Science manuscript 1147644 by Dyudina et al.
Response to the reviews
Review 1
> This is an interesting paper that describes a fascinating phenomenon
> at Saturn's South Pole. The paper is concise and presents interesting
> observations, but I find it difficult to believe that this is really
> an analogy to a terrestrial hurricane.
We agree that the environments on Saturn and Earth are very different and excluded direct parallels between Saturn polar vortex (SPV) and hurricane throughout the paper.
>On the top of page 3 it is
> stated that the latter are sustained by latent heat release, and
> although this explanation is given in most text books, it is probably
> wrong. It has become abundantly clear over the past few decades that
> terrestrial hurricanes are sustained by enthalpy fluxes across the
> air-sea interface; this is why they die upon landfall even though the
> surrounding atmosphere may be very moist. In numerical experiments,
> if the temperature of the environmental radiative-convective
> equilibrium state is reduced in successive numerical experiments,
> while keeping the thermodynamic disequilibrium between the surface
> and the atmosphere constant, and maintaining the same temperature
> difference across the troposphere, the resulting vortex has the same
> intensity in each case, though its structure changes. It is perfectly
> possible to have a dry hurricane, -- which is what happens in the
> low-temperature limit - as long as there is enough enthalpy jump
> across the boundary.
We excluded latent heat release as a mechanism maintaining the SPV
From the paper.
> The hurricane works on a feedback between the surface
> enthalpy flux and the boundary-relative wind, because there is always
> a layer next to the surface in which the heat fluxes are carried by
> mechanically driven turbulence, which is the rate limiting factor and
> depends on the boundary-relative flow. Without such a boundary, this
> feedback is not possible and the fundamental mechanism of the
> hurricane is missing.
In the new version of the paper we do not attempt to explain the driving mechanism for the SPV.
> I do have a suggestion for what might be going on, that
> is based on the observations of the convective vortices presented in
> the paper. It is well known that intense vortices embedded in a
> large-scale gradient of (potential) vorticity tend to self-migrate,
> owing to the advection of the background (potential) vorticity
> gradient by the vortex flow. Cyclonic vortices migrate poleward,
> while anticyclonic ones migrate equatorward, assuming that the
> background gradient is of the same sign as the gradient of planetary
> vorticity. Convective updrafts produce intense cyclones at lower
> levels, and these may be expected to migrate poleward. The net effect

> is to produce a poleward vorticity flux. I might add that this effect
> is well known and observed in terrestrial hurricanes. Thus, over
> time, vorticity might accumulate at the poles, while equatorward of
> the convective maximum the flux of vorticity would act to reduce the
> overall gradient.
> Such an effect may be evident in numerical experiments on
> convection on a rotating sphere, as long as the convection is of high
> amplitude (very supercritical Rayleigh numbers). In a quick search, I
> came across one paper (Christensen, 2002, J. Fluid Mech., 470,
> 115-133) that seems to indicate that prograde jets might form near
> poles when the convection is strong enough (see their Figure 3d). In
> any event, it might pay to research the literature on convection on
> rotating spheres.
We thank the reviewer for offering this explanation. We agree that it may be one of the possible mechanisms. However our data do not detect vortices drifting systematically in the meridional direction, and we do not include this explanation in the paper.
> Minor points:
> Page 3, first sentence of last paragraph: it is not clear from this
> sentence whether the vortex did not exist before 2004 or whether
> there were no observations before 2004.
Corrected, thanks.
> Page 3, three lines from bottom: "Deep clouds" has a specific
> meteorological meaning which implies large vertical extent. I do not
> think that is what the authors mean here.
We replaced the word "deep" with "low".
> Review 2
> This paper presents a study of the South Polar Vortex of Saturn based
> on Cassini data. This feature was discovered and characterized from
> previous ground-based thermal infrared images and Cassini images
> (ref. 4, 6). The new data the authors present are a higher-resolution
> version of both. I find particularly relevant and interesting the
> analysis of the `eye' feature, where new material is presented, as
> for example the oval shape and rotation of the inner eyewall
> (impressive), the cloud altitudes derived from sunlight shadows
> (figures S2 and S3) and the detailed temperature map (Figures 3 and
> S5). It is on these new data that the authors should focus their
> paper. The interpretation of this feature as a `possible terrestrial
> hurricane analog' is speculative and risky since no modelling is
> presented. In summary, I see this paper interesting enough to be

