A Modeling Study of Stratospheric Waves Over the Southern Andes and Drake Passage

1668 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70

A Modeling Study of Stratospheric Waves over the Southern Andes and Drake Passage

QINGFANG JIANG,JAMES D. DOYLE, AND ALEX REINECKE Naval Research Laboratory, Monterey, California

RONALD B. SMITH Department of Geology, Yale University, New Haven, Connecticut

STEPHEN D. ECKERMANN Naval Research Laboratory, Washington, D.C.

(Manuscript received 26 June 2012, in ﬁnal form 20 November 2012)

ABSTRACT

Large-amplitude stratospheric gravity waves over the southern Andes and Drake Passage, as observed by the Atmospheric Infrared Sounder (AIRS) on 8–9 August 2010, are modeled and studied using a deep (0–70 km) version of the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) model. The simulated tropospheric waves are generated by flow over the high central Andes ridge and the Patagonian peaks in the southern Andes. Some waves emanating from Patagonia propagate southeastward across Drake Passage into the stratosphere over a horizontal distance of more than 1000 km. The wave momentum flux is characterized by a tropospheric maximum over Patagonia that splits into two comparable maxima in the stratosphere: one located directly over the terrain and the other tilting southward with altitude. Using spatial ray-tracing techniques and flow conditions derived from the numerical simulation, the authors find that waves that originate from the high ridge in the Central Andes are absorbed by a critical level in the lower stratosphere. The three-dimensional waves originating from Patagonia could be separated into three families—namely, a northeast-propagating family, which is absorbed by a critical level between 15 and 20 km; a localized family, which breaks down in the stratosphere and lower mesosphere directly above Patagonia; and a southeast-propagating family, which forms the observed linear stratospheric wave patterns oriented across Drake Passage. The southward group propagation, assisted by lateral wave refraction due to persistent meridional shear of the zonal winds, leads to stratospheric wave breaking and drag near 608S, well south of the parent orography.

1. Introduction Accurate parameterizations require in turn a fundamental understanding of gravity wave dynamics, from Gravity waves entering into the stratosphere and me- generation at the source to propagation and dissipation sosphere play an important role in driving the general elsewhere in the atmosphere. Major tropospheric grav- circulation, enhancing vertical mixing, and contributing ity wave sources identified by previous studies include to polar stratospheric cloud formation, which has further mountains, convection in tropical areas, lower-tropospheric implications for ozone depletion over polar regions (e.g., frontal activity, and upper-tropospheric unbalanced jet Carslaw et al. 1998). Owing to finite computing resources, streams, each of which has been the subject of extensive global climate and weather models cannot run at spatial studies [see review by Fritts and Alexander (2003)]. Par- resolutions needed to resolve gravity waves, so their ticularly, our knowledge of gravity waves generated by effects must be parameterized (e.g., Kim et al. 2003). flow over mountains has been significantly advanced through several large field campaigns conducted over major Corresponding author address: Qingfang Jiang, Naval Research barriers such as the Rocky Mountains [Wave Momentum Laboratory, 7 Grace Hopper Ave., Monterey, CA 93940-5502. Flux Experiment (WAMFLEX); Lilly and Kennedy 1973], E-mail: [email protected] the European Alps [Mesoscale Alpine Programme (MAP);

DOI: 10.1175/JAS-D-12-0180.1

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Smith et al. 2007], and the Sierra Nevada range [Sierra The remainder of this paper is organized as follows. Waves Project (SWP) 1954 and Terrain-Induced Rotor The wave event and wave properties deduced from Experiment (T-REX); Grubisic et al. 2008]. Mountain satellite and radiosonde observations and the scientific waves over high-latitude southern regions, such as the issues to be pursued by this study are set forth in section southern Andes, have received much less attention. 2. Section 3 contains a description of the model config- Over the past decade, the advent of high resolution uration and an overview of the synoptic conditions satellite sensors has provided new insights into the during this wave event. The simulated wave character- global distribution of long-wavelength gravity wave ac- istics including spatial and temporal variations, wave tivity in the stratosphere (Wu et al. 2006). Observations spectra, and wave momentum fluxes are presented in from both limb and nadir sensors have revealed a strik- section 4. Wave dynamics is further examined in section ing maximum in stratospheric gravity wave variances 5 through ray-tracing calculations. The results and con- over the southern tip of the Andes, the Antarctic Pen- clusions are summarized in section 6. insula, and Drake Passage (Eckermann and Preusse 1999; McLandress et al. 2000; Jiang et al. 2002; Wu 2004; 2. The 8–10 August 2010 wave event Wu and Eckermann 2008; Alexander et al. 2008; Yan et al. 2010). A number of studies have demonstrated that The Atmospheric Infrared Sounder (AIRS) on the the high orography of the Andes and Antarctic Penin- National Aeronautics and Space Administration Aqua sula generates many of the intense stratospheric gravity satellite acquires radiances by scanning the atmosphere waves observed here, some of which appear to propa- symmetrically about nadir in a repeating cycle aligned gate downstream and meridionally to produce activity orthogonal to the orbit vector (Aumann et al. 2003). A over Drake Passage (e.g., Preusse et al. 2002; Jiang et al. number of previous studies have demonstrated that 2002; Alexander and Teitelbaum 2007; Baumgaertner gravity waves with long vertical wavelengths and hori- and McDonald 2007; Plougonven et al. 2008; Yamashita zontal wavelengths .40 km can be resolved as a two- et al. 2009; Shutts and Vosper 2011). However, others dimensional perturbation structure in swath radiance have questioned the presumed dominance of orographic imagery of certain stratospheric channels uncontaminated forcing in generating enhanced wave activity in this re- by high-tropospheric cloud (e.g., Wu et al. 2006; Alexander gion (e.g., de la Torre and Alexander 2005). For example, and Barnet, 2007; Eckermann et al. 2007). Here we use some studies have identified tropospheric convection and a channel-averaged AIRS radiance product registered jet stream instabilities as the sources of waves observed in at a series of heights from 100 to 2 hPa and summarized this same region (e.g., Yoshiki and Sato 2000; Yoshiki in Table A2 of Gong et al. (2012). We remove large- et al. 2004; de la Torre et al. 2006; Spiga et al. 2008; Hei scale backgrounds to isolate gravity wave perturbations et al. 2008; Llamedo et al. 2009). Still other studies have using techniques described by Eckermann and Wu argued that instabilities in the stratospheric vortex jet (2012). generate upward- and downward-propagating gravity Figure 1 shows the resulting brightness temperature waves that also contribute to this enhanced local wave (radiance) perturbations at several pressure levels on 8–9 activity (Sato and Yoshiki 2008; Moffat-Griffin et al. August 2010 within a focused region over the southern 2011). Clearly the origins and dynamics of the rich and Andes and Antarctic Peninsula. Linear wave patterns highly energetic gravity wave fields encountered in this are evident in the swath imagery over the southern tip of remote region of the planet require further research to the Andes and Drake Passage with at least three pairs of better understand and parameterize. wave crests and troughs discernible. Note that, while The research in this paper is also motivated by satellite these observed radiance perturbations are directly re- observations of stratospheric gravity waves in this region, lated to actual gravity-wave-induced temperature struc- which frequently reveal linear wave patterns over the ture in terms of the two-dimensional phase structure, the southern Andes and Drake Passage. The objectives of this brightness temperature amplitudes are a lower bound, study are twofold. First, we want to explore the capability and likely a considerable underestimate, of the actual of the Coupled Ocean–Atmosphere Mesoscale Prediction temperature amplitudes of these waves, owing to the System (COAMPS) in simulating stratospheric gravity vertical averaging effect of the broad nadir weighting waves by extending its model top from the previous functions that yield these channel radiances (Alexander capability at the 30-km level (i.e., lower stratosphere) to and Barnet 2007). The waves evident in Fig. 1 share the ;70 km MSL (i.e., lower mesosphere). Second, we want to following properties: 1) they extend across Drake Pas- advance our understanding of characteristics and dy- sage with phase lines oriented northwest–southeast; 2) namics of gravity waves over the southern Andes and Drake while the wave crests (troughs) vary in length at differ- Passage through examination of the simulated waves. ent levels, their northern edges are always anchored

