Venus Express radio occultation observed by PRIDE
T. M. Bocanegra-Bahamon, G. Molera Calves, L.I. Gurvits, G. Cimo, D. Dirkx, D.A. Duev, S.V. Pogrebenko, P. Rosenblatt, S. Limaye, L. Cui, P. Li, T. Kondo, M. Sekido, A.G. Mikhailov, M.A. Kharinov, A.V. Ipatov, W. Wang, W. Zheng, M. Ma, J.E.J. Lovell, J.N. McCallum
AAstronomy & Astrophysics manuscript no. paperVEX c (cid:13)
ESO 2019March 6, 2019
Venus Express radio occultation observed by PRIDE
T. M. Bocanegra-Bahamón , , , G. Molera Calvés , , L.I. Gurvits , , G. Cimò , , D. Dirkx , D.A. Duev , S.V.Pogrebenko , P. Rosenblatt , S. Limaye , L. Cui , P. Li , T. Kondo , , M. Sekido , A.G. Mikhailov , M.A.Kharinov , A.V. Ipatov , W. Wang , W. Zheng , M. Ma , J.E.J. Lovell , and J.N. McCallum Joint Institute for VLBI ERIC, P.O. Box 2, 7990 AA Dwingeloo, The Netherlands.e-mail: [email protected] Department of Astrodynamics and Space Missions, Delft University of Technology, 2629 HS Delft, The Netherlands. Shanghai Astronomical Observatory, 80 Nandan Road, Shanghai 200030, China. University of Tasmania, Private Bag 37, Hobart, Tasmania, 7001, Australia Netherlands Institute for Radio Astronomy, P.O. Box 2, 7990 AA Dwingeloo, The Netherlands. California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA. ACRI-ST, 260 route du Pin Montard, F06904 Sophia-Antipolis Cedex, France. Space Science and Engineering Center, University of Wisconsin, Madison, WI, USA. Xinjiang Astronomical Observatory, CAS, 150 Science 1-Street, Urumqi, Xinjiang 830011, China. NICT Kashima Space Technology Center, 893-1, Kashima, Ibaraki, 314-8501, Japan. Institute of Applied Astronomy of Russian Academy of Sciences, 191187 St. Petersburg, Russia.March 6, 2019
ABSTRACT
Context.
Radio occultation is a technique used to study planetary atmospheres by means of the refraction and absorption of a space-craft carrier signal through the atmosphere of the celestial body of interest, as detected from a ground station on Earth. This techniqueis usually employed by the deep space tracking and communication facilities ( e.g.,
NASA’s Deep Space Network (DSN), ESA’sEstrack).
Aims.
We want to characterize the capabilities of the Planetary Radio Interferometry and Doppler Experiment (PRIDE) technique forradio occultation experiments, using radio telescopes equipped with Very Long Baseline Interferometry (VLBI) instrumentation.
Methods.
We conducted a test with ESA’s Venus Express (VEX), to evaluate the performance of the PRIDE technique for thisparticular application. We explain in detail the data processing pipeline of radio occultation experiments with PRIDE, based on thecollection of so-called open-loop Doppler data with VLBI stations, and perform an error propagation analysis of the technique.
Results.
With the VEX test case and the corresponding error analysis, we have demonstrated that the PRIDE setup and processingpipeline is suited for radio occultation experiments of planetary bodies. The noise budget of the open-loop Doppler data collectedwith PRIDE indicated that the uncertainties in the derived density and temperature profiles remain within the range of uncertaintiesreported in previous Venus’ studies. Open-loop Doppler data can probe deeper layers of thick atmospheres, such as that of Venus,when compared to closed-loop Doppler data. Furthermore, PRIDE through the VLBI networks around the world, provides a widecoverage and range of large antenna dishes, that can be used for this type of experiments.
Key words.
Radio occultation, PRIDE, Venus, Venus Express
1. Introduction
The Planetary Radio Interferometry and Doppler Experiment(PRIDE) is a technique based on the adaptation of the tradi-tional far-field very long baseline interferometry (VLBI) astro-metric technique applied to near-field targets - spacecraft insidethe solar system - with the main objective of providing pre-cise estimates of the spacecraft state vectors. This is achievedby performing precise Doppler tracking of the spacecraft carriersignal and near-field VLBI observations in phase-referencing mode (Duev et al. 2012, 2016; Bocanegra-Bahamón et al. 2018).PRIDE is suitable for various applications in planetary and spacescience, such as determination of planetary ephemerides (Dirkxet al. 2017), characterization of the interplanetary plasma (Mol-era et al. 2014) and detection of interplanetary coronal mass ejec-tion (ICME) (Molera et al. 2017). In this work we present an-other application: the characterization of planetary atmospheresand / or ionospheres by means of radio occultation observations. Article number, page 1 of 15 a r X i v : . [ a s t r o - ph . I M ] M a r & A proofs: manuscript no. paperVEX
The implementation and application of radio occultation ex-periments to planetary science has been widely discussed in theliterature ( e.g.
Phinney & Anderson 1968; Fjeldbo & Eshleman1968; Fjeldbo et al. 1971; Jenkins et al. 1994; Yakovlev 2002;Pätzold et al. 2007; Tellmann et al. 2009; Withers et al. 2014). Aplanetary radio occultation experiment involves a ‘central’ body(a planet or a natural satellite), the atmosphere (or ionosphere)of which is to be studied, and two radio elements: a transmit-ter onboard a spacecraft orbiting (or performing a flyby about)the central body and, one or multiple ground stations on Earth.At certain geometries, the spacecraft is occulted by the centralbody with respect to the line of sight of the receiving groundstation. As the spacecraft gets gradually occulted by the cen-tral body, the spacecraft carrier signal cuts through successivelydeeper layers of the planet’s atmosphere, experiencing changesin its frequency and amplitude before being completely blockedby the body. This phase is known as ingress. Then the same phe-nomena is observed as the signal emerges from behind the body.This phase is known as egress. The refraction that the signalundergoes due to the presence of the atmosphere can be deter-mined from the frequency shift observed throughout the occul-tation event. In addition to this, accurate estimates of the space-craft state vector are needed to obtain the refractivity as a func-tion of the radius from the occultation geometry. In the case ofPRIDE, the receiving element is not a single station but a net-work of Earth-based radio telescopes. PRIDE provides multiplesingle-dish Doppler observables that are utilized to derive theresidual frequencies of the spacecraft carrier signal, and addi-tionally interferometry observables that are used, along with theDoppler observables, as input to determine the spacecraft statevector. The final product of this experiment is the derivation ofvertical density, pressure, and temperature profiles of the centralbody’s atmosphere.The purpose of this paper is to evaluate the performance ofthe PRIDE setup for radio occultation experiments of planetaryatmospheres. We note that the radio occultation technique can beproductive for studies of atmosphereless celestial bodies as well( e.g. , the Moon, Saturn’s rings), enabling the characterization ofthe shape of the occulting body. However, we do not discuss thisapplication here. As a test case, we analyze several observationsof ESA’s Venus Express (VEX) spacecraft using multiple radiotelescopes from the European VLBI Network (EVN), AuScopeVLBI array (Australia) and NICT (Japan), during April 2012,May 2012 and March 2014. The VEX orbiter was launched in2005.11.09, arriving at Venus in April 2006 and remained in or-bit around the planet until end of 2014. The operational orbit ofthe spacecraft was a highly elliptical ( e = . i = ∼ ◦ ) with a ∼ ff es et al. 1994; Jenk-ins et al. 1994; Hinson & Jenkins 1995), ESA’s VEX (Pätzoldet al. 2004, 2007; Tellmann et al. 2009, 2012; Peter et al. 2014;Girazian et al. 2015) and recently with JAXA’s Akatsuki (Ima-mura et al. 2017; Ando et al. 2017). The composition of Venus’ionosphere is primarily O + and smaller amounts of CO + , O + andother trace species (Girazian et al. 2015). Although radio occul-tation experiments cannot be used to determine the specific com-position of the ionosphere, the radio waves are sensitive to theelectron distribution and therefore density profiles of the iono-spheric plasma can be derived down to ∼
100 km. Similarly, forVenus’ neutral atmosphere density and temperature profiles canbe derived assuming the composition of the atmosphere (96.5%CO , 3.5% N ) (Kliore 1985; Sei ff et al. 1985). In the case ofVenus’ atmosphere, radio occultation data provide a vertical cov-erage of ∼ ∼
65 km (Limaye et al. 2017).In this paper we present the results of VEX occultation obser-vations obtained with radio telescopes equipped with VLBI dataacquisition instrumentation. We explain the processing pipelinecarried out with the PRIDE setup and present the correspond-ing error propagation analysis. Sections 2.1 and 2.2 present thetheoretical background of the radio occultation method and theapproximations taken into account when formulating the obser-vation model. Section 2.3 shows the theoretical derivation of theatmospheric profiles from the carrier signal frequency residuals.Section 3 presents the overall description of the experiment andthe results found. Section 3.1 describes the setup of the experi-ment, describing the observations used and the data processingpipeline. Section 3.2 present the resulting Venus’ atmosphericprofiles using the PRIDE setup. Section 3.3 presents the errorpropagation analysis, through the processing pipeline, from theDoppler observables to the derived atmospheric properties. Sec-tion 4 presents the conclusions of this technology demonstration.
