ClimateandWeatherof theSun-EarthSystem(CAWSES):SelectedPapers fromthe2007KyotoSymposium,Edited by T. Tsuda, R. Fujii, K. Shibata, and M. A. Geller, pp. 279–293.c© TERRAPUB, Tokyo, 2009.

Gravity wave coupling from below: A review

Robert A. Vincent

School of Chemistry and Physics, University of Adelaide, Adelaide, SA 5005, AustraliaE-mail: robert.vincent@adelaide.edu.au

Gravity waves efficiently couple energy and momentum from source regions in thelower atmosphere to the middle and upper atmosphere. Wave dissipation results ina drag that drives meridional circulations that can profoundly affect the state of themiddle atmosphere. New developments in various observing techniques, as well as abetter appreciation of the limits imposed by observational selection, allow for a betterunderstanding of the role of gravity waves in the atmosphere. Here we summarise re-cent advances in the measurement of wave parameters, especially those obtained bysatellite and in situ techniques. Of particular importance is the development of tech-niques to measure momentum fluxes on a hemispheric or even global scale. Improvedunderstanding of gravity wave coupling processes into the thermosphere-ionospherehas resulted from better formulations of dissipation effects. Allied with new rapidincoherent scatter measurements it may soon be possible to identify sources of smalland medium scale ionospheric travelling disturbances that are not linked to auroralphenomena.

1 IntroductionGravity waves, or more accurately buoyancy waves, are ubiquitous in the atmo-

sphere. Wave periods range from minutes to hours and spatial scales extend up tothousands of km. They are important because they efficiently couple energy and mo-mentum from their source regions in the lower atmosphere to the middle and upperatmosphere. Their presence in the lower atmosphere has been noted for over onehundred years, but is only relatively recently that their importance in the middle andupper atmosphere has been appreciated.

Wavelike perturbations in the ionospheric F-region are often referred to as trav-elling ionospheric disturbances (TIDs). Both early and more recent studies of TIDsrecognized that they are often not generated by geomagnetic disturbances but havepossible links to meteorological sources in the lower atmosphere (e.g. Munro, 1958;Waldock and Jones, 1987). It was the realization that TIDs were the manifestation ofgravity waves that led in part to the seminal paper by Hines (1960) whose pioneeringwork also helped establish the importance of wave transfer of energy and momentumfrom the lower to the middle and upper atmosphere (Hines, 1974).

The last decade has seen new techniques brought to bear in the study of grav-ity waves and their effects in the middle atmosphere and thermosphere-ionosphere.

279

280 R. A. Vincent

Fig. 1. Polar stratospheric clouds observed using a downward viewing lidar on the Calipso satellite asit passed over the Patagonian Andes and the Antarctic. The dashed lines show the phase fronts of aquasi-monochromatic gravity wave with an approximate vertical wavelength of about 10 km.

Satellite observations provide a global perspective and wave effects can be observedin somewhat unexpected ways. For example, Fig. 1 shows lidar signals transmittedfrom the Calipso satellite that are backscattered from polar stratospheric clouds dur-ing a pass over the Antarctic Peninsula. Gravity waves modulate the cloud density, asindicated by the dashed lines, with the tilt of the constant phase surfaces characteris-tic of upward propagating waves. These wave effects in the middle stratosphere areprobably manifestations of mountain waves produced by the strong winter eastwardflow over the Antarctic Peninsula.

Transfer of momentum by gravity waves is particularly important. The quantityρo u′w′, where ρo is atmospheric density and u′ and w′ are the horizontal and verticalperturbation amplitudes, is conserved in the absence of wave dissipation. Momen-tum deposition associated with wave breaking or dissipation exerts a body force onthe atmosphere (Andrews et al., 1987). The zonal-average zonal wind momentum

Gravity Wave Coupling 281

Fig. 2. Cartoon of the gravity wave driven summer-to-winter pole circulation at the mesopause.

equation is∂u

∂t− f v = − 1

ρo

∂(ρo u′w′)

∂z(1)

At mid- to high-latitudes at the solstices the acceleration of the mean zonal wind uis small and there is a balance between the Coriolis term and flux divergence. At thesolstices the wave drag drives a pole-to-pole circulation in the mesosphere that pro-foundly changes the thermal structure of this region. The upwelling over the summerpole (Fig. 2) and the associated adiabatic cooling produces temperatures that can beas low as 100 K at heights near 85 km. The cold temperatures lead to freezing ofeven the small quantities of water vapour present in the mesosphere and this is mani-fest in such phenomena as noctilucent clouds and polar mesospheric summer echoesobserved with ground-based radars (e.g. Rapp and Lubken, 2004). The associatedsinking of air over the winter pole leads to a warming whose effects can be felt as lowas 20 km (Garcia and Boville, 1994).

