Clouds and Haze in Saturn`s Troposphere

Transcription

Clouds and Haze
in Saturn’s Troposphere
Cécile Merlet
Trinity Term 2011
Lady Margaret Hall
Atmospheric, Oceanic and Planetary Physics
Department of Physics
University of Oxford
Word count =12 824
Page count = 63
Contents
1 Introduction
1
2 VIMS Near-IR Spectrum of
2.1 VIMS data . . . . . . . . .
2.2 Thermal Spectrum . . . .
2.3 Reflection Spectrum . . .
2.4 Scattering Model . . . . .
2.5 Aerosol-free Atmosphere .
3 Tropospheric Clouds
3.1 Cloud Vertical Structure
3.1.1 Fitting strategy .
3.1.2 Results . . . . . .
3.2 Limb-darkening . . . . .
3.2.1 Methodology . .
3.2.2 Results . . . . . .
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Saturn
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4 Tropospheric Haze
4.1 Sensitivity to Model Parameters . . .
4.2 Optical and Physical Haze Properties
4.3 Vertical Structure . . . . . . . . . . .
4.3.1 Sensitivity Tests . . . . . . . .
4.3.2 Opacity clearing . . . . . . . .
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5 Conclusion and Future Work
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Bibliography
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ii
List of Figures
1.1
1.2
1.3
1.4
Historical Survey . . . . . . . . . . . . . .
The Cassini Cruise Trajectory to Saturn. .
Both Sides View of the Cassini Spacecraft.
VIMS-VIS and VIMS-IR Layouts. . . . . .
2.1
2.2
2.3
2.4
2.5
2.6
2.7
VIMS Image and Spectra of Saturn at Near-IR Thermal Wavelengths . .
Altitude Sensitivity of the the VIMS Thermal Spectrum of Saturn . . . .
VIMS Near-IR Reflection Images and Spectrum of Saturn. . . . . . . . .
Comparison of VIMS and SpeX Near-IR Reflection Spectra of Saturn . .
Weighting Functions for Aerosol-free Opacity . . . . . . . . . . . . . . . .
Henyey-Greenstein Phase Functions . . . . . . . . . . . . . . . . . . . . .
Doubling Method for the Computation of Radiance in a Multiple Scattering
Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Effects of Rayleigh Scattering on Saturn’s Near-IR Spectrum . . . . . . .
2.8
3.1
3.2
3.3
3.4
3.5
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3.8
4.1
4.2
4.3
4.4
4.5
4.6
4.7
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Vertical Locations and Compositions of Clouds in Saturn’s Atmosphere
based on Thermochemical Equilibrium Theory . . . . . . . . . . . . . . .
Retrieval of Cloud Pressure Level and Particle Size for the Compact Cloud
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Limb-darkening Observations of Saturn. . . . . . . . . . . . . . . . . . .
Limb-darkening Analysis for a Compact Ammonia Cloud Model . . . . .
Limb-darkening Analysis for a Compact Ammonium Hydrosulfide Cloud
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Limb-darkening Analysis for an Extended Ammonia Cloud Model. . . . .
Limb-darkening Analysis for a Continuous Aerosol Model. . . . . . . . .
Limb-darkening Analysis for a Compact Ammonia Cloud and a Compact
Haze Layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 31
Sensitivity of Nemesis to Atmospheric Parameters . . . . . . . . .
Retrieval of Optical and Physical Haze Properties . . . . . . . . . .
Retrieval of Opacity for Various Aerosol Sizes . . . . . . . . . . . .
Retrieval of Particle Size for an Ammonia Haze . . . . . . . . . . .
Complex Refractive Indexes of Haze Candidates . . . . . . . . . . .
Sensitivity of Saturn’s Reflection Spectrum to Haze Pressure Levels
Tests on the Haze Vertical Profile . . . . . . . . . . . . . . . . . . .
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Chapter 1
Introduction
“The primary goal of Cassini-Huygens is to conduct an in-depth exploration of the Saturnian System”, NASA (1989)
Visible to the naked eye, Saturn was observed before the beginning of Christianity by the
most ancient civilizations as a moving point on the sphere of fixed stars1 . Nevertheless,
it is really with the start of telescopic astronomy in 1609 that Saturn was seen not as
an ordinary round planet but as a much more complex system. In July 1610, Galileo
pointed his telescope, an instrument with an aperture of around 2cm, 20× magnification
and imperfect optics, at Saturn and noted that the planet was triple (North, 1974). He
shared his discovery in the most cryptic way by the use of an anagram: “smaismrmilmepoetaleumibunenugttauiras”. Combined in the right order, the letters revealed their true
meaning: Altissinum planetum tergeminum observavi [I have observed the highest planet
to be triple-bodied].
It is only in 1655 that the Dutch astronomer Christiaan Huygens correctly interpretated
Galileo’s observations with the discovery of Saturn’s rings. He also discovered, in the same
year, Saturn’s largest moon, Titan. A few years later, the Italian-French astronomer Giovanni Domenico Cassini would discover the satellites Iapetus (1671), Rhea (1672), Tethys
(1684) and Dione (1684), as well as the division between the A ring and B ring of Saturn
(1675).
The development of modern astronomy and space exploration has made it possible to
enhance our knowledge of the Saturnian system. The first space missions to Saturn,
Pioneer 11 (1979), Voyager 1 (1980) and 2 (1981), only flew rapidly by the planet, its
moons and its rings. They provided a unique insight into the Saturnian system, but they
also raised many new questions to planetary scientists. Following the Galileo mission to
Jupiter (1995-2000), the Cassini-Huygens mission to the ringed world was the next logical
step.
1
The very first recorded observations of Saturn were made by the Assyrian an Babylonian civilizations
in ∼ 800 BC.
1
CHAPTER 1. INTRODUCTION
2
Figure 1.1: Left: Saturn as sketched by Galileo in 1616. Middle: Portrait of Giovanni
Domenico Cassini (1625-1712). Right: Portrait of Christiaan Huygens (1629-1695).
The Cassini-Huygens spacecraft is a joint NASA/ESA/ASI2 interplanetary mission aimed
at studying the Saturnian system. The spacecraft is made of two main components: the
Cassini orbiter, which surveys Saturn, its moons and its rings, and the Huygens probe,
which landed on Titan’s surface on 14 January 2005. NASA provided the Cassini orbiter,
the launch vehicule, the mission operations and the telecommunication systems via the
Deep Space Network (DSN). The development of the Huygens probe was carried out by
ESA. The Italian Space Agency was in charge for the supply of the orbiter’s hardware
systems, as well as instruments for both the orbiter and the probe.
The Cassini-Huygens spacecraft was launched on 15 October 1997, using a Titan IVBCentaur rocket at Cape Canaveral Air Force Station, Florida. On its way to Saturn, the
spacecraft performed four gravity assist flybys of Venus on 26 April 1998 and 24 June
1999, Earth on 18 August 1999, and Jupiter on 30 December 2000 (see Fig. 1.3). The
Cassini-Huygens spacecraft reached Saturn’s satellite Phoebe on 11 June 2005, 19 days
before sucessfully entering Saturn’s orbit on 1 July 2004. During the first four years
of mission, also known as the Prime Mission, Cassini orbited 74 times around Saturn,
executed close targeted flybys of Titan (×44), Enceladus (×3), Phoebe, Hyperion, Dione,
Rhea and Iapetus, and made distant flybys of other major moons. The huygens probe
was released from the Cassini orbiter on 25 December 2004, and entered Titan’s upper
atmosphere 20 days later. The Prime Mission ended on 30 June 2008 and was extended
until September 2010 under the name of Cassini Equinox Mission as the mission coincided
with Saturn’s equinox. The mission is currently known as the Solstice Mission and will
end at the summer soltice of Saturn’s nothern hemisphere in 2017.
2
The ASI is the Italian Space Agency (Agenzia Spaziale Italiana)
3
Figure 1.2: The Cassini cruise trajectory to Saturn.
With a total mass at launch of 5636 kg3 and height of 6.87 m, Cassini-Huygens is one of the
largest interplanetary spacecraft ever built, and the third heaviest one after the two Soviet
Union spacecraft Phobos4 . The Cassini orbiter is equipped with 12 science instruments,
which have been designed to meet 27 science investigations. Half of these instruments
undertake in situ measurements of the plasma, dust and magnetic field in the Saturnian
system: CAssini Plasma Spectrometer (CAPS), Cosmic Dust Analyze (CDA), Ion and
Neutral Mass Spectrometer (INMS), MAGnetometer (MAG), Magnetospheric IMaging
Instrument (MIMI) and Radio and Plasma Wave Science (RPWS). The other half consists of remote sensing instruments operating at optical and radio wavelengths: Composite
InfraRed Spectrometer (CIRS), Imaging Science Sunsystem (ISS), UltraViolet Imaging
Spectrograph (UVIS), Visible and Infrared Mapping Spectrometer (VIMS), RADAR, and
Radio Science Subsystem (RSS). The Huygens probe carries 6 science instruments: Gas
Chromatograph and Mass Spectrometer (GCMS), Aerosol Collector and Pyrolyzer (ACP),
Descent Imager and Spectral Radiometer (DISR), Huygens Atmospheric Structure Instrument (HASI), Doppler Wind Experiment (DWE) and Surface Science Package (SSP).
The topic of this thesis is to investigate the physical and optical properties of aerosols
in Saturn’s atmosphere, as well as their vertical structure, which is addressed using the
VIMS instrument. Therefore, the technical capabilities and main science objectives of the
VIMS instrument are briefly described here.
3
The total mass includes the propellant mass at launch of 3132 kg.
The two spacecrafts Phobos 1 and 2 were sent to Mars and its moons Phobos and Deimos on July
1988. They weighed each 6220 kg with their orbital insertion hardware attached.
4
4
Figure 1.3: Both sides view of the Cassini spacecraft.
The Visual and Infrared Mapping Spectrometer (VIMS) is an imaging spectrometer measuring scattered and emitted light from surfaces and atmospheres in the 0.35-5.1 µm
wavelength range. It consists of two distinct 64×64 pixel cameras in the visible and
near-infrared: VIMS-VIS and VIMS-IR. Each pixel corresponds to a spectrum with 352
wavelengths, 96 in the visible and 256 in the infrared. VIMS-VIS operates in the 0.35-1.0
µm spectral range, and can reach a maximum spectral and spatial resolution of respectively 1.46 nm and 167 µrad in the high-resolution mode. In the normal mode VIMS-VIS
operates at a resolution of 7.3 nm (5 pixel summing) and 500 µrad (3×3 pixel summing).
