoskins and Karoly 1981; Simmons 1982; Branstator 1983; Simmons et al. 1983; Held and Kang 1987) because barotropic modes can propagate to high turning latitudes. However, the tropical heat source associated with ENSO does not directly force a barotropic response. In the central and eastern tropical Pacific, ENSO is associated with tropospheric temperature anomalies that can be well described by baroclinic equatorial wave dynamics, with the response to heating tending to approximately resemble a baroclinic Rossby wave straddling the equator and a Kelvin wave at the equator (Kiladis and Diaz 1989; Wallace et al. 1998; Chiang and Sobel 2002; Su and Neelin 2002; Kumar and Hoerling 2003). Interactions between baroclinic and barotropic modes then force the barotropic Rossby wave trains that dominate the ENSO teleconnections in the North Pacific and North America.
In view of the vertical structure of teleconnections into midlatitudes, pure barotropic models have been widely used for their study (e.g., Hoskins and Karoly 1981; Simmons 1982; Simmons et al. 1983; Held and Kang 1987). Applications of this methodology, however, typically have prescribed a vorticity source or “Rossby wave source” (RWS; Sardeshmukh and Hoskins 1988). The prescribed source can be based, for instance, on the specification of baroclinic divergence at upper levels or on baroclinic transient motions diagnosed from a GCM simulation (Held and Kang 1987). Many components of a fixed source in this approach come from dynamical processes whose scales, spatial form, and so on depend on the interaction of the baroclinic mode with the basic state in ways that can be interesting to elucidate.
The motivation of our work is to investigate the complex baroclinic-to-barotropic pathway in the tropics-to-midlatitudes teleconnection process through baroclinic–barotropic interactions during ENSO. In the equation for the barotropic component of the flow, the interactions with the baroclinic component are formally similar to the term traditionally described as a Rossby wave source, but their structure can be quantitatively and conceptually quite different than those based on upper-level divergent flow. For instance, if there is no vertical shear and no damping on the baroclinic mode associated with surface stress, then upper-level divergence in the baroclinic mode does not produce any linear forcing of the barotropic mode. At the same time, by explicitly modeling the gravest baroclinic mode, the teleconnection pathway can be followed as the two modes interact. To maintain consistency with the earlier literature while emphasizing the systematic projection on the barotropic mode, the term “barotropic Rossby wave source” is used here. This is shorthand for “baroclinic–barotropic interaction terms in the barotropic vorticity equation.” Potential caveats on viewing these terms as a fixed source/sink of barotropic vorticity will be provided in discussion of the results, while arguing for the usefulness of the RWS as a diagnostic of the pathway between direct baroclinic response to SST in the tropics and the barotropic contribution to the response.
Multilevel linear, steady-state wave models with both baroclinic and barotropic components (Hoskins and Karoly 1981; Ting and Held 1990; DeWeaver and Nigam 2004) can capture at least some aspects of the tropical/baroclinic–midlatitude/barotropic transition. Held et al. (1985) show how a geostrophic barotropic mode is modified to an external mode in the presence of shear, as further discussed in section 2b. Lee et al. (2009) use a simple two-level model to analyze the interaction of baroclinic and barotropic components in response to ENSO-like heating, as well as the importance of vertical background wind shear in exciting the barotropic response in midlatitudes. Majda and Biello (2003) emphasize the central role of baroclinic mean shear for sufficiently rapid nonlinear exchange of energy between the tropics and midlatitudes. Biello and Majda (2004a) explain how the dissipative mechanisms arising from radiative cooling and atmospheric boundary layer drag create barotropic (baroclinic) spinup (spindown) in the teleconnection process. Interactions with baroclinic transient eddies (Held et al. 1989; Hoerling and Ting 1994; Straus and Shukla 1997) also alter the teleconnection pattern in a manner that is not easily captured by stationary wave models.
