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1 Icarus 221 (2012) Contents lists available at SciVerse ScienceDirect Icarus journal homepage: Microwave absorptivity by sulfuric acid in the Venus atmosphere: First results from the Venus Express Radio Science experiment VeRa J. Oschlisniok a,, B. Häusler b, M. Pätzold a, G.L. Tyler c, M.K. Bird a,d, S. Tellmann a, S. Remus e, T. Andert b a Abteilung Planetenforschung, Rheinisches Institut für Umweltforschung, Universität zu Köln, Cologne, Germany b Institut für Raumfahrttechnik, Universität der Bundeswehr München, Neubiberg, Germany c Department of Electrical Engineering, Stanford University, Stanford, CA , USA d Argelander Institut für Astronomie, Universität Bonn, Bonn, Germany e European Space Astronomy Center (ESAC), Villanueva, Spain article info abstract Article history: Received 27 March 2012 Revised 21 September 2012 Accepted 24 September 2012 Available online 13 October 2012 Keywords: Venus, Atmosphere Occultations Radio observations The Venus Express (VEX) Radio Science experiment VeRa utilizes radio occultation techniques to investigate the Venus atmosphere over a wide range of latitudes. Radio attenuation measurements with the VEX 3.6 cm (X-band) signal provide information on the absorptivity distribution within the Venus cloud deck. The combined results from 6 years of occultation measurements reveal a distinct latitudinal variation in absorptivity in the altitude range from 50 to 55 km. Enhanced absorptivity is observed at equatorial and mid-latitudes (0 50 S), exceeding db/km on the dayside and 0.01 db/km on the nightside of the southern hemisphere. Poleward of 50 S latitude a decrease in the absorptivity is observed, reaching minimal values at polar latitudes (>70 S), where the absorptivity did not exceed db/km on the dayside and db/km on the nightside. The main absorber of radio waves in the Venus atmosphere, gaseous sulfuric acid, can serve as a tracer for atmospheric motions. The inferred absorptivity was used to determine the abundance of gaseous sulfuric acid. Abundances of about 1 2 ppm are found between 0 S and 70 S latitude in the altitude range from 50 to about 52 km, sometimes increasing to values of about 3 ppm on the dayside and 5 ppm on the nightside near 50 km. The abundance at polar latitudes (>70 S) did not exceed 1 ppm within the considered altitude range. The absorptivity and gaseous sulfuric acid height profiles are compared with previous measurements. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction Corresponding author. address: joschlis@uni-koeln.de (J. Oschlisniok). Earth s nearest planetary neighbor Venus is shrouded by thick clouds extending from an altitude of approximately 48 km above the surface up to an altitude of about 70 km. The cloud deck is divided into three layers according to the particle size over this range of altitudes. The upper cloud layer is located between 60 and 70 km, the middle cloud layer between 50 and 60 km and the lower cloud layer between 48 and 50 km (Zasova et al., 2007). Only subtle contrast variations are seen in the upper cloud deck boundary at visible wavelengths. Observations in the ultraviolet, however, reveal brightness variations caused by strong atmospheric dynamics. The superrotating Venus atmosphere circumvents the planet in only 4 5 days (Young and Schubert, 1973) at velocities in excess of 100 m/s near an altitude of 65 km (Counselman et al., 1980). Superimposed on the zonal rotation is a much weaker meridional motion with wind velocities an order of magnitude smaller than the zonal velocities (Counselman et al., 1980; Rossow et al., 1980). Sulfuric acid is the primary constituent in the clouds (Hansen and Hovenier, 1974; Palmer and Williams, 1975; Young, 1973), existing in both gaseous and liquid states. Liquid sulfuric acid is predominantly found within the main clouds (50 70 km), while gaseous sulfuric acid forms a haze layer below the clouds extending to an altitude of about 35 km (Kolodner and Steffes, 1998). A possible H 2 SO 4 cycle embedded within the meridional motion in the venusian atmosphere has been described by Krasnopolsky and Pollack (1994) and Imamura and Hashimoto (2001). Liquid sulfuric acid is formed within the upper cloud layer by condensation of photochemically produced sulfuric acid at equatorial latitudes. The resulting droplets are transported poleward by the Hadley circulation. Downward transport at higher latitudes into the hot lower atmosphere causes evaporation to gaseous H 2 SO 4. Meridional equatorward flow beneath the clouds transports the resulting sulfuric acid vapor back to lower latitudes, where convective cells transport the vapor up to the colder atmosphere within the middle cloud layer. Droplets formed there by condensation fall back to the cloud base near 50 km due to their large size and sub /$ - see front matter Ó 2012 Elsevier Inc. All rights reserved.