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FIG. 1. 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 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. above the southern Andes; 3) the horizontal wave- peaks higher than 3 km MSL. The coincidence between lengths (i.e., the horizontal distance between two adja- the northwestern end of the wave field and these high cent crests or troughs in the direction normal to the peaks, as well as the nearly stationary nature of these waves) exhibit a weak dependence on altitude, tend to waves, suggests an orographic origin. It is noteworthy increase with the distance from their northern edges, that there are wavelike features to the west of Drake and are in the range of 300–700 km; and 4) these waves Passage discernible at least at the 7- and 2.5-hPa levels, are nearly stationary with respect to the ground and which may be generated by active baroclinic storms in the penetrate throughout the full depth of the stratosphere. troposphere (Fig. 4) rather than by flow over orography Further inspection indicates that the northwestern end (e.g., Zhang 2004). of the wave field is approximately located above the The wind profiles derived from the radiosondes Patagonian ice sheet, which comprises several mountain launched from Puerto Montt (PM, 41.438S) and Punta

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Arenas (PA, 53.008S) during this time period provide 3. Numerical configuration further evidence of an orographic origin of these waves a. Numerical configuration (Fig. 2, with station locations depicted in Fig. 3). Around 1200 UTC 9 August, Fig. 2 reveals moderate low-level The atmospheric component of Coupled Ocean– southwesterlies directed toward the southern Andes— Atmosphere Mesoscale Prediction System1 (Hodur 1997; a condition typically conducive to the generation of Doyle et al. 2000) has been applied to the study area mountain waves. Wavelike variations in the horizontal (Fig. 3) to simulate this wave event. COAMPS is a fully wind profiles suggest that these radiosondes may have compressible, nonhydrostatic terrain-following meso- ascended through gravity waves that emanated from the scale model. The finite difference schemes are of second- southern Andes (Fig. 3). For example, at PA, both u and order accuracy in time and space in this application. The y components reveal a wavelike variation between 3 km boundary layer and free-atmospheric turbulent mixing and the tropopause (;12 km), suggesting a possible and diffusion are represented using a prognostic equation gravity wave with a dominant vertical wavelength for the turbulence kinetic energy (TKE) budget (Mellor of ;9 km, which is comparable to that of a linear hy- and Yamada 1974). The surface heat and momentum drostatic wave (i.e., lz 5 2pU/N ; 9.4 km, with the fluxes are computed following the Louis (1979) and Louis troposphere-averaged cross-mountain wind speed U ; et al. (1982) formulations. The grid-scale evolution of 2 2 15 m s 1 and the buoyancy frequency N ; 0.01 s 1). moist processes is explicitly predicted from budget equa- Uncertainties associated with deriving wave character- tions for cloud water, cloud ice, rainwater, snowflakes, and istics from a single radiosonde (Shutts et al. 1988) appear water vapor (Rutledge and Hobbs 1983), and the subgrid- to be less an issue here as the drift distance of the ra- scale moist convective processes are parameterized using diosonde is far smaller than the horizontal wavelengths. an approach following Kain and Fritsch (1993). The Fu– More wave properties can be deduced from the cor- Liou four-stream approximation is used for the shortwave responding wind hodographs (Fig. 2b) by assuming that and longwave radiation processes (Fu et al. 1997). these wavelike perturbations were related to a mono- The model is initialized at 0000 UTC 8 August and chromatic wave and using a linear dispersion relation for integrated over 36 h, after a 12 h spinup. The initial inertia–gravity waves (IGWs). The hodographs derived fields for the model are created from multivariate opti- from the pair of soundings are characterized by looping mum interpolation analysis of upper-air sounding, sur- (or spiral) patterns, which are typical for observations face, commercial aircraft, and satellite data that are obtained from radiosondes ascending through IGWs quality controlled and blended with previous 12-h (e.g., Tsuda et al. 1994; Eckermann 1996). The radio- COAMPS forecast fields. An incremental update data sonde from PA intercepts a much-larger-amplitude assimilation procedure is used, which enables mesoscale wave with u and y perturbations ranging around 25– phenomena to be retained in the analysis increment 2 30 m s 1 in the troposphere (i.e., the primary loop), fields. Lateral boundary conditions for the outermost although the tropospheric jet stream shear might dis- grid mesh are derived from the Navy Operational tort these IGW ellipses somewhat. The counterclock- Global Atmospheric Prediction System forecast fields. wise rotation with height in the Southern Hemisphere The computational domain contains two horizontally implies that waves have a downward phase speed and nested grid meshes of 151 3 151 and 256 3 355 grid an upward group velocity (e.g., Tsuda et al. 1994). The points, and the corresponding horizontal grid spacings orientation of the primary loop implies that the hori- are 45 and 15 km, respectively. There are 92 vertical zontal wave phase line is oriented from northwest to levels with grid spacing increasing from 20 m at the southeast above PA. The smaller amplitude wave ob- lowest model level to 400–750 m in the upper tropo- served at PM propagates upward as well. However, the sphere and stratosphere. The model top is located at major axis of the ellipsis implies that the horizontal approximately 70 km MSL and a sponge boundary phase line is oriented southwest–northeast (Fig. 2). condition is applied to the top 12 km to reduce down- Finally, it is worth noting that we inspected wave ward reflection of gravity waves. It is worth noting that patterns in the stratospheric AIRS radiances over this several additional numerical experiments have been region each day throughout the July–September 2010 carried out to test the sensitivity of the simulated waves period. Similar wave patterns to those in Fig. 1 are ob- to the horizontal grid spacing (e.g., triple-nested grid served on many days during this 3-month period, im- meshes with grid spacings of 45, 15, and 5 km) and upper plying that such waves occur frequently and may have significant contributions to the wave variance maximum over Drake Passage, as suggested by previous studies 1 COAMPS is a registered trademark of the Naval Research (e.g., Jiang et al. 2002). Laboratory.

