Icarus 177 (2005) 18–31
www.elsevier.com/locate/icarus
Meridional variations of temperature, C2H2 and C2H6 abundances
in Saturn’s stratosphere at southern summer solstice
Thomas K. Greathouse a,1,∗ , John H. Lacy b,1 , Bruno Bézard c , Julianne I. Moses a ,
Caitlin A. Griffith d , Matthew J. Richter e,1
a Lunar and Planetary Institute, 3600 Bay Area Boulevard, Houston, TX 77058-1113, USA
b University of Texas at Austin, Department of Astronomy, Austin, TX 78712, USA
c Observatoire de Paris, Section de Meudon, 92195 Meudon cedex, France
d Lunar and Planetary Laboratory, Tucson, AZ 85721, USA
e University of California Davis, Davis, CA 95616, USA
Received 22 September 2004; revised 11 February 2005
Available online 22 April 2005
Abstract
Measurements of the vertical and latitudinal variations of temperature and C2 H2 and C2 H6 abundances in the stratosphere of Saturn can
be used as stringent constraints on seasonal climate models, photochemical models, and dynamics. The summertime photochemical loss
timescale for C2 H6 in Saturn’s middle and lower stratosphere (∼40–10,000 years, depending on altitude and latitude) is much greater than
the atmospheric transport timescale; ethane observations may therefore be used to trace stratospheric dynamics. The shorter chemical lifetime
for C2 H2 (∼1–7 years depending on altitude and latitude) makes the acetylene abundance less sensitive to transport effects and more sensitive
to insolation and seasonal effects. To obtain information on the temperature and hydrocarbon abundance distributions in Saturn’s stratosphere,
high-resolution spectral observations were obtained on September 13–14, 2002 UT at NASA’s IRTF using the mid-infrared TEXES grating
spectrograph. At the time of the observations, Saturn was at a LS ≈ 270◦ , corresponding to Saturn’s southern summer solstice. The observed
spectra exhibit a strong increase in the strength of methane emission at 1230 cm−1 with increasing southern latitude. Line-by-line radiative
transfer calculations indicate that a temperature increase in the stratosphere of ≈10 K from the equator to the south pole between 10 and
0.01 mbar is implied. Similar observations of acetylene and ethane were also recorded. We find the 1.16 mbar mixing ratio of C2 H2 at −1◦
−7 and 2.5+1.8 × 10−7 , respectively. The C H mixing ratio at 0.12 mbar is found to
and −83◦ planetocentric latitude to be 9.2+6.4
2 2
−3.8 × 10
−1.0
−5 at −1◦ planetocentric latitude and 2.6+1.3 × 10−6 at −83◦ planetocentric latitude. The 2.3 mbar mixing ratio of C H
be 1.0+0.5
2 6
−0.3 × 10
−0.9
−6 and 1.0+0.3 × 10−5 at −1◦ and −83◦ planetocentric latitude, respectively. Further observations,
inferred from the data is 7.5+2.3
−1.7 × 10
−0.2
creating a time baseline, will be required to completely resolve the question of how much the latitudinal variations of C2 H2 and C2 H6 are
affected by seasonal forcing and/or stratospheric circulation.
 2005 Elsevier Inc. All rights reserved.
Keywords: Infrared observations; Saturn; Atmosphere; Abundances
1. Introduction
* Corresponding author. Fax: +1 281 486 2162.
E-mail address: [email protected] (T.K. Greathouse).
1 Visiting Astronomer at the Infrared Telescope Facility, which is oper-
ated by the University of Hawaii under cooperative agreement NCC 5-538
with the National Aeronautics and Space Administration, Office of Space
Science, Planetary Astronomy Program.
0019-1035/$ – see front matter  2005 Elsevier Inc. All rights reserved.
doi:10.1016/j.icarus.2005.02.016
Saturn, like the Earth, undergoes seasonal variations due
to an axial tilt of ≈27◦ to its orbital plane. Changes in insolation with latitude over a saturnian year cause latitudinal variations of temperature and photochemistry. Saturn’s
stratosphere is very similar to Jupiter’s, where it has recently
been shown that C2 H2 and C2 H6 are the dominant coolants
Saturn’s temperature and abundances of C2 H2 and C2 H6
(Yelle et al., 2001). These molecules are photochemical byproducts of methane photolysis, so their abundance versus
latitude may be tied to seasonally varying insolation. To
understand how seasons affect the meridional temperature
profile and photochemical production and loss rates requires
knowledge of the temperature and abundances of these key
photochemical molecules as a function of latitude and time.
In 1973, spatially resolved N/S scans of Saturn, taken at
12 µm in the ν9 band of ethane, showed a gradual increase
in emission from north to south and a substantial peak in
emission over the south pole during Saturn’s southern summer (Gillett and Orton, 1975; Rieke, 1975). Variations in
ethane emission could be attributed to either temperature or
abundance variations. Later, in 1975 and 1977, Tokunaga et
al. (1978) made spatially resolved N/S scans at other wavelengths, including within the ν4 band of methane at 7.9 µm.
They observed a similar increase in emission with increasing southern latitude in the methane band as was seen earlier
in the ethane-band observations. Because it is controlled by
diffusion and transport rather than by photochemistry, the
methane vertical distribution is not expected to exhibit noticeable variations in abundance with latitude. Therefore, the
variable emission observed in the CH4 ν4 band provided
evidence that the emission enhancement was caused by a
temperature increase towards high-southern latitudes. Cess
and Caldwell (1979) constructed a stratospheric seasonal
model attempting to describe the physics behind the variable emission seen in these early observations. Their model
successfully accounted for the emission trends observed by
Tokunaga et al. (1978), with the predicted stratospheric temperature being higher at the south pole than at the equator.
However, the model indicated the temperature at the south
pole should be lower than that at the equator during the 1973
observations, whereas Gillett and Orton (1975) and Rieke
(1975) observed enhanced 12-µm emission at the south pole.
Cess and Caldwell (1979) therefore suggested that the observed south polar enhancement of 12-µm emission in 1973
could have been caused by enhanced ethane abundances
rather than enhanced temperatures.
During the Voyager missions in 1980 and 1981, shortly
after Saturn’s northern spring equinox, LS ≈ 0◦ , the infrared spectrometer IRIS provided spatially and spectrally
resolved measurements of thermal emission (e.g., Hanel et
al., 1981, 1982). Using temperatures retrieved from the inversion of Voyager infrared spectra, Conrath and Pirraglia
(1983) showed that Saturn’s tropospheric temperature at the
150-mbar level exhibited a warming trend from north to
south, but this trend was not present at the 290- or 730mbar levels. They explained that this difference was caused
by the variation in thermal inertia with altitude producing
a phase lag in the thermal response. Due to observational
limitations (see Hanel et al., 1981, 1982), stratospheric temperature maps have never been derived from the Voyager
IRIS data. Similarly, although latitudinal variations in hydrocarbon emissions were observed by IRIS, no analysis of
the abundance variations has ever been published, perhaps
19
because of the difficulty in separating the individual roles
of temperature and abundance in contributing to the emission (see Courtin et al., 1984; Bjoraker et al., 1985). Using
the Voyager IRIS data as a constraint, Bézard and Gautier
(1985) improved upon previous seasonal models by incorporating a radiative transfer treatment and including ring
shadowing effects on the insolation of Saturn. By calculating
latitudinally dependent heating and cooling rates modulated
by the saturnian season, they showed that at 5-mbar seasonal
variations of insolation could produce peak temperature variations from pole to pole of 30 K, three to five years following
the solstices.