The VIMS-VIS total field of view (FOV) is 2.4◦ ×2.4◦ , however the visible channel covers
an effective FOV of 1.8◦ ×1.8◦ in order to match the VIMS-IR total FOV. The infrared
channel VIMS-IR covers the 0.85-5.1 µm wavelength range. The instrument has a maximum spectral resolution of 16.6 nm and covers an effective FOV of 500 µrad. The optics
of the visible and infrared channels are thermally isolated from the Cassini spacecraft
and cooled down in order to reduce the effects of noise. VIMS-VIS and VIMS-IR are
mounted together on the same palette so that they are optically aligned. Data from both
the visible and infrared channel are combined into the instrument’s electronics, and so a
single spectrum is produced simultaneously in the whole 0.35-5.1 µm wavelength range.
The VIMS instrument has been measuring the spectrum of Saturn at various latitudes
and longitudes and for many emission, solar and azimuthal angles. Therefore, it allows
us not only to map atmospheric features all over the surface of Saturn, but also to constrain numerical models by considering a specific area of the planet observed at different
viewing geometries. VIMS can also perform measurements of Saturn’s spectrum at a very
high spatial resolution. Thus the instrument capabilities has made it possible to track
distinctive features such as storms in the planet’s atmosphere. The list of science objectives for the VIMS instrument is extensive. In particular, VIMS observations of Saturn’s
5
Figure 1.4: VIMS-VIS (left) and VIMS-IR (right) layouts.
atmosphere are expected to provide new insight on:
i. The structure of clouds and haze in the troposphere and stratosphere, as well as their
optical and physical properties.
ii. The nature of tropospheric aerosols by spectral detection of cloud features.
iii. The distribution of gas species, including condensables (such as ammonnia and perhaps water) and disequilibrium species (such as phosphine).
iv. The bolometric bond albedo.
v. The role of solar energy in the dynamics of the planet.
vi. The three-dimensional distribution of lighting.
The analysis of VIMS data in Oxford has been undertaken using the numerical code Nemesis (Irwin, 2008). The Non-linear Optimal Estimator for MultivariatE spectral analySIS
model was initially designed for the analysis of CIRS spectra of Saturn, but is also applicable to any planets and many other instruments, such as VIMS. NEMESIS is a retrieval
algorithm which undertakes two main tasks. First, the algorithm calculates the synthetic
spectrum for an assumed atmospheric structure through the radiative transfer equation.
Then, the synthetic spectrum is directly compared to the measurements and NEMESIS
adjusts the atmospheric structure so as to match more closely the observations. This
process is iterated a number of times until convergence of the solution. NEMESIS is particularly useful for studying the cloud and haze distribution in Saturn’s atmosphere since
the algorithm can model both the reflected and thermal radiation in a multiple-scattering
atmosphere. NEMESIS can also compute synthetic spectra for many viewing geometries,
including limb observations of the planet.
In the next section, we review the main characteristics of the infrared spectrum of Saturn
measured by the VIMS instrument, as well as its relevance for the investigation of aerosol
properties in the troposphere of the planet.
Chapter 2
VIMS Near-IR Spectrum of Saturn
2.1
VIMS data
VIMS raw cubes can be downloaded directly from the Planetary Data System (PDS)
which stores scientific data from NASA planetary missions. VIMS data are stored into
archive volumes containing the raw spectral images, the instrument pointing and navigation, as well as the calibration files and software. VIMS data were released for the first
time to the whole scientific community on 1 July 2005. To date there are 43 volumes
available, and the next release is expected on 1 October 2011.
The data calibration was performed by using the calibration pipeline provided by the
PDS. The software ISIS was used to add all the backplane data in the cubes. They provide information on the geometry of observations such as the phase angle, emission angle,
solar incidence angle, as well as the latitude, longitude, pixel resolution and line resolution. In addition, the VIMS team at the University of Arizona developed continuously
their own calibration pipeline. However this version of the pipeline is not available and we
only have a few cubes calibrated with the updated algorithm. Extensive testing was made
to compare VIMS data calibrated with the PDS and the University of Arizona pipelines.
By using new flatfields files measured in 2009, both pipelines provide identical calibrated
data. The new flatfields files were incorporated in the PDS pipeline to calibrate all VIMS
data.
The spectral cubes are provided without error measurements. The photon noise has been
estimated to be less than 1 DN, which corresponds to a relative error on the flux of around
0.1 %. However, folding in all of the other errors (especially, absolute calibration errors of
how the instrument responds), the measurement errors are more likely to be a few percent.
In particular, the measurement errors should be at least as large as the solar irradiance
uncertainty in the near-infrared. Colina et al. (1996) estimated this error to be around
3-5 %. The measurement errors are greater where water absorbs in particular since the
calibration was done on Earth where water exists (K. Baines, personal communication,
November 2008). Therefore, it is generally agreed to set up the measurement errors at
10% of the mean flux (Sromovsky et al., 2010).
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CHAPTER 2. VIMS NEAR-IR SPECTRUM OF SATURN
2.2
7
Thermal Spectrum
The spectrum of Saturn between 4.6 and 5.1 µm is formed mainly by the thermal radiation
emitted from the deepest layers of the planet’s atmosphere and absorbed by the two main
opacity sources, i.e. aerosols and gases. In this spectral region, the gaseous absorption is
dominated by phosphine (PH3 ) with smaller contributions from ammonia (NH3 ), arsine
(AsH3 ), germane (GeH4 ), deuterated methane (CH3 D), carbon monoxide (CO) and water
(H2 O) (Fletcher et al., 2009).
Figure 2.1: VIMS image and spectra of Saturn at near-IR thermal wavelengths. Left:
VIMS image at 5.06 µm extracted from the VIMS spectral cube CM1524383985 and
acquired on 22 April 2006 on the nightside. The spectral cube was calibrated with the
PDS pipeline. The thermal image of Saturn shows significant latitudinal structure, as
well as the presence of bright and dark spots. Here the dark pixels correspond to region
of high opacity where the internally generated heat radiation is absorbed by aerosols and
gases. In contrast, bright pixels correspond to region of relatively low opacity. Right:
Typical VIMS thermal spectra at different northern latitudes extracted from the same
cube CM1524383985.
The weighting functions for a cloud-free and a typical cloud model are shown on Fig.
2.2. For a cloud-free atmosphere, only gases are responsible for the absorption of thermal
radiation. Most of the gaseous absorption occurs at around 4-5 bar in the upper limit
of the wavelength range investigated here. Note that the thermal spectrum of Saturn
is still sensitive to pressure levels up to 500 mbar, especially at lower wavelengths. The
weighting functions for a tropospheric cloud located at 2 bar1 are shifted higher up in
the atmosphere at the exact position of the cloud. Therefore, VIMS data in the 4.6-5.1
µm wavelength range are particularly valuable for sounding the cloud structure and gas
distribution at deep tropospheric levels.
1
Thermochemical models predict the formation of ammonia ice between 1 and 2 bar (Atreya et al.,
2004)
8
Figure 2.2: Altitude sensitivity of the VIMS thermal spectrum of Saturn. left: The
weighting functions are calculated for a cloud-free atmosphere. The dark colours show
the pressure levels at which gaseous absorption is significant. At a given wavelength,
the thermal spectrum is not sensitive to pressure levels below the peak of the weighting
function. right: One compact cloud is present at 2 bar. The weighting functions are
shifted to the altitude of the cloud layer. In this case, the tropospheric cloud contributes
the most to the opacity sources, and any other aerosol or gas opacity below the 2 bar
level would contribute very little to the thermal spectrum.
We focused our analysis of the VIMS thermal spectrum of Saturn on retrieving cloud and
gas opacities from nightside measurements. There is still a signal at dayside in Saturn’s
thermal spectrum. Nevertheless, dayside data are more difficult to interpret because
physical phenomena such as scattering of sunlight can have a significant impact on the
thermal spectrum of Saturn. NEMESIS can perfectly model the scattering of sunlight
by the tropospheric clouds2 , however it would add another level of complexity and new
degeneracies in the model.
2.3
Reflection Spectrum
The near-infrared spectrum of Saturn at 0.8-3.5 µm is made of six distinctive peaks (see
Fig. 2.3). These features are the result of strong absorption of the continuum3 at 0.90,
1.01, 1.17, 1.40, 1.75, and 2.25 µm (Clark et al., 1979). Methane is the main gaseous
absorber with many absorption bands in the 0.8-3.5 µm wavelength range. Ammonia,
hydrogen, and phosphine also contribute to the absorption of the continuum at these
wavelengths (Baines et al., 2005 ; Butler et al., 2005). In particular, 1-0 band pressureinduced absorption due to molecular hydrogen dominates the 2.0-2.5 µm spectral region.
2
Tropspheric gases also scatter the sunlight but at shorter wavelengths than those considered here.
The continuum refers to the spectrum at wavelengths where there is no absorption. It is also the
continuous solar spectrum reflected by a non-absorptive surface and measured at the viewing geometry
of VIMS instrument.
3
9
Figure 2.3: VIMS near-IR reflection images and spectrum of Saturn. Top: Near-IR images
of Saturn at 1.07 µm (left) and 1.40 µm (right). These images were extracted from the
VIMS cube CM1469004529 acquired on 23 March 2004. The bright pixels in the 1.07 µm
image correspond to the reflection of sunlight by the planet’s haze and rings. In contrast
to Saturn’s image at 5.06 µm, radiation at 1.07 µm is homogeneously distributed over
the whole dayside area of the planet (here, on the left side of VIMS image). The sunlight
scattered by tropospheric aerosols is absorbed at 1.40 µm by gaseous methane located at
higher altitude levels. So the planet appears black at this wavelength, while scattering of
sunlight by Saturn’s rings is still measured. Bottom: Near-IR spectrum of Saturn from
0.8 to 3.5 µm. The spectrum was extracted from the same spectral cube as the images
above. The selected spectrum was measured at a latitude of 4◦ N and at an emission angle
of 61◦ . There is no signal at nightside from 0.8 to 3.5 µm. This dayside spectrum was
obtained at a relatively high solar angle of 51◦ and at an azimuthal angle of 58◦ .
10
Note that the signal between 1.60 and 1.65 µm has a very low quality due to an overlap of
filters at 1.64 µm, and so this spectral range can be ignored in further analysis of VIMS
data. There is also another joint at 2.98 µm. Sromovsky et al. (2010) noticed another
VIMS artefact in the thermal spectrum of Jupiter. They observed an enhancement of
radiance at 2.3 µm probably due to light scattered by the grating of the infrared channel.
This feature is not present in the VIMS spectrum of Saturn. Indeed, no significant signal
in the gaseous absorption bands was measured by the VIMS instrument except in the
methane absorption band at 1.01 µm. The VIMS spectrum was compared to Saturn’s
reflection spectrum measured by the SpeX instrument mounted on the NASA Infrared
Telescope Facility (IRTF) in Mauna Kea (see Fig. 2.4). A similar feature is observed in
the SpeX spectrum which means that the high reflectance at 1.01 µm is not an artefact
specific to VIMS instrumentation. This feature is likely to be due to the presence of
scatterers at higher altitude levels where methane absorption is less significant4 .
