Statistical and computational uncertainties in atmospheric profiles from radio occultation: Mariner 10 at Venus

Radio occultation studies of planetary atmospheres and ionospheres are based on measurements of the frequency and amplitude of the received radio signal. These measurements have random errors due to noise in the receiving system and linearly mapped into atmospheric profiles to give uncertainties can be estimated from the data and linearly mapped into atmospheric profiles to give uncertainties in temperature, T, pressure, p, and absorption profiles. For Mariner 10 occultation immersion at Venus, the standard deviations of T and p due to receiver noise are less than 2° K and 2 mbar over the range of radii from 6087 to 6140 km, based on our reduction from analog, “ open-loop” data. The temperature has a systematic error due to boundary uncertainty, estimated to be 50°K at 6140 km, that decays rapidly with depth; below 6117 km, it is less than 0.5°K. For the attenuation profile, systematic errors incurred during our calculations are more important than statistical errors. We estimate an upper bound to the uncertainty which is 32% at the peak value of absorption, which is about 0.01 db/km and occurs at a radius of 6096 km. A calculation of the 95% confidence limits for T profiles indicates that the local deviations are statistically significant to about 1°K or less. We have also analyzed “closed-loop” data to give temperature profiles which deviate from the open-loop results by less than 0.2°K below 6110 km but by as much as 2°K in the upper atmosphere. For the same occultation and the same boundary conditions, our closed-loop T-p profile is within 2°K of that of P. D. Nicholson and D. O. Muhleman but differs from those derived by A. J. Kliore by as much as 10°K. We cannot account for deviations as large as the latter by minor differences in trajectory information or computational methods.     

Turbulence in planetary occultations: III. Effects on atmospheric profiles derived from intensity measurements

The intensities of radio and optical signals observed during spacecraft and stellar occultations by planets scintillate due to atmospheric turbulence. The combined effect of turbulent fluctuations in refractivity and the average atmospheric gradient are found to produce slightly smaller signal intensity scintillations than the homogeneous case when there is no gradient, in contrast to a prediction that the scintillations would be markedly increased. Profiles of atmospheric temperature and pressure derived from intensity measurements are found to have much larger errors due to turbulence than do the corresponding profiles derived from radio Doppler frequency measurements. However, such errors are still small in the limit of weak scattering, which is assumed here. Radio and optical occultation experiments tend to be complementary since the generally shorter distances involved in the former mean that the radio experiments can probe relatively deeply into the atmosphere, while the optical experiments are limited to tenuous atmospheric regions. Because the radio experiments generally have a much greater dynamic measurement range, they are more likely to encounter conditions where strong scattering occurs than will the optical occultation experiments, provided the rms turbulent refractivity increases with depth approximately as the refractivity of the quiescent atmosphere.     

Scintillations during occultations by planets I. An approximate theory

Fluctuations are observed during occultations of both stars and spacecraft by planetary atmospheres. Existing treatments of spacecraft scintillations ignore a major effect unique to occultations: the severe flattening of the Fresnel zone or source image by defocusing. Other large effects, due to “saturation” of the scintillation, have also been ignored. The deeper portions of atmospheric temperature and density profiles inferred from occultation data are seriously in error if other planets' atmospheres are as turbulent as our own. Thus, profiles obtained from entry probes (e.g., the Soviet Venera series) are probably more accurate than those from radio occultation (Mariner 5 and 10) data. Scintillation greatly reduces the information obtainable from occultation observations; much of the detail attributed to layering in published profiles is probably due to aliasing of turbulence. This paper gives an approximately correct theoretical treatment that is a substantial improvement over published theories, and shows how a more accurate theory could be constructed. Some methods for a more accurate determination of atmospheric structure are proposed.     

