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Open Access Discussions Chemistry and Physics Atmospheric 1000 m) are a very com- < z measured by the radar can λ 2 N 2 are clearly observed by the radar and 2 N ). Here, we present a case study of typical N , and P. Dalin 31252 31251 E). The waves are seen most clearly in radar- 2 ◦ N, 21.10 ◦ , J. Arnault 2 , S. Kirkwood 1 200 m. The model and the hodograms indicate horizontal wave- + . Large-amplitude wave signatures in 2 derived from and by radar shows the validity of the radar determination N 2 This discussion paper is/has beenand under Physics review (ACP). for Please the refer journal to Atmospheric the Chemistry corresponding final paper in ACP if available. Laboratoire de l’Atmosphère et desSwedish Cyclones, Institute La of Réunion Space University, La Physics, Réunion, Box 812, France 981 28 Kiruna, Sweden of 700 lengths between 37 andamplitudes 100 indicated km by and thethe intrinsic model observations. periods are We between show however, 6be an finally and used that order 9 to the of h. profilesmomentum estimate The magnitude fluxes of wave wave less which amplitudes, are than consistent horizontal in with wavelengths, the estimates intrinsic from periods the radiosondes. and for the wave amplitude) shows thatare the closely model associated gives realistic totem. results the and Hodographs upper-level that of the front the waves inpropagate upward an fluctuations in upper-troposphere from the the jet–frontin lower radiosondes, sys- stratosphere the show confirming troposphere. that that The the the waves observations origin and of modelling the all waves is indicate vertical wavelengths waves from the 21 FebruaryN to the 22 Februaryof 2007. Very good agreementthe between radiosondes in the lowermostprofiles stratosphere, of from horizontal 9 wind km components to andshow potential 14–16 the km height. from same the Vertical waves. radiosondes casting Mesoscale (WRF) simulations model with are theagreement carried Weather between out Research the to and radar complement Fore- and the analysis radiosonde of measurements the and waves. the Good model (except Inertia-gravity waves with very shortmon vertical feature wavelength of ( the lowermost stratospherenorthern as Scandinavia observed by (67.88 the 52derived MHz radar profiles ESRAD of in buoyancy frequency ( Abstract Atmos. Chem. Phys. Discuss., 13, 31251–31288,www.atmos-chem-phys-discuss.net/13/31251/2013/ 2013 doi:10.5194/acpd-13-31251-2013 © Author(s) 2013. CC Attribution 3.0 License. Short vertical-wavelength inertia-gravity waves generated by a jet–frontArctic system latitudes at – VHF radar,and radiosondes numerical modelling A. Réchou 1 2 Received: 27 September 2013 – Accepted: 11Correspondence November 2013 to: – A. Published: Réchou 2 ([email protected]) December 2013 Published by Copernicus Publications on behalf of the European Geosciences Union. 5 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | N), ◦ , vertical wave- 1 − er the best possibility ff ects and convection (Smith, ff N and S) inertia-gravity waves in the stratosphere, and low in- N over the Pacific to study the ◦ ◦ 1 − –90 ◦ is the Coriolis parameter). In later modelling f 31254 31253 . They used a ray-tracing model to show that f N) over the North Atlantic, showed inertia-gravity ◦ (where 40 and 2 f ∼ f and 2 f S). They found waves with vertical wavelength between about 1 and 7 km ◦ ths and Reeder, 1996), diabatic heating (Hooke, 1986), (Rosenthal and ffi Measurements from satellites are today often considered to o A number of observational and modelling studies have suggested that the polar The properties of gravity waves are very dependent on the processes that cause for global, climatological studies of gravity waves. Certainly, characterization of gravity Island (54 and intrinsic periods between waves propagating into the lowersystem stratosphere to probably had the theirduration SW source balloon in of a flights the jet–front atwith island. very non-orographic Finally, high sources, in latitudes suggestedcomparable a (60 to importance be recent to orographic jet–front study waves systems, regardingflux using their were in contribution a the found to lower to number momentum stratosphere be (Vincent of of et long- al., 2007). correlated with the jetward stream. energy In propagation (clockwise the rotation stratosphere, ofby downward the the propagation, wind waves consistent vector) with were and the dominated dominant inbeing source the by at for troposphere inertia-gravity up- tropopause waves level.high-resolution At upper-air high soundings southern of wind latitudes, and Guest temperature and released al. from Macquarie (2000) examined teristics of the wave generationin by the the jet vicinity stream. ofassociated Lane an et inertia-gravity al. intense waves. (2004) They jet/frontto used also system dropsondes 2.3 km. found near Using short 40 8Vaughan vertical yr and of wavelengths, Worthington observations from (2007) from 1 period determined the quasi-monochromatic oscillations UK the in MST occurrence theity radar and wind waves. at properties They vector Aberystwyth found identified of that (52 withlengths long the inertia around waves grav- 2 km, had and typical that amplitudes waves 1–2 with ms 6–8 h (ground-based) periods were strongly troposphere, closely correlated in space withwind regions of speeds strongest curvature in and an highest generally upper-troposphere 2–3 km, jet. small The amplitude, wavestrinsic typically had periods, 2–4 between short ms verticalwork wavelengths, (Plougonven and Snyder, 2007), they were able to reproduce the main charac- wave packets propagating upward in the lower stratosphere and downward in the mid- diosoundings at mid-latitudes ( Fritts and Alexander, 2003,study, and Kirkwood et specifically al., at 2010b; Réchou theGri et al., location 2013), considered fronts (Ekerman in andLindzen, the Vincent, 1983; 1993; present Fritts, 1982;jet Lott et (Ucellini al., and 2009) Koch,generated and 1987). by instability In the of jet the the at present high upper-tropospheric study, latitudes. we focusjet on inertia-gravity stream waves (in thegravity waves. upper-troposphere For example, at Plougonven et mid- al. or (2003), using high a latitudes) very large can number generate of ra- inertia- wave-generation processes and the spectrumcrucial of for the waves accuracy that of they global produce models. is therefore them. Known sources1979; of Lilly waves et include al., 1982; topographic Bretherton e and Smolarkiewitcz, 1989; Shutts and Gray, 1994; et al., 2002). Gravitythe waves also atmosphere have (Holton a et stronglevels to influence al., the on 1995) middle the byIn and general this upper the circulation way, levels of transport they of change ofthe the the horizontal momentum atmosphere dynamics and (Fritts and from and vertical thermal theresolved Alexander, balance scales in 2003). lower of of atmospheric the General most atmosphere. Circulationsrameterized gravity Since Models in waves the (GCMs), are models. the The too waves uncertaintytial small must of uncertainties be to such in pa- parameterizations be the causes models explicitly substan- (Morgenstern et al., 2010). A detailed understanding of Gravity and inertia gravity wavessphere play a and very mesosphere. important For role example,displacements in in induced the the physics by high-latitude of mountain stratosphere, the10 waves K strato- large can and vertical reduce can locally lead to by the up formation to of polar stratospheric clouds in winter (Dörnbrack 1 Introduction 5 5 25 20 10 15 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ) N, N ◦ cient ffi 300 m) > z λ ) can be measured with high N 31256 31255 E). This radar has been operating in a mode capa- ◦ N, 21.10 ◦ 64 m and pointing vertically. Echo power and Doppler shift (vertical wind) ) and cannot be reliably determined using short-vertical-resolution mea- 1 × − E) near Kiruna in northern Sweden. The radar has a peak transmitter power of and the assumption that the wave amplitudes are at the wind-shear instability ◦ 2 N The radar usually (since 2005) operates in two modes with vertical sampling 150 m In this paper, we examine whether inertia-gravity waves from the upper-troposphere mates only of echo power and Doppler, not of horizontal wind. Buoyancy frequency ( The radar insuch general as provides , informationin waves, on turbulence the the troposphere and dynamic and layering,Chilson state lower et from of al. stratosphere. about (1999), Further the updated 1 km technical in atmosphere Kirkwood details to et can al. 20 kmand (2010a). be altitudes 600 found m, in respectively. Thecorresponds mode to with a 150 Gaussian-weightedwidth m about sampling average 200 over is m. a used For height here. heights Each interval above sample about with 5 half-power km, this mode provides accurate esti- 21.10 72 kW and an antenna array consistingarea of of 284, 72 5-element Yagi antennas spreadare over an measured using thehorizontal whole winds array. and The turbulence array is parameters divided to into be 6 determined sub-arrays using to interferometry. allow in limit (Gubenko et al., 2008, 2011). 