Piccialli-2012.Pdf

Icarus 217 (2012) 669–681

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Icarus

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Dynamical properties of the Venus mesosphere from the radio-occultation experiment VeRa onboard Venus Express ⇑ A. Piccialli a,c, , S. Tellmann b, D.V. Titov a,c, S.S. Limaye d, I.V. Khatuntsev e, M. Pätzold b, B. Häusler f a Max Planck Institute for Solar System Research, Max Planck Strasse 2, 37191 Katlenburg-Lindau, Germany b Institut für Geophysik und Meteorologie, Universität zu Köln, Albertus-Magnus-Platz, D-50923 Köln, Germany c ESA, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands d Space Science and Engineering Center, University of Wisconsin-Madison, 1225 West Dayton Street Madison, WI 53715, USA e Space Research Institute, Russian Academy of Sciences, Profsoyuznaya ul. 84/32, Moscow 117997, Russia f Institut für Raumfahrttechnik, Universität der Bundeswehr München, D-85577 Neubiberg, Germany article info abstract

Article history: The dynamics of Venus’ mesosphere (60–100 km altitude) was investigated using data acquired by the Available online 5 August 2011 radio-occultation experiment VeRa on board Venus Express. VeRa provides vertical profiles of density, temperature and pressure between 40 and 90 km of altitude with a vertical resolution of few hundred Keyword: meters of both the Northern and Southern hemisphere. Pressure and temperature vertical profiles were Venus used to derive zonal winds by applying an approximation of the Navier–Stokes equation, the cyclostroph- Atmospheres, dynamics ic balance, which applies well on slowly rotating planets with fast zonal winds, like Venus and Titan. The Radio observations main features of the retrieved winds are a midlatitude jet with a maximum speed up to 140 ± 15 m s1 which extends between 20°S and 50°S latitude at 70 km altitude and a decrease of wind speed with increasing height above the jet. Cyclostrophic winds show satisfactory agreement with the cloud-tracked winds derived from the Venus Monitoring Camera (VMC/VEx) UV images, although a disagreement is observed at the equator and near the pole due to the breakdown of the cyclostrophic approximation. Knowledge of both temperature and wind fields allowed us to study the stability of the atmosphere with respect to convection and turbulence. The Richardson number Ri was evaluated from zonal field of measured temperatures and thermal winds. The atmosphere is characterised by a low value of Richardson number from 45 km up to 60 km altitude at all latitudes that corresponds to the lower and middle cloud layer indicating an almost adiabatic atmosphere. A high value of Richardson number was found in the region of the midlatitude jet indicating a highly stable atmosphere. The necessary condition for barotropic instability was verified: it is satisfied on the poleward side of the midlatitude jet, indicating the possible presence of wave instability. Ó 2011 Elsevier Inc. All rights reserved.

1. Introduction surface and reaching a maximum value of 100 m s1 at cloud top, corresponding to a rotation period of 4 Earth days (60 times Venus’ mesosphere (60–100 km altitude) is a transition region faster than Venus itself). The processes responsible for maintaining characterised by an extremely complex dynamic: strong retro- the zonal super-rotation in the lower atmosphere and its transition grade zonal winds dominate in the troposphere and lower meso- to the solar–antisolar circulation in the upper atmosphere are still sphere while a solar–antisolar circulation can be observed in the unknown (Schubert, 1983; Gierasch et al., 1997; Limaye, 2007; upper mesosphere. Tracking of the UV markings, descent probes, Schubert et al., 2007). and Vega balloon trajectories (Schubert et al., 2007) all showed Different techniques have been used to obtain direct observa- that the super-rotation extends from the surface up to the cloud tions of wind at various altitudes: tracking of clouds in ultraviolet top with wind speeds of only few meter per second near the (365 nm) and near infrared (980 nm) images can give information on the wind speed at the cloud top (70 km altitude) (Rossow et al., 1990; Limaye, 2007; Sánchez-Lavega et al., 2008; Moissl ⇑ Corresponding author. Present address: ESA, ESTEC, Keplerlaan 1, 2201 AZ et al., 2009) and within the clouds (47 km, 61 km) (Sánchez- Noordwijk, The Netherlands. Fax: +31 (0) 71 565 4697. Lavega et al., 2008) while ground-based measurements of Doppler E-mail addresses: [email protected] (A. Piccialli), [email protected] shift in CO2 band at 10 lm(Sornig et al., 2008) and in several CO (S. Tellmann), [email protected] (D.V. Titov), [email protected] (S.S. Limaye), millimeter lines (Rengel et al., 2008) provide wind speeds above [email protected] (I.V. Khatuntsev), [email protected] (M. Pätzold), Bernd. [email protected] (B. Häusler). the clouds up to 110 km of altitude. In the mesosphere (60–