2 J. Oschlisniok et al. / Icarus 221 (2012) sequently evaporate into gaseous H 2 SO 4. Precipitation within the middle cloud layer followed by evaporation near the cloud base, combined with the ascending sulfuric acid haze from below the clouds, results in accumulation of H 2 SO 4 vapor near 50 km at lower latitudes. Further down (between 35 and 40 km), the gaseous H 2 SO 4 dissociates thermally into H 2 O and SO 3 (Kolodner and Steffes, 1998). The radio occultation method is used to monitor absorbing gases like H 2 SO 4, which is responsible for a strong decrease in the radio signal intensity (Jenkins and Steffes, 1991; Jenkins et al., 1994; Steffes and Eshleman, 1982). The received signal intensity is used to derive radio absorptivity profiles. A distinct latitudinal variation of the 13 cm radio wave absorptivity within the Venus northern atmosphere was inferred from observations made by the Pioneer Venus Orbiter radio occultation experiment (Jenkins and Steffes, 1991). The implied variable distribution of the trace gas H 2 SO 4 with planetary latitude was taken as evidence for atmospheric dynamics. Absorptivity profiles are therefore a valuable tool for revealing atmospheric motions. Radio occultation experiments were performed with the Venus Express spacecraft during nine occultation seasons between 2006 and 2011 (Pätzold et al., 2007, 2009; Tellmann et al., 2009). The Radio Science Experiment VeRa onboard Venus Express probes the atmosphere of Venus at 13 cm (S-band: 2.3 GHz) and 3.6 cm (X-band: 8.4 GHz) wavelengths (Häusler et al., 2006a). The orbit and occultation geometry allow sounding the atmosphere over a wide range of latitudes within each occultation season. The radio signals are recorded at ground stations on Earth using both closed-loop and open-loop techniques (Häusler et al., 2006b). The closed-loop system uses a phase-locked loop in the receiver for the purpose of signal tracking. The amplitude and frequency of the downlink signal are recorded, but are not always reliable at altitudes below 50 km, where the signal can exhibit strong dynamical effects. The open-loop system performs a down conversion of the received frequency to baseband and the entire pass band is recorded for later processing. Useful observations can be recovered by the open-loop system during dynamic signal conditions. These data are currently under evaluation for the study of the deep Venus atmosphere. Signal intensity measurements of the 3.6 cm radio signals from 122 occultations were processed to derive height profiles of atmospheric absorptivity in the atmosphere of Venus at many latitudes, solar zenith angles and local times. The abundance of gaseous sulfuric acid was then inferred from these profiles. 2. Method The radio occultation technique is well suited to study planetary atmospheres. It was first used during the Mariner IV flyby of Mars in 1965 (Kliore et al., 1965) and developed further with the Mariner V observations of Venus in 1967 (Mariner Stanford Group, 1967). Further observations of Venus with the radio occultation technique have been performed with the spacecraft Mariner 10 (Eshleman et al., 1980; Howard et al., 1974; Kliore et al., 1979; Lipa and Tyler, 1979), Pioneer Venus (Cimino et al., 1980; Jenkins and Steffes, 1991; Kliore and Patel, 1982), Venera 15/16 (Yakovlev et al., 1991; Gubenko et al., 2001, 2008), and Magellan (Jenkins et al., 1994; Steffes et al., 1994). Observations of radio signals propagating through the Venus atmosphere to Earth are recorded at times prior to the start of the occultation of the spacecraft by Venus and during the emergence as seen from the Earth. The dense Venus atmosphere has a strong influence on the radio ray path. The phase advance in the ionosphere and phase retardation in the neutral atmosphere caused by the bending of the radio ray path is seen as a shift of the carrier frequency. The observed frequency Fig. 1. Radio ray path geometry during an occultation. The radio ray path from the spacecraft to the ground station along the ray asymptotes R 1 and R 2 reaches the closest distance to the center of the planet at the ray periapsis