1
Supplementary Information for
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3
Strong Temporal Variation Over One Saturnian Year:
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From Voyager to Cassini
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Liming Li1*, Richard K. Achterberg2, Barney J. Conrath3, Peter J. Gierasch3, Mark A. Smith1,
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Amy A. Simon-Miller4, Conor A. Nixon2, Glenn S. Orton5, F. Michael Flasar4,
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Xun Jiang1, Kevin H. Baines5, Raúl Morales-Juberías6, Andrew P. Ingersoll7,
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Ashwin R. Vasavada5, Anthony D. Del Genio8, Robert A. West5, Shawn P. Ewald7
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We explore the temporal variation of Saturn’s atmosphere between two time periods,
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which are separated by one Saturnian year (i.e., ~29.5 Earth years). Therefore, we basically
12
select the data sets with observational times separated by one Saturn year. Here, we describe
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different data sets, which include atmospheric spectra and images in the tropic region (i.e., 30S-
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30N) of Saturn’s upper troposphere (i.e., 50-750 mbar). We also introduce the data processing
15
and the corresponding measurements for the different data sets. In addition, a modified thermal
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wind equation, which is developed to explore the vertical structure of zonal winds in the tropic
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region, is discussed. In particular, we provide the uncertainty estimates for the retrieved
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temperature, measured zonal winds, and integrated thermal winds in this Supplementary
19
Information.
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S1. Retrieved Temperature From Nadir Observations and Uncertainty
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The atmospheric temperature in the plane of latitude (y) and altitude (z) is mainly based
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on the observations from the Infrared Spectrometer (IRIS) on Voyager1 and the Composite
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Infrared Spectrometer (CIRS) on Cassini2. The basic characteristics of the infrared spectrometers
1
1
are described by the previous studies1, 2. For the Voyager/IRIS observation, the content
2
information outside the pressure range of 50-750 mbar is not good enough to be used for
3
retrieving atmospheric temperature. Therefore, only the atmospheric temperature between 50
4
mbar and 750 mbar (i.e., upper troposphere) was retrieved from the spectra recorded by the
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Voyager/IRIS. The spectral coverage is wider in the Cassini/CIRS than in the Voyager/IRIS, so
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the good content information has larger vertical extension in the Cassini/CIRS spectra than in the
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Voyager/IRS spectra. To be consistent, only the retrieved CIRS temperature in the pressure
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range of 50-750 mbar is discussed. The Voayger/IRIS observations cover both of the two
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hemispheres. For the Cassini/CIRS observations, each of high-spatial-resolution Cassini/CIRS
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maps covers one hemisphere only. In order to get the complete picture of the tropic region (i.e.,
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30S-30N), we combine two CIRS maps covering the Northern Hemisphere (NH) and the
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Southern Hemisphere (SH), respectively.
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Table S1. Zonal-Mean Temperature from Voyager/IRIS and Cassini/CIRS.
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Voyager (1 & 2)/IRIS
Cassini/CIRS
Voyager 1: November 11-13, 1980
NH: November 4, 2009
Voyager 2: August 25-August 26, 1981
SH: October 19, 2010
Solar longitude
Voyager 1: 8.6
NH: 3.0
Voyager 2: 18.2
SH: 14.6
-1
Wave-number
180-2500 cm (4-55 m)
10-1400 cm-1 (7-1000 m)
Emission Angle
Voyager 1 & 2: 0-60
NH & SH: 0-75
Spatial Resolution (y and z) 1 and ~ 1 scale height
1 and ~ 1 scale height
Formal Retrieval Errors
~ 1K
0.5-1.5K
Note: The solar longitude, which is defined as the angular distance along Jupiter’s orbit around
Time
24
Sun measured from a reference point in the orbit (i.e., the zero of solar longitude at northern
25
spring equinox), is used to track the different seasons. The other errors (e.g., varying optical
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depth and helium volume mixing ratio) are not included in the formal retrieval errors.