100 km altitude), at altitudes where direct observations of wind The stability of the atmosphere with respect to convection and tur- are not possible, the only way to characterise the circulation is to bulence was analysed using knowledge of both temperature and derive zonal wind field from the vertical thermal structure using wind fields. a special approximation of the Navier–Stokes equation: the cyclostrophic balance. Earlier studies (Leovy, 1973; Schubert, 1983) have 2. Mesospheric thermal structure from VeRa radio-occultation shown that on slowly rotating planets, like Venus and Titan, strong sounding zonal winds at the cloud top can be assumed to be in cyclostrophic balance in which equatorward component of centrifugal force is The Venus Express Radio Science Experiment VeRa uses one- balanced by meridional pressure gradient. This equation gives a way radio carrier signals at two coherent frequencies (X-band at possibility to reconstruct the zonal wind if the thermal structure 8.4 GHz and S-band at 2.3 GHz) for the radio sounding of the ion- is known. osphere and the neutral atmosphere of the planet received at the The temperature structure of the middle atmosphere of Venus ground station with the closed loop receiver system (Häusler was observed remotely by thermal emission spectrometry and et al., 2006, for details). Open loop data require further investiga- radio occultation experiment on board Pioneer Venus and tion and were not used for this study (Tellmann et al., 2009). An Venera-15 orbiters (Seiff, 1983; Taylor et al., 1983; Lellouch Ultrastable Oscillator (USO) provides an on board reference source et al., 1997; Zasova et al., 2007). Two prominent features of the with a relative frequency stability of 1013. The measurements temperature field were observed: an increase of temperature from are performed during so-called ‘‘Earth occultation’’ opportunities. equator to pole above 70 km altitude, known as the ‘‘warm polar As seen from the Earth, the spacecraft disappears behind the plan- mesosphere’’, and an inversion in the vertical temperature profiles etary disk and emerges on the opposite limb of the planet. The around 65° latitude at the cloud top (65 km altitude), known as radio signal propagates through the ionosphere and the neutral the ‘‘cold collar’’. atmosphere of the planet during the entry (‘‘ingress’’) and the exit The mesospheric temperature field retrieved from the Pioneer (‘‘egress’’) phases of the occultation event. The propagation direc- Venus (Taylor et al., 1983), Venera-15 (Zasova et al., 2007) and tional path of the radio link bends in response to the local gradient Galileo (Roos-Serote et al., 1995) radiance measurements has been of the refractive index while the radio beam slices through the alti- used to derive the cyclostrophic wind (Limaye, 1985; Roos-Serote tude regions of the planetary ionosphere and atmosphere. This et al., 1995; Zasova et al., 2007). In most case the zonal wind exhib- causes a corresponding frequency shift of the radio carrier signal its a strong midlatitude jet centered around 50° latitude with a on ground. The data used here were recorded at the ground station 1 maximum speed ranging from 110 m s (Zasova et al., 2000) in the closed loop receiver technique with a sample rate of 1 sam- 1 to 160 m s (Newman et al., 1984); a decline of the wind speed ple/s (Häusler et al., 2006). The standard retrieval method for radio with altitude above the jet is also observed. Although the cyclos- occultations is based on geometrical optics assuming spherical trophic balance seems to clearly describe the observed state of symmetry. The resulting profiles of the bending angle and the Venus super-rotation showing that winds are tightly coupled to ray periapsis is used to retrieve refractivity profiles l(h) as a func- temperature field, it does not explain neither what originally tion of altitude h via an inverse Abel transform (Fjeldbo et al., brought the atmosphere to this state, nor which mechanisms 1971). Below 100 km the planetary neutral atmosphere dominates maintain the vertical wind shear. the effect on the radio signal. The neutral number density profile After a pause of more than a decade, Venus atmosphere is being n(h) is directly proportional to the refractivity explored again: the first European mission to the planet Venus, Ve- nus Express (VEx), is acquiring new data since 2006 (Svedhem lðhÞ¼C1 nðhÞk ð1Þ et al., 2007, 2009; Titov et al., 2009). Venus Express payload is where k is the Boltzmann constant and C is a constant factor especially very well suited for atmospheric studies with a special 1 depending on the composition of the atmosphere (for details see regard to atmospheric dynamics and circulation: atmospheric Tellmann et al., 2009). Temperature profiles T(h) are derived assum- dynamics is investigated by observing clouds at different levels ing hydrostatic equilibrium from (Eshleman, 1973; Jenkins et al., and by deriving zonal winds from thermal profiles (Svedhem 1994; Ahmad and Tyler, 1997): et al., 2009). The quasi-polar orbit of the spacecraft provides a com- Z plete latitudinal coverage and gives the best compromise for allow- hup lup m 0 0 0 ing both high-resolution observations near pericenter and global TðhÞ¼ Tup þ nðh Þgðh Þdh ð2Þ lðhÞ k nðhÞ h observations during the apoapse part of the orbit (Titov et al., 2006). Two experiments on board the European Venus Express where the mean molecular mass of the atmosphere is given by (VEx) orbiter are sounding the thermal structure of the Venus m ; gðhÞ represents the altitude dependent acceleration of gravity mesosphere: the Visible and Infrared Thermal Imaging Spectrome- (Lipa and Tyler, 1979). The integration constant Tup for the temper- ter (VIRTIS) provides vertical temperature profiles of the Venus ature at the upper end at 100 km of the sensible atmosphere has to

Southern hemisphere in the altitude range 65–90 km with a very be estimated. Usually, the values Tup = 170 K, 200 K and 230 K are good spatial and temporal coverage (Drossart et al., 2007; Grassi chosen. Typically, the influence of the selected boundary value is et al., 2008, 2010). The radio science experiment (VeRa) probes negligible below an altitude of approx. 90 km (Tellmann et al., both north and south hemispheres to derive vertical profiles of 2009). The pressure profile is derived from the temperature and density, temperature and pressure between 40–90 km of altitude the neutral number density by using the ideal gas law. The VeRa with a vertical resolution of 500 m (Häusler et al., 2006; Tell- profiles cover the altitude range between approx. 90 and 40 km mann et al., 2009). In addition, the Venus Monitoring Camera with a vertical resolution of only few hundred meters (500 m). (VMC) acquires ultraviolet (UV) images used for direct measure- The uncertainties in the retrieved profiles decrease with decreasing ments of wind speed by cloud-tracking (Markiewicz et al., 2007; altitude and are in the order of a fraction of a Kelvin in the temper- Moissl et al., 2009). VEx gives for the first time the opportunity ature profile at the lowest detectable levels (40 km). A more de- to verify the cyclostrophic hypothesis by comparing cloud-tracked tailed description of error analysis can be found in Tellmann et al. and balanced zonal winds. Here we present retrievals of the cyclos- (2009), Appendix B. More than 280 profiles of the ionosphere and trophic wind in Venus mesosphere derived from VeRa/VEx thermal the neutral atmosphere were retrieved during the nominal and first soundings (Tellmann et al., 2009) and their comparison to the extended mission of Venus Express. First results can be found in cloud-tracked winds to validate the cyclostrophic assumption. Pätzold et al. (2007, 2008) and Tellmann et al. (2009). A. Piccialli et al. / Icarus 217 (2012) 669–681 671