Ground-based infrared images obtained by Gezari et
al. (1989) have revealed a latitudinal gradient in 7.8-µm
methane emission increasing from the equator to the north
pole. This reversal of the emission gradient from the early
1973 and 1975 observations was successfully predicted by
the seasonal climate models of Bézard and Gautier (1985),
Bézard et al. (1984), and Cess and Caldwell (1979). More
recent observations of seasonal effects on Saturn were attempted by Ollivier et al. (2000). The observations, taken in
1992 during Saturn’s northern summer, exhibited brightness
variations in their mid-infrared circular-variable-filter (CVF)
images similar to those observed by Gezari et al. (1989).
Ollivier et al. (2000) attempted retrievals of temperature and
abundances of C2 H2 and C2 H6 . However, their observations
could not constrain the temperature at the 2-mbar level independently from the abundance of C2 H2 or C2 H6 .
In this paper we attempt to derive the stratospheric
temperature using independent information from that used
to derive the abundances of C2 H2 and C2 H6 in Saturn’s
stratosphere. We use high-resolution spectra of the ν4 band
of methane to derive stratospheric temperatures. Methane is
the most abundant trace molecule in Saturn’s atmosphere;
however, its mixing ratio is still uncertain due to the
derivations being somewhat model dependent. Using recent
Cassini CIRS observations of CH4 pure rotational lines,
Flasar et al. (2004) determined the methane tropospheric
mixing ratio to be 4.5 ± 0.9 × 10−3 . This result is in excellent agreement with that of Courtin et al. (1984) who
−3 for the
derived a constant mixing ratio of 4.5+2.4
−1.9 × 10
lower stratosphere using Voyager IRIS observations. Other
determinations have ranged from ∼1.7 × 10−3 to ∼4.2 ×
10−3 (Tomasko and Doose, 1984; Trafton, 1985; Killen,
1988; Karkoschka and Tomasko, 1992; Kerola et al., 1997;
Lellouch et al., 2001). The CH4 mixing ratio is expected
to remain roughly constant in the lower stratosphere until it
declines due to diffusive separation above the methane homopause (e.g., Festou and Atreya, 1982; Smith et al., 1983).
In addition, the methane abundance is affected primarily
by diffusion and not by chemistry in the middle and lower
stratosphere. The methane distribution is therefore expected
to be homogeneous with latitude and longitude throughout
much of the stratosphere, and variations in the strength of its
emission lines must then be due to thermal variations. This
assumed uniformity, along with the fact that CH4 emits on
20
T.K. Greathouse et al. / Icarus 177 (2005) 18–31
the Wien side of Saturn’s blackbody curve, makes methane
a very sensitive temperature probe. After deriving temperatures from the methane data, we use those temperature
profiles to derive abundances of C2 H2 and C2 H6 , the key
hydrocarbon coolants and main photochemical products in
Saturn’s stratosphere.
2. Observations
We measured spectra along Saturn’s central meridian on
September 13 and 14, 2002, UT at NASA’s Infrared Telescope Facility to look for variations in the emission of CH4 ,
C2 H2 , and C2 H6 with latitude. The slit was oriented along
the celestial N/S direction. Saturn’s rotational axis was tilted
by −5.29◦ to celestial N/S, and the sub-Earth and sub-solar
point were both near planetocentric latitude −26◦ . Saturn’s
equatorial diameter was 18.2 arcsec. Our spatial resolution
along the slit, due to diffraction and seeing, was 1.1 arcsec, allowing 16 independent latitudinal bins to be probed.
However, due to the extinction of the rings and the weakness of the methane emission near the equator, we were
unable to derive reliable temperature information from the
northern hemisphere. Only the southern hemisphere will be
covered in this paper. We achieved a resolving power, R =
ν̃/ν̃ ≈ 80,000, using TEXES (Lacy et al., 2002) in highresolution cross-dispersed mode with a 1.4 arcsec wide slit.
Spectrally separated emission lines from the ν4 band of CH4 ,
between 1228 and 1231.6 cm−1 (Fig. 1), were used to derive
information on the stratospheric temperature profile. Observations of the ν5 Q branch of C2 H2 at 730 cm−1 (Fig. 2)
and the ν9 band of C2 H6 at 820 cm−1 (Fig. 3) were used
to derive their respective mixing ratios. In each of the above
spectral settings 13 C isotopic variants of the respective molecules were seen along with a few CH3 D emission lines in the
methane observations. A small number of lines are as yet
unidentified in our C2 H6 spectrum (see the residuals plotted
in Fig. 3). We include plots of the integrated line fluxes from
various emission lines versus latitude to aid in comparing
our observations to previous spectrally unresolved observations. We normalized the peak of the integrated fluxes to 1
for ease of comparing the trends between different molecules
and lines of differing opacities (see Fig. 4).
Due to the fact that Earth exhibits strong methane features
in its spectrum, we were required to observe Saturn as near
quadrature as possible, to maximize the Doppler shift for the
separation of Saturn’s CH4 emission from Earth’s CH4 absorption. We observed when Saturn exhibited a −28 km s−1
Doppler shift (Fig. 1). The need for a large Doppler shift
reduced the amount of time per night that Saturn was observable. This, along with the fact that Saturn is extremely faint
at 1230 cm−1 , forced us to spend all of the first half-night
observing CH4 to acquire the S/N required for our analysis. Due to the long integration time required, the methane
spectrum at a given latitude is an average over ≈100◦ in
longitude. Therefore, after modeling of the data, we retrieve
Fig. 1. A methane spectrum taken at −80◦ planetocentric latitude. The data
points (crosses) have been overplotted by the model (solid line). The dashed
line is the atmospheric transmission (divided by 5). The high spectral resolution of TEXES allows us to observe the strong methane emission line at
1228.8 cm−1 Doppler shifted by the Earth/Saturn motion to 1228.91 cm−1 ,
cleanly separating it from the telluric methane absorption.
Fig. 2. A spectrum of the C2 H2 Q branch taken at −80◦ planetocentric
latitude. The data points (crosses) have been overplotted by the model
(solid line). The dashed line is the atmospheric transmission (multiplied
by 4). Note the C2 H2 hot band l = 0 ν4 + ν5 − ν4 at 731.15 cm−1 has
many closely spaced lines making what looks like a squared-off shoulder
to the Q(20) line at 731.11 cm−1 . Gaps in the data exist due to opaque
atmospheric absorption, e.g., 731.6 cm−1 , and because of the incomplete
spectral coverage of TEXES beyond 11 µm, e.g., 729.4 and 730.75 cm−1 .
an approximately longitudinally averaged temperature profile for each latitude probed. However, little integration time
was required for the C2 H6 observations since ethane emits
in a very clear part of the atmosphere and the emission from
Saturn is exceedingly strong at 820 cm−1 . As a result, the
ethane observations are averaged over only ≈6◦ in longitude. In addition, the methane data and C2 H2 and C2 H6 data
were taken on consecutive nights; the temperatures were
found using an average methane observation ≈180◦ in longitude away from the other hydrocarbon observations. If the
Saturn’s temperature and abundances of C2 H2 and C2 H6
thermal structure is variable with longitude, the temperatures
sampled from the methane data may differ from those sampled by the ethane and acetylene data. We have assumed in
21
this paper that the variations of temperature and hydrocarbon abundances with longitude are much smaller than their
variations with respect to latitude.
All the spectra were sky subtracted, flat fielded and flux
calibrated by an ambient temperature blackbody following
the procedure in Lacy et al. (2002). To remove the effects
of telluric absorption we divided the Saturn observations by
observations of the asteroid Ceres.