2. The radio occultation experiment
In a radio occultation experiment, the carrier signal of thespacecraft experiences refraction, absorption and scattering asit passes behind the visible limb of the planetary body due to itspropagation through the planet’s atmosphere on its way to thereceiving ground station on Earth. The physical properties of theplanetary atmosphere can be inferred by analyzing the changesin frequency and amplitude of the received carrier signal.
During the occultation event, the spacecraft carrier signal propa-gates through the atmosphere of the celestial body, experiencinga modulation of phase and a decrease in amplitude. The variationin phase is proportional to the real part of the medium’s complexrefractive index and the decrease in amplitude is proportional tothe imaginary part of the medium’s complex refractive index,also known as absorption factor (Eshleman 1973). These refrac-tive and absorptive radio e ff ects are caused by the presence ofneutral gases and plasma in the atmosphere and ionosphere. Inthe study at hand, only the frequency changes in the carrier signal Article number, page 2 of 15. M. Bocanegra-Bahamón et al.: Venus Express radio occultation observed by PRIDE are analyzed. Therefore, the amplitude data from which absorp-tivity profiles are derived, are not treated in this paper.As the spacecraft signal gets refracted crossing the di ff erentlayers of the planet’s atmosphere, the variation of the real part ofcomplex refractive index (treated simply as the refractive indexin the remainder of this paper) as a function of altitude can bedetermined, for a particular cross section of the atmosphere. Be-fore establishing the relation between the frequency changes ofthe received carrier signal and the planet’s atmospheric refractiveindex as a function of altitude, let us consider some approxima-tions that simplify the models used to relate these quantities.As for most planets, the variations in the electrical proper-ties of Venus’ atmosphere occur at scales much larger than thespacecraft signal wavelength (Fjeldbo et al. 1971). Hence, theradio wave can be treated as a light ray and its trajectory can bedetermined by geometric optics. As in previous radio occulta-tion experiments of Venus, such as Fjeldbo et al. (1971); Jenkinset al. (1994); Tellmann et al. (2012), we assume the planet’s at-mosphere can be modeled as a spherically symmetric medium,made of concentric shells, each of them with a constant refractiveindex. From geometric optics the propagation path of the signalcan be described as a ray r ( s ) parameterized by an arclength s that satisfies the following di ff erential equation (Born & Wolf1999), dds (cid:32) n d r ds (cid:33) = ∇ n (1)where n ( r ) is the refractive index, which for the case of sphericalsymmetry is a function of radial distance only. Hence, the raytrajectory, as it bends through the medium, can be traced giventhe medium refractive index as a function of the radius. This isknown as the forward problem. However, we are interested inthe inverse problem, where based on the ray path parameters, -the bending angle and the impact parameter-, the refractivity ofprofile of the atmosphere is retrieved. In the radio domain the bending that the signal undergoes as itcrosses the planet’s ionosphere and neutral atmosphere cannotbe measured directly. However, it can be retrieved from the fre-quency shift experienced by the received signal at the groundstations. In this section, we will first introduce the relation be-tween the frequency shift and the ray parameters of the receivedsignal, to then establish the relation between ray parameters andrefractive index as a function of radius.
The geometry of the occultation is determined by the occultationplane ( i.e. , the plane defined by the center of the target planet,the position of tracking station and the position of the space-craft, each with respect to the target planet) as shown in Figure1. The reference frame used has its origin at the center of massof the target planet, with the negative z -axis pointing to the posi-tion of the tracking station at reception time, the n -axis parallelto the normal of the occultation plane and the r -axis perpendic-ular to both the z - and n - axis. In this scenario, the target bodyis assumed to have a spherically symmetric and stationary at-mosphere and the ray path refraction occurs on the occultationplane, reducing it to a two-dimensional problem as shown in Fig-ure 2. The bending of the refracted ray path is then parameterized with respect to the free-space ray path by means of the angles δ r and β r . The angle δ r is defined between the position vector ofthe spacecraft at transmission time with respect to the trackingstation at reception time and the ray path asymptote in the direc-tion the radio wave is received at the tracking station at receptiontime. The angle β r is defined between the position vector of thetracking station at reception time with respect to the spacecraftat transmission time and the ray path asymptote in the directionthe radio wave is transmitted by the spacecraft at transmissiontime (see Figure 2).This description of the occultation geometry is based onFjeldbo et al. (1971), where the approach that will be discussedin this section was first introduced. Multiple authors have ex-panded on this approach ( e.g., Lipa & Tyler 1979; Jenkins et al.1994; Withers et al. 2014) including the relativistic correctionsinto the analysis.
To isolate the perturbation that the spacecraft signal experienceswhen propagating through the media along the radio path, weevaluate the di ff erence between the detected carrier frequencyand the prediction of the received frequency at the ground sta-tion, assuming for the latter that the signal is propagating throughfree-space (including geometrical e ff ects, such as relative posi-tion and motion between the spacecraft and ground station, Earthrotation and relativistic corrections). If perturbations due to thesignal propagation through the Earth’s atmosphere, ionosphereand interplanetary medium are accounted for, then the remain-ing observed perturbation is solely due to the atmosphere andionosphere of the planet of interest.As shown by Kopeikin & Schäfer (1999, Eq. 266), the fre-quency received at a tracking station on Earth f R at a receptiontime t R is given by, f R = f T − k R · v R / c − k T · v T / c R ( v R , v T , t R , t T ) (2)where c is the free-space velocity of light, f T is the spacecrafttransmission frequency at the transmission time t T , v R and v T are the barycentric velocity vectors of the receiving station at t R and of the spacecraft at t T , respectively, k R and k T are theunit tangent vectors in the direction along which the radio wavepropagates at t T and t R , respectively, and the term R gives thespecial and general relativistic corrections: R ( v R , v T , t R , t T ) = (cid:34) − ( v T / c ) − ( v R / c ) (cid:35) / (cid:34) a ( t T ) a ( t R ) (cid:35) / b ( t R ) b ( t T ) (3)where the terms a and b are derived as explained in Section 2.2of Bocanegra-Bahamón et al. (2018). All position and velocityvectors are expressed in the solar system barycentric frame.The frequency residuals are subsequently found by evalu-ating the di ff erence between detected frequency f R , detected andthe predicted frequency in free-space f R , f ree − space received at theground station at t R , as follows: ∆ f = f R , detected − f R , f ree − space (4)assuming that f R , detected has been corrected for the e ff ects ofpropagation through interplanetary plasma and the Earth’s atmo-sphere and ionosphere. Article number, page 3 of 15 & A proofs: manuscript no. paperVEX
In the case of free-space, the direction along which the radiosignal propagates is the same at t R and t T , hence k R = k T in Eq2, and δ r = β r =
0. When the signal gets refracted by theatmosphere of the target planet, k R and k T become the two raypath asymptotes shown in blue in Figure 2. Hence, the ray pathasymptotes for both cases can be defined as follows: − k R , f ree − space = ˆr sin δ s + ˆz cos δ s (5) − k T , f ree − space = ˆr cos β e + ˆz sin β e (6) − k R , detected = ˆr sin ( δ s − δ r ) + ˆz cos ( δ s − δ r ) (7) − k T , detected = ˆr cos ( β e − β r ) + ˆz sin ( β e − β r ) (8)Fig. 1: Sketch of the occultation plane. The occultation plane isdefined by the center of mass of the target planet, the positionof tracking station and the position of the spacecraft, each withrespect to the target planet.Hence, a relation between the frequency residuals and theangles that parameterize the bending of the ray path can be es-tablished by replacing Eq. (2) and Eqs. (5) to (8) into Eq. (4), ∆ f = R f T (cid:32) c + v r , R sin ( δ s − δ r ) + v z , R cos ( δ s − δ r ) c + v r , T cos ( β e − β r ) + v z , T sin ( β e − β r ) − c + v r , R sin δ s + v z , R cos δ s c + v r , T cos β e + v z , T sin β e (cid:33) (9)where v r , R is the r -component of v R and v z , R is the z -componentof v R at reception time t R , v r , T is the r -component of v T and v z , T is the z -component of v T at transmission time t T . The angles β e and δ s are defined between the position vector of the spacecraftat t T with respect to the ground station at t R , and the r -axis and z -axis, respectively ( β e + δ s = π/ a from the