1. Introduction
Gravity waves entering into the stratosphere and mesosphere play an important role in driving the general circulation, enhancing vertical mixing, and contributing to polar stratospheric cloud formation, which has further implications for ozone depletion over polar regions (e.g., Carslaw et al. 1998). Owing to finite computing resources, global climate and weather models cannot run at spatial resolutions needed to resolve gravity waves, so their effects must be parameterized (e.g., Kim et al. 2003). Accurate parameterizations require in turn a fundamental understanding of gravity wave dynamics, from generation at the source to propagation and dissipation elsewhere in the atmosphere. Major tropospheric gravity wave sources identified by previous studies include mountains, convection in tropical areas, lower-tropospheric frontal activity, and upper-tropospheric unbalanced jet streams, each of which has been the subject of extensive studies [see review by Fritts and Alexander (2003)]. Particularly, our knowledge of gravity waves generated by flow over mountains has been significantly advanced through several large field campaigns conducted over major barriers such as the Rocky Mountains [Wave Momentum Flux Experiment (WAMFLEX); Lilly and Kennedy 1973], the European Alps [Mesoscale Alpine Programme (MAP); Smith et al. 2007], and the Sierra Nevada range [Sierra Waves Project (SWP) 1954 and Terrain-Induced Rotor Experiment (T-REX); Grubišić et al. 2008]. Mountain waves over high-latitude southern regions, such as the southern Andes, have received much less attention.
Over the past decade, the advent of high resolution satellite sensors has provided new insights into the global distribution of long-wavelength gravity wave activity in the stratosphere (Wu et al. 2006). Observations from both limb and nadir sensors have revealed a striking maximum in stratospheric gravity wave variances over the southern tip of the Andes, the Antarctic Peninsula, and Drake Passage (Eckermann and Preusse 1999; McLandress et al. 2000; Jiang et al. 2002; Wu 2004; Wu and Eckermann 2008; Alexander et al. 2008; Yan et al. 2010). A number of studies have demonstrated that the high orography of the Andes and Antarctic Peninsula generates many of the intense stratospheric gravity waves observed here, some of which appear to propagate downstream and meridionally to produce activity over Drake Passage (e.g., Preusse et al. 2002; Jiang et al. 2002; Alexander and Teitelbaum 2007; Baumgaertner and McDonald 2007; Plougonven et al. 2008; Yamashita et al. 2009; Shutts and Vosper 2011). However, others have questioned the presumed dominance of orographic forcing in generating enhanced wave activity in this region (e.g., de la Torre and Alexander 2005). For example, some studies have identified tropospheric convection and jet stream instabilities as the sources of waves observed in this same region (e.g., Yoshiki and Sato 2000; Yoshiki et al. 2004; de la Torre et al. 2006; Spiga et al. 2008; Hei et al. 2008; Llamedo et al. 2009). Still other studies have argued that instabilities in the stratospheric vortex jet generate upward- and downward-propagating gravity waves that also contribute to this enhanced local wave activity (Sato and Yoshiki 2008; Moffat-Griffin et al. 2011). Clearly the origins and dynamics of the rich and highly energetic gravity wave fields encountered in this remote region of the planet require further research to better understand and parameterize.
The research in this paper is also motivated by satellite observations of stratospheric gravity waves in this region, which frequently reveal linear wave patterns over the southern Andes and Drake Passage. The objectives of this study are twofold. First, we want to explore the capability of the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) in simulating stratospheric gravity waves by extending its model top from the previous capability at the 30-km level (i.e., lower stratosphere) to ~70 km MSL (i.e., lower mesosphere). Second, we want to advance our understanding of characteristics and dynamics of gravity waves over the southern Andes and Drake Passage through examination of the simulated waves.
The remainder of this paper is organized as follows. The wave event and wave properties deduced from satellite and radiosonde observations and the scientific issues to be pursued by this study are set forth in section 2. Section 3 contains a description of the model configuration and an overview of the synoptic conditions during this wave event. The simulated wave characteristics including spatial and temporal variations, wave spectra, and wave momentum fluxes are presented in section 4. Wave dynamics is further examined in section 5 through ray-tracing calculations. The results and conclusions are summarized in section 6.
