Saturn`s South Polar Vortex - Division of Geological and Planetary

Saturn’s South Polar Vortex: A Gas-Giant Analog to a
Terrestrial Hurricane
Ulyana A. Dyudina,1∗ Andrew P. Ingersoll,1 ,Shawn P. Ewald,1
Ashwin R. Vasavada2 and other authors TBD
1
150-21, Geological and Planetary Sciences, Caltech, Pasadena, CA, 91125, USA,
2
∗
Jet Propulsion Laboratory, Caltech, Pasadena, CA, 91125, USA
To whom correspondence should be addressed; E-mail: [email protected].
Intended for submission to Science.
Version as of June 15, 2007
For co-authors only
The author list is preliminary. Please send your suggestions.
Number of manuscript text pages: 8, Figures: 7
Temporary remarks are shown in bold font and will be removed later.
My suggestions are marked UD at the end of the note. Ulyana
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Previous studies have shown that Saturn’s south pole has a circular vortex
that spins in a cyclonic direction - clockwise, like a southern hemisphere hurricane. Also like a hurricane, the vortex has a warm core that extends into
the lower stratosphere. Here we extend the hurricane analogy with additional
observations: A central eye with eyewall clouds that extend two scale heights
above their surroundings, an outside ring whose absolute vorticity is constant,
numerous small-scale cumulus clusters whose vorticity suggests a convective
origin, and a suggestion of excess cyclonic rotation not balanced by the inward pressure force, implying outward flow at high altitudes. The obvious
differences - the vortex is fixed to the pole and does not have a liquid ocean to
support it - may appear less serious as we come to understand the interaction
of Saturn’s moisture-laden interior with winds in the troposphere.
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A hurricane (typhoon, tropical cyclone) is a warm-core vortex sustained by release of latent
heat when in-flowing air in the boundary layer picks up water vapor from the ocean (1; 2; 3).
The vortex has a central low pressure at low altitudes that becomes weaker at high altitudes due
to thermal expansion of the air at the center. Condensation and release of latent heat are greatest
in a ring of clouds surrounding the central eye, which is sometimes clear and sometimes partly
cloud covered. The eyewall clouds tower two scale heights, about 15 km, above the surface.
Hurricanes dissipate quickly when they leave the ocean and run over the land.
What would a hurricane look like on a giant planet, which has no ocean although it does
have a moisture-laden atmosphere at depth, where temperatures are too warm for the moisture
to condense? One would expect some significant differences, but at what point would the similarities outweigh the differences, so that it would be worthwhile studying such a structure for
comparison with terrestrial hurricanes? These are the questions addressed in this paper.
The warm central core and the wind profile at intermediate spatial resolution were reported
earlier (4; 5; 6). Here we present high-resolution data taken by the Cassini spacecraft over a
three-hour period on October 11, 2006. Figure 1 is a false-color image (7) that shows cloud
heights. The spatial resolution is 20 km/pixel. The blue color plane is made from light at 889
nm where methane gas is a strong absorber. The green color plane is made from light at 727
nm where methane is a moderate absorber. The red color plane is made from light at 750 nm
where the gaseous absorption is minimal and one sees down to the deep clouds. The depth of
penetration depends on clouds and haze, which are uncertain, but for gaseous absorption only,
the incident solar beam penetrates to 0.3 bars at 727 nm and to 0.08 bars at 889 nm (8; 9), since
the beam is only 15 deg above the horizon. Light scattered to the spacecraft exits at 40 deg
above the horizon, so it comes from levels as deep as 0.8 bar and 0.2 bar, respectively.
The central eye looks dark and red in Fig. 1. This indicates a nearly cloud-free upper
atmosphere with some deep clouds at the bottom. The eye has two sharp boundaries, not unlike
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the eyes of terrestrial hurricanes (10). The inner boundary is oblong; the outer one is circular.
Both are concentric with the pole. The diffuse dark band inside each boundary is a shadow cast
by the eyewall clouds that form the boundary. In single-filter images (11) the shadow follows
the sun in a counterclockwise direction as the planet turns during the three-hour period. From
the shadow heights we estimate the height of the outer wall as 40 20 km, and the height of
the inner wall as 70 30 km. The latter value is about twice the pressure scale height (vertical
e-folding distance) of Saturn’s atmosphere, which compares favorably with the eyewall clouds
on Earth.
