the thermal and dynamical state of the atmosphere during

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The thermal and dynamical state of the atmosphereduring polar mesosphere winter echoes

F.-J. Lübken, B. Strelnikov, M. Rapp, W. Singer, R. Latteck, A. Brattli, U.-P.Hoppe, M. Friedrich

To cite this version:F.-J. Lübken, B. Strelnikov, M. Rapp, W. Singer, R. Latteck, et al.. The thermal and dynamicalstate of the atmosphere during polar mesosphere winter echoes. Atmospheric Chemistry and Physics,European Geosciences Union, 2006, 6 (1), pp.13-24. �hal-00295815�

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Atmos. Chem. Phys., 6, 13–24, 2006www.atmos-chem-phys.org/acp/6/13/SRef-ID: 1680-7324/acp/2006-6-13European Geosciences Union

AtmosphericChemistry

and Physics

The thermal and dynamical state of the atmosphere during polarmesosphere winter echoes

F.-J. Lubken1, B. Strelnikov1, M. Rapp1, W. Singer1, R. Latteck1, A. Brattli 2, U.-P. Hoppe2, and M. Friedrich 3

1Leibniz Institute of Atmospheric Physics, Kuhlungsborn, Germany2Norwegian Defence Research Establishment (FFI), Kjeller, Norway3Institute of Communications Networks and Satellite Communications, Graz University of Technology, Austria

Received: 13 July 2005 – Published in Atmos. Chem. Phys. Discuss.: 29 August 2005Revised: 16 November 2005 – Accepted: 30 November 2005 – Published: 2 January 2006

Abstract. In January 2005, a total of 18 rockets werelaunched from the Andøya Rocket Range in Northern Nor-way (69◦ N) into strong VHF radar echoes called “PolarMesosphere Winter Echoes” (PMWE). The echoes were ob-served in the lower and middle mesosphere during large so-lar proton fluxes. In general, PMWE occur much more sel-dom compared to their summer counterparts PMSE (typicaloccurrence rates at 69◦ N are 1–3% vs. 80%, respectively).Our in-situ measurements by falling sphere, chaff, and in-strumented payloads provide detailed information about thethermal and dynamical state of the atmosphere and there-fore allow an unprecedented study of the background at-mosphere during PMWE. There are a number of indepen-dent observations indicating that neutral air turbulence hascaused PMWE. Ion density fluctuations show a turbulencespectrum within PMWE and no fluctuations outside. Tem-perature lapse rates close to the adiabatic gradient are ob-served in the vicinity of PMWE indicating persistent tur-bulent mixing. The spectral broadening of radar echoes isconsistent with turbulent velocity fluctuations. Turbulencealso explains the mean occurrence height of PMWE (∼68–75 km): viscosity increases rapidly with altitude and de-stroys any small scale fluctuations in the upper mesosphere,whereas electron densities are usually too low in the lowermesosphere to cause significant backscatter. The seasonalvariation of echoes in the lower mesosphere is in agreementwith a turbulence climatology derived from earlier sound-ing rocket flights. We have performed model calculations tostudy the radar backscatter from plasma fluctuations causedby neutral air turbulence. We find that volume reflectivitiesobserved during PMWE are in quantitative agreement withtheory. Apart from turbulence the most crucial requirement

Correspondence to:F.-J. Lubken([email protected])

for PMWE is a sufficiently large number of electrons, for ex-ample produced by solar proton events. We have studied thesensitivity of the radar echo strength on various parameters,most important electron number density and turbulence in-tensity. Our observational and theoretical considerations donot provide any evidence that charged aerosol particles areneeded to explain PMWE, in contrast to the summer echoeswhich owe their existence to charged ice particles.

1 Introduction

The existence and the properties of radar echoes can provideimportant information about the background atmosphere, forexample on winds and turbulence. It is therefore crucialto understand their physical origin. It has become clearin recent years that VHF radar echoes from the summermesopause region at mid and high latitudes are directlylinked to charged ice particles which implies that tempera-tures are lower than∼150 K. These radar echoes are called(polar) mesosphere summer echoes, (P)MSE, and were firstobserved in the late 1970’s (Czechowsky et al., 1979). Areview on observations and our current understanding ofPMSE has recently been published byRapp and Lubken(2004). Occasionally, strong radar echoes have also beenobserved in the winter mesosphere and were later called“polar mesosphere winter echoes”, PMWE (Czechowskyet al., 1979; Ecklund and Balsley, 1981; Kirkwood et al.,2002). Since atmospheric temperatures are generally muchtoo high in the winter mesosphere to allow the existenceof ice particles,Stebel et al.(2004) speculate that smallcharged aerosol particles (other than ice) are present and in-fluence the plasma such that radar echoes can occur. Thewinter echoes are much less frequent than their summer

© 2006 Author(s). This work is licensed under a Creative Commons License.