In the tropics, where f ∼ 0, the second term in Eq. (1) is negligible and sogravity waves can drive an acceleration of the zonal-mean zonal wind. Hence gravitywaves probably play important roles in driving the quasi-biennial oscillation (QBO)in the stratosphere and semiannual oscillations near the stratopause and mesopause(Dunkerton, 1997; Baldwin et al., 2001).

Full understanding of the role of gravity waves in the middle and upper atmo-sphere requires improved measurements on a global scale of wave parameters, espe-cially momentum fluxes. Ideally these measurements should be made as a function ofwave phase speed, so that their effects can be fully incorporated in numerical climate

282 R. A. Vincent

models and vertical coupling effects properly understood. Hamilton (1999) providesa background to early gravity wave observations and theoretical developments whileFritts and Alexander (2003) provide a recent and comprehensive review of gravitywave theory and effects. Here we review recent observations of gravity waves madeusing a variety of techniques as well as coupling effects.

2 Observations2.1 Observational selection

A wide variety of techniques, ranging from ground-based to in-situ balloon-bornemeasurements and space-based measurements, are used to study gravity waves andtheir characteristics. However, no technique is perfect; it is not possible for onemethod to measure wave parameters across the whole wave spectrum (Alexander,1998). For example, Alexander and Barnet (2007) discuss the response of varioussatellite viewing systems, as illustrated in Fig. 3. Satellite instruments that view alongthe limb, such as HIRDLS, have excellent vertical resolution, but relatively poor hori-zontal resolution. In contrast, a nadir-viewing instrument such as AIRS has excellenthorizontal resolution compared with the vertical. Alexander et al. (2008b) made adetailed investigation of the application of the GPS radio occultation technique togravity wave studies. Their analysis shows that best retrievals occur for waves withquasi-horizontal phase surfaces, i.e. for waves with quasi-inertial frequencies. Theyconclude that caution must be used in using occultation data to retrieve GW parame-

Fig. 3. Illustration of space-based observations of gravity waves. The background colours show tem-perature perturbations of modelled gravity waves, while the ovals illustrate the weighting functioncross-sections for various satellite viewing modes. Those on the left are for downward viewing satel-lites, while the ovals on the right are for limb viewing geometries. (From figure 3, Alexander and Barnet(2007). See their paper for more details.)

Gravity Wave Coupling 283

ters.Gravity wave dispersion is another selection factor that needs to be taken into

account. Just because a gravity wave packet is in the viewing region of a particularinstrument it does not necessarily mean that accurate measurements of wave ampli-tude and fluxes can be made. Short-period gravity waves tend to propagate verticallymuch faster than longer period waves. Consequently, a high frequency wave packetwill propagate up through a region of observation more quickly than a longer periodpacket (Alexander and Barnet, 2007) so that observations of long-period waves arefavoured.2.2 Satellite observations

The advent of microsatellites in low earth orbit, such as GPS/MET, CHAMP andthe COSMIC constellation, has allowed gravity wave activity to be studied globallyusing the GPS occultation technique (e.g. Tsuda et al., 2000; de la Torre et al., 2004,2006; Ratnam et al., 2004; Baumgaertner and McDonald, 2007; Hei et al., 2008). Asa low earth orbit satellite sets, the signals from an occulting GPS satellite are refractedby the intervening atmosphere and ionosphere. The resulting ray bending gives infor-mation on the vertical distributions of electron density, temperature and, low in theatmosphere, humidity. Gravity wave potential energy per unit mass information isderived from the temperature profiles

Ep = 1

2

g2

N 2

T ′2

T 2o

, (2)

where N is the Brunt frequency, g is the acceleration due to gravity and T ′ and To

are the temperature perturbation and mean temperature, respectively. As shown inFig. 4, all the necessary information to compute Ep can be derived from the GPS

Fig. 4. GPS estimates of gravity wave perturbation amplitudes. (From Baumgaertner and McDonald,A gravity wave climatology for Antarctica compiled from Challenging Minisatellite Payload/GlobalPositioning System (CHAMP/GPS) radio occultations, J. Geophys. Res., 112, D05103, 2007. Copyright2007 American Geophysical Union. Reproduced by permission of American Geophysical Union.)