r 0. The ray impact parameter a is defined as the distance between the ray asymptote and the center of planet. The refraction angle d is the angle between the ray asymptotes R 1 and R 2 of the radio ray link. shift and the occultation geometry are used to determine the refraction angle d and the ray impact parameter a (Fig. 1). The ray periapsis r 0 (Fig. 1), the closest approach of the refracted ray to the center of the planet, is related to the impact parameter by a ¼ nðr 0 Þr 0 : The refractivity n(r 0 ) is derived from an inverse Abel transform, assuming a spherically stratified atmosphere (Fjeldbo et al., 1971) lnðnðr 0 ÞÞ ¼ 1 p Z 1 aðr 0 Þ ð1þ dðaþda q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : ð2þ a 2 aðr 0 Þ 2 The temperature and pressure are computed assuming hydrostatic equilibrium for a well mixed atmosphere of known composition (Lipa and Tyler, 1979). The measurements of the received signal power are used to derive the attenuation of the signal intensity by the atmosphere, which is assumed to be caused by the combination of refractive defocusing, absorption and mispointing of the spacecraft antenna. The total loss P(r 0 ) of the radio signal, expressed in db, is written as Pðr 0 Þ¼Lðr 0 Þþsðr 0 Þþmðr 0 Þ; where L(r 0 ) is the decrease in signal intensity due to refractive defocusing, s(r 0 ) is the residual attenuation and m(r 0 ) is the decrease in signal intensity due to mispointing of the spacecraft antenna. If the residual attenuation is due only to absorption, then s(r 0 ) is the integrated absorption coefficient a along the ray path. Refractive defocusing is caused by the radial gradient in the refractivity, leading to differential refraction of the radio beam. If I 0 is the free space signal intensity recorded at the ground station and I the received signal intensity after passing through the atmosphere, then the decrease in signal intensity due to refractive defocusing L(r 0 ) is computed from the ratio I/I 0. Applying geometrical optics as shown in the plane of refraction in Fig. 1, it can be shown that L(r 0 ) is given by (Lipa and Tyler, 1979) Lðr 0 Þ¼10 log 10 ð/ 1 / 2 Þ; where / 1 represents the focusing effect caused by the compression of the radio beam in the plane perpendicular to the plane of refraction. Rays that pass by the planet at the asymptotic distance a before refraction are compressed into the distance r = a secd D tand, where D is the distance of the spacecraft behind the planet (Fig. 1). The focusing effect is then given by (Lipa and Tyler, 1979) / 1 ¼ a r ¼ 1 sec d D a tan d : The factor / 2 in Eq. (4) represents the defocusing that occurs in the plane of refraction. The distance Da of separated incident rays before refraction increases to the distance Dr cosd, where Dr =(@r/@a) Da +(@r/@d)(dd/da) Da after refraction. The refractive defocusing is then given by (Lipa and Tyler, 1979) ð3þ ð4þ ð5þ

3 942 J. Oschlisniok et al. / Icarus 221 (2012) Da / 2 ¼ Dr cos d ¼ 1 : ð6þ 1 þðatan d D sec dþ dd After removing the defocusing loss L(r 0 ) and the signal decrease due to mispointing of the spacecraft antenna m(r 0 ) from the observed total signal attenuation P(r 0 ) the residual attenuation s(r 0 ) remains, which is expressed as an integral over the radius by using Bouger s rule (Lipa and Tyler, 1979) and rewritten in the form of an Abel transform (Jenkins and Steffes, 1991). The absorptivity, given by the absorption coefficient a(r 0 ), is derived by applying the inverse Abel transform to s(r 0 ) and multiplying the result by the refractivity n(r 0 )(Jenkins and Steffes, 1991): 2 3 aðr 0 Þ¼ nðr 0Þ p aðr 0 Þ d Z 1 6 sðaþada qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 7 4 5: ð7þ da aðr 0 Þ a 2 aðr 0 Þ 2 The remaining absorptivity a H2 SO 4, after correcting for the contributions of carbon dioxide, nitrogen and sulfur dioxide, is used to determine the abundance of gaseous sulfuric acid as the main absorber of radio waves. The correction a H2 SO 4 ¼ a a CO2 ; N 2 a SO2 ð8þ da Fig. 2. Comparison of the total signal loss at 3.6 cm (solid line) and calculated refractive defocusing loss (dashed line) computed from closed loop