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The process of retrieving atmospheric temperature from the infrared spectra recorded by
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the Voyager/IRIS and the Cassini/CIRS is based on a retrieval algorithm developed by the co2
1
authors (i.e., Conrath, B. J. and Geirasch, P. J) and described in a previous study3. In this
2
retrieval algorithm, the atmospheric temperature and para hydrogen are simultaneously retrieved
3
from the spectral measurements within the S(0) (centered at 354 cm-1) and S(1) (centered near
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600 cm-1) hydrogen absorption lines. This retrieval algorithm has already been coded and
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extensively used in some of our previous studies3,4. All recorded spectra within each latitude bin
6
with a width of 1 are averaged and applied to the retrieval algorithm3. So the retrieved
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temperature from the Voyager/IRIS and the Cassini/CIRS (this study) has a spatial resolution of
8
1 in the meridional direction, which equates to the width of latitude bin. Such a resolution (i.e.,
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1) is only for the retrieved temperature, which is different from the spatial resolution of the raw
10
data from the Voyager/IRIS and Cassini/CIRS. The spatial resolution of the raw data depends on
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the varying distance between spacecrafts and Saturn and the field of view of focal planes in
12
spectrometers, which is ~ 2-5 and ~ 0.5-8 for Voyager/IRIS5 and Cassini/CIRS6, respectively.
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The formal retrieval errors of the retrieved temperature are estimated by considering the
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number of spectra within each latitude bin, the signal strength, and the observational geometry3,
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~ 1K and 0.5-1.5 K for the Voyager/IRIS and the Cassini/CIRS, respectively. Such errors are
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much smaller than the temporal variation of atmospheric temperature discussed in the text. But
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they will affect temperature gradient and hence thermal winds, which is discussed in Section S4
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of this Supplementary Information. The other important error sources affecting the retrieved
20
temperature include varying optical depth and the helium volume mixing ratio, which were both
21
discussed in one previous study7. In the previous study, the optical depth of Saturn’s atmosphere,
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which is possibly modified by some dynamical processes (e.g., storms, waves, and so on), was
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tested in a very wide range (i.e., 0.0-5.0). The errors related to the varying optical depth for the
. The formal errors of the retrieved temperature in the upper troposphere (i.e., 50-750 mbar) are
3
1
retrieved temperature in the upper atmosphere is estimated to have a magnitude of ~ 1.7K7.
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Regarding to the helium volume mixing ratio (i.e., He/H2), the retrieved temperature from the
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Voayger/IRIS was based a value of He/H2 ~ 0.07 from a previous study3. On the other hand, the
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retrieved temperature of the Cassini/CIRS was based on a refined estimate8 of He/H2 ~ 0.135.
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The influence of varying ratio of He/H2 to the retrieved Saturn’s temperature was also discussed
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in the previous study7, which suggests that the variation of He/H2 from 0.07 to 0.135 will induce
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~1.4K errors in the upper atmosphere (i.e., 50-750 mbar). However, the errors due to the varying
8
optical depth and the varying helium volume mixing ratio are systematic, which does not affect
9
the temperature gradient and hence thermal winds. The retrieved temperature from the infrared
10
spectra recorded by the Voyager/IRIS and Cassini/CIRS is summarized in Table S1.
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S2. Retrieved Temperature From Radio Occultation Observations and Uncertainty
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To validate the retrieved temperature from the nadir observations by Voyager and Cassini,
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we examine some independent observations in the epochs of Voyager and Cassini. We first
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search for the independently simultaneous observations to validate the nadir observations by the
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Voyager/IRIS in 1980-81. The independent radio-occultation measurements by Voyager are used
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to validate the retrieved temperature from the nadir observations by the Voyager/IRIS. Here, we
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mainly use a previous analysis9 of the radio occultation measurements by Voyager 1 and 2
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(1980-81) 10, 11. The process of retrieving the atmospheric temperature from the radio occultation
20
measurements is pretty standard, which was described in the Voyager observations9. The basic
21
idea of the retrieval process is to convert the refractivity data from the radio occultation
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experiments to the number densities by assuming the atmospheric compositions and referring the
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available experiments of relating refractivity to gas density12. Then the number density
4
1
distributions are used to compute the vertical pressure profiles by integrating the equation of
2
hydrostatic equilibrium. Finally, the gas temperature is estimated by the equation of state with
3
known number density and pressure.
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The estimated errors of the retrieved temperature from the radio occultation experiments
5
by Voyager are the standard deviations of the computed temperature9, which reflect the
6
fluctuations of the refractivity data (Table S2). The other important error source is the
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assumption of atmospheric compositions, which is used in the process of retrieval the
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atmospheric temperature from the refractivity data. In the following table (Table S2) and Fig.2 in
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the text, the helium volume mixing ratio He/H2 is set as 0.06, which is close to the value used in
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the retrieval temperature from the Voyager/IRIS. The radio occultation experiments by Voyager
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are summarized in Table S2.
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Table S2. Temperature From the Radio-Occultation Measurements by Voyager and Cassini.