planet’scenter of mass to the tangent at any point along the ray path is aconstant a , a = | z R | sin ( δ s − δ r ) = ( r T + z T ) / sin ( β e − γ − β r ) (10)where a is called the ray impact parameter. Eqs. (9) and (10) canbe solved simultaneously for the two ray path angles δ r and β r - assuming that the state vectors of the spacecraft and trackingstation are known - using the numerical technique introduced byFjeldbo et al. (1971). Once the values of δ r and β r are deter-mined, the total bending angle of refraction α of the ray path isobtained by adding them (see Figure 2). α = δ r + β r (11)Applying this procedure, for every ∆ f obtained at each sampledtime step (Eq. 4) the corresponding ray path parameters, bend-ing angle α and impact parameter a , are derived. We follow thesign convention adopted by Ahmad & Tyler (1998) and With-ers (2010) where positive bending is considered to be toward thecenter of the planet. In this section we will establish the relations that link the raypath parameters to the physical properties of the layer of the at-mosphere the radio signal is sounding. Following Born & Wolf(1999), assuming a radially symmetric atmosphere representedby K concentric spherical layers each with a constant refractiveindex n , the bending angle α is related to n through an Abeltransform: α ( a k ) = − a k r = ∞ (cid:90) r = r k d ln( n ( r )) dr dr (cid:113) ( n ( r ) r ) − a k (12)where r is the radius from the center of the planet to the ray andthe subscripts represent the k -th layer, the deepest layer each raypath reaches, which corresponds to a specific reception time atthe receiver.As explained in Fjeldbo et al. (1971), Eq. (12) can be invertedto have an expression for the refractive index n in terms of α and a :ln n k ( a k ) = π a (cid:48) = ∞ (cid:90) a (cid:48) = a k α ( a (cid:48) ) da (cid:48) (cid:113) a (cid:48) − a k (13) n ( r k ) = exp π (cid:90) α (cid:48) = α (cid:48) = α ( a k ) ln a ( α (cid:48) ) a k + (cid:32) a ( α (cid:48) ) a k (cid:33) − / d α (cid:48) . (14)Using the total refraction bending angles found as explained inSection 2.2, the refractive index for the k -th layer can be deter-mined by performing the integration over all the layers the rayhas crossed: n k ( a k ) = exp π a (cid:90) a ˜ α da (cid:48) (cid:113) a (cid:48) − a k + ... + π a k − (cid:90) a k ˜ α k da (cid:48) (cid:113) a (cid:48) − a k (15)where ˜ a i is the average value of the bending angles α i in a layer:˜ α i = α i ( a i ) + α i − ( a i − )2 with i = ... k . (16)A ray with impact parameter a will cross the symmetric atmo-sphere, down to a layer k of radius r k . This minimum radiusis found via the Bouguer’s rule, which is the Snell law of re-fraction for spherical geometries. As explained in Born & Wolf(1999) and Kursinski et al. (1997), r k is related to a k by: Article number, page 4 of 15. M. Bocanegra-Bahamón et al.: Venus Express radio occultation observed by PRIDE
Fig. 2: Geometry of the radio occultation depicted on the occultation plane. In this case, the figure shows the ray path as it getsrefracted by the planet’s ionosphere (in gray), where it gets bent by an angle α from its original path. r k = a k n k (17)The refractivity as a function of the radius depends on the localstate of the atmosphere. The total refractivity of the atmosphere µ is given by the sum of the components due to the neutral at-mosphere and ionosphere. For each layer the total refractivity isgiven by (Eshleman 1973): µ k = ( n k − = µ n , k + µ e , k (18)where µ n is the refractivity of the neutral atmosphere: µ n = κ N n (19)where κ is the mean refractive volume and N n is the neutral num-ber density, and µ e is the refractivity of the ionosphere: µ e = − N e e π m e (cid:15) f (20)where e is the elementary charge, m e is the electron mass, (cid:15) isthe permittivity of free-space, f is the radio link frequency and N e is the electron density.In the ionosphere, the electron density is high and the neutraldensities can be several orders of magnitude lower, therefore inthe ionosphere µ e is dominant and µ n is negligible. On the otherhand, at lower altitudes, the situation is the opposite: the neutraldensities are high and electron densities are low. Hence in prac-tice, if the value of µ is negative, µ e is assumed to be equal to µ and if µ is positive, then µ n is assumed to be equal to µ .Assuming hydrostatic equilibrium, the vertical structure ofthe neutral atmosphere can be derived from the neutral densityprofile N n ( h ) and the known constituents of the planetary atmo-sphere. The pressure in an ideal gas is related to the temperature T ( h ) and number density of the gas by: p ( h ) = kN n ( h ) T ( h ) (21)where k is the Boltzmann’s constant. Using Eq. (21) and theequation for hydrostatic equilibrium the temperature profile can be found from the following formula (Fjeldbo & Eshleman1968): T ( h ) = T ( h ) N ( h ) N ( h ) + ¯ mkN ( h ) h (cid:90) h g ( h (cid:48) ) N ( h (cid:48) ) dh (cid:48) (22)where ¯ m is the mean molecular mass, g ( h ) is the gravitationalacceleration and h is an altitude chosen to be the top of the at-mosphere for which the corresponding temperature T ( h ), takenfrom the planet’s reference atmospheric model, is assigned asboundary condition. From Eq.(22) it can be seen that the sen-sitivity of T ( h ) to the upper boundary condition T ( h ) rapidlydecreases due to the N ( h ) / N ( h ) factor.
3. PRIDE as an instrument for radio occultationstudies: a test case with Venus Express
The PRIDE technique uses precise Doppler tracking of thespacecraft carrier signal at several Earth-based radio telescopesand subsequently performs VLBI-style correlation of these sig-nals in the so-called phase referencing mode (Duev et al. 2012).In this way, PRIDE provides open-loop Doppler observables, de-rived from the detected instantaneous frequency of the spacecraftsignal (Bocanegra-Bahamón et al. 2018), and VLBI observables,derived from the group and phase delay of the spacecraft signal(Duev et al. 2012), that can be used as input for spacecraft orbitdetermination and ephemeris generation. During a radio occul-tation experiment, the Doppler observables are utilized to derivethe residual frequencies of the spacecraft carrier signal. Theseare subsequently used to derive atmospheric density profiles, asexplained in Section 2. Both, the Doppler and VLBI observables,can be used for orbit determination, allowing the accurate es-timation of the spacecraft state vectors during the occultationevent. In this paper, we will focus on the error propagation inthe frequency residuals obtained with the open-loop Doppler ob-servables derived with PRIDE, and will use the VEX navigationpost-fit orbits derived by the European Space Operations Center(ESOC) , which do not include PRIDE observables, to calculatethe spacecraft state vectors in the occultation plane. ftp: // ssols01.esac.esa.int / pub / data / ESOC / VEX / Article number, page 5 of 15 & A proofs: manuscript no. paperVEX
The current data processing pipeline of the PRIDE radio occul-tation experiment is represented in Figure 3. The first part ofthe software comprises three software packages developed toprocess spacecraft signals (the software spectrometer
SWSpec ,the narrowband signal tracker
SCtracker and the digital phase-locked loop
PLL )(Molera et al. 2014) and the software correla-tor SFXC (Keimpema et al. 2015) which is able to perform VLBIcorrelation of radio signals emitted by natural radio sources andspacecraft. These four parts of the processing pipeline are usedfor every standard PRIDE experiment (yellow blocks in Figure3). The output at this point are open-loop Doppler and VLBIobservables. The methodology behind the derivation of theseobservables using the aforementioned software packages is ex-plained by Duev et al. (2012); Molera et al. (2014); Bocanegra-Bahamón et al. (2018). The second part of the software wasdeveloped for the sole purpose of processing radio occultationexperiments. It consists of three main modules: the frequencyresiduals derivation module, the geometrical optics module andthe Abelian integral inversion module. From these three modulesthe vertical density profiles, and subsequently, temperature andpressure profiles of the target’s atmosphere can be derived. Thefrequency residuals module uses the output of the