The radio occultation method for the study of planetary atmospheres

Planets, the Moon and the Sun have a number of ‘atmospheres’ which may be measured by the radio occultation method, using radio links to spacecraft which are being occulted by the body as seen from Earth. Molecular atmospheres, ionospheres, magnetospheres, particulate atmospheres and several general-relativistic atmospheres can all affect radio signal charecteristics. Measured Doppler frequencies, signal amplitudes and wave polarizations contain information on these atmospheres. From such occultation measurements it is possible, for example, to derive profiles which are related to the changes with height of temperature, pressure, density, free electron concentration and the fractional volume occupied by particulate matter. Important clues for identifying molecular or particulate constituents can also be obtained. Even though one type of measurement may be sensitive to several different atmospheric characteristics, these characteristics can often be separated due to differences in their dependence on radio wavelength or on height above the surface.     

A re-analysis of the 1971 Beta Scorpii occultation by Jupiter: study of temperature fluctuations and detection of wave activity

Data from the 13 May 1971 β Scorpii occultation by the southern polar region of Jupiter (Vapillon et al., 1973, Astron. Astrophys. 29, 135-149) are re-analyzed with current methods. We correct the previous results for an inacurrate background estimation and calculate new temperature profiles, that are now consistent with the results of other observers of this occultation, as well as with the current knowledge of the jovian atmosphere. The characteristics of the profiles of temperature gradient and the spectral behavior of the temperature fluctuations are found to be similar to the results of previous investigations of planetary atmospheres and in agreement with the presence of atmospheric propagating gravity waves in the jovian atmosphere. We use a wavelet analysis of the temperature profiles to identify the dominant modes of wave activity and compare the reconstructed temperature fluctuations to model-generated gravity waves.     

A seasonal climate model of the atmospheres of the giant planets at the voyager encounter time: I. Saturn's stratosphere

A radiative seasonal model which incorporates a multilayer radiative transfer treatment at wave-lengths longward of 7 μm is presented and applied to Saturn's stratosphere. Opacities due to H₂-He, CH₄, C₂H₂, and C₂H₆ are included. Season-dependent insolation is shown to produce a strong hemispheric asymmetry decreasing with depth at the Voyager encounter times, and seasonal amplitudes of 30°K at the poles are predicted in the high stratosphere. The ring-modulated dependence of the insolation and the orbital eccentricity are shown to have a significant effect. Calculations agree closely with the Voyager 1 and 2 radio occultation ingress profiles recorded at 76°S and 36.5°S for CH₄/H₂ = 3.5 + 1.4/? 1.0 × 10^?3;the estimated errors include modeling systematic errors and uncertainties in the occultations profiles. The possible role of aerosols in the stratospheric heating is analyzed. The Voyager 2 egress profile recorded at 31°S cannot be reproduced by calculations. Some constraints on the C₂H₂ and C₂H₆ abundances are derived. The upper portion of the occultation profiles (p < 3mbar) can be matched for C₂H₂/H₂ = 1.0 + 1.3/?0.6 × 10^?7, C₂H₆/H₂ = 1.5 + 1.8/?0.9 × 10^?6 at 76°S and C₂H₂/H₂ = 4 + 6/?4 × 10^?8, C₂H₆/H₂ = 6 + 9/?6 × 10^?7 at 36.5°N. At the northern occultation latitude, the discrepancy with the concentrations derived from analysis of IRIS spectra by R. Courtin, D. Gautier, A. Marten, B. Bézard, and R. Hanel (1984, Astrophys. J.287) can be explained by a sharp variation of the mixing ratios of these gases with altitude in the upper stratosphere. Other interpretations are discussed.     

Statistical analysis of the results of champ occultation data processing at Shanghai astronomical observatory

With the development of the CPS (Global Positioning System) it has become possible to retrieve accurate profiles of atmospheric temperature, pressure and moisture from CPS occultation data. Using the inversion module developed in Shanghai Astronomical Observatory, (SHAG), we obtained atmospheric profiles from more than 2700 CHAMP occultation events observed in the period 2002 Aug. 1–17. The retrieved profiles are compared with the data of the European Center for Medium-range Weather Forecasts (ECMWF), and their errors are analyzed. An optimal method of statistical analysis is proposed and applied. The statistical results show that GPS occultation data may contribute valuably to numerical weather forecast and long-term monitoring of the earth's climate.     