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21 FIG. 2. (a) Horizontal wind components (m s ) and potential temperature (K) proﬁles from the 1200 UTC soundings on 9 Aug 2010 from Puerto Montt (PM) (41.438S, 73.108W; solid) and Punta Arenas (PA) (53.008S, 70.858W; dashed). (b) Corresponding wind hodographs are shown with the sense of rotation with height indicated by thin arrows. boundary conditions (e.g., simulations with a deeper model conﬁgurations. The terrain data are based on sponge layer or a radiation boundary condition follow- the Global Land One-km Base Elevation (GLOBE) ing Klemp and Durran 1983) and the simulated waves dataset, and the terrain in the 15-km mesh is shown are found to be relatively insensitive to the changes in in Fig. 3.

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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. In the stratosphere (Figs. 4e,f), nearly steady and very strong westerlies are evident between 508 and 708S associated with the polar vortex. Pronounced negative meridional shear of the zonal wind (i.e., ›U/›y , 0, where y is the meridional distance) exists between 408 and 608S. In contrast, the stratospheric winds equator- ward of 308S are much weaker. The southern tip of the Andes, a possible mountain wave source, is located be- neath the northern edge of the polar vortex, where relatively strong westerlies and lateral shear are present. In the vicinity of PA, the simulated strong southwesterly jet extends from the mountaintop level (i.e., ;2 km) to the lower stratosphere over the southern Andes, which is in qualitative agreement with the proﬁles derived from the radiosonde from PA after ﬁltering out wave perturbations (Fig. 2).

4. Characteristics of simulated waves The objective of this section is to characterize the

FIG. 3. Topography in the 15-km grid domain is shown in gray simulated gravity waves with emphasis on spatial and shading (interval 0.5 km): locations of the two radiosonde stations, temporal variations of inertia–gravity waves and vertical PM and PA, are indicated by black triangles. 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 b. Synoptic conditions the Antarctic Peninsula) and also has a horizontal grid The synoptic conditions associated with this wave spacing that is fine enough to resolve the mesoscale event are illustrated in Fig. 4. During this event, the waves of interest. lower troposphere was characterized by complex syn- a. Wave characteristics and time dependence optic patterns, including pressure troughs and cutoff lows associated with baroclinic waves (Figs. 4a,b). A We begin with a qualitative comparison between the southwesterly jet arrives at the southern Andes at simulated wave patterns evident in the plan views of the 1200 UTC 8 August and reaches its maximum strength vertical velocity and those in the AIRS images in Fig. 1. approximately 24 h later, during which the low-level Figures 5b–d are plots of simulated wave fields at model winds gradually become more westerly. It is noteworthy levels that correspond approximately to the 80, 10, and that, according to linear theory and field observations, 2.5-hPa levels, respectively, of the AIRS imagery in Fig. strong cross-mountain low-level winds are favorable to 1. The simulated vertical velocity field is characterized the launching of large-amplitude mountain waves (e.g., by quasi-linear wave patterns in the stratosphere, ori- Doyle et al. 2009). This jet, characterized by generally ented northwest–southeast across Drake Passage in a positive vertical wind shear, extends throughout the tro- manner qualitatively similar to the AIRS brightness posphere and provides a favorable condition for stationary temperature patterns (Fig. 1). The zonal wavelengths mountain waves to enter the stratosphere (Figs. 4c,d) (i.e., east–west distance between two adjacent wave owing to the absence of zero-wind critical levels. Equa- crests or toughs) exhibit some variations in the vertical torward of 308S, a weaker low-level jet impinges on the and meridional directions and are in the range of high central Andes ridge (;6 km MSL) and becomes 300–700 km, in agreement with those estimated from the progressively stronger during the study period, implying AIRS images. The northern edges of these linear wave that the central Andes might be another wave source. patterns are anchored over the southern tip of the Andes Consistent with this, the lower-left panel of Fig. 1 clearly as well. The qualitative agreement between the satellite

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FIG. 4. Synoptic ﬂow patterns from the 45-km grid mesh. Horizontal wind speed [color, increment is (a)–(d) 2 2 5ms 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.

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21 FIG. 5. Plan views of the vertical velocity [color, increment is (a)–(c) 0.2 and (d) 0.3 m s ] 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. observations and COAMPS simulated wave patterns Passage generally increases with the altitude, as would provides the basis for further diagnosis of the wave be expected for freely propagating nondissipating waves properties and exploration of the underlying dynamics. due to the density effect. However, in the troposphere According to the COAMPS simulation, the amplitude there are only quasi-stationary waves locally over the of the stratospheric–mesospheric waves across Drake leeside of the central and southern Andes and no