Figure 2.4: Comparison of VIMS and SpeX near-IR reflection spectrum of Saturn. Left:
The two VIMS spectra were extracted from the spectral cube CM1564373828 acquired on
29 July 2007 at a latitude of 20◦ S and 35◦ N. SpeX spectra were measured on May 2007
and co-added along the central meridian (Rayner et al., 2009). All spectra are scaled to
the VIMS spectrum measured at a latitude of 20◦ S. The change in reflectance at 1.50
µm is due to latitudinal variations of aerosol opacity. The high reflectance in the first
absorption band at 1.01µm is observed in all VIMS measurements and also in the Spex
spectrum. Therefore, this feature is not a VIMS artefact and is probably formed by
scattering of sunlight by upper level hazes. Right: Retrieval of aerosol concentration from
VIMS specta at a latitude of 20◦ S and 35◦ N. The aerosol opacity retrieved at 35◦ N latitude
is significantly less than at 20◦ S. The cumulative optical depth increases slowly at 35◦ N
latitude, therefore the reflection spectrum is also sensitive to deeper atmospheric levels.
In particular, the increase of opacity around 2 bar might affect the relative intensity of
the six reflection peaks.
The source of emission for the continuum is scattering of sunlight in Saturn’s atmosphere,
so spectral features at 0.8-3.5 µm are only present in dayside spectra. The sunlight is
continuously scattered back into the direction of the spacecraft, except at specific wave4
Stratospheric aerosols have smaller sizes and so they can only be detected at lower wavelengths.
Therefore, no signal in the other absorption bands was measured at higher wavelengths.
11
lengths corresponding to gaseous absorption bands5 . Therefore, the 0.8-3.5 µm spectrum
and the individual peaks can be equally referred to as the reflection spectrum and the
reflection peaks.
A limit on the vertical location of the scatterers can be inferred by mapping the weighting
function for an aerosol-free atmosphere (see Fig. 2.5). Assuming no aerosols are present
in Saturn’s atmosphere, gaseous absorption only contributes to the total opacity of the
planet’s atmosphere, and so the two-way weighting functions6 show the pressure levels at
which gases absorb the reflected sunlight. At the reflection peaks, absorption is significant
below 1 bar, and so only scatterers located above this level can contribute to the reflection spectrum. In between the reflection peaks, absorption starts above the tropopause at
∼100 mbar and extends throughout the lower stratosphere up to ∼10 mbar. Therefore,
the scatterers are located deeper than the 10 mbar level, or else they would contribute
significantly to the spectrum in the absorption bands7 . The analysis of Saturn’s spectrum
at 0.8-3.5 µm is then particularly relevant for surveying the nature and vertical distribution of scatterers located between 1 and 10 bar. Towards this end, a scattering model
needs to be properly defined and implemented in Nemesis.
Two-way Weighting Function
Aerosol-free model
0.001
1.0
Pressure (bar)
0.010
0.100
0.5
1.000
0
10.000
1.0
1.5
2.0
Wavelength (µm)
2.5
3.0
3.5
Figure 2.5: Weighting functions for aerosol-free opacity. The weighting functions at each
wavelength were derived from the two-way transmission, i.e. the transmission to and
from each atmospheric level. The calculation was made assuming that no aerosols are
present in Saturn’s atmosphere, so the only source of opacity is gaseous absorption. The
dot-dashed lines show the position of the reflection peaks. The weighting functions were
normalized to 1.
5
The sunlight is still scattered back from upper level hazes, but this is not detected in the 0.8-3.5 µm
spectrum except at 1.01µm
6
The two-way weighting functions are derived from the transmission functions to and from the reflective layers.
7
Aerosols can be present higher in the stratosphere, but Fig. 2.4 shows that they are only detected at
1.01µm and contribute very little to other wavelengths.
2.4
12
Scattering Model
In planetary atmospheres, particles are sufficiently far away from each other to be considered as independent scatterers. Therefore, Saturn’s atmosphere can be treated as a
sum of small volume elements with individual scattering properties (Hansen et al., 1974).
The theory describing light scattering within these small volume elements is known as
single scattering. Light scattering in the entire atmosphere is then computed by multiple
scattering algorithms. Rayleigh scattering and Mie scattering are both implemented in
Nemesis.
Rayleigh scattering
Rayleigh scattering applies to small particles with size much less than the incident wavelength of the incident radiation. This condition implies that individual particles can be
treated as being in a homogeneous external electric field. Another condition for Rayleigh
scattering to apply is that the ratio between the wavelength and the complex refractive
index should be larger than the particle size. The incident radiation polarizes the particles’s own field. The dipole moment induced by the incident radiation is proportional
to the external electic field. The second condition means that the time of polarization in
response to incident radiation is short compared to the period of the incident wave. The
Rayleigh phase matrix8 is as follows (Chandrasekhar, 1950):






3
(1
4
+ cos2 α)
− 34 sin2 α
0
0
− 43 sin2 α
3
(1 + cos2 α)
4
0
0
0
0
3
cos α
2
0
0
0
0
3
cos α
2






where the phase angle α is the angle between the incident and emission angles. Rayleigh
scattering theory is particularly relevant for understanding light scattering by molecular
gas.
Mie scattering
Light scattering by spherical particles with size of the same order of the incident wavelength is described by Mie theory. The Mie phase function is a function of the size
distribution and complex refractive index, n = nr + ini of particles. The refractive index is a complex number and carries important information on the optical and physical
properties of particles. The real and imaginary parts of the index represent respectively
the phase velocity of radiation and absorption by scatterers. Mie scattering theory provides an analytical solution for spherical particles interacting with plane waves, therefore
scatterers are modelled as single spheres in numerical codes. Nemesis computes the radiation absorbed and scattered by spherical particles with various size distributions. Here
the scatterers are assumed to have a standard gamma size distribution
8
Radiation polarized by Rayleigh scatterers is represented by a phase matrix in the I, Q, U, and V
Stokes vector. The solution is for isotropic Rayleigh particles.
n(r) ∝ r(1 − 3b)/b exp(−
13
r
),
ab
where a and b are respectively the mean radius and the variance.
Figure 2.6: Henyey-Greenstein phase functions. Top: Simple Henyey-Greenstein functions
for forward (g = 0.5), isotropic (g = 0.01), and backward scattering (g = −0.5). Bottom:
Combined Henyey-Greenstein functions. The three phase functions have both forward
and backward peaks with variable relative strengths. By tuning the values for f , g1 , and
g2 , a wide range of phase functions can be modelled including the specific case where both
forward and backward scattering are simultaneously present. Note that for f = 0, 1, the
phase functions are identical to the single Henyey-Greenstein functions.
The Mie phase function is calculated by Nemesis and then fitted with the HenyeyGreenstein function in order to make the computation of radiance more efficient within
the retrieval code. The Henyey-Greenstein phase function is given by
p(θ) =
1 − g2
1
,
4π (1 + g 2 − 2g cos θ)3/2
where θ is the scattering angle9 and g the asymmetry factor.
The Henyey-Greenstein function can account for strong forward, strong backward, and
isotropic scattering (see Fig. 2.6). However, the function cannot properly model all the
possible phase functions. In particular, there is no Henyey-Greenstein phase function
9
Here the definition of the Henyey-Greenstein function implies that forward scattering occurs for
θ ∈ [− π2 , π2 ], and backward scattering for θ ∈ [−π, − π2 ] ∪ [ π2 , π].
14
that can describe both strong forward and backward scattering simultaneously. Since
most atmospheric scatterers are likely to have both forward and backward scattering
peaks, Nemesis uses instead the combined Henyey-Greenstein function
p(θ) =
f
1 − g12
1−f
1 − g22
+
,
4π (1 + g12 − 2g1 cos θ)3/2
4π (1 + g22 − 2g2 cos θ)3/2
where f is a fraction between 0 and 1, and {g1 , g2 } are the asymmetry factors of the two
contributing functions.
The Rayleigh and Mie phase functions are calculated for each small volume element within
Saturn’s atmosphere. A multiple scattering code is needed to compute the radiation emitted at the top of the atmosphere after being scattered by all volume elements. Nemesis
uses a doubling or adding method which consists in calculating the reflection, transmission
and source function for individual layers. Adjacent layers are then combined to derive the
the reflection, transmission, and source functions for the two layers. This process can be
iterated until all the layers are successively integrated in the numerical code.
Consider one homogeneous layer with bottom and top boundaries indexed by 0 and 1
respectively (see Fig. 2.7). For any incident, emission and azimuth angle (θ0 , θ, φ), the
coefficients of reflection and transmission, and the source function due to thermal emission
within the layers are given by rαβ , tαβ and Jαβ for {α, β} ∈ {0, 1}. The flux emitted at
the top and bottom layers are given by
I1+ (µ, φ) =
I0− (µ, φ) =
2π
Z
1
Z
Z02π Z01
0
0
I0+ (µ0 , φ0 )t01 (µ, µ0 , φ0 − φ)µdµdφ +
I0+ (µ0 , φ0 )r01 (µ, µ0 , φ0 − φ)µdµdφ +
Z
2π
Z
1
Z0 2π Z0 1
0
0
I1− (µ0 , φ0 )r10 (µ, µ0 , φ0 − φ)µdµdφ + J01 (µ, φ)
I1− (µ0 , φ0 )t10 (µ, µ0 , φ0 − φ)µdµdφ + J10 (µ, φ)
where µ = cos θ and µ0 = cos θ0 . In Nemesis, the integral equations are replaced by the
matrix equations
+
I1+ = t01 I0+ + r10 I1− + J01
+
I0− = r01 I0+ + t10 I1− + J10
Similar equation as those shown above can also be written for the second layer boundered
by the surfaces indexed by 1 and 2. Then the flux emitted by the combination of the
layers is
+
I2+ = t02 I0+ + r20 I1− + J02
+
I0− = r02 I0+ + t20 I1− + J20
where the coefficients of reflection and transmission, and the source function for the
combined layer are
r02 = r21 + t12 (E − r10 r12 )−1 r10 t21
t02 = t12 (E − r10 r12 )−1 t01
+
−
+
+
= J12
+ t12 (E − r10 r12 )−1 (J02
+ r10 J21
)
J02
15
Figure 2.7: Doubling method for the computation by Nemesis of radiance in a multiple
scattering atmosphere.
2.5
Aerosol-free Atmosphere
The main scatterers in planetary atmospheres are molecular gas and particles in condensed phase, commonly referred to as aerosols. Depending on the physical and chemical
processes that lead to their formation, aerosols can also carry many other names such as
clouds, haze, dust,etc. In Saturn’s atmosphere, clouds are expected to form at deeper
tropospheric levels than those considered in this analysis (Atreya et al., 1999). On the
other hand, hazes might form in the troposphere above the cloud layers, and also in the
stratosphere (Ortiz et al., 1995). Thus, the generic term of haze will be used to refer to
aerosols located between 1 and 10 bars.