data. The excess attenuation (dashed dotted line) along the radio ray path is the difference between total signal loss and defocusing loss. The ray periapsis r 0, stated as radius, is the closest distance of the refracted radio ray path to the center of the planet (see Fig. 1). The profiles were obtained from ingress measurement during Orbit 87 in 2006 at southern equatorial latitudes (15.32 S) on the dayside of the planet (solar zenith angle: ). is implemented by using the expression, a CO2 ;N 2 ¼ 1: q 2 CO 2 þ 0:25 q CO2 q N2 þ 0:0054 q 2 N 2 f 2 ðp 1: Þ 2 T 5 ð9þ for the CO 2 and N 2 contribution (Ho et al., 1966) and a SO2 ¼ 4: f 2 ðp 1: Þ 1:28 T 2:91 q SO2 ð10þ for the SO 2 contribution (Janssen and Poynter, 1981; Steffes and Eshleman, 1981; Fahd and Steffes, 1992; Suleiman et al., 1996), where a is the total absorptivity derived from Eq. (7) in db/km, f the carrier frequency (GHz), p the pressure (Pa), T the temperature (K), and q is the number mixing ratio of the gas ðq CO2 ¼ 0:965; q N2 ¼ 0:035Þ. All empirical expressions here are in SI units. The mixing ratio of sulfur dioxide q SO2 is taken for this work as an average from Venera, VEGA and Pioneer Venus observations (de Bergh et al., 2006; Bertaux et al., 1996; Bézard et al., 1993; Krasnopolsky and Pollack, 1994; Marcq et al., 2008). Expression (10) is a best fit to the 3.5 cm absorptivity results given by Suleiman et al. (1996). The residual absorptivity attributed to H 2 SO 4 is then used to compute the sulfuric acid mixing ratio q H2 SO 4 from an empirical formula derived by Kolodner and Steffes (1998) from laboratory measurements Fig. 3. Signal loss caused by mispointing of the spacecraft high gain antenna 1 for the orbit 87. a H2 SO 4 ð3:6 cmþ¼443:570 ðp1: Þ 1:302 3:00:2 553 q T : ð11þ H2SO4 3. Results and discussion Fig. 2 shows the total attenuation jpj, the defocusing loss jlj and the excess attenuation jsj of the 3.6 cm radio signal as a function of altitude h = r 0 R, with respect to a planetary mean radius of R = km at equatorial southern latitudes (15.23 S) on the dayside of the planet. Fig. 3 shows the decrease in signal strength due to mispointing of the spacecraft high gain antenna jm(h)j. It is evident that the decrease in signal intensity above 50 km is mainly caused by defocusing. Fig. 4 shows the corresponding absorptivity a as a function of h calculated from Eq. (7). The associated uncertainty was estimated by applying linear error propagation and is discussed in detail in Appendix A. Signal noise was smoothed out by using a moving average filter. In order to suppress the effects Fig. 4. Absorptivity of the 3.6 cm radio signal computed by applying the inverse Abel transform to the excess attenuation (Eq. (7)) in Fig. 2. of noise amplification by the derivatives in (6) and (7), a smooth and noise-robust differentiator ( was used. A low-pass filter was applied to the excess attenuation s(r 0 ) and the derived Abel transform in Eq. (7). Based on the radio signal attenuation in Fig. 2 two altitude regions can be distinguished: (i) Above an altitude of about 55 km, the observed radio attenuation is dominated by refractive defocusing, in general agreement with previous observations e.g. (Lipa and Tyler, 1979). Attenuation of the radio signal by mispointing of the Venus Express high gain antenna plays only a minor role

4 J. Oschlisniok et al. / Icarus 221 (2012) (see Fig. 3). The defocusing loss fluctuates strongly with highest amplitudes between about 55 and 70 km altitude. Since the observed total signal attenuation above 55 km altitude is mostly caused by refractive defocusing, these fluctuations are also visible in the received signal intensity. The varying defocusing loss results from irregularities of the refractive index implying that the observed intensity variations must be attributed to the varying refractive index. Signal intensity variations in radio occultation experiments, known as intensity scintillations were first observed by Mariner 5 (Woo et al., 1974) and by Mariner 10 (Woo, 1975), the Veneras (Kolosov et al., 1979; Gubenko et al., 2001), Pioneer Venus (Woo et al., 1980) and the