2 Methods 2.1 VHF radar We use measurements from the 52 MHz radar ESRAD, located at Esrange (67.88 high resolution non-hydrostatic mesoscale modelcasting WRF Model, (Weather Skamarock Research and andwaves Klemp, obtained Fore- 2008) by the are model made areacteristics compared and of to the the the characteristics waves, observations. we To of determine useanalysis spectral the the analysis char- (radiosonde (observations winds) and and, model), for hodograph the radar data, the amplitude of the perturbations from 21 to 22 February 2007. To complement the observations, simulations with the characteristics of gravity waves obtained by the radar and by collocated radiosondes ally used for gravity-wave climatologieswind based on perturbations fluctuations associated in(a horizontal with few winds. jet-source The ms IGW’ssurements are at expected ESRAD. to However, buoyancy-frequencyprecision be ( (see very Appendix) and small showstical strong wavelengths wave (Kirkwood signatures, et particularly al., 2010a,most for b; short of Réchou the ver- et time, al., poleward 2013).Atlantic of, The storm but radar close is tracks located, to, so the thereistics jet-stream is of associated the jet-induced with potential the waves. for northern In climatological this study of first the step, character- we make a case study. We analyse the jet can be observed andin characterised North by Sweden the (67.88 VHFble radar of ESRAD, located resolving near perturbationsgravity Kiruna waves, associated continuously with since short-vertical-wavelength 2005. The ( radar is less powerful than those gener- Hei et al., 2008). However, theby lower limit such of satellite vertical measurements wavelengths is whichto can 2–4 km study be (Preusse resolved the et jet-related al.,vertical inertia-gravity 2008) wavelengths waves which less as is than observations not 2 showin su km. that case Another they studies possibility can might (e.g. have 2004; be O’Sullivan Plougonven to and and use Snyder, Dunkerton, modelling, 2007).elling 1995; as However, for it Wu climatological is and not studies Zhang,domain practicable due sizes. to 2004; to use Zhang, the such necessity mod- of both high resolution and large ground-based observations areobservations. relatively Both sparse, climatologies thanks andsatellite case-studies to instruments have high-resolution (e.g. been satellite Limb made Atmospheric Sounder, using Infrared Alexander data Sounder/High and from Administration Teitelbaum; Resolution Advanced 2011; Microwave Dynamics National Sounding, Wu, Oceanic 2004 and and Atmopsheric GPS radio occultation; waves has been much improved in recent years, particularly in polar regions where 5 5 20 25 15 10 25 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (1) and . The 2 2 N 6 h) and N , even as > 2 g N T is the atmospheric scale H in Eq. (1) has been found by with co-located radiosoundings A 2 N , the raw values of potential temper- 2 in both the upper troposphere and the 2 N N rather than the more usual wind fluctuations from the sondes with the values measured by 2 31258 31257 , for the location of the ESRAD radar are shown 2 N 2 N 1 km, and long ground-based period, N for that sonde. Fluctuations about the average are < 2 z N λ ) by: r P E. Conditions at the outer boundaries were defined by ECMWF 2 ◦ / 1 r P ) is a calibration factor which can be found either by technical calibration of z/H A is the height from which the echo is returned, exp( z N and 10–50 2400 km in area covering Scandinavia and western Russia, between about ◦ Az × = In this study, we use fluctuations in The period 21/22 February 2007 was chosen for study due to the presence of inertia- 2 of the short-vertical-wavelength wave-fronts, seen in Fig. 1, is re-produced well by the was configured for this2700 case study as50–75 a non-hydrostatic modelmodel-level with analysis. a In single the domain together model with domain, 251 a vertical levels horizontalvertical between resolution resolution the is surface of and 90–100 6 m 24 km km abovethick was 800 height. damping m Corresponding layer used, height, was and used 26–89reflections. at m The the below modelled top that. values of A of the 5000in m model Fig. domain 2, to for prevent the spurious same wave time interval as the radar data shown in Fig. 1. The morphology sondes. Further analysis of the radiosonde measurements is considered2.3 in Sect. 5. WRF Model The Weather Research and Forecasting model (WRF, Skamarock and Klemp, 2008) comparison with the sonde atagreement 02:00 UTC in on average 22 value February, of independently so measured there is by necessarily the good north two or techniques. On northwest this afterof occasion, launch the the reaching tropopause. sondes They horizontal drifted then18–20 distances km drifted 20–35 height. km back The toward at two the sondes theto at radar, the height 02 passing radar and within beam 05:00 3–20 UTC in kmtively. on the The at 22 lower agreement February stratosphere passed between – closest regards the coming small radar-derived as fluctuations and close in as the the 3 sonde-derived height and profiles, 5 is km, very respec- good, particularly for those two The lower panels of Fig.the 1 radar. compare Profiles fromThe the vertical radar lines represent on 1tal h the lines averages top on following panel the the indicateeach sonde lower the sonde. panels launch. times The show of value the launch. of lapse-rate the The tropopause proportionality dashed height horizon- constant determined from varies from 6 m toature 9 were m. smoothed For to the calculation have of the same height resolution (200 m) as the radar data. thin black line atis around 9 the km height radar-based followsmeasurements estimate the is of maximum considered vertical in the Sect. gradient tropopause 5. in height. Further2.2 analysis of Radiosondes the radar Five radiosondes were launchedand from at 02:00 Esrange, UTC, at 05:00raw UTC, data 21:00 UTC 12:00 were UTC sampled on and at 21 17:00 2 UTC s February intervals, on 2007 resulting 22 in February an uneven 2007. height The resolution, which gravity wave signatures whichwith are short typical vertical wavelength, forthe this availability site of (clear avertical number descending resolution. of wave The closely fronts top collocated panel radiosonde in measurements Fig. with 1 high shows the radar measurements of (in the present case, wethe use absence radiosoundings). of Equation humidity, i.e. (1) in isthat the stratosphere. strictly the However, previous method applicable studies only gives have in accurate shown lower estimates stratosphere of (e.g. Kirkwood et al., 2010a; Arnault and Kirkwood,measured 2012). by the radarhigher precision to in characterize the thefound relevant in waves conditions. the A since Appendix. more this detailed can discussion be of measured this can with be N Where height and the radar or by comparison of the derived profile of is derived form echo power ( 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | in ◦ latitude in A–B, 55 ◦ below about 10 km) separates 2 N ected by strong cyclonic winds re- ff ect and will be discussed later. 