284 R. A. Vincent

Fig. 5. HIRDLS observations at 25 km for May 2006. (Left) Temperature perturbations. (Right) Abso-

lute momentum flux, ρo

∣∣∣u′w′∣∣∣. (From Alexander et al., Global estimates of gravity wave momentum

flux from High Resolution Dynamics Limb Sounder (HIRDLS) observations, J. Geophys. Res., 113,D15S18, 2008. Copyright 2008 American Geophysical Union. Reproduced by permission of AmericanGeophysical Union.)

measurements, although as noted by Alexander et al. (2008b), caution is required inderiving GW parameters from occultation data.

Using several years of CHAMP data, Baumgaertner and McDonald (2007) wereable to study the seasonal cycle in GW Ep in the Antarctic lower stratosphere atheights between ∼10 and 35 km. There is an annual cycle in Ep with largest am-plitudes in winter, a result similar to that reported by Zink and Vincent (2001) forthe SH mid-latitude site of Macquarie Island. Baumgaertner and McDonald (2007)also reported an interesting longitudinal variation of wave activity, as well as a strongenhancement of wave energy at the edge of the polar vortex. Their results show astrong relationship between gravity wave activity and geographic location, indicat-ing that topography is a strong source for wave activity, especially over the AntarcticPeninsula and the Southern Andes. Mountain waves from this region have even beenlinked to disturbances in the lower ionosphere (Hocke et al., 2002). On the otherhand, an analysis by Hei et al. (2008) of 5 years of GPS data from the CHAMP satel-lite for both polar regions indicates the limited geographical extent of topographicallyforced waves and the importance of waves that they ascribe to gravity generation byplanetary wave transience and/or breaking.

In the equatorial stratosphere, Tsuda et al. (2000), Alexander et al. (2002) andde la Torre et al. (2006) all report a maximum in GW Ep extending between about1◦S and 10◦N. However, the Ep variations show significant geographic as well asinterannual variability. de la Torre et al. (2006) found interannual enhancements inwave activity related to the QBO, similar to the findings of Vincent and Alexander(2000) made using radiosonde observations at Christmas Island (12◦S) in the IndianOcean. Geographic variability was discussed by Tsuda et al. (2000), who reportedincreases in Ep in regions with strong convection, such as the Maritime Continent inthe Western Pacific.

Local enhancements in Ep, however, do not necessarily mean correspondinglylarge momentum fluxes. As discussed by Ern et al. (2004) and Alexander et al.

Gravity Wave Coupling 285

(2008a), the relation between absolute momentum flux and temperature variance is

∣∣u′w′∣∣ = 1

2

λz

λh

g2

N 2

T ′2

T 2o

, (3)

where λz and λh are the GW vertical and horizontal wavelengths, respectively. Com-parison of vertical temperature profiles derived from adjacent scans through the at-mosphere by the HIRDLS instrument, Alexander et al. (2008a) were able to estimateboth λz and λh and so derive absolute fluxes. This is illustrated in Fig. 5, which showsaverage values of T ′ and ρo

∣∣u′w′∣∣ for May 2006 (SH early winter). Note not onlythe relatively high values of T ′ over Southeast Asia, but also the correspondinglysmall flux values. In contrast, there are large temperature perturbations and largefluxes over the southern Andes. These geographic variations in flux can be ascribedto source-related differences in the ratio of λz and λh , which is an important factor indetermining GW momentum via Eq. (3). Furthermore, using HIRDLS data Alexan-der et al. (2008a) were also able to follow waves generated over the southern Andesup to heights in the lower mesosphere.2.3 In-situ observations2.3.1 Radiosonde observations

A relatively inexpensive way to derive information on gravity wave activity inthe lower stratosphere is to use conventional radiosonde soundings made by nationalweather agencies (Allen and Vincent, 1995). High vertical resolution (∼20–50 m)soundings are now routinely made and archived by many weather agencies. Anal-ysis of these data enables GW to be resolved, although selection of short verticalwavelength (λz < 7 km) waves is favoured (Alexander, 1998).