The synthetic reflection spectrum for an atmosphere free of aerosols was generated by
Nemesis (see Fig. 2.8). The only scatterers present in this atmospheric model are then
molecular gas, which can deviate the sunlight through Rayleigh scattering. Rayleigh
theory states that the ratio between emitted and incident radiation decreases with wavelength. The synthetic spectrum shows two distinctive signals at the spectral position of
the first two peaks. The radiances for these peaks are respectively ∼ 4 and ∼ 2 µW
cm−2 sr−1 µm−1 . Comparison with VIMS spectra measured at the same latitude and longitude, and for the same solar and emission angles shows that Rayleigh emission from
molecular gas is small comparing to measurements . Therefore, this effect cannot account
for the 0.8-3.5 µm spectrum and so aerosols are the main scatterers at these wavelengths.
16
Rayleigh Scattering Spectrum in the Near-IR of Atmospheric Molecular Gas
70
Measured by VIMS
Modelled with NEMESIS
Radiance (µW cm-2 sr-1 µm-1)
60
50
40
30
20
10
0
0.80
1.07
1.33
1.60
1.86
2.13
2.39
Wavelength (µm)
2.66
2.92
3.19
3.45
Figure 2.8: Effects of Rayleigh scattering on Saturn’s near-IR spectrum. The spectrum
was extracted from VIMS image cube CM1524386400 measured on 16 April 2006 at
a latitude of 19◦ S. The solar and emission angles are respectively 76◦ and 38◦ . In this
chapter, analysis of Saturn’s reflection spectrum is based on this particular data set unless
otherwise stated.
Chapter 3
Tropospheric Clouds
The knowledge of cloud and haze distribution in Saturn’s atmosphere is particularly valuable since aerosols are key ingredients in many atmospheric processes such as the radiative
transfer, the energy balance, microphysical reactions and stratospheric photochemistry.
Aerosols can also be used as passive tracers of wind motion. Theoretical expectations of
aerosol formation and structure are based mainly on thermochemical equilibrium theory
and photochemistry. Thermochemical models predict the formation of clouds by condensation of a gaseous phase into an aqueous or solid solution. In Saturn’s atmosphere,
oxygen, nitrogen, and sulphur are expected to combine with hydrogen to form clouds in
the troposphere, from the tropopause down to the 20 bar pressure level (Lewis, 1969 ;
Weidenschilling and Lewis, 1973 ; Atreya et al., 2004). We mentioned in the previous
section that the thermal spectrum of Saturn between 4.6 and 5.1 µm is not sensitive
to opacity sources located below 5 bar. Ammonia (NH3 ) and ammonium hydrosulphide
(NH4 SH) are the only molecules expected to condense above this pressure level (see Fig.
3.1).
Figure 3.1: Vertical locations and compositions of clouds in Saturn’s atmosphere based
on thermochemical equilibrium theory (Atreya et al., 2004)
17
CHAPTER 3. TROPOSPHERIC CLOUDS
3.1
3.1.1
18
Cloud Vertical Structure
Fitting strategy
The first part of the analysis of VIMS thermal spectrum focused on the retrieval of aerosol
and gas opacities from one single spectrum at a given viewing geometry. Data were extracted from nightside spectral cubes at low emission angles. The last condition makes
the computation of radiance by Nemesis more efficient since limb-darkening effects are
negligible. The temperature and para-ortho ratio profiles were derived from CIRS observations at similar latitude and emission angle as for the selected VIMS spectra.
Sensitivity tests showed that the atmospheric parameters most affecting the Saturn’s
thermal spectrum are the aerosol opacity, and the phosphine and ammonia gaseous abundances. In the spectral range considered for this analysis, Saturn’s spectrum is sensitive
to phosphine and ammonia at pressure levels where they have homogeneous distribution.
Therefore scaling factors to their a priori values in the deep troposphere were retrieved
from the VIMS thermal spectrum.
A Mie scattering model was used to generate the cloud absorption coefficient, the single
scattering albedos and the scattering phase functions at all wavelengths. The HenyeyGreenstein parameters were fitted to the Mie phase function. The complex refractive
indexes for ammonia (Martonchik et al., 1984) and ammonium hydrosulfide (Howett et
al., 2007) are known from laboratory measurements1 . The five optical parameters were
calculated for a few wavelengths between 4.6 and 5.1 and for particle sizes ranging from
100 nm to 10 µm, and then implemented in the retrieval algorithm.
The cloud opacity, phosphine and ammonia abundances were retrieved simultaneously
with Nemesis for various cloud models:
i.: Vertical structure: two models were tested in this analysis, one compact and one extended structure for the cloud. For the compact cloud model, the aerosol density is zero
everywhere except at one pressure level. The retrieval code derived the cloud opacity
at this specific pressure level which provides the best fit to the observations. For the
extended cloud model, there are two free parameters, the base pressure and the extension
of the cloud2
1
The presence of ammonia and ammonium hydrosulphide clouds is expected from thermochemical
equilibrium theory. However no spectral signatures have been detected for either of these molecules. The
first results show that VIMS near-IR spectrum of Saturn is mainly sensitive to the vertical distribution of
aerosols and the particle size. Since there are less constraints on the complex refractive index, the values
for ammonia and ammonium hydrosulphide have been used so far for the analysis of the VIMS thermal
spectrum.
2
The extension above the pressure level at which condensation occurs can be defined either by the
height of the cloud in kilometres or by a fractional scale height ranging from 0 to 1.
19
ii.: Composition: Retrievals were performed assuming the cloud is made of either ammonia or ammonium hydrosulphide particles
iii.: Interaction radiation-matter: Radiation can be scattered by clouds and gases located
above the source of thermal emission. This effect was tested by fitting the VIMS spectrum
for scattering and purely absorptive opacity sources in the troposphere.
iv.: Number of clouds: Thermochemical equilibrium models predict the formation of two
clouds above the 5 bar level. Therefore, the analysis of the VIMS thermal spectrum was
carried out for 1 and 2 aerosol layers.
3.1.2
Results
The results for one compact cloud made of ammonia ice are shown on Fig. 3.2. We found
that we can fit the VIMS thermal spectrum equally well for both a scattering and a purely
absorptive atmosphere. In both cases, we also found that the cloud base pressure needs
to be less than 3.2 bar in order to fit the observations properly. The top boundary of
the cloud is less constrained, except for a scattering atmosphere. In that case, we could
not fit the VIMS spectrum with clouds above the 2.5 bar pressure level. Best fits are
obtained for a cloud pressure base at 2.7 bar for both purely absorptive and scattering
aerosols, however there are less constraints on the particle size. In a purely absorptive
atmosphere, only particles with sizes ranging from 300 nm to 2 µm can model the VIMS
spectrum. There are no such constraints for a scattering atmosphere in the range of size
investigated, and particles of all sizes are potential candidates in the retrieval problem.
Similar values for the mean opacity of the compact cloud, and for the deep volume mixing ratios (VMR) of phosphine and ammonia3 were retrieved for the range of parameters
providing a good fit to the observations. For a cloud at 2.7 bar made of purely absorptive
particles of one micrometre size, optimum fit to the thermal VIMS spectrum was obtained
for a mean opacity of 10.9, a deep phosphine VMR of (7.03 ± 0.36) × 10−6 and a deep
ammonia VMR of (2.48±0.40)×10−3 . For a scattering cloud, these values are respectively
14.5, (6.84 ± 0.35) × 10−6 and (2.03 ± 0.34) × 10−3 . The values retrieved for the deep
phosphine VMR are in good agreement with recent measurements from Cassini/CIRS.
Fletcher et al. (2009) derived an average value of (6.4 ± 0.4) × 10−6 from the analysis of
high-resolution spectra of Saturn in the 600-1430 cm−1 wavenumber range. Nevertheless,
typical values for the deep ammonia VMR are of one order smaller than the values derived
here. Davis et al (1996) retrieved a value of 10−4 from ISO observations of Saturn in the
far-infrared.
3
The mean opacity is averaged over all the wavelengths. As seen on Fig. 3.2 there is actually little
variation of the optical depth at the cloud pressure level. Deep VMR values for phosphine and ammonia
correspond to pressure values above ∼500 mbar and ∼2 bar respectively.
20
We found that the optical depth value retrieved by the algorithm depends on the cloud
model. Clouds detected by remote sensing instruments have optical depth of typically a
few units, so the values found here are very likely to be overestimated. This is due to
the simplicity of the compact cloud model. Since the aerosol concentration is assumed to
be zero everywhere except at the base pressure level, Nemesis retrieved a high optical
depth so as to account for the absorption and scattering of thermal emission. We also
found that the optical depth for a scattering cloud is higher than for a purely absorptive
cloud. This was observed for all cloud models and can be explained as follow: Thermal
emission scattered by the troposphoric cloud is spread over many emission angles, and so
the VIMS instrument for a specific viewing geometry measures less flux than for a purely
absorptive cloud.
As mentioned in the previous section, many cloud models were tested in our analysis of
one single thermal spectrum. In particular, we managed to fit the VIMS spectrum equally
well for a compact and an extended cloud. It should be noted that an extended cloud
adds another free parameter in the aerosol model. In Nemesis, the cloud extension can
be parametrized by either a fractional scale height between 0 and 1 or a cloud height
in kilometres. Significantly smaller values of the optical depth were retrieved for an extended cloud. Nevertheless, the range of atmospheric parameters that can possibly fit the
observations is larger than for a compact cloud, and so the extended cloud model turns
out to be highly degenerate.
Thermochemical theory predicts the condensation of ammonium hydrosulphide below the
ammonia ice layer at ∼ 5 bar (see Fig. 3.1). At this pressure level, clouds are difficult to
detect due to gaseous absorption (see Fig. 2.2). Nevertheless, the ammonium hydrosulfide cloud is expected to extend up to the 3 bar level where aerosol opacity contributes
significantly to the thermal spectrum of Saturn. For that reason, the same analysis of one
single thermal spectrum was carried out for a compact and extended ammonium hydrosulphide cloud. The conclusions drawn for an ammonium hydrosulphide cloud are very
simlar to those for an ammonia cloud model, therefore we cannot distinguish between the
two models. Furthermore, neither ammonia nor ammonium hydrosulphide cloud features
have been spectrally detected so far. So we cannot exclude the possibility of a more complicated model for the complex refractive indexes. This obviously adds a higher level of
degeneracy in the retrieval problem.
Finally, we did not constrain either the number of clouds necessary to match the observations. In conclusion, the retrieval problem is highly degenerate and many possible
solutions can be found to fit one single VIMS thermal spectrum. One way to break the
degenerencies of the retrieval problem is to look at independent measurements simultaneously. This is done by combining spectra of the same area in Saturn’s atmosphere but
observed at different viewing geometries.
21
Figure 3.2: Retrieval of cloud pressure level and particle size for a purely absorptive (left)
and scattering (right) cloud model. The Saturn’s spectrum used here was extracted from
the VIMS cube CM1524383985 (see Fig. 2.1), and measured at a latitude of 0.2◦ N and
emission angle of 10◦ . The results are shown for one compact cloud made of ammonia ice.