31260 31259 ff ) is at about 12 km altitude on the equatorward 2 N ), i.e. close to the times of the ECMWF analyses in Fig. 3. from the WRF model results, at 00:00 UTC on the 21 and 22 February, respec- 2 N Finally, we note that the horizontal cross sections at 12 km altitude in Figs. 5 and 6 Figures 5 and 6 show vertical and horizontal (at 12 km altitude) cross sections of wind they are close to theA–B. jet This is axis likely along a C–D, propagation/wind but e spread out further from the jet-axis along axis of the jet, andthe sloping upper-level upwards towards front. the Thewind north latter poleward shear of between start the the jet, atin parallel jet about both with axis vertical 10 km and sections,in altitude the A–B C–D. upper in The and level wave-fronts the C–D, parallel front. butlocation. region with Similar It shifted the of is patterns a upper-level clear strong front few are fromthe are degrees seen poleward/eastward the those edge towards horizontal seen of the cross-section the at that jet/front south vicinity the system these of radar from waves Leningrad the extend and north all Moscow. of In along Scandinavia the to horizontal the plane, the wave fronts are curved – 4 Source of the wave inFigures the 5 lower stratosphere and 6jet–front show system signatures are the of wave several fronts, waves. sloping Those upwards towards most the clearly south, related over the to main the C–D. show cyclonic (north westerly)Fig. winds 3, this over means the that,22 north at the February of location reversed Scandinavia. of direction ESRAD Comparingand and or with the further stalled stratosphere. north, between the This theorographic wind means on lower waves) that 21 part would and any be of wavesupwards the generated blocked to in by the troposphere, stratosphere. the the troposphere wind (e.g. reversal, and would not propagate strength at 00:00 UTC on22 21 February. February, and A has sharpstronger almost winds front disappeared to by (sloping 00:00 the UTC layerthe south sharp on of poleward from boundary high slower in the windsupwards clouds to to (Fig. the 4) the at tropopause, north. about reaching 5 This km the altitude front tropopause and coincides at continues with 65–67 side of the jet, and around 10 km on the poleward side. In A–B the jet has maximum 20 February, 01:24 UTC onhttp://www.sat.dundee.ac.uk 21 February and 01:14 UTC on 22 February 2007 (from Figure 3 presents00:00 UTC the on synoptic 22 February situationaltitude. 2007, On each from 24 the h, 00:00 20th, computed UTClated with the on ECMWF to location analyses 20 of the atwinds ESRAD 6 lower February km due is pressure to 2007 a the to to highseen the pressure across to the east, southern the and part north.jet of Strong on at Scandinavia, westerly-north-westerly the 00:00 with winds UTC a 21st are vanced on region Very and of High the strong Resolution 22nd 21st, curvature RadiometerNOAA-17 in moving by (AVHRR) this images satellite further anticyclonic taken in by east the the by polar thermal the orbiting infrared 22nd. (10.3–11.3 µm) Figure channel 4 4 shows at Ad- 01:35 UTC on are discussed in more detail in Sects. 3–5. 3 Synoptic situation model (Fig. 2), although the amplitudes in the model are clearly smaller. Model results letter “E” on theof horizontal highest cross sections), wind the speed5–12 eastern in km line the altitude, C–D in jet. intersects the Theary the southern vertical between region part low sections and of clearly high each shows values cross-section. the of The jet, tropopause between (bound- and tively. The vertical cross sectionsthe are horizontal cross taken section. along The two westernradar line lines, location A–B (marked marked provides by A–B a the cross and vertical section C–B line through on the on the left-hand panels and by the circle and We particularly draw attention to theland band and of the clouds south stretching of across Scandinavia,aligned the with front north a at sharp of the border Scot- lower to levels,also the below show north the the indicating jet progression a stream of NW–SE shown the in system Fig. eastward 3. over The the cloud course images of the study interval. 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | s 4 − 10 × 1.3511 = f N), and the angular from the model and ◦ 2 N 67.88 = φ . This gives 1 from the model is lower than for − 2 N rads are significantly shorter than found in 5 z − λ 10 × 31262 31261 from the radar and from the model (Figs. 1 and 2 are reached) along C–D than along A–B. As we , we applied a classical multi taper algorithm (Per- 7.292 z N 2 λ N Ω = ) (2) φ sin Ω (2 π/ are summarized in Table 1, where the uncertainties are taken as the half- 2 z λ = is the Coriolis parameter at the radar latitude ( f π/f 2 = The inertial period at the latitude of ESRAD is: The waves directly over the main jet, tilting equatorward with height, are very simi- A complete set of figures, the same as Figs. 5 and 6, but for eachIt 20 can min also from be noticed that the amplitude of the waves poleward of the jet/front is f where rotation frequency of the Earth The ground-based period isfrom obtained the from radar the data time09:00 over UTC, series the at of time 12 km intervalfurther height. 21 that Both February the show 05:00 model UTC a reproduces to the dominant the dominant peak 22 waves at seen February by 7.5 h the radar. (Fig.T 8), confirming ported. However, previous studies have beennecessarily at expect much the lower same latitudes, wave characteristics, soradar and we based some would previous results not studies of (e.g.resolve the such Vaughan short and wavelengths. Worthington, 2007) may not5.2 have been able Ground-based period to for the times ofin the the two time/height sondes presentations where of 2), the the waves energy were clearest. ofthe As the radar can or spectrum the also of radiosondes. befor fluctuations However, for seen vertical in each method wavelengths there between areresults 0.4 clear for and spectral peaks 0.8 kmwidths (with of a the peak spectral atprevious peaks. around studies The 600 (see m). values introduction) for The where 1–2 km has typically been the shortest re- To obtain the vertical wavelength, cival and Walden, 1993) toquency from obtain the the radar spectrum (at the of(at times the the of height the radar radiosondes), profiles location, the at of radiosondes and the buoyancy the fre- times model of the radiosondes). Results are illustrated in Fig. 7 5.1 Vertical wavelengths simulation and in thewe measurements, next and examine the their wave significance parameters – for wavelength, momentum frequency transport, and amplitude. slightly better horizontal resolutionet al. than (2004), present there are WRFfronts indications modelling. parallel of to In weak waves the Fig.jet-core in upper were the 7a stronger lower level of and stratosphere front. were Lane with At the wave- focus the of same that time, study. the waves5 directly over the Characteristics of the wave inIn the order lower stratosphere to better understand the characteristics of the waves as they appear in the ing poleward from the poleward edgeclear of from the Figs. 5 jet and werealso not 6 identified that rather in they short have, those not studies. horizontalused only It wavelengths, by short is less Plougonven vertical and than wavelengths (Fig. Snyder 100resolve 2), km. (2007), these but at The waves. best horizontal The 25 km, resolution simulations may not of have Lane been et enough al. to (2004), on the other hand used higher (more extreme valuesnoted of earlier, the simulationsthis under-estimate may the be amplitude arepresented problem at accurately of the enough the by radar thethe exact location, ECMWF simulation. location so analysis of which the is frontal used as system, the which inputlar may to in not morphology be andPlougonven location and (relative Snyder to (2007) the and jet) Lane to et those al. found (2004). in However, the the simulations waves propagat- by 12:00 UTC on 20 FebruaryThese clearly to show 24:00 the UTC propagation on ofstarting wave 22 between packets the February northward jet over is axis thecontinuation included radar and of location, as the the upper Supplement. front, level front, and propagating continuing through further the poleward. upward 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | k (4) (5) , from by this R k . k quoted in the i T and can be found using , we find the intrinsic i h (Eq. 4), or the ratio of ω λ 2 is the dot product of the ) frequencies is given by k/m N g k ω . So, even if we have mea- · 7.5 h, of the same order as k U = g T K, while the absolute variation of ◦ ), and g 1 to 1 − π/T is the ratio of amplitudes of the wind fluc- (Eq. 3), or the ratio of horizontal to vertical R U 31264 31263 and ) and ground-based ( i are the magnitudes of horizontal and vertical 2 ω z m , and the wave vector ). Best fit ellipses have been found by least-squares ◦ U  π/λ 2 2 k = m . Hodographs have been plotted in the lower panels of Fig. 9. 