A series of near-equatorial radio occultations of Cassini by Saturn occurred in 2005 and again in 2009–2010. Comparison of the temperature-pressure profiles obtained from the two sets of occultations shows evidence of a descending pattern in the stratosphere that is similar to those associated with equatorial oscillations in Earth's middle atmosphere. This is the first time that this descent has been observed in another planetary atmosphere. If absorption of upwardly propagating waves drives the descent, the implied absorbed flux is 0.05 m2 s−2, at least as large if not greater than on Earth.
 Recent reports of ground-based [Orton et al., 2008] and Cassini spacecraft [Fouchet et al., 2008] observations in the mid-infrared have described an equatorial oscillation in the zonal mean temperature and winds in Saturn's stratosphere. The ground-based data had very limited vertical resolution, and the oscillation was deduced from the differences in brightness temperatures near the equator and at 13° planetocentric latitude in both hemispheres. Covering a period of 27 years, the record implied a period of approximately 15 years, about one half Saturn's orbital period. The Cassini data were obtained from limb-sounding measurements with the Composite Infrared Spectrometer (CIRS). These data had better vertical resolution, and they showed a vertically stacked pattern of warm and cold “anomalies” in the equatorial region. Application of the thermal wind equation implied an alternating decrease and increase of the zonal wind with altitude, having a peak-to-peak amplitude of nearly 200 m s−1. The vertical “periodicity” of the temperature anomalies and winds was 4–5 pressure scale heights. Similar evidence for an equatorial oscillation in Jupiter's stratosphere was provided by ground-based measurements [Orton et al., 1991; Friedson, 1999] and CIRS nadir sounding [Flasar et al., 2004] during Cassini's 138 RJ swing by at the end of 2000. The ground-based observations implied a 4–5 year cycle.
 Equatorial oscillations in zonal-mean temperatures and winds have been well documented in Earth's middle atmosphere, from rocket- and radio-sonde data and observations from orbiting satellites. The oscillations are characterized by reversals of the zonal winds with altitude, and an attendant variation in the equatorial temperatures consistent with the thermal wind equation. The vertical pattern descends with time. Two classes of oscillation have been observed to have a dynamical origin: a semi-annual oscillation (SAO) and a quasi-biennial oscillation (QBO), whose “period” is irregular, repeating at intervals ∼22–34 months [see, e.g., Garcia et al., 1997; Baldwin et al., 2001].
 The Jupiter and earlier Saturn observations from CIRS were essentially snapshots within a limited time interval, and they did not show the evolution of the spatial pattern associated with the equatorial oscillations. However, Cassini continues to orbit Saturn, permitting the acquisition of observations that can reveal the change in the equatorial structure. Here we report the results from a series of “diametric” radio occultations near Saturn's equator in 2005 and 2009–2010. In a related paper, Guerlet et al.  compare CIRS limb observations of the equatorial region acquired in 2010 with the earlier data.
 In 2005, a series of 8 radio occultations of Cassini by Saturn sounded within 10 degrees latitude of the equator. The occultations were designed to be as “diametric” as possible. For the first time, three bands, Ka (32 GHz), X (8.4 GHz), and S (2.3 GHz), were used simultaneously. Three of the soundings occurred within 2.5° of the equator. There was another series of nearly diametric occultations in 2009 and 2010, which provided an additional 3 profiles within 2.5° of the equator. Table 1 summarizes the properties of these occultations. The orbit number, date, latitude, longitude, range, and whether the profile is from the ingress or egress side of the occultation is indicated. The latitude and longitude given correspond to the one bar level. Although in general a range of latitudes will be swept out by the successive ray periapses during the course of an occultation ingress or egress, that range was small here, because the occultations were nearly diametric.
Table 1. Properties of the Equatorial Occultation Soundings
Cassini orbit number with I (ingress) or E (egress).
Planetocentric latitude (deg).
E. longitude (deg).
Spacecraft distance to Saturn's center (105 km).
