X. Zhang a, b, *, R.A. West c , D. Banfield d , Y.L. Yung a a
Division of Geological and Planetary Sciences, California Institute of Technology,
Pasadena, CA, 91125, USA b
Department of Planetary Sciences and Lunar and Planetary Laboratory, University of
Arizona, 85721, USA c
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive,
Pasadena, CA 91109, USA d
Department of Astronomy, Cornell University, Ithaca, NY 14853, USA
*Corresponding author at: Department of Planetary Sciences and Lunar and Planetary
Laboratory, University of Arizona, 85721, USA
E-mail address: xiz@lpl.arizona.edu
(X. Zhang)
To be submitted to:
Icarus
1

Abstract
We retrieved global distributions and optical properties of stratospheric aerosols on Jupiter from ground-based NIR spectra and multiple-phase-angle images from Cassini Imaging
Science Subsystem (ISS). A high-latitude haze layer is located at ~10-20 mbar, higher than in the middle and low latitudes (~50 mbar). Compact sub-micron particles are mainly located in the low latitudes between 40 ° 𝑆 and 25° 𝑁 with the particle radius between 0.2 and 0.5 𝜇𝑚 . The rest of the stratosphere is covered by the particles known as fractal aggregates. In the nominal case with the imaginary part of the UV refractive index 0.02, the fractal aggregates are composed of about a thousand 10-nm-size monomers. The column density of the aerosols at pressure less than 100 mbar ranges from ~10
7 cm
-2
at low latitudes to ~10
9
cm
-2
at high latitudes. The mass loading of aerosols in the stratosphere is
~10
-6 g cm
-2
at low latitudes to ~10
-4
g cm
-2
in the high latitudes. Multiple solutions due to the uncertainty of the imaginary part of the refractive index are discussed. The stratospheric haze optical depths increase from ~0.03 at low latitudes to about a few at high latitudes in the UV wavelength (~0.26 𝜇 m), and from ~0.03 at low latitudes to ~0.1 at high latitudes in the NIR wavelength (~0.9 𝜇 m).
2

1. Introduction
Aerosols, or hazes in the stratosphere of Jupiter are of particular interest. First, particular absorbers and scatterers affect the radiative heat budget and the solar energy redistribution in the Jovian stratosphere (West et al., 1992; Moreno and Sadeno, 1997; Zhang et al.,
2013). Second, aerosols are involved in the stratospheric chemical cycle.
They are one of the end products of the photochemistry or ion-chemistry
(Wong et al., 2003). The haze particles shield the UV light and alter the efficiency of photochemistry in deeper layers. Heterogeneous reactions may occur on the particle surfaces. Third, aerosols can serve as ideal tracers for the stratospheric transport (Friedson et al., 1999) and provide valuable information on the stratospheric dynamics. To evaluate the significance of haze, it is important to determine their latitudinal and vertical distribution and optical properties, such as the optical depth, single scattering albedo, and phase function, for the entire wavelength range from ultraviolet (UV) to the near-infrared
(NIR) region.
Taking advantage of the continuum spectra in NIR wavelengths, two attempts have been made to retrieve the global map of haze and clouds on Jupiter. Banfield et al. (1998) retrieved the latitudinal and vertical distributions of stratospheric and tropospheric hazes covering the entire southern hemisphere and northern equatorial region below 25° 𝑁 . They discovered that a low-latitude haze layer is located at ~50 mbar and its altitude level increases sharply to ~20 mbar in the high latitudes (polar hood). The tropospheric haze top is around 0.2 bar and is non-uniform with latitude. Haze density reaches a minimum in the tropopause region, which is unexpected from the previous models (e.g., Kaye and Strobel
1983). Recently, Kedziora-Chudczer and Bailey (2011) used a line-by-line multiple scattering radiative transfer model to simulate the NIR spectra with a much higher resolution. Their data cover the entire disk of Jupiter. They assume a 1.3 𝜇𝑚 particle layer
3

in the troposphere and a 0.3 𝜇𝑚 particle layer in the stratosphere. Their results are generally consistent with Banfield et al. (1998), except for an additional distinct haze layer is discovered around 5 mbar in the polar hoods.
Many studies focused on the aerosol properties in the UV and visible range, from various data sources such as the intensity measurements from spacecraft (e.g., Pioneer 10 in
Tomasko et al. 1978 and Voyager in Hord et al. 1979), space-based telescopes (e.g.,
Tomasko et al. 1986), and ground-based telescopes (e.g., West 1979), and polarization measurements (e.g., Smith 1986). Please see the review in West et al. (2004) for details.
Generally speaking, the low-latitude aerosols are composed of small particles with radii between 0.2-0.5 𝜇𝑚 (Tomasko et al. 1986), while the determination of the high-latitude aerosols is more complicated. Some studies (e.g., Moreno 1996; Barrado-Izagirre et al.
2008) assumed small particles (< 0.1 𝜇𝑚 ) to explain the low phase angle images in the polar region, although small particles in fact are not consistent with high phase angle data
(Rages et al. 1999). Alternatively, West and Smith (1991) proposed that the high-latitude particles are fractal aggregates in order to reconcile both the positive polarization (Smith
1986) and the modest forward scattering (e.g., Tomasko et al. 1978). Details such as the monomer radius, the number of monomers, fractal dimension, and refractive index have not been established. One of the purposes in this study is to test this hypothesis for Jupiter and quantify the aerosol properties.
In this study we combine the information from the ground-based NIR spectra and multiple-phase-angle images in UV to NIR wavelengths from the Imaging Science
Subsystem (ISS) onboard Cassini during its Jupiter flyby in the late 2000 and early 2001.
The ISS acquired ~26000 high-quality time-lapse images of Jupiter during its sixmonths-long flyby from 1 October 2000 to 22 March 2001 (Porco et al. 2003). A proper combination of the images from different filters can be used for a specific purpose. For example, the methane channels and corresponding continuum filters (e.g., MT1/CB1,
MT2/CB2, MT3/CB3) provide vertical structure information of the atmospheric aerosols and clouds. The UV1 filter samples the upper troposphere and stratospheric haze layer.
Furthermore, Cassini ISS provides images from low to high phase angles. Until now only
4

the low phase angle images have been investigated in the polar region (Barrado-Izagirre et al. 2008). In fact valuable information of the phase functions of the stratospheric particles can be obtained from the high phase angle images, as shown by previous studies, e.g., Tomasko et al. (1978) for the Pioneer data and Rages et al. (1999) for the
Galileo data. Therefore, we analyzed the low, middle and high phase angle images together to characterize the size, shape and phase functions of particles on Jupiter. This method also helps distinguish the compact sub-micron (CSM) particles 1 and fractal aggregates.
This paper is structured as follows. In section 2 we revisited the data from Banfield et al.
(1998) and updated the methane absorption coefficients in the original retrieval model and relaxed the previous assumptions, from which the updated stratospheric aerosol map is obtained. Using a new retrieval model is described in section 4, the aerosol and cloud properties are retrieved based on the ISS observations, followed by conclusions and discussions in section 5.
2. Retrieval from NIR Spectra
The NIR spectra from Banfield et al. (1998) were taken on August 14 1995, from the 200inch Hale telescope at Palomar Observatory. The spectra were obtained in broadband H
(1.45-1.8 𝜇𝑚 ) and K (1.95-2.5 𝜇𝑚 ) telluric windows, with the spectral resolution power
~100, covering from 25 ° 𝑁 to the south pole (~80 ° 𝑆 ) of Jupiter. Since the stratospheric aerosol optical depth is small in the H and K bands, Banfield et al. (1996) developed a direct retrieval technique based on the single-scattering approximation for the NIR spectra, under which the radiative transfer inversion problem is linear. Therefore a simple and effective retrieval technique can be applied to minimize the difference between the
1
In our study we cannot distinguish spherical and compact non-spherical particles in that size regime and so we use the term “CSM particles”.
The optical properties of the CSM particles small compared to the wavelength can be calculated using Mie theory even if they are not spheres. This is clearly not true for the fractal aggregates and large crystalline ice cloud particles in the troposphere.
5