The composition and vertical structure of the lower cloud deck on Venus

The opportunity to determine the planetwide temperature and cloud structure of Venus using radio occultation techniques arose with Pioneer Venus. Amplitude and Doppler data provided by the radio occultation experiment offered a unique and powerful means of examining the atmospheric properties in the lower cloud region.Absorption due to gaseous components of the atmosphere was subtracted from the measured absorption coefficient profiles before they were used to compute cloud mass contents. This absorption was found to represent a small part of the total absorption, depending on the latitude. In the main cloud deck, gaseous absorption contributes 10 to 20%, however, at the bottom of the detected absorption layer the sulfuric acid vapor contributes up to 100% due to increased vapor pressures. The clouds are the primary contributing absorbers in the 1- to 3-bar level of the Venus atmosphere. Below about 3 bars, depending on the latitude, absorption due to sulfuric acid vapor dominates.If a cloud particle model consisting of a solid nonabsorbing dielectric sphere with a concentric liquid sulfuric acid coating is invoked, the absorptivity of the particles increases from that of a pure sulfuric acid liquid sphere, and the mass content derived from the absorption coefficient profiles decreases. As the ratio of the core radius to the total radius (q) increases, absorption increases by more than a factor of 10 for high values of q. In the case of pure sulfuric acid droplets, the conductivity is sufficiently high that some of the field is excluded from the interior of the droplet thereby reducing the absorption. When a dielectric core of nonabsorbing material is introduced, the surface charge density is reduced and the absorption increases.The mass contents for all orbits in the equatorial region of Venus were calculated using values of q from 0 to 1. The resulting profiles match the probe mass content profiles at similar locations when a q of 0.97 is chosen.The wavelength dependence of the absorption for the spherical shell model varies with q from 1/λ² for pure liquid to λ^0.2 for a large core. A q of from 0.96 to 0.98 results in a wavelength dependence of 1/λ^1.0 to 1/λ^1.4 which matches the radio occultation absorption wavelength dependence and the microwave opacity wavelength dependence.Mass content profiles using a q of 0.97 were determined for occultations in the polar, collar, midlatitudinal, and equatorial regions assuming q remains constant over the planet. The results show considerable variability in both the level and the magnitude of the lower cloud deck. The cloud layer is lowest in altitude in the polar region. This might be expected as the temperature profile is cooler in the polar region than over the rest of the planet. The mass content is greatest in the polar and collar regions; however, many of the collar profiles were cut off due to fluctuations resulting from increased turbulence in the collar region. The mass contents are least dense in the midlatitude regions. There is a sharp lower boundary at about 1.5 bars in the equatorial and midlatitude regions and at about 2.5 bars in the polar region. Measurements made by the Particle Size Spectrometer and nephelometers also showed sharp lower cloud boundaries at this level.     

The structure of Neptune's upper atmosphere: The stellar occultation of 24 May 1981

Observations of the 24 May 1981 occultation of an uncatalogued star by Neptune made at the Cerro Tololo Inter-American Observatory have been analyzed to yield temperature profiles of Neptune's upper atmosphere for number densities near 5 × 10¹³ cm^?3. The mean temperatures at immersion (latitude ?56°) and emersion (latitude ?16°) obtained by numerical inversion were 140 ± 10°K and 154 ± 10°K, respectively. The immersion and emersion profiles are remarkably similar in overall shape, suggestive of global atmospheric layering. From the astrometry of the event, precise relative positions of Neptune and the occulted were obtained.     

On the mass motions and the atmospheric states of moustaches

Analyses of broad moustache profiles of Balmer lines and Ca ii H and K lines are performed based upon our spectroscopic observation under good seeing conditions. Hα emission profiles are found to consist of three components, i.e., a central absorption, a Gaussian core and a power-law wing. Each of them has a different Doppler shift from others. From the data of Doppler shifts, mass motions with velocity of about 6 km s^?1 are found to be present in chromospheric levels of moustache atmospheres. Computations of Hα emission profiles radiated from a variety of model atmospheres are made. Comparison of computed profiles with the observed ones leads us to the conclusion that a broad Hα profile is due to a formation of heated (ΔT = 1500 K) and condensed (?/? ₀ = 5) chromospheric layers relative to the normal.     