26 Jun 2005
2 Aug 2005
20 Aug 2005
26 Dec 2009
27 Jan 2010
27 Jan 2010
2. Data Analysis and Temperature Retrievals
 During ingress and egress, the signal from the spacecraft was recorded by at least one Deep Space Network station. Cassini was oriented so that the spacecraft's high-gain antenna tracked the “virtual Earth”, that point on Saturn where the radio ray is bent by Saturn's atmosphere so that it arrives at the Earth one light travel time later. Had this is not been done, the signal would have been lost because of the resultant pointing error rather than from atmospheric extinction, as the virtual Earth wandered successively out of the Ka, X, and S beams. At least one 34-meter antenna was used to record in the X and Ka bands simultaneously, and usually a 70-meter antenna was used to record in the S and X bands simultaneously. The signals from the spacecraft were mixed with a locally generated predict frequency to mix them into a low-frequency (audio) band, and then digitally sampled at a rate of 1 kHz, 16 kHz, and 50 kHz for each of the S, X, and Ka band signals. The predict frequencies were precomputed by a code using a model Saturn atmosphere. The signal was recorded until well after it was lost at all bands from absorption in Saturn's atmosphere. Depending on the exact occultation geometry, this occurred for Ka band at about 0.8–0.9 bar, for X band at about 1–1.1 bar, and at S band at about 1.4–1.6 bar.
 This work uses 16-kHz sampling, and the process of determining the structure of Saturn's atmosphere begins with dividing each digital record into 0.256 s segments, and the data within each Fourier transformed to determine the frequency in the audio band at which the received signal is the strongest. Overlapping segments were used so that each frequency point was 0.032 s apart. Knowledge of the mixing frequency enables one to reconstruct the “sky frequency” at which the signal arrived at the DSN station. This differs from the emitted signal frequency in the rest frame of the spacecraft, because of the relative motion of the spacecraft high-gain antenna and the receiving station antenna, the gravitational red shift of Saturn, the Sun, and the Earth, the phase shifts that occur from the radio signal's traversal of the interplanetary plasma and Earth's atmosphere, and those from the refraction occurring during the traversal of Saturn's atmosphere and ionosphere. It is this last phase shift that needs be isolated to analyze Saturn's atmospheric and ionospheric structure.
 To proceed, several assumptions about the atmosphere of Saturn have been made. The atmosphere is assumed to be axisymmetric and barotropic. This means that a gravitocentrifugal potential exists, and that the surfaces of constant density, pressure, and potential coincide. The potential is:
where r is the spherical radius, θ is the planetocentric colatitude, Pn is the nth Legendre polynomial, Jn are constant expansion coefficients for the gravitational field of Saturn, and a is a reference equatorial radius. Q, the centrifugal part of the potential, is computed from
where ω is the angular velocity containing both the constant rotational component Ω and the part due to the wind angular velocity vw(R)/R, and R is the cylindrical radial coordinate perpendicular to the planetary rotation axis [Tassoul, 1978]. Q is precomputed numerically after choosing a wind model. We use the wind model of Sanchez-Lavega et al. , which was derived from Voyager data using automated feature tracking. vw(R) is computed by taking those wind values and assuming they are valid at a single pressure level at the cloud tops. Because of the ring shadow during the Voyager encounters, there is a gap in the winds between 1.7–8.8°S, and therefore we use the northern hemispheric wind profile for both north and south in the occultations we describe here. The expansion coefficients for the potential and the rotation rate and mass of Saturn are obtained from a PCK (planetary constants kernel) computed by the Cassini Navigation team. Throughout this paper, we use GM = 3.79312077 × 107 kg3 s−2, Ω = 1.6378499 × 10−4 rad s−1, a = 60330 km, J2 = 1.6291419485 × 10−2, J4 = −9.30059692 × 10−4, and J6 = 9.2794848 × 10−5.
 The winds and how they are incorporated determine the shapes of the surfaces of constant potential U. Because of the barotropic assumption, these are coincident with surfaces of constant density and constant index of refraction n and refractivity N = 106(n − 1). The gradient of the refractivity provides the “force” that deflects the rays as they travel through the atmosphere of Saturn. The shape of the atmospheric “lens” through which we view Cassini during the course of an occultation is of the utmost importance in analyzing the radio occultation data.
 The structure of the atmosphere is determined by ray tracing. Our technique is very similar to that of Lindal  except that we assume the atmosphere is barotropic. The ephemeris, provided as binary kernels by the Cassini Navigation Team, is queried for the position and velocity of the spacecraft, the position and velocity of Saturn and the orientation its rotation axis, and the position and velocity of the various Deep Space Network antennas that are recording the occultation, with appropriate light travel time corrections applied. The atmosphere is built up of layers of constant refractivity gradient from the outside in. Each successive ray is traced through the previously known layers, and then the refractivity gradient of the new unknown layer is adjusted so that the ray reaches the DSN antenna with the actual received frequency.