Magellan spacecraft (Hinson and Jenkins, 1995). Leroy and Ingersoll (1995) showed that those intensity scintillations may be associated with vertically propagating gravity waves. The highest amplitudes of gravity waves are located in the stable atmosphere above an altitude of about 60 km. Another source of small-scale amplitude fluctuations is multipath propagation occurring in the venusian atmosphere. Multipath effects have been identified in power spectra of open-loop data occurring near an altitude of 60 km. The multipath propagation phenomenon at Venus will be described in detail in a future publication. The excess attenuation in Fig. 2 reveals increased values above 55 km altitude which lead to fluctuations in the absorptivity profile visible in Fig. 4. The most probable cause of these fluctuations are intensity variations caused by gravity waves and multipath effects rather than absorption. Increased absorptivity above about 55 km altitude has also been reported by Gubenko et al. (2001) in Venera 15 and 16 radio occultation measurements at 5 cm wavelength as well as in Pioneer Venus radio occultation measurements by Jenkins and Steffes (1991) at 13 cm wavelength. Fig. 5 shows the averaged 13 cm absorptivity profiles derived from season 10 from July through December 1986 (Jenkins and Steffes, 1991) in the northern hemisphere. (ii) Below an altitude of about 55 km a divergence of the total attenuation from the defocusing loss is visible, indicating an increase in the absorptivity a. Fig. 4 reveals a strong gradient in the computed absorptivity near the cloud base. Similar behavior was observed in Pioneer Venus 13 cm absorptivity measurements (Fig. 5) particularly in the equatorial region. According to the Eqs. (9) (11) the gaseous components CO 2,SO 2 and H 2 SO 4 are the main absorbers of the 3.6 cm radio signal in the lower altitude range. The contribution by cloud material within this altitude range is of the order of 10 4 db/km (Cimino, 1982) and can be neglected. Fig. 5. Averaged 13-cm absorptivity profiles measured by Pioneer Venus radio occultation experiments in the northern hemisphere of Venus, taken from Jenkins and Steffes (1991), who distinguished different latitudinal regions: equatorial (10 20 N); mid-latitudes (35 45 N); 60S (59 68 N); 70S (72 80 N); polar (>80 N). Fig. 6 shows a latitudinal, time-averaged absorptivity map of the 3.6 cm radio signal within the Venus atmosphere as a function of southern latitude and altitude for the dayside (solar zenith angle SZA <90 ) and the nightside (SZA >90 ). The absorptivity maps are computed using data from the years 2006 to 2011 from nine occultation seasons with a total of 61 height profiles from the dayside and 61 height profiles from the nightside. A moving average filter was applied to each individual absorptivity profile in order to suppress any unrealistic negative values (see Fig. 4). In order to provide a uniform data grid, the hemisphere was subdivided into equal latitudinal bins of 5 each. Measurements located within each bin have been averaged to one absorptivity profile. A distinct difference in the absorptivity is visible on the dayside and nightside of the planet. The strongest absorptivity is observed at equatorial and midlatitudes (0 50 S) below 53 km altitude on both the dayside and the nightside. Maximal mean absorptivity values are 9 (14) 10 3 db/ km on the dayside (nightside) near the cloud base at 50 km. Sulfuric acid is assumed to be the main absorber of radio waves at 3.6 cm wavelengths at these altitudes. The increased level of absorptivity indicates either the presence of a higher cloud base level (Jenkins and Steffes, 1991) or the result of accumulated sulfuric acid vapor within this region (Krasnopolsky and Pollack, 1994; Imamura and Hashimoto, 2001). Fig. 6. Atmospheric absorptivity map of the 3.6 cm signal between 50 and 55 km altitude on the dayside (left panel) and nightside (right panel) of the southern hemisphere. A total of 61 profiles on the dayside and 61 profiles on the nightside (ingress and egress) from the years 2006 to 2011 were averaged within equal latitudinal bins of width 5.