3. Radiative transfer
Fig. 3. An ethane spectrum taken at −80◦ planetocentric latitude. The data
points (crosses) have been overplotted by the model (solid line). The dashed
line is the atmospheric transmission (multiplied by 3). This is the ν9 band of
C2 H6 along with the ν12 band of 13 C12 CH6 at 821.63 cm−1 . A plot of the
residuals of our model fit compared to the data is included at the bottom of
each plot offset by −0.5. Most of the wiggles seen are due to a slight stretch
of the spectrum. Small gaps existing at 816.83, 817.5, 818.18, etc., are due
to incomplete coverage of the spectral orders at wavelengths longer than
11 µm, by TEXES. The weak emission lines observed between 820.8 and
821.1 cm−1 and between 818.1 and 818.4 cm−1 have yet to be identified.
We modeled the data with a line-by-line radiative transfer code assuming a plane-parallel 75-layer atmosphere with
equal log(P ) spacing between 1.8 and 1 × 10−7 bar. Local
thermodynamic equilibrium (LTE) was assumed throughout. The variation of saturnian airmass and gravity for each
observed latitude was included in the calculation. Line positions, intensities and energies for NH3 , CH3 D, 12 C2 H2 ,
12 C13 CH , 12 C H and 12 C13 CH were taken from the
2
2 6
6
GEISA databank (Jacquinet-Husson et al., 1999), and those
for 12 CH4 and 13 CH4 come from the TDS spectroscopic
databank (Tyuterev et al., 1994). H2 and He mole fractions
were 0.877 and 0.118, respectively (Conrath and Gautier,
2000). The H2 –H2 and H2 –He collision-induced transitions
were calculated following the formalism of Borysow et al.
(1988). The mean molecular mass was set to 2.226 g mol−1 .
Fig. 4. Plots of the normalized integrated flux of selected emission lines. Due to Saturn’s axial tilt at the time of our observations, all longitudes at latitudes south
of −80◦ were visible. The region north of 7◦ latitude was obscured by Saturn’s rings. In the CH4 plot the solid line represents the emission at 1228.81 cm−1 ,
the dashed line is the moderate strength CH4 line at 1229.47 cm−1 , and the dot-dashed line is the optically thin 13 CH4 line at 1229.71 cm−1 . In the C2 H6
plot the solid line represents the peak of emission at 822.34 cm−1 . At this wavelength the C2 H6 becomes optically thick at high airmass, causing the emission
to slightly decrease between the −80◦ observation and the −83◦ latitude bins which straddle the south pole but are at different airmasses. This is in contrast
to the other two lines plotted, which correspond to the emission from 821.06 cm−1 and the peak of the ν12 band of 13 C12 CH6 at 821.56 cm−1 . These lines
are optically thin, causing them to peak near the saturnian limb where the airmass is largest. In the C2 H2 plot the solid line and the dashed line represent the
Q(9) and Q(21) lines at 729.55 and 731.22 cm−1 , respectively, whereas the dot-dashed line is the integrated flux over a few blended lines of the ν4 + ν5 − ν4
Q branch at 731.08 cm−1 . The solid and dashed vertical lines through all three plots represent the sub-solar point at −26◦ and the south pole, respectively.
Wavenumbers quoted here are the rest frame values.
22
T.K. Greathouse et al. / Icarus 177 (2005) 18–31
Fig. 5. The mixing ratio profiles of CH4 (solid line), C2 H2 (dashed line),
and C2 H6 (dot-dashed line) from Moses et al. (2000). We derive temperatures using the CH4 mixing ratio profile as it is plotted here. We vary
the entire mixing ratio profile of C2 H6 by a multiplicative factor to fit the
820 cm−1 data, and the mean and slope of the entire C2 H2 profile in order
to fit the 730 cm−1 data.
The ratio of the abundances of 12 C–13 C hydrocarbon species
was set to the terrestrial value appropriate for a 12 C–13 C ratio of 89 (Sada et al., 1996), and the D/H ratio in methane
was set to 1.7 × 10−5 (Lellouch et al., 2001). These isotopic values were not allowed to vary. The model spectra
were calculated with a sampling of 25 times the resolution
of the data, i.e., a velocity resolution of ≈0.16 km sec−1 , and
then convolved with a measured line profile taken from lowpressure gas-cell data measured on the same observing run
as the data presented here. A Lorentzian convolution with a
FWHM of 1.5 km sec−1 was used to mimic the effect of the
convolution of our beam profile across the slit and Saturn’s
rotation.
4. Modeling and results
The strength of stratospheric emission from Saturn depends predominantly on the vertical distribution of the emitting molecule and the temperature profile of the stratosphere.
The effects of the temperature and abundance of the emitting
molecule on the observed molecular emission are often difficult if not impossible to separate. This was the case in the
work by Ollivier et al. (2000), where they were unable to derive a unique solution; that is their derived abundances for
C2 H2 and C2 H6 were dependent on their assumed temperature profiles. However, we describe here a method to derive
the stratospheric thermal profile independently from any assumptions regarding the abundances of C2 H2 and C2 H6 .
Because methane has a long photochemical lifetime in
the middle and lower stratosphere of Saturn and has no appreciable destruction pathway in the observable atmosphere,
we assume that its mixing ratio does not vary with latitude
or longitude. Eddy and molecular diffusion do affect its altitude variation, however, especially in the upper stratosphere.
Fig. 6. A plot of the temperature profile from Moses et al. (2000) shown
with symbols and line. The initial temperature profile for the modeling
program is the long-dashed line. We include the derived temperature profiles for planetocentric latitudes of −83◦ (solid), −69◦ (dashed), and −29◦
(dot-dashed).
Thus, it is possible that coupling between meridional circulation and vertical gradients could cause the methane mixing ratio in the upper stratosphere to vary with latitude, but
our data cannot simultaneously constrain both the methane
mixing ratio and the stratospheric temperature. For our calculations we adopt the methane mixing ratio profile from the
photochemistry/diffusion model of Moses et al. (2000) with
a CH4 mixing ratio of 4.5 × 10−3 at 10 mbar (Fig. 5). Having fixed the methane abundance in our line-by-line radiative
transfer model, we can derive the temperature at each latitude by producing synthetic spectra that reproduce our highresolution spectra taken in the ν4 band of methane. Then,
holding the derived temperature profiles fixed in the model,
we vary the abundances of C2 H2 and C2 H6 to produce synthetic spectra that closely resemble the observed emission
spectra near 730 and 820 cm−1 , respectively.
4.1. Approach to fitting the spectra
To derive the temperature profile at each latitude, we run
the radiative transfer model using an initial guess thermal
profile created by using the thermal profile from Moses et
al. (2000) below the 10 mbar level and assuming a constant
temperature above this level (Fig. 6). The program measures
the goodness of fit of our model spectrum to an observed
CH4 spectrum, producing a χ 2 given by:
2
n
τ (i)
2
χ =
,
data(i) − model(i)
[1.1 − τ (i)]1/2
i=1
where data(i) is the measured radiance in erg s−1 sr−1 cm−2
per cm−1 , model(i) is the radiance at the ith pixel in the
same units as the data, Doppler shifted to account for the radial velocity of Saturn, and τ (i) is the telluric transmission
at spectral pixel i. The sum is over all spectral pixels, i.e.,
Saturn’s temperature and abundances of C2 H2 and C2 H6
Fig. 7. Contribution functions illustrating the pressure levels that are responsible for the observed flux at a given wavenumber. These functions were
calculated assuming the temperature and mixing ratio profiles from Moses
et al. (2000), a latitude of −60◦ , and a saturnian airmass of 1.0. When modeling the TEXES data, we take advantage of all the different contribution
functions in the observed spectrum by minimizing the χ 2 between data and
model with respect to all the spectral points in a given spectrum. The three
plots contain a few contribution functions from separate resolution elements
showing the range and variation of pressure levels probed by the different
spectral regions. Due to the high-spectral resolution achieved by TEXES,
we begin to resolve the wings of the strongest emission lines in the CH4
and C2 H2 spectral regions. The double peak contribution functions exhibit
a high-altitude peak due to the Doppler core and a low altitude peak due to
the pressure broadened wings of the emission lines. Using the large number of spectrally separated lines in the CH4 setting, their various intensities
and energies, we are able to derive mean stratospheric temperature, slope
and curvature of the temperature profile between 10 and 0.01 mbar. Using
similar information found in the C2 H2 and C2 H6 spectral settings plus the
derived temperature profiles from the CH4 data, we were able to retrieve
the mean and slope of the C2 H2 and the mean of the C2 H6 mixing ratio
profiles.