simulated spectra and the observations in the least-square sense, with a Tikhonov-type regularization term (a two-point Gaussian correlation matrix) in the cost function to smooth the inverted profiles. The retrieval result is called f value, which is proportional to the product of phase function, cross section, single scattering albedo and mixing ratio of the particles. In the entire spectral region, any pixel with reflectivity ( I/F ) greater than 0.075 was removed to make sure the single scattering approximation is robust. Note that Banfield et al. (1996) assumed the retrieved f value is constant with wavelength. Banfield et al.
(1998) relaxed the assumption by incorporating the spectral shape of the aerosol extinction efficiency, but still assumed a constant particle size of 0.3 𝜇𝑚 with latitude and altitude.
See Banfield et al. (1996; 1998) for details of the observations, calibrations and the inverse model.
In this study, we improved the retrieval technique by (1) updating the CH
4
absorption coefficient, and (2) allowing the aerosol size to be varied with latitude. We use the correlated-k method to calculate the atmospheric transmission, which is accurate enough for the NIR low-resolution spectra and broadband filters for Cassini ISS images. We adopt the state-of-art CH
4
absorption coefficients from Karkoschka and Tomasko (2010), which are constructed from both visible and NIR CH
4
bands, based on the laboratory data and observed spectra from the Huygens probe on Titan and Hubble Space Telescope observations. The upper panel of Fig. 1 shows the total optical depth of CH
4
and H
2
-H
2
and
H
2
-He collisional induced absorption (CIA, based on Borysow et al. 1989a; 1989b; 1992;
2002) from the top of the atmosphere to 100 mbar. The old CH
4
coefficients in Banfield et al. (1998) generally overestimate the CH
4
opacity and the band shapes are also slightly different.
Banfield et al. (1998) found the spectra are actually not very sensitive to the particle size.
This is generally true except for the polar region. Fig. 2 compares the two optimized solutions based on the prescribed 0.3 and 0.7 𝜇𝑚 aerosols for 70 ° 𝑆 and the equator. The equatorial spectrum is relatively insensitive to the particle size. However the 0.3 𝜇𝑚 particle fails to fit the polar region spectrum below 2.1 𝜇𝑚 , while the 0.7 𝜇𝑚 particle is able to reproduce the observations. Therefore, we improve the retrieval technique by
6

varying the aerosol size with latitude. Through a grid search method, an optimal solution can be obtained for each latitude. The observations require larger particles (>0.6 𝜇𝑚 ) in the polar stratosphere (poleward of 60 ° 𝑆 ), but in the other regions the spectra are not able to distinguish the larger and smaller particles. One of the solutions in Rages et al. (1999) from the analysis of the Galileo measurements in the north polar region (60 ° N ) is 1.3 𝜇𝑚 particle radius at the 1 mbar level, which seems consistent with our solution for the south polar region, although one can ask whether these large particles are sustainable against sedimentation in the 1 mbar region or higher (Rages et al. 1999). An alternative solution by
Kedziora-Chudczer and Bailey (2011) is a two-mode haze model, in which they assume the lower layer (tropospheric haze or cloud) is composed of the 1.3 𝜇𝑚 particles and the upper layers (stratospheric haze) are composed of the 0.3 𝜇𝑚 particles. Therefore, the 0.7 𝜇𝑚 particle size in the polar region may be an average of the mixture of the 1.3 𝜇𝑚 tropospheric haze and 0.3 𝜇𝑚 stratospheric particle size, although our broadband data could not tell the difference.
The retrieved aerosol map ( f value) is shown in Fig. 3. This map generally agrees with the result from Banfield et al. (1998), except the aerosol layers are shifted slightly downward.
This is because the new CH
4
absorption coefficients are slightly smaller than the old ones.
The pressure level of the haze layer decreases from about 50 mbar at the equator to above
20 mbar at the south pole. The haze layers are found concentrated within one or two scale heights. Note that this map shows a clear region around the tropopause (~100 mbar), consistent with Banfield et al. (1998). It is contrary to the hydrazine photochemical model results by Kaye and Strobel (1983). It might be attributed to a deep source in the troposphere without strong upward transport or the fast fallout of heavy particles around the tropopause region, but a satisfactory physical explanation is still lacking (Banfield et al.
1998). The clear region is also found by Kedziora-Chudczer and Bailey (2011). The locations of the haze layers in their selected band and zones are generally consistent with our results. They found a very high stratospheric haze layer above 10 mbar that is beyond our sensitivity region. However, Kedziora-Chudczer and Bailey (2011) does not provide detailed latitudinal and vertical aerosol profiles and therefore we will use the updated aerosol map (Fig. 3) from Banfield’s data to model the haze (section 3).
7

3. Retrieval from Cassini Images
3.1. ISS data Description
Three Cassini ISS filters used in this work, CB3, MT3 and UV1 channels, are located near the two ends of our wavelength range from NIR to UV for the heating rate calculation. The lower panel of Fig. 1 shows the CH
4
and Rayleigh scattering optical depth at 100 mbar from UV to NIR region. The Rayleigh scattering optical depth is based on Chan and Dalgarno (1965): 𝜏/𝑝 = 0.0083(1 + 0.014𝜆 −2 + 0.00027𝜆 −4 )𝜆 −4
, for wavelength 𝜆 in 𝜇𝑚 and pressure 𝑝 in 𝑏𝑎𝑟 . Due to the oblateness of Jupiter, this expression can be corrected by a factor of 24.40/g to any latitude (West et al., 2004). The
CB3 filter (0.938 𝜇𝑚 ) is the continuum channel sampling the methane-free wavelength.
The MT3 filter is located in a strong methane absorption band centered at 0.889 𝜇𝑚 . This channel is designed to sample the upper atmosphere. The MT3/CB3 filters are sensitive to the location of the tropospheric haze layer and the aerosol properties at ~10 mbar in the high phase angle images. The UV1 filter is centered at 0.258 𝜇𝑚 , not affected by CH
4
but by strong Rayleigh scattering. Fig. 1 shows that the Rayleigh scattering optical depth at the UV1 channel is roughly the same as the methane optical depth in MT3 channel.
Therefore the UV channel is also more sensitive to the higher hazes.
We selected 38 Cassini ISS images, covering all the latitudes of Jupiter from 70 ° S to
70 ° N, and phase angles from 0.9
° to 141 ° . All images are calibrated according to West et al. (2010). The detailed information of the image index numbers from the Planetary
Data System (PDS) and mean phase angles are shown in Table 1. Fig. 4 shows some selected ISS images from the three filters. A significant latitudinal contrast is seen in the MT3 images, revealing brighter bands near the equator and the polar region, and that the northern hemisphere is brighter than the southern hemisphere. The brighter regions imply some combination of higher cloud top and thicker stratospheric haze in the equatorial region and northern high latitudes. The contract of small-scale features at low and high latitudes in the UV1 images is diminished by Rayleigh scattering above
8