Our focus in the present study is on the forcing of the midlatitude barotropic response to ENSO by three barotropic–baroclinic interaction processes: 1) shear advection (Wang and Xie 1996; Neelin and Zeng 2000; Majda and Biello 2003; Biello and Majda 2004b; Lee et al. 2009), 2) surface drag (Neelin and Zeng 2000; Biello and Majda 2004a), and 3) vertical advection (Neelin and Zeng 2000; Bacmeister and Suarez 2002). Recently, Ji et al. (2014) analyzed in detail the roles that these three terms play in interhemispheric teleconnections from tropical heat sources. Moreover, Ji et al. (2015) examined the effects of these three terms in generating the sea level pressure anomalies in the western Pacific during El Niño, which are an integral part of the Southern Oscillation pattern. Here, we examine the ENSO composites of baroclinic–barotropic interaction terms [the barotropic Rossby wave source] calculated from NCEP–NCAR reanalysis. The NCEP RWS is then prescribed in the barotropic vorticity equation of a quasi-equilibrium tropical circulation model (QTCM; see model description in section 2c) used in previous studies to perform a set of diagnostic experiments. The barotropic teleconnection responses in these experiments are then compared to ENSO composites of the NCEP–NCAR reanalysis winds.
The remainder of the text is organized as follows. Section 2 gives a brief introduction of the datasets, model, and methodology used in this study. Section 3 presents ENSO composite anomalies of tropospheric temperature, and of the baroclinic and barotropic components of wind, based on data from the NCEP–NCAR reanalysis. Section 4 presents the results of QTCM experiments in response to ENSO composite anomalies of the barotropic Rossby wave source—the baroclinic–barotropic interaction terms—computed using NCEP–NCAR reanalysis and further analysis of the dominant component of the Rossby wave source. Section 5 consists of a summary and discussion.
2. Datasets, model, and methodology
a. Datasets
We use monthly mean air temperature and zonal and meridional winds from the NCEP–NCAR reanalysis (Kalnay et al. 1996), which covers the period from 1948 to the present. Using this dataset we created composite plots corresponding to six El Niño events (1982/83, 1986/87, 1991/92, 1997/98, 2002/03, and 2009/10).
b. The barotropic Rossby wave source
Interpreting the individual terms on the rhs of (4), the contributions of baroclinic–barotropic interaction in such a barotropic Rossby wave source are: 1) 
Because the ENSO anomaly terms represent averages over a specific set of months with ENSO conditions (e.g., a composite of December–February over a set of El Niño years) minus the long-term climatological average, there will also be contributions from nonlinear interactions of transient motions at shorter time scales over the ENSO conditional average minus their climatological average. These transient term anomalies are denoted as 
Finally, vorticity source terms tend to emphasize small scales, which can be distracting for visualizing components that are important to the large-scale stationary wave response. One common approach is to filter with an inverse Laplacian, but this tends to overemphasize the larger scales. We use two approaches to addressing this visualization problem. The primary approach is to display the RWS anomaly as a vorticity source, but then to also display the response of an intermediate complexity model to the RWS, as discussed in section 2c. As a secondary method specifically for the discussion of leading terms in (6) and (7), we display terms both with and without taking the curl. For zonally elongated features, such as the El Niño subtropical jet anomalies in the eastern Pacific that are of particular interest here, this corresponds to diagnosing the zonal acceleration term, similar to the approach used by Straus and Shukla (1997).
c. QTCM
The QTCM belongs to a class of tropical atmospheric models of intermediate complexity that occupies a niche between GCMs and simple models. The model takes analytical solutions that hold approximately under quasi-equilibrium (QE) conditions and employs them as leading basis functions to represent the vertical structure of the flow. The primitive equations are then projected onto these simplified vertical structures, with self-consistent nonlinear terms retained in advection, moist convection, and vertical momentum transfer terms, among others. A more detailed model description can be found in Neelin and Zeng (2000). The QTCM has been used to analyze the moist dynamics of ENSO teleconnections in a number of contexts (Su et al. 2001, 2003, 2005; Neelin and Su 2005; Lintner and Chiang 2007).