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Time
Solar longitude
Wavelength
Voyager 1 & 2
Cassini
Voyager 1: November 13, 1980
Jan 27, 2010
Voyager 2: August 26, 1981
(ingress and egress)
Voyager 1: 8.6
5.7
Voyager 2: 18.2
3.6 cm (X band)
0.9 cm (Ka band)
& 13.0 cm (S band)
3.6 cm (X band) & 13.0 cm (S
band)
Ingress/Egress latitude
Voyager 1: 3.0S (egress)
1.8S (ingress)
Voyager 2: 31.2S (egress)
2.6N (egress)
Vertical Resolution
~2-6 km
~6-7 km
Estimated Errors
~2-3 K
~1-2 K
Note: Latitudes shown here are planetographic latitudes. The estimated errors shown here are
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for the pressure range of 50-750 mbar, which is the effective pressure range of the Voyager/IRIS.
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The ingress latitudes of Voyager 1 and 2 are outside of the tropic regions (i.e., 30S-30N),
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which are not included in this table. The other measurements in the equatorial region from the
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Cassini radio occultation, which are before 2010, are not included in this table either.
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1
In the Cassini epoch, there are also independent radio-occultation measurements
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available to validate the nadir observations by Cassini in 2009-10. The temperature profiles
3
retrieved from the radio-occultation measurements by Cassini were presented in a previous
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study13, which are used in the study. The retrieving process in the radio-occultation
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measurements by Cassini is basically same as the method we described for the radio-occultation
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measurements by Voyager, which is introduced above. In addition, the retrieval process in the
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epoch of Cassini is also described in detail in some previous studies9, 13, 14. The major source of
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the uncertainties in the retrieved temperature from the radio-occultation measurements by
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Cassini is the thermal noise13. Such uncertainties were used to quantitatively estimate the errors
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in the retrieved temperature13, which are shown in Table S2 and Fig.2 in the text. The second
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error source is the assumption of Saturn’s atmospheric composition. In the previous study of the
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radio-occultation measurements by Cassini13, the helium volume mixing ratio He/H2 is set as
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0.11, which is based on a study conducted by Conrath and Gautier8. The retrieved temperature
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from the nadir observations by the Cassini/CIRS is based on the same reference8 but with a little
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bit different value (0.135). There are still other possible error sources in the retrieved temperature
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from the radio-occultation measurements by Cassini, but they are thought to be smaller than the
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major error due to the thermal noise13.
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We select the two measurements in 2010 from the radio-occultation measurements by
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Cassini, which are the closest to the average solar longitude of the nadir observations by the
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Cassini/CIRS, to validate the Cassini nadir observations. The two measurements and the
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corresponding estimated errors are shown in panels C and D in Fig. 2 in the text. It should be
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mentioned that there are limb observations conducted by the Cassini/CIRS in 2009 and 201015.
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Unfortunately, the Cassini limb observations only cover the upper atmosphere above troposphere
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1
(i.e., 0.001-30 mbar). Such limb observations do not help validate the retrieved temperature in
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the upper troposphere (i.e., 50-750 mbar) from the Cassini/CIRS nadir observations, so we do
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not include the Cassini limb observations in this study.
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S3. Cloud-Tracking Zonal Winds From Images and Uncertainty
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The cloud-tracking winds are mainly used as the boundary condition of a modified
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thermal wind equation (see the following section). The cloud-tracking winds in this study are
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based on the observations from the Imaging Science Subsystem (ISS) on Voyager16 and
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Cassini17. The image-processing (i.e., navigation and calibration) of the ISS images has been
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described previously16,
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and extensively used in our previous studies18,
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previous measurements of zonal winds on Saturn based on the images recorded by the ISS on
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Voyager and Cassini. Here, we basically select the data sets from Voyager and Cassini with
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observational times separated by one Saturnian year. The Voyager observations are mainly in
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1980-81, so we select the Cassini observations in 2010, which is ~ one Saturnian year later than
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the Voyager epoch.
. There are many
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By tracking the visible cloud features on the green-filter (560 nm) images by the
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Voyager/ISS, Sanchez-Lavega et al.20 systematically measured the zonal winds at the pressure
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level of visible clouds in the Voyager epoch (1980-81). The Cassini/ISS also has a similar green
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filter (568 nm) as that in the Voyager/ISS. In addition, the Cassini/ISS has some continuum
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bands (i.e., CB1, CB2, and CB3). The images taken in the green filter and the continuum bands
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probe the same pressure level of visible clouds. Our measurements show that the zonal winds are
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basically same between the results measured by the green filter and the results measured by the
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continuum bands. However, the cloud features are much clearer to the Cassini/ISS in the
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1
continuum-band images than in the green-filter images. Furthermore, there are many more
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observations taken in the continuum bands than in the visible filters for the Cassini/ISS.