over all observed ν̃. The quotient at the end of the equation
is a measure of how the noise in the spectrum varies with
wavelength. By including this term, we give higher weight
to spectral regions exhibiting low telluric absorption. In the
thermal infrared, the dominant noise is photon noise from
sky and telescope emission. After dividing the source spectrum by an asteroid spectrum to remove the effects of telluric
absorption on the spectrum, the noise in the source spectrum
is equal to the square root of the telluric emission divided by
the telluric transmission. We approximate the telluric emission by 1.1—the telluric transmission since the combination
of the instrument window and the telescope have an emissivity of ≈10%.
After finding the χ 2 of the initial model (χ02 ), the program adjusts the temperature profile with a constant T ,
where T is in Kelvin, above 10 mbar (see Fig. 7 for sensitivity information) and derives a new χ 2 for both a positive
and negative T shift. The slope of the χ 2 surface can then
be found by
∂χ 2 χ+2 − χ−2
=
.
∂T
2T
23
Fig. 8. A contour plot of stratospheric temperature derived from radiative
transfer modeling of the ν4 band of CH4 . The sub-solar latitude is indicated by the vertical line at −26◦ latitude. The temperature is assumed to
be constant above 0.01 mbar. Between 0.01 and 10 mbar, only the mean
temperature and its first and second derivatives with log(P ) were allowed
to vary at each latitude.
We also derive the second difference by
∂ 2 χ 2 χ+2 + χ−2 − 2χ02
=
.
∂T 2
(T )2
If the second difference is positive, the attempted change to
the original temperature profile in order to improve the fit is
∂χ 2 ∂ 2 χ 2
T = Tprev −
∂T
∂T 2
between 10 and 0.01 mbar, i.e., the temperature is changed
by the first derivative divided by the second derivative, which
should adjust T to the value where χ 2 is minimized if other
parameters are kept fixed. The methane data are insensitive to temperature variations at altitudes below the 10-mbar
level and at altitudes above the 0.01-mbar level (Fig. 7).
Thus, the temperature below the 10-mbar level is not allowed
to vary and the temperature above the 0.01-mbar level is set
2 2
equal to that of the 0.01-mbar level. If ∂∂Tχ2 is negative the
temperatures are changed by ±5 K, whichever is in the direction of decreasing χ 2 . Using this new temperature profile,
a new model is run and a new χ 2 derived. If χ 2 increases,
the original profile is changed by only half of the previous
correction, and the new profile is tested. Once χ 2 is found to
decrease the whole process is repeated, taking the last model
as the initial guess and looking for a better solution. Once the
program’s suggested temperature change becomes less than
the test step, T equal to 0.005 K in this work, the program
is assumed to have converged.
The next step is to try not only a constant shift of the
temperature profile, but also a change in slope. We test all
permutations of a positive and negative change in slope with
2
a positive and negative constant offset. We derive the ∂χ
∂T ,
∂χ 2 ∂ 2 χ 2 ∂ 2 χ 2
∂2χ 2
∂M , ∂T 2 , ∂T ∂M , and ∂M 2 , where M
is the slope of the tem-
24
T.K. Greathouse et al. / Icarus 177 (2005) 18–31
perature profile (M = dT /d(log P )). The second derivative
values are placed into a matrix
 ∂ 2χ 2
∂ 2χ 2 
∂T ∂M 
.
∂ 2χ 2
∂M 2
 ∂T 2
S=
∂ 2χ 2
∂M∂T
2 2
2 2
∂ χ
∂ χ
The terms ∂T
∂M and ∂M∂T are equal. The slope and constant
offset are then adjusted by
δT = S −1 · (−∇χ 2 ),
where in this case the elements of the array δT are δT1 = δT
and the δT2 = δM. If δT · ∇χ 2 is greater than zero then the
suggested move is along the gradient rather than opposite it.
If this occurs or if the inversion of the matrix S produces a
singular matrix, the gradient approach is applied, where
δT = −5K ×
∇χ 2
|∇χ 2 |
and the 5K is an arbitrary constant. The adjustment to the
temperature profile between 10 and 0.01 mbar would then
be
T = Tprev + (δT2 ) × log(P ) + δT1 .
The program can use this methodology with any number
of free parameters. After running a series of sensitivity tests,
we found that the methane data could constrain the mean,
slope, and curvature of the temperature profile between 10
and 0.01 mbar. Higher-order terms were not considered.
To derive the abundances of C2 H2 and C2 H6 , we follow
the same procedure as outlined above with a few minor, yet
notable, variations. First, we vary the abundances by multiplicative factors instead of additive variations as was done
for the temperature. Instead of changing the fitting program,
which works in linear temperature space versus log pressure space, we converted the mixing ratios into the log of
the mixing ratio. By operating in log mixing ratio versus log
pressure space, an additive constant to the mixing ratio in
log space is the same as a multiplicative change in linear
mixing ratio space. Secondly, we only allowed variations in
the mean and slope of the entire C2 H2 mixing ratio profile,
and only the mean of the entire C2 H6 mixing ratio profile to
minimize χ 2 . For our initial guess, we used the abundance
profiles for C2 H2 and C2 H6 derived in Moses et al. (2000)
from globally averaged ISO observations (Fig. 5).
The error analysis of the model fit to the data was carried
out using the χ 2 values the program derived after having
converged on the final solution to the temperature or mixing
ratio profile it was modeling. We assume that the χ 2 space is
continuous and can be described by a quadratic function with
respect to each free parameter. Using the minimum value
2 2
of χ 2 , the ∂x∂ i χ∂xj , and the number of free parameters (Np ),
we solve for χ 2 over a broad range of all xi and xj values
to derive a χ 2 surface. The value of χ 2 for a given set of
Fig. 9. A line plot taken from Fig. 8. The vertical solid line marks the position of the sub-solar latitude. The sloping solid lines are linear regressions
to the 3 pressure levels, excluding the 3 points nearest the sub-solar latitude,
displaying the general trend of temperature versus latitude. The interior error bars represent the 1-sigma uncertainties due to the possible variation of
the mean, slope and curvature parameters in fitting each individual spectrum
(Section 4.1). The exterior error bars include the modeling, flux calibration,
atmospheric division and methane abundance uncertainties (Section 4.2).
parameters can be found by
Np Np
2 2 1 ∂ χ
2
χ =
(δxi )(δxj )
+ min(χ 2 ).
2
∂xi ∂xj
i=1 j =1
Using this equation, we solve for all possible combinations of free parameters that yield a value of χ 2 less than
the minimum value of χ 2 multiplied by (1 + 1/N ), where
N is the number of independent spectral elements in the
observed spectrum. This provides an estimate of the uncertainty in the retrieved parameters at the 1-sigma level. The
value of χ 2 used here has an unknown scaling factor, since
we only know how the noise varies across the spectrum, not
its absolute value. This derivation of the error does not include possible observational errors such as flux calibration
or the removal of telluric absorption, but it does show the
range of values that are possible solutions for the model profile given the free parameters and the data spectrum used to
constrain those parameters.