The present study uses the first-generation QTCM (QTCM1), version 2.3. This version retains a single basis function for the vertical structure of temperature, with two components in the vertical structure of velocity: barotropic 
We perform several experiments with the QTCM to analyze the pathway of atmospheric teleconnections in the Pacific from tropical ENSO heating to the mid- and high latitudes. In these experiments, the ENSO December–February (DJF) composite anomalies of monthly baroclinic–barotropic interaction terms are used as the forcing, instead of ENSO SST anomalies. Then the barotropic teleconnections in response to those interaction terms are compared to the teleconnection patterns calculated as the ENSO composite anomalies in the NCEP–NCAR reanalysis. These experiments provide a way of interpreting the large-scale barotropic wave response to ENSO forced by those baroclinic–barotropic interactions. Although we keep the barotropic-to-baroclinic feedback in the QTCM, the results here should be reproduced using a pure barotropic model. The caveats are that, as waves propagate far from the source, the accurate simulation of background zonal wind becomes essential. The QTCM uses its own background field, which is shown below (Fig. 1) to have good agreement with that from the NCEP–NCAR reanalysis. Because of model limitations in simulating the basic state, we should not completely trust the far-field response; however, the wave response close to the source in this self-consistent baroclinic–barotropic decomposition model should compare reasonably well with that from the NCEP–NCAR reanalysis and other models prescribing the reanalysis background winds.
DJF climatology of (a) NCEP barotropic zonal wind 
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0053.1
Figure 1 shows the DJF-mean climatology of barotropic zonal wind and baroclinic zonal wind at 200 hPa from the NCEP–NCAR reanalysis and a 100-yr QTCM run with climatological SSTs. Recall that the barotropic component is independent of p and is represented as the vertical mean in the NCEP–NCAR reanalysis. The baroclinic component is calculated as the departures from vertical mean at each level. We choose to present 200-hPa baroclinic wind because this level is important for steering storms that impact the California coast during ENSO and is also a typical level selected for representing the basic-state flow in previous studies using simpler barotropic models. The most noticeable feature in Fig. 1 is that the barotropic and baroclinic components reinforce each other in the subtropical jet region in the northern Pacific. The background winds generally agree well between the reanalysis and model simulation, in regard to the jet location in the western Pacific, the extended easterlies in the tropics, and the westerlies in the subtropical North Atlantic, although the jet has a broader structure in the NCEP–NCAR reanalysis compared to the model simulations.
3. ENSO composites in the NCEP–NCAR reanalysis
Figure 2 shows ENSO DJF composite anomalies of the tropospheric temperature and baroclinic vector wind at 200 hPa from the NCEP–NCAR reanalysis. The most prominent feature of these temperature anomalies is consistent with a baroclinic Rossby wave straddling the equator in the eastern Pacific and a Kelvin wave–like structure extending to the east. There are also statistically significant temperature anomalies in the North Pacific and North America region. The baroclinic wind anomalies at 200 hPa are roughly consistent with geostrophic thermal wind balance in the subtropics and midlatitudes. The baroclinic shear advecting the baroclinic wind anomalies in both tropics and subtropics forces the barotropic response in ENSO teleconnections (which we will discuss in further detail in Fig. 4).
NCEP ENSO DJF composite anomalies of vertically averaged tropospheric temperature 
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0053.1
Figure 3 shows ENSO DJF composite anomalies of upper-level (200 hPa) and lower-level (1000 hPa) zonal winds and their baroclinic components from the NCEP–NCAR reanalysis. The upper-level easterlies on the equator in 200-hPa zonal wind, together with the lower-level westerlies in 1000-hPa zonal wind, indicate a dominant baroclinic structure in the deep tropics. In the subtropical Pacific, the wind anomalies associated with ENSO have a substantial barotropic component, indicated by anomalous westerlies throughout the troposphere in the 200- and 1000-hPa winds. In the subtropics and midlatitudes, at 1000 hPa, the barotropic contribution to the surface wind (Fig. 4) cancels the baroclinic contribution (Fig. 3d) to a large extent, as one would expect when surface drag is effective at reducing the near-surface wind, and spinning up a strong barotropic component.
NCEP ENSO DJF composite anomalies of (a) zonal wind at 200 hPa 
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0053.1
NCEP ENSO DJF composite anomaly of barotropic component of zonal wind 
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0053.1
Figure 4 shows ENSO DJF composite anomalies of barotropic zonal wind from the NCEP–NCAR reanalysis. The barotropic component is substantial in the subtropics, where the subtropical jet extends between 20° and 30°N off the U.S coast, with a magnitude similar to the baroclinic component (Fig. 3b). The barotropic contribution in the tropics is also nonnegligible.