14 F.-J. Lubken et al.: Polar mesosphere winter echoes

Fig. 1. Volume reflectivityη detected by the ALWIN VHF radaron 20 January 2005, from 08:00–15:00 Universal Time (=09:00–16:00 local time). The vertical lines indicate launch times of fallingspheres. On the color scale we also give the backscatter power inrelative units (dB). The conversion fromη to dB is correct only at65 km. However, the error is small (<4 dB) in the height range50-80 km.

counterparts (occurrence rates of 1–3% and∼80%, respec-tively, at polar latitudes). This makes it extremely difficult toexperimentally determine their characteristics and to studythe physical processes involved. PMWE appear approxi-mately between 55 and 80 km with a maximum occurrencearound 68–75 km (see Zeller et al., 20051, for more de-tails). Nearly all of these echoes have been observed whenthe Sun photo-ionizes the mesosphere and when solar and/orgeomagnetic activity provides an additional source of elec-trons.

In January 2005 we launched a sequence of meteorologicaland instrumented rockets into PMWE at high latitudes. Con-sidering the very low occurrence rate of PMWE this oppor-tunity was due to very favorable circumstances. These newmeasurements provide unique information about the condi-tions in the neutral and charged atmosphere. In this paper wesummarize the temperature and wind measurements of themeteorological rockets (falling sphere and chaff) and providesome important results from the instrumented rockets. Wewill present observational and theoretical evidence that neu-tral air turbulence alone (i.e., without the presence of chargedaerosols) can create PMWE.

2 The ROMA/PMWE campaign

In January 2005 a series of rockets were launched from theAndøya Rocket Range (69◦) while the co-located ALWINVHF radar detected strong echoes in the mesosphere. This

1Zeller, O., Zecha, M., Bremer, J., Latteck, R., and Singer, W.:Mean characteristics of mesosphere winter echoes at mid and highlatitudes, J. Atmos. Solar Terr. Phys., submitted, 2005.

Table 1. Rockets launched during the ROMA/PMWE campaign in2005.

date time (UT) label

18 Jan. 11:36:30 RWMM01” 12:06:00 RWMM02” 12:36:00 RWFS03” 13:15:00 RWFS04” 13:58:00 RWCH05” 14:42:00 RWFS06” 15:31:00 RWFS07” 16:07:00 RWCH08” 16:54:00 RWFS09” 17:24:00 RWFS101)

” 17:57:00 RWCH11” 18:35:00 RWFS12

20 Jan. 08:46:00 RWFS13” 09:16:00 RWCH14” 11:00:00 RWFS15” 11:30:00 RWFS16” 12:19:00 RWFS17

21 Jan. 13:06:00 RWFS18

25 Jan. 01:30:00 RWFS19” 03:30:00 RWFS20” 05:30:00 RWFS21” 07:30:00 RWFS22

27 Jan. 12:22:00 RWFS23

RW = ROMA/Winter, FS = falling sphere, CH = chaffMM = Mini-Midas; 1) RWFS10 was a failure

campaign was part of a project called “Rocket borne Obser-vations in the Middle Atmosphere” (ROMA). The dates andtimes of rocket launches are listed in Table1. The ALWINradar is part of the ALOMAR observatory (Arctic lidar ob-servatory for middle atmosphere research) and is describedin more detail elsewhere (Latteck et al., 1999). The radaroperates at 53.5 MHz which corresponds to a Bragg scaleof `Br=λ/2∼3 m. The power-aperture product of the radaris 5.3·107 W·m2 and the two-way beam half-width is 2.55◦.Only the vertical beam is available during the winter period.In Fig. 1 the radar signal on 20 January 2005 is shown, whena series of 5 falling spheres were launched. A strong PMWEis observed with maximum backscattered power of more than24 dB above noise floor (volume reflectivity: 4·10−15/m.).Such strong backscatter is observed rather seldom with ourradar. The echoes come from an altitude range of roughly 55to 75 km, in agreement with typical occurrence heights.

In Fig. 2 typical profiles of volume reflectivity for winter(PMWE) and summer (PMSE) echoes are shown. As canbe seen from this figure the winter echoes are weaker andlower compared to summer (η∼10−15/m at 60–70 km, rela-tive to 10−12 at 82–90 km, respectively). In both cases theechoes have been integrated for approximately 1/2 h. As can

Atmos. Chem. Phys., 6, 13–24, 2006 www.atmos-chem-phys.org/acp/6/13/

F.-J. Lubken et al.: Polar mesosphere winter echoes 15

be seen from Fig.1 the echoes in the period shown in Fig.2are rather strong but can on occasion be significantly weaker.We found that typical PMWE strengths are on the order of10−16–10−15/m during our campaign.

A total of 17 falling spheres, 4 chaff, and 2 instrumentedrockets were launched from 18 to 27 January, most of them(12, 4, 2, respectively) during PMWE. On 25 and 27 January,i.e., during the last five rocket launches, the ALWIN radar didnot detect any PMWE.