 The spacecraft oscillator frequency in its rest frame is set by choosing a “baseline,” a period of time before the atmosphere is reached where the signal from the spacecraft to the DSN antenna is traveling through vacuum. The relation between the spacecraft oscillator frequency and the earth received frequency,
is averaged to obtain the constant spacecraft oscillator frequency that will be used in the subsequent analysis. Here U(r) is the gravitational potential at the point r, including all important contributions, fa is the earth received frequency, fs is the spacecraft oscillator frequency, va is the velocity of the receiving antenna, vs is the velocity of the spacecraft, and ns (na) is the unit vector in the direction of the emitted (received) ray. Of course, in vacuum ns = na.
 The use of multiple frequencies during these occultations enables one to remove the refraction effects of the ionosphere from the neutral atmosphere profiles. If the refractivity derived from S band data nS is assumed to consist of two parts, n0 independent of frequency and ni(f) a function of frequency, and similarly for the X band refractivity nX, then n0 = (nS − [ni(fS)/ni(fX)]nX)/(1 − ni(fS)/ni(fX)) [Schunk and Nagy, 2000]. Since ni ∝ f−2 for free electrons ni(fS)/ni(fX) = fX2/fS2 = (11/3)2, one can use the X and S bands, (or any other two bands with the appropriate values), to extract the refractivity n0 of the neutral gas alone. Since S band is most strongly affected by the presence of ions, it's also the band where the ion removal is most necessary. Here we have used S and X, but the Ka-band results are used as a check on this procedure, since they are virtually unaffected by the ionosphere.
 The ray tracing yields profiles of refractivity vs. potential. Converting this to the temperature - pressure profiles requires a specification of the atmospheric composition. We assume that the atmosphere of Saturn is composed entirely of hydrogen and helium, and that the number fraction of He to H2 is 0.11 [Conrath and Gautier, 2000]. The refractivities per molecule of hydrogen and helium used are 5.0558 × 10−18 cm−3 and 1.3 × 10−18 cm−3, respectively [Mohammed and Steffes, 2003]. This converts the refractivity profiles to density profiles. Next, we solve the equation of hydrostatic equilibrium
where P is the pressure, h a distance along the local direction of the gradient of the potential, g the gravitational acceleration obtained from the potential of equation (1) by taking the magnitude of the gradient, and ρ is the density. Finally, the ideal gas equation of state yields a temperatures from the pressures and densities. Equation (4) requires a boundary condition, which is set at the top of the atmosphere [Lipa and Tyler, 1979]. Instead of pressure at a fixed altitude, we specify the temperature T = 150 K at 0.1 mbar.
 The vertical resolution of the retrieved profiles is set by the Fresnel scale, approximately the geometric mean of the radio wavelength and the distance of the spacecraft to the occulting limb. Since the profiles were derived by combining both X- and S-band retrievals, the longer wavelength of S band (13 cm), sets the effective Fresnel scale. The spacecraft range to the center of Saturn during the occultations (Table 1) was 5–7 Saturn equatorial radii (a). At these distances the range and the distance to the limb are nearly the same, implying Fresnel scales of 6–7 km. For comparison, the pressure scale height is 34 × (T/90) km, where T is in degrees Kelvin.
Figure 1 shows all six of the near equatorial temperature-pressure profiles. The error bars shown are estimates of the effects of thermal noise from Monte Carlo calculations that add additional noise to the system. The individual profiles exhibit small-scale structure that could indicate zonal variability and atmospheric wave propagation. However, there is a commonality of structure among the profiles separately in the earlier and later sets of occultations. Given the different longitudes sampled, this probably reflects changes in the zonal-mean atmosphere between the two periods. These large-scale changes are quite noticeable above the 100-mbar level. Between 100 mbar and 10 mbar, the atmosphere has significantly cooled, in effect broadening the tropopause region (where the temperature is minimum between the troposphere and stratosphere). Despite the larger errors, it is clear that the atmosphere between 0.1 mbar and 3 mbar has also cooled. Temperatures, however, have become much warmer between 3 mbar and 10 mbar. This is the region where temperatures increase strongly with altitude, and the impression given is that the profiles have descended between 2005 and 2009–10, by approximately 0.6 pressure scale heights. Nonetheless, it is clear from the overall structure in the tropopause region and stratosphere that the thermal pattern in the descent is not rigid. Little change is evident below the 100-mbar level, in the upper troposphere. Note that the merging of all the profiles at T = 150 K at 0.1 mbar reflects the common upper boundary condition.