5 944 J. Oschlisniok et al. / Icarus 221 (2012) Fig. 7. Absorptivity of the 3.6 cm radio signal within the equatorial and midlatitudinal (0 50 S) of the Venus cloud layer in the southern hemisphere as a function of altitude and solar zenith angle (left panel) and local true solar time (right panel). Seventy-eight absorptivity profiles (ingress and egress) were averaged in 5 bins in SZA between 15 and 155 and 0.5 h bins between 3 h and 22 h. The dashed lines in both maps indicate the terminator separating the dayside from the nightside of the planet. Fig. 8. Averaged absorptivity profiles of the 3.6 cm signal on the dayside (left panels) and nightside (right panels) from low latitudes (upper row), cold collar latitudes (middle row) and polar latitudes (lower row). The strongest absorption of the 3.6 cm signal, attributed to sulfuric acid vapor, occurred just above 50 km at low latitudes on the dayside and nightside of the planet. Fig. 7 shows the absorptivity within the equatorial and midlatitudinal region (0 50 S) as a function of solar zenith angle SZA (left) and local true solar time LTST (right). Analogous to Fig. 6, the absorptivity map in Fig. 7 represents the averaged absorptivity over 6 years, where 78 absorptivity profiles were averaged in 5 bins in SZA (left) and 0.5 h bins in LTST (right). It can be clearly

6 J. Oschlisniok et al. / Icarus 221 (2012) Fig. 9. Sulfuric acid vapor abundance between 50 and 55 km altitude on the dayside (left panel) and nightside (right panel) of the southern hemisphere of Venus derived from 3.6 cm absorptivity data (Fig. 6). A total of 61 profiles on the dayside and 61 profiles on the nightside (ingress and egress) from the years 2006 to 2011 were averaged in equal latitudinal bins of 5 width. Increased abundances are observed at low and mid-latitudes (0 50 S) near 50 km. Fig. 10. Averaged sulfuric acid vapor abundances derived from 3.6 cm absorptivity data (profiles in Fig. 8) on the dayside (left panels) and nightside (right panels) from low latitudes (upper row), cold collar latitudes (middle row) and polar latitudes (lower row).

7 946 J. Oschlisniok et al. / Icarus 221 (2012) seen that the absorptivity remains strong over a wide range of SZA ( ) and LTST (3 22 h). We conclude that increased absorptivity is present in the equatorial and midlatitudinal region all around the planet. A decrease in the absorptivity is observed poleward of 50 S latitude, reaching minimal values of db/ km on the dayside and db/km on the nightside in the polar region (>70 S). A latitudinal variation in the 13 cm absorptivity was also observed in the northern hemisphere in Pioneer Venus radio occultation studies (Fig. 5). The strong absorptivity in the equatorial region at about 50 km (6100 km) is not observed at higher latitudes. Observations from the first and second Pioneer Venus season also reveal a latitudinal gradient in the 13 cm signal absorptivity at about 50 km (Cimino, 1982). The Venus Express and Pioneer Venus absorptivity studies imply a symmetric sulfuric acid vapor distribution within the considered altitude range in the northern and southern hemispheres. The absorptivity maps in Fig. 6 represent an averaged absorptivity of the 3.6 cm radio signal within the Venus southern cloud layer. Examples of averaged absorptivity profiles and their associated uncertainties in various latitude ranges are shown in Fig. 8. An analysis of the uncertainty in the absorptivity profiles is presented in Appendix A. It is evident that the uncertainty is largest at lower latitudes, indicating a larger variability in equatorial absorptivity data. Fig. 9 shows the latitudinal and time-averaged gaseous sulfuric acid abundance in the southern hemisphere. The abundance was derived from the smoothed absorptivity profiles used for the contour maps (Fig. 6) by applying Eq. (11). The left panel of the H 2 SO 4 map shows the dayside and the right panel the nightside of the southern hemisphere. Values of about 1 2 ppm are found between 0 and 70 S latitudes in the altitude range from 50 to about 52 km on the dayside and nightside. At equatorial and midlatitudes (0 50 S) the H 2 SO 4 abundance near the cloud base may reach 3 ppm on the dayside and about 5 ppm on the nightside. At polar latitudes (>70 S) the sulfuric acid vapor abundance does not exceed 1 ppm either on the dayside or on the nightside of the planet within the considered altitude range. The gaseous sulfuric acid abundances derived from Venus Express radio occultation data generally agree with the values reported by Kolodner and Steffes (1998) within a comparable altitude range. Fig. 10 shows