the cloud and haze layers. A darker band in the equatorial region also implies some combination of a higher cloud top and darker particles. The strong evidence for the higher stratospheric haze layer in the polar region comes from the bright polar caps in the MT3 images and corresponding darker polar region in the UV1 images because only the higher stratospheric haze layer can overcome the CH
4
absorption and Rayleigh scattering. That the polar haze layers reside in the higher stratosphere is consistent with the results from the NIR retrieval results in section 2.
The spectral information from the three filters is not enough for retrieving a high-resolution vertical profile of the haze layer. Therefore we incorporate the vertical profiles from the
NIR retrieval results in section 2 and retrieved a total column abundance of aerosols for each latitude. For the region northward of 25 ° 𝑁 where the NIR retrieval results are not available, we assume that the shape of the vertical aerosol profile is the same as its conjugated latitude in the southern hemisphere. This assumption is justified according to the haze layer locations in zones and bands revealed by Kedziora-Chudczer and Bailey
(2011). We divided the whole globe evenly into 29 latitude bins from 70 ° 𝑆 to 70 ° 𝑁 , with a width of 5 ° in each bin. For each latitude, we randomly sampled I/F values for 10 pixels spread over longitude to represent the limb darkening profile. We tested different samples to validate our results.
3.2. Retrieval Model Description
We developed a retrieval model for the ISS data. The model is composed of two parts: the forward module and the optimization module. The forward module consists of a radiative transfer module and an aerosol optical property module. The optimization module is based on a nonlinear least square optimization to minimize the difference between model and observations (see, eg., Chapter 6 in Goody and Yung 1989). The details are presented in the following.
The radiative transfer module simulates the reflectivity (I/F) for a specific incident angle, viewing angle and phase angle using DISORT (DIScrete Ordinates Radiative Transfer
9

Program for a Multi-Layered Plane-Parallel Medium). DISORT (Stammes et al., 1988) employs the discrete ordinates method and has recently been translated into a C-language version by T. Dowling (2010, personal communication). Compared with the original single-precision Fortran code, the new version of the DISORT, called C-DISORT, is using double precision and has removed possible spurious numerical spikes, and its speed is 3-4 times faster than the original version. We use 32 streams to characterize the intensity angular distribution, the results from which display almost no difference from the 64stream cases.
As illustrated by Fig. 5, our forward module includes several atmospheric layers, including the haze layer, the cloud layer and the gas layers, from 1 mbar to the tropospheric cloud top. Typically above the cloud top our model has 12 vertical layers, which are enough to approximate the vertical profile of the stratospheric haze layer from the NIR retrieval. We do not use a CSM particle to approximate the optical properties of the tropospheric cloud layer which is probably consist of large crystalline ice cloud particles such as ammonia ice
(West et al. 2004). Instead, since we mainly focus on the stratospheric hazes, for simplicity, we parameterized the CH
4
absorption, Rayleigh scattering, aerosols and clouds in the troposphere all together as a semi-infinite “effective cloud layer” (or a bottom scattering layer), which can be characterized by its single scattering albedo (SSA) and a double
Henyey-Greenstein (DHG) phase function (Tomasko et al. 1978):
𝑃(𝜃) = 𝑓
1
4𝜋 (1 + 𝑔
1
2
1 − 𝑔
1
2
− 2𝑔
1 𝑐𝑜𝑠 𝜃) 3/2
+
1 − 𝑓
1
4𝜋 (1 + 𝑔
2
2
1 − 𝑔
2
2
− 2𝑔
2 𝑐𝑜𝑠 𝜃) 3/2 where 𝑃 is the phase function and 𝜃 is the scattering angle. The three parameters in the
DHG phase function are: the partition factor 𝑓
1
, the forward asymmetry factor 𝑔
1
, and the backward asymmetry factor 𝑔
2
. We considered two types of clouds: one for the NIR
(CB3/MT3) filters and the other for the UV1 filter. Due to strong tropospheric CH
4 absorption in the MT3 filter but little in the CB3 filter, we also retrieved the photon mean free path (PMFP) in the cloud in the MT3 channel, defined as the path length of a photon that travels in the cloud before a scattering event. Besides the optical properties, the effective cloud top is also a free parameter in the model.
10

For the haze optical property simulator, we choose two models: the “CSM model”, in which we assume the aerosols are CSM particles; and the “AGG model”, in which we assume the aerosols are fractal particles aggregated from a number of tiny monomers. The phase function and cross sections of CSM particles are calculated on the basis of Mie theory, and that of the fractal aggregates can be accurately calculated from the electromagnetic scattering computation using the multi-sphere methods, for example, by the MSTM code from Mackowski and Mishchenko (2011). However, it is computationally too expensive to meet our retrieval needs even with the help of parallel computing. Instead, we adopt a useful parameterization method for the aggregates with a fractal dimension of 2
(Tomasko et al. 2008)
2
. This empirical code has been validated with the rigorous multisphere calculations in a large parameter space, spanning the size parameter of the monomer from 10 −4
to 1.5 and number of monomers from 2 to 1024. For the monomer size parameter smaller than 0.5, the model is robust for even larger number of monomers
(~4028). Based on this empirical code, Tomasko et al. (2008) were able to fit the descent imager/spectral radiometer (DISR) instrument aboard the Huygens probe for Titan and found that the fractal aggregates in the Titan lower atmosphere are composed of thousands of 0.05𝜇𝑚 radius monomers. Therefore, we adopt the code in Tomasko et al. (2008) as our
AGG model.
The optimization module is a nonlinear least square optimization package, MPFIT, in
Interactive Data Language (IDL) language (Markwardt 2008). The algorithms were translated from the original Fortran code, MINPACK-1, a minimization routine (Moré
1978). The algorithm is based on the Levenberg–Marquardt iteration scheme (Levenberg
1944; Marquardt 1963), and the errors are calculated from the posterior covariance matrix.
This algorithm does not require any a priori knowledge, which is typically suitable for our purpose due to the poor knowledge about Jovian aerosols. The IDL package supports the upper and lower constraints for the retrieved parameters that are bounded within their physically allowed region. For instance, the single scattering albedo should be less than or
2 A typo has been found in their equation (A. 12b). The correct expression should be (personal communication with M. Lemmon): depol_11 = C_p11_m_3*M0*taus_out E_p11_t_1 .
11

equal to unity. See Moré (1978) and Markwardt (2008) for details of the code and its numerical scheme. The initial guess is sometimes crucial, so we tried different initial guesses and chose the best fitting results. From our synthetic data tests, the minimization package approaches the true values quickly and shows a robust behavior. The detailed computational time depends on the choice of the optical property module, the initial guess, and the number of data points, but a typical retrieval case in this study converges within 20 iterations in several hours, with the help of parallel computing.
3.3. Retrieval Results
In principle, retrieval is performed individually for each latitude bin to obtain the bestfitting parameters: cloud top pressure, haze column density, particle shape parameters, particle refractive indices, photo mean free path in the cloud, cloud phase functions and single scattering albedos. However, multiple solutions exist because there are not sufficient information and constraints to define a unique solution. In order to retrieve the common properties of the haze and cloud, we set up two cases for each retrieved parameter. In one case all the latitudes share the same value of that parameter, and in the other case the parameter is allowed to vary with latitude. If the performances of the two retrieval cases are as good as each other, we conclude the retrieved parameter behaves uniform along the latitudes based on the observations. We found that all the latitudes can share the same cloud phase functions for the NIR and UV filters, respectively, and only two types of stratospheric hazes are needed to explain the ISS data: CSM particles in the low latitudes
(40 °𝑆 − 25°𝑁 ), and fractal aggregated particles in the middle and high latitudes (70 °𝑆 −
45 °𝑆 and 30 °𝑁 − 70°𝑁 ). The low latitude boundaries are determined empirically on the bais of best-fit results; a CSM model is appropriate inside but an AGG model is required outside. In fact the low latitude boundaries can be seen from the MT3 and UV1 images in
Fig. 4.
The retrieved results for the nominal cases are summarized in Tables 2 and 3. Since the ISS data in our study are not very sensitive to the refractive index, we fix its real part based on
Khare et al. (1984). For the imaginary part that determines the haze albedo, in our nominal
12