1 − , and the (mean) buoyancy frequency, and 2 ) h k/m 3 ms determined by Eq. (5), horizontal wavelength , we cannot determine the intrinsic period unless we know at a fixed height, the horizontal wavelength can easily be determined ) (3) and the background wind ± i U k k/m 2 6.8–8.9 h are close to the ground-based period, consistent with the wind π/λ · ( k ω 2 2 N = U is the ground based frequency (2 i N = 12.92 h. So the ground-based wave period g − + k g = ω 2 f ω π/ω f f /R ( T 2 = = = Further, as described for example in Guest et al. (2000), the linear theory of gravity For the radiosondes, hodograph analysis and Eq. (5) are used to determine the in- To calculate the intrinsic period, we need to know the magnitude and direction of the From the dispersion and polarisation relations for hydrostatic inertia-gravity waves = 2 i i i i propagating inertia gravity wave traces an elliptical path, which rotates clockwise in the with mean and standard deviationsTable. of With the resulting estimates of Eq. (4), as alsorameters shown found in by Table theuncertainties 1. are hodograph There quite analysis large. is In andmakes good some those the hodographs agreement the from uncertainties between ellipses the arelarge. in the nearly model, wave determining circles although pa- which the the direction of thewaves wave in a vector uniform background particularly flow predicts that one vertical wavelength of an upward- wave, and the ratio ofwave frequency the (Eq. major 5). to Wavefrom the parameters derived minor the by axes first fitting of three ellipsesmethod the to has sondes ellipse the an is are hodograms ambiguity proportional givenfitting of to to in 180 intervals the Table of 1 600 m (note (overlapping by that 300 m) the for the direction entire of height range 10–14 km, the radar location. trinsic frequency. Figure 9 showsstratosphere fluctuations (from of the 10 km temperature to anddes. wind 14 Variations km) in of associated the temperature with lower oscillatewind the from is waves from about theAccording five to radioson- the linear theoryellipse of of the gravity hodograph waves, the is orientation aligned with of the the horizontal major wave axis vector of of the the inertia gravity the vertical wavelength as describedperiods in given Sect. in 5a, Table to 1. The calculate (perpendicular orientation to of the the wave wave fronts fronts),T also listed gives also the in direction Table of direction 1. being The close intrinsic to periods perpendicular we to find, the direction of wave propagation at 12 km at in the vicinity of the radar site and at the times of radiosonde launches, together with By plotting from the spacing between wave fronts. Using a height of 12 km (as in Figs. 5 and 6), where wavenumbers, respectively, tuations along and perpendicular to the direction of wave propagation. wave vector wave numbers, wind fluctuations perpendicular andthe hodogram parallel ellipse, to Eq. 5). the This direction is of easiest to propagation do ( for the model results, using Eq. (4). (e.g. Sato et al., 1997) we can write: ω ω The relationship between intrinsic ( ω where mean background wind vector, surements of the inertial period, indicatingthis is that really the determined wave byground-based the may period intrinsic be due period an to which Doppler may inertia-gravity be shifting wave, longer by although or the shorter background5.3 wind. than the Intrinsic frequency and horizontal wavelengths and 5 5 25 15 20 10 25 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (6) (7) as 2 N using the f , where the am- 2 N in the height profile. . Average values of z 2 λ by the change of wind N ff  0.5  2 i /ω 31266 31265 2 f +  1  2 min 2 , relative to the background wind using information on N + k + 1 2 max N  by the relatively poor resolution of the measurements (a Gaus- are the maximum and minimum values of 2 0.5  N 2 min . 2 i over the time interval 00:00 UTC on 21 February and 12:00 UTC on N 2 2 min /ω N 2 N f and − + is calculated separately for each 20 min averaged profile between 10 km and is the relative amplitude of the wave, which can be written in terms of 1 e has been calculated using Eq. (6), horizontal wave number can be computed 2 max 2 e max  i a a N 2 N ω   and mean = = Here For the radar data, we base our analysis on the method developed by Gubenko There has been much criticism of the hodograph method. For example, Zhang e e e 22 February, and their standard deviationwith are the given in vertical Table wavelength 1. to TheseAs are calculate can used intrinsic be together frequency seen and in horizontal Tabletal 1, wavelength. wavelength there is from good the consistencythe sondes with the and direction wave from of period and the wave-vector mean horizon- model. wind Finally, (here it available is fromto possible radiosondes) the to and sign estimate Eq. of (2). thein angle The Table with 1. result respect One is to of ambiguous the these as background matches wind, well so the two results results from are the quoted model and the sondes. 14 km heights. A correctionextreme factor values of of 1.1 is appliedsian to weighted account height for smoothing-out averagea of with the width 200 m) compared to where a where Once using Eq. (4). stability fluctuations. In thisthe case, wave, there and is the a intrinsic relation frequency: between the relative amplitudea of be reached without instability resulting from the wave-induced wind-shear and static plitude does not grow with height, correspond to the maximum amplitude which can tain waves and, indirection any at case, the tropopause. any So such wetem can waves be was would confident dominant. be that Plougonven the and cut wave Teitelbaumtechnique from (2003) o the also has jet–front showed limitations sys- that in theappropriate conditions hodogram for with a strong part background of windin the the shear present wave and spectrum cases, is at (low only the frequency, radar long site, wave the limit). wind However, shearet was weak al. and (2008, the frequencysinusoidal 2011). low. fluctuations in This a method height-profile of assumes temperature, density that or gravity waves, observed as quasi- to apply band-pass filters toto the near data to monochromatic ensure oscillations, that asin the done hodograph our by analysis cases Vaughan is and confined therea Worthington problem. was (2007), Since but a the singlecase wind comes dominant in from the vertical the lower north-east, wavelength levels which so is around rather this the flat, radar should we would location not not in expect be the strong moun- present indication of upward propagation (althoughwindshear it was could present, but in this principle is be not misleading the if case strong here). et al. (2004) simulatedMM5 mesoscale a model, and near found that, monochromaticthe in vertical a wave wavelength region of could of be background intrinsicnor wind accurately shear, the period determined, although horizontal neither 3 the wavelength could intrinsicmethod breaks frequency be down reliably when derived. there They is further a showed superposition how of waves. the One possibility would be propagating wave, the rotation is anti-clockwisein in the the Northern Southern Hemisphere Hemisphere). (clockwise Theevery hodograph radiosonde of shows the a windsondes, between which clockwise means 10 rotation km that to the ofdownward 14 waves km the progression are for with propagating wind, time upward most of in the the clearly stratosphere. wavefronts in The in the the radar first data 3 (Fig. 1) is also an Northern Hemisphere (anti-clockwise in the Southern Hemisphere). For a downward 5 5 20 10 15 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (8) (9) (10) 