Unauthenticated | Downloaded 10/07/21 05:33 PM UTC 1676 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70 discernible waves over Drake Passage (Fig. 5a). The During the 36-h study period, the simulated waves vertical variation of the simulated waves is more evident evolved with time in accordance with the slowly in Fig. 6, which shows vertical cross sections of zonal changing synoptic conditions evident in Fig. 4. Right velocities u, vertical velocities w, and potential tem- above the Patagonian peaks, a nearly stationary wave is perature u along three west-to-east sections oriented present over the lee slope, characterized by a crest and across the central and southern Andes and Drake Pas- trough pair and the wave amplitude becomes much sage, respectively (i.e., approximately along the pre- stronger over the last 24 h of the simulation (Fig. 7a), vailing wind direction), and shown in Fig. 5a. Mountain consistent with enhancement of the cross-mountain waves emanate from the high central Andes ridge and wind component at the mountaintop level near Pata- propagate up to the tropopause (;12 km MSL). The gonia during the same time period (Fig. 4). In the zonal winds at these lower latitudes are characterized stratosphere, there are three crest–trough pairs over the by a strong easterly shear across the tropopause and leeside of the Patagonian peaks (Fig. 7b) likely due to lower stratosphere, where wave breaking and critical dispersion of the IGWs, and the characteristic wave- level absorption occur. Above 20 km the zonal winds length is noticeably longer than in the troposphere. In become weaker, and no waves are distinguishable (Figs. contrast to the steady waves at the mountaintop level, 6a,b). In contrast, deep westerlies are present over the the wave amplitude and location of the wave phase lines southern Andes (Fig. 6c). Accordingly, the mountain slowly oscillate, initially moving upstream and then waves that emanate from the southern Andes (i.e., Pat- downstream in the last 24 h. The evolution of the zonal agonian glacial sheet) propagate through the entire wind upstream of Patagonia from the troposphere to stratosphere and into the mesosphere with increasing lower mesosphere and the corresponding leeside wave wave amplitude aloft due to the decrease of the air den- response are shown in Figs. 7c and d, respectively. The sity (Fig. 6d). The wave amplitudes in terms of vertical zonal wind component in the troposphere exhibits a mini- velocity and zonal wind perturbations reach maxima mum approximately from 10 to 20 h, separating the 36-h between 50 and 60 km MSL where a zonal wind reversal period into a weakening phase (i.e., 0–12 h) and occurs in accordance with the wave-induced steepened strengthening phase (;12–24 h, Fig. 7c). The corre- isentropes (Fig. 6c)—a typical signature of breaking sponding wave phase lines descend more than 5 km in the gravity waves. A useful dimensionless diagnostic of wave first 12 h while the wave amplitude weakens substantially, saturation or breaking is the steepness (or vertical dis- then ascend throughout the remainder of the forecast pe- L5 h placement gradient) N m/U (Lindzen 1981), where riod as the waves reintensify (Fig. 7d), approximately in N is the ambient buoyancy frequency, U is the ambient phase with evolution of the tropospheric westerlies. The horizontal wind speed, and hm denotes the maximum downward and upstream (upward and downstream) vertical displacement of density surfaces or isentropes. movement of the phase lines during the weakening Wave breaking may occur when L exceeds unity, and (strengthening) phase of the synoptic-scale westerlies in may then give rise to dissipation and mixing that restores the x–z space is consistent with the idealized study of Chen stable stratification and accordingly keeps the maximum et al. (2005) of the influence of transient synoptic-scale L near or less than unity. For a stationary linear two- winds on orographic wave forcing and evolution. dimensional gravity wave of the form (w, h) 5 h p l b. Wave momentum fluxes (wm, m) sin(2 x/ x), the wave-induced vertical displacement can be estimated using the linear wave relation, A key property of gravity waves is the vertical flux of 5 ›h › L5 l p 2 w U / x,whichyields N xwm/(2 U ). Using the horizontal momentum, defined by values estimated from Fig. 6c at the level of 50 km MSL— ðð 5 21 l 5 5 21 namely, N 0.02 s , x 300 km, wm 5ms ,andU 0 0 0 0 2 0 0 0 0 2 5 r y 5 1r y 5 1 L; (Fx, Fy) a(w u , w ) A a (w u , w ) dx dy, 70 m s —we obtain 1.0, implying that vigorous A wave breaking may be occurring around 50 km MSL (1) over the southern Andes. Along the Drake Passage, gravity waves are evident in the stratosphere and, again, where (u0, y0, w0) 5 (u 2 U, y 2 V, w 2 W) denotes the there is no discernible wave signal in the troposphere perturbation velocity with respect to the synoptic-scale r 5 r (Figs. 6e,f). Compared to waves over Patagonia, the velocity (U, V, W) and a a(z) is the mean air density, waves over Drake Passage are characterized by smaller which decreases approximately exponentially with alti- amplitudes and longer wavelengths. Further inspection tude. The synoptic-scale velocity at each model grid suggests wave breaking occurs at ;55 km MSL, as in- point is obtained by applying a moving average over dicated by steepened isentropes, TKE maxima, and flow a square area centered at the grid point with an area of reversal in the direction normal to the wave phase line. 900 3 900 km2. It is noteworthy that the choice of this

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21 FIG. 6. Cross sections of (left) zonal [increment is (a) 5 and (c),(e) 10 m s ] and (right) vertical [increment is 2 (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.

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21 FIG. 7. Distance–time (Hovmoller)€ diagrams of the vertical velocity at (a) 4 km (increment 0.2 m s ) and 2 (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 2 distance). Time–height diagrams of (c) the upstream zonal winds (increment 5 m s 1; see Fig. 5a for location) and 2 (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. area is largely based on trial and error, and is consistent is deposited into the mean flow. The evolution and with the traditional assumption that the characteristic vertical variation of the domain-average Fx is shown in horizontal wavelengths of extratropical gravity waves Fig. 8. It is evident that Fx is negative everywhere, re- are usually far less than 1000 km and the length scales flecting the easterly propagation of these quasi-stationary for synoptic patterns are typically longer than 1000 km. waves with respect to the background westerlies. The The calculation has been repeated with the average magnitude of Fx exhibits a sharp decrease between ap- square area equal to 600 3 600 km2 and 1200 3 proximately 15 and 20 km MSL, likely associated with 1200 km2, and the resulting synoptic and perturbation the easterly wind shear here (Fig. 6a). In the stratosphere fields are qualitatively similar. and lower mesosphere, the amplitude of Fx decreases For a steady irrotational inviscid vertically propagat- much more gradually with altitude. The momentum flux ing gravity wave, the vertical momentum flux should be also shows two separate maxima in time in the strato- constant with height (Eliassen and Palm 1961) up to a sphere, corresponding to the first 12 h and last 24 h, level where dissipation (i.e., wave breaking or critical respectively, consistent with the evolution of the level absorption) occurs and some wave momentum flux stratospheric waves in Fig. 7.

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FIG. 9. Vertical cross section of vertical ﬂuxes of the zonal mo- FIG. 8. Time–height plots of the vertical ﬂux of zonal momentum mentum (b) for the lowest 15 km and (a) between 15 and 60 km (Fx) averaged over the southern Andes and Drake Passage. (b) For MSL valid at 0000 and 1200 UTC 9 Aug 2010, respectively. 22 2 the troposphere the range is from 20.06 to 0 N m with an in- The color scale intervals are 7.5 3 103 Nm 1 for (a) and 45 3 22 2 crement of 0.005 N m and (a) for the stratosphere the range is 103 Nm 1 for (b). 2 2 from 20.012 to 0 N m 2 with an increment of 0.001 N m 2.

To examine the meridional variation of the wave the high central Andes ridge, likely because of stronger momentum flux, the zonally averaged verticalÐ flux of zonal winds over Patagonia in the lower troposphere. h i 5 r 0 0 5 r L 0 0 zonal momentum, Fx aw u a 0 w u dx/L, The maximum over the Antarctic Peninsula is centered where L is the zonal width of the 15-km model grid, for approximately at 8 km MSL, pointing to baroclinic wave the final hour of the simulation is shown in Fig. 9. The adjustment as a possible source of this wave activity. simulated tropospheric momentum fluxes are charac- A substantial portion of the wave momentum flux that terized by three local maxima in absolute value over the originates from the Patagonian peaks extends well into high ridge of central Andes, the Patagonian peaks in the the stratosphere and even lower mesosphere. In con- southern Andes, and the Antarctic Peninsula, re- trast, the momentum flux from the central Andes is spectively. These maxima over the central Andes and mostly absorbed in the upper troposphere and lower Patagonia decay monotonically with altitude, implying stratosphere, on account of the backward vertical shear their orographic origins. The maximum over the Pata- of zonal winds. This is consistent with observations, in gonian peaks is substantially stronger than the one over Fig. 1, that show wave activity in the lower stratosphere