 Thermal noise turns out to be the major source of error for these Saturn occultations, based on Monte Carlo studies of both thermal noise and other sources of error (ephemeris error) that are assumed randomly distributed. Another class of potential errors, composition error (an incorrect [He]/[H2]) ratio or a wind model different from the assumed wind model, cause global shifts of all profiles to the left or right on Figure 1, but will not affect our conclusions. Other potential sources, such as modeling error (for example, the atmosphere is only approximately barotropic or axisymmetric, or some additional minor molecule in the atmosphere that over-contributes to the index of refraction at radio wavelengths) should also be kept in mind but are harder to quantify, although we estimate that they should be smaller than the error bars we show.
 Although the descending pattern of equatorial zonal winds and temperatures has been well documented for the QBO and SAO in Earth's middle atmosphere, the Saturn observations provide the first direct evidence of analogous behavior at another planet. The descent observed in the QBO is thought to result from the absorption of a combination of vertically propagating waves having westerly (i.e., eastward) and easterly phase velocities. Wave absorption also plays an important role in driving the SAO, but zonal momentum transports by the seasonally varying cross-equatorial meridional circulation are thought to be important in maintaining easterly jets and possibly setting the semi-annual clock. Wave absorption occurs through viscous or radiative damping, and the momentum deposition is such that the background mean atmospheric flow is accelerated toward the zonal phase velocity of the absorbed wave. A ray tracing analysis (in which the wave is assumed to propagate in a slowly varying medium) of the simplest case, zonal-vertical wave propagation in an axisymmetric zonal flow, indicates that the damping is most effective when the upwardly propagating wave approaches the level at which its zonal phase velocity approaches the mean zonal wind velocity, where both the vertical wavelength and vertical group velocity vanish. Following the analysis of the QBO by Plumb  (see also Figure 7 of Baldwin et al. ), consider the case with an initial zonal wind profile having a westerly jet in the lower stratosphere and a pair of upwardly propagating waves with easterly and westerly phase velocities of comparable magnitude. Then the westerly wave is preferentially absorbed lower in the stratosphere, in the vicinity of the jet, because its phase velocity is closer to the zonal wind velocities. The easterly wave propagates to higher levels before it is absorbed. Since absorption of that wave accelerates the zonal winds in an easterly direction, an easterly jet develops at altitudes higher than the westerlies. As the jets increase in magnitude (up to the phase velocities of the waves), most of the momentum fluxes of the easterly and westerly waves are absorbed below their respective jet maxima. This leads to the downward movement of the wind pattern as well as that of temperatures, because winds and temperatures are coupled by the thermal wind equation. As the jets descend and grow in magnitude, the jets tend to become thinner in altitude, and a lower “ledge” develops, particularly at the lower, westerly jet. In Plumb's laboratory simulation, viscous diffusion dissipates the narrow westerly jet, and the process continues, with the easterly jet now being the lowest. Analogous diffusive mixing may act similarly in planetary atmospheres, but when the lower jet reaches the troposphere, the more vigorous vertical mixing there should also hasten the jet's demise.
 The descent rate of pattern of jets and temperatures constrains the upward wave momentum flux absorbed by the winds. If dz/dt is the descent rate of the lower ledge of a jet, and Δu is the peak-to-peak amplitude of the zonal wind change, then the absorbed zonal wave flux Fuvert is [Dunkerton, 1991]:
For Saturn, dz/dt ≈ 0.6 H/4 years (Figure 1), and Δu ≈ 200 m s−1 [Fouchet et al., 2008], implying Fuvert ∼ 0.05 m2 s−2. Representative values for the terrestrial QBO in the lower stratosphere are dz/dt ∼ 20 km/26 months, and Δu ∼ 30 m s−1 [Baldwin et al., 2001], yielding smaller absorbed fluxes, Fuvert ∼ 0.009 m2 s−2. The terrestrial SAO exhibits more complex behavior, but in the upper mesosphere, dz/dt ∼ 20 km/6 months, Δu ∼ 30 m s−1 [Garcia et al., 1997], implying Fuvert ∼ 0.04 m2 s−2, more comparable to the value for Saturn.
 Which waves could provide the mechanical forcing to drive the observed descent remain to be determined. There is certainly a suggestion of waves with small vertical wavelengths (≪H) in Figure 1, and this merits further study. Observations by CIRS [Flasar et al., 2004] can also be used to search for waves. However, because the amplitudes of any interacting waves will attenuate in the vicinity of zonal winds with velocities close to the wave zonal phase velocities, the spatial distribution of the waves will likely be complex. Observing the subsequent evolution of the descent will also provide important diagnostics, and additional occultations will occur in Saturn's equatorial region in 2012 and 2017.
 The Editor thanks Darrell Strobel and an anonymous reviewer for their assistance in evaluating this paper.