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

Saturn’s South Polar Vortex: A Possible Gas-Giant
Analog to a Terrestrial Hurricane
Ulyana A. Dyudina,1∗ Andrew P. Ingersoll,1 ,Shawn P. Ewald,1
Ashwin R. Vasavada2, Robert A. West2 , Anthony Del Genio3 , John Barbara3,
Carolyn C. Porco4, Richard Achterberg 5, F. Michael Flasar 5
Amy A. Simon-Miller5 , Leigh N. Fletcher6
1
150-21, Geological and Planetary Sciences, Caltech, Pasadena, CA, 91125, USA,
2
3
Jet Propulsion Laboratory, Caltech, Pasadena, CA, 91125, USA
NASA/Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025, USA
4
CICLOPS/Space Science Institute, Boulder, CO, USA
5
NASA Goddard Space Flight Center, Code 693, Greenbelt, MD, 20771
6
Atmospheric, Oceanic and Planetary Physics, Department of Physics,
University of Oxford, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK
∗
To whom correspondence should be addressed; E-mail: ulyana@gps.caltech.edu.
Intended for submission to Science.
Version 3 as of July 5, 2007
For co-authors only
The author list is preliminary. Please send your suggestions.
Number of manuscript text pages: 8, Figures: 3
Temporary remarks are shown in bold font and will be removed later.
My suggestions are marked UD at the end of the note. Ulyana
Red indicates corrections by UD after the second draft. UD
1
Previous studies have shown that Saturn has a warm-core vortex centered on
the South pole that spins in a cyclonic (clockwise) direction like a southern
hemisphere hurricane. Winds are 160 m s−1 , and the temperature anomaly is
2.5 K. Here we report additional observations suggestive of terrestrial hurricanes: a central eye 4200 km in diameter with large relative vorticity, an outer
region where relative vorticity is near zero, a temperature anomaly within the
eye that extends high into the stratosphere, concentric eyewall clouds that extend 70 km above their surroundings, numerous small-scale cloud clusters
whose anticyclonic vorticity implies a convective origin, and a suggestion, at
high altitudes, of excess cyclonic rotation not balanced by the inward pressure
force, implying outward flow. Besides differences of scale, the main differences
from Earth are that the vortex is fixed to the pole and does not have a liquid
ocean to support it.
2
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 central eye, typically 20-100 km in diameter, is warmer than its surroundings to the
height of the tropical tropopause at 15 km and is relatively cloud-free. A ring of clouds, the
eyewall, surrounds the eye up to the tropopause. This height is about twice the pressure scale
height (vertical e-folding distance) of the atmosphere. Sometimes there are multiple concentric
eyewalls. Winds are greatest in the eyewall and can reach speeds of 85 m s−1 . The relative
vorticity ζ, which is the vertical component of the curl of the velocity associated with motion
relative to the planet, is large out to the eyewall and small in the region beyond, where the
tangential velocity decays to zero. The vorticity at the center is cyclonic - clockwise in the
southern hemisphere and counterclockwise in the northern hemisphere
What would a hurricane look like on a giant planet, which has no ocean although it does
have a deep moisture-laden atmosphere below the clouds? Would it be a hurricane if it had an
eye, an eyewall, evidence of convective clouds, a warm core, and a cyclonic circulation? At
what point would the similarities outweigh the differences, so that studying such a structure
would be worthwhile for comparison with terrestrial hurricanes? These are the questions addressed in this paper.
The warm central core and the wind profile observed in 2004 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. As far as can be judged from the
2004 observations, the polar vortex remained unchanged over the two-year period (7). Figure
1 is a false-color image that shows cloud heights (8; 9; 10). The spatial resolution is ∼20
km/pixel. The central eye looks dark and red in Fig. 1. This indicates a nearly cloud-free
3
upper atmosphere with some deep clouds at the bottom. The blue-green ring outside the eye
indicates high clouds and haze. The eye has two concentric boundaries, not unlike the eyes of
terrestrial hurricanes (3), except on Saturn the boundaries are not contracting with time (7; 11).
The inner boundary is oblong; the outer one is circular, measuring 2000 and 4200 km in diameter respectively. In the original images the sun was ∼16 ◦ above the horizon, and the eyewall
clouds cast shadows towards the pole (12). The shadows follow the sun in a counterclockwise
direction as the planet turns during the three-hour period. From the shadow lengths we estimate
the height of the outer wall as 40±20 km, and the height of the inner wall as 70±30 km relative
to the cloud tops inside the eye (12). The latter value is about twice the pressure scale height
of Saturn’s atmosphere, which compares favorably with the eyewall clouds on Earth. From the
opacity of Saturn’s atmosphere in the three wavelengths used to construct the image, it appears
that the eyewall clouds may extend up to the tropopause, which is at the ∼100 mbar level (12).