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Therefore, measurements of the zonal winds from the continuum-band observations are more
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robust than measurements from the green-filter observations in the epoch of Cassini. Here, we
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selected the Cassini/ISS images taken at a continuum-band at 736 nm (i.e., CB2) in 2010 (Table
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S3), which is roughly one Saturnian year after the Voyager epoch in 1980-81, to measure the
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zonal winds in the Cassini epoch. Some previous studies21, 22, 23, 24, 25 of wind measurements in
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the epoch of Cassini are also based on the Cassini ISS continuum-band images.
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By tracking cloud features that do not substantially alter their shape over time in a series
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of images taken by the Voyager/ISS and the Cassini/ISS, we can convert their movements into
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the zonal winds. Then the cloud-tracking winds are averaged in each latitude bin. In the
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Voyager/ISS cloud-tracking wind measurements conducted by Sanchez-Lavega et al.20, the
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width of latitude bin is ~ 0.5. In the cloud-tracking wind measurements with the Cassini/ISS
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images in 2010 (this study), the width of latitude bin is 1, which is consistent with the latitudinal
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spatial resolution of the retrieved temperature from the Voyager/IRIS and the Cassini/CIRS
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(Table S1). Therefore, the 0.5 zonal winds from the Voyager/ISS20 are also averaged to 1 to be
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consistent with the 1 retrieved temperature from the Voyager/IRIS. It should be mentioned that
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the spatial resolution of measured zonal winds is different from the spatial resolution of the raw
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ISS images from the Voyager and Cassini. The spatial resolution of the raw ISS images depends
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on the varying distance between spacecrafts and Saturn and the field of view of the cameras. The
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Voyager/ISS raw images have a spatial resolution ~ 50-150 km (~0.01-0.3 at the equator) per
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pixel, and the Cassini/ISS raw images have a spatial resolution ~ 60-130 km (~ 0.01-0.3 at the
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equator) per pixel.
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3
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Table S3. Cloud-Tracking Zonal Winds From the Voyager/ISS and the Cassini/ISS.
Voyager 1 & 2/ISS
Cassini/ISS
Voyager 1: November 5-12, 1980
time 1: April 29, 2010
Voyager 2: August 19-September 4, 1981
time 2: September 15,
Time
2010
Solar longitude
Voyager 1: 8.6
time 1: 8.7
Voyager 2: 18.2
time 2: 13.5
Filter
Green
CB2
Effective Wavelength
560 nm
750 nm
Spatial Resolution (y)
0.5
1
Standard Deviation
5-20 m/s
5-15 m/s
Note: There are two pairs of Cassini/ISS image in April 29, 2010 (time 1), and there is one pair
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of Cassini/ISS images in September 15, 2010. The two images in each of the three pairs are
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separated by ~ 10 hours (i.e., ~ one Saturn rotation period), which make them to be suitable to
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measure zonal winds by the cloud-tracking method.
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Figure S1 shows that the zonal winds at the pressure level of visible clouds in 2010,
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which are basically equivalent to the zonal winds measured in the previous years of the Cassini
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epoch (i.e., 2004-08)21,
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pressure level of visible clouds did not change significantly during the time period of 2004-2010.
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The comparison of zonal winds between 1980-81 and 2010 is roughly consistent with the
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comparison between 1980-81 and 2004-08 in a previous study24, which suggests that the
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equatorial winds at the pressure level of visible clouds decreased ~ 100 m/s from the Voyager
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epoch to the Cassini epoch.
22, 23, 24, 25
. Such an consistency suggests that the zonal winds at the
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The errors of wind measurements in the previous Voyager/ISS analysis were estimated
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by the standard deviation of the wind measurements in each latitude bin20. For the wind
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measurements by the Cassini/ISS, we also use the standard deviation of multiple measurements
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within each latitude bin as the estimated errors. The zonal winds and the corresponding errors
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from the measurements by the Voyager/IRIS and the Cassini/CIRS are shown in Fig.S1. In
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1
Fig.S1, the cloud-tracking zonal winds and the corresponding errors in the Voyager epoch comes
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from the study by Sanchez-Lavega et al. 20. For the wind profile in the Cassini epoch shown in
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Fig.S1, most of the zonal winds (blue solid lines) are based on the images taken in 2010 (this
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study). The zonal wind within 8°S-5°N in Fig. S1 (blue dashed lines) are based on the images
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taken in 2004-08, which comes from a previous study by Garcia-Melendo et al.24.