Figure 2A shows the zonal (positive eastward) velocity u measured by tracking clouds over
the 3-hour period. Each point is an individual cloud. The smooth curve assumes absolute
vorticity, ζ + f is constant between latitudes -73.5 ◦ and -85◦ . Here ζ is the vertical component
of vorticity due to motions relative to the rotating planet and f = 2Ωsin(φ) is the vertical
component of vorticity due to the planet’s rotation. The value of the constant is f 0 , the value of
f at latitudeφ0, which we take to be -73.5◦ . This latitude is the only free parameter, since we
impose boundary conditions u = 0 and ζ = 0 at φ = φ 0 to be consistent with the observations at
more northerly latitudes.
Constant absolute vorticity is consistent with rings of air moving poleward without friction
and without expansion or contraction in the vertical. A terrestrial hurricane has much the same
structure. Friction is important to the overturning circulation, but it is less important to the tangential circulation. As the distance r from the center of the vortex approaches zero, u increases
as 1/r, so the flow regime has to change. In a terrestrial hurricane, vertical motion takes over
as the air rises within the eyewall clouds.
The solid line of Fig. 2B shows the relative vorticity ζ estimated from the measured u.
Consistent with the solid curve of Fig. 2A, ζ is close to zero up to the edge of the eyewall.
The points of Fig. 2B show the relative vorticity of the little red spots (cumulus clusters) seen
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in Fig. 1. To make the measurements, we constructed a series of 14-frame movies that span
the 3-hour time interval. We centered each spot in the movie and dialed in a variable amount
of backwards rotation until the spot appeared not to rotate. Twice this angular velocity is the
vorticity of the spot. We repeated the procedure three times for each spot and assigned error
bars from the residuals.
Figure 2B shows that the little red spots are anticyclones, with vorticities in the range 1 ±
1 × 10−4 s−1 , which is ∼1/3 the magnitude of f but of opposite sign. This is consistent with
a convective origin, since parcels rising from the adiabatic interior will have Ertel potential
vorticity (Ref) equal to zero. They would then have ζ ≈ −f when they spread out in the upper
troposphere, except for entrainment, which dilutes this anticyclonic vorticity with ambient air.
In this respect the cumulus clusters are like the shower zones of a terrestrial hurricane.
One might ask why the large-scale vorticity, i.e., the solid curve of Fig. 2B, is not the
average of the small-scale vorticity represented by the points of Fig. 2B. The answer must be
that each cumulus cluster has a zone of opposite-signed vorticity surrounding it. This could
happen if the flow around each cluster decays away exponentially with a length scale equal to
the radius of deformation (12), as expected for flow in the stably stratified upper troposphere.
Figure 3 shows a high-resolution map of temperatures at the 50-mbar level (13). This is
the lower stratosphere, but it shows a dramatic concentration of warm air within 1.5 deg of the
vortex center. This puts the warm core inside the outer eyewall of Fig. 1. Another figure (14)
shows that this warm core extends up to the 0.5-mbar level.
We have no direct evidence of the sign or magnitude of the overturning circulation. The
blue-green haze of Fig. 1 just outside the outer eyewall is consistent with air that has been
lifted. The eyewall itself is consistent with rising motion, since clouds form on updrafts. We
made a 4-frame color movie (15) of images like the one in Fig. 1, and we searched for a
difference in u between levels, expecting to find the cyclonic wind growing weaker with altitude.
5
This expectation is based on the weakening of the central low pressure and is described by
the thermal wind equation (12). In fact we found no difference in the wind with altitude, at
least at -84◦ where there were features in the blue-green haze suitable for tracking. This could
be evidence of an overturning circulation, since the failure of the wind to weaken means the
centrifugal force at high altitudes is not completely balanced by the inward pressure force.
This unbalanced force could drive an outward flow balanced by friction, consistent with the
overturning circulation of a terrestrial hurricane.
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References and Notes
1. E. Palmen, C. W. Newton, Atmospheric Circulation Systems (Academic Press, New York
and London, 1969).
2. R. A. Anthes, Tropical Cyclones. Their evolution, structure and effects, vol. 19 of Meteorological Monographs (American Meteorological Society, 1982).