Studies of Planetary Atmospheres by Stellar Occultations: Application to Mars and Venus

We consider the application of the stellar occultation method to the studies of planetary atmospheres and its history and briefly describe the instruments designed for such measurements (SPICAM/Mars-96, GOMOS/ENVISAT). In comparison with solar occultations, this method allows the profiles to be measured almost at any time of the day and at any location of the planet, irrespective of the orbit of the spacecraft from which observations are carried out. Based on the measuring characteristics of the SPICAM-Light UV spectrometer for the spectral range 118–320 nm with a resolution of 0.9 nm (for the ESA Mars Express Mission; launched in June 2003), we simulate the capabilities of the method to study the Martian atmosphere. In stellar occultation measurements, the stellar spectrum changes because of the absorption by CO₂ and O₃, other gases, and aerosols. The profiles of the CO₂ and O₃ density (and, hence, the temperature) and the aerosol content can be restored by solving the inverse problem. Observations of bright stars (no fewer than 30) three to five times in a turn allow us to measure the atmospheric density at altitudes 10–150 km with an accuracy of about 2% and the temperature at altitudes 20–130 km with an accuracy of 3 K. Ozone is measured with an accuracy of several percent at altitudes 25–40 km or lower, depending on the conditions. Optically thin clouds and hazes, particularly on the nightside where no measurements are possible in reflected light, can be studied. The SPICAV experiment, which is similar to SPICAM-Light, is part of the Venus Express (to be launched in 2005) scientific payload. On Venus, stellar occultations can be used to measure the atmospheric temperature and density above clouds at altitudes up to 130–150 km and to study the SO₂ profile. The results of our simulations can be easily extended to instruments with different measuring characteristics.     

Strong turbulence and atmospheric waves in stellar occultations

Many of the problems of stellar occultation observations stem from the difficulty of determining the effects of realistic atmospheric structure on the lightcurves. General techniques for producing model lightcurves for a variety of realistic atmospheric irregularities, including turbulence and inertia-gravity waves, are presented and applied. Using numerical simulations which model the propagation of a wave through a phase-changing screen, the limit of strong scintillations for one-dimensional, Kolmogorov-like turbulence, both for a point source and for extended sources, is investigated in some detail, and significant departures from the behavior in the weak scintillation regime are found. The results are compared with published analytical results and recent occultation data. The effects of large-scale atmospheric waves with realistic horizontal structure are examined, and the reliability of the numerical inversion method of retrieving the true atmospheric vertical structure under circumstances of strong ray crossing and horizontal inhomogeneities is assessed. The simulations confirm that large-scale layered features of the atmosphere are accurately recovered; horizontally inhomogeneous structures (including turbulence) with coherence scale $\text{L ? (2πRH)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ (where R = planetary radius and H = scale height) have little effect on the derived temperature profiles. It is concluded that analysis of occultations may eventually allow us to determine both the quasiglobal atmospheric structure and the statistical characteristics of small-scale refractivity variations.     

The 2003 November 14 occultation by Titan of TYC 1343-1865-1: II. Analysis of light curves

We observed a stellar occultation by Titan on 2003 November 14 from La Palma Observatory using ULTRACAM with three Sloan filters: u^′, g^′, and i^′ (358, 487, and 758 nm, respectively). The occultation probed latitudes 2° S and 1° N during immersion and emersion, respectively. A prominent central flash was present in only the i^′ filter, indicating wavelength-dependent atmospheric extinction. We inverted the light curves to obtain six lower-limit temperature profiles between 335 and 485 km (0.04 and 0.003 mb) altitude. The i^′ profiles agreed with the temperature measured by the Huygens Atmospheric Structure Instrument [Fulchignoni, M., and 43 colleagues, 2005. Nature 438, 785–791] above 415 km (0.01 mb). The profiles obtained from different wavelength filters systematically diverge as altitude decreases, which implies significant extinction in the light curves. Applying an extinction model [Elliot, J.L., Young, L.A., 1992. Astron. J. 103, 991–1015] gave the altitudes of line of sight optical depth equal to unity: 396±7 and 401±20 km (u^′ immersion and emersion); 354±7 and 387±7 km (g^′ immersion and emersion); and 336±5 and 318±4 km (i^′ immersion and emersion). Further analysis showed that the optical depth follows a power law in wavelength with index 1.3±0.2. We present a new method for determining temperature from scintillation spikes in the occulting body's atmosphere. Temperatures derived with this method are equal to or warmer than those measured by the Huygens Atmospheric Structure Instrument. Using the highly structured, three-peaked central flash, we confirmed the shape of Titan's middle atmosphere using a model originally derived for a previous Titan occultation [Hubbard, W.B., and 45 colleagues, 1993. Astron. Astrophys. 269, 541–563].     