1.3– 0.03– = 0.012– | = 0 = v represent | /ρ z , ph λ 1 F ph − F (parallel and per- 0 v . This gives and 2.5–2.7 ms 3 0 − = u is the atmospheric density. | 0 u ρ | , and assuming sinusoidal fluc- so that the wave will be readily 0 u 1 ) − , the momentum flux per unit mass, 0.4 kgm = /ρ k/m ( ρ ph − F = 0 and 5 km, so the waves with shorter w | 31268 31267 0 > v | z , λ | , being consistent with both radiosonde and radar- 0 2 u 2, this gives | − / s 2 per day, which represents a significant forcing. ) (11) | 2 0 1 m u | − (2 = mean ) 0 k/ 2 w | 0 0 mean u ): ) u ( | 0 h i i F w 0.03–0.04 m 2 2 0 ) ) 0.4–0.5 ms i i u = . These show low values, a few ms = N/π N/π z z /k h /ρ i ) λ λ f /ω f /ω (12–16 mPa) according to the observations. This is similar to the lower- F ) ) ( ( is the atmospheric scale height (taken as 7 km). For ω ph , e e 2 are the fluctuations in vertical velocity, and F 2 − − ρH a − a = ( − , 0 1 1 H 1 s / − h − h h w − 2 C ph ρ ρ (2 (1 F = = = = ∼ | | The amplitudes of the inertia-gravity waves do not increase with height, rather they Also shown in Table 1, are estimates of the magnitude of the horizontal phase ve- For comparison with other studies, we can also express the momentum flux, for ex- 0 0 h ph ph u v locity, Doppler shifted and the wavefronts distorted, by the background wind. For example, ac- energy and momentum at aet rate al. which keeps (1997), their this amplitudewave leads propagation constant. ( to Following Sato an expression for theF wave driven force in the directionWhere of 0.04 m 2011; Vincent et al., 2007), butlatitudes. they are probably less common, at least at high northern are fairly constant (between 10–14 km).would Since be reduced density expected towards to higher lead altitudes to increased amplitude, this means that they are shedding et al. could only resolvean waves addition with to thiszonal flux. fluxes It suggested is to also comeresolving about from model an wintertime study order jet–front of ofspheric systems Sato magnitude in balloon et more the al. flights than gravity-wave (2009),a by the or common Vincent average in occurrence et the at al. analysisa the large of (2007). area, radar long-duration Since they strato- site, can theage and be sense. waves expected the Orographic identified to model waves make here over showsmagnitude a major are significant that more mountain contribution, they to ranges even extend the in can over an momentum contribute aver- an flux order when of they occur (Alexander and Teitelbaum, ample at 12 km height, in absolute0.016 Nm terms using stratosphere momentum fluxwinter estimates jet-streams) for by the Ern corresponding et al. regions (2004), (high-latitude which suggested 10–20 mPa. However, Ern based estimates. However, thea model factor 5, underestimates and the the momentum wave flux amplitude by at by least about an order of magnitude. tuations so that ( F Estimates of the wave amplitudes are given in Table 1 for eachthe method. We radiosondes can see and that there the is2.0 good ms radar-based agreement between estimates, with F where Substituting the polarization relationship hodograms as described above.et For al., ESRAD 2008) as: they are calculated (following| Gubenko | The vertical flux ofestimated horizontal as momentum (Fritts in and the Alexander, 2003) direction of wave propagation can be Wave amplitudes in termspendicular of to horizontal the wind direction fluctuations by of examination of wave propagation) theFor have fluctuations the been between radiosondes, estimated 10–14 km wind for height the fluctuations at model are the ESRAD determined location. from the elliptical fits to the 5.4 Wave amplitude, momentum flux and wave-driven force 5 5 25 15 20 10 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , or 1 − alone. 2 is greater N gh 0.09 ms C N). This means ∼ ◦ z g C N), while poleward of 1 km), located above ◦ (at 65 > 1 − (70 700 m, 1 − = at 12 km altitude, just poleward z 15 ms λ k − 3 ms · in wind perturbation along the di- − U 1 − by the ESRAD radar in northern Swe- 2 N) and , as the primary variable to illustrate the ◦ N . So it should take about 12 h for the wave N) and 2 1 ◦ 113 km and N − = 31270 31269 (65 (at 60 h 1 λ 1 − − or 52 kmh 8.8 h, 1 = − i T so that the disturbance can propagate poleward even when , h 2 − C s 15 ms 3 ∼ −  gh  10 3 2 C × m i m i ω ω , which determine how quickly a wave packet moves away from it’s source. 0.42 / 2 gh , while = k/ k 1 C 2 2 2 − N N N and = = z z High vertical-resolution measurements of The model clearly shows the source of the waves as a jet–front system, with the jet Finally we calculate the magnitudes of the vertical and horizontal group velocities, g g gh length and the vertical flux of horizontal momentum, from vertical profiles of in earlier studies of inertia-gravityof wave generation the by same jet–front parts systems. of Earlier2004) jet–front studies have systems (e.g. reported Plougonven waves andthe Snyder, with jet 2007; longer core. Lane These et vertical waves al., the wavelengths are high also ( northern seen latitude in of our the simulation radar but site. they doden not propagate often to show similarused wave a signatures method to proposedassumptions, those by to Gubenko shown derive et here. wave al. In parameters, (2008, this including 2011), study based intrinsic we on period, have wave horizontal saturation wave- core moving across thesite southern appear to part originate of on thealtitude, Scandinavia. upper, between The poleward/eastward edge the waves of latitude reaching the jet, ofabout the at 200–300 the km about radar jet 10 poleward km of core the andtical jet wavelengths, the emanating core from upper-level at this front 10 source km which region, height. appear is Waves not with located to such have short been ver- reported The amplitudes observed by theflux radar of and horizontal radiosondes momentum give inhigher estimates the than for range estimates the 12–16 vertical of mPa,tudes which the (e.g. is Vincent average et an for al., order non-orographic-source 2007;of of Sato waves the et magnitude at type al., 2009). similar identified This lati- here,will shows with that be inertia-gravity vertical intermittent, waves wavelengths can lessthe provide than lower significant stratosphere. 1 contributions km, to even though momentum-flux they budgets in 60–100 km are consistent with alland three radiosondes methods are although the large uncertainties (severalgive using 10 s radar similar of estimates km). for Radarrection amplitude, and of radiosonde about propagation. measurements The 3 ms amplitudeless, in but the higher model amplitudes at are the found radar location at is other a locations factor within of the 5 same wave packet. wavelength 500–700 m and intrinsic period 6–9 h. Horizontal wavelengths in the range waves as this can bepropagating, used inertia-gravity for waves all over three the methods. radar/radiosonde All launch methods find site, dominating, with upward vertical the ground-based phase velocity is Doppler-shifted to zero by the background wind. 6 Summary and conclusions We have investigated thethe source lower of stratosphere short over verticalhigh-resolution northern wavelength non-hydrostatic Scandinavia inertia using modelling, gravity VHF waveshave for in radar, used a radiosondes squared and 2 buoyancy day frequency, period in February 2007. We 326 mh disturbance to travel upwardsthe from maximum height its where source itsame above is time clearly the it seen jet will inthan around have the the travelled 10 observations, phase km 600 velocity, around km height, 14 horizontally. km. to The In group the velocity C In the hydrostatic inertial gravity wave assumption, this isC given by C Using of the jet along A–Dthe is jet between along 0 ms C–D itthat is between the 0 wavefronts ms movestationary poleward further at to the the radarfronts east, location seen e.g. in (along along the A–B), C–D. horizontal This but sections explains are in the Figs. almost curvature 5 and in 6. the wave cording to the model, at 00:00 UTC on 22 February, 5 5 25 20 10 15 25 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | λ (A2) profiles 2 N erences between ff , which is a reason- 1 − ects and