2. The 8–10 August 2010 wave event
The Atmospheric Infrared Sounder (AIRS) on the National Aeronautics and Space Administration Aqua satellite acquires radiances by scanning the atmosphere symmetrically about nadir in a repeating cycle aligned orthogonal to the orbit vector (Aumann et al. 2003). A number of previous studies have demonstrated that gravity waves with long vertical wavelengths and horizontal wavelengths >40 km can be resolved as a two-dimensional perturbation structure in swath radiance imagery of certain stratospheric channels uncontaminated by high-tropospheric cloud (e.g., Wu et al. 2006; Alexander and Barnet, 2007; Eckermann et al. 2007). Here we use a channel-averaged AIRS radiance product registered at a series of heights from 100 to 2 hPa and summarized in Table A2 of Gong et al. (2012). We remove large-scale backgrounds to isolate gravity wave perturbations using techniques described by Eckermann and Wu (2012).
Figure 1 shows the resulting brightness temperature (radiance) perturbations at several pressure levels on 8–9 August 2010 within a focused region over the southern Andes and Antarctic Peninsula. Linear wave patterns are evident in the swath imagery over the southern tip of the Andes and Drake Passage with at least three pairs of wave crests and troughs discernible. Note that, while these observed radiance perturbations are directly related to actual gravity-wave-induced temperature structure in terms of the two-dimensional phase structure, the brightness temperature amplitudes are a lower bound, and likely a considerable underestimate, of the actual temperature amplitudes of these waves, owing to the vertical averaging effect of the broad nadir weighting functions that yield these channel radiances (Alexander and Barnet 2007). The waves evident in Fig. 1 share the following properties: 1) they extend across Drake Passage with phase lines oriented northwest–southeast; 2) while the wave crests (troughs) vary in length at different levels, their northern edges are always anchored above the southern Andes; 3) the horizontal wavelengths (i.e., the horizontal distance between two adjacent crests or troughs in the direction normal to the waves) exhibit a weak dependence on altitude, tend to increase with the distance from their northern edges, and are in the range of 300–700 km; and 4) these waves are nearly stationary with respect to the ground and penetrate throughout the full depth of the stratosphere. Further inspection indicates that the northwestern end of the wave field is approximately located above the Patagonian ice sheet, which comprises several mountain peaks higher than 3 km MSL. The coincidence between the northwestern end of the wave field and these high peaks, as well as the nearly stationary nature of these waves, suggests an orographic origin. It is noteworthy that there are wavelike features to the west of Drake Passage discernible at least at the 7- and 2.5-hPa levels, which may be generated by active baroclinic storms in the troposphere (Fig. 4) rather than by flow over orography (e.g., Zhang 2004).
Small horizontal-scale brightness temperature anomalies (K) extracted from multichannel AIRS radiances peaking at the indicated altitudes of (from bottom to top) 80, 30, 7, and 2.5 hPa [see Table A2 and accompanying discussion of Gong et al. (2012) for details] from the ascending and descending overpasses of the southern Andes region on 8 and 9 Aug 2010. These perturbations were isolated using the algorithms described by Eckermann and Wu (2012). A 3 × 3 point smoothing of radiance anomalies in neighboring footprints was applied in these plots to suppress channel noise and accentuate the geophysical wave perturbations. Data from overpasses on ascending and descending orbits (different local times) are plotted in separate panels.
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
The wind profiles derived from the radiosondes launched from Puerto Montt (PM, 41.43°S) and Punta Arenas (PA, 53.00°S) during this time period provide further evidence of an orographic origin of these waves (Fig. 2, with station locations depicted in Fig. 3). Around 1200 UTC 9 August, Fig. 2 reveals moderate low-level southwesterlies directed toward the southern Andes—a condition typically conducive to the generation of mountain waves. Wavelike variations in the horizontal wind profiles suggest that these radiosondes may have ascended through gravity waves that emanated from the southern Andes (Fig. 3). For example, at PA, both u and υ components reveal a wavelike variation between 3 km and the tropopause (~12 km), suggesting a possible gravity wave with a dominant vertical wavelength of ~9 km, which is comparable to that of a linear hydrostatic wave (i.e., λz = 2πU/N ~ 9.4 km, with the troposphere-averaged cross-mountain wind speed U ~ 15 m s−1 and the buoyancy frequency N ~ 0.01 s−1). Uncertainties associated with deriving wave characteristics from a single radiosonde (Shutts et al. 1988) appear to be less an issue here as the drift distance of the radiosonde is far smaller than the horizontal wavelengths.
(a) Horizontal wind components (m s−1) and potential temperature (K) profiles from the 1200 UTC soundings on 9 Aug 2010 from Puerto Montt (PM) (41.43°S, 73.10°W; solid) and Punta Arenas (PA) (53.00°S, 70.85°W; dashed). (b) Corresponding wind hodographs are shown with the sense of rotation with height indicated by thin arrows.