The two figures at the top correspond to the goodness-of-fit [χ2 /(number of wavelengths)]
as a function of the cloud pressure level and particle size. Optimum fits to the observations
are obtained for typical χ2 /nλ values . 1.0, so values above 5.0 are omitted here. The
synthetic and VIMS spectra are shown on the middle panel for optimum values of the
cloud pressure level (Pb = 2.7 bar) and particle size (radius = 1 µm). The bottom panel
shows the cumulative optical depth from the top of the atmosphere to all pressure levels.
3.2
3.2.1
22
Limb-darkening
Methodology
Many cloud models have been found to fit individual VIMS spectra perfectly well. In
this section, we focus on the analysis of spectra emitted from the same region of Saturn
but viewed at different angles. This extra information is expected to constrain the cloud
structure and composition. As the planet rotates, the VIMS instrument keeps measuring
spectra and so the same area on the planet can be observed at different emission angles.
Therefore the time difference between two measurements of the flux emitted by the same
area of the planet, but at different emission angles is relatively small4 . The variations of
aerosol structure and abundance are expected to be negligible over such a short period of
time, and so spectra can be considered as independent measurements of the same physical
quantity.
We show in Fig. 3.3 how thermal spectra of the same area of Saturn viewed at different emission angles can be seen as independent measurements and so why they can be
treated simultaneously in order to constrain the atmospheric structure of the planet. Four
spectra were extracted from the VIMS spectra cubes CM1523880874, CM1523879088,
CM1523877318 and CM1523875542. The cubes were all acquired on 16 April 2006 between 10:15:22.999 and 11:44:14.964 (UTC). All spectra were emitted from a latitude of
21◦ S and a longitude 113◦ in the System III West, but measured at different emission
angles ranging from 27◦ to 76◦ . The cloud opacity, as well as the phosphine and ammonia VMRs were retrieved with Nemesis from the spectrum at 27◦ emission angle. As
expected from the previous section, we managed to fit quite well the low emission angle spectrum for various cloud structure and composition. The atmospheric structure of
Saturn was updated with the retrieved values of cloud opacity and gaseous VMRs, and
the synthetic spectra a higher emission angles were then calcucated. This time, we could
not fit any of the high emission angle spectra measured with the VIMS instrument. If all
spectra were non-independent measurements of the same physical quantity, the solution
found at lower emission angle should also be a solution at higher emission angles. As seen
on Fig. 3.3, this is clearly not the case, and so the analysis of each spectum individually
provides independent sets of solutions to the retrieval problem. By retrieving Saturn’s
cloud opacity and gas VMRs from all spectra simultaneously, we can find the common
solutions and hopefully exclude many atmospheric structures that were found to fit VIMS
spectra individually.
4
In this report, the measurements of VIMS specta of the same area viewed at different emission angles
are only a few hours. Therefore, the aerosol opacity and volume mixing ratios of tropospheric gases are
unlikely to undergo large variations over such a short time. Over larger time scales, the atmospheric
structure in belts and perhaps zones might vary and so we avoided analysing such data simultaneously.
23
Figure 3.3: Limb-darkening Observations of Saturn. Top: VIMS images CM1523880874
(left) and CM1523875542 (right) µm at 5.06 µm acquired on 16 April 2006 at 11:44:14.964
and 10:15:22.999 (UTC) respectively. The red squares show the same area [latitude =
21◦ S , longitude = 113◦ (System III West)] on the night side of the planet observed at
an emission angle of 27◦ (left) and 76◦ (right). Middle-left: VIMS thermal spectra of
Saturn at a latitude of 21◦ S and a longitude of 113◦ , measured at an emission ange of 27◦ ,
45◦ , 65◦ and 76◦ . The four spectra are extracted from the VIMS cubes CM1523880874,
CM1523879088, CM1523877318 and CM1523875542 measured on 16 April 2006. The
cubes CM1523879088 and CM1523877318 were acquired at 11:14:28.976 and 10:44:58.987
(UTC) respectively. Middle-right: Goodness-of-fit as a function of the emission angle for
various cloud models. The cloud opacity as well as the phosphine and ammonia VMRs
were retrieved from Saturn’s spectrum at 27◦ emission angle, and their values updated
in the atmospheric structure of the planet. The synthetic spectra at higher emission
angles were then calculated and directly compared to VIMS data. The atmospheric
structure retrieved from the spectrum at low emission angle provides very poor fits to
the observations at higher emission angles. So spectra of the same area measured at
different emission angles can be seen as independent measurements and should be analysed
simultaneously in order to narrow the constraints on Saturn’s atmospheric structure.
Bottom: VIMS and synthetic spectra of Saturn for various cloud models at an emission
angle of 27◦ (left) and 76◦ (right).
3.2.2
24
Results
One compact ammonia cloud model
Saturn’s thermal spectra at a latitude of 21◦ S and a longitude of 113◦ measured at 27◦
and 76◦ emission angles were analysed simultaneously. The two spectra were extracted
from the VIMS spectral cubes CM1523880874 and CM1523875542 acquired on 16 April
2006 (see Fig. 3.3). The aerosol model was first assumed to be one single compact cloud
made of ammonia ice. The aerosol opacity, and the phosphine and ammonia VMRs were
retrieved with Nemesis for various particle sizes and cloud pressure levels (see Fig. 3.4).
For purely absorptive aerosols, the lowest χ2 /nλ values are obtained for a cloud pressure
level between 2 and 3 bar. We show on Fig. 3.4 the synthetic spectra at low and high
emission angles for a cloud pressure level at 2.3 bar and a particle size of 1 µm. The fit to
the observations is quite poor especially at higher wavelengths. Therefore, VIMS spectra
at low and high emission angles cannot be modelled simultaneously by one purely absorptive cloud made of ammonia ice. This was not the case for a single spectrum measured
at one specific viewing geometry. Indeed, while we found many possible solutions to the
retrieval problem from the analysis of a single spectrum (see Fig. 3.2), by combining data
at different emission angles we managed to discriminate the compact cloud model made
of purely absorptive ammonia ice.
The same analysis was carried out for one compact cloud made of scattering ammonia
ice. The minimum χ2 /nλ values correspond to a cloud pressure either less than 2 bar or
more than 1.5 bar. The synthetic spectra are shown for a particle size of 1 µm, and a
cloud pressure level at 0.94 bar and 2.3 bar. The fit to the observations is slightly better
than for purely absorptive ammonia ice. In particular, we managed to get a better fit at
higher wavelengths between 5.0 and 5.1 µm. Therefore, these results show that scattering
effects are very likely to be important in the wavelength range considered here. The next
step is to refine the atmospheric structure, and especially the aerosol model, in order to
match VIMS observations more closely.
One compact ammonium hydrosulfide cloud model
The atmospheric structure was modelled with one compact cloud made of ammonium
hydrosulphide particles. Both purely absorptive and scattering aerosols were considered
as in the previous section. The conclusions that can be drawn for the ammonium hydrosulphide cloud are similar to those for an ammonia cloud. The main difference is that
minimum χ2 /nλ values for scattering ammonium hydrosulfide particles are obtained for
a cloud pressure level between 2 and 3 bar. Otherwise, even though scattering aerosols
provide a better fit to the observations, the compact cloud model still fails at exactly
matching VIMS spectra at low and high emission angles simultaneously.
25
Figure 3.4: Limb-darkening analysis for a compact ammonia cloud model. Top:
Goodness-of-fit as a function of the cloud pressure level and the particle size for a purely
absorptive (left) and scattering (right) cloud. The synthetic and VIMS spectra at low
and high emission angles are shown for optimum χ2 /nλ values on the bottom panels.
26
Figure 3.5: Limb-darkening analysis for a compact ammonium hydrosulfide cloud model.
Top: Goodness-of-fit as a function of the cloud pressure level and the particle size for a
purely absorptive (left) and scattering (right) cloud. The synthetic and VIMS spectra at
low and high emission angles are shown for optimum χ2 /nλ values on the bottom panels.
27
One extended ammonia cloud model
Our first revision of the cloud model was to consider an extended cloud. Indeed, Lewis
et al. (1969) predict from thermochemical theory that clouds should extend above the
pressure level at which condensation starts. Although most of the cloud opacity is found
at the base pressure, the layers above might contribute significantly to the absorption
and scattering of thermal emission. For simplicity, we often considered a compact cloud
model and managed to fit quite well VIMS spectra individually. Nevertheless, since we
cannot fit VIMS spectra simultaneously at different viewing angles, the next logical step
is to consider an extended cloud model. The cloud vertical distribution is set by the
base pressure and the cloud extension in kilometres. The analysis of limb-darkening data
was carried out for an ammonia and an ammonium hydrosulphide cloud made of purely
absorptive and scattering aerosol particles. The cloud opacity, as well as the VMRs of
gaseous ammonia and phosphine were retrieved with Nemesis for a wide range of particle
size, cloud base pressure and cloud extension.
The results are shown on Fig. 3.6 for an extended ammonia cloud made of scattering
particles. The best fits were obtained for a deep cloud at pressure higher than 2.5 bar
with an extension of at least 25 kilometres, and for a particle size between 1 and 3 µm.
We show the synthetic spectra at low and high emission angles for a base pressure of 2.7
bars, an extension of 25 kilometres and a particle size of 2 µm. The fit to the observations
is significantly better than all the compact cloud models considered so far. We also
show the aerosol concentration in particles per litre retrieved for this specific atmospheric
structure. The concentration at the base pressure was scaled to its theoretical value
derived by Atreya et al. (2004) from thermochemical theory (see Fig. 3.1). This was done
by assuming an homogeneous particle mass of 1 µg, and so the units are now expressed
in g.l−1 The aerosol concentration derived from our analysis decreases significantly slower
than predicted by thermochemical theory. In particular, we found an aerosol concentration
of 10−3 g.l−1 at 500 mbar while Atreya et al. predicted a value around 10−6 g.l−1 . As
mentioned above, 25 kilometres is the minimum cloud extension providing a good fit to the
observations, and so 10−3 g.l−1 is also a minimum estimation of the aerosol concentration
value at 500 mbar. By assuming an extended cloud made of ammonium hydrosulphide
particles, similar conclusions can be drawn and the aerosol concentration at 500 mbar is
still overestimated by comparison with theoretical models. Finally by considering purely
absorptive ammonia or ammonium hydrosulphide particles, we could not fit the VIMS
spectra simultaneously at low and high emission angles. This is not surprising since we
concluded in the previous section than scattering is very likely to be necessary for limbdarkening analysis. The results for a scattering extended cloud show that a source of
opacity above the cloud base is needed in order to fit all spectra simultaneously. The
high value retrieved here for the cloud extension suggests that this opacity source is to be
found at higher altitudes in the troposphere. Photochemical and microphysical models
predict the existence of haze at pressure levels around a few hundred millibars, and so a
tropospheric haze was tested as a potential candidate for the secondary opacity source.