the characteris- ff 75 ms = for parameters which could be , is the variance in the individual 2) σ max x 2 ( V σ is generally dominated by the antenna ff e θ 0.2 s for the corresponding maximum wind speed, erence between two estimates of the same ff 31272 31271 = max ective angular half-width (in degrees) of the po- V ff max T ∆ the e ff e θ ) (A1) , this gives ff ◦ e 2) θ x 2 ( σ max , which can be assumed equal to is the variance of the di + V is the sampling time, 1) ( x 2) 1) 2 ( x x λ/ 2 ( σ − can be expected at the ESRAD location (due to orographic waves), corre- max σ 1 T x 1 4.8 2 ( = − ∆ σ = 2) x − 1 max Figure A1 shows estimated standard deviations When fully operational, ESRAD uses 6 separate receivers, each connected to a sep- For Doppler wind measurements (used for vertical wind at ESRAD), the sampling x T 2 ( used to characterize waves in the UTLS. Results from the analysis of a whole month of the wind (and thesibility other to parameters) determine at each thethose height precision pairs and of of time. the measurements This using gives measurements us the from the statistical theσ pos- relation di where parameter, estimates. SNR is achieved afterfor about wind 1 s estimates and integration 1 time. s So for echo we power. use integrationarate times segment of of 0.2 s needed the to antenna determine array. the Since horizontal only wind, 3 we receivers/antenna can segments make are two independent estimates Where the radar wavelength, and lar diagram of thetics scatter of the (including sacatterers). both For antennabeam-width, ESRAD, where about beam 2 e able upper limit forfrequency, the longer coherent UTLS. integration For times can echo betime power used, of measurements, limited the only used echoes. by to the For correlation typical find UTLS buoyancy conditions at ESRAD, we find that no increase in lation between sampling time and maximumthis technique wind has speed been which addressed can by beas Holdsworth measured and using Reid (1995). It can be estimated ∆ Horizontal winds at ESRAD are measured using the full correlation technique. The re- to 3 ms sponding to a Doppler shift of 1 Hz, requiring maximum sampling times less than 0.50 s. components which are in-phasetransmitted or pulse in are quadrature added separately). comparedpower This to to leads the to noise initial an power increase phase (SNR)The in of by the number a the ratio of factor of signal equal coherentetition to integrations rate the which (determined number can of byESRAD coherent be the during integrations. used maximum winter) height depends andmaximum coverage on sampling on needed, the time the typically is pulse maximum determined 30 rep- km sampling by at the time application. whichrate can has be to used. be The at least twice the maximum Doppler shift expected. Vertical winds up fluctuations in the parameterRAD, which echoes is from to thepower be upper than used. troposphere the For a background andtronic) and single noise, lower external radar (interference which stratosphere and pulse has galactic) havesignal from sources. levels, contributions much In echoes ES- order from from lower to a large achieve both measurable number internal of radar (elec- pulses are integrated coherently (i.e. wave, including seasonal variations in the momentum flux. Appendix A Precision of ESRAD measurements In order to characterizements wave with fluctuations, a precision the which radar is better must than be the expected able amplitude to of the make wave-induced measure- The agreement found hereand between those wave from parameters radiosondes derivedsynoptic and from modelling context radar show of that thebe the waves, method predominantly it is towards is useful. the likelyare Given north-east. that available the Since from the almost ESRAD, direction it 10 yr of will of be the suitable possible momentum to observations flux make will a statistical study of this type of 5 5 25 15 20 10 25 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ff the 2 N could be 2 in horizontal N 1 − 1 but increases > 10.5194/amt-4-2153- , 2002. , 2012. ects in the middle atmosphere, ff when SNR , 2008. 1 − , 2003. 0.5, which would include about half . This makes observations of 2 > N is 2–3 ms σ 10.1029/2001JD000452 31274 31273 at SNR . 1 − 10.1029/2007JD008920 10.3402/tellusa.v64i0.17261 10.1029/2001RG000106 , 2004. , 2011. This research has been partly funded by the Swedish Research Council financed by CNRS-INSU. The publication of this article is for lower SNR. Since most of the observations in this height region ) in vertical wind and 80 % in 1 1 − − cannot be reliably determined. Smaller fluctuations could be detected in 1 − , 2011. 10.1029/2004JD004752 10.1029/2011JD016151 The waves studied in the current paper have amplitudes of 2–3 ms 2011 Rev. Geophys., 41, 1003, doi: the lower stratosphere over Macquarie Island, J. Atmos. Sci., 57,other wave 737–752, parameters 2000. from aGeophys. single Res., vertical 113, temperature D08109, or doi: density profile measurement, J. internal gravity wave parameters from radiofiles occultation in retrievals the of Earth’s vertical atmosphere, Atmos. temperature Meas. pro- Tech., 4, 2153–2162, doi: 1982. ity wave momentumdoi: flux derived from satellite data, J. Geophys. Res., 109, D20103, honey, M.: Evidence for inertia-gravitydinavia, waves J. forming Geophys. Res., polar 107, stratospheric 8287, clouds doi: over Scan- cold fronts over southern Australia, J. Atmos. Sci., 50, 785–806, 1993. Mountains in Antarctica: radar observations,analysis, fine-scale Tellus A, modelling 64, and 17261, kinetic doi: energy budget trainment around cumulus clouds, J. Atmos. Sci., 46, 740–759,procedure 1989. for range validation using balloons, Radio Sci., 34, 427–436, 1999. tain wavesdoi: observed by satellite: a case study, J. Geophys. Res., 116, D23110, Alexander, M. J. and Teitelbaum, H.: Three-dimensional properties of Andes moun- References of the availabledetected measurements. more Wave that signatures 90 % as of the small time. aswind 10 % components, 10–15 in times less0.15–0.30 ms (by the ratio ofmost vertical suitable to for horizontal characterizing the wavelengths, waves using ESRAD. for the estimates. Forto horizontal several ms winds. have lower SNR, thisa few means ms that wave-inducedvertical horizontal winds, wind down fluctuations to of 0.2–0.3 ms only (April 2009, when all 6 receivers were operating) at heights 11–13 km have been used Gubenko, V. N., Pavelyev, A. G., and Andreev, V. E.: Determination of the intrinsic frequency and Gubenko, V. N., Pavelyev, A. G., Salimzyanov, R. R., and Pavelyev, A. A.: Reconstruction of Guest, F. M., Reeder, M. J., Marks, C. J., and Karoly, D. J.: Inertia-gravity waves observed in Fritts, D. C. and Alexander, M. J.: Gravity wave dynamics and e Fritts, D. C.: Shear excitation of atmospheric gravity waves, J. Atmos. Sci., 39, 1936–1952, Ern, M., Preusse, P., Alexander, M. J., and Warner, C. D.: Absolute values of grav- Eckermann, S. D. and Vincent, R. A.: VHF radar observations of gravity-wave production by Dörnbrack, A., Birner, T., Fix, A., Flentje, H., Meister, A., Schmid, H., Browell, E., and Ma- Chilson, P. B., Kirkwood, S., and Nilsson, A.: The esrange MST radar: a brief introduction and Arnault, J. and Kirkwood, S.: Dynamical influence of gravity waves generated by theBretherton, Vestfjella C. S. and Smolarkiewicz, P. K.: Gravity waves, compensating subsidence and de- for technical support. Thanksthe also first to author. the University of Réunion for giving a sabbatical year to (grants 621-2007-4812 and 621-2010-3218). ESRADtion is with maintained Swedish and Space operated Corporation, in Esrange. collabora- Particular thanks are due to the Esrange sta Acknowledgements. Supplementary material related to thishttp://www.atmos-chem-phys-discuss.net/13/31251/2013/ article is available online at acpd-13-31251-2013-supplement.zip 5 5 25 30 20 15 10 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , 10.5194/acp-10-3583- , 2003. , 2004. 10.1029/2007JD009682 , 2013. 10.1175/JAS3305.1 10.1029/2003JD003535 . 31276 31275 , 2008. 10.5194/angeo-31-239-2013 , 2009. , 2003. , 2010. erent baroclinic life cycles, J. Atmos. Sci., 64, 2502–2520, ff , 2007. 