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
Topography in the 15-km grid domain is shown in gray shading (interval 0.5 km): locations of the two radiosonde stations, PM and PA, are indicated by black triangles.
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
More wave properties can be deduced from the corresponding wind hodographs (Fig. 2b) by assuming that these wavelike perturbations were related to a monochromatic wave and using a linear dispersion relation for inertia–gravity waves (IGWs). The hodographs derived from the pair of soundings are characterized by looping (or spiral) patterns, which are typical for observations obtained from radiosondes ascending through IGWs (e.g., Tsuda et al. 1994; Eckermann 1996). The radiosonde from PA intercepts a much-larger-amplitude wave with u and υ perturbations ranging around 25–30 m s−1 in the troposphere (i.e., the primary loop), although the tropospheric jet stream shear might distort these IGW ellipses somewhat. The counterclockwise rotation with height in the Southern Hemisphere implies that waves have a downward phase speed and an upward group velocity (e.g., Tsuda et al. 1994). The orientation of the primary loop implies that the horizontal wave phase line is oriented from northwest to southeast above PA. The smaller amplitude wave observed at PM propagates upward as well. However, the major axis of the ellipsis implies that the horizontal phase line is oriented southwest–northeast (Fig. 2).
Finally, it is worth noting that we inspected wave patterns in the stratospheric AIRS radiances over this region each day throughout the July–September 2010 period. Similar wave patterns to those in Fig. 1 are observed on many days during this 3-month period, implying that such waves occur frequently and may have significant contributions to the wave variance maximum over Drake Passage, as suggested by previous studies (e.g., Jiang et al. 2002).
3. Numerical configuration
a. Numerical configuration
The atmospheric component of Coupled Ocean–Atmosphere Mesoscale Prediction System1 (Hodur 1997; Doyle et al. 2000) has been applied to the study area (Fig. 3) to simulate this wave event. COAMPS is a fully compressible, nonhydrostatic terrain-following mesoscale model. The finite difference schemes are of second-order accuracy in time and space in this application. The boundary layer and free-atmospheric turbulent mixing and diffusion are represented using a prognostic equation for the turbulence kinetic energy (TKE) budget (Mellor and Yamada 1974). The surface heat and momentum fluxes are computed following the Louis (1979) and Louis et al. (1982) formulations. The grid-scale evolution of moist processes is explicitly predicted from budget equations for cloud water, cloud ice, rainwater, snowflakes, and water vapor (Rutledge and Hobbs 1983), and the subgrid-scale moist convective processes are parameterized using an approach following Kain and Fritsch (1993). The Fu–Liou four-stream approximation is used for the shortwave and longwave radiation processes (Fu et al. 1997).
The model is initialized at 0000 UTC 8 August and integrated over 36 h, after a 12 h spinup. The initial fields for the model are created from multivariate optimum interpolation analysis of upper-air sounding, surface, commercial aircraft, and satellite data that are quality controlled and blended with previous 12-h COAMPS forecast fields. An incremental update data assimilation procedure is used, which enables mesoscale phenomena to be retained in the analysis increment fields. Lateral boundary conditions for the outermost grid mesh are derived from the Navy Operational Global Atmospheric Prediction System forecast fields. The computational domain contains two horizontally nested grid meshes of 151 × 151 and 256 × 355 grid points, and the corresponding horizontal grid spacings are 45 and 15 km, respectively. There are 92 vertical levels with grid spacing increasing from 20 m at the lowest model level to 400–750 m in the upper troposphere and stratosphere. The model top is located at approximately 70 km MSL and a sponge boundary condition is applied to the top 12 km to reduce downward reflection of gravity waves. It is worth noting that several additional numerical experiments have been carried out to test the sensitivity of the simulated waves to the horizontal grid spacing (e.g., triple-nested grid meshes with grid spacings of 45, 15, and 5 km) and upper boundary conditions (e.g., simulations with a deeper sponge layer or a radiation boundary condition following Klemp and Durran 1983) and the simulated waves are found to be relatively insensitive to the changes in model configurations. The terrain data are based on the Global Land One-km Base Elevation (GLOBE) dataset, and the terrain in the 15-km mesh is shown in Fig. 3.