4.2. Temperature and its variation with latitude
As can be seen in Fig. 4, the integrated emission of a
number of the observed methane emission lines show a gradual increase from the equator to ≈ −65◦ latitude, at which
point the emission ramps up at a significantly faster rate to
peak at the south pole. This rise in emission is similar to
that observed by Gillett and Orton (1975) and Rieke (1975).
They, like us, observed Saturn during or slightly after Saturn’s southern summer solstice, except their observations
were taken 30 years earlier. Observations made by Gezari
et al. (1989) just after northern summer solstice show a similar variation of brightness with latitude except reversed; i.e.,
Saturn’s temperature and abundances of C2 H2 and C2 H6
the north pole is bright with emission decreasing to the equator. So from the earliest infrared scans of Saturn taken during
the 1970’s, observations have been made of Saturn over a full
saturnian year. These observations of hydrocarbon emission
show distinct trends with the changes in season, such that
the hydrocarbon emission peaks at the summer poles and
the emission decreases towards the equator.
Ollivier et al. (2000) using CVF observations taken in
1992, found that Saturn still exhibited a north polar peak
in emission at wavelengths corresponding to the emissions
of C2 H2 and C2 H6 ≈5 years after northern summer solstice. This suggests the possibility of a lag in the thermal
response in Saturn’s stratosphere, as suggested by Tokunaga
et al. (1978). Such a lag is in direct agreement with the
stratospheric seasonal model produced by Bézard and Gautier (1985).
Previous determinations of Saturn’s stratospheric temperature profile have come from stellar (Hubbard et al., 1997;
Cooray et al., 1998) or Voyager occultations (Lindal et al.,
1985). The stellar occultations are primarily sensitive to the
µbar level, which is higher in the stratosphere than our CH4
observations probe (Fig. 7). The Voyager radio occultation
data constrain temperature profiles between 0.2 mbar and
1.3 bar. All of these measurements sample spatially distinct
regions of Saturn giving information on the variation of temperature from place to place on Saturn. However, only a
finite number of occultation experiments were carried out by
the two Voyager spacecraft, and observers must take what is
offered by random stellar occultation events. This makes it
difficult to carry out a methodic program to unravel the variations of temperature with latitude. In principle Voyager IRIS
observations containing CH4 emission could have been used
to derive stratospheric temperatures in the mbar region at
many different latitudes and longitudes, but the low brightness temperature of Saturn along with the low sensitivity of
the IRIS instruments at 8 µm made this derivation unfeasible
(Hanel et al., 1981, 1982).
Recently, ISO observations of CH4 were successfully
used by Moses et al. (2000) and Lellouch et al. (2001) to
derive the temperature of Saturn in the 0.4–5-mbar region,
but these measurements were global averages giving no information on the latitudinal variations of temperature.
Fig. 8 presents a contour plot of the retrieved temperatures, from our CH4 data, of Saturn’s stratosphere with respect to latitude and pressure. Line plots of temperatures at a
given pressure level versus latitude are shown in Fig. 9. The
dominant trend at pressures between 10 and 0.01 mbar is that
of increasing temperature with increasing southern latitude.
Superimposed on this trend is a small perturbation centered
at the sub-solar latitude seen as a temperature increase above
the general trend at pressures larger than 1 mbar and as a
decrease in temperature relative to the general trend at pressures lower than 1 mbar. Fitting a line to the data points in
Fig. 9, ignoring the 3 data points centered about the subsolar point, we find that the temperature variation between
the equator and the south pole is +8.7 ± 0.5 K at 3 mbar,
25
Fig. 10. A plot of the zonal mean winds as a function of latitude and pressure. Velocities are in m s−1 with positive corresponding to winds moving
from west to east. We have assumed zero wind velocity at 10 mbar at all
latitudes and have integrated the thermal wind equation upward from that
level. Our data set was insufficient to constrain Saturn’s tropospheric temperature, which is required in order to integrate the thermal wind equation
from the level of wind measurements derived from cloud tracking as in
Sánchez-Lavega et al. (2004).
+9.7 ± 0.7 K at 0.3 mbar, and +10.8 ± 0.5 K at 0.03 mbar.
The increase in the temperature variation with decreasing
pressure, although not highly significant, is consistent with
the thermal inertia time scale decreasing with decreasing
pressure. We suggest that the perturbation to this general
trend at the sub-solar latitude is dynamically forced either by
existing winds below the 10 mbar level or vertically propagating waves. It has been shown by Conrath and Pirraglia
(1983) that the temperature at the 150 mbar level, derived
from Voyager 1 and 2 IRIS data, displayed a general northto-south thermal gradient, which they believed to be seasonal
in nature. This trend however was overlaid by smaller scale
variations which they argued were dynamically forced.
Uncertainties in the derived temperature profiles are dominated by possible errors in flux calibration and the assumed
CH4 abundance. These errors affect the derived temperature profiles at all latitudes in the same manner. Thus, the
latitudinal variations shown in Figs. 8 and 9 should be unaffected by these errors. Errors in flux calibration tend to
change the derived temperatures by increasing or decreasing the temperature profile by a constant offset, whereas
variations of the CH4 abundance change the slope of the
temperature profile while keeping the mean constant. An increase/decrease in the assumed CH4 abundance causes an
increase/decrease of the derived temperature above ≈1 mbar
and a decrease/increase of the derived temperature below
≈1 mbar. The combined effects of the uncertainty in flux
calibration, atmospheric correction, and plausible CH4 mixing ratios between 3.6 × 10−3 and 5.3 × 10−3 give error bars
of +1.4/−1.2 K at 0.03 mbar, +1.2/−1.1 at 0.3 mbar, and
±1.1 K at 3 mbar.
We have carried out a comparison of the temperature retrievals described in Flasar et al. (2004) with this data set
and a more recent data set taken using TEXES on the IRTF
26
T.K. Greathouse et al. / Icarus 177 (2005) 18–31
4.3. Stratospheric winds
Fig. 11. A plot of the derived C2 H6 mixing ratio at 2.3 mbar (triangles)
versus planetocentric latitude, compared to the 1-D photochemical model
predictions (Moses and Greathouse, 2005) for the mixing ratio at the same
pressure level and at southern summer solstice, (solid line). The solid vertical line represents the sub-solar latitude at −26◦ . The dashed line is a linear
regression to the data points. The error bars represent the uncertainty in the
ethane mixing ratio due to uncertainties in flux calibration, atmospheric division and the uncertainties of the temperature profiles (Section 4.4). The
modeling 1-sigma statistical errors (Section 4.1) on the fit of the mean C2 H6
abundance to the data have not been plotted since they are smaller than the
individual data points.
in October 2004. The temperature profiles from Flasar et
al. (2004) produce CH4 emission lines that are significantly
stronger and broader than either of the TEXES data sets indicates. Our data suggest that the Flasar et al. (2004) temperature profiles are much too warm in the lower stratosphere
between ≈0.4 and 4 mbar at the latitudes tested. It seems
unlikely that time variability could explain this effect, especially regarding the comparison to our October 2004 data.