3. K. Emanuel, Divine Wind - The History and Science of Hurricanes (Oxford University
Press, 2005).
4. G. S. Orton, P. A. Yanamandra-Fisher, Science 307, 696 (2005).
5. A. R. Vasavada, et al., Journal of Geophysical Research (Planets) 111, 5004+ (2006).
6. A. Sánchez-Lavega, R. Hueso, S. Pérez-Hoyos, J. F. Rojas, Icarus 184, 524 (2006).
7. C. C. Porco, et al., Space Science Reviews 115, 363 (2004).
8. M. G. Tomasko, R. A. West, G. S. Orton, V. G. Teifel, Clouds and aerosols in Saturn’s
atmosphere (in: Saturn, 1984), pp. 150–194. University of Arizona Press,Tucson, AZ.
9. E. Karkoschka, Icarus 133, 134 (1998).
10. R. A. Houze, S. S. Chen, B. F. Smull, W.-C. Lee, M. M. Bell, Science 315, 1235 (2007).
11. The details of the eyewall height measurement are provided in the supporting online material (attached at the end of this .pdf file UD).
12. probably the reference to Holton’s book UD.
13. F. M. Flasar, et al., Space Science Reviews 115, 169 (2004).
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14. Another CIRS figure for 0.5 mbar in the online supporting material. I do not have it
yet. UD.
15. The movie in the online supporting material
http://www.gps.caltech.edu/∼ulyana/iss/polar movie/movies/color 4frm%
c ompressed.aviUD.
1. This research was supported by the NASA Cassini Project.
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Figure 1: False-color image of Saturn’s south polar clouds taken by the Cassini imaging system
(7). An image at 889 nm, where methane gas is a strong absorber, is projected onto the blue
plane. An image at 727 nm, where methane is a moderate absorber, is projected onto the green
plane. An image at 750 nm, where the gases of Saturn’s atmosphere are transparent, is projected
onto the red plane. The red ”eye” in the center indicates a clear atmosphere over deep clouds.
The blue-green ring outside the eye indicates high clouds and haze. The puffy pink clouds are
deep, but they are overlain by thin clouds and haze. The clouds around the inner eye tower 70
km above the clouds inside. This figure will be marked by latitudes and longitudes later.
For now, see Fig.4 for coordinate reference.
See my .doc version 5 for changes to this caption
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Figure 2: Profiles of zonal velocity (eastward) and cyclonic vorticity (clockwise) around Saturn’s south pole. (A). Zonal velocity measured by tracking clouds in a sequence of images
over a 3-hour period. The resolution of the images is 20 km/pixel. The solid curve is from a
model that assumes constant absolute vorticity starting at latitude -73.5 ◦ , with zonal velocity
and relative vorticity set to zero at that point. (B). Relative vorticity, assumed positive when the
direction is cyclonic - clockwise in the southern hemisphere. The solid curve is a cubic spline
fit to the velocity data of Fig. 2A. The points are the puffy pink clouds of Fig. 1. Their vorticity
is anticyclonic and falls in the range 1 ± 1 × 10−4 s−1 , which is about 1/3 of the local planetary
vorticity but of opposite sign. Anticyclonic vorticity suggests the pink clouds have convective
origin
See my .doc version 5 for changes. I eliminated redundancy with the text
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Figure 3: This is a preliminary figure. It will be combined with the greyscale image from
ISS UD Temperature map at the 50-mbar level derived from the Cassini infrared spectrometer
(13). Consistent with infrared images from Earth taken at lower resolution, the gases at the
pole are ∼2.5 K warmer than their surroundings. The warm core, the cyclonic circulation with
constant absolute vorticity, and the small convective features are reminiscent of a terrestrial
hurricane.
This figure is OK for the version we are sending around. It may be OK in
general. The worst thing is the faint lettering. That will have to be changed
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Supporting online material
1 Windspeeds.
Cassini took repeated images of the pole during the 3-hour observation. High spatial resolution
and good temporal sampling of 14 images in continuum
band filter (the wavelength of the best
the continuum
contrast for small features) allowed tracking of
clouds
to obtain accurate wind velocities. A movie
clouds
combined from these images
1
shows the winds increasing towards the pole. The cyclone’s
eye rotates by ∼ 60◦ within the 3 hours. Figure 2 shows zonal windspeeds measured by cloud
tracking. Two tracking techniques were used. Outside the -84.5 ◦ latitude circle the windspeeds
automatic
were obtained byan
automatic
feature tracker. Inside the -84.5◦ the automatic tracker failed to
obtain accurate wind speeds because of high speeds, curved trajectories, and multiple linear
features. For the circle inside the -84.5◦ latitude we manually tracked individual features 2 .