b. Synoptic conditions
The synoptic conditions associated with this wave event are illustrated in Fig. 4. During this event, the lower troposphere was characterized by complex synoptic patterns, including pressure troughs and cutoff lows associated with baroclinic waves (Figs. 4a,b). A southwesterly jet arrives at the southern Andes at 1200 UTC 8 August and reaches its maximum strength approximately 24 h later, during which the low-level winds gradually become more westerly. It is noteworthy that, according to linear theory and field observations, strong cross-mountain low-level winds are favorable to the launching of large-amplitude mountain waves (e.g., Doyle et al. 2009). This jet, characterized by generally positive vertical wind shear, extends throughout the troposphere and provides a favorable condition for stationary mountain waves to enter the stratosphere (Figs. 4c,d) owing to the absence of zero-wind critical levels. Equatorward of 30°S, a weaker low-level jet impinges on the high central Andes ridge (~6 km MSL) and becomes progressively stronger during the study period, implying that the central Andes might be another wave source. Consistent with this, the lower-left panel of Fig. 1 clearly shows a two-dimensional mountain wave at 80 hPa directly above the Andes near these latitudes. Between these two jets, the tropospheric winds are weak, associated with an approaching cutoff low from the west of the Andes ridge.
Synoptic flow patterns from the 45-km grid mesh. Horizontal wind speed [color, increment is (a)–(d) 5 m s−1 and (e),(f) 10 m s−1], wind vectors, and pressure contours at the 4-, 10-, and 35-km levels valid at (left) 1200 UTC 8 Aug and (right) 1200 UTC 9 Aug 2010 are shown. Pressure contour intervals are 5 hPa for the 4- and 10-km levels and 0.5 hPa for the 35-km level.
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
In the stratosphere (Figs. 4e,f), nearly steady and very strong westerlies are evident between 50° and 70°S associated with the polar vortex. Pronounced negative meridional shear of the zonal wind (i.e., 
4. Characteristics of simulated waves
The objective of this section is to characterize the simulated gravity waves with emphasis on spatial and temporal variations of inertia–gravity waves and vertical wave momentum transfer. We use the simulation results from the 15-km grid, which covers the area of interest (i.e., southern Andes, Drake Passage, and a portion of the Antarctic Peninsula) and also has a horizontal grid spacing that is fine enough to resolve the mesoscale waves of interest.
a. Wave characteristics and time dependence
We begin with a qualitative comparison between the simulated wave patterns evident in the plan views of the vertical velocity and those in the AIRS images in Fig. 1. Figures 5b–d are plots of simulated wave fields at model levels that correspond approximately to the 80, 10, and 2.5-hPa levels, respectively, of the AIRS imagery in Fig. 1. The simulated vertical velocity field is characterized by quasi-linear wave patterns in the stratosphere, oriented northwest–southeast across Drake Passage in a manner qualitatively similar to the AIRS brightness temperature patterns (Fig. 1). The zonal wavelengths (i.e., east–west distance between two adjacent wave crests or toughs) exhibit some variations in the vertical and meridional directions and are in the range of 300–700 km, in agreement with those estimated from the AIRS images. The northern edges of these linear wave patterns are anchored over the southern tip of the Andes as well. The qualitative agreement between the satellite observations and COAMPS simulated wave patterns provides the basis for further diagnosis of the wave properties and exploration of the underlying dynamics.
Plan views of the vertical velocity [color, increment is (a)–(c) 0.2 and (d) 0.3 m s−1] and horizontal wind vectors at (a) 4, (b) 10, (c) 17, and (d) 30 km MSL, valid at 1200 UTC 9 Aug 2010. The three thick lines and blue star in (a) indicate the locations of the three cross sections shown in Fig. 6 and the location for the time–height diagram in Fig. 7c, respectively.