We also compare our results with the predictions of the
stratospheric radiative seasonal climate model produced by
Bézard and Gautier (1985). We first note that their model
was produced using the Voyager data as constraints, and
that the model extends to a minimum pressure of 0.1 mbar,
which is below the altitude where we measure the peak in the
stratospheric temperature. The Bézard and Gautier model
predicts that, at the time of our observations, the temperature at 5 mbar should decrease slightly from the equator to
the south pole. In the model, a few years following the southern summer solstice, this trend reverses and the temperature
increases from equator to pole. In contrast we observe a distinct increase of temperature from equator to pole at southern
summer solstice. The discrepancy between model and observations may be due to the different abundance profiles
of C2 H2 and C2 H6 derived here compared to those used in
Bézard and Gautier (1985), and to the fact that the model
does not include the effects of stratospheric circulation. This
discrepancy indicates a need for new and improved seasonal
climate models for Saturn. Future observations, supplying a
measure of the temporal variation of the temperature measurements made here, will shed light on the question of the
time scale of thermal variations at a given latitude and will
help constrain the magnitude of the thermal inertia in Saturn’s stratosphere.
Due to the lack of visible tracers in Saturn’s stratosphere,
direct studies of zonal winds in Saturn’s atmosphere have
been restricted to the troposphere where cloud features
can be seen and tracked in visible image data sets (Smith
et al., 1981; Smith et al., 1982; Ingersoll et al., 1984;
Sánchez-Lavega and Rojas, 2000; Sánchez-Lavega et al.,
2003; Sánchez-Lavega et al., 2004). However, using temperatures along a constant pressure surface and the thermal
wind equation, one can indirectly measure the wind shear at
the given pressure level. This indirect method was first used
on Saturn data by Conrath and Pirraglia (1983). By inverting
Voyager IRIS measurements, Conrath and Pirraglia (1983)
were able to derive the variation of temperature with latitude at 150 mbar. Employing the thermal wind equation they
were then able to infer the zonal wind shear at the 150 mbar
level. They found that the wind shear was in the sense as
to dampen Saturn’s jet structure. Using a similar approach,
we derive the zonal wind shear in the southern hemisphere.
By applying the thermal wind equation (e.g., Wallace and
Hobbs, 1977) to our derived temperature map, we infer the
zonal wind shear between 10 and 0.01 mbar. We display our
results in Fig. 10. In this analysis we have no information
on the wind shear between the cloud top measurements presented by Sánchez-Lavega et al. (2004) at ≈100 mbar and
our temperature measurements starting at 10 mbar. Since this
large gap exists between the two measurements, we make the
assumption that the wind at 10 mbar at all latitudes is equal
to zero. This allows us to display the behavior of the winds
above the 10-mbar level by integrating the calculated thermal wind shear from 10 to 0.01 mbar (Fig. 10). The actual
winds will differ from our derived winds by a latitudinally
dependent additive factor of the wind velocity at the 10-mbar
level.
Two fairly distinct regions are found in Fig. 10. The first
consists of latitudes south of −25◦ where we find wind values that are predominantly negative. This behavior is expected since the southern hemisphere is experiencing its
summer, and our measured temperatures show a clear trend
of decreasing from the south pole to the equator. The other
distinct region is that north of −25◦ latitude. Here we see
multiple reversals of the wind shear with latitude and pressure. A possible explanation is that these are manifestations
of vertically propagating waves.
We compare our results with the linear radiative-dynamical model results presented in Conrath et al. (1990). The
only temperature and zonal wind maps of Saturn presented
by Conrath et al. (1990) are for Saturn’s northern spring
equinox, LS = 0, and Saturn’s northern summer solstice,
LS = 90. Since our observations were taken at Saturn’s
southern summer solstice, LS = 270, we will compare our
results in the southern hemisphere with the LS = 90 results
in the northern hemisphere assuming that the seasonal effects are close to symmetrical. We find a larger latitudinal
temperature gradient from pole to equator (compare Fig. 8
Saturn’s temperature and abundances of C2 H2 and C2 H6
Fig. 12. The photochemical loss time scale for C2 H6 (thick lines) and C2 H2
(thin lines) as a function of pressure at Ls = 273◦ (near southern summer
solstice) from the photochemical model of Moses and Greathouse (2005).
The solid lines are for −8◦ , the dashed lines for −29◦ , and the dotted lines
for −81◦ latitude. The vertical dot-dashed line demarks Saturn’s orbital period and is included for reference. The star represents an estimate of the time
scale for meridional transport, assuming the effective meridional eddy diffusion coefficient Kyy on Saturn is similar to that derived from the evolution
Shoemaker–Levy 9 gaseous debris on Jupiter. Note that the photochemical
lifetime for C2 H6 is greater than both the estimated transport time scale
and a saturnian season, whereas the lifetime for C2 H2 is less than, but of
the same order as, both.
in this paper with Fig. 9b in Conrath et al. (1990)) and thus
a larger wind shear (compare Fig. 10 in this paper to Fig. 9e
in Conrath et al. (1990)) than that found by Conrath et al.
(1990). This discrepancy implies that the radiative time constant, tr , is less than the orbital time constant, torb , rather than
tr = torb inferred by Conrath et al. (1990). The discrepancy
might also result from their use of latitudinally independent
abundance profiles for C2 H2 and C2 H6 and their omission of
aerosol heating and ring shadowing effects.
It must be emphasized that the plotted wind speeds
are calculated with the assumption that the wind speed at
10 mbar is equal to zero everywhere. This assumption is
probably incorrect, but we lack the data to connect our
stratospheric data set with tropospheric wind measurements.
However, if the wind speed was known at the 10-mbar level
from some other method, the 10-mbar wind field could be
added to Fig. 10 to find the actual zonal wind velocity at
pressure levels between 10 and 0.01 mbar. Future TEXES
and Cassini observations will help unravel the time variations of the zonal winds. These time variations will constrain
the possible forcing mechanisms that are the cause of the
wind patterns we find.
4.4. C2 H6 abundance and latitudinal variation
Some of the earliest observations of Saturn in the midinfrared were done in a bandpass containing emission due to
C2 H6 , in large part because the 12-µm region is a very clear
portion of Earth’s atmospheric spectrum. Like our observa-
27
Fig. 13. A plot of the derived C2 H2 mixing ratio at 1.16 mbar (triangles)
and 0.12 mbar (diamonds) compared to the 1-D photochemical model predictions (Moses and Greathouse, 2005) for the mixing ratio at the same
pressure levels and at southern summer solstice, solid line and dashed line,
respectively, versus planetocentric latitude. The two dot-dashed lines are
linear regressions of the data to emphasize the dominant trend. The solid
vertical line is a reference to the sub-solar point at −26◦ latitude. The small
error bars are the 1-sigma uncertainties in the fit of the model to the data
(Section 4.1). The total uncertainty in the measurements due to modeling,
flux calibration, atmospheric division and errors in the derivation of temperatures are indicated by the large error bars (Section 4.5).
tions, the observations of Gillett and Orton (1975), Rieke
(1975), Tokunaga et al. (1978), Tokunaga et al. (1979) and
Sinton et al. (1980) at this wavelength show a general increase in emission with increasing southern latitude. This
trend in 12-µm emission was shown by Gezari et al. (1989)
to have reversed with the reversal of the saturnian season.
Using the temperature profiles derived in Section 4.2, we
modeled the C2 H6 spectra and inferred mixing ratio profiles
at multiple latitudes. We found the 2.3 mbar mixing ratio of
−5
ethane at −83◦ planetocentric latitude to be 1.0+0.3
−0.2 × 10 .
A linear regression of the variation of the mixing ratio with
latitude indicates a decrease of the C2 H6 mixing ratio from
the south pole to the equator by a factor of 1.8, shown in
Fig. 11.