PLL which arethe time averaged carrier tone frequencies detected at each tele-scope. To produce the frequency residuals the predictions of thereceived carrier signal frequency at each telescope is computedas described in (Bocanegra-Bahamón et al. 2018), and then thefrequency residuals are corrected with a baseline fit to accountfor the uncertainties in the orbit used to derive the frequencypredictions (Section 3.3). In the geometrical optics module thestate vectors retrieved from VEX navigation post-fit orbit aretransformed into a coordinate system defined by the occultationplane as explained in Section 2, and using the frequency resid-uals found in the previous step, the bending angle and impactparameter at each sample step is found using Eqs. (9) to (11)using the procedure described in Section 2. The refractivity pro-file is derived in the Abelian integral inversion module, wherethe integral transform that relates the bending angle with the re-fractive index (Eq. 12) is solved by modeling the planet’s atmo-sphere as K concentric spherical layers of constant refractivityand applying Eq. (15), as explained in Section 2. The number oflayers and their thickness is defined by the integration time stepof the averaged carrier frequency detections. In the atmosphericmodel, each sample is assumed to correspond to a ray passingtangentially through the middle of the n -th layer, as described inFjeldbo et al. (1971) (Appendix B).To provide a noise budget of PRIDE for radio occulta-tion experiments we used five observation sessions in X-band(8.4 GHz) with Earth-based telescopes between 2012.04.27 and2012.05.01, and one in 2014.03.23, when VEX was occulted byVenus. Table 1 shows a summary of the telescopes involved inthe observations and Table 2 shows a summary of the observa-tions and participating telescopes per day. The observations wereconducted in three scans : in the first scan the antennas pointingto the spacecraft for 19 minutes up to ingress where there is lossof signal, in the second the antennas pointing to the calibratorsource for 4 minutes, and in the third pointing back to the space-craft starting right before egress for 29 minutes. The exceptionbeing the 2014.03.23 session where the ingress and egress weredetected in one single scan (no calibrator source was observed in https: // bitbucket.org / spacevlbi / A scan is the time slot in which the antenna is pointing to a specifictarget ( i.e , a spacecraft or a natural radio source) between, because there was no loss of signal throughout the oc-cultation). Figure 4 shows the signal-to-noise ratio (S / N) of thetwo spacecraft scans, ingress and egress, as recorded by the 32-m Badary telescope on 2012.04.30. Usually, for orbit determina-tion purposes, the part of the scan where the S / N of the detectionsstarts dropping due to the signal refraction in the planet’s atmo-sphere is discarded. However, this is precisely the part of thescan that is of interest for radio occultation experiments. For thecase of VEX, during radio occultation sessions the spacecraftwas required to perform a slew manoeuvre to compensate forthe severe ray bending due to Venus’ thick neutral atmosphere(Häusler et al. 2006).As explained in Bocanegra-Bahamón et al. (2018), whenprocessing the observations a polynomial fit is used to model themoving phase of the spacecraft carrier tone frequencies alongthe time-integrated spectra per scan. In order to provide an ap-propriate polynomial fit to the low S / N part of the detection, af-ter running
SWSpec the scan is split in two parts: right beforethe signal starts being refracted in the case of the ingress, andright after it stops being refracted in the case of the egress (Fig-ure 4). The initial phase polynomial fit and the subsequent stepswith
SCtracker and
DPLL are conducted as if they were twoseparate scans.Fig. 3: Radio occultation processing pipeline. The first part ofthe software, which comprises the
SWSpec , SCtracker , PLL and
SFXC correlation software, (in yellow blocks in Figure 3) is usedfor every standard PRIDE experiment. This part of the process-ing pipeline gives open-loop Doppler and VLBI observables asoutput. The second part of the software was developed for thesole purpose of processing radio occultation experiments. It con-sists of three main modules: the frequency residuals derivationmodule, the geometrical optics module and the Abelian integralinversion module. The output of this second part are vertical den-sity, temperature and pressure profiles of the target’s atmosphere.
Figure 5a shows an example of the frequency residuals found forUr and Sh during ingress for the 2012.04.27 session in compari-son with those of NNO, as provided by ESA’s planetary sciencearchive (PSA) . From ∼ ftp://psa.esac.esa.int/pub/mirror/VENUS-EXPRESS/VRA/ Article number, page 6 of 15. M. Bocanegra-Bahamón et al.: Venus Express radio occultation observed by PRIDE
Fig. 4: Example of the S / N of a signal detection during a radio occultation. This is the VEX signal detection obtained with Bd inthe session of 2012.04.29. At around 19400 s the S / N starts rapidly decreasing marking the beginning of the occultation ingress,which lasts for ∼ ∼ / N after egress corresponds to theclosest approach of VEX to the center of mass of Venus. A higher S / N is typically observed during VEX’s radio science observationphase (scheduled around the pericenter passage) because the telemetry is o ff during this phase. During the tone tracking part of theprocessing, in order to provide an appropriate polynomial fit to the low S / N part of the detection, the ingress and egress scan aresplit in two. For this particular example, for the ingress scan at 19400 s and for the egress scan at 21080 s.Table 1: Summary of the radio telescopes involved in the obser-vations.
Observatory Country TelescopeCode Diameter (m)Sheshan (Shanghai) China Sh 25Nanshan (Urumqi) China Ur 25Tianma China T6 65Badary Russia Bd 32Katherine Australia Ke 12Kashima Japan Ks 34 by the ionosphere, as shown in Figure 5b, and from ∼ ∼ ∼ × m − and altitude ∼
140 kmand the secondary layer has density ∼ × m − and altitude ∼
125 km. This nightside (SZA =
142 deg) profile is consistentwith other observations of the deep nightside ionosphere ( e.g. ,Kliore et al. (1979); Pätzold et al. (2007)).Figure 6 shows an example of the resulting ingress profilesof Venus’ neutral atmosphere from the Doppler frequency resid-uals corresponding to the session of 2012.04.29. Figure 6 showsthe refractivity, neutral number density, temperature and pres-sure profiles derived with Eqs. (18), (19), (22) and (21), respec-tively. Despite the fact that both NNO and Bd have similar an-tenna dish sizes, with Bd the spacecraft signal is detected downto a lower altitude. During this observation the elevation of Bdwas between 50-58 deg while for NNO it was 20-25 deg. Severalnoise contributions at the antenna rapidly increase, such as theatmospheric and spillover noise, at low elevation angles, whichresult in lower S / N detections. Besides this, the profiles corre-sponding to Bd and Ke were derived from the open loop Dopplerdata obtained with the PRIDE setup, while the profiles of NNO were derived using the frequency residuals obtained from ESA’sPSA, corresponding to closed loop Doppler tracking data. Theadvantage of using open loop Doppler data for radio occultationresides in the ability of locking the signal digitally during thepost-processing. This allows the estimation of the frequency ofthe carrier tone at the deeper layers of the atmosphere. This is notthe case with closed-loop data, since once the system goes out oflock the signal is lost. Figure 7 shows the frequency detectionsobtained by the 65-m Tianma during the session of 2014.03.23,where the carrier signal of the spacecraft is detected throughouta complete occultation, including the time slot where the plane-tary disk is completely occulting the spacecraft. This is possiblebecause of the extremely strong refraction the signal undergoeswhile crossing Venus’ neutral atmosphere. The fact that there isno loss-of-signal (LOS) in this particular session highlights theadvantage of using both large antenna dishes and open loop dataprocessing for radio occultation experiments. On one hand, thelarge antenna dishes have low thermal noise allowing higher S / Ndetections throughout the occultation, and on the other hand, theopen-loop processing allows the detection of the carrier signalthrough thick media. It is worth to mention, however, that for thesession 2014.03.23 the closed-loop Doppler data of NNO is notcurrently publicly available, therefore Tianma’s results could notbe compared with those of NNO.Table 3 gives the location and depth of the radio occultationprofile obtained during the di ff erent sessions. Figure 8 shows theneutral atmosphere temperature profiles obtained using Eq. (22)throughout the di ff erent sessions in 2012, displaying the ingressand egress profiles separately. Besides the assumption of a spher-ically symmetric atmosphere, the radio occultation method asdiscussed in this paper, also assumes hydrostatic equilibrium anda known composition. The composition is assumed to be con-stant in a spherically homogeneous well-mixed atmosphere be-low the altitude of the homopause ( < ∼
125 km). For the analysisin this paper, atmospheric composition of the neutral atmosphereis assumed to be 96.5% CO , 3.5% N (Kliore 1985; Sei ff et al.1985). In order to derive the temperature profiles, an initial guessfor the boundary temperature ( T ( h ) in Eq. 22) of 170 K at 100km altitude was used. In the case of Venus, the boundary tem-perature is typically chosen to be between 170-220 K at 100 kmaltitude, with an uncertainty of 35 K. These values are taken fromthe temperature profiles of the Venus International Reference At-mosphere (VIRA) model (Sei ff et al. 1985; Keating et al. 1985) Article number, page 7 of 15 & A proofs: manuscript no. paperVEX