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^ FIG. 10. Two-dimensional horizontal wavenumber spectra of the vertical ﬂux of zonal momentum [Fx(k, l)] at (a) 12, (b) 20, (c) 45, and 2 (d) 55 km MSL valid at 1200 UTC 9 Aug 2010. Shading intervals are 0.15, 0.08, 0.05, and 0.03 N m 2, and contour intervals are 0.3, 0.16, 2 0.1, and 0.06 N m 2; negative values are dashed. The horizontal (vertical) axes correspond to zonal (meridional) wavenumbers. Only 22 21 wavenumbers in the range 1 # k # 23km and 221km # l # 21km are shown, where km 5 2p/(256Dx). The wavenumber k or l 5 10 km is labeled (horizontal dashed line) for reference.

over the central Andes (bottom-left panel) but no ac- with negative values around (k, l) 5 (6km,4km)and tivity higher up. It is also noteworthy that the momentum (4km, 22km), corresponding to the waves with northwest– flux over the Antarctic Peninsula reduces to virtually zero southeast- and southwest–northeast-oriented phase lines, at and above 10 km MSL. Interestingly, in the strato- respectively (Fig. 10a), where km 5 2p/L and L 5 sphere the momentum flux maximum over Patagonia 256Dx. In addition, there are positive flux values near (0, splits into two separate maxima with the primary one 2km), a plausible source of which is the projection of extending vertically upward and the second with mesoscale waves onto synoptic flow variations. As a comparable amplitude tilting southward over Drake shown in Fig. 4, synoptic flow patterns are rather com- Passage, indicative of a southward transfer of the wave plicated in the troposphere, implying difficulty in sepa- momentum flux with height. At 60 km MSL, the center rating mesoscale wave perturbations and synoptic-scale of the second maximum is located approximately 1000 km variations, particularly at these larger scales. The con- to the south of Patagonia. tribution to momentum fluxes from the synoptic-scale To further examine the dependence of the momentum variability can be either positive or negative. It has been flux on horizontal wavenumbers, the momentum flux in demonstrated by Chen et al. (2005) that positive mo- the wavenumber space is computed for a 256 3 256 mentum flux can be generated by interaction between subdomain of the 15-km grid, which includes the southern mountain waves and evolving large-scale patterns. It is Andes and Drake Passage (Fig. 5d). The momentum flux noteworthy that, in the troposphere, even the centers of is analyzed using a two-dimensional Fourier transform of enhanced negative momentum flux may be contami- fields at a given model level. Figure 10 displays the vertical nated by contributions from synoptic-scale flow pat- fluxes of the zonal momentum in this two-dimensional terns. This is much less of an issue in the stratosphere horizontal wavenumber space, defined by where momentum fluxes are predominantly negative (Figs. 10b–d). In addition, the maxima in flux mag- r nitude are centered above l 5 0, implying that the F^ (k, l) 5 Re(u^w^*), (2) x 2 southwest–northeast oriented waves evident in the troposphere are absent in the midstratosphere, likely where the caret denotes Fourier component variables due to critical level absorption associated with the

(i.e., u, w,andFx) and the terms with the asterisk rep- vertical wind shear in the tropopause and lower resent the corresponding complex conjugates. There stratosphere. This is consistent with the wave patterns are two centers of enhanced absolute ﬂux values, each in Fig. 4, phase lines of which are mostly northwest–

Unauthenticated | Downloaded 10/07/21 05:33 PM UTC JUNE 2013 J I A N G E T A L . 1681 southeast oriented. At 20 km MSL the momentum flux where maximum is centered approximately at (6km,6km), corresponding to wavelengths (640 km, 640 km). From d › g 5 1 (U 1 c ) $ the lower to middle stratosphere, the momentum flux dt ›t g maximum tends to shift toward slightly larger wavenumbers. For example, at 45 km MSL the maximum is denotes changes along a ray path, cgi 5 ›v/›ki is the in- centered near (8km,9km), corresponding to wavelengths trinsic group velocity, and the index i 5 1, 2, and 3 of (480 km, 426 km). The shortening of the horizontal corresponds to the three dimensions, x, y, and z. Using wavelengths with height may result from differences in the Wentzel–Kramers–Brillouin (WKB) approxima- the vertical group velocity; in general, shorter waves tion, the dispersion relation for a linear hydrostatic IGW propagate faster (e.g., Tan and Eckermann 2000; Chen can be written as et al. 2005). The amplitude of the momentum flux tends to decrease slowly with altitude and a sharp decrease 2 2 occurs between 45 and 55 km (Figs. 10c,d), likely asso- v2 5 N K 1 2 2 f , (4) ciated with wave breaking over Patagonia (see Fig. 6d). m It is noteworthy that the momentum fluxes are pre- where dominantly negative in the stratosphere, implying a lack of down-going secondary waves often generated by in- g ›u tense wave breaking (Smith et al. 2008). A plausible ex- N2 5 u ›z planation is that the wave breaking examined in this study is relatively moderate, and secondary wave generation is is the buoyancy frequency squared, K2 5 k2 1 l2 is the insignificant. Stratospheric wave breaking in the Tan and total horizontal wavenumber squared, k and l are zonal Eckermann (2000) study generated downward-propa- and meridional wavenumber components, m is the gating secondary waves, but this result is likely affected vertical wavenumber, f is the Coriolis parameter, by the simplicity of their two-dimensional simulations, v 5 V 2 k U is the intrinsic frequency, and V is the since the present study reveals important three-di- Eulerian wave frequency, which is zero for steady waves. mensional aspects to the wave field evolution with The density scale-height term and acoustic branch are height. ignored in (4) for simplicity. The group velocity (cg) can be written as 5. Ray-tracing calculation N2 The analysis in section 4 suggests that the observed c 5 [k, l, 2K2/m]. (5) g vm2 stratospheric/mesospheric wave patterns over Drake Passage likely originate from the Patagonian peaks in Using dki/dt 52›v/›xi and (4), we obtain the equations the southern Andes. It also raises a number of inter- that govern refraction of the wavenumber vector (e.g., esting questions regarding the influence of lateral and Marks and Eckermann 1995): vertical wind shear, stratification variation, and the earth’s rotation on wave propagation, refraction, evolu- d k ›U ›V K2 ›N2 tion, and possible absorption. In this section, we attempt g 52k 2 l 2 , (6) dt ›x ›x 2m2 ›x to address these questions through three-dimensional ray-tracing calculations using the COAMPS output d l ›U ›V K2 ›N2 f df g 52k 2 l 2 2 , (7) from the 15-km grid. dt ›y ›y 2m2 ›y v dy a. Three-dimensional ray paths of inertia–gravity d m ›U ›V K2 ›N2 g 52k 2 l 2 . (8) waves dt ›z ›z 2m2 ›z The ray-tracing technique has been frequently used Equations (6)–(8) imply wave refraction occurs asso- in the study of stratospheric gravity waves (e.g., ciated with lateral and vertical wind shears, horizontal Dunkerton 1984). A ray group trajectory is given by and vertical stratification gradients, and the b effect. In (Lighthill 1978) the remainder of this section, several groups of inertia– gravity wave ray solutions are calculated using (3), (4), dgxi (6), and (7) using background wind and buoyancy fre- 5 U 1 c , (3) dt i gi quency fields derived from the COAMPS simulation.