We will present only the main idea of the various in-situexperiments since they have been described in more detailelsewhere (Widdel, 1990; Schmidlin, 1991; Lubken, 1999;Friedrich et al., 2004; Brattli et al., 20052). From the fallingsphere technique (FS), mass densities, temperatures, and hor-izontal winds from 95 to 35 km are derived using the decel-eration and horizontal deflection of an inflated Mylar spherewhich is transported to the lower thermosphere by a smallrocket. The altitude resolution is 1–5 km depending on thealtitude. The chaff technique relies on a foil cloud consist-ing of several thousand small aluminum strips slowly driftingthrough the atmosphere. This gives horizontal winds withmuch better resolution compared to FS, but in a rather lim-ited height range of typically 15–20 km.

Electron density profiles were measured using a rocketborne radio wave propagation experiment based on theFaraday rotation/differential absorption technique (see e.g.,Mechtly et al., 1967). Because of the large electron densityonly the higher frequency (3.883 MHz) yielded data, whereas1.3 MHz was already absorbed at the altitude where the an-tennas deployed.

Ion densities were measured using a positive ion probe(PIP) located in the front of each of the two instrumentedpayloads. An electric field in a spherical grid rejects elec-trons and collects positive ions with very high temporal andspatial resolution (2.44 kHz and<1 m, respectively). Meanion densities are consistent with electron densities obtainedfrom the wave propagation instrument.

It is obvious from the overall occurrence statistics ofPMWE that a sufficient number of free electrons is requiredfor these echoes. In wintertime these electrons come from so-lar radiation (as long as the Sun is above the horizon at meso-spheric altitudes) and from solar and geomagnetic activity.The latter sources completely dominate over solar radia-tion during disturbed conditions. During the ROMA/PMWEcampaign altitudes above 70 km were sunlit from∼07:00–15:00 UT (=08:00–16:00 LT). All PMWE observed duringour campaign appeared during this time of day. Furthermore,the GOES-11 satellite showed strong energetic proton fluxesin the period 17–21 January which were enhanced by about3 orders of magnitude compared to quiet conditions. In addi-

2Brattli, A., Hoppe, U.-P., Rapp, M., Lubken, F.-J., Singer, W.,et al.: In-situ measurements of plasma parameters within polarmesosphere winter echoes, Atmos. Chem. Phys. Discuss., to besubmitted, 2005.

10−18

10−16

10−14

10−12

50

55

60

65

70

75

80

85

90

95

100

Reflectivity η [m−1]

Hei

ght [

km]

20−Jan−200509:30−09:59

10−18

10−16

10−14

10−12

50

55

60

65

70

75

80

85

90

95

100

Reflectivity η [m−1]

Hei

ght [

km]

06−Jul−200412:46−13:10

Fig. 2. Volume reflectivities deduced from the ALWIN radarbackscatter power for a typical winter echo from 20 January 2005(left panel), and for a summer echo on 6 July 2004 (right panel). Inboth cases the radar signal was averaged for∼1/2 h.

tion, on 18 January we observed strong riometer absorptionat 38.2 MHz (∼3 dB) above our launch site and large fluc-tuations in magnetometer recordings both at Andenes andTromsø (6K-indices=54), indicating strong particle precipi-tation from the magnetosphere. Furthermore, on 20 Januarya very strong X-ray event of class X7.1 at 0.1–0.8 nm (corre-sponding to 7.1·10−4 W/m2) was observed by GOES-11. Wesummarize that the PMWE during our campaign occurredduring a period of strong solar and geomagnetic disturbanceleading to enhanced electron densities. This scenario sup-ports the observations byKirkwood et al.(2002), namely thatPMWE can occur only if the number density of free elec-trons, Ne, is sufficiently large. We will later demonstratein more detail the crucial importance ofNe for a quantita-tive understanding of PMWE and will use measured electronnumber densities to calculate volume reflectivities.

3 Experimental results

In Fig. 3 all 11 temperature profiles measured during PMWEare shown. We designate the launches on 18, 20, and 21January as PMWE launches, although during a few of theseflights the PMWE had just disappeared or was very weak.We also take into account that the horizontal distance be-tween the atmospheric volume measured by the radar (sound-ing vertically) and the falling spheres and chaff is typically30–50 km. There is a clear tendency in the profiles shownin Fig. 3 for a steep temperature gradient in the 50–70 kmheight range. In some cases the temperature gradient is closeto the adiabatic lapse rate. We argue that these steep gra-dients are an indication of turbulent mixing (see below for

www.atmos-chem-phys.org/acp/6/13/ Atmos. Chem. Phys., 6, 13–24, 2006


Fig. 3. Temperature profiles from falling spheres in the presence ofPMWE. Profiles from flights RWFSxx, xx=03, 04, 06, 07, 09, 12,13, 15, 16, 17, 18 are shown (see Table 1 for more details). Thedotted line shows the frost point temperature. The dashed-dottedline is the mean January temperature profile from the FS climatol-ogy of Lubken and von Zahn(1991). The dashed line indicates anadiabatic temperature lapse rate of 9.8 K/km.