Table 2: Summary of observations.Station time Telescopes Solar elongation Distance to S / C(UTC) Code (deg) (AU)2012-04-27 05:10 - 06:05 Ur,Sh 41 0.472012-04-29 05:10 - 06:05 Bd,Ke 40 0.462012-04-30 05:10 - 06:05 Bd 40 0.452012-05-01 05:10 - 06:05 Bd,Ks 39 0.442014-03-23 02:50 - 03:16 T6 46 0.68Table 3: Summary of location and depth of the radio occultation profiles obtained during the di ff erent sessions.Date Station Mode Minimum altitude Latitude LST(km) (deg) (hh:mm:ss)2012-04-27 Ur Ingress 46.2 -20.2 01:48:19Egress 43.7 83.4 23:19:29Sh Ingress 45.8 -20.0 01:48:08Egress 44.7 83.5 23:08:122012-04-29 Bd Ingress 42.7 -19.7 01:59:55Egress 44.0 83.6 23:17:13Ke Ingress 47.8 -23.6 01:57:49Egress 44.3 83.6 23:12:252012-04-30 Bd Ingress 41.0 -19.3 02:05:49Egress 42.0 83.7 23:12:392012-05-01 Bd Ingress 41.9 -22.0 02:10:27Egress 43.1 83.7 23:35:13Ks Ingress 45.1 -26.8 02:07:31Egress 47.2 83.8 23:13:372014-03-23 T6 Ingress 54.9 33.3 00:02:07Egress 54.9 33.3 00:02:07and the empirical model of Venus’ thermosphere (VTS3) (Hedinet al. 1983).As shown in Figure 8, the troposphere is probed down to alti-tudes of ∼
41 km. From this altitude to about ∼
58 km the temper-ature decreases as altitude increases. Performing a linear fit from43 to 58 km, the mean lapse rate found for the egress profiles is9.5 K / km. For the ingress profiles, a fit was performed from 41to 50 km that resulted in a mean lapse rate of 6.4 K / km and an-other fit was made from 50 to 58 km that resulted in a mean lapserate of 9.3 K / km. From the VIRA model, the mean lapse rate be-tween 41-58 km from the surface is 9.8 K / km (Sei ff et al. 1985).At about ∼
58 km the linear trend experiences a sharp change,which is identified as the tropopause, where the upper bound-ary of the middle clouds is present (Sei ff et al. 1985; Tellmannet al. 2012). From the altitudes 60 to 80 km, where the middle at-mosphere extends, there is a clear di ff erence between the ingressand egress profiles. This is due to the di ff erence in latitudes of theoccultation profiles, which are ∼ ◦ S and ∼ ◦ N for the ingressand egress, respectively, for the sessions from 2012.04.27 to2012.05.01. For the egress profiles, the region between ∼
65 to ∼
70 km is approximately isothermal, and from 70 km to 80 kmthe temperature decreases at a much lower lapse rate than atthe troposphere. For the ingress profile, this isothermal behav-ior only extends for a couple of kilometers from ∼
62 km. Thedi ff erence in lapse rate between the ingress and egress profilesalong the altitude range from 60 to 80 km can be attributed to dynamical variations on local scales, eddy motions or gravitywaves (Hinson & Jenkins 1995). It is desired to start the inte-gration of the temperature profiles (Eq. 22) as high as possible.However, at high altitudes (above ∼
100 km) there is not enoughneutral gas detected and the noise introduced by the measure-ments is large with respect to the estimated refractivity values.For this reason, the upper boundary is chosen to be at an alti-tude of ∼
100 km, where the standard deviation of the refractiv-ity is ∼ / T ( h ) rapidly decreases with altitude due tothe factor N ( h ) / N ( h ). Therefore, it was found that when usingdi ff erent upper boundary temperatures (170 K, 200 K and 220 K)at 100 km for the detections of a single station, the temperatureprofiles of that particular station converge at ∼
90 km. When us-ing the same upper boundary for all stations participating in oneobservation ( e.g. , the temperature profile shown in Figure 6c forthe 2012.04.29 session), the temperature profiles of the di ff er-ent stations converge at ∼
80 km. This is due to the e ff ect of thenoise fluctuations of the refractivity profile, where the standarddeviation in refractivity drops from 10% of the estimated valueat 100 km to ∼ .
1% at ∼
80 km.
Article number, page 8 of 15. M. Bocanegra-Bahamón et al.: Venus Express radio occultation observed by PRIDE(a) (b)(c) (d)(e)
Fig. 5: Frequency residuals retrieved from open-loop data from Ur and Sh compared to the residuals from closed-loop data fromNNO, during occultation ingress in the session of 2012.04.27. Panel (a) shows the frequency residuals of the detected signal up toLOS. Panel (b) zooms in the frequency residuals showing when the signal starts getting refracted by Venus’ ionosphere at around19605 s. Panel (c) and (d) show the corresponding altitude probed versus the frequency residuals of the data shown in panel (a) and(b), respectively. Panel (e) shows the corresponding electron density profile, where the secondary V1 layer and main V2 layer ofVenus’ ionosphere are identified.
In order to quantify the performance of the PRIDE techniquefor the purpose of radio occultation experiments we carry out anerror propagation analysis. To this end, we begin by propagatingthe frequency residual uncertainties derived from the open-loop Doppler data of the VLBI stations, through the multiple steps ofdata processing pipeline (Figure 3) to derive the uncertainties inthe atmospheric properties of Venus measured during the radiooccultation observations.The frequency residual uncertainty σ ∆ f in time is the un-certainty of the di ff erence between the observed frequency (also Article number, page 9 of 15 & A proofs: manuscript no. paperVEX
Fig. 6: Refractivity, neutral number density, temperature and pressure profiles of the 2012.04.29 session. The profiles correspondingto the 32-m Bd and 12-m Ke were derived from the open loop Doppler data obtained with the PRIDE setup, and the profiles of the35-m NNO were derived using the frequency residuals obtained from ESA’s PSA, corresponding to closed loop Doppler trackingdata. Despite the fact that both NNO and Bd have similar antenna dish sizes, with Bd the spacecraft signal is detected down to alower altitude, due to the fact that the Doppler data obtained with Bd is open loop, while for NNO is closed loop.Fig. 7: Detection of the carrier signal of the spacecraft through-out a complete occultation, using the open-loop Doppler data re-trieved by the 65-m T6 during the session of 2014.03.23. The leftpanel shows the S / N throughout the detection, showing that thereis no LOS during the whole occultation. The right panel showsthe frequency residuals, which show from 10650 to 11100 s theingress followed by the egress from 11100 to 11450 s. Thismeans that T6 was able to detect the signal while the planetarydisk was completely occulting VEX.known as the sky frequency) f sky , and the predicted frequency f pred , the latter derived as explained in Bocanegra-Bahamónet al. (2018). The σ ∆ f is evaluated before the signal starts gettingrefracted by the planet’s atmosphere (referred to in this paperas the frequency residuals in ‘vacuum’ for the sake of simplic-ity), that is, in the first part of the two-part split ingress scan, orthe second part of the split egress scan. In practice, the standarddeviation is calculated after performing a baseline correction tothe frequency residuals in vacuum. While the uncertainty of thesky frequency is random, the uncertainty of the predicted fre-quency is systematic, reflecting the errors of the estimated statevectors of the spacecraft and ground stations, and the errors inthe ephemerides of Venus and the Earth, used to generate theDoppler predictions, and the errors in the estimation of the nom-inal spacecraft transmission frequency at transmission time. In the absence of these systematic errors, the frequency residuals invacuum would be the remaining Doppler noise of the signal (dueto the random uncertainties) with zero mean value, as shown inFigure 5a up to 19600 s. The presence of systematic errors inthe frequency residuals in vacuum results in a non-zero meanconstant trend. This e ff ect is corrected by applying a baselinecorrection based in the algorithm described by Gan et al. (2006).For this reason, the σ ∆ f , after baseline correction, is assumed tobe solely due to σ f sky .The uncertainty of the f sky derived with the procedure shownin Bocanegra-Bahamón et al. (2018) depends on the integrationtime used, the noise introduced by the instrumentation on theground stations and onboard the spacecraft, and the noise intro-duced by the propagation of the signal, σ prop , through the inter-planetary medium, and, the Earth’s ionosphere and troposphere.In the case of one-way Doppler the instrumental noise is given bythe thermal noise, σ th , introduced by the receiver at the groundstations and the limited power received at downlink, the noiseintroduced by the spacecraft USO, σ US O , the noise introducedby frequency standard used at the ground stations, σ FS , and theantenna mechanical noise, σ mech . The modeled σ ∆ f is calculatedby, σ ∆ f = ( σ th + σ US O + σ FS + σ mech + σ prop ) f (23)where f is the carrier tone frequency which is ∼ σ th ( τ ) ≈ (cid:113) BS φ / π f τ (24)where S φ is the one-sided phase noise spectral density of thereceived signal in a 1 Hz bandwidth, B is the carrier loop band-width which is 20 Hz for this experiment, f is the nominal fre-quency of the Doppler link and τ is the integration time, which inthis case has the value of 1 s. The relative noise power of the car-rier tone is given by S φ , which is approximated by 1 / (S / N) where
Article number, page 10 of 15. M. Bocanegra-Bahamón et al.: Venus Express radio occultation observed by PRIDE