examples of averaged sulfuric acid vapor abundance profiles along with their associated uncertainties in various latitude ranges on the dayside and nightside of the planet. The uncertainties represent the linear error propagation of the sulfuric acid vapor abundance profiles located within each latitudinal bin of 10. Considering the CO 2,N 2 and SO 2 contribution to the total absorptivity can sometimes lead to negative H 2 SO 4 vapor values in regions of weak absorptivity, particularly in the polar regions (Fig. 9). This may indicate either an overestimated contribution by the major gases to the total absorptivity in these regions, explained by lower pressure levels at the poles and generally above 54 km, or an underestimated total absorptivity. 4. Conclusions Radio occultation measurements from 122 height profiles during the years provide information on the absorptivity of the 3.6 cm radio signal within the southern hemisphere of Venus. Distinct altitude and latitude variations of the absorptivity are found on both the dayside and nightside. Weak or no absorption of 3.6 cm radio waves is observed above an altitude of about 55 km, where the signal attenuation is dominated by refractive defocusing. Enhanced fluctuation of the signal strength is observed, with highest amplitudes between 55 and 70 km altitude. These intensity scintillations must be attributed to atmospheric gravity waves (Leroy and Ingersoll, 1995) for which the greatest activity is known to exist within the upper clouds. Temperature inversions and multipath effects, observed in this range of altitudes in the Venus atmosphere, are also capable of affecting the signal intensity. Increased absorptivity is observed below an altitude of about 55 km revealing a distinct latitudinal gradient. The strongest absorptivity is detected in equatorial and midlatitudes (0 50 S) near 50 km altitude, reaching maximal values of db/km on the dayside and db/km on nightside. The increased level of absorptivity indicates either the presence of a higher cloud base level (Jenkins and Steffes, 1991) or the result of accumulated sulfuric acid vapor within this latitudinal and altitudinal region (Krasnopolsky and Pollack, 1994; Imamura and Hashimoto, 2001). Sulfuric acid vapor abundances of about 1 2 ppm are observed within this region reaching maximal values near 50 km of 3 ppm on the dayside and about 5 ppm on the nightside. Low absorptivity was detected in the polar region (>70 S) with values of db/km on the dayside and db/km on the nightside, resulting in a maximal sulfuric acid vapor abundance of 1 ppm. A latitudinal variation in the 13 cm absorptivity was also observed in the northern hemisphere in Pioneer Venus radio occultation studies (Jenkins and Steffes, 1991; Cimino, 1982). This implies a symmetric sulfuric acid vapor distribution within the considered altitude range in the northern and southern hemispheres. Moreover the inferred sulfuric acid vapor abundances in Fig. 9 agree well with the H 2 SO 4 (g) values derived by Kolodner and Steffes (1998) within the overlapping altitude range. Acknowledgments The Venus Express Radio Science experiment VeRa is funded by the Deutsches Zentrum für Luft-und Raumfahrt (DLR) Bonn under grant 50QM1004. Support for Venus Express Radio Science activities at Stanford University is provided by NASA through a JPL Contract. We thank P. Varanasi, S. Asmar and T. W. Thompson for their support at JPL. We also thank the personal of the Venus Express project at ESTEC, ESOC, ESAC, JPL and the ESTRACK ground station antennas for their continuous support. We particularly thank the VEX Project scientist H. Svedhem and the VEX Mission Operations Manager F. Jansen. Appendix A. Error analysis The basic expression used to estimate the uncertainty of the computed absorptivity a and the sulfuric acid vapor abundance q H2 SO 4 was derived by considering the first order in the Taylor series Dy i ¼ XN j Dx j ; ða:1þ where Dy i is the uncertainty of the ith sample y i, and N is the number of variables x j in y i with their uncertainties Dx j. Eq. (A.1) forms the standard formalism in studying the influence of Dx j on y i when the uncertainty Dx j is small compared to x j. The error bars placed on the vertical absorptivity and sulfuric acid vapor profiles represent the square roots of the diagonal elements of the symmetric matrix C y ¼ Dy Dy T ; ða:2þ where Dy is a (i 1)-vector consisting of the elements Dy i. In order to compute the uncertainty of the absorptivity and the sulfuric acid vapor profiles, it is necessary to estimate the uncertainty of all Dx j, where the x j are the ray impact parameter Da, the bending angle Dd, the signal strength DP, the ray periapsis