more details). In Fig.3 we also show the mean tempera-ture profile for January from the climatology ofLubken andvon Zahn(1991), hereafter referred to as L&vZ. This cli-matology is based on FS measurements, i.e., on the sameexperimental technique as used here. The mean tempera-ture gradient at PMWE altitudes is significantly smaller inthe L&vZ-climatology compared to the measurements in ourcampaign. This indicates that the thermal structure duringour rocket flights was considerably different compared to theclimatological mean. We note, however, that the tempera-ture gradient in the L&vZ climatology is smaller (i.e., morenegative) in the 60–70 km altitude range, compared to aboveand below. Therefore, the atmosphere is closer to instabilityin this height range. It is important to note that the FS tech-nique is not influenced by the presence of aerosol particles(if there should be any) since they cannot exert a noticeabledrag on the sphere. In contrast, temperature profiles deducedfrom lidar measurements might be influenced by aerosols ashas been demonstrated, for example, inStebel et al.(2004)in their Figs. 3 and 4.

In Fig. 4 we show Richardson numbersRi=ω2B/(∂u/∂z)2

calculated from the falling sphere temperatures, and windsfrom chaff and falling sphere, respectively (ωB=Brunt-Vaisala frequency;u=mean horizontal wind). Since the al-titude resolution of the falling sphere winds is significantly

Fig. 4. Richardson number calculated from chaff winds (RWCH14)and falling sphere temperatures (RWFS17, solid line). Dashedline: same but using winds and temperatures from falling sphere(RWFS17). Note the change of scales for negativeRi numbers.The dotted vertical line indicatesRi=1/4. There is a time differenceof ∼3 h between the two rocket launches.

poorer compared to chaff, the wind shears are systemati-cally smaller and the Richardson number is larger. As canbe seen from Fig.4 the difference is typically one order ofmagnitude. This implies that FS winds have to be consid-ered with great care when identifying instability regions ashas been done inKirkwood et al.(2003). Richardson num-bers from chaff winds in Fig.4 are very structured and showlayers with small values indicating instability roughly above70 km. Unfortunately, the chaff profile does not cover theentire range of PMWE. Taking into account the limitationsabout FS winds mentioned above, we still see thatRi is verysmall (and even negative) at altitudes around 60 km. We willlater come back to a comparison ofRi with PMWE.

We have used a wavelet analysis to determine power spec-tral densities (PSD) of relative ion density fluctuations de-fined as1Ni= (Ni− 〈Ni〉) / 〈Ni〉, whereNi is ion numberdensity, and〈Ni〉 is a running mean ofNi over 6 rocketspin periods (Torrence and Compo, 1998; Strelnikov et al.,2003). Figure 5 shows two spectra from the downleg offlight RWMM01. One of the spectra is from an altituderange within PMWE (58.5–59.0 km), the other from outsidePMWE (68.0–68.5 km). Power spectral densities are muchlarger inside PMWE which implies large fluctuations. Thespectrum from inside PMWE shows a slope close tok−5/3,compatible with an inertial subrange of a Kolmogorov tur-bulence spectrum. On the other hand, the PSD from out-side PMWE is much smaller and “flat”, basically determinedby instrumental noise. The spectra from the second flight(RWMM02, not discussed here) show a similar characteristic



behavior. We note, though, that both flights are only 30 minapart, i. e., they are presumably launched into a single event.We conclude that spectra of ion density fluctuations are con-sistent with turbulence inside PMWE, and no turbulence out-side.

4 Theory of turbulent PMWE

The theory of coherent radar backscatter from a weakly ion-ized plasma is summarized inTatarskii(1961) and yields thefollowing expression for the volume reflectivity:

ηcoh= 8π2

(e2 Ne

2 ε◦ me c2

)2

· 8Ne(κ) (1)

wheree is the elementary charge,Ne is the mean electrondensity,ε◦ is the dielectric constant of vacuum,me is theelectron mass,c is the speed of light, and8Ne(κ) is thethree-dimensional power spectral density (PSD) of the rel-ative electron density fluctuations at the radar Bragg wavenumberκ=2 · (2π/λ)=2π/`Br . A general expression for8Ne was given byDriscoll and Kennedy(1985) and was laterapplied to in-situ measurements of neutral and electron den-sity fluctuations (Lubken et al., 1994; Giebeler, 1995). Atscales within the inertial subrange (and smaller) the follow-ing expression for the radar reflectivity was derived:

η = 16 · π2

(e2 Ne

2 ε◦ me c2

)2

Q9/2 A Nϑ ε−1/3η11/3Kol (2)

·

(y−11/3

+ y−3)

· exp

{−

α

Q2Sc

(3

2y4/3

+ y2)}

wherey=Q3/2· ηKol · k (k=wavenumber),ηKol=(ν3/ε)1/4

is the Kolmogorov micro scale,ν is the kinematic viscosityof air, ε is the turbulent energy dissipation rate,Nϑ is the dis-sipation rate of fluctuations, Sc=ν/D is the Schmidt number,D is the diffusivity of the tracer, andQ=2, A=0.033 · a2,a2