4. The barotropic RWS and QTCM experiments
Figure 5 shows ENSO DJF composite anomalies of the barotropic RWS (Fig. 5a) [i.e., the rhs of (4)], together with each of the three components: shear advection (Fig. 5b), vertical advection (Fig. 5c), and surface drag (Fig. 5d) from the NCEP–NCAR reanalysis. Figure 5e shows the residual calculated by subtracting the barotropic RWS from 
NCEP ENSO DJF composite anomalies of (a) the barotropic RWS, (b) shear advection contribution, (c) vertical advection contribution, (d) surface drag contribution, (e) the residual, and (f) the barotropic RWS plus the residual (total). The box indicates the Pacific region where the forcing is applied in the QTCM experiments; values outside the region are set to zero. The units are ×10−11 s−2. Stippling denotes regions where the anomaly passes a two-sided t test at the 95% significance level.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0053.1
We next present results from pairs of 100-yr QTCM simulations: one is the control or climatological run, and the other is performed with ENSO DJF composite anomalies of each forcing source in Fig. 5 added to the rhs of the barotropic vorticity equation (RWS run). Both runs use monthly mean climatological SSTs. Differences between each pair are thus due to the response to each forcing anomaly within the Pacific region. The 100-yr simulation length is used to obtain statistically significant results.
Figure 6 shows the QTCM DJF barotropic wind anomalies in response to each forcing source in Fig. 5. The barotropic wind responses to the barotropic RWS show qualitatively good agreement with the DJF composite anomalies of barotropic wind from the NCEP–NCAR reanalysis in Fig. 4, in the tropical central Pacific, the subtropical northern Pacific, and the North America region. The contributions from each of the three baroclinic–barotropic interaction terms are not negligible, and they alternately cancel and reinforce each other in different regions. That being said, the vertical advection contribution is noticeably smaller among the three, even in the tropics. This is in contrast to traditional assumptions that upper-level divergence is an important forcing term. The shear advection contribution is larger among the three, modified by the other two sources, especially by surface drag in the western Pacific. In the region off the California coast, where the subtropical jet extends farther east in ENSO, the three interaction terms reinforce each other. For the case of residual forcing shown in Fig. 6e, there is a substantial response off the U.S. coast. Last, in Fig. 6f, we show the barotropic wind response to the sum of the barotropic RWS and the residual. In this case, the response off the U.S. coast is qualitatively similar to the case forced by the barotropic RWS in Fig. 6a, with a larger amplitude.
QTCM DJF barotropic wind anomalies 
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0053.1
While we have to be cautious about the residual calculation since it can include finite-differencing errors, a leading contribution is presumed to be due to the nonlinear effects of departures from the monthly averages as a result of high-frequency storm transients, 
We now turn to the key stage of the tropical-to-subtropical, baroclinic–barotropic interaction by breaking down contributions of the RWS anomaly. To identify the dominant component of shear advection forcing, we examine each of the four components of the linearization (6). We find the largest component is the first term 
Shear advection term decomposition: (a) the largest term in the shear advection Rossby wave source anomaly 
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0053.1
If we assume that the response to the barotropic RWS is approximately linear, we can explore how large the contribution is from different regions. We perform two experiments with the barotropic RWS in two narrower boxes: one is in the tropics (15°N–15°S, 160°E–80°W); the other is in the subtropics (15°–40°N, 160°E–100°W). We find that off the U.S. coast, roughly half of the jet response is due to forcing in the subtropics locally, and half is due to forcing in the tropics (figures not shown). From the previous analysis on shear advection decomposition, it is easy to see that, while such experiments are easy to do and may help us to understand the relative contribution of different parts of the Rossby wave source, the separation into tropics and subtropics is artificial. The barotropic teleconnections in the subtropical jet region result from the basic-state baroclinic wind advection acting on the baroclinic response to ENSO seen in the flow pattern in Fig. 2, which spreads by baroclinic wave dynamics from the deep tropics into subtropics on the scale of equatorial radius of deformation. Figure 8 illustrates some aspects of this interaction. The baroclinic response spreads from the ENSO heating to yield the characteristic baroclinic stationary wave pattern in the tropics and subtropics. At particular locations, the climatological baroclinic shear interacts strongly with this anomalous ENSO pattern, yielding the barotropic Rossby wave source that projects on the barotropic component. The response to this plus surface drag contributions yields the barotropic contribution to the ENSO response. Rather than assuming a forcing by the sensitive divergent component of the flow, diagnosing the pathway under this view emphasizes the role of the baroclinic dynamics in setting up the ENSO anomaly and puts the focus on interactions of these anomalous wind patterns with surface drag and the basic-state shear.