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
According to the COAMPS simulation, the amplitude of the stratospheric–mesospheric waves across Drake Passage generally increases with the altitude, as would be expected for freely propagating nondissipating waves due to the density effect. However, in the troposphere there are only quasi-stationary waves locally over the leeside of the central and southern Andes and no discernible waves over Drake Passage (Fig. 5a). The vertical variation of the simulated waves is more evident in Fig. 6, which shows vertical cross sections of zonal velocities u, vertical velocities w, and potential temperature θ along three west-to-east sections oriented across the central and southern Andes and Drake Passage, respectively (i.e., approximately along the prevailing wind direction), and shown in Fig. 5a. Mountain waves emanate from the high central Andes ridge and propagate up to the tropopause (~12 km MSL). The zonal winds at these lower latitudes are characterized by a strong easterly shear across the tropopause and lower stratosphere, where wave breaking and critical level absorption occur. Above 20 km the zonal winds become weaker, and no waves are distinguishable (Figs. 6a,b). In contrast, deep westerlies are present over the southern Andes (Fig. 6c). Accordingly, the mountain waves that emanate from the southern Andes (i.e., Patagonian glacial sheet) propagate through the entire stratosphere and into the mesosphere with increasing wave amplitude aloft due to the decrease of the air density (Fig. 6d). The wave amplitudes in terms of vertical velocity and zonal wind perturbations reach maxima between 50 and 60 km MSL where a zonal wind reversal occurs in accordance with the wave-induced steepened isentropes (Fig. 6c)—a typical signature of breaking gravity waves. A useful dimensionless diagnostic of wave saturation or breaking is the steepness (or vertical displacement gradient) 
Cross sections of (left) zonal [increment is (a) 5 and (c),(e) 10 m s−1] and (right) vertical [increment is (b) 0.3, (d) 1, and (f) 0.5 m s−1] wind components oriented across (top) the central Andes, (middle) Patagonia, and (bottom) Drake Passage (see Fig. 5a for locations) valid for 1200 UTC 9 Aug 2010. The zero contours of the zonal wind are shown as green in (a) and (c), and areas with zonal wind reversal in the stratosphere are indicated by white arrows.
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
During the 36-h study period, the simulated waves evolved with time in accordance with the slowly changing synoptic conditions evident in Fig. 4. Right above the Patagonian peaks, a nearly stationary wave is present over the lee slope, characterized by a crest and trough pair and the wave amplitude becomes much stronger over the last 24 h of the simulation (Fig. 7a), consistent with enhancement of the cross-mountain wind component at the mountaintop level near Patagonia during the same time period (Fig. 4). In the stratosphere, there are three crest–trough pairs over the leeside of the Patagonian peaks (Fig. 7b) likely due to dispersion of the IGWs, and the characteristic wavelength is noticeably longer than in the troposphere. In contrast to the steady waves at the mountaintop level, the wave amplitude and location of the wave phase lines slowly oscillate, initially moving upstream and then downstream in the last 24 h. The evolution of the zonal wind upstream of Patagonia from the troposphere to lower mesosphere and the corresponding leeside wave response are shown in Figs. 7c and d, respectively. The zonal wind component in the troposphere exhibits a minimum approximately from 10 to 20 h, separating the 36-h period into a weakening phase (i.e., 0–12 h) and strengthening phase (~12–24 h, Fig. 7c). The corresponding wave phase lines descend more than 5 km in the first 12 h while the wave amplitude weakens substantially, then ascend throughout the remainder of the forecast period as the waves reintensify (Fig. 7d), approximately in phase with evolution of the tropospheric westerlies. The downward and upstream (upward and downstream) movement of the phase lines during the weakening (strengthening) phase of the synoptic-scale westerlies in the x–z space is consistent with the idealized study of Chen et al. (2005) of the influence of transient synoptic-scale winds on orographic wave forcing and evolution.
Distance–time (Hovmöller) diagrams of the vertical velocity at (a) 4 km (increment 0.2 m s−1) and (b) 40 km (increment 0.5 m s−1) MSL along the same Patagonia cross section as in Figs. 6c,d (but over a shorter distance). Time–height diagrams of (c) the upstream zonal winds (increment 5 m s−1; see Fig. 5a for location) and (d) vertical velocity (increment 1 m s−1) superimposed with the corresponding isentropes (increment 100 K) on the lee side. The time period is from 0000 UTC 8 Aug to 1200 UTC 9 Aug 2010.
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
b. Wave momentum fluxes
For a steady irrotational inviscid vertically propagating gravity wave, the vertical momentum flux should be constant with height (Eliassen and Palm 1961) up to a level where dissipation (i.e., wave breaking or critical level absorption) occurs and some wave momentum flux is deposited into the mean flow. The evolution and vertical variation of the domain-average 
Time–height plots of the vertical flux of zonal momentum (Fx) averaged over the southern Andes and Drake Passage. (b) For the troposphere the range is from −0.06 to 0 N m−2 with an increment of 0.005 N m−2 and (a) for the stratosphere the range is from −0.012 to 0 N m−2 with an increment of 0.001 N m−2.