28
Figure 3.6: Limb-darkening analysis for an extended ammonia cloud model. Top:
Goodness-of-fit as a function of the cloud pressure level and the particle size for a scattering (right) cloud. The results are shown for a cloud extension of 5, 10, 15, 20, 25 and
30 kilometres. Bottom-left: Synthetic and VIMS spectra for an ammonia cloud at 2.7
bar with an extension of 25 km and particle size of 2 µm. The aerosol concentration in
particles.l−1 retrieved for this atmospheric structure is shown on the bottom-right figure.
The profile was converted in g.l−1 by assuming an homogeneous particle mass of 1 µg.
The ad hoc value for the particle mass was chosen so that the concentration at the base
pressure would be similar to the value derived from thermochemical models (see Fig. 3.1).
29
Continuous cloud model
One difficulty is that we have little knowledge of the location and composition of the haze.
Also, the cloud at deep topospheric levels is probably the main opacity source and can be
parametrized by many free parameters, such as the refractive indexes, the pressure base,
the cloud extension and the particle size. We started our analysis by considering a simple
aerosol model: the particles are assumed to have a complex refractive index of 1.4 +0.001i
and a size of 1 µm. Indeed, the value used here for the refractive index is typical for most
materials and especially for ammonia and ammonium hydrosulfide particles. Finally, our
results from both the analysis of single and limb-darkening data provided an optimum fit
to the observations for a particle size of around one micrometre.
The aerosol vertical distribution was initially set to a continuous a priori profile. The
aerosol concentration at each pressure level, as well as the phosphine and ammonia VMRs
were retrieved for various a priori profiles. The results are shown on Fig. 3.7. Two main
opacity sources were retrieved with Nemesis: One deep tropospheric cloud with a base
pressure between 2 and 3 bar, and a haze layer below the tropopause at around 200 mbar.
Similar profiles were retrieved for all tested a priori profiles and provided a very close fit
to VIMS spectra both at low and high emission angles. The non-cumulative optical depth
at each pressure level shows that the deep tropospheric cloud contributes the most to the
opacity sources, and so the features apparent on Saturn’s images at ∼ 5 µm are associated
with the deep cloud. Nevertheless, our results show that Saturn’s thermal spectrum is
still sensitive to the haze located higher up in the troposphere.
Two compact clouds model
One main issue with the continuous model is that Nemesis derives the aerosol concentration at each pressure level which increases significanty the number of free parameters in
the retrieval algorithm. To break some degenerencies inherent to the continuous aerosol
profile, we considered the cloud and haze model as follows: One compact ammonia cloud
made of 1 µm scatterers and one compact haze layer made of scattering particles with
1.4 + 0.001i refractive index and 1 µm size. We retrieved the cloud and haze opacity,
and phosphine and ammonia VMRs for a wide range of pressure levels for both the cloud
and haze layers. The results are shown on Fig. 3.8. The best fits to the observations
are obtained for a deep ammonia cloud between 2.5 and 4 bar, and for a haze layer at
pressures higher than 500 mbar.
In conclusion, the thermal spectrum of Saturn is sensitive to the tropospheric haze, and so
we need to know the haze structure in order to better constrain the physical and optical
properties of the clouds at deeper tropospheric levels. To that end, we oriented our
analysis to the near-infrared reflection spectum of Saturn which is particularly relevant
for the study of tropospheric haze.
30
Figure 3.7: Limb-darkening analysis for a continuous aerosol model. The complex refractive index and particle size are respectively 1.4 + 0.001i and 1 µm. Top-left: A continuous
aerosol distribution (solid line) is retrieved from three different a priori profiles (dotted line). The fit to the VIMS spectra at low and high emission angles are shown for
the three aerosol profiles retrieved with Nemesis. Bottom: Cumulative (left) and local
(right) optical depth.
31
Figure 3.8: Limb-darkening analysis for a compact ammonia cloud and a compact haze
layer. The cloud and haze particles have a size of one micrometre. The haze particles
have a complex refractive index of 1.4 + 0.001. Top: Goodness-of-fit as a function of the
ammonia cloud and haze layer. Bottom: Synthetic and VIMS spectra for an ammonia
cloud at 2.7 bar and a haze layer at 0.16 bar.
Chapter 4
Tropospheric Haze
Karkoschka et al. (1996, 2005) analysed Saturn’s images at methane bands and nearby
continuum wavelengths between 0.6 and 0.96 µm. These images acquired with the Hubble
Space Telescope between 1991 and 2004 were used to retrieve the aerosol vertical structure
in the troposphere and stratosphere of the planet. They found that the best fits to the
observations were obtained for a tropospheric haze layer located above the condensate
clouds.
Most theories of the formation of stratospheric haze involve photochemical processes and
bombardment by energetic particles, as well as microphysical reactions such as the nucleation, sedimentation and coagulation of haze particles. However, little is known on
the mechanisms leading to the formation of haze in the troposphere of Saturn. To better
understand these mechanisms, it is necessary to know the optical and physical properties
and vertical stucture structure of the tropospheric haze.
Following the work done by Karkoschka et al., only a few papers investigating the properties of the upper tropospheric haze have been published (Baines et al., 2006 ; Ortiz et
al., 1996 ; Peres-Hoyos et al., 2005). Nevertheless, these studies focus on the analysis
of visible and near-infrared images in a few filters, and so many ad-hoc assumptions are
made in the atmospheric stucture in order to fit properly the observations.
In this section, we used VIMS data sets in the near-infrared between 0.8 and 3.5 µm to
analyse the particle haze size, opacity, complex refractive index, and vertical distibution
in Saturn’s upper troposphere. As seen on Fig. 2.5, the near-infrared reflection spectum of Saturn is sensitive to pressure levels above the condensate clouds, and so VIMS
spectra are particularly relevant for the investigation of tropospheric haze. VIMS reflection spectra are made of 146 spectral points and were acquired at many different viewing
geometries and observation times. Therefore, VIMS data offer a unique opportunity to
better constrain the haze properties in the upper troposphere of Saturn.
32
CHAPTER 4. TROPOSPHERIC HAZE
4.1
33
Sensitivity to Model Parameters
Temperature
The ratio to the initial reflection spectrum after perturbing the temperature is below
1.1 and increases with wavelength. This dependency with wavelength is due to thermal
emission which dominates Saturn’s near-IR spectrum at higher wavelengths. For the first
four peaks, the variations in temperature have very little effect on the spectrum (less than
1%). However, changes up to 10% of the radiance are observed for the last two peaks.
The effects on the spectrum are particularly significant at the edge of the peaks where
the signal is low, and for large temperature variations, which are less likely to occur in
Saturn’s atmosphere. Therefore the temperature profile will be set to the profile retrieved
from CIRS thermal spectra measured at similar times.
Complex refractive index
Tests on the real and imaginary parts of the refractive index were carried out for nr ∈ [1, 2]
and ni ∈ [0, 0.1]. These ranges of values embrace refractive indexes for most materials at
any wavelength, and so no specific composition of tropospherice haze is a priori assumed.
The ratio is very close to 1.0 for most values of ni 1 . Most importantly, the ratio to the
initial spectrum is nearly uniform for most imaginary refractive indexes and so there is
no apparent correlation with wavelengths. That is to say, variations in the imaginary
refractive index should affect the overall spectrum uniformly. On the other hand, the
ratio for the real refractive index can vary between 0.9 and 1.4 for the same value of the
index. Thus the effects on the spectrum can be large and have a wavelength dependency
Aerosol size
The aerosol size significantly affects the near-IR reflection spectrum at lower wavelength.
There is a clear wavelength dependent effect of the size perturbation on the ratio, and
this is observed for all radii ranging from 100 nm to 1 µm2 . For one specific particle size,
the change in radiance can vary between 0% and up to 600%. Consequently, the particle
size affects both the amplitude and shape of the reflection spectrum, while the complex
refractive index has the main effect on the amplitude3 . The problem is partly uncorrelated
since the aerosol size can be tuned to match the shape of the synthetic spectrum to
VIMS spectrum; then adjustment is made by varying the complex refractive index. The
problem is only partly uncorrelated since both the real and imaginary refractive indexes
are unknown parameters in the model.
1
The largest variations are seen for "extreme” values of the refractive index. e.g. an imaginary index
of 0.1 leads to significant changes of the reflection spectrum, however it is statistically unlikely that this
value should be relevant since most materials have very small imaginary index below 0.1.
2
Here also typical values for aerosol sizes were used. Note that contrary to the refractive index, the
dependency with wavelengths is not a statistical bias since all the radius show a similar trend.
3
This also applies to the real part of the complex refractive number. Even though variations in radiance
up to 50% are observed, this is for extreme values of the index and is still relatively small compared to
effect of the particle size.
34
Sensitivity of Saturn’s Near-IR Reflection Spectrum to Real Refractive Index
Sensitivity of Saturn’s Near-IR Reflection Spectrum to Temperature
1.5
1.10
2.0
20
1.4
15
1.8
1.3
5
1.2
0
1.6
Ratio
10
Ratio
1.05
1.1
1.00
1.4
-5
1.0
-10
1.2
0.95
1.0
1.5
2.0
Wavelength (µm)
2.5
-15
0.9
-20
0.8
3.0
1.0
1.0
Sensitivity of Saturn’s Near-IR Reflection Spectrum to Imaginary Refractive Index
1.5
2.0
Wavelength (µm)
2.5
3.0
Sensitivity of Saturn’s Near-IR Reflection Spectrum to Particle Size
10
8
10-1
10 µm
8
4 µm
10-2
6
2 µm
6
Ratio
Ratio
10-3
4
900 nm
4
700 nm
10-4
500 nm
2
2
10-5
300 nm
0
0
1.0
1.5
2.0
Wavelength (µm)
2.5
3.0
0
100 nm
1.0
1.5
2.0
Wavelength (µm)
2.5
3.0
Figure 4.1: Sensitivity of Nemesis to atmospheric parameters. A synthetic reflection spectrum
was generated with Nemesis for an atmospheric profile made of tropospheric aerosols. Aerosols
were assumed to have a size of 1 µm with a variance of 0.05, and a refractive index of 1.4+0.001i.
The temperature profile was retrieved from the CIRS thermal spectrum of Saturn measured at
about the same time period (Fletcher et al., 2010). A volume mixing ratio (VMR) of 4.5 × 10−3
was chosen for methane (Flasar et al., 2005). For each perturbation of the temperature, real
refractive index, imaginary refractive index and aerosol size, the synthetic spectrum was recalculated and then compared to the initial spectrum. The four figures show the ratio between
the re-calculated and initial radiances at the six reflection peaks. Perturbations of temperature
are expressed as a shift ∆T ∈ [−20, 20] homogeneously applied to the initial profile. The colorbars
for the other parameters show their actual values after perturbation.