Global average observations of Saturn from ISO indicate
a mixing ratio of 9 ± 2.5 × 10−6 at the 0.5-mbar level (Moses
et al., 2000). Using the updated global-average temperature
profile derived from ISO data by Lellouch et al. (2001), the
ISO-derived ethane mixing ratio from Moses et al. (2000)
should be updated to 1.3 ± 0.3 × 10−5 . In order to compare
our data to that of ISO we averaged the ethane mixing ratio
over all our latitude bins giving us a global average value of
−5 at 0.5 mbar, in good agreement within the
1.5+0.5
−0.3 × 10
errors of the updated ISO measurement.
Because we have made a concerted effort to separate
the contributions of temperature and abundance in terms of
their effects on the emission intensities, these measurements
provide the first quantitative description of the latitudinal
variation of C2 H6 mixing ratios. No published observations
exist with which we can compare our results. In addition, no
two- or three-dimensional photochemical models are available for comparison. Fig. 11 illustrates how our derived
28
T.K. Greathouse et al. / Icarus 177 (2005) 18–31
ethane mixing ratios compare with the one-dimensional latitudinal/seasonal model of Moses and Greathouse (2005).
This time-variable photochemical model accounts for variations in ultraviolet flux due to orbital position, solar cycle,
ring-shadowing effects, and latitude/season. Both the thermal structure and the eddy diffusion coefficient profile in the
model are assumed to be latitude invariant, and winds and
horizontal eddy diffusion are ignored. Therefore, variations
with latitude are solely due to changes in solar insolation.
At high altitudes, the model predicts that the ethane mixing
ratio will remain roughly constant with latitude in the summer hemisphere due to the nearly constant daily averaged
solar insolation in the summer hemisphere at solstice. However, due to the long vertical diffusion time scales in Saturn’s
stratosphere, the otherwise dramatic seasonal changes do not
propagate very far into the stratosphere. Fig. 11 shows that
the latitude variation in the lower stratosphere is expected to
mimic the yearly average solar insolation rather than the insolation of the current season. One would therefore expect
the C2 H6 mixing ratio to decrease with increasing latitude
in the summer hemisphere if meridional winds were not a
factor (see Fig. 11). The observed increase in the C2 H6 mixing ratio with increasing latitude at these altitudes provides
clear evidence for the importance of meridional transport on
Saturn.
Ethane is a long-lived photochemical byproduct of methane photolysis; its photochemical loss time scale at −29◦
latitude at Ls = 273◦ (near summer solstice) is ∼2000 years
at 2 mbar (i.e., the level at which the C2 H6 contribution
function peaks). Although the loss time scale is altitude and
latitude dependent, ethane survives longer than the ∼29-year
saturnian year at all pressures greater than the few-microbar
level (see Fig. 12). The photochemical lifetime is relatively
short in its peak production region at ∼4 × 10−4 mbar; however, ethane will take ∼40 years to diffuse from its peak
production region to the 2-mbar level, where it is observed.
Given the long vertical diffusion time scale and the long
photochemical lifetime of ethane in the middle and lower
stratosphere, abundance variations due to seasonally varying
insolation are expected to be confined to high altitudes.
There are no current observations that can help us determine meridional transport time scales at relevant stratospheric altitudes on Saturn. On Jupiter, however, meridional
transport time scales were determined from observations of
the spreading of the Shoemaker–Levy 9 debris after the 1994
impact of the comet with Jupiter (e.g., Sánchez-Lavega et al.,
1998; Friedson et al., 1999; Lellouch et al., 2002; Moreno
et al., 2003; Griffith et al., 2004). From observations of the
spreading of comet-derived gas in the 0.1–0.5 mbar region
of Jupiter, Lellouch et al. (2002), Moreno et al. (2003), and
Griffith et al. (2004) determined the effective meridional
eddy diffusion coefficient Kyy to be 2.0–2.5 × 1011 cm2 s−1 .
If transport in Saturn’s stratosphere behaves in a similar
manner as on Jupiter with a similar Kyy , we estimate the
meridional transport time scale τlat to be L2 /Kyy , where L
is an effective length scale taken to be the equator to pole
distance of ∼90,000 km; thus, τlat ≈12 years in Saturn’s
middle stratosphere. Note that our estimated τlat is much
shorter than the photochemical lifetime of C2 H6 . We therefore expect ethane to be strongly affected by meridional
transport on Saturn, and C2 H6 should be a good tracer for
stratospheric dynamics.
More realistic 2-D or 3-D photochemical models that include meridional transport will be needed to address the
C2 H6 model-data discrepancies shown in Fig. 11; observational errors clearly are not large enough to account for the
discrepancies. Possible errors in flux calibration and in the
derivation of the temperature profiles would lead to uncertainties in abundance of a factor of ∼1.3 at 2 mbar. These
errors should be regarded as affecting an offset for the entire
data set; they will not alter the latitudinal trend significantly.
4.5. C2 H2 abundance and latitudinal variation
Our observations of the C2 H2 ν5 Q-branch show little variation in emission with latitude except for a minor
peak in emission at the south pole (Fig. 4). However, the
ν4 + ν5 − ν4 hot band, measured in the same spectral setting
as the Q-branch (Fig. 2) shows substantial variations with
latitude (Fig. 4). Our observations agree with the observations taken at wavelengths corresponding to C2 H2 emission
by Tokunaga et al. (1978). These early observations did not
resolve the weak hot band features and so only exhibited a
slight peak in emission at the south pole. In their CVF images, taken in late northern summer, Ollivier et al. (2000)
observe a slight emission peak at high-northern latitudes in
the filter settings corresponding to C2 H2 emission, but the
data also exhibit a stronger peak between 10◦ and 30◦ latitude. This mid-latitude brightening is, to some extent, due
to tropospheric thermal effects, not stratospheric, since they
observe a similar ∼17◦ latitude peak in their 10.91-µm observations.
Both, Winkelstein et al. (1983) and Courtin et al. (1984),
analyzed their respective ultraviolet and infrared data with
C2 H2 abundance profiles such that the mixing ratios were
assumed constant above 20 mbar, and zero at lower altitudes. The derived C2 H2 mixing ratios were (9 ± 3) × 10−8
(Winkelstein et al., 1983) and 2.1 ± 1.4 × 10−7 (Courtin
et al., 1984). From the most recent measurements by ISO,
Moses et al. (2000) were not only able to retrieve the abundance of C2 H2 , but also the slope to the abundance profile
−6
with altitude. Their measured values were 1.2+0.9
−0.6 × 10
−7
at 0.3 mbar and 2.7 ± 0.8 × 10 at 1.4 mbar. Using the updated global-average temperature profile from Lellouch et al.
(2001), the ISO-derived acetylene mixing ratio from Moses
−6 at 0.3 mbar
et al. (2000) should be updated to 1.4+1.0
−0.7 × 10
−7 at 1.4 mbar. If we again average our deand 3.2+1.0
−0.9 × 10
rived C2 H2 abundances over all latitude bins observed, we
−6 and at
derive a global average at 0.3 mbar of 2.0+1.0
−0.7 × 10
+2.9
1.4 mbar of 4.1−1.7 × 10−7 , in agreement within the errors
with the ISO measurements.