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21 FIG. 11. (a) Plan view of the 24-h average true zonal (grayscale, increment 10 m s ) and meridional (contour, 2 increment 5 m s 1; negative dashed) wind components at 10 km MSL. (b) Vertical cross section [location indicated 2 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 .

The objective of these calculations is to understand the a range of latitudes along the main Andes ridge using vertical and lateral group propagation of inertia–gravity winds and potential temperature averaged over the last waves, the influence of lateral wind shear and the earth’s 24 h of the integration. The 24-h averaged fields are rotation effects on IGW propagation, and the evolution further smoothed to remove mesoscale perturbations, of IGWs in a time-evolving synoptic flow. The in- which may introduce strong wind shear and cause diffi- tegration of a ray terminates under one of the following culties with the integration (i.e., essentially a spurious five conditions: 1) when it reaches lateral boundaries or wave–wave interaction). This is done using the same the model top, 2) when the nondimensional parameters two-dimensional 900 3 900 km2 smoother as in the wave momentum flux calculation. Furthermore, the model dk d 5 1 i . wind direction at each grid point is rotated from the i 2 1, ki dxi model north to true north to remove errors associated with the map projection. The smoothed and corrected 3) when v changes sign, 4) when v2 2 f 2 , 0, and 5) zonal winds are characterized by a stratospheric jet when the magnitude of m is too large. Condition 2 states that peaks approximately at 50 km MSL (Fig. 11b). To that the variation of wavenumbers should be slow, which the south of 308S there is a positive vertical shear (i.e., is required by the WKB approximation (Marks and dU/dz . 0) and negative lateral shear (i.e., dU/dy , 0). Eckermann 1995; Chen et al. 2005). The sign change of These rays are launched approximately along the v implies that the ray is traveling across a critical level. main southern Andes ridge (Fig. 12) at 6 km MSL to Condition 4 represents an inertial critical level where further minimize the impact of mountain-induced me- wave energy is absorbed or reflected (Wurtele et al. soscale perturbations. The initial horizontal wave- j j 21 1996). When m is too large, the vertical group velocity numbers are k0 5 l0 5 2p/400 km , which are chosen is small, implying that the ray is approaching a critical based on the spectral analysis in section 4. As shown in level. It is noteworthy that (8) is redundant given the Fig. 12, these ray paths behave quite differently, de- dispersion relation (4). In our code, the vertical wave- pending on their initial meridional locations. For rays numbers are calculated using (4) and (8) separately for initiated over the high central Andes ridge north of 358S, the purpose of consistency checking. the vertical group velocity decreases toward zero between 15 and 20 km, in accordance to the backward b. Ray paths in steady state flow vertical shear of the westerly winds above the tropo- To examine the latitudinal dependence of wave pause (Fig. 11b), suggestive of critical level absorption. characteristics, we first calculate rays launched from Although the wave packets launched between 358 and

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FIG. 12. Ray paths in the y–z plane calculated using the 24-h average COAMPS winds and buoyancy frequency: these rays are initiated at x 5 105 (in grid points) and z 5 6 km with 21 k0 5 2p/400 km . Two sets of ray paths are shown; the solid rays correspond to y 5 20n (n 5 1, 2, 3 ...) in model grid points and l0 5 k0, and the dashed rays correspond to y 5 20n 1 10 and l0 5 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.

408S are able to avoid the critical level, partially due to waves from this area have little contribution to the their southward propagation, they reach the eastern simulated stratospheric waves aloft. Farther south, no model boundary and, hence, are terminated before rays are shown as the intrinsic frequency changes sign reaching the polar jet. These waves are of less interest near the surface due to the complex tropospheric wind because of the slow zonal wind in the lower troposphere patterns (Figs. 4a,b), implying a ﬂow condition unfavor- and the relatively low quasi-two-dimensional ridge be- able for mountain wave generation. tween 308 and 408S. The rays initiated between 408 and As an example, a group of ray paths corresponding to 21 528S experience the largest southward group propaga- k0 5 2p/400 km and l0 5 0 are calculated and included tion (i.e., 500–1200 km) and are able to propagate into in Fig. 12. These rays bifurcate approximately at 478S, the core of the stratospheric jet. It is noteworthy that, just to the north of Patagonia. To the north of 478S, the above the zonal jet, the group velocity decreases, asso- waves propagate northward in the troposphere owing to ciated with the transition to backward shear of the zonal lateral refraction by the positive meridional shear in the wind, which should eventually lead to wave breaking. zonal wind and are absorbed by critical levels aloft. To The southward bending of the ray paths that originate the south, the rays propagate southward associated with from the high Patagonian peaks is consistent with the refraction from the negative meridional shear of the bifurcation of the vertical ﬂux of the zonal momentum, zonal wind that leads to an increase of l (i.e., positive l in Fig. 9b, and suggests that the Patagonian peaks are and accordingly negative meridional group velocity) likely the source of the impressive stratospheric/meso- aloft. In general, this group of rays shows less southward spheric waves over Drake Passage, revealed by the bending than the corresponding rays with k0 5 l0. For AIRS brightness temperature images in Fig. 1. These example, at 45 km MSL the wave packets with k0 5 2p/ 21 results are consistent with similar spatial ray-tracing 400 km and l0 5 0 launched from Patagonia are ap- simulations of mountain wave propagation over the proximately located at 150 km to the south of the wave southern Andes by Preusse et al. (2002). Between 528 source. and 628S the waves propagate nearly vertically with More ray paths over a range of wavenumbers from much less lateral displacement. There is no high terrain Patagonia are shown in Fig. 13. Along each ray path, the within this latitudinal range and, accordingly, mountain meridional wavenumber increases, primarily because