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
To examine the meridional variation of the wave momentum flux, the zonally averaged vertical flux of zonal momentum, 
Vertical cross section of vertical fluxes of the zonal momentum (b) for the lowest 15 km and (a) between 15 and 60 km MSL valid at 0000 and 1200 UTC 9 Aug 2010, respectively. The color scale intervals are 7.5 × 103 N m−1 for (a) and 45 × 103 N m−1 for (b).
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
A substantial portion of the wave momentum flux that originates from the Patagonian peaks extends well into the stratosphere and even lower mesosphere. In contrast, the momentum flux from the central Andes is mostly absorbed in the upper troposphere and lower stratosphere, on account of the backward vertical shear of zonal winds. This is consistent with observations, in Fig. 1, that show wave activity in the lower stratosphere over the central Andes (bottom-left panel) but no activity higher up. It is also noteworthy that the momentum flux over the Antarctic Peninsula reduces to virtually zero at and above 10 km MSL. Interestingly, in the stratosphere the momentum flux maximum over Patagonia splits into two separate maxima with the primary one extending vertically upward and the second with a comparable amplitude tilting southward over Drake Passage, indicative of a southward transfer of the wave momentum flux with height. At 60 km MSL, the center of the second maximum is located approximately 1000 km to the south of Patagonia.
Two-dimensional horizontal wavenumber spectra of the vertical flux of zonal momentum [
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
5. Ray-tracing calculation
The analysis in section 4 suggests that the observed stratospheric/mesospheric wave patterns over Drake Passage likely originate from the Patagonian peaks in the southern Andes. It also raises a number of interesting questions regarding the influence of lateral and vertical wind shear, stratification variation, and the earth’s rotation on wave propagation, refraction, evolution, and possible absorption. In this section, we attempt to address these questions through three-dimensional ray-tracing calculations using the COAMPS output from the 15-km grid.
a. Three-dimensional ray paths of inertia–gravity waves
b. Ray paths in steady state flow
To examine the latitudinal dependence of wave characteristics, we first calculate rays launched from a range of latitudes along the main Andes ridge using winds and potential temperature averaged over the last 24 h of the integration. The 24-h averaged fields are further smoothed to remove mesoscale perturbations, which may introduce strong wind shear and cause difficulties with the integration (i.e., essentially a spurious wave–wave interaction). This is done using the same two-dimensional 900 × 900 km2 smoother as in the wave momentum flux calculation. Furthermore, the model wind direction at each grid point is rotated from the model north to true north to remove errors associated with the map projection. The smoothed and corrected zonal winds are characterized by a stratospheric jet that peaks approximately at 50 km MSL (Fig. 11b). To the south of 30°S there is a positive vertical shear (i.e., dU/dz > 0) and negative lateral shear (i.e., dU/dy < 0).
(a) Plan view of the 24-h average true zonal (grayscale, increment 10 m s−1) and meridional (contour, increment 5 m s−1; negative dashed) wind components at 10 km MSL. (b) Vertical cross section [location indicated by the straight (N–S) line in (a)] of the true zonal wind component (grayscale, increment 10 m s−1) and isentropes (increment 100 K) oriented north–south approximately along the Andes ridge .
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
These rays are launched approximately along the main southern Andes ridge (Fig. 12) at 6 km MSL to further minimize the impact of mountain-induced mesoscale perturbations. The initial horizontal wavenumbers are k0 = l0 = 2π/400 km−1, which are chosen based on the spectral analysis in section 4. As shown in Fig. 12, these ray paths behave quite differently, depending on their initial meridional locations. For rays initiated over the high central Andes ridge north of 35°S, the vertical group velocity decreases toward zero between 15 and 20 km, in accordance to the backward vertical shear of the westerly winds above the tropopause (Fig. 11b), suggestive of critical level absorption. Although the wave packets launched between 35° and 40°S are able to avoid the critical level, partially due to their southward propagation, they reach the eastern model boundary and, hence, are terminated before reaching the polar jet. These waves are of less interest because of the slow zonal wind in the lower troposphere and the relatively low quasi-two-dimensional ridge between 30° and 40°S. The rays initiated between 40° and 52°S experience the largest southward group propagation (i.e., 500–1200 km) and are able to propagate into the core of the stratospheric jet. It is noteworthy that, above the zonal jet, the group velocity decreases, associated with the transition to backward shear of the zonal wind, which should eventually lead to wave breaking. The southward bending of the ray paths that originate from the high Patagonian peaks is consistent with the bifurcation of the vertical flux of the zonal momentum, in Fig. 9b, and suggests that the Patagonian peaks are likely the source of the impressive stratospheric/mesospheric waves over Drake Passage, revealed by the AIRS brightness temperature images in Fig. 1. These results are consistent with similar spatial ray-tracing simulations of mountain wave propagation over the southern Andes by Preusse et al. (2002). Between 52° and 62°S the waves propagate nearly vertically with much less lateral displacement. There is no high terrain within this latitudinal range and, accordingly, mountain waves from this area have little contribution to the simulated stratospheric waves aloft. Farther south, no rays are shown as the intrinsic frequency changes sign near the surface due to the complex tropospheric wind patterns (Figs. 4a,b), implying a flow condition unfavorable for mountain wave generation.