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Figure S1. Comparison of zonal winds between Voyager and Cassini. There are no
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measurements for the latitude range of 2.0°S-10°S in the previous Voyager studies, which is
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therefore linearly interpolated from the neighboring measurements (red dashed lines). Cassini’s
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cloud-level winds are based on the feature-tracking measurements with the ISS CB2 images in
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2010. For the wind profile in the Cassini epoch (2010) shown in Fig.S1, the rings blocked and
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blurred the latitude band around the equator (8°S-5°N). Therefore, the winds within 8°S-5°N
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(blue dashed lines) come from the averaged winds over the time period of 2004-2008 in a
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previous study24.
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1
It should be mentioned there are other possible sources of errors in the wind
2
measurements, which include the errors due to the navigation procedure and the uncertainty
3
related to locating cloud features when conducting the cloud-tracking wind measurements. These
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error sources were discussed in the Supplementary Information of one of our previous studies25.
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In general, the navigation of ISS images, which is conducted by fitting the observed planetary
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limb to its predicted location, has a precision smaller than one pixel. The procedure introduces
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small systematic errors due to imprecise knowledge of the altitude of limb-defining opacity.
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Such errors are mitigated by the relative wind measurements conducted with the same
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navigation. Therefore, the navigation procedure does not introduce significant uncertainty to the
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wind measurements based on the ISS images. The other error source is the uncertainty related to
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locating cloud features in the ISS images. Most of the cloud features used in the cloud-tracking
12
method have sizes of a few pixels. Here, we simply assume that the uncertainty related to the
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locating of cloud features is ~ 1 pixel. The time separation between the pair of images from the
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Voyager/ISS and the Cassini/ISS is ~ 10 hours (i.e., ~ the rotation period of Saturn). Therefore,
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one pixel (i.e., ~ 50-150km for the Voyager/ISS and ~ 60-130 km for the Cassini/ISS) separated
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by 10 hours will induce errors of zonal wind ~ 1.4-4.2 m/s and 1.7-3.6 m/s for the Voyager/ISS
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and the Cassini/CIRS, respectively. Such errors are much smaller than the standard deviation of
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wind measurements, which are not included in Table S3.
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In order to use the cloud-tracking winds as the boundary condition for the thermal wind
20
equation, we have to determine the pressure level of visible clouds. In the Voyager epoch, the
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pressure level of visible clouds was estimated around 360 mbar26, 27, 28, 29 with an uncertainty of 
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140 mbar29. In the Cassini epoch, the pressure level of visible clouds was estimated as ~300
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mbar with an uncertainty of  50 mbar29. A follow-up study30 suggests that some individual
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1
cloud features shown in the Cassini/ISS images can reach deeper levels in the troposphere. To be
2
consistent with the Voyager results, we set the pressure level of visible clouds as 360 mbar in
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this study. Such a pressure level (i.e., 360 mbar) is used as the boundary level with the known
4
cloud-tracking winds for the vertical integration of the thermal wind equation (see the next
5
section). It should be mentioned that the integrations of thermal wind equation by varying the
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boundary level (i.e., the pressure level of visible clouds) in a wide range should introduce the
7
errors in the computed zonal winds from the thermal wind equation, which is discussed in the
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next section.
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S4. Zonal Winds Computed From Thermal Wind Equation and Uncertainty
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The measurements by the Voyager/ISS and the Cassini/ISS, which are discussed in the
12
previous section, provide important information about the zonal winds at the pressure level of
13
visible clouds. Furthermore, the zonal winds at the pressure level of visible clouds (i.e., 360
14
mbar) can be used as the boundary condition to integrate the thermal wind equation with the
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retrieved temperature from the Voyager/IRIS and the Cassini/CIRS. Such integrations will help
16
us explore the vertical structure of zonal winds above and below the pressure level of visible
17
clouds.
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The classical thermal wind equation31, 32 relates the vertical wind shear to the horizontal
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temperature gradient along isobaric surfaces, and thus it can be used to derive the vertical
20
structure of zonal winds from the atmospheric temperatures with the known zonal winds at the
21
boundary level. However, one limitation is that the classical thermal wind equation31, 32 stops
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working at low latitudes because the geostrophic balance, which is one assumption behind the
23
standard thermal wind equation, ceases to be valid close to the equator. More importantly, some
12
1
forces discarded in the geostrophic balance and the hydrostatic balance (i.e., the other
2
assumptions of the classical thermal wind equation), are not negligible when approaching the
3
planet’s equator. Thus a modified thermal wind equation is developed33, 34, which is applicable to
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both low and high latitudes of planets. The modified thermal wind equation, which is already
5
validated by Earth’s observed wind and temperature fields34, can be expressed as
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 U 2  2Urc  R p T


z rc 
rc
 p r r 
(S1)
p
7
where z is an unit vector along the rotation axis, rc is the cylindrical radius, U is the zonal wind,
8

 is the angular speed of rotation of planets, R is the specific gas constant, P is the pressure, r
9
 , and  is the latitude. 