case we fix it as 0.001 and 0.02 in NIR and UV filters, respectively. Multiple solutions corresponding to different choices of the imaginary index are investigated.
3.3.1. Low Latitudes: CSM Model Results
As in Tomasko et al. (1986), we are not able to determine the stratospheric particle size accurately in the low latitude region because they are optically thin and most of the photons are scattered by clouds in the troposphere. The approximate particle radius range found in this study is between 0.2 and 0.5 𝜇𝑚 , consistent with Tomasko et al. (1986). Therefore we fixed the CSM particle properties in the CSM model, in which we use the two-parameter gamma function for the aerosol size distribution. A different type of size distribution does not significantly influence the retrieval results. A typical CSM-model fit with a 0.3𝜇𝑚 radius particle is shown in Fig. 6 (solid lines) for different filters and various low and high phase angles at the equator. For the other intermediate phase angles (not shown in the plot) the fitting is also good. The dashed lines in Fig. 6 show that the AGG model fails to reproduce the limb-darkening profile.
Multiple solutions exist for the stratospheric particle size and refractive index. For example,
Table 4 shows two different solutions at the equator. Solution A is our nominal case in
Tables 2 and 3, and solution B corresponds to the UV imaginary refractive index 0.18
(Khare et al., 1984) and a particle size of 0.5 𝜇𝑚 . Although the aerosol properties are different, both solutions can fit the limb-darkening profiles. But the total aerosol optical depths above 100 mbar are more or less the same, about ~0.026 (NIR) and ~0.025 (UV) for solution A and ~0.034 (NIR) and ~0.022 (UV) in solution B. The total column density above 100 mbar is ~ 2 × 10 7 cm -2 for solution A and ~ 2.4 × 10 7 cm -2 for solution B.
Multiple solutions with a CSM particle of 0.3 𝜇𝑚 are shown in Fig. 7. We explored the
NIR imaginary refractive index from 0.0001 to 0.01 for the NIR filter with the UV imaginary refractive index fixed as 0.02, and the UV imaginary refractive index from 0.002 to 0.01 with the NIR imaginary refractive index fixed as 0.001. Changing the refractive
13

index would only change the single scattering albedo within a factor of 2, so the stratospheric haze optical depth is around 0.02-0.03 and the mass loading is around 2 𝜇𝑔 𝑐𝑚 −2
, consistent in all solutions. On the other hand, a CSM model with haze optical depth ~0.1 will significantly overestimates the high phase angle reflectivity, as shown by the dotted lines in Fig. 6.
3.3.2. Middle and High Latitudes: AGG Model Results
Outside the low latitude region (40 °𝑆 − 25°𝑁 ), the CSM model fails (Fig. 8, dashed lines).
Although the CSM model with particle radius of 0.1 𝜇𝑚 might be able to fit the low phase angle data, as also shown by previous studies (Moreno 1996; Barrado-Izagirre et al. 2008), it does not fit the high phase angle data simultaneously. On the other hand, fractal aggregates are able to reproduce the limb-darkening profiles in all filters and phase angles
(solid lines in Fig. 8).
The optical properties of the fractal aggregates depend on the monomer size and number of monomers. Smaller monomer leads to larger UV haze optical depth, and larger number of monomers increases the forward scattering. Provided that the imaginary part of UV refractive index is 0.02, all the observations in the middle and high latitudes can be explained with the same kind of fractal particle that is composed of a thousand 10nanometer monomers. The monomer size in the southern hemisphere appears slightly smaller than that in the northern hemisphere. Fig. 9 shows that the models with 50-nm monomer (dashed) or 200 monomers with any size (dotted) cannot simulate the midlatitude observations very well, especially when the phase angles are high.
In the nominal case, the total haze optical depths above 100 mbar are about 2-3 in UV and
~0.1 in the NIR wavelengths in the high latitudes, with the mass loading on the order of 10
-
4 g cm
-2
. Compared with the low latitudes, the high-latitude haze is optically thicker by one to two orders of magnitude. The dotted lines in Fig. 8 show a sensitivity test case in which we performed the optimization with the optical depth fixed as five times smaller than the best solution, the high phase angle data in the MT3 filter are significantly underestimated.
14

The solutions depend on the choice of imaginary part of the refractive index that affects the haze single scattering albedo. Multiple solutions for 60 ° 𝑆 are shown in Fig. 10. When fixing the NIR imaginary index as 0.001, we found decent fits exist if the UV imaginary index is between 0.006 and 0.08 (blue dots in Fig. 10). If we fixed the UV imaginary index as 0.02, our model requires the NIR imaginary index less than ~0.005 (orange dots in Fig.
10). In fact both of them can vary and so they do not provide as tight a constraint on the mass loading and microphysical parameters as this figure might imply. Fig. 8 shows that an
AGG model with UV imaginary index equal to 0.2 would not be able to explain the limbdarkening profiles. The haze optical depths in UV and NIR wavelengths are roughly consistent in all the solutions. The retrieved haze parameters do not vary significantly with the NIR imaginary index because the cloud NIR albedo change is enough to compensate most of the haze absorption change. The monomer radius increases with the UV imaginary index in order to keep the UV to NIR optical depth ratio roughly constant. The number of monomers deceases with the monomer radius increase so that the total particle size and phase function do not change significantly. The total column density and mass loading decease as the UV imaginary index increases due to the scattering efficiency increase with the monomer radius. Therefore, within the uncertainty range of the UV imaginary index, the monomer radius could vary from 5 nm to 40 nm, and accordingly, the number of monomers changes from 10000 to 100. The total aerosol mass loading in the 65°𝑆 ranges from ~ 2 × 10 -5 g cm -2 to ~10 -3 g cm -2 . But the stratospheric haze optical depths only differ less than 30% among all the solutions. The single scattering albedos of the polar haze are
~0.8 and 0.8-0.95 in the UV and NIR wavelengths, respectively, consistent in all the solutions.
3.3.3. Summary of the ISS Retrieval Results
Fig. 11 shows the latitudinal distributions of the effective cloud top, cloud single scattering albedo, aerosol optical depths, and total mass loading in the nominal case. The effective cloud top is around 200 mbar, roughly consistent with the result from NIR spectrum inversion (Fig. 3). The cloud top does not change dramatically from latitude to latitude, but
15

the equatorial zone and the northern mid-latitudes shows a higher effective cloud top.
Although the cloud is barely seen in the higher latitudes from the high phase angle images, the low phase angle images seem to imply the northern polar region tends to have lower effective cloud top than the southern polar region, but there is a large uncertainty associated with it. This conclusion is qualitatively consistent with the tropospheric haze tops retrieved from the low phase angle images from other ISS filters and Hubble Telescope observations
(Barrado-Izagirre et al. 2008). The cloud top retrieved by Kedziora-Chudczer et al. (2011) also appears higher at high northern latitudes than at high southern latitudes.
The belts and zones at low latitudes can be seen from the cloud SSA in all three filters because the clouds contribute the most to the reflectivity. The zones tend to be brighter and the belts tend to be darker in the NIR filter and the opposite behavior exhibits in the UV1 filter. This might be expected because cloud scattering in the UV1 channel is mixed with conservative Rayleigh scattering. The PMFP in the cloud is around 100-200 mbar in the
NIR (Table 3). It seems the cloud/tropospheric haze at low latitudes is optically thicker than the high-latitude cloud based on the retrieval results that (1) shorter photon scattering path at low latitudes and (2) higher cloud albedo in the UV wavelengths at high latitudes.
This is consistent with the NIR retrieval results in Fig. 3. The thickest tropospheric haze
(smallest PFMP) is located between 0 ° to 10 ° N, consistent with the Galileo observations
(West et al., 2004). This high and thick tropospheric haze layer in the equatorial region is likely associated with a strong upwelling from the hydrogen ortho-para fraction data as suggested by Banfield et al. (1998).
The aerosol optical depths in the UV and NIR wavelengths at low latitudes in the nominal case are roughly the same. The NIR continuum optical depth increases continuously towards the high latitudes until it is comparable to the CH
4
optical depth (~0.2) in MT3 wavelengths latitudes ± 70 degrees. The UV optical depth shows discontinuities at about
30 ° N and near 45 ° S, where it exceeds the Rayleigh scattering optical depth (~0.2 at 100 mbar). The UV/NIR extinction ratio in the middle and high latitudes is roughly constant
(~35), mainly because they share the same monomer size (~10 𝑛𝑚 ).
16