For this work 116 temperature and pressure profiles were used, 3. Wind retrievals they were acquired between December 2006 and January 2009. The highly elliptical polar orbit of Venus Express allows to cover al- 3.1. Retrieval method most all latitudes and local times. Profiles were selected in order to have a complete latitudinal coverage of the Southern hemisphere; Leovy (1973) first noticed that the strong zonal winds in Venus’ measurements in the Northern hemisphere are mainly constrained mesosphere are well described by the cyclostrophic approxima- to high latitudes. Comparison between temperature profiles tion. Cyclostrophic balance is a special approximation of the acquired in the Northern and Southern hemisphere shows that Navier–Stokes equation which applies well on slowly rotating observations taken in the two hemispheres are very similar. There- planets with fast zonal winds, like Venus and Titan. It allows one fore, hereinafter hemispheric symmetry will be assumed. Different to neglect the Coriolis force and the role of eddies and turbulent local times are covered ranging from late night (0:00 h) to early motions, and assumes the balance between the equatorward com- morning (10:00 h). Temperature profiles do not show any signifi- ponent of the centrifugal force and the meridional pressure gradi- cative trend due to local time. A lack of full local time coverage pre- ent force (Eq. (3)): cludes a complete analysis of diurnal variations. u2 tan / 1 @p Individual profiles were interpolated to a standard pressure grid ¼ ð3Þ chosen to retain as much detail of the original data set as possible. r q @y Each vertical temperature profile is spread over a latitude and lon- where / is latitude, u is zonal wind velocity in m s1, r is radius of gitude interval up to 8°. Generally, the latitudinal coverage of each the planet, q is density, p is pressure and y is poleward Cartesian vertical temperature profile is retained, however, in order to plot coordinate. contours of temperature field a nominal location for temperature If, as in the case of the radio-occultation experiment, the verti- profiles is taken at the pressure level of 1 bar. cal pressure profiles p(y) can be measured, then the zonal wind Figs. 1 and 2 show examples of several typical temperature pro- speed can be derived directly by the equation: files at different locations and the latitude-altitude temperature g @z field retrieved from VeRa observations. Data from Northern and u2 ¼ ð4Þ Southern hemispheres and for all local times were considered. tan / @/ p Observations are in a very good agreement with previous radio occultation measurements (Newman et al., 1984). The main fea- obtained from Eq. (3). Eq. (4) was first used by Limaye (1985) to de- tures which can be observed in the temperature structure are the rive zonal wind directly from meridional slope of pressure surfaces. cold collar and the warm polar mesosphere. Altitude pressure profiles retrieved by VeRa were used to derive zonal wind velocities using Eq. (4). The meridional gradient of the 0.1 height of the pressure surfaces has been evaluated by binning 90 height profiles to a 5° latitudinal grid and then by smoothing over 1.0 10° latitude intervals (Fig. 3). 80 Fig. 4 shows the meridional cross section of the meridional gra-

dient of the height of isobaric surfaces @z/@/jp=const. At locations 10.0 70 where the gradient is positive (represented in grey in Fig. 4) the right hand side term in Eq. (4) becomes negative thus precluding 100.0 60 the computation of the cyclostrophic wind. This can be seen espe- Pressure, [mbar] cially at low latitudes, as observed also by Limaye (1985). Uncer- Approx. altitude, [km] 50 1000.0 tainties on the gradient due to scatter in the pressure profiles were qualitatively calculated. Regions of positive gradient seem 150 200 250 300 350 400 not to be significantly affected. However, due to the increasing of Temperature, [K] uncertainties on pressure profiles with increasing altitude, only gross features should be taken in account above 1 mbar. Fig. 1. Vertical temperature profiles at four different latitudes: (black) 7°S; (blue) 33°S; (green) 68°S; (red) 85°S. Error bars showing the noise of the measurements Eq. (3) can also be re-written in a form that directly relates the were added to one of the profiles. zonal wind speed u(z) to the vertical temperature structure T(y). We have followed the same method used by Newman et al. (1984) to derive from Eq. (3) the thermal wind equation (Eq. (5)): 1 @u R @T 2u ¼ ð5Þ 190. 80 @n tan / @/ p¼const

1 10 200. 210. where u is the zonal wind speed in m s , n = lnp/pref is the loga- 240. 220. 70 rithmic pressure vertical coordinate, R is the gas constant and 230. (@T/@/)p=const is the latitudinal temperature gradient. Eq. (5) gives a possibility to reconstruct the zonal wind u directly from temper- 100 250. 300. 60 230. 260. ature retrievals, together with a suitable boundary condition on u. Pressure, [mbar] 280.320. 260. Since Eq. (4) does not require a lower boundary velocity, compari-

280. Approx. Altitude [Km] son between zonal wind fields obtained from both retrieval meth- 340. 320. 50 1000 360. 340. 380. 360. ods allows to test the sensitivity of the zonal wind derived from -20 -30 -40 -50 -60 -70 -80 Eq. (5) on the choice of the lower boundary condition. Latitude, [deg] Fig. 5 shows examples of latitude dependence of temperatures at constant pressure levels. The fitting curves used to evaluate the latitudinal temperature gradient are also shown in this figure. Fig. 2. Meridional cross section of atmospheric temperature (K) obtained combin- In order to determine the fitting curves, the retrieved temperatures ing 116 VeRa profiles. Hemispherical symmetry and local time independence has been assumed. Contours have been smoothed. Contours interval is 10 K, some were first binned to a 5° latitudinal grid and then smoothed over contours have been removed to render the plot clearer. 10° latitude intervals. 672 A. Piccialli et al. / Icarus 217 (2012) 669–681

Pressure level: 4 mbar Pressure level: 20 mbar 81 73

80 72

79 71 Height, [km] Height, [km] 78 70

77 69 0 -20 -40 -60 -80 0 -20 -40 -60 -80 Latitude, [deg] Latitude, [deg] Pressure level: 40 mbar Pressure level: 90 mbar 70

65 69

64 68

63 67 Height, [km] Height, [km]

66 62

0 -20 -40 -60 -80 0 -20 -40 -60 -80 Latitude, [deg] Latitude, [deg] Pressure level: 200 mbar Pressure level: 500 mbar 56 61 55 60

54 59 Height, [km] Height, [km]

58 53

0 -20 -40 -60 -80 0 -20 -40 -60 -80 Latitude, [deg] Latitude, [deg]

Fig. 3. Altitude of constant pressure levels as function of latitude derived from VeRa radio occultation. Fitting curves are also shown (red line). (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