10.1029/2007JD008938 , 2010b. 10.1029/2009GL039908 10.1029/2003GL017716 10.1175/JAS3953.1 10.1029/2009JD013728 ths, M., and Reeder, M. J.: Stratospheric inertia-gravity waves generated in a numerical ffi Ann. Geophys., 31, 239–250, doi: On thedoi: origins of mesospheric gravity waves, Geophys. Res. Lett., 36, L19801, tal wavelength gravity waves, J. Geophys. Res., 113, D24104, doi: convective origin over Arctic Scandinavia – VHF radar observations and numerical modelling, stratosphere revealed by three-weekRes. continuous Lett., observation 24, 1739–1742, with 1997. the MU radar, Geophys. 2008. I: Results, J. Atmos. Sci., 40, 509–520, 1983. spheric midlatitude jet assoundings, J. given Geophys. by Res., 108, the 4686, Fronts doi: and Atlantic Storm? Track Experiment radio Akiyoshi, H., Austin, J.,perfield, Baumgaertner, M. A. P., Cugnet, J.A., D., G., Hardiman, Dameris, Bekki, S. M., S., C., Dhomse, Braesicke, Hegglin, P., S., M. Brühl, Frith, I., C., S. Chip- Jöckel, M., P., Garny, Kinnison, H., D. Gettelman, E., Lamarque, J.-F., Mancini, seen in thedoi: ECMWF analyses and from radiosondes, Geophys. Res. Lett., 30, 1954, and numerical simulations of inertia–gravitya waves jet and stream, shearing J. instabilities Atmos. in Sci., the 61, vicinity 2692–2706, of doi: and middle stratosphere: method andLMDz-GCM, J. comparison Atmos. between Sci., the 66, ERA-40 1327–1346, re-analysis 2009. and the and fronts.doi: Part I: Di tain waves over Northern ScandinaviaWRF – mesoscale a case model, study2010 Atmos. using Chem. the ESRAD Phys., VHF 10, radar and 3583–3599, the doi: ments of wave momentum flux108, over 625–642, the 1982. Colorado Rocky Mountains, Q. J. Roy. Meteor. Soc., cycle of baroclinic instability, J. Atmos. Sci., 52, 3695–3716, 1995. Conventional Univariate Techniques, Cambridge University Press, Cambridge, 1993. Kumar, S.: Fresnel scatterArctic, the revisited-comparison Tropics and of Antarctica,http://www.ann-geophys.net/28/1993/2010/ Ann. 50 MHz Geophys., 28, radar 1993–2005, and 2010a, radiosondes in the E., Manzini, E., Marchand,G., M., Plummer, Michou, D. M., A.,Tian, Nakamura, W., Rozanov, T., and E., Nielsen, Yamashita, Y.:chemistry J. Scinocca, Review climate E., J. of models Olivié, and the F., associated D., Smale, formulationdoi: external Pitari, forcings, of D., J. present Geophys. Teyssédre, Res., generation H., 115, stratospheric D00M02, Toohey, M., 1280, 1995. Boston, Amer. Meteor. Soc., 272–288, 1986. London, 1995. and application to the full correlation analysis of spaced antenna data, Radio Sci., 30, 1263– polar regions revealed byD04107, GPS doi: radio occultation data with CHAMP, J. Geophys. Res., 113, model of frontogenesis I: Model solutions, Q. J. Roy. Meteor. Soc., 122, 1153–1174, 1996. Sato, K., Watanabe, S., Kawatani, Y., Tomikawa, Y., Miyazaki, K., and Takahashi, M.: Sato, K., O’Sullivan, D. J., and Dunkerton, T. J.: Low-frequency inertia-gravity waves in the Preusse, P., Eckermann, S. D., and Ern, M.: Transparency of the atmosphere to shortRéchou, horizon- A., Arnault, J., Dalin, P.,and Kirkwood, S.: Case study of stratospheric gravity waves of Rosenthal, A. J. and Lindzen, R. S.: Instabilities in a stratified fluid having one critical level. Part Plougonven, R., Teitelbaum, H., and Zeitlin, V.: Inertia gravity wave generation by the tropo- Morgenstern, O., Giorgetta, M. A., Shibata, K., Eyring, V., Waugh, D. W., Shepherd, T. G., Plougonven, R. and Teitelbaum, H.: Comparison of a large-scale inertia–gravity wave as Lott, F., Kuttippurath, J., and Vial, F.: A Climatology of the gravest waves in the equatorial lower Plougonven, R. and Snyder, C.: Inertia–gravity waves spontaneously generated by jets Kirkwood, S., Mihalikova, M., Rao, T. N., and Satheesan, K.: Turbulence associated with moun- Lane, T. P., Doyle, J. D., Plougonven, R., Shapiro, M. A., and Sharman, R. D.: Observations Lilly, D. K., Nicholls, J. M., Chervin, R. M., Kennedy, P. J., and Klemp, J. B.: Aircraft measure- Percival, D. B. and Walden, A. T.: Spectral Analysis for Physical Applications: Multitaper and O’Sullivan, D. J. and Dunkerton, T. J.: Generation of inertia–gravity waves in a simulated life Kirkwood, S., Belova, E., Satheesan, K., Narayana Rao, T., Rajendra Prasad, T., and Satheesh Holton, J. R.: An Introduction to Dynamic , 3rd edn., Elsevier Academic Press, Hooke, W. H.: Gravity waves, in: Mesoscale Meteorology and Forecasting, edited by: Ray, P.S., Holdsworth, D. A. and Reid, I. M.: A simple model of atmospheric radar backscatter: description Hei, H., Tsuda, T., and Hirooka, T.: Characteristics of atmospheric gravity wave activity in the Gri 5 5 30 20 25 30 15 10 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | and 1 0.5 0.3 0.4 0.7 − h z ± ± ± ± ms λ 2 0.03 2.2 0.01 2.8 0.04 1.8 0.01 3.4 − the Coriolis /ρ C s ± ± ± ± 2 ph F f , k . sonde1/model1 the vertical flux of 3.5 0.06 1.4 0.04 3.2 0.07 2.2 0.03 k i T ± ± ± ± , 2007. /ρ ph F i 0.27 6.0 0.11 7.7 0.24 5.8 0.17 8.8 ± ± ± ± f /ω 48 0.68 49 0.46 26 0.59 34 0.45 is mean squared buoyancy fre- h ± the direction of ± ± ± 2 m q N , 8 113 , 2007. 43 46 38 37 k 60 78 ± ± ± ± the ground based wave period, the amplitudes of the wind fluctuations θ λ | 98) 125) g 138) 124) 0 N of E km H m − − T − − ◦ v | , 2 10.1029/2007GL031072 N 1 0.8 42 ( 0.4 82 ( 0.7 56 ( 0.6 33 ( − and 0 ± ± ± ± v | ms 0 u 31277 31278 | 10.1002/qj.142 1 erent methods. Values in bold are directly estimated 0.9 1.4 0.7 1.6 1.5 1.5 0.2 1.9 − 0 ± ± ± ± ff u the intrinsic period of the wave, the horizontal phase speed parallel to i T h 200 2.7 C z ± λ , 600 3.1 700 2.8 700 0.4 0.3 29 100 0.69 8.9 0.002 3.1 500 3.3 700550 0.5 0.5 0.3 0.3 28 25 66 76 0.52 0.67 6.8 8.7 0.004 0.002 2.7 2.4 k , 1994. , 2004. g H m ms T 0.10 7.5 700 e ± a 0.81 4 − 4 4 4 4 4 4 10 − − − − − − × 2 10 10 10 10 10 10 2 m − × × × × × × N s 0.3 the intrinsic frequency, ± 4.0 4.1 4.5 4.1 4.2 4.2 i 4.2 the relative amplitude of the wave in w e Wave parameters from three di a 10.1029/2004JD005090 10.1002/qj.49712051903 the vertical and horizontal wavelengths, sonde3 10–14 km sonde2 10–14 km model1 12 km radar 10–14 km 0–36 h sonde1 10–14 km model2 12 km model3 12 km to retrieve gravity waveL11110, characteristics doi:10.1029/2004GL019841, from 2004. individual soundings, Geophys. Res. Lett., 31, tems, J. Atmos. Sci., 61, 440–457, 2004. with satellite observationsdoi: and a mesoscale model,acterization and Radiometric J. Calibration for Geophys. Remote Sensing, Res., Logan, Utah, 109, August 2004. D22104, J. Roy. Meteor. Soc., 133, 179–188, doi: measurements of gravity-wave momentumspheres, Geophys. fluxes Res. Lett., in 34, the L19804, doi: polar stratosphere of both hemi- Geophys., 21, 87–230, 1979. justment process followingdoi: deep convection, Q. J. Roy.mesoscale Meteor. gravity wave Soc., events, Mon. 120, Weather Rev., 1145–1178, 115, 721–729, 1987. research and forecasting applications, J. Comp. Phys., 227, 3465–3485, 2008. h horizontal momentum parallel to parallel and perpendicular to the horizontal wave vector parameter, λ from the observed orpersion modelled and fluctuations, polarization other relations parameters asquency, are described calculated in using Sect. wave 5. dis- Table 1. are at 21:00 UTC onon 22 21 February. Februry, All sonde2/model2 model at results 02:00 for UTC the on vicinity 22 of the February, at radar. 05:00 UTC Zhang, F. Q., Wang, S. G., and Plougonven, R.: Uncertainties in using the hodograph method Zhang, F.: Generation of mesoscale gravity waves in the upper-tropospheric jet–front sys- Wu, X.: Operational Calibration of AVHRR/3 Solar Reflectance Channels, Conference on Char- Wu, D. L. and Zhang, Z.: A study of mesoscale gravity waves over the North Atlantic Vaughan, G. and Worthington, R. M.: Inertia-gravity waves observed by the UK MST radar, Q. Vincent, R. A., Hertzog, A., Boccara, G., and Vial, F.: Quasi-Lagrangian superpressure balloon Shutts, G. J. and Gray, M. E.Uccellini, B.: L. W. A and numerical Koch, S. modelling E.: study The synoptic of setting the and possible geostrophic source ad- mechanisms for Smith, R. B.: The influence of mountains on the atmosphere, edited by: Saltzman, B., Adv. Skamarock, W. C. and Klemp, J. B.: A time-split nonhydrostatic atmospheric model for weather 5 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