The manual and automatic tracking agree outside the -84.5 ◦ circle. The wind increases towards
pole
theeyewall
outerat -87.8◦ latitude. There are no trackable features between the
the pole
untilup
theto
outer
outer wall and latitude of ∼-88.5◦ just outside the inner eye wall. Between latitudes -86.5 ◦ and
-89 ◦ the winds reach thair maximum linear speed of ∼ 150 ± 20 m/s. The features inside the
delete◦ are
~ drifting at 20-30 degrees per hour with various speeds not strongly correlated with
∼-88.5
latitude.
The winds measured in July 2004 Cassini images at - 87 ◦ were 160±10 m/s (6). This is
give reference to Sept-Oct
consistent with our measurements at this latitude. In September-October 2004 the linear speed
associated with the rotation of the inner eyewall at -88.5 ◦ latitude was 80 to 135 m/s. This is
smaller than our 130-160 m/s winspeeds for this latitude. Although this difference may be real,
1
http://www.nasa.gov/mpg/162357main pia08332.mpg
To obtain accurate zonal windspeed manually we played modified movies combined from the 14 maps. In each
modified movie the maps were rotated back relative to the clouds’ windspeed at some angular velocity around the
pole. At particular angular velocity the the cloud feature rotation and the movie’s back rotation cancels out and
stops the motion of the feature. For each of the test angular velocities we picked the features that stopped their
motion in the modified movies, which produced the data points in Fig. 2
2
12
high
the uncertinty in the windspeed measurements is rather
hight to assert this windspeed change
with confidence.
turned out to
We also measured the meridional component of the clouds’ motion which turned to be zero
within the errors for all the clouds except the ones in the inner eye. The features in the inner eye
display a non-systematic drift North or South which is small compared to their zonal motion.
The main mechanism forming terrestrial hurricanes involves inward motion of the air towards
the eye. It is possible that on Saturn similar inflow exists, but is slow and thus undetectable.
The multiple-filter observations shown in Fig. 1 are repeated four times during the three
hours. The four frame color movie3 combined from the images similar to Fig. 1 shows that the
clouds at different heights (appearing in different colors) move at the same velocities. It should
be noted though that inside -86 ◦ latitude only one color plane has small trackable features. Thus
it is impossible to tell if the windspeeds near the eye are the same at all heights. The oval shape
of the inner eye rotates coherently in all colors. It is unclear though if the eye wall shape tracks
the wind motion or acts as a wave.
2 Vorticity.
The zonal wind profile from Fig. 2 can be used to calculate the vorticity of the zonal flow.
Also, multiple smaller clouds around the cyclone’s eye show detectable individual rotation.
To compare the vorticity in the small clouds with the background zonal flow we measured
the rotation of these smaller clouds. Figure 4 shows the locations and vorticity values for the
individual clouds that have detectable rotation. The vorticities of the clouds are calculated
a procedure
as their angular velocity multiplied by two. The angular velocity was obtained
by procedure
similar to the manual feature tracking used for the zonal windspeeds, which involves picking an
3
http://www.gps.caltech.edu/∼ulyana/iss/polar movie/movies/color 4frm compressed.avi
13
appropriate stopped motion movie from the set of the test movies 4 . Often it is uncertain which
of the movies matches the rotation of the cloud. To test the uncertainty and to increase the
times, picking
precision of the vorticity measurements we measured vorticity of each cloud 3-4 times picking
the range of reasonably good matches. The vorticity values (colors of the asterisks in Fig. 4)
are the averages of those 3-4 measurements. Nearly all small clouds rotate counterclockwise
(anticyclonic
(positive vorticity). Remarkably, the largest features (the two dark spots at the upper left corner
vorticity)
of the map) rotate the fastest. For the smaller clouds the relation between the size and rotation
is not systematic.