Ray paths in the y–z plane calculated using the 24-h average COAMPS winds and buoyancy frequency: these rays are initiated at x = 105 (in grid points) and z = 6 km with k0 = 2π/400 km−1. Two sets of ray paths are shown; the solid rays correspond to y = 20n (n = 1, 2, 3 … ) in model grid points and l0 = k0, and the dashed rays correspond to y = 20n + 10 and l0 = 0. The time interval between two adjacent symbols (i.e., circles for set 1 and crosses for set 2) is 1 h. The maximum terrain height is profiled at the bottom.
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
As an example, a group of ray paths corresponding to k0 = 2π/400 km−1 and l0 = 0 are calculated and included in Fig. 12. These rays bifurcate approximately at 47°S, just to the north of Patagonia. To the north of 47°S, the waves propagate northward in the troposphere owing to lateral refraction by the positive meridional shear in the zonal wind and are absorbed by critical levels aloft. To the south, the rays propagate southward associated with refraction from the negative meridional shear of the zonal wind that leads to an increase of l (i.e., positive l and accordingly negative meridional group velocity) aloft. In general, this group of rays shows less southward bending than the corresponding rays with k0 = l0. For example, at 45 km MSL the wave packets with k0 = 2π/400 km−1 and l0 = 0 launched from Patagonia are approximately located at 150 km to the south of the wave source.
More ray paths over a range of wavenumbers from Patagonia are shown in Fig. 13. Along each ray path, the meridional wavenumber increases, primarily because of the negative lateral shear of the westerlies (i.e., 
(a) Ray paths in the y–z plane and (b) horizontal wavenumbers (k, l) along each ray path for four pairs of wave packets with k0 = 2π/100, 2π/200, 2π/400, and 2π/600 km−1 and l0 = 0 and k0, respectively. In (b) the k (solid) and l (dashed) curve are shown in the same color as in (a) for each wave packet.
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
Finally, we briefly discuss the sensitivity of the ray path corresponding to k0 = l0 = 2π/400 km−1 generated by flow over Patagonia to the Coriolis parameter, buoyancy frequency, vertical wind shear, and meridional winds. Although the spatial variation of the buoyancy frequency and Coriolis parameter appears in (3)–(8), their impact on wave refraction is rather insignificant over the parameters examined here (Fig. 14). This is consistent with Dunkerton (1984), who calculated ray paths of IGWs with an analytical zonal jet profile similar to the mean profile shown in Fig. 11b. According to (3), the squared ratio of the Coriolis parameter and the wave intrinsic frequency, 
(a) Ray paths in the y–z plane and (b) wavenumbers are shown for k0 = l0 = 2π/400 km−1. The other five pairs of curves correspond to paths and wavenumbers calculated from the identical parameters except for f = 0, Uy = 0, Ux = Uy = Vx = Vy = 0, V = 0, or N = 0.015 s−1, respectively.
Citation: Journal of the Atmospheric Sciences 70, 6; 10.1175/JAS-D-12-0180.1
6. Discussion and conclusions
A gravity wave event characterized by long linear wave patterns oriented northwest–southeast across Drake Passage in the stratosphere and lower mesosphere has been examined using a COAMPS simulation, and the simulated wave patterns bear close resemblance to those revealed by AIRS brightness temperatures.