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FIG. 13. (a) Ray paths in the y–z plane and (b) horizontal wavenumbers (k, l) along each ray path for four pairs of 21 wave packets with k0 5 2p/100, 2p/200, 2p/400, and 2p/600 km and l0 5 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. of the negative lateral shear of the westerlies (i.e., refraction associated with the strong meridional shear of ›U/›y , 0) and the zonal wavenumber becomes slightly zonal winds aloft. The stratospheric momentum flux smaller, presumably from (6), because of accumulating maximum right above the Patagonian peaks is associated effects of wind gradients in the zonal direction. In gen- with relatively short waves (i.e., lx ; 300 km or shorter). eral, shorter waves (i.e., lx , 300 km) propagate faster The wavelength dependence of the southward ray group in the vertical with little southward bending. This is es- propagation is consistent with the observed and simulated pecially true for the packets with l0 5 0, whose ray paths increase of wave lengths aloft with distance away from the are nearly vertical. Longer waves (i.e., lx 5 400 and wave source (i.e., Patagonia). 600 km) propagate upward more slowly. The slow up- Finally, we briefly discuss the sensitivity of the ray 21 ward propagation allows for a greater accumulation of path corresponding to k0 5 l0 5 2p/400 km generated lateral wavenumber refraction via (7), which in turn al- by flow over Patagonia to the Coriolis parameter, lows wave groups to propagate farther south in the buoyancy frequency, vertical wind shear, and meridio- stratosphere and mesosphere, via (3). It is noteworthy nal winds. Although the spatial variation of the buoy- that, even for l0 5 0, the rays of longer waves (i.e., lx ; ancy frequency and Coriolis parameter appears in (3)– 600 km or longer) exhibit substantially more southward (8), their impact on wave refraction is rather in- refraction associated with the increase of the meridional significant over the parameters examined here (Fig. 14). wavenumber along each ray and slower vertical group This is consistent with Dunkerton (1984), who calcu- velocity. In summary, the ray path calculation suggests lated ray paths of IGWs with an analytical zonal jet that the northwest–southeast-oriented waves over Drake profile similar to the mean profile shown in Fig. 11b. Passage are likely one branch of the diverging three- According to (3), the squared ratio of the Coriolis pa- dimensional ‘‘ship’’ waves from Patagonia (Smith 1980), rameter and the wave intrinsic frequency, f 2/v2, pro- while the other branch is largely absorbed by critical vides a useful measure of the importance of the Coriolis levels to the north of Patagonia. The southward transfer parameter in wave refraction. We can define a wave 2 5 v2 2 of wave momentum flux is enhanced by lateral wave Rossby number squared, Rw /f , which reduces to

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21 FIG. 14. (a) Ray paths in the y–z plane and (b) wavenumbers are shown for k0 5 l0 5 2p/400 km . The other ﬁve pairs of curves correspond to paths and wavenumbers calculated from the identical parameters except for f 5 0, Uy 5 21 0, Ux 5 Uy 5 Vx 5 Vy 5 0, V 5 0, or N 5 0.015 s , respectively.

2 5 2 2 Rw (Uk) /f after ignoring the meridional wind. As an lateral shear of the zonal wind (i.e., Uy) aloft plays a key 2 2 2 example, for f 521.2 3 10 4 s 1, U 5 30 m s 1, and role in increasing the meridional wavenumber along a 5 p 21 2 ; k 2 /400 km , we have Rw 16 1, implying that given ray path and therefore enhancing the southward the Coriolis parameter effect is negligible. It is noteworthy wave refraction, consistent with previous studies (e.g., that the Coriolis parameter becomes important when Dunkerton 1984; Marks and Eckermann 1995). The (Uk 1 lV)2 and f 2 are comparable. This could happen difference in the meridional ray locations at 60 km MSL for longer waves or Uk and lV are comparable but of for the wave packets with the modeled V and with V 5 opposite signs. One such example is a wave excited by 0 is small because V is positive in the troposphere (i.e., northwesterly winds over Patagonia (i.e., k, l . 0, U . 0, southwesterlies) and negative in the stratosphere; the and V , 0). Another example is northward propagating contributions from the two effects partially cancel each waves originating from the Antarctic Peninsula associ- other. ated with a southwesterly jet (i.e., k . 0, l , 0, U . 0, and V . 0). The buoyancy frequency N is between 0.008 and 2 2 6. Discussion and conclusions 0.016 s 1 with an average value of around 0.01 s 1 in the 2 lowest 10 km, between 0.016 and 0.028 s 1 in the A gravity wave event characterized by long linear 2 stratosphere, and 0.016 and 0.02 s 1 in the mesosphere. wave patterns oriented northwest–southeast across 2 When replacing the local N with a constant 0.015 s 1, Drake Passage in the stratosphere and lower meso- the ray path exhibits noticeably less refraction due to the sphere has been examined using a COAMPS simulation, faster upward propagation in the troposphere. It is in- and the simulated wave patterns bear close resemblance structive to compare the terms corresponding to the to those revealed by AIRS brightness temperatures. meridional shear in zonal wind and the meridional N2 According to the numerical simulation, the linear variation in (6): the former is substantially larger than stratospheric wave patterns over Drake Passage likely the latter. Accordingly, the horizontal variation of N2 is originate from interaction between Patagonian orog- found to have little impact on wave refraction. The raphy and a southwesterly tropospheric jet. Waves