From Eq. (5) it is possible to observe that generally an increase

0.1 -50. (decrease) of temperature towards the pole corresponds to a de- 50. crease (increase) of zonal wind speed with height. Hence, solving

-50. Eq. (5), we expect an increase of zonal wind in the altitude region 0. 1.0 0. -100. -50. -100. 200–30 mbar enhanced by the negative latitudinal temperature gradient in the latitude range 30–65°S and a deceleration of wind above 20 mbar as a result of the warm polar mesosphere. The ref- 10.0 erence pressure p was ﬁxed at 1700 mbar (45 km altitude) and -200. -250. -150. ref -150. the velocity used as the lower boundary condition is the cloud- -250. tracked wind proﬁle retrieved from VIRTIS/VEx 1.74 lm images

Pressure, [mbar] 100.0 -100. corresponding to a nominal altitude of 47 km (Sánchez-Lavega -50. -200. et al., 2008). -50. 1000.0 0. 3.2. Balanced zonal ﬂow -20 -40 -60 -80 Latitude, [deg.] Assuming cyclostrophic balance, zonal wind (Fig. 6) was derived from the latitudinal gradient of the height of pressure sur- Fig. 4. Contours of the latitudinal gradient of the height of the isobaric surfaces 1 1 1 1 faces in Fig. 3. Vertical wind shear du/dn was also calculated @z/@/jp=const (10 m rad ). Contour interval is 50 10 m rad . Regions of positive values of @z/@/jp=const are represented in grey. (Fig. 7). As can be seen in Fig. 6, the main feature of the wind ﬁeld A. Piccialli et al. / Icarus 217 (2012) 669–681 673

Pressure level: 4 mbar Pressure level: 20 mbar

230 240 220

210 230

200 220 190

180 210

0 -20 -40 -60 -80 0 -20 -40 -60 -80

Pressure level: 40 mbar Pressure level: 90 mbar 250 250

240 240

230 230 220 Temperature [K]

220 210

200

0 -20 -40 -60 -80 0 -20 -40 -60 -80

Pressure level: 200 mbar Pressure level: 500 mbar 270 310

260 300

250 290

240 280

230 270

220 0 -20 -40 -60 -80 0 -20 -40 -60 -80 Latitude, [deg.]

Fig. 5. Atmospheric temperature at constant pressure levels as function of latitude. Fitting curves are also shown (solid lines). is a midlatitude jet with a maximum speed of 140 m s1 centred greater altitudes (65–70 km) at midlatitudes (25–60°S) com- at an altitude of 68 km and extending between 50°S and 20°S pared to higher and lower latitudes. latitude. Although the cyclostrophic approximation may be mathemati- The zonal wind field derived from VeRa temperature profiles cally valid, it should be pointed out that for latitudes lower than (Fig. 5) using Eq. (5) is also shown in Fig. 8. 20° and higher than 80°, where a highly variable polar vortex The main features of the cyclostrophic wind are reproduced in is observed, other forces, such as eddies, waves and turbulent mo- good agreement with the zonal wind derived from Eq. (4). A mid- tions, may play a more important role in the original Navier–Stokes latitude jet is clearly evident at the cloud top with a maximum equation and thus preclude the cyclostrophic balance from giving a speed of 140 m s1; the jet extends from 30° to 55°S latitude. reliable description of the zonal circulation. Applying Eq. (5), the jet is directly calculated from the negative latitudinal temperature gradient observed in the altitude range 50– 3.3. Uncertainties in wind speeds 65 km which produces a positive wind shear in the same altitude range (Fig. 7). Above 70 km of altitude, the negative vertical wind A qualitative analysis has been done to determine uncertainties shear, which forces the wind to decrease to zero at high latitudes in the derived wind speeds; we followed the same approach of above the midlatitude jet, is the result of a positive latitudinal tem- Newman et al. (1984). The main source of uncertainties on wind perature gradient (Eq. (5)). The positive wind shear layer reaches speed is due to scatter in temperature profiles, therefore we have 674 A. Piccialli et al. / Icarus 217 (2012) 669–681

1 Pressure level: 90 mbar 80. 60.70. 40. 130. 90. 80. 70. 80 100. 90. 100. 50. 110. 60. 250 120. 110. 10 120. 70 240 230 130. 100 100. 60 110. 220

Pressure, [mbar] 90. 80. 70. Temperature, [k]

Approx. Altitude, [Km] 210 80. 60. 50. 40. 50 1000 100. 90. 10. 20. 30. 200 -20 -30 -40 -50 -60 -70 -80 0 -20 -40 -60 -80 Latitude, [deg.] Latitude, [deg]

Fig. 6. Latitude–height cross section of zonal wind speed (m s1) derived from VeRa Fig. 9. Plot of temperatures vs latitudes at a pressure level of 90 mbar. The ﬁtting vertical pressure proﬁles assuming cyclostrophic balance (Eq. (4)). Contour interval curve is represented in black together with ±1r,±2r curves. is 10 m s1.

Zonal wind speeds have been derived from ±1r and ±2r curves 1 to determine the error in wind velocity. For all cases, the position -10. 80 of the jet is not changed within 5° latitude. The wind speed re- 1 -20. -30. trieved from curve 1r show a max jet velocity of 137 m s at

-10. 10 -10. -20. 42° latitude. Wind ﬁeld obtained from curve 1r has a jet speed 0. 70 of 151 m s1 at 42°. Jets for curves ±2r present a speed of -10. 1 1 10. 0. 129 m s at 47° and 157 m s at 38° respectively. It seems thus reasonable to assume as uncertainty in the derived wind ﬁeld an 100 10. 60 1 20. 30. error of ±15 m s . -20. Pressure, [mbar] 20. 10. 10.