In our nominal case, the haze column density above 100 mbar is ~10
7
cm
-2
at low latitudes and ranges from ~10
8
cm
-2
in the mid-latitudes to ~10
9
-10
10
cm
-2
in the polar region.
Assuming that the mass density is about 1 g cm
-3
, the mass loading of the particles is ~10
-6 g cm
-2
in the low latitudes and ~10
-4
g cm
-2
in the high latitudes.
The derived column density and mass loading at mid-latitudes are roughly consistent with Tomasko et al.
(1986), who estimated aerosol mass loading on the order of 10
-6
g cm
-2
in the low latitudes and on the order of 10 -5 g cm -2 in the middle latitudes, and the total column density at
45 ° 𝑁 is about 5 × 10
8
cm
-2
. Our results also generally agree with the global map of aerosol volume density per unit gas abundances in West et al. (1992). But we have shown that the column density and mass loading of the fractal aggregates could vary by one or two order of magnitudes due to the uncertainty of the refractive index in the UV wavelengths, as discussed in previous sections.
Fig. 12 shows the aerosol number density map on Jupiter. The maximum aerosol number density also changes dramatically from low latitudes to high latitudes. At equator, the aerosol number density peaks at about 50 mbar, with the value of ~10 cm
-3
. In the polar region, for instance, at 65 ° 𝑁 , the aerosol number density peaks at about 20 mbar, with the value of ~10
4
cm
-3
. The values are different from the Galileo high phase angle results
(Rages et al., 1999), which show the number density ~0.15 cm
-3
at 100 mbar, and ~0.1 cm
-3 and 0.7 cm -3 at 20 mbar for the equatorial region and 60 ° 𝑁 , respectively. The difference is mainly due to the different vertical aerosol profile and particle shape. In this study, the aerosol distribution shows a clear region at 100 mbar so the particle number density near the 100 mbar is low (Fig. 3). At ~20 mbar, in fact the number density in our equatorial model is also roughly ~0.1 cm
-3
. But the peak is actually located around 50 mbar. For the polar region, the required UV optical depth is ~10, provided the extinction cross section of the aggregates is of the order of 10
-9
cm
2
at the UV wavelength and the total column density is required to be ~10 10 cm -2 . Since we have a very concentrated particle haze layer from the NIR retrieval and the layer thickness is usually within one or two atmospheric scale heights (~25-50 km), the number density is ~ 10 4 cm -3 . The particle density profiles provide useful constraints to chemical and microphysical models.
17

The aerosol and cloud phase functions are plotted in Fig. 13. The aerosol phase functions in low latitudes and high latitudes look similar in the forward peak in both the NIR and UV filters, respectively. The low-latitude haze appears to have stronger back scattering than the high-latitude particle, but note that the phase function of the low-latitude particle depends on the particle size. The tropospheric haze/cloud phase function over the UV-visible wavelengths seems not change too much, as the derived phase functions are roughly consistent with that from Pioneer 10 observations in the RED filter (0.64 𝜇𝑚 ) at the north component of the South Equatorial Belt (SEBn) of Jupiter (Tomasko et al., 1978). Detailed analysis of the clouds may require more cloud channel data to separate the tropospheric haze from the bottom layer clouds.
4. Concluding Remarks
In this study, we analyzed two types of observations to retrieve the Jovian aerosols. The spectral shape of the ground-based NIR data in the CH
4
bands are used to derive the latitudinal and vertical profiles of the aerosols, from which we can further determine the particle size, shape and optical properties in the optical wavelengths based on the UV and visible-IR limb-darkening profiles at multiple phase angles from Cassini ISS. We obtained an aerosol number density map by combining the two pieces of information.
Only one type of tropospheric haze/cloud layer is needed to explain the limb-darkening profiles for all the latitudes. The effective cloud top is located at ~200 mbar, consistent in both NIR and Cassini ISS retrievals. The north polar cloud layer appears to be deeper than it is in the south high latitudes. The PMFP in the cloud is around 100-200 mbar in the NIR.
It appears that the tropospheric hazes/clouds at low latitudes is optically thicker than the high latitude cloud and the equatorial clouds are the thickest.
We distinguished two types of aerosols in the stratosphere of Jupiter. CSM particles are located in the low latitudes between 40 ° 𝑆 and 25° 𝑁 , with a radius between 0.2 and 0.5 𝜇𝑚 . The rest of the stratosphere is covered by the fractal aggregated particles composed of a thousand 10-nm monomers, provided that the imaginary part of the UV refractive index is
18

0.02. The polar haze is one to two orders of magnitude optically thicker than the lower latitude haze. The column density of the aerosols ranges from ~10
7 cm
-2
at low latitudes to
~10
10
cm
-2
in the polar region. The mass loading of aerosols in the stratosphere is from ~10
-
6 g cm
-2
at the low latitudes to ~10
-4
g cm
-2
in the high latitudes.
Multiple solutions exist due to the uncertainty of imaginary part of the refractive index.
Changing the imaginary part of the refractive index does not change much of the scattering efficiency in the high phase angles. Therefore, under different choices of imaginary index, the stratospheric haze optical depth remains roughly the same, i.e., around 0.02-0.03 at low latitudes and about a few at high latitudes, consistent in all solutions. In order to maintain roughly same scattering efficiency and phase function, one can adjust the monomer radius and number of monomers of the high-latitude aerosol particles to fit the spectra, and thus lead to multiple solutions. We found that the monomer radius could vary from 5 nm to 40 nm, the number of monomers from 10000 to 100, and the total aerosol mass loading from
~10
-5
g cm
-2
to ~10
-3
g cm
-2
, corresponding to different UV imaginary indices.
We also constrained the UV imaginary index within the range of 0.006-0.08 from the highlatitude images. The derived value in the UV wavelengths from Moreno and Sedano (1997) is about 0.02-0.04 in the high latitudes. Note that their values are based on spherical particles and the low phase angle images only, and we use fractal aggregates and both low and high phase angle images are included. The upper limit of the NIR imaginary index from this study is ~0.004. Very few previous laboratory measurements focused on the refractive index for the aerosols in the hydrogen dominant environment. Khare et al. (1987) measured the imaginary part of the refractive index of thin hydrocarbon films produced in the mixture of 7% CH
4
and 93 percent H
2
from the charge particle irrradiation at 0.13 mbar pressure from 0.4 to 2.5 𝜇𝑚 (Fig. 14). Their values in the NIR region are located within the error bar of our retrieval results (Fig. 14). In the UV region, the values derived in this study imply that particles produced in the H
2
environment have weaker absorptivity than that from the N
2
environment, as shown by the comparison of our results with the widely used tholin refractive index measured by Khare et al. (1984) in a Titan-like environment. The change of the absorptivity might be related to the unpaired electrons of nitrogen interacting
19