Wang and Geller (2003) and Wang et al. (2005) exploited routine high-resolutionsoundings of winds and temperatures made at more than 90 stations to study GWactivity in the troposphere and lower stratosphere over the continental USA, Alaskaand islands in the Pacific and the Caribbean. Analysis of a 4-year dataset that cov-ers a wide variety of terrain ranging from oceanic to mountainous enabled them todistinguish source from propagation effects. Wang and Geller (2003) reported anoverall decrease of stratospheric wave activity with increasing latitude, similar toprevious studies (e.g. Allen and Vincent, 1995) in the Australian region. Seasonally,stratospheric wave amplitudes are larger in winter than in summer. Interestingly, tro-pospheric amplitudes are not always well correlated with stratospheric amplitudes.For example, in the troposphere there are clear GW energy maxima over the RockyMountains, whereas in the stratosphere maxima occur over the southeastern UnitedStates.

Combining wind and temperature profiles gives propagation directions in boththe vertical and horizontal (Vincent et al., 1997). Using the US radiosonde datasetWang et al. (2005) showed that at least 75% of wave energy is up going in the lowerstratosphere. They also report that the ratio of mean intrinsic frequency to inertialfrequency is ∼2.4–3, with a weak latitudinal dependence. These results are consistentwith previous studies. The dominance of low intrinsic frequency waves is probably

286 R. A. Vincent

c d

a b

-12.5

-7.5

-2.5

2.5

7.5

12.5mPa

Fig. 6. Average values of momentum fluxes from SPB observations for the Arctic (top) and Antarctic(bottom). Panels a and c refer to zonal fluxes, while panels b and d show meridional values. Note thelarge fluxes over Greenland and the Antarctic Peninsula.

an observational effect, since the ∼5 m s−1 ascent rate of radiosondes is inadequatefor sampling long vertical wavelength, high phase speed waves—i.e. this is anothermanifestation of the “observational selection” issue discussed by Alexander (1998)and Alexander and Barnet (2007).2.3.2 Superpressure balloon observations

Superpressure balloons (SPB) provide a powerful means for studying GW in thelower stratosphere (Hertzog and Vial, 2001). The envelope of an SPB is inextensibleso when it is injected with a fixed amount of gas the pressure inside is greater thanambient pressure at the float level. Hence the balloon floats on a constant density(isopycnic) surface. The advantage of the SPB technique over ground or space-basedtechniques is that the balloons are advected by the background wind and hence mea-sure the frequency of waves relative to the background flow, the so-called intrinsicfrequency, ω. It is ω that determines wave properties (e.g. Fritts and Alexander,2003).

SPB developed by CNES, the French Space Agency, have 8 and 10-m diametersand float at pressure levels between 75 and 55 hPa, corresponding to altitudes ofabout 17 and 18 km, respectively. The balloons carry a small gondola to measurepressure p and temperature T as well as position using GPS techniques. Early results

Gravity Wave Coupling 287

296 298 300 302 304Longitude (deg)

15

16

17

18

19

Ver

tical

Dis

plac

emen

t (km

)

170

180

190

200

210

Tem

pera

ture

(K

)

1500 m ASL

Fig. 7. Vertical displacement (blue, left scale) and temperature (red, right scale) recorded on an 8-m di-ameter SPB during its passage over the Antarctic Peninsula. The shaded region shows the cross-sectionthrough the Peninsula.

were limited by the accuracy of the GPS measurements and by the relatively slow15-min sampling interval dictated by the rate at which data could be transmitted backto ground stations via the Argos satellite system. More information about the SPBtechnique and how the data are converted to GW momentum fluxes is given in Vincentet al. (2007), while Boccara et al. (2008) provide a detailed error analysis of theretrieved fluxes and phase speeds.