Schematic based on the ENSO temperature and wind anomalies of Fig. 2 and the regions of large shear interaction in Fig. 7, indicating relationships between the ENSO baroclinic wind anomalies and the baroclinic climatological shear. Black ovals correspond to those in Fig. 7c, highlighting regions of strong 
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0053.1
Similar to what we did for shear advection, we examine the linearization of the vertical advection term [see (7)] and identify the dominant component as 
Vertical advection term decomposition: (a) the largest term in vertical advection: 
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0053.1
5. Conclusions
To understand the complex baroclinic-to-barotropic pathway in the tropical-to-midlatitude ENSO teleconnection process, it can be useful to examine an approach that considers a systematic modal breakdown of baroclinic and barotropic modes. In this view, the barotropic mode is forced by the baroclinic–barotropic interaction terms, which yield the barotropic Rossby wave source (RWS). These RWS interaction terms are diagnosed from the NCEP–NCAR reanalysis data to create ENSO anomalies. Unlike in the classic studies that assume that a diagnosed upper-level vorticity source forces a barotropic mode, the barotropic RWS in our approach represents the forcing on the barotropic component evaluated through the atmospheric column (here, 200 hPa to the surface). Under these approximations, baroclinic and barotropic components of ENSO wind anomalies are examined as composites from the NCEP–NCAR reanalysis. The barotropic component is substantial even in the tropical Pacific, implying that a purely baroclinic mode representation of ENSO would be incomplete even within the forcing region. In the subtropical Pacific off the U.S. West Coast, which can be important for ENSO impacts on North America, the baroclinic contribution remains substantial, but the barotropic mode contribution doubles the subtropical jet response to ENSO.
Composite ENSO anomalies of the barotropic RWS as vorticity source contributions that appear on the rhs of barotropic vorticity equation can be interpreted directly, but it can also be useful to see the associated wind solutions. For this, the QTCM, a model with an explicit baroclinic barotropic mode breakdown, is used to diagnose the response. In these QTCM experiments, the barotropic vorticity equation of the model is forced by the composite ENSO anomaly barotropic RWS diagnosed from the NCEP–NCAR reanalysis. The resulting zonal wind anomalies (compared to the wind in a control run) are qualitatively in good agreement with those of the ENSO composite barotropic wind response from the NCEP reanalysis, including in the subtropics off the U.S. coast. Although there are nontrivial impacts of transients in the barotropic wind response to ENSO, qualitatively, the barotropic response near the coast of North America is set up by the barotropic Rossby wave source term as diagnosed from monthly means for ENSO anomaly composite response. Among the three barotropic Rossby wave source contributions (shear advection, vertical advection, and surface drag), vertical advection contributions arise from anomalous vertical velocity in regions where there is climatological baroclinic shear, but these terms tend to be smaller than the others. This is in contrast to traditional assumptions that upper-level divergence is an important forcing term. The surface drag contribution alternately tends to cancel or reinforce the shear advection in different regions through damping on the baroclinic mode, which spins up a barotropic response. The dominant contributions are from the shear advection. Further decomposition of the shear advection term shows that the mean baroclinic zonal wind advecting the anomalous baroclinic zonal wind is the most important component. Shear advection in both the tropics and subtropics contributes to the subtropical response, but both are an integral part of basic-state advection of the baroclinic ENSO flow pattern. In this view, the barotropic Rossby wave source in the subtropics simply arises from the basic-state baroclinic flow acting on the well-known baroclinic ENSO flow pattern that spreads from the deep tropics into the subtropics over a scale of the equatorial radius of deformation. This is inseparably connected to the leading deep tropical Rossby wave source that arises from eastern Pacific basic-state baroclinic winds advecting the tropical portion of the same ENSO flow pattern.
Acknowledgments
This work was supported in part by National Science Foundation Grants AGS-1540518 and AGS-1041477 and the National Oceanic and Atmospheric Administration Grant NA14OAR4310274. We thank J. Meyerson for graphical assistance.
APPENDIX
QTCM Equations
As in Fig. 6, but for QTCM DJF 200-hPa baroclinic wind anomalies (
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0053.1
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