with the delocalized π electrons from aromatics (Imanaka et al. 2004).
The similarity between the mid- and high-latitude aerosols implies the source of the midlatitude particles might be in the polar region, possibly due to the complex hydrocarbon synthesis driven by the energetic particle precipitation in the aurora region (e.g., Hord et al.
1979; Pryor and Hord 1991; Wong et al. 2003). This hypothesis is also consistent with the
NIR retrieval results (Fig. 3), which show the polar haze layer is at ~10-20 mbar, higher than the middle and low latitudes (~50 mbar) in the southern hemisphere, implying an efficient transport from the polar region to the middle latitudes. Another line of evidence is from the boundaries of the CSM particle zone (or the low optical depth zone) at low latitudes, which are not symmetric about the equator. It has been hypothesized to correlate with the hemispheric asymmetry of the auroral precipitation, since the auroral main oval extends to lower latitudes in the northern polar region (West et al., 2004). On the other hand, the difference between the mid-latitude and low-latitude particles, although they reside on the same pressure levels from the NIR observations, suggests that the low-latitude particles might be generated via a different chemical pathway, e.g., by the neutral photochemical processes driven by the UV photons instead of high energetic particles in the high latitudes.
The polar particles can be transported by eddy mixing or wind advection. The Stokes sedimentation timescale of the particles at 10 mbar is about an Earth year (Banfield et al.,
1998), which is smaller than the horizontal eddy mixing timescales (10-100 years) estimated from the SL-9 debris data (Friedson et al., 1999) and C
2
H
2
and C
2
H
6
distributions from Cassini (Liang et al., 2005). The aerosol heating in the polar region is large, which might induce a circulation from poles to the mid-latitudes. However, the advection by the mean residual circulation from previous studies (timescale ~100 years, e.g., West et al.,
1992) is not fast enough to transport the polar fractal aggregates to the mid-latitudes. A detail chemical-transport model has yet to be developed to explain the particle transport in the high latitudes.
20

Previous studies on the aerosol solar heating rate are not consistent with each other. Based on the latitudinal distribution of aerosols from the observations by Voyager and
International Ultraviolet Explorer (IUE), West et al. (1992) calculated the aerosol heating rate map in the stratosphere of Jupiter and found that the aerosol heating effect is so large, especially at the polar region, that it might drive a circulation from the poles to the midlatitudes. However, Moreno and Sedano (1997) derived the aerosol properties based on a microphysical model and the Hubble Space Telescope (HST) images. They found that the aerosol heating rate is significantly smaller than that in West et al. (1992), especially in the northern polar region. However, the vertical profile of the Jovian stratospheric aerosol was not well determined until the study by Banfield et al. (1998). Now we know the derived aerosol vertical profile from the NIR spectra (Banfield et al. 1998) differs significantly from the microphysical model results in Moreno and Sedano (1997). Since the details of the fractal aggregates were not revealed before, both the sub-micron particles in West et al.
(1992) and the tiny particles (<0.1 𝜇𝑚 ) in Moreno and Sedano (1997) are not consistent with the observations. In light of the aerosol global map and particle properties derived in this study, a renewed effort on aerosol heating in the stratosphere of Jupiter is justified.
Acknowledgements
We thank M. Lemmon for the parameterization model for the aggregated particles, T.
Dowling for the C-DISORT program, M. Line for helpful discussions. This research was supported by the Outer Planets Research program via NASA grant JPL.1452240 to the
California Institute of Technology. YLY was supported in part by NASA NNX09AB72G grant to the California Institute of Technology. XZ was supported in part by the Bisgrove
Scholar Program in the University of Arizona.
21

References
Banfield, D., Gierasch, P.J., Squyres, S.W., Nicholson, P.D., Conrath, B.J., Matthews, K.,
1996. 2 𝜇 m spectrophotometry of Jovian stratospheric aerosols-scattering opacities, vertical distributions, and wind speeds. Icarus 121, 389-410.
Banfield, D., Gierasch, P., Bell, M., Ustinov, E., Ingersoll, A., Vasavada, A., West, R.A.,
Belton, M., 1998. Jupiter's cloud structure from Galileo imaging data. Icarus 135, 230-
250.
Barrado-Izagirre, N., Sánchez-Lavega, A., Pérez-Hoyos, S., Hueso, R., 2008. Jupiter's polar clouds and waves from Cassini and HST images: 1993-2006. Icarus 194, 173-185.
Borysow, A., Frommhold, L., 1989a. Collision-induced infrared spectra of H
2
-He pairs at temperatures from 18 to 7000 K. II-Overtone and hot bands. The Astrophysical
Journal 341, 549-555.
Borysow, A., Frommhold, L., Moraldi, M., 1989b. Collision-induced infrared spectra of
H
2
-He pairs involving 0-1 vibrational transitions and temperatures from 18 to 7000 K.
The Astrophysical Journal 336, 495-503.
Borysow, A., 1992. New model of collision-induced infrared absorption spectra of H
2
-He pairs in the 2-2.5 μm range at temperatures from 20 to 300 K: An update. Icarus 96,
169-175.
Borysow, A., 2002. Collision-induced absorption coefficients of H
2
pairs at temperatures from 60 K to 1000 K. Astronomy and Astrophysics 390, 779-782.
Chan, Y., Dalgarno, A., 2002. The dipole spectrum and properties of helium. Proceedings of the Physical Society 86, 777.
Friedson, A.J., West, R.A., Hronek, A.K., Larsen, N.A., Dalal, N., 1999. Transport and mixing in Jupiter's stratosphere inferred from Comet SL-9 dust migration. Icarus 138,
141-156.
22

Goody, R.M., Yung, Y.L., 1995. Atmospheric radiation: theoretical basis, Oxford
University Press, USA, p. 259.
Hord, C.W., West, R.A., Simmons, K.E., Coffeen, D.L., Sato, M., Lane, A.L., Bergstralh,
J., 1979. Photometric observations of Jupiter at 2400 angstroms. Science 206, 956-
959.
Karkoschka, E., Tomasko, M.G., 2010. Methane absorption coefficients for the jovian planets from laboratory, Huygens, and HST data. Icarus 205, 674-694.
Kaye, J.A., Strobel, D.F., 1983. HCN formation on Jupiter: The coupled photochemistry of ammonia and acetylene. Icarus 54, 417-433.
Kedziora-Chudczer, L., Bailey, J., 2011. Modelling the near-IR spectra of Jupiter using line-by-line methods. Monthly Notices of the Royal Astronomical Society 414, 1483-
1492.
Khare, B., Sagan, C., Thompson, W., Arakawa, E., Votaw, P., 1987. Solid hydrocarbon aerosols produced in simulated uranian and neptunian stratospheres. Journal of
Geophysical Research 92, 15067-15015,15082.
Khare, B.N., Sagan, C., Arakawa, E., Suits, F., Callcott, T., Williams, M., 1984. Optical constants of organic tholins produced in a simulated titanian atmosphere: from soft Xray to microwave frequencies. Icarus 60, 127-137.
Levenberg, K., 1944. A method for the solution of certain problems in least squares.
Quarterly of applied mathematics 2, 164-168.
Liang, M.C., Shia, R.L., Lee, A.Y.T., Allen, M., Friedson, A.J., Yung, Y.L., 2005.
Meridional transport in the stratosphere of Jupiter. The Astrophysical Journal Letters
635, L177.
Mackowski, D., Mishchenko, M., 2011. A multiple sphere T-matrix Fortran code for use on parallel computer clusters. Journal of Quantitative Spectroscopy and Radiative
Transfer 112, 2182-2192.
Markwardt, C.B., 2008. Non-Linear Least Squares Fitting in IDL with MPFIT. in proc.
Astronomical Data Analysis Software and Systems XVIII, Quebec, Canada, ASP
Conference Series, 411, eds. D. Bohlender, P. Dowler & D. Durand (Astronomical
Society of the Pacific: San Francisco), 251-254.
23