is the radius of planets, T is the temperature
10
Based on the retrieved atmospheric temperature at isobaric surfaces from the
11
Voyager/IRIS and the Cassini/CIRS (Fig. 1 in the text), we can compute the gradient of
12
atmospheric temperature in the latitude direction ( T   P ) in Eq. S1. With the temperature
13
gradient and a suitable boundary condition, Eq. S1 will be integrated along the cylindrical
14

routines (i.e., rc ) to explore the zonal winds
(i.e., U ) at different isobaric surfaces. As we
15
discussed before, the integration boundary is set as the pressure level of visible clouds on Saturn.
16


In general,
the thermal wind equation is integrated upward to explore the vertical structure of
17
zonal winds above the pressure level of visible clouds. Here, we also integrate the modified
18
thermal wind equation downward from the pressure level of visible clouds to explore the zonal
19
winds below the visible clouds. The vertical structure of zonal winds, which are computed from
20
the integration of the retrieved temperature from the Voyager/IRIS and the Cassini/CIRS are
21
shown in Fig. 3 in the text. In principle, the modified thermal wind equation (Eq. S1) works for
22
all latitudes from equator to pole. The narrow gaps in the equatorial regions in Fig. 3 (i.e., the
13
1
regions within the black lines) are due to the cylindrical integration routines (i.e., rc ), which do
2
not pass the narrow regions close to the equator when integrating upward and downward along
3
the cylindrical routines34.

4
Next we estimate the errors in the computed thermal winds (Fig.3 in the text) from the
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modified thermal wind equation. There are three dominant error sources: (1) the uncertainty in
6
the measurements of the cloud-tracking zonal winds (Fig. S1), which will be used to be the
7
boundary condition of the thermal wind equation; (2) the uncertainty in the altitude location of
8
the cloud-tracking zonal winds, which will affect the thermal winds by changing the altitude of
9
the boundary level; and (3) the uncertainty in the retrieved temperature from the Voyager/IRIS
10
and the Cassini/CIRS, which will influence the temperature gradient and hence affect the
11
integration of the thermal winds.
12
The first errors are straightforward and constant, which will be brought to each of the
13
pressure levels above and below the pressure level of visible clouds when integrating the thermal
14
wind equation upward and downward. The second errors are related to the uncertainty in the
15
altitude location of the cloud-tracking zonal winds. The comparisons between the observed
16
reflectivity from Voyager/Cassini images and the simulations by radiation models29 suggest that
17
altitude location of the cloud-tracking zonal winds is 360140 mbar in the Voyager epoch. The
18
uncertainty in the altitude location of the cloud-tracking zonal winds is relative small (60 mbar)
19
in the Cassini epoch. Here, we use the relatively larger uncertainty (140 mbar) to test the
20
influence of different boundary levels on the computed thermal winds. Based on the large
21
uncertainty, we have the upper limit and lower limit of the altitude location of the cloud-tracking
22
zonal winds as 220 mbar (i.e., 360-140 = 220 mbar) and 500 mbar (i.e., 360+140 = 500 mbar),
23
respectively. First, we use Eq. S1 to re-compute the thermal winds in both the Voyager epoch
14
1
and the Cassini epoch by replacing the boundary level of 360 mbar (Fig. 3 in the text) with the
2
upper limit (i.e., 220 mbar) and the lower limit (i.e., 500 mbar), respectively. Figure S2 shows
3
the thermal winds with the upper limit of 220 mbar (panels A and B) and the lower limit of 500
4
mbar (panels C and D), which suggests that the structure and magnitude of the computed zonal
5
winds basically do not change when the altitude location of the cloud-tracking zonal (i.e.,
6
boundary level) varies during the pressure range of 220-500 mbar.
7
8
Figure S2. Computed zonal winds with different boundary levels. The zonal winds in Saturn’s
9
upper troposphere (i.e., 50-750 mbar) are computed with Eq. S1 and the retrieved temperature
10
from the Voyager/IRIS and the Cassini/CIRS. The regions within the black lines are left blank
11
because the cylindrical routines of the modified thermal wind equation do not pass the regions.