The occultation of Mariner 10 by Mercury

An analysis of the Mariner 10 dual frequency radio occultation recordings has yielded new information on the radius and atmosphere of Mercury. The ingress measurements which were conducted near 1.1° North latitude and 67.4° East longitude on the night side of the planet, gave a value for the radius of 2439.5 ± 1 km. Egress near 67.6° North latitide and 258.4° East longitude in the sunlit side yielded a radius of 2439.0 ± 1 km. The atmospheric measurements showed the electron density to be less than 10³ cm^?3 on both sides of the planet. From the latter result one may infer an upper limit to the dayside surface gas density of 10⁶ molecules per cm³.     

火星电离层无线电掩星探测仿真研究

对中俄联合火星星-星电离层掩星技术体制进行了分析和介绍,采用三维射线追踪方法对电离层掩星事件的电波观测值进行了模拟计算,并利用模拟的掩星观测数据进行了电子密度廓线反演,结果说明仿真算法可靠.利用仿真的方法,分别对掩星电波相位观测误差和卫星轨道误差等带来的反演误差进行了个例计算和分析,结果得到:5%周的相位测量误差对白天电离层掩星探测结果的影响可以忽略,而夜间电子密度测量的绝对误差小于4×108 m-3;卫星轨道误差对掩星的主要影响是导致电离层高度抬升或下降.结果表明,中俄联合火星电离层掩星探测技术体制先进,可望获得高精度的电子密度廓线;其技术体制也可以用于月球电离层环境的探测.     

Martian occultation of ϵ Gem as observed from the C. E. Kenneth Mees observatory

Ground-based observations of the occultation of ? Gem by Mars on April 8, 1976 have been reduced in the manner of French et al. [Icarus 33, 186–202 (1978)] to yield the scale height and temperature profiles of the Martian atmosphere for number densities between 10¹³ and 10¹⁵ cm^?3. The deduced variations in temperature are remarkably similar to those obtained by Elliot et al. [Astrophys. J.217, 661–679 (1977)] and to the in situ measurements from the Viking landers.     

On the structure of Mars' atmosphere at 120–220 km

Altitude dependences of [CO₂] and [CO₂⁺] are deduced from Mariner 6 and 7 CO₂⁺ airglow measurements. CO₂ densities are also obtained from n_e radio occultation measurements. Both [CO₂] profiles are similar and correspond to the model atmosphere of Barth et al. (1972) at 120 km, but at higher altitudes they diverge and at 200–220 km the obtained [CO₂] values are three times less the model. Both the airglow and radio occultation observations show that a correction factor of 2.5 should be included into the values for solar ionization flux given by Hinteregger (1970). The ratio of [CO₂⁺]/n_e is 0.15–0.2 and, hence, [O]/[CO₂] is ～3% at 135 km. An atmospheric and ionospheric model is developed for 120–220 km. The calculated temperature profile is characterized by a value of T ≈ 370°K at h ? 220 km, a steep gradient (～2°/km) at 200-160 km, a bend in the profile at 160 km, a small gradient (～0.7°/km) below and a value of T ≈ 250°K at 120 km. The upper point agrees well with the results of the Lyman-α measurements; the steep gradient may be explained by molecular viscosity dissipation of gravity and acoustical waves (the corresponding energy flux is 4 × 10^?2 erg cm^?2sec^?1 at 180 km). The bend at 160 km may be caused by a sharp decrease of the eddy diffusion coefficient and defines K ≈ 2 × 10⁸cm²sec^?1; and the low gradient gives an estimate of the efficiency of the atmosphere heating by the solar radiation as ? ≈ 0.1.     