Marquardt, D.W., 1963. An algorithm for least-squares estimation of nonlinear parameters.
Journal of the Society for Industrial & Applied Mathematics 11, 431-441.
Moré, J. 1978. The Levenberg-Marquardt Algorithm: Implementation and Theory. in
Numerical Analysis 630, ed. G. A. Watson, Springer-Verlag: Berlin.
Moreno, F., 1996. The structure of the stratospheric aerosol layer in the equatorial and south polar regions of Jupiter. Icarus 124, 632-644.
Moreno, F., Sedano, J., 1997. Radiative balance and dynamics in the stratosphere of
Jupiter: Results from a latitude-dependent aerosol heating model. Icarus 130, 36-48.
Porco, C.C., West, R.A., McEwen, A., Del Genio, A.D., Ingersoll, A.P., Thomas, P.,
Squyres, S., Dones, L., Murray, C.D., Johnson, T.V., 2003. Cassini imaging of
Jupiter's atmosphere, satellites, and rings. Science 299, 1541-1547.
Pryor, W.R., Hord, C.W., 1991. A study of photopolarimeter system UV absorption data on
Jupiter, Saturn, Uranus, and Neptune: Implications for auroral haze formation. Icarus
91, 161-172.
Rages, K., Beebe, R., Senske, D., 1999. Jovian stratospheric hazes: The high phase angle view from Galileo. Icarus 139, 211-226.
Smith, P.H., 1986. The vertical structure of the Jovian atmosphere. Icarus 65, 264-279.
Stamnes, K., Tsay, S.C., Jayaweera, K., Wiscombe, W., 1988. Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. Applied Optics 27, 2502-2509.
Tomasko, M., Doose, L., Engel, S., Dafoe, L., West, R., Lemmon, M., Karkoschka, E.,
See, C., 2008. A model of Titan's aerosols based on measurements made inside the atmosphere. Planetary and Space Science 56, 669-707.
Tomasko, M., Karkoschka, E., Martinek, S., 1986. Observations of the limb darkening of
Jupiter at ultraviolet wavelengths and constraints on the properties and distribution of stratospheric aerosols. Icarus 65, 218-243.
Tomasko, M., West, R., Castillo, N., 1978. Photometry and polarimetry of Jupiter at large phase angles: I. Analysis of imaging data of a prominent belt and a zone from pioneer
10. Icarus 33, 558-592.
West, R., Friedson, A., Appleby, J., 1992. Jovian large-scale stratospheric circulation.
Icarus 100, 245-259.
24

West, R., Knowles, B., Birath, E., Charnoz, S., Di Nino, D., Hedman, M., Helfenstein, P.,
McEwen, A., Perry, J., Porco, C., 2010. In-flight calibration of the Cassini imaging science sub-system cameras. Planetary and Space Science 58, 1475-1488.
West, R.A., 1979. Spatially resolved methane band photometry of Jupiter: II. Analysis of the South Equatorial Belt and South Tropical Zone reflectivity. Icarus 38, 34-53.
West, R.A., Smith, P.H., 1991. Evidence for aggregate particles in the atmospheres of Titan and Jupiter. Icarus 90, 330-333.
West, R.A., Baines, K.H., Friedson, A.J., Banfield, D. Ragent, B., Taylor, F., 2004. Jovian
Clouds and Haze. In Jupiter - The Planet, Satellites and Magnetosphere. F. Bagenal, T.
Dowling and W. McKinnon, Eds., Cambridge University Press.
Wong, A.S., Yung, Y.L., Friedson, A.J., 2003. Benzene and haze formation in the polar atmosphere of Jupiter. Geophysical research letters 30, 1447.
Zhang, X., Nixon, C.A., Shia, R.L., West, R.A., Irwin, P., Yelle, R., Allen, M., and Yung
Y.L., 2013, Radiative Forcing of the Stratosphere of Jupiter, Part I: Atmospheric
Cooling Rates from Voyager to Cassini, submitted
25

Table 1. Selected Cassin ISS images in this work.
CB3 Filter MT3 Filter
Image
Number
Mean
Phase
Angle
Image Number Mean
Phase
Angle
N1352917174
N1355181340
N1355181726
N1355182081
N1355182442
N1356751773
N1356754443
N1358257928
N1358258182
N1360176531
N1360177530
N1363092160
17.548
N1352917145
3.503
N1355181377
3.458
N1355181763
3.699
N1355182101
3.731
N1355182462
52.915
N1355366470
53.065
N1355716697
119.584
N1355717439
119.580
N1359305173
136.444
N1359306172
136.445
N1363092096
140.988
UV1 Filter
Image Number
17.549
N1352917104
3.503
N1355181442
3.457
N1355182158
3.699
N1355182519
3.730
N1355720416
0.936
N1355720779
6.471
N1355723337
6.470
N1357558433
131.917
N1358243072
131.921
N1358243326
140.987
N1358855316
N1358856323
N1358860176
N1358861183
N1363187297
Mean
Phase
Angle
17.548
3.507
3.703
3.731
6.442
6.592
6.568
99.774
119.323
119.318
128.024
128.021
128.066
128.062
141.022
26

Low-latitude Particle
High-latitude Particle
Cloud NIR Phase Function
Cloud UV Phase Function
Mean Radius 𝐫 eff 𝐯 eff
(𝜇𝑚 )
Imaginary Part of the Refractive Index NIR (~0.9
𝜇𝑚 )
UV (~0.25 𝜇𝑚 ) 𝑓
1 𝑔
1 𝑔
2 𝑓
1 𝑔
1 𝑔
2
(𝜇𝑚
Monomer Radius ( 𝑛𝑚
Number of Monomers
)
)
0.3
0.1
~10 (north)
~8 (south)
~1000
1 × 10 -3
2 × 10 -2
0.9675
0.6650
-0.5954
0.8303
0.8311
-0.3657
*
We use a two-parameter gamma distribution for the low-latitude particles, characterized
Table 2.
Latitudin allyinvariant
Paramete rs in the best-fit model. by r eff
and v eff
:
𝑁(𝑟) =
(𝑟 r 𝑒𝑓𝑓
1/v eff
−3 𝑣 𝑒𝑓𝑓
) exp (−
1/v eff
−2 𝑟 𝑟 𝑒𝑓𝑓 𝑣 𝑒𝑓𝑓
)
𝛤(1/v eff
− 2)
, where 𝑟 is the radius and 𝛤 is the gamma function.
27

eters.
-10
-5
0
5
10
15
Latitude Column density above 100 mbar
(10 6 cm -2 )
-70
-65
-60
-55
-50
-45
-40
-35
-30
-25
-20
-15
9410.3 ± 218.0
4618.4 ± 70.7
2282.1
1172.9
795.3 ± 17.0
242.3 ± 7.3
7.9
8.1 ± 0.5
7.2
±
±
±
±
39.6
18.4
0.4
0.7
12.0
± 0.7
19.3
± 0.8
15.1 ± 0.7
9.7
± 0.7
16.1 ± 0.9
19.8 ± 0.7
13.3 ± 1.3
12.7 ± 0.7
5.0 ± 1.1
232
226
235
243
197
144
113
113
239
190
201
194
219
237
213
163
233
189
Cloud Top
(mbar)
CB3
Albedo
MT3
PMFP
(mbar)
0.9990
248
0.9941
141
0.9824
134
0.9810
237
0.9855
230
0.9862
240
0.9848
200
0.9902
153
0.9928
137
0.9937
115
0.9920
109
0.9866
149
0.9849
125
0.9914
112
0.9933
79
0.9897
90
0.9854
121
0.9878
192
UV1
Albedo
0.9800
0.9800
0.9800
0.9702
0.9725
0.9370
0.8679
0.8963
0.9168
0.9214
0.9279
0.9396
0.9324
0.9301
0.9124
0.9166
0.9357
0.9470
Table
3.
Retrie ved
Latitu dinall yvaryin g
Param
28