30. 20. Approx. Altitude, [Km] -10. 0. 10. 10. -10.-20. 10. 0.-10.-50.-40. -10. 50 3.4. Sensitivity to the lower boundary condition 1000 -30.-10.-30. 10. 0. 10. -50.-40. -30. 20. 10. 30. 20.-50. 0.-40. -20. 10. 30. 20. 0. 20.30. 0. -20 -30 -40 -50 -60 -70 -80 The sensitivity of the zonal wind derived from Eq. (5) to the Latitude, [deg.] lower boundary condition has been analysed: zonal wind has been calculated using four different lower boundary conditions (Fig. 10); Fig. 7. Contours of vertical wind shear du/dn (m s1). Negative shear regions are winds derived from Pioneer Venus entry probes at an altitude of 1 represented in grey. Contour interval is 10 m s . 45 km are also included for comparison. In Fig. 11 we plotted for better clarity the difference between the zonal wind obtained from VeRa temperature proﬁles using VIR-

50. TIS cloud-tracking wind as lower boundary condition and that 1 60. 70. 70. 30. 20. 60. 50. 40. 10. derived using respectively the solid body rotation function: 80. 80 1 90.100. 110. u0 = u0(/ = 0)cos/ where u0(/ = 0) = 20, 40, 60 m s (Fig. 11A–C).

80. Winds appear to be only slightly dependent on the choice of the 120. 10 90. base wind: as can be observed in Fig. 11 a maximum difference of 70 30 m s1 occurs for all cases at high altitudes due to the strong de-

120. 130. crease of wind. In the region of the midlatitude jet (42° latitude) a 1 100 110. maximum difference of 15 m s can be seen, showing that the 90. 100. 60 choice of lower boundary condition does not affect signiﬁcantly

Pressure, [mbar] 70. 80. 70. 60. 50. 40.

60. Approx. Altitude [Km] 30. 50 1000 20. 70 -20 -30 -40 -50 -60 -70 -80 60 1 Latitude [deg.] 50 2 Fig. 8. Latitude–height cross section of zonal thermal wind speed (m s1) derived 40 from VeRa temperature profiles assuming cyclostrophic balance (Eq. (5)). The 3 velocity used as lower boundary condition is the cloud-tracked wind profile 30 retrieved from VIRTIS/VEx 1.74 lm images (Sánchez-Lavega et al., 2008). Contour interval is 10 m s1. 20 4 Wind speed, [m/s] 10 PV probes 0 proceeded as follow. On each pressure level temperature profiles 0 -20 -40 -60 -80 were binned to 5° latitude intervals and standard deviation was Latitude, [deg] calculated for every interval. An approximating curve was fitted through the standard deviations and added to the original temper- Fig. 10. Velocities used as lower boundary condition. Curve 1 is the cloud-tracked wind derived from VIRTIS/VEx images (Sánchez-Lavega et al., 2008). Curves 2, 3 and ature’s fitting curve to produce the 1r curve. The 1r and ±2r 4 correspond to the solid body rotation function u0 = u0(/ = 0)cos/, where u0(/ were calculated in the same way. Fig. 9 shows that almost all data = 0) = 20, 40, 60 m s1. Curve 1 is used for the nominal case. Winds derived from lie within ±2r curves. Pioneer Venus probes are also added. A. Piccialli et al. / Icarus 217 (2012) 669–681 675

1 5. 80 20. 10. 10 15. 70

5. 100 60 A 5. 10. 50 1000 15. 20. 1 10. 5. 15. 30. 15. 80 20. 10 15. 10. 70 10. 100 5. 60 15. Pressure, [mbar] 20. 15. Approx. altitude, [km] B 50 1000 20. 30. 1 10. 15. 30. 80 20. 10 15. 10. 70 15. 100 20. 60 15. 30. 20. 50 1000 C 30. -20 -30 -40 -50 -60 -70 -80 Latitude, [deg.]

Fig. 11. Contours of the difference absolute value (m s1) between the zonal wind derived from VeRa temperature proﬁles using VIRTIS cloud-tracked wind as lower boundary condition and those obtained assuming (a) u0 = 60 cos/; (b) u0 = 40 cos/; (c) u0 = 20 cos/ as lower boundary conditions.

the jet. This result is consistent with the form of the thermal wind u0 = (45 sech((/ 56)/9) + 75)cos/ (Piccialli et al., 2008). VIRTIS equation (Eq. (5)) as the vertical integral of the left-hand side of Eq. temperatures used to derive the wind are a combination of five or- (5) is proportional to the difference of the square of the zonal bits acquired between July 2006 and August 2008. Orbits were se- velocity at the higher atmosphere level, minus that at the bottom lected in order to have a complete latitudinal coverage of the boundary. Southern hemisphere (15–85° latitude) and a good local time Comparison of zonal winds obtained from Eqs. (4) and (5) illus- coverage of the nightside (18:00–06:00 h). The main feature ob- trate also the role of boundary conditions. Eq. (4) does not require a served in both figures is the midlatitude jet: the VeRa jet (Fig. 12, lower boundary velocity, thus, it allows one to test the sensitivity left) has a maximum speed of 130 m s1 at the cloud top around of the zonal wind derived from Eq. (5) on the choice of the lower 40°S latitude, the VIRTIS wind field (Fig. 12, right) presents a jet boundary condition. The comparison between the zonal wind with a maximum speed of 100 m s1 centred around 50°S lati- fields in Figs. 6 and 8 shows a good agreement, therefore, validat- tude at 67 km of altitude. ing the method based on Eq. (5) and confirming the independence Analysis shows that this discrepancy could be the result of sev- of the retrieved zonal wind field on the lower boundary condition. eral factors:

4. Discussion Peculiarities of temperature sounding techniques: VeRa radio-occultation data provide temperature structure with 4.1. Comparison with other thermal wind retrievals vertical resolution of few hundred meters that allows the measurements to completely resolve deep temperature inver- In addition to the radio science experiment, a second instru- sions typical for the cold collar regions. Vertical resolution in ment on board Venus Express is sounding the atmospheric struc- VIRTIS thermal emission spectroscopy in the 4.3 lmCO2 bands ture of Venus: the Visible and Infrared Thermal Imaging does not exceed few kilometers. This smoothes tempera- Spectrometer (VIRTIS) provides vertical temperature profiles on ture inversions and effectively reduces the latitudinal gradi- the night side of the planet covering the altitude range from 65 ent of temperature from which the wind is estimated (see Eq. to 85 km (100–1 mbar) (Drossart et al., 2007). A comparison be- (5)). tween the zonal wind field derived from VeRa temperature profiles Effect of clouds: it is important to notice that VeRa temperature using Eq. (5) and that obtained from VIRTIS temperature retrievals sounding is not sensitive to clouds; on the contrary, the cloud (Grassi et al., 2008) is shown in Fig. 12. structure is assumed in VIRTIS temperature retrievals and For a better comparison the same lower boundary condition uncertainty in the cloud model results in systematic temperature retrieval errors (see Lee et al. (2010) for a more detailed was chosen for both wind fields: it was fixed at 58 km of altitude discussion). (275 mbar) and the velocity used as lower boundary was 676 A. Piccialli et al. / Icarus 217 (2012) 669–681

1 20.