A major SPB campaign was made from McMurdo (78◦S) in the SH spring of2005 during which 27 balloons were launched to study the evolution of the vortex. Inpreparation for this campaign a number of test flights were made from Kiruna (68◦N).Results from Vorcore and the Kiruna test flights enable GW momentum fluxes in thenorthern and southern polar lower stratospheres to be compared. Figure 6 showsdensity-weighted (ρo u′w′, ρo v′w′) momentum fluxes for flights in the Arctic andAntarctic (Vincent et al., 2007). Note the large flux values in the vicinity of mountainranges, such as eastern Greenland, the southern Andes and the Antarctic Peninsula.Overall, however, when the fluxes are zonally averaged over regions of high topog-raphy and oceanic regions it is found that the fluxes are comparable in magnitude(Hertzog et al., 2008).

Wave amplitudes observed over mountainous regions appear to be significantlymore intermittent than values measured over the oceans, with very large fluxes some-times observed over mountains (Hertzog et al., 2008). Figure 7 illustrates an extreme

288 R. A. Vincent

case where an 8-m diameter balloon suffered an approximate 1.5 km vertical dis-placement during a severe mountain wave event over the Antarctic Peninsula. Thecorresponding peak-to-peak temperature change was about 15 K. From the estimated1 hr intrinsic period and approximate horizontal and vertical perturbation velocities of10 m s−1 and 0.7 m s−1, respectively, it is possible to estimate an average momentumflux of 0.7 Pa. This is a factor of about 70 times larger than the average flux in thisregion. Plougonven et al. (2008) provide a more detailed analysis of this event. Suchlarge amplitude waves will break low in the stratosphere, whereas weaker amplitudewaves can penetrate well into the middle atmosphere before breaking and depositingtheir momentum (e.g. Alexander et al., 2008a).

3 Gravity Wave Coupling into the ThermosphereLarge-scale gravity waves associated with magnetic storms are a well-known fea-

ture of the ionosphere. After a major storm wave disturbances can produce iono-spheric effects on a global scale (e.g. Karpachev et al., 2007). Smaller scale wavespropagating from sources such as tropical convection in the lower atmosphere havebeen suggested as the cause of equatorial spread-F (e.g. McClure et al., 1998;Prakash, 1999), although Kudeki et al. (2007) recently questioned the need for gravitywave seeding of spread-F .

Identifying the sources of waves observed in the thermosphere-ionosphere is achallenging problem. To ray-trace backwards a wave observed in the ionosphere toa lower atmospheric source requires good knowledge of the intermediate wind andtemperature fields. These cause the waves to be refracted and advected horizontally.The problem is particularly acute in the region near 100 km where there are oftenlarge amplitude tidal wind and temperature fluctuations and very large wind shears(Larsen, 2002). Molecular viscosity and thermal diffusive damping effects also be-come important in the region above 100 km. This complicates the application of GWray-tracing techniques.

Recently, Vadas and Fritts (2005) provided an improved form of the GW dis-persion relation that incorporates kinematic effects. Applying this new formulationVadas and Fritts (2004) employed a linear model to study the thermospheric responseto a GW spectrum generated by vertical motions induced in a tropospheric mesoscaleconvective complex. Molecular viscosity and thermal diffusivity act as selective fil-ters on a GW spectrum, allowing only the high-frequency, largest vertical wavelength,waves to propagate to the highest altitudes (Vadas and Fritts, 2005). Strong bodyforces can be induced by the resulting momentum flux deposition at heights well intothe thermosphere. There is also a significant solar cycle effect. GWs penetrate tomuch higher altitudes during active solar conditions when thermospheric tempera-tures are high compared with solar minimum conditions (Vadas and Fritts, 2006).This is in part because kinematic viscosity decreases more slowly with altitude whentemperature increases, and in part due to the increase in λz associated with the highertemperatures.