20
25
0.6
30 440.3 ± 16.3
35 715.9 ± 19.5
40
45
50
15.7 ±
12.4 ± 0.7
1301.6
2219.7 ± 29.1
3242.7
±
±
24.8
49.6
55
60
65
70
5384.1 ± 90.6
6010.6 ± 132.9
7455.9 ± 172.0
8035.7 ± 204.1
229
225
131
133
137
175
194
272
291
387
484
Table 4. Best-fitted CSM model results for the Equator.
0.9933
120
0.9890
143
0.9924
165
0.9889
178
0.9893
210
0.9880
242
0.9848
240
0.9855
240
0.9845
239
0.9841
184
0.9917
140
0.9297
0.9067
0.9472
0.9393
0.9661
0.9800
0.9800
0.9800
0.9800
0.9800
0.9800
29

Figures
Mean Particle Radius r eff
( 𝜇𝑚 )
Size Distribution Parameter v eff
(
NIR Imaginary Refractive Index 𝜇𝑚 )
UV Imaginary Refractive Index
Total Column above 100 mbar (cm -2 )
Cloud NIR Phase Function
0.1
0.1
1 × 10 -3
2 × 10 -2
1 . 6 × 10
1.86
× 10
-3
-1
(1.98
± 0.07) × 10 7 (2.4
± 0.2) × 10 7 f
1
0.9675
0.9207
g
1
0.3
0.6650
0.5
0.8507
g
2
-0.5954
f
1
0.8303
-0.1000
0.7230
Cloud UV Phase Function g
1
0.8311
0.8574
Troposheric SSA at CB3
PMFP at MT3 (mbar)
Troposheric SSA at UV1 g
2
-0.3657
0.9933
79
0.9124
-0.2767
0.9974
49
0.9109
30

Fig. 1. Total gas optical depth including CH
4
and H
2
-H
2
and H
2
-He CIA at 100 mbar.
Upper panel shows the difference between the results based on the old correlated-k coefficients (red dashed line) used in Banfield et al. (1998) and the new data (black solid line) from Karkoschka and Tomasko (2010) for the H and K bands in the NIR region.
Lower panel shows the comparison between the CH
4
optical depth (black) and Rayleigh scattering optical depth (blue) from 0.2 to 1.0 𝜇𝑚 . The three vertical dashed lines correspond to the ISS filters used in this study, CB3 (0.938 𝜇𝑚 ), MT3 (0.889 𝜇𝑚 ), and
UV1 (0.258 𝜇𝑚 ), respectively.
31

Fig. 2. Comparison of the best solutions with prescribed 0.3 and 0.7 𝜇𝑚 particles, for 70 ° 𝑆
(upper panel) and the equatorial region (lower panel), respectively. The observed spectra from Banfield et al. (1998) are shown in black with error bars.
32

Fig. 3. Retrieved aerosol map ( f value) in the stratosphere and upper troposphere of Jupiter, based on the ground based NIR measurements.
33

CB3
M T3
UV1
Fig. 4. Sample images from three Cassini ISS filters. From top to bottom: CB3 (0.938 𝜇𝑚 ),
MT3 (0.889 𝜇𝑚 ), UV1 (0.258 𝜇𝑚 ). For each filter, we show a low phase angle (~17.5
° ) image on the left and a high phase angle (~141 ° ) image on the right.
34

Fig. 5. Illustration of the structure of the retrieval model.
35

Fig. 6. Atmospheric reflectivity (I/F) as a function of longitude in the equatorial region for multiple phase angles indicated in the upper left of each panel. Circles are the observations and lines are the model results. Black, orange and blue colors correspond to CB3, MT3, and UV1 filters, respectively. Solid lines: best-fitting CSM model results in the nominal case; dashed lines: best-fitting AGG model results; dotted lines: best-fitting CSM model results with the haze optical depth fixed as five times of that in the nominal case.
36

Fig. 7. Multiple solutions for the equatorial region as functions of the imaginary part of the refractive indices in the NIR (orange) and UV (blue) filters. Each dot represents a solution.
Left: total aerosol optical depth at 100 mbar in the NIR (open circle) and UV filters (filled circle); right: total aerosol mass loading (assume the density is 1 𝑔 𝑐𝑚 −3
) above 100 mbar.
I t is important to keep in mind that the UV refractive index was held constant when generating the plotted points for the NIR, and the NIR refractive index was held constant when generating the results for the UV.
37

Fig. 8. Atmospheric reflectivity (I/F) as a function of longitude at 60 ° 𝑆 for multiple phase angles indicated in the upper left of each panel. Circles are the observations and lines are the model results. Black, orange and blue colors correspond to CB3, MT3, and UV1 filters, respectively. Solid lines: best-fitting AGG model results in this work (Tables 3 and 4); dashed lines: best-fitting CSM model results with particle radius fixed at 0.1 𝜇𝑚 ; dotted lines: best-fitting AGG model results with the haze optical depth fixed at a fifth of that in the nominal case; dash-dotted lines: best-fitting AGG model results with the imaginary part of the refractive index at UV1 filter fixed at 0.2.
38

Fig. 9. Atmospheric reflectivity (I/F) as function of longitude in the middle latitudes (45 °𝑁 ) for multiple phase angles indicated in the upper left of each panel. Circles are the observations and lines are the results from the AGG model. Black, orange and blue colors correspond to CB3, MT3, and UV1 filters, respectively. Solid lines: best-fitting model results in this work (Tables 3 and 4); dashed lines: best-fitting model results with monomer radius fixed at 50 nm ; dotted lines: best-fitting model results with monomer number fixed as 200.
39

Fig. 10. Multiple solutions for the south-pole region (60 ° 𝑆 ) as functions of the imaginary part of the refractive index in the NIR (orange) and UV (blue) filters. Each dot represents a solution. Upper left: monomer radius; upper right: total aerosol optical depth at 100 mbar in the NIR (open circle) and UV filters (filled circle); lower left: number of monomers; lower right: total aerosol mass loading (assume the density is 1 𝑔 𝑐𝑚 −3
) above 100 mbar. It is important to keep in mind that the UV refractive index was held constant when generating the plotted points for the NIR, and the NIR refractive index was held constant when generating the results for the UV.
40

Fig. 11. Summary of important retrieved parameters as function of latitude with a 5 ° bin width. From top to bottom: (a) effective cloud top in the troposphere. (b) Cloud SSA in the
CB3 (black) and UV1 (blue) filters. The dashed line in (b) indicates the fixed values in the retrieved model because they are less well constrained. (c) Total aerosol optical depth at
100 mbar in the NIR (orange solid) and UV filters (blue solid), with the CH
4
optical depth for the MT3 filter (orange dashed) and Rayleigh scattering optical depth at UV1 filter (blue dashed) at 100 mbar. (d) Total aerosol mass loading (assume the density is 1 𝑔 𝑐𝑚 −3
) above 100 mbar as function of latitude.
41

Fig. 12. Zonally averaged number density map of stratospheric aerosols ( 𝑐𝑚 −3
) on Jupiter, as a function of pressure and latitude.
42

Fig. 13. Retrieved phase functions of the stratospheric aerosol (upper panel) and tropospheric cloud (lower panel) for NIR and UV filters. The dotted vertical lines indicate the scattering angles associated with the ISS images. Blue dashed curve in the lower panel is the cloud phase function derived from Pioneer 10 observations in the RED filter (0.64 𝜇𝑚 ) at the north component of the South Equatorial Belt of Jupiter (Tomasko et al., 1978).
43

Fig. 14: Real (upper panel) and imaginary (lower panel) part of the refractive index of aerosols from laboratory measurements. Retrieved imaginary refractive index for the ISS
NIR and UV filters are plotted for comparison (red).
44