12
(A) Zonal winds derived from the Voyager/IRIS temperature (1980-81) with the boundary level
13
of 220 mbar. (B) Zonal winds derived from the Cassini/CIRS temperature (2009-10) with the
15
1
boundary level of 220 mbar. Panels (C) and (D) are same as panel (A) and (B) except for a
2
different boundary level of 500 mbar.
3
Figure 3S further displays the difference between the computed zonal winds with the
4
boundary level of 360 mbar (Fig. 3 in the text) and the computed zonal winds with the boundary
5
levels of 220/500 mbar (Fig. S3), which can be used to estimate the errors of the computed zonal
6
winds due to the uncertainty in the altitude location of the cloud-tracking winds. Figure S3
7
implies that the errors are larger in the computed zonal winds with the boundary level varying
8
between the upper limit (i.e., 220 mbar) and 360 mbar than with the boundary level varying
9
between the lower limit (i.e., 500 mbar) and 360 mbar. In addition, the errors due to the
10
uncertainty in the altitude location of the cloud-tracking winds are basically less than 10 m/s.
11
Such errors are smaller than the errors due o the uncertainty in the measurements of the cloud-
12
tracking zonal winds (Fig. S1), which have a magnitude of ~ 20 m/s.
13
14
Figure S3. Difference between computed zonal winds with different boundary levels. The
16
1
computed zonal winds with the boundary level of 360 mbar (Fig. 3 in the text) are subtracted
2
from the computed zonal winds with different boundary levels (Fig. S2) to test the errors
3
introduced by the uncertainties in the altitude location of the cloud-tracking zonal winds. (A)
4
Difference between the computed zonal winds with the boundary level of 360 mbar and the
5
computed zonal winds with the boundary level of 220 mbar for the Voyager/IRIS temperature
6
(1980-81). (B) Same as panel A except for the Cassini/CIRS temperature. (C) Difference between
7
the computed zonal winds with the boundary level of 360 mbar and the computed zonal winds
8
with the boundary level of 500 mbar for the Voyager/IRIS temperature (1980-81). (D) Same as
9
panel C except for the Cassini/CIRS temperature.
10
The third error source of the computed zonal winds, which is related to the uncertainties
11
in the retrieved temperature, is complicated. The uncertainty in the retrieved temperature from
12
the Voyager/IRIS and the Cassini/CIRS, which has a magnitude ~ 1 K (Table S1), will induce
13
the errors in the temperature gradient (i.e., T   P ) and hence influence the integrated zonal
14
winds from the thermal wind equation. Here, we estimate such errors by adding the random
15
 the magnitude of the formal retrieval errors in Table S1) to
errors with a magnitude of 1K (i.e.,
16
the retrieved temperature (Fig. 1 in the text) and test the computed zonal winds from the thermal
17
wind equation. First, we create 100 different 2-dimentioanl (2-D) random temperature errors in
18
the plane of latitude and altitude with a magnitude of 1 K and a normal distribution. Then we add
19
the 100 2-D random temperature errors to the retrieved temperature from the Voyager/IRIS and
20
the Cassini/CIRS (Fig. 1 in the text) to create 100 different temperature fields with 1-K random
21
errors. Finally, the 100 different temperature fields are applied to the modified thermal wind
22
equation (Eq. S1). The mean zonal winds averaged from the 100 computed zonal winds with the
23
100 different temperature fields are taken as the final thermal winds, which are shown in Fig. 3
17
1
in the text. The standard deviation of the 100 computed zonal winds is used to estimate the errors
2
of the computed thermal winds due to the uncertainties in the retrieved temperature, which are
3
displayed in Fig. S4.
4
5
Figure S4. Propagating errors in the computed zonal winds, which are related to the errors in
6
the retrieved temperature (second errors). (A) Errors in the computed zonal winds related to the
7
errors in the retrieved temperature by the Voyager/IRIS (1980-81). (B) Errors in the computed
8
zonal winds related to the errors in the retrieved temperature by the Cassini/CIRS (2009-10).
9
The errors are estimated by the standard deviation of the 100 computed zonal winds with the
10
random temperature errors.
11
Figure S4 shows the large errors are concentrated in a narrow latitude band around the
12
equator (i.e., 10N-10S). The figure also suggests that the errors increase with the increasing
13
distance from the boundary level (i.e., 360 mbar). There are two reasons for such a spatial pattern
14
shown in Fig.S4: (1) The zonal winds are stronger in the narrow latitude band (i.e., 10N-10S)
15
than in other latitudes, which makes the corresponding standard deviation of zonal winds is
18
1
larger in the narrow latitude band than in the other latitudes; and (2) The wind errors due to the
2
errors of retrieved temperature accumulate along the integration routine starting from the
3
boundary level (i.e., 360 mbar), so the errors in the computed zonal winds are magnified when
4
integrating the thermal wind equation upward/downward from the boundary level.