Fig. 8: Compilation of the temperature profiles obtained with all participating stations during the session of 2012.04.27 to2012.05.01. The left panel shows the ingress temperature profile corresponding to latitudes around 20 deg S. The right panel showsthe egress temperature profiles corresponding to latitudes around 84 deg N.S / N is the signal-to-noise ratio of the signal evaluated in a 1 Hzbandwidth. The thermal noise values estimated with Eq. (24) ofthe X-band Doppler detections for the di ff erent radio telescopesused during the study at hand are summarized in Table 4. Theuncertainties found correspond to values ranging from 1.6 mHzfor the lowest thermal noise, found at the 65-m T6, to 10.4 mHzfor the highest thermal noise, found at the 34-m Ks (higher thanthe one found for the 12-m Ke). As reported by Häusler et al.(2007), the USO that provided the reference frequency for theVEX transponder has an Allan deviation of ∼ × − at inte-gration times 1-100 s, which corresponds to σ US O f < . σ ∆ f for each station is calculated using Eq. (23) and displayed in Ta-ble 4, along with the measured σ ∆ f of the signal detections at1 s integration time (derived by taking the mean standard devi-ation of the frequency residuals in vacuum). All VLBI stationsare equipped with a hydrogen maser frequency standard that pro-vide a stability of < × − at τ = σ FS f < . ff ects, the noiseinduced by the Earth’s ionosphere is calibrated using the totalvertical electron content (vTEC) maps (Hernández-Pajares et al.2009) and the noise introduced by the Earth’s troposphere is cali-brated using the Vienna Mapping Functions VMF1 (Boehm et al.2006). These two corrections are applied to the Doppler predic-tions before deriving the frequency residuals ∆ f . The noise in-troduced by the remaining errors after calibration with the vTECand VMF1 maps are not quantified in the work at hand. Fur-thermore, the interplanetary plasma noise was not characterizedin this study due to the fact that only X-band detections wereobtained. However, an estimate of the Allan deviation of the in- terplanetary phase scintillation noise can be derived using theapproach described in Molera et al. (2014). Based on the analy-sis of multiple tracking campaigns of the VEX signal, in S- andX-band, at di ff erent solar elongations, a relation (Eq. 6 in Mol-era et al. (2014)) was formulated to estimate the expected phasevariation of the received signal as a function of TEC, σ expected = TEC4000 · (cid:32) . f obs (cid:33) · (cid:18) τ nod s (cid:19) m + [rad] , (25)where TEC is Venus-to-Earth total electron content along theline-of-sight, τ nod is the nodding cycle of the observations, f obs is the observing frequency and m is the spectral index. Since thephase power spectrum S φ is of the form S φ = A f − m , where m is the spectral index and A is a constant, the scintillation contri-bution in the spectral power density can be characterized using afirst order approximation on the logarithmic scale, as explainedin Molera et al. (2014) (Eq. 5). Using this approximation the ex-pected phase variation can be expressed as follows, σ expected = (cid:34) A f − mc · f c m + (cid:35) m + (26)where f c is the cut-o ff frequency of the spectral power densityof the phase fluctuations (usually ∼ < m < S φ = A f − m is (Armstrong et al. 1979), σ y ( τ ) = A τ m π f τ (cid:90) ∞ sin ( π z ) z m dz (27)Based on the results presented in Molera et al. (2014), it is as-sumed a Venus-to-Earth TEC along the line-of-sight of 10 tecu Article number, page 11 of 15 & A proofs: manuscript no. paperVEX at 40 deg elongation (Fig. 6 of Molera et al. (2014)) and a spec-tral index of 2 .
4, which is the average spectral index of more thanhundred observing sessions. Using these values and Eqs. 25 to27 the estimated Allan deviation is of 2 . × − at τ = σ prop f = . ff erence between the measuredand the modeled variances. In the case of T6 the predominantnoise comes from the USO. For Bd, both the thermal noise andthe USO noise represent each ∼
30% of the total frequency resid-uals measured. This indicates that for one-way radio occultationexperiments the noise introduced by the USO is larger than thenoise introduced by the thermal noise of the ground stations,when using antennas with a diameter larger than ∼
30 m. Thislimiting noise source could be avoided by performing two-waytracking during occultations, however this would limit the oc-cultation detections only to ingress passes since the transmittingsignal would be out of lock during egress. The thermal noise ofSh is estimated to be higher than the thermal noise of Ur, whichcoincides with the larger frequency residuals obtained with Sh,despite the fact that both stations have the same antenna diame-ter. The thermal noise of Ke corresponds to ∼
70% of the noisebudget. This is reasonable when compared to the thermal noiseof the other stations, given the fact the Ke has a 12-m diame-ter. On the other hand, the modeled thermal noise for Ks cor-responds to almost 80% of its noise budget, which is extremelyhigh for a 34-m antenna. This was corroborated with the systemtemperature readings for the session of 2012.05.01 (also the onlysession where Ks participated), which were much higher than itsreported nominal system temperature (Campbell, Robert 2018).For this reason the data retrieved with Ks should be discarded.The modeled noise attributed to interplanetary plasma phasescintillation, estimated for elongation angles of ∼
40 degrees, canbe corrected for when multifrequency observations are available(Bertotti et al. 1993; Tortora et al. 2004). For T6 this would cor-respond to a calibration of ∼
20% of the Doppler noise. The noiseintroduced by the ground stations frequency standard in the over-all noise budget is marginal compared to the other sources ofnoise.As shown in Table 4 the modeled noise for the di ff erent tele-scopes is consistently lower than the measured noise. This can beattributed to unmodeled noise ( e.g. , antenna mechanical noise)and errors in the estimates of the propagation noise and the noiseintroduced by the USO. The estimate of the propagation noisegiven in Table 4 includes only the plasma scintillation noise, butnot the remaining errors after calibration of the Earth’s iono-spheric and tropospheric propagation e ff ects. As for the USO,the Allan deviation given in Table 4 represents the nominal fre-quency stability of the USO, hence, not the actual measurementsduring the observations.Regarding the choice of integration time to process the ra-dio occultation scans, there is a trade-o ff to be made betweenvertical resolution and frequency residual noise. The choice of asmall integration time results in a better vertical resolution, butalso results in larger frequency residuals noise. Furthermore, thevertical resolution of the profiles derived using geometrical op-tics are di ff raction limited to the Fresnel zone diameter (Hinsonet al. 1999), which is ≈ √ λ D , where λ is the signal wavelength, D = R cos( β e − γ − β r ), and R , β e , γ and β r are defined as shownin Figure 2. To be consistent with this inherited vertical reso-lution limit of the model the sample spacing should be kept as close to √ λ D as possible, which for this experiment should belarger than ∼
470 m. When processing the signal detections, itwas noticed that the minimum integration time for which thiscondition would be satisfied was 0.1 s down to ∼
50 km from thesurface, since from this altitude on the bending angle of the raypath largely increases. Hence, the integration time was chosen tobe 0.1 s down to an altitude of 50 km and then from this pointdown to lowest altitudes probed an integration time of 1.0 s wasused.Fig. 9: Percentage of the modeled noise sources in the total mea-sured frequency residuals. In the case of T6 the predominantnoise comes from the USO. For Bd, both the thermal noise andthe USO noise represent each 30% of the total frequency resid-uals measured. Although Ur and Sh have the same antenna sizethe thermal noise of Sh is higher than that of Ur. The modeledthermal noise of Ke corresponds to almost 70% of the budget,which in comparison to other stations is reasonable since its an-tenna diameter is only 12 m and the station has an uncooled re-ceiver. On the other hand, in the case of the 34-m Ks, the ther-mal noise corresponds to 80% of the budget which given its sizeindicates an under-performance of the station during the obser-vations it was involved in. In the overall budget, the noise in-troduced by the frequency standard is considered to be marginalwith respect to the other sources of noise.Once the frequency residual uncertainties have been cal-culated we proceed to propagate them through the process-ing pipeline. We assume that the sampled f sky are indepen-dent and uncorrelated, hence the frequency covariance matrix C f = (cid:104) ∆ f ∆ f T (cid:105) is diagonal. In order to derive the uncertainties ofthe ray path parameters, the equations that describe the occulta-tion geometry (Eqs. 10 and 11) are linearized with respect to theray path angles δ r and β r as described by Fjeldbo et al. (1971),and using the standard propagation of errors (Brandt 1997), thecovariance matrix between the bending angle α and the impactparameter a , C α a , can be derived as follows, C α a = M α f C f M Ta f (28)where, M α f = ∂α ∂ f ∂α ∂ f · · · ∂α ∂ f n ∂α ∂ f ∂α ∂ f · · · ∂α ∂ f n ... ... . . . ... ∂α n ∂ f ∂α n ∂ f · · · ∂α n ∂ f n f = ¯ f Article number, page 12 of 15. M. Bocanegra-Bahamón et al.: Venus Express radio occultation observed by PRIDE
Table 4: Noise budget of X-band Doppler detections of the VLBI stations during the radio occultation sessions.