=1.74,α=0.83 are numerical constants. Further explana-tions on the quantities introduced in Eq. (2) are given in thereferences mentioned above and inLubken(1992). Note thatthe size of the aerosol particles enters through a reduced dif-fusivity, D, which increases the Schmidt numberSc=ν/D tovalues larger than unity. The normalization of8Ne in Eq. (2)is such that the integral of the PSD gives the total variance ofthe fluctuations:

〈ϑ′2〉 =

∞∫−∞

∞∫−∞

∞∫−∞

8Ne(k) dkx dky dkz (3)

In Fig. 6 we have plotted various cases of Eq. (2), keepingthe energy dissipation rate constant (ε=0.1 W/kg) and vary-ing Ne, Sc, andNϑ . A value of ε=0.1 W/kg was chosensince it is a moderate value and it is consistent with modelresults (Becker, 2004). As can be seen from Fig.6 the PSD

Fig. 5. Power spectral density of relative ion fluctuations as mea-sured by the PIP instrument during flight RWMM01. Upper panel:spectrum from an altitude range within PMWE. The straight lineindicates a−5/3 power law expected from classical turbulence the-ory. Lower panel: spectrum from an altitude range without PMWE.The prominent peaks in the spectra (dashed lines) are caused by thepayload spin frequency and its harmonics.

at 3 m varies strongly withNe and to a lesser extent withNϑ

and with Sc. We will discuss the sensitivity of the volumereflectivity in more detail below.

It is important to note that the “breaks” in the spectra inFig. 6 vary strongly with kinematic viscosity,ν ∝ 1/ρ, andtherefore with altitude. The scale corresponding to the breakis defined as (seeLubken, 1997):

`H◦ = 9.90 · ηKol = 9.90 ·

(ν3

ε

)1/4

(4)



Fig. 6. Volume reflectivity as a function of wave number for variouscases of electron densitiesNe, Schmidt number Sc, andNϑ . Stan-dard case (thick solid curve):Ne=1·1010/m3, Nϑ =1·10−5/s, andSc=1. Relative to the standard case the electron density has beendecreased by a factor of 10 (dotted line),Nϑ has been increased bya factor of 100 (dashed line), and the Schmidt number has been in-creased by a factor of 100 (thin solid line). The energy dissipationrate isε=0.1 W/kg and the kinematic viscosity isν=0.245 m2/s forall curves. The value forν is representative for an altitude of 70 km.The thin vertical line corresponds to the Bragg scale of the ALWINradar.

In Fig. 7 we show turbulent energy dissipation ratesε andthe corresponding heating rates (dT/dt) required to fulfill thecondition`H

◦ =`Br , which is a very rough criterion to allowturbulence producing substantial fluctuations for radar wavescatter. From Eq. (4) we see thatε∼ν3

∼1/ρ3, i.e., the re-quired turbulence intensity increases rapidly with altitude. Itis obvious from this plot that unrealistic strong turbulence(heating rates of up to 1 million K/d!) would be required toproduce fluctuations at VHF radar scales in the upper meso-sphere, whereas moderate or even small turbulence (heatingrates: 0.1–10 K/d) is sufficient in the lower mesosphere.

We have systematically studied the sensitivity of the vol-ume reflectivity,η, on electron number densities,Ne, turbu-lent energy dissipation rates,ε, Schmidt numbers, Sc, andon Nϑ . The variation ofη with N2

e comes from the factthat relative electron density fluctuations are considered inderiving Eqs. (1) and (2), whereas the radar signal comesfrom absoluteelectron number density fluctuations. We ar-gue that relative electron (and ion) density fluctuations cre-ated by neutral air turbulence are fairly similar in all casesof turbulence, whereas absolute electron density fluctuationscan vary substantially depending on the mean backgroundelectron density. This idea comes from the simple considera-tion that the “mixing ratio” of ions and electrons (relative toneutrals) is constant when an air parcel is moved vertically.Since the background gradient in the plasma is normally dif-

Fig. 7. Turbulent energy dissipation rates derived from the condi-tion `H

◦ =`Br (`Br=3 m) which is a very rough criterion to allowturbulence producing substantial fluctuations for radar wave scatter.The upper axis shows the corresponding heating rates calculatedfrom dT /dt=ε/cp (cp=heat capacity of air at constant pressure).

ferent from the neutral atmosphere, relative ion fluctuations(1Ni/Ni) are larger compared to neutrals (1n/n). Simplescale height considerations lead to the following relationship(seeThrane and Grandal, 1981, for more details):

1Ni

Ni

=1

F·1n

n; F =

γHp

Hn− 1

γHp

Hi− 1

(5)

whereHp, Hn andHi are the scale heights of pressure, neu-tral density, and ion density, respectively. Indeed, there havebeen several in-situ measurements of ion and electron num-ber densities during winter conditions which show fluctua-tions on the order of 1–5% (much larger than neutral airfluctuations) and conversion factors (1/F) of approximately5–10 (Thrane and Grandal, 1981; Thrane et al., 1985, 1994;Lubken et al., 1987, 1993; Blix et al., 1990a,b).