4.2
Optical and Physical Haze Properties
The haze vertical distribution was retrieved from a continuous a priori profile with Nemesis. The input parameters in the retrieval code relevant for the analysis of Saturn’s
near-IR spectrum are: the extinction coefficient, the scattering albedo, and the three
Henyey-Greenstein coefficients f , g1 , and g2 . Each parameter is expected to vary with
wavelength; so assuming that there are N wavelengths in the spectrum, the retrieval problem has 5N free parameters. It is unlikely that all sets of parameters would fit the VIMS
spectrum, but it is practically impossible to try all of them4 . Furthermore, the problem
might be highly degenerate and so many solutions could potentially fit the data. This
4
The full 0.8-3.5 µm VIMS spectrum was retrieved. There are 146 wavelengths in VIMS spectrum,
which gives more than 730 degrees of freedom to the retrieval problem for this particular data set. Also,
we do not know a priori the values for each parameter which means that there is an infinite number of
parameter sets.
35
is even more true for a large spectrum spread over many wavelengths, such as Saturn’s
reflection spectrum. A high number of measurements further increases the constraints on
the retrieval solutions but also introduces a wavelength dependency of the parameters in
the model. Finally, very little is known about the actual values of the parameters and
their dependency with wavelength, and so it is very likely that no distinction could be
made amongst all possible solutions.
Another approach was used in this analysis, in order to break the degeneracies inherent to
the retrieval problem. The extinction coefficient, the scattering albedo, and the HenyeyGreenstein coefficients can be pre-calculated in Mie theory assuming a particular size
distribution and complex refractive index. The number of degrees of freedom then reduces
to 1 + 2N instead of 5N (The aerosol size accounts for one degree of freedom). It can still
be a large number especially if a full spectral range is retrieved with Nemesis, but more
importantly there is some information available on these three parameters:
i. Atmospheric aerosols have typical sizes ranging from a few nanometers to a few microns.
ii. The imaginary refractive index has a typical value below 1 (see Fig. 4.5).
iii. The real refractive index of most materials ranges between 1 and 2.
iv. The complex refractive index shows low variability with wavelength and so is uncorrelated to the the aerosol size at first order.
v. The aerosol size has the most effect on both the amplitude and the shape of the near-IR
reflection spectrum.
The first step consisted in fitting the shape of VIMS reflection spectrum. Towards this
end, the synthetic spectrum was calculated with Nemesis for all aerosol sizes ranging
from 100 nm to 10 µm, and then compared to the VIMS spectrum. The real refractive
index was set up to 1.4, which is a typical order value shared by many materials. Since
the range of physical values for the imaginary part of the refractive index is typically
much larger than for the real part, both the imaginary refractive index and the aerosol
size were retrieved simultaneously5 (See Fig. 4.2).
5
In the ideal case, the real refractive index, the imaginary refractive index, and the aerosol size should
be varied all simultaneously. Although this is actually a work in progress, the time order for running
Nemesis on the full 0.8-3.5 µm spectrum is around one day.
36
Variation of the Goodness-of-fit with Aerosol Size and Imaginary Refractive Index
Variation of the Goodness-of-fit with Aerosol Size and Real Refractive Index
10.0
10.0
15
30
90
80
70
60
50
40
30
20
15
20
20
60
9
15
10
Aerosol size
15
20
10
80
90
20
30
40
50
60
70
80
90
15
20
30
5070
6040
8090
10-4
10-3
Imaginary refractive index
10-2
10-1
0.1
1.00
50
181007906400
00
60
50
30
10-5
15
20
40
1.07
1.15
1.23
0
19000 0 0
7805604
10-6
15
30
70 60
50
40
0.1
10-7
9
1.32
1.41
1.52
Real refractive index
1.62
1.74
96080570
10100
0
10
30
9
10
1.0
40
Aerosol size
50
10
9
1.0
1.87
Retrieval of Aerosol Vertical Profile from VIMS Near-IR Reflection Spectrum
50
Measured by VIMS
Modelled with NEMESIS
40
HAZE MODEL
*************
particle size = 700 nm
refractive indice = 1.4 + 0.001*i
30
20
10
0.80
1.07
1.33
1.60
1.86
2.13
2.39
Wavelength (µm)
2.66
2.92
3.19
3.45
0.001
Pressure (bar)
0.010
0.100
1.000
10.000
10-4
10-3
10-2
10-1
100
101
-3
Aerosol concentration (cm )
102
103
Figure 4.2: Retrieval of optical and physical haze properties. Top-left: Goodness-of-fit as
a function of aerosol radius and imaginary refractive index. The real index is set to 1.4.
Parameters for which the χ2 /nλ value is above 100 are ignored since optimal fit is found
for values below ∼ 10. Top-right: Goodness-of-fit as a function of aerosol radius and
real refractive index. The imaginary index is set to 0.001. Middle: Synthetic spectrum
calculated with Nemesis for aerosol size of 700 nm and a refractive index of 1.4 + 0.001i.
Bottom: Retrieved haze vertical distribution from a continuous a priori profile (solid line).
The retrieval errors are shown in dotted lines.
104
2.00
37
By plotting all the synthetic spectra against the VIMS spectrum, it can be easily seen that
any set of parameters with χ2 /nλ values above 10 cannot properly fit the observations
(See Fig. 4.3). Therefore, the optimum fit to the VIMS spectrum fit is obtained for a
narrow range of aerosol sizes between 600 nm and 1.5 µm and for any imaginary refractive
index below 0.001. The low value for the imaginary refractive index corresponds to high
single scattering albedo values. Indeed, the imaginary index represents the absorption of
sunlight by scatterers, and so low absorption corresponds to high scattering strength for
a given extinction coefficient. The single scattering albedo was found to vary significantly
with wavelengths between 0.8 and 3.5 µm, though most values are above 0.90. The
fact that the single scattering albedo is a variable function of the wavelength shows the
difficulty of choosing this parameter as a free variable in the model. The fitting strategy
used in this analysis of VIMS reflection spectrum has proved to be efficient in reducing
the range of possible solutions to the retrieval problem, and especially strong constraints
on the aerosol size were obtained6 . It has been mentionned that the real refractive index
was set to the constant value of 1.4. Although most materials have typical values around
1.4 for the real index, the use of a specific value for this parameter implies that the nature
of scatterers is known a priori. The synthetic spectrum was calculated for real refractive
indexes between 1 and 2 and for particle sizes between 100 nm and 10 µm. The imaginary
refractive index was set to 0.001. The best fits to VIMS spectrum were obtained for real
indexes between 1.1 and 1.8 and for particle sizes between 600 nm and 2 µm. A similar
range for the aerosol size has been retrieved while varying the real and imaginary parts
of the complex refractive index. Thus the particle size is well constrained by the analysis
of Saturn’s near-IR spectrum, and is quite uncorrelated with both the real and imaginary
indexes.
Another way to break some degeneracies in the model is to consider the optical depth.
For each set of parameters, a different vertical profile for the aerosol concentration is
found and so this actually adds a new degenerated parameter in the model7 . For example,
aerosol concentrations for particle sizes between 600 nm and 1.5 µm have a similar vertical
structure, but with different absolute values especially at the peak around 200 mbars. This
result is somewhat expected since larger particles have a higher extinction cross-section,
and so fewer particles/cm−3 are needed to fit the observations. However the aerosol
concentration and the extinction coefficient can be combined into the optical depth and
it has been found that this parameter is similar for all sets of possible solutions (See Fig.
4.3). Below 200 mbars, the optical depth becomes larger than 10, and so no information
on the atmospheric structure can be retrieved at these pressure levels. At the peak,
the optical depth ranges between 2 and 3 and shows little variation with wavelength.
Consequently, the two main parameters that can be the most accurately retrieved from
VIMS near-IR reflection spectrum are so far the aerosol size and the optical depth.
6
The physical explanation for the narrow range of aerosol size solutions is currently under investigation.
Preliminary tests have shown so far that particles with backward scattering (small particles) or with strong
forward scattering (large particles) cannot fit properly the observations.
7
It actually adds a number of degenerated parameters equal to the number of vertical levels chosen in
the model
PRESSURE = 0.00126525 bar
0.2
0.1
1.0
1.5
2.0
2.5
3.0
WAVELENGTH (MICRONS)
1.5
1.0
0.5
0.0
0.5
3.5
15
10
5
1.5
2.0
2.5
3.0
10
5
0
0.5
OPTICAL DEPTH
80
60
40
1.0
1.5
2.0
2.5
3.0
400 nm
500 nm
1.0
1.5
2.0
2.5
3.0
5
0
0.5
3.5
3.5
80
60
40
600 nm
1.0
1.5
2.0
2.5
3.0
700 nm
1.0
1.5
2.0
2.5
3.0
3.5
120
100
20
0
0.5
3.5
10
120
100
1.5
2.0
2.5
3.0
15
3.5
1.0
15
OPTICAL DEPTH
1.0
5
0
0.5
3.5
OPTICAL DEPTH
OPTICAL DEPTH
OPTICAL DEPTH
1.5
2.0
2.5
3.0
20
OPTICAL DEPTH
1.0
10
20
20
0
0.5
15
OPTICAL DEPTH
0.3
0
0.5
2.0
OPTICAL DEPTH
OPTICAL DEPTH
0.4
0.0
0.5
38
3.5
800 nm
120
100
80
60
40
20
0
0.5
1.0
1.5
2.0
2.5
3.0
900 nm
3.5
1 µm
Figure 4.3: Retrieval of opacity for various aerosol sizes. Top: Synthetic (red lines)
and VIMS (blue line) spectra for particle sizes between 400 nm and 10 µm. A complex
refractive index of 1.4 + 0.001i was used to generate the extinction, scattering albedo and
Henyey-Greenstein phase functions. Middle: Aerosol profiles retrieved with Nemesis for
each particle size. Bottom: Cumulative optical depth calculated from the top of the
atmosphere to various pressure levels.
39
The dependency of the real refractive number with wavelength, and both the imaginary
index and aerosol size is still work in progress. This should be particularly relevant since
the nature of scatterers can be inferred from their real refractive indexes8 . Preliminary
results are shown on Fig. 4.4. The haze is assumed to be made of ammonia particles and
so the complex refractive indexes in the near-IR are included in Nemesis (Martonchik et
al., 1984). The synthetic spectrum is calculated for various particle sizes ranging from 100
nm to 10 µm and then compared to the VIMS spectrum. The best fits to VIMS data are
found for particle sizes between 500 nm and 2 µm, which are similar values to the optimum
sizes retrieved for a constant refractive index. The particle size is still well constrained,
even though the complex refractive index varies with wavelength. The real and imaginary
indexes of ammonia particles have typical values similar to those that have been found to
fit the VIMS spectrum. Thus the synthetic spectrum for an ammonia haze matches quite
well the VIMS reflection spectrum. However the haze formation is a complex process
involving many different components and the retrieval problem is degenerate, so it is
very unlikely that ammonia particles only account for the tropospheric haze in Saturn’s
atmosphere.