Station Thermal USO Frequency Plasma phase Modeled Measurednoise standard scintillation σ ∆ f σ ∆ f σ th σ th f σ USO σ USO f σ FS σ FS f σ prop σ prop f (mHz) (mHz) (mHz) (mHz) (mHz) (mHz)T6 1 . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − and, M a f = ∂ a ∂ f ∂ a ∂ f · · · ∂ a ∂ f n ∂ a ∂ f ∂ a ∂ f · · · ∂ a ∂ f n ... ... . . . ... ∂ a n ∂ f ∂ a n ∂ f · · · ∂ a n ∂ f n f = ¯ f where n is the number of sampled sky frequencies.The uncertainties associated with the refractive index µ aredetermined as explained in (Lipa & Tyler 1979), using the co-variance matrix C α a . First, Eq. (14) is solved using the trape-zoidal approximation and the embedded exponential function islinearized about zero. Then the result is linearized with respectto α and a yielding, ∆ µ i = K (cid:88) k = i ( M µα, k ∆ α + M µ a , k ∆ a ) (29)for the i -th concentric spherical layer, where M µα, k = h k − − h k and M µ a , k = ( ∂ h k /∂ a k )( a k + − α k ) + ( ∂ h k − /∂ a k )( α k − α k − ) are thelinear transformations (to the first order) relating µ and α , and, µ and a , respectively, where h = ln (( a k + + a k ) / a i ).The covariance matrix of µ , C µ , is given by, C µ = (cid:104) ∆ µ k ∆ µ j (cid:105) = K (cid:88) i = [ V α i M µα, ji M µα, ki + V a M µ a , ji M µ a , ki + C α a , i ( M µα, ki M µ a , ji + M µα, ji M µ a , ki )] (30)where V α and V a are the variances of α and a , respectively.From Eq. (22) two types of uncertainty can be identified forthe temperature profile. The first term from the right side of Eq.(22) results in a systematic error due to the uncertainty of theboundary temperature. The uncertainty resulting from the sec-ond term is due to the statistical fluctuation of the refractivity.Using the linearized transformations of Eq. (22) and Eq. (21),the covariance matrices for temperature C T and pressure C P arederived using Eq. (30) as described by Lipa & Tyler (1979) (Ap-pendix C), C T = (cid:104) ∆ T k ∆ T j (cid:105) = B (cid:88) r = k B (cid:88) s = j b r b s (cid:32) N r N s N k N j (cid:33) (cid:32) C µ, rs N r N s − C µ, ks N k N s − C µ, r j N r N j + C µ, k j N k N j (cid:33) (31) C P = (cid:104) ∆ P k ∆ P j (cid:105) = kN B B (cid:88) r = k B (cid:88) s = j b r b s C µ, rs (32)where b = g ( h i + − h i ) / k , g is the gravitational acceleration of thecentral body, which is assumed to be constant, k is Boltzmann’sconstant and B corresponds to the layer centered at h given bythe upper boundary condition in Eq. (22).Figure 10 shows the resulting uncertainties in the refractiv-ity, neutral number density, temperature and pressure profiles,from the error propagation of the Doppler frequency residualsfor the stations Bd and Ke during the session of 2012.04.29.These uncertainties correspond to the profiles shown in Figure6. The minimum values for σ µ , σ nn and σ P are found at an al-titude of ∼
78 km, which corresponds to the altitude where thetemperature profiles of the di ff erent stations converge in Fig-ure 10 (where the temperature di ff erence between stations dropsbelow 1 K). The refractivity and neutral number density uncer-tainties increase approximately linearly from 78 km to 67 km.From this altitude to about 63 km sharp changes are observedat the same altitudes for both stations, which correspond to thealtitudes where there are also large changes in the lapse rate asshown in the temperature profile of Figure 6. At ∼
58 km, wherethe tropopause is expected, the refractivity and neutral numberdensity uncertainties start increase at a larger rate as the alti-tudes decreases to 50 km in the case of Bd, and 55 km in thecase of Ke. The rate at which the uncertainties increase is higherfor Ke than for Bd. The sudden drop at 50 km and 55 km, forBd and Ke, respectively, are related to the change of integrationtime from 0.1 s to 1.0 s during the processing. The temperatureuncertainties are 15 K and 23 K, for Bd and Ke, respectively, at90 km and rapidly drop below 1 K at an altitude of ∼
85 km. Theobserved temperature uncertainties above 85 km explain the dif-ferences observed around ∼
90 km in the profiles of Bd and Ke,as shown in Figure 6c. Above 85 km the main contribution to theresulting temperature uncertainty is given by the systematic er-ror induced by the choice of the boundary temperature at 100 km.As the refractivity increases, this value gets highly damped be-low the 85 km.
Article number, page 13 of 15 & A proofs: manuscript no. paperVEX
It is important to take into account that Figure 10 is com-paring the residuals obtained with a 32-m antenna with thoseof a 12-m antenna. Badary at an integration time of 0.1 s has afrequency residual uncertainty of σ ∆ f = . σ ∆ f = . σ nn = . × m − at 51.2 km forBd and σ nn = . × m − at 55.7 km for Ke. While the ra-tio of the frequency uncertainties between these two stations is2, the ratio of the largest neutral number density uncertainties is1.1. Tellmann et al. (2009) reported neutral density uncertainties σ nn = . × m − at 50 km with NNO.
4. Conclusions
With the VEX test case exposed in this work and the correspond-ing error analysis, we have demonstrated that the PRIDE setupand processing pipeline is suited for radio occultation experi-ments of planetary bodies. The noise budget indicated that theuncertainties in the derived neutral density and temperature pro-files remain within the range of uncertainties reported in previ-ous Venus radio occultation experiments ( e.g. , Tellmann et al.(2009)). Summing up the results of all the observations with thedi ff erent telescopes, we found that at 1 bar level the frequencyresiduals vary between 4800-5000 Hz with uncertainties of 3.7-11.8 mHz, which result in uncertainties in the neutral numberdensities of 2.7-3.9 × m − and in temperature of ∼ ff erent sources of Doppler noise, itwas found that for one-way radio occultation experiments thenoise introduced by the USO can dominate over the thermalnoise of large dish antennas ( > ff elsberg or the 305-m Arecibo. Additionally, due to the widecoverage of the networks, the setup can be optimized to ensurehigh S / N signal detections. For instance, by choosing as receiv-ing stations VLBI telescopes that can track the spacecraft at thehighest antenna elevations, when the deep space station has lim-itations in terms of antenna elevation.As demonstrated with the detection of Bd, open-loopDoppler data as the one produced with PRIDE allows soundingdeeper layers of planetary bodies with thick atmospheres whencompared to closed-loop Doppler data. The main advantage ofopen loop data for radio occultation experiments is that duringthe post-processing the frequency of the carrier signal can be es-timated with precision wideband spectral analysis. Even if thereare large unexpected changes in the carrier frequency due to, forinstance, large refractivity gradients in the deep atmosphere orinterference e ff ects such as multipath propagation. This is notthe case with closed-loop detections, since in this scheme thesignal is received at much narrower bandwidth. Using a feed-back loop, the detection bandwidth is gradually shifted around acentral frequency, that is the predicted Doppler signal for the ex-periment. In case of large unexpected changes in frequency, thesignal will no longer be detected by the tracking station becauseof a loss-of-lock in the closed-loop scheme. With the widebandspectral analysis of PRIDE, we showed that even with small an-tennas, such as the 12-m Ke, the signal can be detected belowVenus’ clouds layer. Acknowledgements.