60. 10.

0 .

0 10.

2 40. 0

20. 60. 1 100. 80. 40. 80

120. 0 40.

. 70. 10

60.

80. 130. 70

60.

10. Pressure, [mbar]

100.

2 20. Approx. Altitude [Km]

10. 80. 120. 90.

100.

100 10. 20.

40.

70. 40. 60 60. -20 -30 -40 -50 -60 -70 -80 -20 -30 -40 -50 -60 -70 -80 Latitude, [deg.]

Fig. 12. Meridional cross sections of zonal thermal winds derived from (left) VeRa and (right) VIRTIS temperature proﬁles applying cyclostrophic approximation (Eq. (5)). The lower boundary condition was ﬁxed for both zonal wind at 58 km of altitude (275 mbar), the velocity used as lower boundary condition is the function u0 = (45 sech((/ 56)/9) + 75).

Earlier studies have shown a similar discrepancy: zonal winds derived from Venera-15 Fourier spectrometer temperature retrievals display a maximum jet speed of 90–100 m s1 (Zasova et al., 2000), while winds derived from Pioneer Venus radio occultation data present a maximum speed of 140–160 m s1 (Newman et al., 1984; Limaye, 1985).

4.2. Validity of cyclostrophic approximation

Combination of temperature sounding and imaging observations on board Venus Express gives a unique chance to compare balanced wind field with cloud-tracked winds measured in the same temporal period; this allows validation of the cyclostrophic balance. Winds have been derived from the tracking of cloud features in the VMC and VIRTIS UV images at 66–70 km altitude and in the VIRTIS near infrared images at altitudes of 48 km and 61 km (Sánchez-Lavega et al., 2008; Moissl et al., 2009). Fig. 13 shows a VMC–UV image of Venus together with the balanced zonal flow derived from VeRa temperature retrievals. The VMC image (Fig. 13) offers a global view of the Venus disk with Fig. 13. Global view of Venus in UV observed from the Venus Monitoring Camera the Southern pole at the bottom. The presence of mottled and pat- (VMC) on board Venus Express. Latitude–altitude cross section of the zonal chy cloud patterns at low latitudes indicates that convection and cyclostrophic wind derived from VeRa temperature soundings is also displayed. turbulence play an important role in these regions. Around 50°S streaky features start to prevail over the mottled clouds, indicating a transition to quasi-laminar flow at high latitudes VeRa cyclostrophic wind at 61 km altitude shows a better agree- where a bright midlatitude band can be also observed (Titov ment with cloud-tracking winds. The difference between cyclos- et al., 2012). As pointed out by Titov et al. (2012), cloud morphol- trophic and cloud-tracked UV winds appears comparable to the ogy gives a ‘‘visual’’ indication of the midlatitude jet at the edge of scatter in cloud-tracked winds. As presented by Khatuntsev et al. the bright midlatitude band. (2010), VMC cloud-tracked winds show a orbit-to-orbit variability The zonal wind profile determined from VIRTIS data at 48 km with some orbits characterised by a pronounced jet. This orbit-to- altitude has been used as the lower boundary condition to solve orbit variability could be due to real variations in the zonal flow or the thermal wind equation (Eq. (5)) for VeRa temperature retri- be the consequence of cloud top altitude changes. evals. Cloud-tracked winds from VMC images at 66 km have been Also, as reported previously by Limaye (2007), a disagreement compared to the balanced flow derived from the VeRa thermal between zonal winds derived from the cyclostrophic assumption sounding at the same altitude. Fig. 14 displays the comparison be- and cloud-tracked winds was observed in earlier studies. Zonal tween cloud-tracked winds derived from the VMC images and cycl- winds obtained from the direct application of cyclostrophic bal- ostrophic winds derived from VeRa pressure retrievals at three ance (Eq. (4))(Limaye, 1985) and from the thermal wind equation different altitudes. (Eq. (3))(Newman et al., 1984) applied to Pioneer Venus tempera- VeRa cyclostrophic winds at 69 and 65 km altitudes display a ture retrievals displayed a similar zonal flow structure with a mid- 1 strong midlatitude jet with a maximum speed up to 150 m s1. latitude jet speed up to 140 m s . Venera 15 and Galileo NIMS A. Piccialli et al. / Icarus 217 (2012) 669–681 677

Fig. 14. Comparison between the latitudinal proﬁles of cyclostrophic wind derived from VeRa pressure retrievals at altitudes of 69 km, 36 mbar (black curve); 65 km, 79 mbar (black dotted curve); 61 km, 177 mbar (black dashed curve) and the VMC cloud-tracked wind.