A major difference is that the diameter of the eye is ∼20 times larger than that of a terrestrial
hurricane, though Saturn itself is ∼9 times larger than the Earth.
Figure 2A shows the mean zonal velocity ū (positive eastward)
Constant absolute vorticity is consistent with horizontal stirring by eddies. Without the
frictional losses by eddies, rings of air moving inward would produce a profile with constant
angular momentum. As in a terrestrial hurricane, angular momentum decreases toward the center. On Earth, rings of air flowing inward lose angular momentum to the lower boundary and
to the outflowing air above (1; 2; 3). On Saturn there is no lower boundary, but rings of air
could lose angular momentum to the deep atmosphere below. The latter is vigorously stirred
by internal heat convected up from Saturn’s interior and therefore could act as a large sink of
angular momentum.
4
The solid line of Fig. 2B shows the relative vorticity ζ estimated from the measured ū (12).
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 puffy red clouds seen in Fig. 1 (12).
The puffy red clouds are anticyclones, with vorticity in the range −1 ± 1 × 10 −4 s−1 , which is
∼1/3 the magnitude of the planetary vorticity f but of opposite sign. This is consistent with a
convective origin, since parcels rising from the convective interior should have ζ + f = 0 when
they spread out in the upper troposphere (13; 14), except that entrainment dilutes this anticyclonic vorticity with ambient air. In this respect the puffy red clouds are like the rain bands of a
terrestrial hurricane. The rain bands usually form spirals around the hurricane, which is not the
case for the puffy red clouds. However, ”annular hurricanes” (15), long-lived and symmetric
terrestrial hurricanes, do not show spiral rain bands and may be a closer analogue to the polar
vortex on Saturn.
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 may be that
each cloud cluster has a zone of opposite-signed vorticity surrounding it. This is expected for
quasi-geostrophic flow (14) in a rotating system: The velocity decays away exponentially with
a length scale equal to the radius of deformation (14).
Figure 3 shows a high-resolution map of temperatures at the 200-mbar level (16). This is
near the tropopause at 100 mbar (12), and it shows a dramatic concentration of warm air inside
the eye. Another figure (12; 17) shows that in 2005 this warm core was strongest (5 K warmer
than the surroundings) at ∼ 250 mbars. In terrestrial hurricanes the strongest warm core indicates the layer of outflow just below the tropopause (3). The warm core on Saturn extends up
in the stratosphere unlike the cores of terrestrial hurricanes (3; 12)
5
Evidence of an overturning circulation is indirect. First, the blue-green haze of Fig. 1 just
outside the outer eyewall is consistent with air that has been lifted. Second, the eyewall itself
is consistent with rising motion, since clouds form on updrafts. Third, the warm central core
means that the central low pressure, and with it the cyclonic circulation, should weaken with
altitude. We searched for this effect using a 4-frame color movie (12) of images like the one in
Fig. 1, and found no difference in the wind with altitude, at least at -84 ◦ where there were features in the blue-green haze suitable for tracking (12). 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, consistent with the overturning circulation
of a terrestrial hurricane (1; 2).
The Saturn vortex is distinctly different from Jupiter’s Great Red Spot and similar ovals on
the giant planets, which are anticyclonic, calm at the center, and do not have eyes. It is different
from the winter polar vortex in the Earth’s stratosphere at 1 - 10 mbar, which is a cold-core
vortex with no eye and no eyewall clouds (14). It could be similar to a polar low (18), which is
a high-latitude feature that resembles a hurricane. On Saturn the poles are not necessarily colder
than the equator. The deep atmosphere, which is stirred by internal heat, acts as a thermostat
that maintains all parts of the planet at nearly the same temperature (19). Saturn’s polar vortex
could be an organized cyclonic structure that uses moisture to convey this internal heat to the
surface as do terrestrial hurricanes and polar lows.
6
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, Annual Review of Earth and Planetary Sciences 31, 75 (2003).
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. The same double-wall structure as in this study is seen in ∼50 km/pixel Cassini polar
observations taken in September-October 2004 (5), and in ∼30 km/pixel observations taken
in July 2004 (6). The elliptical shape of the inner eyewall looks remarkably unchanged
between the 2004 and 2006 observations. As in this study, there are many small clouds
outside and a few small clouds inside the inner eyewall in both 2004 and 2006 images.