We thank the referee for her / his constructive comments andcorrections of our manuscript, which resulted in an overall improvement of thepaper. The European VLBI Network is a joint facility of independent European,African, Asian, and North American radio astronomy institutes. Scientific re-sults from data presented in this publication are derived from the following EVNproject codes: v0427, v0429, v0430, v0501 and v0323. This study made use ofdata collected through the AuScope initiative. AuScope Ltd is funded under theNational Collaborative Research Infrastructure Strategy (NCRIS), an AustralianCommonwealth Government Programme. Venus Express (VEX) was a missionof the European Space Agency. The VEX a priori orbit, Estrack and DSN track-ing stations transmission frequencies, and the events’ schedules were suppliedby the ESA’s Venus Express project. The authors would like to thank the per-sonnel of all the participating radio observatories. In particular, the authors aregrateful to Eiji Kawai and Shingo Hasagawa for their support of observationsat the Kashima radio telescope. The authors are grateful to the Venus ExpressRadio Science team, the VeRa PI Bernd Häusler and Venus Express Project Sci-entists Dmitri Titov and Håkan Svedhem for their e ff orts, advice and cooperationin conducting the study presented here. Tatiana Bocanegra-Bahamón acknowl-edges the NWO–ShAO agreement on collaboration in VLBI (No. 614.011.501).Giuseppe Cimò acknowledges the EC FP7 project ESPaCE (grant agreement263466). Lang Cui thanks for the grants support by the program of the Lightin China’s Western Region (No. YBXM-2014-02), the National Natural ScienceFoundation of China (No. 11503072, 11573057,11703070) and the Youth Inno-vation Promotion Association of the Chinese Academy of Sciences (CAS). References
Ahmad, B. & Tyler, G. L. 1998, Radio Science, 33, 129Ando, H., Imamura, T., Sugimoto, N., et al. 2017, Journal of Geophysical Re-search: Planets, 122, 1687Armstrong, J., Woo, R., & Estabrook, F. 1979, The Astrophysical Journal, 230,570Barnes, J. A., Chi, A. R., Cutler, L. S., et al. 1971, Instrumentation and Measure-ment, IEEE transactions on, 1001, 105Bertotti, B., Comoretto, G., & Iess, L. 1993, Astronomy and Astrophysics, 269,608Bocanegra-Bahamón, T., Molera Calvés, G., Gurvits, L., et al. 2018, Astronomy& Astrophysics, 609, A59Boehm, J., Werl, B., & Schuh, H. 2006, J. Geophys. Res., 111, B02406,doi:10.1029 / ff action of Light, 7th edn. (Cambridge UniversityPress)Brace, L. & Kliore, A. 1991, Space Science Reviews, 55, 81Brandt, S. 1997, Statistical and computational methods in data analysis.(Springer Verlag, New York)Campbell, Robert. 2018, , EVN status table II. Accessed on March 7 2018Dirkx, D., Gurvits, L., Lainey, V., et al. 2017, Planetary and Space Science, 147,14Duev, D. A., Molera Calvés, G., Pogrebenko, S. V., et al. 2012, Astronomy &Astrophysics, 541, A43Duev, D. A., Pogrebenko, S. V., Cimò, G., et al. 2016, Astronomy & Astro-physics, 593, A34Eshleman, V. R. 1973, Planetary And Space Science, 21, 1521Fjeldbo, G. & Eshleman, V. R. 1968, Planetary and Space Science, 16, 1035Fjeldbo, G., Kliore, A. J., & Eshleman, V. R. 1971, The Astronomical Journal,76, 123Fox, J. L. & Kliore, A. J. 1997, Venus II, 161Gan, F., Ruan, G., & Mo, J. 2006, Chemometrics and Intelligent LaboratorySystems, 82, 59Girazian, Z., Withers, P., Häusler, B., et al. 2015, Planetary and Space Science,117, 146Gubenko, V. N., Andreev, V. E., & Pavelyev, A. G. 2008, Journal of GeophysicalResearch: Planets, 113, E3Häusler, B., Pätzold, M., Tyler, G., et al. 2007, ESA Special Publications, 1295,1Häusler, B., Pätzold, M., Tyler, G., et al. 2006, Planetary and Space Science, 54,1315Hedin, A., Niemann, H., Kasprzak, W., & Sei ff , A. 1983, Journal of GeophysicalResearch: Space Physics, 88, 73Hernández-Pajares, M., Juan, J., Sanz, J., et al. 2009, Journal of Geodesy, 83,263Hinson, D., Simpson, R., Twicken, J., Tyler, G., & Flasar, F. 1999, Journal ofGeophysical Research: Planets, 104, 26997Hinson, D. P. & Jenkins, J. M. 1995, Icarus, 114, 310Howard, H., Tyler, G., Fjeldbo, G., et al. 1974, Science, 183, 1297 Article number, page 14 of 15. M. Bocanegra-Bahamón et al.: Venus Express radio occultation observed by PRIDE
Fig. 10: Uncertainties in the refractivity, neutral number density, temperature and pressure profiles, from the error propagation ofthe Doppler frequency residuals for the stations Bd and Ke during the session of 2012.04.29. These uncertainties correspond to theprofiles shown in Figure 6. The sudden drop at 50 km and 55 km, for Bd and Ke, respectively, are related to the change of integrationtime from 0.1 s to 1.0 s during the processing.
Imamura, T., Ando, H., Tellmann, S., et al. 2017, Earth, Planets and Space, 69,137Jenkins, J. M., Ste ff es, P. G., Hinson, D. P., Twicken, J. D., & Tyler, G. L. 1994,Icarus, 110, 79Keating, G., Bertaux, J. L., Bougher, S. W., et al. 1985, Advances in Space Re-search, 5, 117Keimpema, A., Kettenis, M., Pogrebenko, S., et al. 2015, Experimental Astron-omy, 39, 259Kliore, A., Levy, G. S., Cain, D. L., Fjeldbo, G., & Rasool, S. 1967, Science,158, 1683Kliore, A., Patel, I., Nagy, A., Cravens, T., & Gombosi, T. 1979, Science, 205,99Kliore, A. J. 1985, Advances in Space Research, 5, 41Kliore, A. J. & Luhmann, J. G. 1991, Journal of Geophysical Research: SpacePhysics, 96, 21281Kliore, A. J. & Patel, I. R. 1980, Journal of Geophysical Research: SpacePhysics, 85, 7957Kliore, A. J. & Patel, I. R. 1982, Icarus, 52, 320Kolosov, M., Yakovlev, O., Efimov, A., Pavelyev, A., & Matyugov, S. 1979, Ra-dio Science, 14, 163Kopeikin, S. M. & Schäfer, G. 1999, Physical Review D, 60, 124002Kursinski, E., Hajj, G., Schofield, J., Linfield, R., & Hardy, K. R. 1997, Journalof Geophysical Research: Atmospheres (1984–2012), 102, 23429Limaye, S. S., Lebonnois, S., Mahieux, A., et al. 2017, Icarus, 294, 124Lipa, B. & Tyler, G. L. 1979, Icarus, 39, 192Mariner, S. G. 1967, Science (New York, NY), 158, 1678Molera Calvés, G., Kallio, E., Cimo, G., et al. 2017, Space Weather, 15, 1523Molera Calvés, G., Pogrebenko, S., Cimò, G., et al. 2014, Astronomy & Astro-physics, 564, A4Pätzold, M., Häusler, B., Bird, M., et al. 2007, Nature, 450, 657Pätzold, M., Neubauer, F., Carone, L., et al. 2004, ESA Special Publications,1240, 141Peter, K., Pätzold, M., Molina-Cuberos, G., et al. 2014, Icarus, 233, 66Phinney, R. & Anderson, D. 1968, Journal of Geophysical Research, 73, 1819Rutman, J. & Walls, F. 1991, Proceedings of the IEEE, 79, 952Sei ff , A., Schofield, J., Kliore, A., et al. 1985, Advances in Space Research, 5, 3Ste ff es, P. G., Jenkins, J. M., Austin, R. S., et al. 1994, Icarus, 110, 71Tellmann, S., Häusler, B., Hinson, D., et al. 2012, Icarus, 221, 471Tellmann, S., Pätzold, M., Häusler, B., Bird, M. K., & Tyler, G. L. 2009, Journalof Geophysical Research: Planets, 114, E9Tjoelker, R. L., Prestage, J. D., Burt, E. A., et al. 2016, IEEE transactions onultrasonics, ferroelectrics, and frequency control, 63, 1034Tortora, P., Iess, L., Bordi, J., Ekelund, J., & Roth, D. 2004, Journal of guidance,control, and dynamics, 27, 251Vasilyev, M., Vyshlov, A., Kolosov, M., et al. 1980, Acta Astronautica, 7, 335Withers, P. 2010, Advances in Space Research, 46, 58Withers, P., Moore, L., Cahoy, K., & Beerer, I. 2014, Planetary and Space Sci-ence, 101, 77Yakovlev, O., Matyugov, S., & Gubenko, V. 1991, Icarus, 94, 493Yakovlev, O. I. 2002, Space radio science (CRC Press)es, P. G., Jenkins, J. M., Austin, R. S., et al. 1994, Icarus, 110, 71Tellmann, S., Häusler, B., Hinson, D., et al. 2012, Icarus, 221, 471Tellmann, S., Pätzold, M., Häusler, B., Bird, M. K., & Tyler, G. L. 2009, Journalof Geophysical Research: Planets, 114, E9Tjoelker, R. L., Prestage, J. D., Burt, E. A., et al. 2016, IEEE transactions onultrasonics, ferroelectrics, and frequency control, 63, 1034Tortora, P., Iess, L., Bordi, J., Ekelund, J., & Roth, D. 2004, Journal of guidance,control, and dynamics, 27, 251Vasilyev, M., Vyshlov, A., Kolosov, M., et al. 1980, Acta Astronautica, 7, 335Withers, P. 2010, Advances in Space Research, 46, 58Withers, P., Moore, L., Cahoy, K., & Beerer, I. 2014, Planetary and Space Sci-ence, 101, 77Yakovlev, O., Matyugov, S., & Gubenko, V. 1991, Icarus, 94, 493Yakovlev, O. I. 2002, Space radio science (CRC Press)