, from 2 −

(colour) in s 2 N , from the WRF model experiment (same time 2 − 31280 31279 (colours) in s 2 N

Figure 1. , between radar (red) and radiosondes (black) launch at the radar site at 21:00 UTC 2 N Top panel: time-height diagram of squared buoyancy frequency, Time-height diagram of is given by the coloured bar on the right of the top row. Lower panels: comparison of pro- 2 N Figure 2. Fig. 2. and height axes as Fig. 1). ESRAD observations. The horizontal axis2007 gives to the 18:00 time UTC in 22 hoursfor February from 00:00 2007, UTC and 21 the February files vertical of axis gives the height in km. The scale Fig. 1. 21 February 2007, 02:00 UTC,lines on 05:00, the 12:00 top and panel 17:00 show UTC the 22 times February of the 2007. radiosonde Vertical launches. black Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

31282 31281 ). , from left to right, at 00:00 UTC on 20, 21 and 22 February 2007, from 1 −

Horizontal cross-sections at 6 km altitude of pressure (colour) in hPa and horizontal Advanced Very High Resolution Radiometer (AVHRR) images taken by the polar orbit-

Figure 4. http://www.sat.dundee.ac.uk Figure 3.

Fig. 4. ing NOAA-17 satellite in01:35 UTC the 20 thermal February infra-red 2007,(from 01:24 (10.3–11.3 UTC µm) 21 channel February 4, 2007 from and 01:14 left UTC to 22 February right, 2007 at ECMWF analyses. The pressurescale scale by is the given arrow by atof the the ESRAD coloured bottom radar. right bar corner to of the each right, panel. and The the black wind cross gives the location Fig. 3. winds (arrows) in ms Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | the (b) and Vertical cross- Vertical cross- (a) (b) (a) at the model level which is at 2 N 31284 31283 Horizontal cross section for (c) . , vertical black line indicates the radar location. (c) (c)

. Black contours and arrows show wind speed and direction. In 2 −

Figure 6.

Figure 5.

in s

2 Results from the WRF model for 00:00 UTC on 21 February 2007 Results from the WRF model as in Fig. 5, but for 00:00 UTC on 22 February 2007. N

Fig. 6. Fig. 5. section along line A–B in section along line C–D in arrows show the wind component in the plane of the cross-section. 12 km altitude at theshows radar site (marked by a black circle), and for wind at 10 km. Colour scale Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

31286 31285 in vertical profiles from 10 km to 14 km height, from for time-series at 12 km height from ESRAD and from 2 2 N N

Spectrum of fluctuations of Spectrum of fluctuations of

Figure 8. .

Figure 7.

Fig. 8. the WRF model22 at February the 2007. ESRAD location, from 05:00 UTC on 21 February to 09:00 UTC on Fig. 7. ESRAD, the WRF05:00 UTC model on 22 and February 2007. radiosondes, for the times of two radiosondes, 02:00 and

Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 0.30 -

5 0.1 for lower at SNR > 0.5, 1 1 - - s ( April 2009, is buoyancy s

m m N 0.3 the most suitable for – 2 in horizontal wind 1 - s m cannot be reliably determined. 3 1 - - s m

using 0.2 s and 1.0 s coherent are zonal, meridional and vertical cal to horizontal wavelengths, N but increases to several for parameters which could be used to 13 km have been used for the estimates.

- w σ

) fluctuations from the five radiosondes m the analysis of a whole month T and SNR >1 v ,

u This makes observations of N

when .

2 1 - s by the ratio of verti 31288 31287 dard deviations m 3 - 80% in N is 2

σ and ) and temperature ( the current paper have amplitudes of 2 V s. , 15 times less ( U – could be detected more that 90% of the time.

2 r fluctuations could be detected in vertical winds, down to 0.2 r fluctuations could be detected in vertical winds, induced horizontal wind fluctuations of only a few cterizing the waves using ESRAD. - ) in vertical wind 1 -

s

The waves studied in components, 10 m chara estimates. Figure A1 shows estimated stan characterize waves in the UTLS. Results fro when all 6 receivers were operating) at heights 11 For horizontal wind region have lower SNR, this means that SNR. Since most of the observations in this height wave Smalle signatures as small as measurements. Wave which would include about half of the available 10% in N Standard deviation of measured parameters as a function of SNR, and distribution of

Figure 9. Vertical profile of wind ( frequency. Dashed andintegration solid times, black respectively. lines show results for wind components, respectively, all measured using 0.2 s coherent integration. Fig. A1. SNR, for ESRAD usingrecords experiment covering the mode whole fca_150, month altitudes of April 11–13 km 2009). (based on 1 min data Fig. 9. in Fig. 1, andheights. corresponding The hodographs lowest for heightdirection the of of wind rotation the fluctuations of hodograph the between is wind 10 vector km marked with and by increasing 14 height. a km red circle and arrows show the