3 Eyewall heights.
The cyclone’s eyewalls are steep and cast shadows on the lower clouds inside the eye. Figure
5 shows that the dark crescent-shaped areas inside the walls follow the Sun as Saturn rotates.
are indeed
shadows
This demonstrates that the dark areas
are the indeed
shadows and not a dark coloration of the
underlying clouds.
Figure 6 shows how we derived the height of the eyewalls from the length of the shadows.
The two maps in the figure are examples of the 9 maps from Fig. 5, which we used for the
eyewall height calculation. We manually picked the points of the apparent end of the shadow
and projected these points along the Sun’s azimuth to the edge of the eyewall. The reader may
judge that the shadow end points are quite uncertain by comparing the left panels of Fig 6 with
the right panels showing the same maps overlaid with our estimated shadow locations. To obtain
the eyewall height we multiplied each shadow length by sine of the solar elevation angle above
4
To obtain each cloud’s angular velocity we first determined its drift around the pole (see the technique description at the footnote in Section 1). Then we made an individual cloud’s movie from the set of 14 maps such that the
center of the movie tracks the cloud in its motion around the pole. Then we made a set of modified back-rotated
movies for a set of possible angular velocities for the cloud. While simultaneously playing the set of back-rotated
movies we picked the
which
stopped
the apparent rotation of the cloud. Because particular clouds are not
theoneone
that
stopped
always covered by all 14 images, some modified movies have less then 14 time steps, down to as few as 2 time
steps.
14
the horizon
which
is around 16◦ for all the images.
horizon,
which
Figure 7 shows the resulting heights for outer and inner eyewalls calculated from the 9 maps.
the longitude
The data are plotted versus longitude at which each shadow point projects to the eyewall. The
at the
respective
longitudes are then adjusted to account for the zonal wind
at respective
latitude. With such an
adjustment the shadows of particular eyewall features (e.g., the ”bulge” of the inner wall oval)
appear at the same longitude for all images. We assumed zero adjustment for the first plot in
Fig. 5, which is also shown in the upper panel of Fig. 6. The longitudes in Fig. 7 refer to that
frame.
The height of the outer wall is about 30-40 km and does not significantly change with
longitude. The height of the inner wall depends on longitude significantly. At longitude ∼180 ◦
the shadows are shorter and the corresponding wall height is ∼30-60 km. Shorter shadows can
be seen in the upper image in Fig.6, which is taken at the time when the Sun illuminated the
image from longitude ∼180 ◦ (up on the map). The Sun proceeds to larger longitudes of 350 ◦ 50◦ with time. The last frame in the time sequence is shown in the lower panels of Fig. 6. The
shadows are longer at those longitudes and the corresponding wall heights are ∼70-120 km.
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Figure 4: Map of the Southern polar vortex combined as a mosaic from 14 maps produced from
individual ISS images. Each image was taken in continuum band filter CB2 with the central
wavelength 750 nm (7). To reduce the effect of varying solar illumination across the image
each color plane is high-pass filtered at the spatial scale of 100 pixels (which is around 200
km). Asterisks show locations of the individual features for which vorticity had been measured.
The value of the vorticity is indicated by the asterisks’ color. The vorticity data are also plotted
in Fig. 2
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Figure 5: A set of the maps showing how the shadow of the cyclone’s eyewall follows the Sun.
The first map is taken on October 11 (DOY 284), 2006 at 19h. 42 min 31 s. The time on the
maps increases from top to bottom panel and then from left to right, as labeled by the time in
hours from the start of the sequence. The white arrow on each panel shows the direction at
which the Sun illuminates the planet. The arrow points from the Sun to the illuminated scene.
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estimated
Figure 6: Two maps demonstrating how the length of the shadowswere
had been
estimated. The left
panels show the map, the right planes show the same map with the cyclone eyewalls outlined in
black and shadow lengths measured on this image shown in white.
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Figure 7: Height of the outer (upper panel) and inner (lower panel) walls of the vortex. The
height is plotted versus longitude of the wall features in the first image of the sequence (first
panel in Fig. 5, or upper panel of Fig. 6). The shadow lengths are taken from all images from
Fig. 5. Then the longitude of the points on the wall casting the measured shadows is adjusted
to account for the zonal velocity of the wall. The zonal velocities are 17 degrees/hr and 20
degrees/hr for the outer and inner walls respectively.
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