According to the numerical simulation, the linear stratospheric wave patterns over Drake Passage likely originate from interaction between Patagonian orography and a southwesterly tropospheric jet. Waves generated by flow over the three-dimensional Patagonian peaks can be separated into three families: namely, the northeast propagating (i.e., k > 0; l < 0), localized (k > 0 and l ~ 0), and southeast propagating (i.e., k > 0; l > 0). For the northeast-propagating waves, their ray paths tend to tilt northward, and these waves are eventually absorbed at the critical level between 15 and 20 km, along with those waves launched from the central Andes. The localized family, including relatively short waves (λx < 300 km; l0 ~ 0), propagates nearly vertically and contributes to a wave momentum flux maximum directly over Patagonia. For this wave family, the increase of the wave amplitude with altitude eventually leads to wave breaking between 50–60 km MSL where the wave saturation criterion (i.e., 
The southward bending of the wave ray paths initiated from Patagonia is found to be sensitive to both wave characteristics and synoptic-scale winds. In general, longer waves exhibit more southward refraction, largely due to their slower vertical propagation. This is consistent with the modeled and AIRS-observed wave patterns over Drake Passage, which show clear increases in the horizontal wavelengths with the distance from the southern Andes. In addition, the southward wave propagation is also dependent on the meridional wind component; a northerly component (i.e., V < 0) enhances the poleward propagation. For this event, however, the contributions from the southerlies in the troposphere and northerlies in the stratosphere largely cancel each other out. Furthermore, the wave refraction is relatively insensitive to the Coriolis parameter and stability gradient. Clearly, the term corresponding to the horizontal variation of the stratification in (4)–(6) is much smaller than the horizontal shear terms. For most waves examined in this study, the wave Rossby number squared, 
It is noteworthy that, compared to the waves observed over major midlatitude barriers such as the European Alps (Smith et al. 2007) and the Sierra Nevada ridge in the United States (Smith et al. 2008; Doyle et al. 2009), the vertical velocity amplitude for the tropospheric waves over the Andes is much weaker. This must be due in part to the longer horizontal wavelengths (hundreds of kilometers), which, through gravity wave polarization and dispersion relations, lead to lower intrinsic frequencies and reduced vertical velocity amplitudes relative to short horizontal wavelength gravity waves. The Patagonian high peaks are located under the northern edge of the deep intense westerly jet associated with the relatively steady polar vortex. Accordingly, waves from Patagonia are able to propagate into the stratosphere and mesosphere without significant amplitude reduction from critical level absorption or wave. In contrast, waves over low- to midlatitude barriers typically encounter some form of critical level in the upper troposphere to lower stratosphere (e.g., a critical level at ~21 km was found over the Sierra Nevada range during T-REX; waves over the Central Andes are absorbed by a critical level between 15 and 20 km MSL in this study). These results highlight the importance of high-latitude topography such as the southern Andes, Antarctic Peninsula, and Greenland in stratospheric/mesospheric drag parameterization. It is also worth noting that the Scandinavian gravity wave imaged and modeled by Eckermann et al. (2007) has a structure, vertical evolution, and dynamics rather similar to the Patagonian waves observed and modeled here, although in that study wind turning with height rather than lateral refraction played a larger role.
In a recent study, McLandress et al. (2012) suggested that the missing orographic wave drag near 60°S could be the cause of stratospheric wind biases in global models. This study suggests that orographic wave drag near 60°S may have a nonlocal source, the Patagonian peaks, and the wave momentum flux is transferred southward by southeast-propagating inertia–gravity waves. The lateral shear of the horizontal wind along the edge of the polar vortex plays a constructive role in the southward momentum transfer largely through increasing the meridional wavenumber. As the dominant refraction term in (7), 
Finally, while the wave characteristics and the ray-tracing calculations are consistent with waves emanated from Patagonia, we cannot rule out other wave sources, such as the jet stream or frontal excitation, which may have contributed to the momentum fluxes. Evidence for such sources in COAMPS was found over the Antarctic Peninsula, for example. This study provides some useful guidance for planning future field observations of gravity waves over the southern Andes and Drake Passage. For example, according to our results, it is difficult for research aircraft to sample orographic waves over Drake Passage using airborne in situ instruments. On the other hand, upward-looking remote sensing instruments on research aircraft flying along Drake Passage may provide much needed insight into the characteristics and dynamics of these stratosphere–mesosphere waves.
Acknowledgments
This research is supported by the Chief of Naval Research through the NRL Base 6.1 Program by PE 0601153N. SDE acknowledges additional support from NASA (NRA NNNH09ZDA001N-TERRAQUA, The Science of Terra and Aqua, Grant NNH11AQ99I). The simulations were made using the Coupled Ocean–Atmospheric Mesoscale Prediction System (COAMPS) developed by U.S. Naval Research Laboratory. Computational resources were supported by a grant of HPC time from the Department of Defense Major Shared Resource Centers. The authors gratefully acknowledge helpful comments and suggestions from two anonymous reviewers.
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