The quantityNϑ determines the total variability of thetracer, together withNe and ε. We have determinedNϑ

from our neutral air turbulence measurements in 12 sound-ing rocket flights and found typical values of 10−8 to10−6/s. From Eqs. (3) and (5) we see that for electronsthe quantityNϑ must be larger by a factor of approximately



Fig. 8. Upper panel: The sensitivity of the volume reflectivity at3 m to electron density and Schmidt number forε=0.1 W/kg andNϑ=1·10−5/s. Lower panel: Same, but for electron density and tur-bulent energy dissipation rate (Sc=1 ;Nϑ=1·10−5/s). A kinematicviscosity ofν=0.245 m2/s is used, representative for an altitude of70 km.

1/F 2∼25...100. We have therefore takenNϑ=1·10−5/s as

our standard case. This number is compatible with a directdetermination ofNϑ from a comparison of neutral air andplasma fluctuation spectra (Lubken et al., 1994; Giebeler,1995).

In Fig. 8 we show the volume reflectivityη3m calculatedfrom Eq. (2) at `Br=3 m. Note that we have used a kine-matic viscosity ofν=0.245 m2/s corresponding to an altitudeof 70 km. It is obvious from Fig.8 that η3m varies muchstronger with electron density than with Schmidt number.Furthermore, the intensity of turbulence (namelyε) playsan important role forη3m. On the other hand, weak turbu-lence can be compensated for by large electron number den-sities. For example, for a volume reflectivity ofη=10−15/m(typical for PMWE) a decrease ofε from 0.1 to 0.01 W/kg

Fig. 9. Electron density profiles measured by the Faraday tech-nique in flights RWMM01 and RWMM02 (thick red lines), prag-matically extended to larger and smaller altitudes (red dotted line).We also show a compilation of daytime electron density measure-ments from the Faraday technique from the auroral zone (thin lines)and a straight line representing “typical” electron densities duringdisturbed conditions (blue line, see text for more details).

can be compensated for by an increase ofNe from 4·109 to1·1011/m3. It is clear from Fig.8 that any speculation aboutthe presence of particles based on Schmidt numbers is onlymeaningful if accompanied by precise measurements of elec-tron number densities and turbulence.

We now apply the theoretical considerations from aboveto our measurements during the ROMA/PMWE campaign.In Fig. 9 the electron density profile measured by the Fara-day instrument during flights RWMM01 and RWMM02 areshown together with a simple analytical approximation andextrapolation to altitudes below and above the actual mea-surements. We also show in that figure a compilation of(possibly all ever measured) daytime electron density mea-surements from rocket borne wave propagation from the au-roral zone. The riometer absorption at the time of these mea-surements varied largely from 0 to 4.5 dB. Typical riometervalues during our salvo are 1.5–3.2 dB. The electron densi-ties measured during our PMWE campaign were indeed ex-ceptionally large, in fact the largest in the entire collection ofcomparable measurements, except for one profile observedat Ft. Churchill (59◦ N) during a polar cap absorption (PCA)event. The extended electron density profile from the Fara-day measurement during our campaign is used to determine



Fig. 10. Upper panel: Volume reflectivity at the ALWIN radarBragg scale for various turbulence strength, namelyε=0.001 (solid),=0.01 (dotted), =0.1 (dashed), and 1. (dashed-dotted). All values inW/kg. The electron density profile from the extended Faraday pro-file in Fig. 9 has been used. Lower panel: Same as upper panel butwith ‘typical’ electron profile from Fig.9. For all profiles we haveusedNϑ=1·10−5/s.

the volume reflectivity from Eq. (2) assuming very weak,weak, moderate, and strong turbulence (ε=0.001, 0.01, 0.1,and 1 W/kg, respectively), independent of altitude. It is im-portant to note that we have assumed that no aerosols andno negative ions are present in the atmosphere, i.e., Sc=1.The results are shown in Fig.10 (upper panel). As can beseen, moderate and even weak turbulence can produce a re-flectivity of 10−14–10−13/m which is even larger than typi-cal PMWE values (see Fig.2). We note, however, that theelectron densities are significantly larger compared to typi-cal disturbed conditions, and to MF and EISCAT measure-ments prior and after the flight (W. Singer, private commu-nication). We have sketched a more typical electron densityprofile during disturbed conditions in Fig.9 which is pre-sumably more representative for general PMWE conditions.The corresponding volume reflectivities are on the order of10−16–10−15/m (see Fig.10, lower panel), in close agree-ment with observations.

5 Discussion

The volume reflectivities shown in Fig.10 nicely agree withthe mean altitude statistics of PWME with a maximum ap-pearance around 70 km. Assuming that turbulence of variousstrengths occurs in the entire mesosphere, the height rangeof PMWE is limited by two effects. Firstly, viscosity is verylarge at higher altitudes and dampens all small-scale fluctu-ations. On the other hand, too few electrons are availablebelow 55 km to allow significant radar backscatter. We note,that the turbulence climatology presented inLubken(1997)shows rather small turbulence in the winter mesosphere withtypical ε values of 0.001–0.01 W/kg. Still, even for weakturbulence the volume reflectivity is large enough to result inPMWE, provided the electron densities are large enough. Weshould keep in mind that the compilation inLubken(1997) isbased on 12 flights only. It is conceivable that on occasionsturbulence can be stronger than in these flights. The maxi-mum volume reflectivity observed by the radar is in quantita-tive agreement with the estimates presented above assumingturbulence without aerosols.