8. C. C. Porco, et al., Space Science Reviews 115, 363 (2004).
9. 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.
10. E. Karkoschka, Icarus 133, 134 (1998).
11. R. A. Houze, S. S. Chen, B. F. Smull, W.-C. Lee, M. M. Bell, Science 315, 1235 (2007).
7
12. The details of the eyewall height measurement, cloud tracking, vorticity measurements,
the cloud movie, and the vertical temperature structure of the warm core are shown in the
supporting online material.
13. Ertel potential vorticity (EPV) is a conserved quantity that is proportional to the dot product of the absolute vorticity and the entropy gradient (14). Since the latter is zero in the
convective interior, EPV must be zero. A rising parcel maintains its value of EPV unless
it mixes with other parcels, so if the parcel rises into a stably stratified layer, it must have
ζ +f =0.
14. J. R. Holton, An introduction to dynamic meteorology, International geophysics series (Academic Press, San Diego, New York, 1992), third edn.
15. J. A. Knaff, J. P. Kossin, M. DeMaria, Weather and Forecasting 18, 204 (2003).
16. F. M. Flasar, et al., Space Science Reviews 115, 169 (2004).
17. L. Fletcher, et al. (2007). In preparation.
18. E. A. Rasmussen, J. Turner, eds., Polar Lows (Cambridge University Press, Cambridge,
UK, 2003).
19. A. P. Ingersoll, C. C. Porco, Icarus. 35, 27 (1978).
This research was supported by the NASA Cassini Project.
Supporting Online Material
SOM text
Fig. S1, S2, S3, S4, and S5
Movies (Will figure out how to reference them UD)
8
Figure 1: False-color image of Saturn’s south polar clouds taken by the Cassini imaging system
in three filters (8). 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 images have been map projected using polar
stereographic projection with planetocentric latitudes. In the original images the sun was 15 ◦
above the horizon at the pole, and attenuation by a factor of e = 2.71... occurs at the 80 mbar
and 300 mbar levels, respectively, for light at 889 nm and 727 nm, which are the blue and green
planes. Thus clouds below 300 mbars appear red, and high thin clouds appear blue or green.
The eyewalls can be seen in all three color planes, and thus extend to ∼80 mbar. To reduce the
effect of varying solar illumination across the image each color plane is high-pass filtered at the
spatial scale of ∼300 km, or ∼0.3 degree latitude.
9
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 solid curve is for constant absolute vorticity ζ + f starting at latitude
φ0 =-73.5, with ū = 0 and ζ = 0 at that point. (B). Relative vorticity ζ, assumed positive when
the direction is cyclonic - clockwise in the southern hemisphere. The solid curve is a spline fit
to the velocity data of Fig. 2A (12). The points are the puffy red clouds of Fig. 1. To determine
the relative vorticity of a puffy red cloud, we track it over the 3-hour time interval and measure
its angular velocity of rotation relative to the rotating planet. Twice this angular velocity is minus the vorticity of the spot. We repeated the procedure three to four times for each cloud and
assigned error bars from the residuals (12).
10
Figure 3: Temperature map at the 200-mbar level derived from the Cassini infrared spectrometer
(16). Consistent with infrared images from Earth taken at lower resolution (4), the gases at the
pole are ∼ 3 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.
11
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 the continuum band filter (the wavelength of the
best contrast for small features) allowed tracking of clouds to obtain accurate wind velocities.
A movie combined from these images (included in the supporting online material) 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 were obtained by an 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 1 . The manual and automatic tracking agree
outside the -84.5◦ circle. The independent cloud tracking by two other co-authors (JB and AW)
agree with the windspeeds in Fig. 2 but have larger uncertainties. We do not include their data
points in Fig. 2. (Co-authors can see the comparison plot at the very end of this .pdf file
UD) The wind increases towards the pole up to the outer eyewall at -87.8 ◦ latitude. There are
no trackable features between the outer wall and latitude of ∼-88.5◦ just outside the inner eye
wall. Between latitudes -86.5◦ and -89 ◦ the winds reach their maximum linear speed of ∼ 150
± 20 m/s.