observations produced similar results (Zasova et al., 2000; Roos- g dT C Ri ¼ T dz ð6Þ Serote et al., 1995). Cloud-tracked winds inferred from Pioneer Ve- @u 2 nus OCPP between 1979 and 1985 did not show any pronounced @z jet at all. It is important to notice, however, that the data used to where C is the dry adiabatic lapse rate, z is height and u is the west- derive the cyclostrophic winds was acquired in a period of time dif- ward zonal wind. If the boundary layer is unstable (numerator of ferent from that in which cloud-tracked winds were measured. Eq. (6) is negative), then Ri < 0 and turbulence is sustained by con- Therefore, one possible reason for their differences is that circula- vection. For stable conditions (numerator is positive) Ri will be tion on Venus is variable. On the contrary, Venus Express’ observa- greater then zero. Small values of Ri could be an indication of the tions used to derive cyclostrophic and cloud-tracking winds were formation of turbulence. From the VeRa temperature structure acquired almost simultaneously. The reason of their disagreement T(z,/) and corresponding balanced wind field U(z,/) we studied dis- is not yet understood, there could be several: tribution of the Richardson number in the Venus mesosphere. Fig. 15 displays meridional cross section of the Richardson num- 1. The midlatitude jet and the UV features used to measure the ber. Note that the calculation of Ri requires the first derivative of a zonal flow could be at different altitudes: uncertainty on the smoothed temperature and wind field: both the stability and the altitude of the UV absorber is one of main source of error on squared vertical wind shear were smoothed twice over 5° latitude cloud-tracked winds. Ignatiev et al. (2009) has mapped the intervals; therefore, only gross features should be taken in account. cloud top altitude and related it to the UV markings. In low The uncertainty in the Richardson number due to measurement and middle latitudes the cloud top is located at 74 ± 1 km. Its uncertainties is hard to define quantitatively. An approach similar altitude decreases poleward from 50° and reaches 63–69 km to that applied to determine uncertainty on zonal wind speed has in the polar region. Due to the variation of cloud top altitude been followed. An uncertainty of about 1–5 has been found in the with latitude, the latitudinal wind profile derived from cloud- altitude range 50–60 km. It is possible to observe a layer where Ri tracking might not refer to a constant altitude. has low values centred at 54 km altitude. This nearly adiabatic 2. Limitation of the cyclostrophic approximation: the cyclostroph- middle cloud layer terminates near 60 km altitude, where Ri in- ic balance gives an approximate relationship between the creases rapidly with altitude. Between 60 and 70 km altitude Ri pressure field and the zonal wind velocity. The approximation reaches very large values, this level is characterised by a larger sta- (Eq. (3)) is applied to zonal flow only and neglects meridional tic stability and it corresponds also to the jet core in the vertical 1 velocity, which is 10 m s , and eddies, turbulent motions profile of the derived thermal wind, where @u/@z ? 0, producing and vertical viscosities which have been shown to play a major therefore a large Richardson number. Thus, this region is character- rule in the maintenance of the circulation. ised by high stability. A similar trend has been observed from Pioneer Venus radio occultation (Allison et al., 1994). In Fig. 15 is also shown approximately the UV cloud top altitude as derived 4.3. Stability studies by Ignatiev et al. (2009). Interestingly, the bottom boundary between layers of low and high values of Ri seems to follow the same The Richardson number is an important stability parameter and behaviour of the latitudinal profile of the cloud top. it is used to indicate dynamic stability and the formation of turbu- The behaviour of Richardson number Ri with latitude and alti- lence. It is defined as the ratio of the static stability and the squared tude is also consistent with observations of the UV cloud morphol- vertical wind shear (Gierasch et al., 1997): ogy by VMC (Titov et al., 2008, 2010). VMC–UV image (Fig. 13) 678 A. Piccialli et al. / Icarus 217 (2012) 669–681

Fig. 15. Latitude–height cross section of Richardson number (Eq. (6)). Dotted line follows the approximate altitude of cloud top (Ignatiev et al., 2009).

displays contrast features that are produced by inhomogeneous 1 @ f ¼ ðru cos /Þð8Þ spatial and vertical distribution of the unknown ultraviolet absor- h r2 cos / @/ ber in the upper cloud. Morphology of the UV markings indicates variations of dynamic state at about 70 km altitude. At low lati- To evaluate fh, VeRa zonal thermal wind u has been used. Because tudes (<40°S) the mottled and patchy clouds indicate significant Venus’ atmosphere can be considered thin compared to the planet’s role of convection and turbulence near the subsolar point. At radius, r can be assumed constant and can be brought outside the 50°S the outer edge of the bright midlatitude band marks a tran- differential term in Eq. (8). The potential temperature h is the tem- sition between the dark and turbulent low latitudes, where zonal perature which a parcel of dry air at pressure p and temperature T wind is almost constant with latitude, and the bright and quiet would have if it were expanded or compressed adiabatically to a midlatitude zone, where zonal wind quickly decreases towards standard pressure p0 and it is defined by (Holton, 2004): the pole. The studies of atmospheric chemical tracers, like carbon p j monoxide, suggest that this transition region could identify the h ¼ T 0 poleward extent of the Hadley cell in the meridional circulation p (Tsang et al., 2008). where p0 is the reference pressure at 1700 mbar and j is the ratio of heat capacities (Cp Cv)/Cp. Values of Cp and Cv at different altitudes 4.4. Ertel potential vorticity have been taken from the VIRA model (Seiff et al., 1985). Fig. 16 shows the meridional cross section of potential temperature. Recent studies on Titan (Teanby et al., 2008) have made use of The 1/p factor causes q to increase exponentially with altitude, potential vorticity maps together with composition measurements making horizontal trends difficult to determine. Therefore, follow- to deduce the presence of a mixing barrier at high latitudes. A sim- ing Read et al. (2006), the potential vorticity has been normalised ilar analysis can be done also for Venus. Studies of carbon monox- on potential temperature surfaces by g h@h/@pi, where hi implies ide (Tsang et al., 2008), an atmospheric chemical tracer, in the the horizontal mean value. Contour plot of scaled Ertel potential Venus atmosphere have shown an enhancement of CO from the vorticity is displayed in Fig. 17. equator to the pole with a peak at 60° latitude at 35 km altitude. As can be observed in this figure, potential vorticity presents the Poleward of 60°S CO decreases with latitude. Tsang et al. (2008) same sign between 30° and 80° latitude and slightly increases from has suggested that the CO enrichment is caused by the descending branch of the Hadley cell which advects the trace gas from the cloud top, where it is produced, to the lower altitude of 35 km. 1300. 1 1200. The decrease of CO from 60° latitude to the pole could be an evi- 1100. 80 dence, as on Titan, of the presence of a mixing barrier. 1000. In order to investigate more in detail this possibility, we esti- 900. mated the zonal mean of the Ertel potential vorticity from VeRa 10 800. thermal zonal mean winds. Under the hydrostatic approximation, 700. 70 the general definition of Ertel potential vorticity (PV) becomes 600. [the following is an excerpt from Read et al. (2006)]: 500. 100 450. 60 400.