The turbulence climatology published inLubken(1997)explains why no echoes are observed in the summer lowermesophere. In summer we have very seldom observed anyturbulence below 76 km in a total of 13 flights. The excep-tion comes from the flights in the summer of 2002 which,however, has been very special in terms of the general atmo-spheric circulation and wave activity (Goldberg et al., 2004;Becker et al., 2004; Rapp et al., 2004). At that time our radardid not yet cover the lower mesosphere, i. e., we don’t knowwhether an echo would have been observed. In the year 2004we have expanded the height coverage of our radar to 50–115 km but have not observed any echo from the lower sum-mer mesosphere since then.



The fact that PMWE are frequently observed once elec-tron densities are large enough indicates that the secondingredient, namely turbulence, is likely to persist in the lowerwinter mesosphere. Unfortunately, our experimental knowl-edge about mesospheric turbulence during winter is very lim-ited. Regarding modeling we refer to recent results on gravitywave saturation which indeed suggests the presence of turbu-lence in the lower winter mesosphere (Fritts and Alexander,2003; Becker, 2004).

There are several indications that turbulence was indeedpresent during PMWE. The PIP instrument detected small-scale fluctuations of positive ion densities which are a goodtracer for neutral air fluctuations. The spectra of thesefluctuations (Fig.5) clearly show strong fluctuations withturbulence spectral characteristics inside the PMWE layer,whereas fluctuations are basically absent outside the layer.

The near-adiabatic temperature profiles shown earlier in-dicate that turbulent mixing must have been present for asubstantial period. In Fig.11 we show the temperature pro-files from flights RWFS16 and RWFS17 together with theradar echoes during these flights. More precisely, the radarecho profiles averaged in a period of approximately 15 minaround the launch times are shown. There is a region of near-adiabatic lapse rates close to the PMWE layer. The slightmismatch in altitude by a few km can be explained by a smalltilt of the layers by∼0.1 km/km. We note that a steep tem-perature gradient is also present in the lidar profile shown inStebel et al.(2004) in the case that no aerosols are present(“Alternative 2” in their Fig. 4).

The apparent absence of radar echoes in the center of theturbulent layer during flight RWFS17 is in agreement withthe theory ofFritts et al.(2003) and has been observed forother tracers in the troposphere (see Fig. 5 in the Fritts etal. (2003) paper). The explanation of this effect is that per-sistent turbulent mixing destroys the background gradient ofthe tracer and thereby inhibits the generation of fluctuationseven if turbulence is still active.

Another indication for turbulence comes from theRichardson numbers in Fig.4 which indicate unstable re-gions (i.e.,Ri smaller as 1/4) at PMWE altitudes and above.In general, regions of PMWE seen in Fig.1 agree with theappearance of instability shown in Fig.4. For example,Ri

is very low in the 60–65 km altitude region, where strongradar echoes are observed. A one-to-one relationship cannotbe expected due to the patchy and intermittent character ofturbulence, the time constants of turbulence production anddestruction, and the horizontal difference between the radarvolume and the rocket probing volume. We note that recentmodel simulations of gravity wave breaking have shown thatturbulence can be generated even if the Richardson numberis significantly larger than unity (Achatz and Schmitz, 2006).

Further evidence for turbulence at PMWE altitudes comesfrom the spectral width of the radar echo shown in Fig.12.Large spectral broadening corresponding to velocity fluctu-ations of up toσobs∼10 m/s are observed within PMWE.

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We hesitate to convert these values to turbulence param-eters since part of the observed broadening might be dueto instrumental effects such as beam and shear broaden-ing (Hocking, 1983). We have used a typical horizontalwind speed from our falling sphere flights of v∼60 m/s toroughly estimate the instrumental broadening and arrive at

σinstr∼v· sin(2.55◦)∼2.7 m/s. Usingσturb=

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leads to somewhat smaller turbulent broadening,σturb. How-ever, a significant part of the observed broadening is causedby atmospheric velocity fluctuations presumably caused byturbulence. We note that we cannot study the aspect sensitiv-ity of backscatter since only the vertical beam was in opera-tion during the campaign.

Our falling sphere temperature measurements clearlyshow that the atmospheric temperature is much larger than



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the frost point temperature (by more than 50 K). In otherwords, it is much too warm to allow the existence of wa-ter ice particles. The question remains whether other ‘large’charged aerosols are present which could influence the radarbackscatter. The observations and the theoretical considera-tions presented above did not give any evidence for aerosols.Contrary to the summer mesopause region, aerosols are notneeded to explain the winter echoes. On the other hand,from our measurements we cannot positively exclude thataerosols are present. Certainly, they cannot be large (ra-dius larger than 20–30 nm) because they would then causea significant enhancement in the lidar signal. Schmidt num-bers significantly larger than unity indicate the presence ofcharged aerosols and have indeed been determined from in-situ measurements of neutral and plasma fluctuations in thevicinity of summer echoes (Lubken et al., 1994). Similar at-tempts would be rather difficult for the winter echoes sincethe Schmidt number is presumably much smaller than insummer because aerosols are smaller (see above).