The winds measured in July 2004 Cassini images at - 87 ◦ were 160±10 m/s (6). This is
consistent with our measurements at this latitude. In September-October 2004 the linear speed
1
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’ motion at some test angular velocity around the
pole. For each cloud there is a particular angular velocity when the cloud rotation and the movie’s back rotation
cancel out, which stops the motion of the cloud. For each of the test angular velocities we picked the clouds that
stopped their motion in the modified movies. This produced the data points in Fig. 2
12
associated with the rotation of the inner eyewall at -88.5 ◦ latitude was 80 to 135 m/s (5). This
is smaller than our 130-160 m/s windspeeds for this latitude. Although this difference may
be real, the uncertainty in the windspeed measurements is rather high to assert this windspeed
change with confidence.
We also measured the meridional component of the clouds’ motion which turned out 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. Although we do not see the inward motion, 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 movie2 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 -84 ◦ 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 follows the phase of the atmospheric wave associated with the eye.
2 Vorticity.
The spline interpolation of the zonal wind profile from Fig. 2 can be used to calculate the
vorticity of the zonal flow. For each pair of consecutive points in the spline curve fited to the
points from Fig. 2A the vorticity is calculated as follows. ζ = (ū 0x0 − ū1 x1 )/((x0 +x1 )/2)/|dl|,
where ū and x are zonal wind and distance to the Saturn’s rotation axis for the first and second
point in the pair, subscribed respectively. |dl| is the distance on Saturn’s surface between these
2
http://www.gps.caltech.edu/∼ulyana/iss/polar movie/movies/color 4frm compressed.avi
13
points along the meridian.
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 as their angular
velocity multiplied by two. The angular velocity was obtained by a procedure similar to the
manual feature tracking used for the zonal windspeeds, which involves picking an appropriate
stopped motion movie from the set of the test movies 3 . Often it is uncertain which of the
movies matches the rotation of the cloud. To test the uncertainty and to increase the 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 and points
in Fig. 2B) are the averages of those 3-4 measurements. Nearly all small clouds rotate counterclockwise (anticyclonic vorticity). Remarkably, the largest features (the two dark spots at the
upper left corner 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. This
demonstrates that the dark areas are indeed shadows and not a dark coloration of the underlying
clouds.
3
To obtain each cloud’s angular velocity we first determined its drift around the pole (see the technique described 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 test angular velocities for that cloud. While simultaneously playing the set of
back-rotated movies we picked the one that stopped the apparent rotation of the cloud. Because individual clouds
are not always covered by all 14 images, some modified movies have less than 14 time steps, down to as few as 2
time steps, which creates additional uncertainty.
14
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
the horizon, which is around 16◦ for the inner eyewall and 17◦ for the outer eyewall for all the
images (as the Sun is 15◦ above the horizon at the pole and the eyewalls are 1◦ and 2◦ away
from the pole.)
Figure 7 shows the resulting heights for outer and inner eyewalls calculated from the 9 maps.
The data are plotted versus the longitude at which each shadow point projects to the eyewall.
The longitudes are then adjusted to account for the zonal wind at the 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.
15
Figure 4: Map of the Southern polar vortex combined as a mosaic of 14 maps produced from
individual ISS images. Each image was taken in continuum band filter CB2 with the central
wavelength 750 nm (8). 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
16
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.
17
Figure 6: Two maps demonstrating how the length of the shadows were estimated. The left
panels show the map, the right planes show the same map with the cyclone’s eyewalls outlined
in black and shadow lengths measured on this image shown in white.
18
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.
19
Temperature (K)
Anomaly (K)
0
-2
-4
2
-6
1
0
0
16
15
2
10
4
0
136
128
-2
2
4
0
96
Pressure (mbar)
144
100
104
1000
-70
112
120
128
136
-75
-80
-85
-90 -70
-75
-80
-85
-90
Planetographic Latitude
Figure 8: Zonal mean temperatures in Saturn’s south polar region derived from Cassini/CIRS
spectra (17) taken on July 30th 2005 from an orbital distance of 28 R s . Tropospheric temperatures in the 70-800 mbar region (bottom left) and stratospheric temperatures between 1-6 mbar
(top left) are derived from the 600-1400 cm−1 region of CIRS mid-IR spectra. The temperature
information originates from fits to the ν 4 CH4 band and the H2 -He collision-induced continuum
at 15.0 cm−1 spectral resolution. Temperature anomalies (right-hand plots) are calculated by
subtracting the zonal temperatures at 84◦ S. The maximum thermal anomaly of 5 K is located
at approximately 250 mbar, just beneath the tropopause (temperature minimum) at 100 mbar.
The stratosphere also demonstrates a warm pole (3-4 K higher than at 84 ◦ S) coincident with the
vortex eye, and warmer than predicted by seasonal radiative models in the absence of dynamics
(17).
20