Unauthenticated | Downloaded 10/07/21 05:33 PM UTC 1686 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70 generated by flow over the three-dimensional Patago- Alps (Smith et al. 2007) and the Sierra Nevada ridge in nian peaks can be separated into three families: namely, the United States (Smith et al. 2008; Doyle et al. 2009), the northeast propagating (i.e., k . 0; l , 0), localized (k the vertical velocity amplitude for the tropospheric . 0andl ; 0), and southeast propagating (i.e., k . 0; l . waves over the Andes is much weaker. This must be due 0). For the northeast-propagating waves, their ray paths in part to the longer horizontal wavelengths (hundreds tend to tilt northward, and these waves are eventually of kilometers), which, through gravity wave polarization absorbed at the critical level between 15 and 20 km, and dispersion relations, lead to lower intrinsic fre- along with those waves launched from the central An- quencies and reduced vertical velocity amplitudes rela- des. The localized family, including relatively short tive to short horizontal wavelength gravity waves. The waves (lx , 300 km; l0 ; 0), propagates nearly vertically Patagonian high peaks are located under the northern and contributes to a wave momentum flux maximum edge of the deep intense westerly jet associated with the directly over Patagonia. For this wave family, the in- relatively steady polar vortex. Accordingly, waves from crease of the wave amplitude with altitude eventually Patagonia are able to propagate into the stratosphere leads to wave breaking between 50–60 km MSL where and mesosphere without significant amplitude reduction L5 h ; the wave saturation criterion (i.e., N m/U 1) is from critical level absorption or wave. In contrast, waves met. The southeast-propagating family includes lon- over low- to midlatitude barriers typically encounter ger waves (i.e., lx . 400 km) with a small or positive some form of critical level in the upper troposphere to meridional wavenumber, l0, and transports wave mo- lower stratosphere (e.g., a critical level at ;21 km was mentum flux poleward while propagating into the found over the Sierra Nevada range during T-REX; stratosphere and mesosphere. The poleward propaga- waves over the Central Andes are absorbed by a critical tion, assisted by refraction associated with the negative level between 15 and 20 km MSL in this study). These meridional shear of the westerlies, allows these waves to results highlight the importance of high-latitude topog- enter into the polar vortex jet in the stratosphere with- raphy such as the southern Andes, Antarctic Peninsula, out suffering any wave breaking. They eventually break and Greenland in stratospheric/mesospheric drag pa- in the lower mesosphere above the vortex jet core where rameterization. It is also worth noting that the Scandi- the westerlies decrease aloft (i.e., ;55 km MSL) with navian gravity wave imaged and modeled by Eckermann momentum deposited into the stratosphere or meso- et al. (2007) has a structure, vertical evolution, and dy- sphere near 608S. namics rather similar to the Patagonian waves observed The southward bending of the wave ray paths initiated and modeled here, although in that study wind turning from Patagonia is found to be sensitive to both wave with height rather than lateral refraction played a larger characteristics and synoptic-scale winds. In general, role. longer waves exhibit more southward refraction, largely In a recent study, McLandress et al. (2012) suggested due to their slower vertical propagation. This is consis- that the missing orographic wave drag near 608S could tent with the modeled and AIRS-observed wave pat- be the cause of stratospheric wind biases in global terns over Drake Passage, which show clear increases models. This study suggests that orographic wave drag in the horizontal wavelengths with the distance from near 608S may have a nonlocal source, the Patagonian the southern Andes. In addition, the southward wave peaks, and the wave momentum flux is transferred propagation is also dependent on the meridional wind southward by southeast-propagating inertia–gravity component; a northerly component (i.e., V , 0) en- waves. The lateral shear of the horizontal wind along the hances the poleward propagation. For this event, how- edge of the polar vortex plays a constructive role in the ever, the contributions from the southerlies in the southward momentum transfer largely through in- troposphere and northerlies in the stratosphere largely creasing the meridional wavenumber. As the dominant cancel each other out. Furthermore, the wave refraction refraction term in (7), 2k›U/›y, needs time to act, the is relatively insensitive to the Coriolis parameter and longer waves with slower vertical group velocity stay in stability gradient. Clearly, the term corresponding to the shearing region long enough to be refracted. In the horizontal variation of the stratification in (4)–(6) general, the above results are consistent with the ray is much smaller than the horizontal shear terms. For path calculations of Preusse et al. (2002), and later by most waves examined in this study, the wave Rossby Sato et al. (2009) using global model data. It is also worth 2 5 2 number squared, Rw (Uk/f ) , is large and, accord- noting that the mere presence of lateral gravity wave ingly, the Coriolis parameter has little impact on the refraction, clearly noted to be relevant to the waves ray solutions. observed and modeled here, has potentially important It is noteworthy that, compared to the waves observed fundamental ramifications for wave–mean flow inter- over major midlatitude barriers such as the European action generally, though previous studies have suggested

Unauthenticated | Downloaded 10/07/21 05:33 PM UTC JUNE 2013 J I A N G E T A L . 1687 it is secondary (Hasha et al. 2008). Clearly, further Baumgaertner, A. J. G., and A. J. McDonald, 2007: A gravity wave studies are needed to quantify and evaluate the clima- climatology for Antarctica compiled from Challenging Minis- tological aspects of the orographic drag maximum over atellite Payload/Global Positioning System (CHAMP/GPS) radio occultations. J. Geophys. Res., 112, D05103, doi:10.1029/ Drake Passage, such as the occurrence frequency, tem- 2006JD007504. poral evolution, and mean amplitudes, so that these Carslaw, K. S., and Coauthors, 1998: Increased stratospheric ozone waves and associated momentum fluxes can be properly depletion due to mountain-induced atmospheric waves. Na- represented in global and climate models (e.g., Shutts ture, 391, 675–678. and Vosper 2011). Chen, C., D. R. Durran, and G. J. Hakim, 2005: Mountain-wave momentum flux in an evolving synoptic-scale flow. J. Atmos. Finally, while the wave characteristics and the ray- Sci., 62, 3213–3231. tracing calculations are consistent with waves emanated de la Torre, A., and P. Alexander, 2005: Gravity waves above from Patagonia, we cannot rule out other wave sources, Andes detected from GPS radio occultation temperature such as the jet stream or frontal excitation, which may profiles: Mountain forcing? Geophys. Res. Lett., 32, L17815, have contributed to the momentum fluxes. Evidence for doi:10.1029/2005GL022959. ——, ——, P. Llamedo, C. Menendez, T. Schmidt, and J. Wickert, such sources in COAMPS was found over the Antarctic 2006: Gravity waves above the Andes detected from GPS ra- Peninsula, for example. This study provides some useful dio occultation temperature: Jet mechanism? Geophys. Res. guidance for planning future field observations of Lett., 33, L24810, doi:10.1029/2006GL027343. gravity waves over the southern Andes and Drake Pas- Doyle, J. D., and Coauthors, 2000: An intercomparison of model- sage. For example, according to our results, it is difficult predicted wave breaking for the 11 January 1972 Boulder windstorm. Mon. Wea. Rev., 901–914. for research aircraft to sample orographic waves over 128, ——, and Coauthors, 2009: Observations and numerical simula- Drake Passage using airborne in situ instruments. On tions of subrotor vortices during T-REX. J. Atmos. Sci., 66, the other hand, upward-looking remote sensing in- 1229–1249. struments on research aircraft flying along Drake Passage Dunkerton, J. T., 1984: Inertia–gravity waves in the stratosphere. may provide much needed insight into the characteristics J. Atmos. Sci., 41, 3396–3404. and dynamics of these stratosphere–mesosphere waves. Eckermann, S. D., 1996: Hodographic analysis of gravity waves: Relationships among Stokes parameters, rotary spectra and cross-spectral methods. J. Geophys. Res., 101 (D14), 19 169– Acknowledgments. This research is supported by the 19 174. Chief of Naval Research through the NRL Base 6.1 ——, and P. Preusse, 1999: Global measurements of stratospheric Program by PE 0601153N. SDE acknowledges addi- mountain waves from space. Science, 286, 1534–1537. tional support from NASA (NRA NNNH09ZDA001N- ——, and D. L. Wu, 2012: Satellite detection of orographic gravity- wave activity in the winter subtropical stratosphere over TERRAQUA, The Science of Terra and Aqua, Grant Australia and Africa. Geophys. Res. Lett., 39, L21807, NNH11AQ99I). The simulations were made using the doi:10.1029/2012GL053791. Coupled Ocean–Atmospheric Mesoscale Prediction ——,J.Ma,D.L.Wu,andD.Broutman,2007:Athree-dimensional System (COAMPS) developed by U.S. Naval Research mountain wave imaged in satellite radiance throughout the Laboratory. Computational resources were supported stratosphere: Evidence of the effects of directional wind shear. Quart. J. Roy. Meteor. 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