8 J. Oschlisniok et al. / Icarus 221 (2012) Dr 0, the refractivity Dn, the pressure Dp and the temperature DT. These uncertainties were assumed to be small scale variations about the vertical profiles. In order to isolate these disturbances, the profiles of a, d, P, r 0, p and T have been smoothed by applying a three point moving average window. The samples become denser with decreasing altitude and the vertical width of the window varies from more than 2 km above the clouds to less than 0.3 km within the clouds. The averaged profiles have been subtracted from the original data and the residuals served as the uncertainty for the corresponding profiles. Atmospheric waves with vertical wavelengths larger than the vertical width of the three point window will not contribute to the estimated uncertainty. The uncertainties may possibly be overestimated in altitude regions where this criterion is not met. The uncertainty profiles achieved in this way, show different types of behavior. While the uncertainty in the signal strength DP and pressure Dp increase with decreasing altitude, the uncertainty in the temperature DT has the opposite behavior. In contrast the uncertainties in the bending angle Dd, ray impact parameter Da and ray periapsis Dr 0 are highest between altitudes of about 60 and 85 km. The uncertainty in the refractivity Dn was achieved by inserting Eq. (A.1) in Eq. (1), yielding minimal values around 100 km and maximal values near 50 km. The method by Jenkins and Steffes (1991) has been adopted for the calculation of the uncertainty in the absorptivity Da. The result of the integral in Eq. (7) is named F. The absorptivity is computed by taking the derivative of F with respect to a, and multiplying the result with n/(2pa). According to Eq. (A.1), the uncertainty is then achieved by DF þ Dn; where the uncertainty DF was computed by Da; and the uncertainty Ds of the excess attenuation s is given by @s DP þ @d Dd: ða:3þ ða:4þ ða:5þ Applying Eq. (A.2) on Eq. (A.3) yields error bars for a single absorptivity profile (Fig. 4). The uncertainty of averaged profiles (Fig. 8) is, according to Eq. (A.1), given by Da ¼ XN 1 X k Da j ¼ j M k¼1a 1 X M Da j ; M j¼1 ða:6þ which represents averaged error bars of M single absorptivity profiles. Error bars displayed on averaged absorptivity profiles (Fig. 8) were achieved by applying Eq. (A.2) on Eq. (A.6) by assuming Da j - Da k 0 for all j = k and Da j Da k = 0 for all j k. This implies that all averaged absorptivity profiles are uncorrelated. The uncertainty in the sulfuric acid vapor abundance Dq H2 SO 4 is according to the Eqs. (11) and (A.1) given by Dq H2 SO 4 H 2 SO 4 H2 SO 4 H 2 SO 4 H2 SO Dp H 2 SO 4 ða:7þ where the uncertainty in the absorptivity by sulfuric acid vapor Da H2 SO 4 can be achieved by applying Eq. (A.1) on Eq. (8) Da H2 SO 4 H 2 SO Da H 2 SO CO2 ;N 2 Da CO2 ;N 2 H 2 SO SO2 Da SO2 : ða:8þ While Da CO2 ;N 2 is the uncertainty of the absorptivity by CO 2 and N 2, achieved by applying Eq. (A.1) on Eq. (9) Da CO2 ;N 2 CO 2 ;N DT CO 2 ;N 2 ða:9þ Da SO2 is the uncertainty in the absorptivity by SO 2 computed by inserting Eq. (A.1) in Eq. (10) Da SO2 SO DT SO 2 Dp: The uncertainty of the temperature and pressure profiles is in the order of DT 10 2 K and Dp 300 Pa between an altitude of about km. The contribution of T and p along with their uncertainties yield values of Da CO2 ;N 2 and Da SO2 in the order of db/km within this altitude range. The uncertainty of the absorptivity by carbon dioxide and nitrogen Da CO2 ;SO 2 as well as by sulfur dioxide Da SO2 can therefore be neglected and Eq. (A.8) becomes Da H2 SO 4 H 2 SO 4 Da ¼ Da: The contribution H2 SO 4 =@T DT H2 SO 4 =@p Dp to the uncertainty of the sulfuric acid vapor mixing ratio Dq H2 SO 4 is in the order of 1 30 ppb, which is negligible compared H2 SO 4 =@a H2 SO 4 Da H2 SO 4. Therefore Eq. (A.7) is reduced to Dq H2 SO 4 ¼ q H 2 SO 4 a H2 SO 4 Da: ða:12þ Eq. (A.12) was used to compute error bars of the averaged sulfuric acid vapor abundance profiles in Fig. 10. The uncertainty Da ¼ Da H2 SO 4 represents the averaged uncertainty computed in Eq. (A.2) and Eq. (A.6). Particularly at polar latitudes and at higher altitudes, the absorptivity computed for carbon dioxide, nitrogen and by sulfur dioxide a CO2 ;N 2 þ a SO2 shows higher values than the absorptivity a derived from the measurements. In this case, the absorptivity by sulfuric acid vapor a H2 SO 4 from Eq. (8) has negative values, leading to negative H 2 SO 4 (g) abundances. 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