Stellar occultation spikes as probes of atmospheric structure and composition

The characteristics of spikes observed in the occultation light curves of β Scorpii by Jupiter are reviewed and discussed. Using a model in which the refractivity (density) gradients in the Jovian atmosphere are parallel to the local gravitational field, the spikes are shown to yield information about (i) the [He]/-[H₂] ratio in the atmosphere, (ii) the fine scale density structure of the atmosphere and (iii) high-resolution images of the occulted stars. The spikes also serve as indicators for ray crossing. Observational limits are placed on the magnitude of horizontal refractivity gradients; these appear to be absent on scales of a few kilometers at altitudes corresponding to number densities less than 2 × 10¹⁴ cm^?3. Spikes are produced by atmospheric density variations, perhaps due to atmospheric layers, density waves or turbulence. To discriminate among these possibilities, future occultation observations should be made from a number of observation sites at two or more wavelengths simultaneously with high time resolution techniques. Given a large telescope and suitable observing techniques, useful information about Jupiter's atmosphere can be obtained from future occultations of early-type stars as faint as V ～ + 6–7.     

Comment on absorbing regions in the atmosphere of Venus as measured by radio occultation

Two recent papers, one by A.J. Kliore, C. Elachi, I.R. Patel, and J.B. Cimeno, Icarus37, 51-2- 72, 1979, and one by B. Lipa and G.L. Tyler, Icarus39, 192–208, 1979, reach fundamentally different conclusions concerning microwave absorption in the atmosphere of Venus, even though they are based on the same Mariner 10 radio occultation data. The Lipa and Tyler results are in general agreement with earlier Mariner 5 measurements analyzed by G. Fjeldbo, A.J. Kliore, and V.R. Eshleman, Astron. J.76, 123–140, 1971. We find that in the Kliore et al. treatment: (1) the effects of measurements and analysis uncertainties in the derived values of absorption are underestimated; (2) an incorrect formula is used for computation of the refractive effects needed to determine the absorption; (3) detailed features of a derived profile of absorption would have been created in an optically thin region by known motions of the spacecraft antenna, if its axial direction were biased about 0.5° from the computed directions; and (4) this particular angular bias is consistent with other available information about an apparent residual difference between true and reconstructed antenna pointing directions. We conclude that: (1) there is no credible evidence for measurable microwave absorption in the atmosphere of Venus at heights greater than 55 km for any of the wavelengths that have been used in radio occultation experiments, even though Kliore et al. indicate that there are significant amounts up to at least 70 km for both Mariner 10 wavelengths (13 and 3.6 cm); (2) absorption in the region 35 to 50 km has been reasonably well determined from the two concordant Mariner 5 and 10 analyses, but only at one wavelength (13 cm); and (3) improved instrumentation and careful planning and analysis will be required for the radio occultation technique to realize its potential for the study of absorbing regions in the atmospheres of Venus and the major planets.     

Independent radio-occultation studies of venus' atmosphere

Two independent analyses of the dual-frequency radio-occultation experiment performed by Mariner 10 at Venus are presented. Using closed-loop frequency data obtained at NASA's Goldstone facility, we have computed S- and X-band pressure-temperature profiles for Venus' neutral atmosphere, and an S-band profile of the nightside ionosphere. Neutral atmosphere dispersion between the two frequencies is negligible (less than 0.1% in refractivity), as expected for a CO₂ atmosphere. The results confirm those obtained by Howard et al. (1974) from the same S-band data with an accuracy of ±5°K at a given pressure level, though there is a discrepancy of 1 km in the radial scale between the two analyses. These two Mariner 10 profiles are compared with the Mariner 5 occultation profile and in situ measurements by Veneras 8, 9, and 10. The occultation was also monitored at the Owens Valley Radio Observatory, though only at X-band. Despite the much lower quality of these data, a reasonable neutral atmosphere refractivity profile above 65 km was obtained from the occultation entry. Uncertainties in the calculated temperatures, however, are too large to permit useful comparison with previous results. The existence of real anomalies in both the amplitude and frequency of the signal during exit from occultation is confirmed.