5
Considering that the three error sources (i.e., the uncertainties in the measurements of the
6
cloud-tracking zonal winds, the uncertainties in the altitude location of the cloud-tracking zonal
7
winds, and the uncertainties in the retrieved temperature) are independent, we estimate the total
8
errors in the computed zonal winds by the square root of the sum of the squares of the three
9
individual errors35. The total errors are shown in panel A and panel B of Fig.5S for the Voyager
10
thermal winds (Panel A of Fig. 3) and the Cassini thermal winds (panel B of Fig. 3),
11
respectively. In the Voyager epoch, the first errors (i.e., the uncertainty in the cloud-tracking
12
zonal winds at the boundary level (Fig. S1)) are larger than the other two errors (i.e., the
13
uncertainties in the altitude location of the cloud-tracking winds (Fig. S3) and the uncertainty in
14
the retrieved temperature (Fig. S4)) at most latitudes, so the spatial pattern of the first errors are
15
dominant. In the Cassini epoch, both the first errors (Fig. S1) and the third errors (Fig. S4) have
16
the maximum in the narrow latitude band around the equator (i.e., 10N-10S), so the total errors
17
are concentrated in such a narrow latitude band.
18
For the errors in the temporal variation of the computed zonal winds from the Voyager
19
epoch to the Cassini epoch (panel C in Fig.3), we refer to the formulation of estimating the error
20
in the sum of two variables36. Therefore, the errors in the temporal variation of the computed
21
zonal winds (panel C of Fig. S5) are estimated by the square root of the sum of the squares of the
22
errors in the Voyager winds (panel A in Fig. S5) and in the Cassini winds (panel B in Fig. S5).
23
The estimated errors in the temporal variation of the computed zonal winds at 750 mbar are also
19
1
used in Fig. 4 in the text.
2
3
Figure S5. Total errors in the computed zonal winds from the modified thermal wind equation.
4
The total errors are based on the three errors discussed above (i.e., uncertainties in the cloud-
5
tracking wind measurements, the uncertainties in the altitude location of the cloud-tracking
6
winds, and the uncertainties in the retrieved temperature). (A) Errors in the computed zonal
7
winds in the Voyager epoch (1980-81). (B) Errors in the computed zonal winds in the Cassini
8
epoch (2009-10). (C) Errors in the temporal variation of zonal winds from the Voyager epoch to
9
the Cassini epoch. The gaps in the latitude range of 2.0°S-10°S (panel A and C) are related to
10
the observational gaps in the Voyager measurements (Fig.S1).
20
1
S5. Temperature Maps in the Horizontal Plane From the Cassini/CIRS
2
To search the large-scale waves in the troposphere of Saturn, we also retrieve the
3
temperature maps in the horizontal plane (latitude and longitude) from the Cassini/CIRS
4
observations. The retrieval process of temperature maps in the horizontal plane was introduced in
5
our previous study of exploring the stratospheric waves on Saturn4. Basically, the retrieval
6
process is similar with the process we introduced in Section S1 except for the Cassini/CIRS
7
spectra are averaged in both the latitude bin (1) and the longitude bin (2) instead of in the
8
latitude bin only. The estimate of the formal retrieval errors in the horizontal temperature maps
9
(latitude and longitude) is also similar to the error estimate in the retrieved temperature in the
10
plane of latitude and altitude (Section S1 in the online Supplementary Information). The errors
11
related to the varying optical depth and the mixing ratio He/H2, which are systematic, do not
12
affect the spatial patterns shown in the horizontal temperature maps.
13
14
Figure S6. Temperature maps in the plane of latitude and longitude. The maps are ~ 100 mbar
15
with spatial resolution 1° and 2° in the latitudinal and longitudinal directions, respectively. The
16
raw spectra for the northern hemisphere were recorded in March 22, 2006, which is different
21
1
from the time of the raw spectra for the southern hemisphere (September 1, 2007).
2
Figure S6 displays the tropical temperature maps at 100 mbar, which show some wave
3
structures in the tropical region of Saturn. It is possible to extract some wave characteristics by
4
examining the large-scale waves shown in the temperature maps from the Cassini/CIRS
5
observations. However, the construction of the relation between the waves and the large-scale
6
atmospheric variations need more observations and theoretical studies.
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
22
1
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(2007).
Please
also
refer
to
a
preliminary
manuscript
online
in
20
26