Figure 4.4: Retrieval of particle size for an ammonia haze
8
Even though scatterers can be identified by their real imaginary part, it becomes harder if many
different types of scatterers are present in Saturn’s atmosphere. Haze formation is a complex process
involving the generation and destruction of many atmospheric components, so the real index of the
"mixture” might hide the individual indexes of each component.
40
The most interesting result from this preliminary analysis is that the variation of complex
refractive index with wavelength has little effect on the retrieval of the particle size. The
real and imaginary indexes between 1 and 5 µm of a few haze candidates are shown on
Fig. 4.5. The variations with wavelength of the complex index in the near-IR are quite
significant for the imaginary part but are small for the real part. Therefore it is very
likely that the imaginary index of aerosols should vary greatly over this spectral range,
while the real part can be considered as a constant function of the wavelength.
Figure 4.5: Complex refractive indexes of haze candidates
4.3
4.3.1
41
Vertical Structure
Sensitivity Tests
In the previous section, it has been mentioned that Nemesis retrieved the haze vertical
distribution from a continuous a priori profile. A series of retrievals was undertaken for
many a priori values and errors. The shape of the retrieved profile turned out to be
always similar to the results shown on Figs. 4.2 and 4.3. This also true for all sets of
particle sizes and refractive indexes that are solutions of the retrieval problem. The main
features of the the haze profile retrieved from Saturn’s near-IR reflection spectrum are:
i. A peak of aerosol concentration at 200 mbar
ii. A sharp decrease of aerosol concentration above the peak until 10 mbar.
iii. An increase of aerosol concentration above 10 mbar.
iv. A decrease of aerosol concentration below the peak. The retrieved profile relaxes to
the a priori profile.
Sensitivity tests on the haze pressure levels (see Fig. 4.6) show that the reflection spectrum
is slightly sensitive to the haze distribution above 10 mbar. In particular, opacity is needed
in the upper stratosphere in order to fit the low signal in the absorption bands. However
the effect on the continuum can be completely neglected, and so the peak at 200 mbars
is contributing most of the reflectance in the near-infrared. Pressure levels between 10
and 200 mbar do not contribute to the reflection peaks. This is because the aerosol
concentration is too low to have significant effect on to the reflectance. As expected, the
peak of opacity at 200 mbar contributes the most the VIMS spectrum. The sharp decrease
of Mie scatterer abundance right above the opacity peak is referred to as a “clearing”. The
existence of a clearing above the opacity peak has been tested by considering differents
models for the haze vertical structure.
Sensitivity of the Near-IR Reflection Spectrum to the Haze’s Top pressure Level
Sensitivity of the Near-IR Reflection Spectrum to the Haze’s Bottom pressure Level
100
80
80
60
χ2
χ2
60
40
40
20
20
0
0.0010
0.0025
0.0063
0.0159
0.0400
0.1004
Top pressure (bar)
0.2523
0.6340
1.5930
4.0023
0
4.002
2.463
1.516
0.933
0.574
0.353
Bottom pressure (bar)
0.217
0.134
0.082
Figure 4.6: Sensitivity of Saturn’s reflection spectrum to haze pressure levels. Left: The
sensitivity to the haze’s top pressure level was tested by removing all points above the
pressure levels shown on the x-axis. Right: The same process but for pressure levels below
those on the x-axis. Note that both figures are not smooth at the concentration peak,
implying that a thin haze layer contributes to the reflection spectrum.
0.051
4.3.2
42
Opacity clearing
The existence of the opacity clearing has been tested by considering the following vertical
haze profiles:
i. A compact profile: the opacity of a single aerosol layer is retrieved for all presure levels.
ii. A block profile: The aerosols have a constant density between two layers, and are absent
elsewhere. All sets of bottom and top pressure levels have been tested in Nemesis.
The particles are assumed to have a size of 700 nm and a complex refractive index of
1.4 + 0.001. For both models, a peak of opacity between 100 and 200 mbar is necessary to
fit the VIMS spectrum (see Fig. 4.7). There is a very tight constraint on the top pressure
level for the block model. Therefore, any synthetic spectrum calculated for a haze profile
with a high opacity above the tropopause cannot fit properly the observations. This is
also true for a haze vertical profile extending down to the deep troposphere. Therefore,
the results from the block haze model suggest that the clearing above the tropopause is
real
Tests on Haze Vertical Profile: Extended Aerosol Layer
Tests on Haze Vertical Profile: Compact Aerosol Layer
100
60
980700
50
0.001
80
χ2
60
40
0.010
0
0.001
0.010
0.100
Pressure base (bar)
1.000
10.000
50
40
30
HAZE MODEL
*************
compact: pB = 0.16 bar
radius = 700 nm
n = 1.4 + 0.001i
20
Top pressure (bar)
pB = 0.16 atm
20
908700
0.100
40
30
6500
40
70
90 80
1.000
10
0.80 0.96 1.11 1.27 1.42 1.58 1.74 1.89 2.05 2.20 2.36 2.51 2.67 2.83 2.98 3.14 3.29 3.45
Wavelength (µm)
0.01
0.10
Bottom pressure (bar)
Figure 4.7: Tests on the haze vertical profile. Left: Compact aerosol layer. right: The
aerosol concentration is constant within two boundary layers, and is assumed to be zero
elsewhere.
1.00
Chapter 5
Conclusion and Future Work
VIMS thermal and reflection spectra in the near-infrared offer a new insight on the clouds
and haze structure in Saturn’s troposphere. We first started the analysis of VIMS data
by looking at single thermal spectra acquired at a specific viewing geometry. We found
that the best fits to the observations were obtained for a cloud base pressure at 2.7 bar.
Nevertheless, we did not manage to distinguish between a purely absorptive and scattering atmospheric model. Also, the aerosol particle size is poorly constrained, and many
sizes can possibly provide a satisfying solution to the retrieval problem. It is necessary to
know the vertical structure of aerosols in order to properly calculate the optical depth.
We found that both a compact and an extended cloud model could fit equally well VIMS
thermal spectra, and so the optical depth values retrieved from these models differ greatly.
Finally, we could not constrain either the cloud composition. The two species expected
to condense at the tropospheric levels considered here, ammonia and ammonium hydrosulphide, were included in the atmospheric model. However, no model provided a better
fit than the other, and so we could not distinguish between both cases. The condensate
of ammonia and ammonium hydrosulphide is predicted by thermochemical theories, however there has been no spectral identification of these species yet. Therefore, we cannot
exclude the possibility of aternative cloud compositions in Saturn’s troposphere. In conclusion, there are many free parameters in the tropospheric cloud model and not enough
measurements constraints in order to find a unique solution to the retrieval problem.
We managed to break some degeneracies inherent to the retrieval problem by considering
different observations of the same area of the planet but at various viewing geometries.
In particular, we carried out the analysis of VIMS spectra simultaneously at low and high
emission angles. We found that a purely absorptive atmosphere cannot properly fit VIMS
data and that scattering needs to be integrated in the numerical code Nemesis. Also,
we managed to exclude the simple cloud model from our set of possible solutions to the
retrieval problem. This applies to a compact cloud made of either ammonia or ammonium
hydrosulphide particles. We could match the observations quite well for an extended cloud
with a base presure higher than 2.5 bar and an extension of at least 25 kilometres, and for
a particle size ranging between 1 and 3 micrometres. Nevertheless, a minimum extension
of 25 kilometres implies tropospheric clouds that extend up to altitude levels significantly
43
CHAPTER 5. CONCLUSION AND FUTURE WORK
44
higher than what is predicted from thermochemical models. Even though the minimum
extension found here is quite unrealistic, it shows that we can fit VIMS observations with
some opacity sources located higher up in the troposphere. This was indeed confirmed by
considering first a continuous aerosol profile and then a two compact clouds model. In
both cases we retrieved two opacity sources: one deep tropospheric cloud between 2 and
4 bar, and one haze layer below the tropopause. We used the VIMS spectum of Saturn
at shorter wavelengths in order to investigate the properties of this haze layer.
The near-infrared spectrum of Saturn in the 0.8-3.5 µm wavelength range was used to
retrieve the optical and physical properties, and the vertical structure of the tropospheric
haze located above the condensate clouds. We retrieved a peak of opacity below the
tropopause at around 200 mbar. Sensitivity tests showed that the opacity clearing above
the peak is very likely to be a realistic feature in Saturn’s atmosphere. Nevertheless, the
cumulative optical depth increases quickly below the peak and so we cannot sound the
haze structure at higher pressure levels. We also found that the real part of the refractive
index should be between 1.1 and 1.8 and the imaginary part below 0.001 in order to mach
VIMS observations. We managed to constrain quite well the particle size range between
600 nm and 2 µm. We are currently applying to VIMS reflection spectra the same multiviewing analysis as described for thermal spectra, in order to narrow the range of possible
solutions to the retrieval problem.
As mentioned above, the next step is to carry out a multi-analysis of VIMS reflection
spectra at various viewing geometries. In that way, we expect to derive a model of
Saturn’s upper tropospheric haze coherent with VIMS data and with the lowest level of
degeneracy. The results from the analysis of VIMS reflection spectra will be combined to
thermal spectra in order to better constrain the condensate cloud properties and vertical
structure. Indeed, by the setting up the haze model in the numerical code, the analysis
of Saturn’s thermal spectum has less free parameters and so we should be able to exclude
many cloud models that were found to fit the observations initially. Once the analysis
of VIMS near-infrared spectra provides a coherent clouds and haze model in Saturn’s
troposphere, the final step will be to investigate spatial and time variations of tropospheric
aerosols, and search for a correlation between the temperature knee and the presence of
tropospheric haze.
CHAPTER 5. CONCLUSION AND FUTURE WORK
Schedule for the next academic year
Term
September 2011
Plan
- Multi-viewing analysis of VIMS reflection spectra. I
am currently analysing reflection spectra measured at
different emission and incident angles.
- Derive a coherent tropospheric haze model including
the vertical structure, particle size, opacity, and complex
refractive index of aerosols.
- Search for potential haze candidates by comparing laboratory measurements with the haze model retrieved
from the multi-viewing analysis.
October 2011
- Test the possibility of a temperature knee generated
by tropospheric haze.
- Investigate the spatial and time variations of the knee
from CIRS observations, and look for possible correlations with the tropospheric haze.
November 2011 - Multi-viewing analysis of thermal spectra assuming a
haze model retrieved from the spectral analysis in the
0.8-3.5 µm wavelength range.
December 2011 - Use the clouds and haze model coherent with the whole
near-infrared spectrum to investigate spatial and time
variations of tropospheric aerosols.
January 2012
- Dynamical study from the variations in clouds and
haze structure over space and time.
February 2012
- Theoretical study of the photochemical and microphysical processes involved in the formation of tropospheric
clouds and haze.
March-May 2012 - Write.
June 2012
- Submit.
July 2012
- Work.
45
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Clouds and Haze in Saturn`s Troposphere

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