We note that the presence of a sufficiently large numberof negative ions will take care of the charge balance withpositive ions and will thereby enhance the mobility of freeelectrons (Stebel et al., 2004; Hill , 1978). This would lead toSchmidt numbers smaller than one. We have not consideredthis case since daylight and particle precipitation inhibits theattachment of electrons to form negative ions. Whether or nota sufficient number of negative ions can form during nightunder geomagnetic disturbed conditions is not yet clear. Wenote, that no electron or negative ion density measurementshave been performed during night in the presence of PMWE.

Apart from turbulence the most crucial requirement forPMWE is a sufficiently large electron number density. Dur-ing disturbed conditions precipitating particles from the Sunor from the Earth’s magnetosphere create electron numberdensities which can be orders of magnitude larger compared

to normal conditions. During night part of these electronsare attached to neutrals to form negative ions. These elec-trons are immediately detached by solar radiation once theSun rises or when proton/electron precipitation occurs. Thisexplains why PMWE are almost exclusively observed dur-ing the day and during strong disturbance, such as solar pro-ton events. On the other hand, a typical value forNe dur-ing undisturbed conditions in the winter lower mesosphereduring daytime is 108/m3, i.e., two orders of magnitude less

than during disturbed conditions. Sinceη ∼ Ne2

this im-plies that PMWE should be smaller by 40 dB, assuming allother parameters to be unchanged. This is much too smallto be detectable by our radar. From Fig.9 we see that elec-tron densities can vary by several orders of magnitude de-pending on the source strength (solar/geomagnetic) and onother factors involving ion-chemistry and photo-chemistry.The sources and sinks cannot be modeled accurately enoughto predict the electron profile for all conditions with suffi-cient accuracy. Therefore, a precise theoretical prediction ofvolume reflectivity from turbulence requires a precise mea-surement of electron number densities, e.g. by the Faradayrotation technique.

6 Summary and conclusions

Various experimental observations support the idea thatPMWE during the ROMA/PMWE campaign are caused byneutral turbulence, namely

– The spectrum of ion density fluctuations shows turbu-lence like characteristics within PMWE, and no fluctu-ations outside PMWE.

– Persistent steep temperature gradients close to the adi-abatic lapse rate in the vicinity of the PMWE layer in-dicate turbulent mixing. In one case we observe a textbook example of fluctuations at the edges of the turbu-lent layer in agreement with theory.

– Temperature measurements from FS and high resolutionwind measurements by chaff show very low Richardsonnumbers indicating instability.

– Spectral broadening of the VHF signal indicates veloc-ity fluctuations of several m/s, presumably due to turbu-lence.

– Turbulence explains the general altitude dependence ofPMWE with a maximum around 70 km (too large vis-cosity above 80 km and too few electrons below 60 km).

– Volume reflectivities calculated from turbulence theoryagrees quantitatively with observations.

– The seasonal variation of turbulence explains the non-existence of echoes in the summer lower mesosphere.



We have based our general considerations about turbulentPMWE on as many measurements of turbulent parametersas available, in particular regardingε andNϑ . Other studieshinge on uncertain estimates of ‘constants’ which are onlypoorly known and further suffer from idealistic assumptionsof turbulence generation etc. Since this leads to uncertain-ties in the calculated volume reflectivities of several ordersof magnitude, a relatively small discrepancy between mea-sured and theoretical values ofη cannot be used to rule outturbulence as a cause of PMWE.

Our observations and theoretical considerations show thataerosols are not needed to explain PMWE (as opposed tosummer echoes). On the other hand, we cannot positively ex-clude their existence from our data as long as they are smallerthan∼20 nm. We have stated earlier that any speculationabout the presence of aerosols based on Schmidt numbers isonly meaningful if accompanied by precise measurements ofelectron number density and turbulence. Since Sc is smalland PMWE occurrence is low, this will be a very difficulttask. It is presumably easier to detect these particles directlyby in-situ techniques as is planned in several projects in thenear future.

Acknowledgements.We thank M. Zecha for providing importantinformation on the mean characteristics of PMWE. We are gratefulto the staff of Andøya Rocket Range and DLR-MORABA for theirprofessional launch services. U.-P. Hoppe and A. Brattli thankS. Olsen and T. Tønnesen, University of Tromsø, for their efficientassistance with the PIP hardware. The radar experiments receivedfunding from the EU 6th framework programme project ALOMAReARI. This project was supported by the Bundesministerium furBildung, Wissenschaft, Forschung und Technologie, Bonn, undergrant 50 OE 99 01.

Edited by: W. Ward

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