ð2X þ r uÞrh ðf þ fhÞ @h @h Pressure, [mbar] q ¼ ’ ’gðf þ fhÞ ð7Þ

q q @z @p Approx. Altitude, [Km] 50 1000 where g is gravitational acceleration, u is the velocity of the ﬂow, f =2Xsin/ is the Coriolis parameter, X is the angular rotation rate -20 -30 -40 -50 -60 -70 -80 of Venus, / is latitude, h is potential temperature, p is pressure, and Latitude, [deg] fh is the vertical component of absolute vorticity calculated at constant potential temperature given by (Teanby et al., 2008): Fig. 16. Potential temperature calculated from the temperature in Fig. 2. A. Piccialli et al. / Icarus 217 (2012) 669–681 679

1 150

20. 30. 40. 80

60. 110 10 70

10. 70 * PVnorm

50. 6 100 40. 60

30. 10 20. 60.70. Pressure, [mbar] 30 Approx. Altitude, [Km]

50. 50 20. 30. 40. 1000 30. 40. 50. 10.20. 50. 20. -10 -30 -40 -50 -60 -70 -80 Latitude, [deg.]

Fig. 17. Contour plot of the Ertel potential vorticity (s1) of the zonal wind ﬁeld of Fig. 6. The zonal wind ﬁeld has been overplotted for comparison.

equator to pole. However, it does not show any region of strong lat- somewhere on a constant potential temperature surface (Houghton, itudinal gradient, as should be expected in presence of a mixing 2002). Fig. 18 shows the contour plot of 1 @ u tan / @u . Eq. (9) is barrier. Yet, this does not exclude completely the possible exis- r @/ @/ tence of a transport barrier, but a more detailed investigation of satisfied on the poleward side of the midlatitude jet. A similar result chemical tracers is needed. For future studies, one possibility could was obtained also by Newman et al. (1984) using Pioneer Venus be to use Venus Express observations of the atmospheric composi- radio occultation data. tion to investigate the possible presence of a mixing barrier. Venus Express uses two techniques to study the atmospheric composi- 5. Conclusions tion. SPICAV/SOIR provides vertical profiles of atmospheric trace gases in the mesosphere (70–110 km altitude). VIRTIS investigates Zonal winds were derived from the VeRa thermal sounding the composition of the low atmosphere (Titov et al., 2009). (Tellmann et al., 2009) by applying the cyclostrophic balance and were compared to the cloud-tracked winds to validate the cyclos- 4.5. Barotropic instability trophic assumption. Thanks to Venus Express capabilities, the variability of zonal wind with latitude and altitude was analysed in Origin of eddies in the Venus atmosphere is an important ques- detail. The main features of the retrieved wind are: (1) a midlati- tion. Previous studies (Young et al., 1984; Michelangeli et al., 1987) tude jet with a maximum speed up to 140 ± 15 m s1 extending be- have investigated the likely existence of barotropic or baroclinic tween 20°S and 55°S latitude at 70 km altitude; (2) the fast instabilities near the midlatitude jet above the clouds. Here, we decrease of the wind speed from 60°S toward the pole; (3) the de- analysed in detail the conditions for barotropic instability to occur. crease of the wind speed with height above the jet (Figs. 6 and 8). Barotropic instability is a wave instability associated with horizon- These results agree well with the balanced zonal flow derived from tal shear in a zonal flow (Holton, 2004). The necessary condition for the earlier mesospheric soundings (Newman et al., 1984; Limaye, barotropic instability, known as Rayleigh’s criterion, is that: 1985; Zasova et al., 2000). 1 @ @u The sensitivity of the zonal thermal wind to the lower boundary u tan / ¼ 0 ð9Þ r @/ @/ condition on u was tested by comparing zonal wind fields obtained from Eqs. (4) and (5) and by applying different velocities as lower boundary condition (Fig. 10). Results showed that zonal thermal winds are only slightly affected by the choice of boundary 1 condition. The synergy between temperature soundings and the imaging -200. -300. 200. 100. 0. 80 -100. observations on board Venus Express gave a unique chance to test the cyclostrophic approximation by comparing the balanced zonal

10 0. flow to the winds derived from tracking UV cloud markings. Cycl- 70 100. ostrophic winds showed satisfactory agreement with the cloud- 0. tracked winds derived from the Venus Monitoring Camera (VMC/ 0. VEx) UV images at 30–70° latitudes (Fig. 14), meaning that the 100 100. 60 cyclostrophic balance governs the circulation at these latitudes. A Pressure, [mbar] disagreement is observed at the equator and near the pole where 200. Approx. Altitude, [Km] 50 the cyclostrophic approximation may be inadequate to describe 1000 100. -300. -300. -100.-200. 0. the zonal circulation. At these latitudes other forces, such as turbu- -30 -40 -50 -60 -70 -80 lent motions, vertical viscosities, and eddies, become dominant in the original Navier–Stokes equation. Latitude, [deg.] From the temperature and balanced wind fields we calculated 1 @ @u 6 1 the Richardson number Ri (Eq. (6)), the parameter characterising Fig. 18. Contour plot of r @/ u tan / @/ ; units are 10 s . Negative regions are represented in grey. VeRa zonal wind field (m s1) has been overplotted for the dynamic stability of the atmosphere. The atmosphere is comparison. characterised by a low value of Richardson number from 40 km 680 A. Piccialli et al. / Icarus 217 (2012) 669–681 up to 60 km altitude at all latitudes that corresponds to the lower Grassi, D. et al., 2008. Retrieval of air temperature profiles in the venusian and middle cloud layer (Fig. 15). Convective regions (Ri < 0) are mesosphere from VIRTIS-M data: Description and validation of algorithms. J. Geophys. Res. (Planets) 113, 342–353, 11 pp. seen only in very shallow layers within the middle cloud deck. A Grassi, D. et al., 2010. Thermal structure of venusian nighttime mesosphere as high value of Richardson number was found in the region of the observed by VIRTIS–Venus Express. J. Geophys. Res. (Planets) 115, 9007. midlatitude jet indicating a highly stable atmosphere. This distri- Häusler, B. et al., 2006. 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