Vadas (2007) recently explored the properties of GW propagating into the thermo-sphere-ionosphere in more detail, including the effects of both vertical and horizontal

Gravity Wave Coupling 289

Fig. 8. Estimated GW spectra as a function of altitude for GWs generated by a deep convective plumeand propagating into a thermosphere with an exospheric temperature of 1000 K. A sudden shear of−100 m s−1 is assumed at z = 120 km. (a) Vertical wavelength spectrum. (b) Horizontal wavelengthspectrum. (c) Ground-based wave period spectrum. (d) Ground-based horizontal phase speed spec-trum. Shading shows regions of strongest amplitude. (From figure 16, Vadas, Horizontal and verticalpropagation and dissipation of gravity waves in the thermosphere from lower atmospheric and thermo-spheric sources, J. Geophys. Res., 112, A06305, 2007. Copyright 2007 American Geophysical Union.Reproduced by permission of American Geophysical Union.)

dispersion. Figure 8 shows the evolution of GW spectra as a function of altitudefor waves generated by a deep convective plume in the lower atmosphere and witha background wind that is westward in the thermosphere. Note how the spectra aredominated by waves with periods ∼15–20 min and that have horizontal scales ofabout 200–400 km. The largest amplitude waves are propagating eastward, againstthe mean flow. It should be noted that the effects of ion drag, wave breaking andeddy viscosity are neglected in this calculation (see Vadas (2007) for more details).Despite these limitations the results are in broad agreement with observations.

Sun et al. (2007) also explored the problem of GW propagation into the ther-mosphere using a three-dimensional transfer function technique. Similar to Vadas(2007) they found that GWs in a 15–30 min period band and horizontal wavelength∼200–400-km were most likely to propagate to the 300-km level.

While these studies have made significant improvements to our understanding of

290 R. A. Vincent

GW propagation into the thermosphere-ionosphere system inclusion of the effects ofthe ionosphere itself are required, since wave motions move charge in the presence ofthe Earth’s magnetic field. This leads in turn to selective damping, depending on thepropagation direction of the waves relative to the magnetic field and the associatedion-drag effects (e.g. Hines, 1968; Tsugawa et al., 2004).

4 Summary and ConclusionsThe past decade has seen a great improvement in our understanding of GW cou-

pling and their role in determining the state of the middle and upper atmosphere.Improvements result from the development and application of new observing tech-niques as well as better appreciation of observational limitations. New satellite andballoon measurements, in particular, provide better understanding of flux variabilityon both regional and global scales.

In summary:

1. The majority of the waves observed in the lower stratosphere couple energyand momentum upward into the middle and upper atmosphere.

2. Largest momentum fluxes are observed over regions of high topography, butthese regions have the greatest wave variability.

3. On a zonally averaged basis, momentum fluxes over mountains and oceans areapproximately equal.

4. Thermospheric GWs are selectively filtered by the kinematic dissipation. Onlythe high frequency, long vertical wavelength components to penetrate to thehighest altitudes.

5. There is a strong solar cycle effect in GW propagation into the thermosphere.GWs propagate to higher altitudes during high sunspot conditions than duringsolar minimum conditions.

Despite the significant progress made in the past decade there are still a number ofuncertainties. While it can be relatively straightforward to identify waves associatedwith topography, it is less easy to identify the GW sources over the ocean. The relativeimportance of different sources, such as shear and geostrophic adjustment, has still tobe established. This is especially true for mid- to high-latitude sources. Convection isthe main GW source in the tropics and there are now a number of models that attemptto specify wave fluxes above convection (e.g. Song et al., 2003; Beres et al., 2004;Lane and Moncrieff, 2008), although the model results have yet to be fully tested byobservation.

With the deployment of new instruments we can expect good progress in under-standing wave coupling into the thermosphere-ionosphere system. New radars, suchas the Advanced Modular Incoherent Scatter Radar (AMISR), makethree-dimensional simultaneous measurements of ionospheric parameters (Nicollsand Heinselman, 2007). This flexibility provides better insight into the relationship

Gravity Wave Coupling 291

between TIDs and gravity waves and outcomes give hope for better identification ofwave sources. In turn, improved appreciation of wave dissipation effects in the ther-mosphere can now be used to provide better understanding of atmospheric parametersin a region that is otherwise difficult to probe. For example, using GW observationsmade with AMISR, Vadas and Nicolls (2008) were able to infer the average back-ground horizontal winds in the 160–240 km height range over Poker Flat, Alaska.

The challenge now is to apply these new instrumental developments, as well asadvances in theory and modelling, to understand better upward coupling by gravitywaves. This will be a major focus of research during CAWSES-II.

Acknowledgments. Discussions with M. J. Alexander, M. Geller, A. Hertzog and A. Kleko-ciuk are gratefully acknowledged.

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