Saturn’s temperature and abundances of C2 H2 and C2 H6
Fig. 13 shows how the derived acetylene mixing ratio
varies with latitude in comparison with the photochemical
model of Moses and Greathouse (2005). The model predicts
that the summer-solstice C2 H2 mixing ratio should drop
from equator to −81◦ latitude by a factor of 1.9 at 1.2 mbar
and by a factor of 2.6 at 0.12 mbar. The overall trends are
qualitatively similar to what is observed, although the models clearly underestimate the abundance of C2 H2 at high
altitudes, and the overall latitudinal gradient and detailed
structure of the data differ from that of the model. The qualitative shape of the latitudinal gradient for both model and
data mimic the average yearly solar insolation at these altitudes rather than the insolation for the current season. The
photochemical loss time scale for C2 H2 at summer solstice is
2–7 years at 1 mbar and 1–6 years at 0.1 mbar, depending on
latitude (see Fig. 12); the results are also dependent on season. If Saturn’s stratosphere has a Kyy similar to Jupiter’s,
these time scales are shorter than the estimated meridional
transport time scale (∼12 years at 0.1–0.5 mbar) and are
slightly shorter than or similar to a saturnian season. Because
acetylene is not as long-lived as ethane, its abundance would
be expected to more closely track insolation values, whereas
the ethane abundance would be less seasonally dependent
and more sensitive to transport effects. Two predictions that
can be made from the current model-data comparisons are
that (1) the seasonal variation of hydrocarbon mixing ratios
will be more pronounced at high-stratospheric altitudes, and
(2) the C2 H2 abundance should exhibit a greater latitudinal
and seasonal variation than the C2 H6 abundance, unless atmospheric transport varies dramatically with season. Note
that the measured mixing ratio at the 1.16 mbar level is
−7 at −83◦ planetocentric latitude and a linear
2.5+1.8
−1.0 × 10
fit to the 1.16 mbar data indicates an increase in the mixing ratio from south pole to equator by a factor of 2.7 (see
Fig. 13). The mixing ratio at −83◦ planetocentric latitude at
−6 and is found to ina pressure of 0.12 mbar is 2.6+1.3
−0.9 × 10
crease from the south pole to the equator by a factor of 2.3.
Uncertainties in the flux calibration and in our measured
temperature profiles due to the uncertainty in CH4 abundance combine to give us an overall uncertainty in the acetylene abundances at 1.16 and 0.12 mbar of a factor of 1.7 and
1.5, respectively. However, these uncertainties do not effect
the latitudinal trends in Fig. 13.
5. Conclusions
By measuring high-resolution emission spectra in the
mid-infrared and modeling these spectra using a line-by-line
radiative transfer code, we have shown that it is possible
to retrieve detailed information on the latitudinal variations
of temperature, winds, and abundances of C2 H6 and C2 H2
in the stratosphere of Saturn. By automating the modeling
process we were able to explore parameter space in an orderly fashion. This automation will allow for the modeling
of larger and more complicated data sets in the future. De-
29
tailed conclusions about the state of Saturn’s stratosphere are
listed below.
(1) We find a dominant trend of the stratospheric temperature decreasing from the south pole to the equator
by ≈10 K between 10 and 0.01 mbar. This confirms
early predictions by Tokunaga et al. (1978), Sinton et
al. (1980) and many others who argued that the increase
in emission at 7.8 µm from equator to the south pole during and after the southern summer solstice was a result
of the stratospheric temperature increasing with southern latitude.
(2) The sharp peak in methane emission south of −59◦ latitude (see Fig. 4) is not due to a sharp increase in the
stratospheric temperature there, but to a combination
of the gradual increase in the stratospheric temperature with increasing southern latitude (Fig. 9) and the
increasing angle of incidence of our observations, i.e.,
increasing airmass.
(3) Application of the thermal wind equation to our latitudinal- and pressure-dependent map of temperatures
allows us to make measurements of the zonal wind shear
in Saturn’s stratosphere. These measurements exhibit
two distinct regions in Saturn’s stratosphere. The winds
in the region between the equator and −25◦ latitude
exhibit variations in wind direction and strength with
latitude and altitude, possibly indicating the presence
of some sort of dynamical forcing within this latitude
range. The region south of −25◦ latitude is much more
quiescent and predominantly displays a trend of east to
west winds (assuming that the winds at 10 mbar are
equal to zero).
(4) The linear fit of C2 H6 mixing ratio versus latitude at
2.3 mbar decreases by a factor of 1.8 from the south
pole to the equator, while the linear fit of mixing ratio
versus latitude at 1.16 and 0.12 mbar of C2 H2 increases
by a factor of 2.7 and 2.3, respectively. The photochemical/seasonal model of Moses and Greathouse (2005)
does a fairly good job of reproducing the trend of C2 H2
mixing ratio with latitude, although the predicted vertical slope of the C2 H2 mixing ratio profile is possibly
too shallow in the model. However, the latitudinal variations in the C2 H6 mixing ratio are not explained by
the Moses and Greathouse (2005) model. We believe
the latitudinal variation of C2 H6 is controlled chiefly by
large scale stratospheric circulation. The data set as a
whole suggests that the dynamical time for stratospheric
circulation at ∼1 mbar lies somewhere in between the
chemical loss time of C2 H2 at ∼7 years and the chemical loss time of C2 H6 at ∼1000 years.
This unambiguous derivation of the variations of temperature, stratospheric zonal winds, and the abundances of
C2 H2 and C2 H6 in the stratosphere of Saturn has illuminated deficiencies in current stratospheric seasonal models
of Bézard and Gautier (1985) and Conrath et al. (1990) and
30
T.K. Greathouse et al. / Icarus 177 (2005) 18–31
a need for a 2-D photochemical model. These models would
benefit from the creation of a stratospheric global circulation model to accurately predict temperatures and latitudinal
variations of long-lived molecules such as C2 H6 .
We find that high-resolution observations in the midinfrared can be used to constrain temperature, zonal winds,
and abundances of key molecules in the atmospheres of the
giant planets. By using high-resolution data, we resolve the
telluric spectrum allowing us to ignore the data contaminated by Earth’s atmospheric absorption and reducing the
uncertainties in flux measurements that can often confuse the
interpretation of lower spectral resolution data. This is important for planetary observations where the rotation of the
planet is large enough to Doppler shift the observed emission
features in and out of telluric absorption features depending
on where on the planet one is observing. This positional dependence of the Doppler shift can modulate the integrated
emission when making observations from the eastern to the
western limb of the giant planets. The high resolution also
offers an increase in sensitivity, relative to lower resolution
data, to extremely weak emission lines caused by molecules
possessing very low abundances. This sensitivity is due to
the fact that the line to continuum ratio increases linearly
with spectral resolution until the line is completely resolved.
Thus, we were able to detect very weak unidentified features
in the C2 H6 emission region (Fig. 3).
It is notable that all of this work may be done from the
ground, allowing for long observing programs that can measure the temporal variations of key parameters required to
understand seasonal variations of the outer planets, which
is impossible to do with short satellite missions (i.e., the
5 year Cassini tour of Saturn) when the time for a full seasonal cycle is approximately 30 years (for Saturn). A second
TEXES observing run, where we can repeat these observations, will be extremely informative since we will be able to
compare it to this work and derive some limits on the temporal variations of the temperature and abundance latitudinal
variations. Our data will complement the lower spectral yet
higher spatial resolution data retrieved from Cassini over the
next 5 years. It will be important to make several ground
based observing runs during that time so that the data retrieved with TEXES can be directly compared to that from
Cassini. In this way TEXES observations after Cassini can
be used to extrapolate trends observed in the Cassini data
with some level of certainty in their correlations. The current data set gives a seasonal context with which the Cassini
team can compare their results.
Acknowledgments
Special thanks to Joe Tufts who had to listen to my ever
changing explanations of what all this data meant. This work
was supported by USRA Grant 8500-98-008, NSF Grant
AST 0205518, and by the Lunar and Planetary Institute,
which is operated by the Universities Space Research Asso-
ciation under NASA CAN-NCC5-679. This paper represents
LPI Contribution 1235.
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