> published in Science but once the authors do a moderate revision of
> its content including probably the title.
We rewrote the paper to focus on the data and to much lesser extent on the interpretation and comparison with hurricanes.
> Here is a list of specific
> comments and suggestions the authors could consider to improve the
> manuscript.
> (1) Page 3. In the second paragraph the authors argue on deep moist
> convection to support the feature. They should first state if the
> moisture is due to ammonia, water or both or to other compound, and
> then the predicted altitude location for their reservoirs and
> abundances. Thermo-chemical models predict water clouds to be deep in
> the atmosphere of Saturn, about 4.5 scale heights below the upper
> clouds (200 km beneath them) and peculiar conditions (humidity,
> condensable abundances, thermal structure) should be present in the
> deep atmosphere for vigorous convection to loft condensable gases up
> to the tropopause.
We keep in mind large uncertainties in understanding convection on Saturn and do not interpret the convection-vortex connection in the new manuscript.
> (2) Page 3 (third paragraph) and Figure 1. The authors describe
> qualitatively the cloud altitudes based on a three colour filter
> combination and cite references (7-9). However, they should consider
> and compare their altitudes with the quantitative analysis presented
> in ref. 6.
We added ref.6 (ref. 3 in new manuscript) to the Fig.1 caption, in which we discuss the cloud heights.
> (3) Page 4 (first paragraph) and Supporting Online Material (section
> 3 and Figures S2-S4). The height from the eyewall clouds shadows and
> the quality of these images is perhaps the most spectacular result of
> the paper. The authors should state that when calculating the
> altitudes from sunlight shadows they are assuming that the cloud
> surface where the shadow projects is flat (i.e. perpendicular to
> rotation axis, not tilted).
Thanks, we added this clarification on p.3, par.2, last sentence.
> I would suggest changing their Figure 1 in the main body of the paper
> by Figure S2 which is by far more interesting, showing the full oval
> eye with the features in rotation and the shadows moving in the
> opposite direction. Figure 1 and S1 do not differ in fact too much
> from previous published work.
We added Figure S2 to the main paper (now Fig.2).
> (4) Pages 4-5 (and Figures 2A-2B) and Supporting Online Material (SOM
> section 2). I'm concerned with the vorticity calculations the authors
> present.
> (a) If I understand correctly, the eastward velocity u drawn by a
> continuous line in Figure 2A results from the integration of the

> equation z+f = f0 (constant) with z =-du/dy (z is the relative
> vorticity or ambient shear, y meridional coordinate), f=2Wsin(phi)
> with W the planet angular velocity, and condition u=0 and z=0 at
> phi0=-73.5 deg (planetocentric). Then du(phi) = (f-f0)dy and its
> integration gives u(phi). Is this OK? I'm asking this because I have
> had some difficulties in reaching this interpretation. I suggest the
> authors to explain more clearly their procedure in the text.
We consider the relative vorticity on the oblate spheroid, which is not –du/dy.
We added detailed equations to our description of vorticity in Section 2 of
SOM.
> Looking to the wind profile in Figure 2A, I see that on the average u
> = 0 for a wide range of latitudes, from -73.5 deg to -80 deg, so the
> boundary condition for f0 seems arbitrary. How your derived curve for
> u(phi) in Figure 2A depends on the assumed value for f0? For example
> how this will change if you take for f0 the latitude -80 deg?
We chose f0 to match the data the best.
In the new figure we plotted two curves for f0=-72 and -73.5 deg to show the effect of changing f0
> (b) In reference to Figure 2B and vorticity.
> First, the formula used to calculate the relative vorticity given in
> SOM (section2, page 3 first paragraph) has a mistake. I think it
> should write: z(x')=[u0(x0)-u1(x1)]/dl being x'= (x0+x1)/2 the
> midpoint where the vorticity is calculated. When correcting it, I
> suggest the use of y instead of x for the meridional coordinate as
> done in textbooks of meteorology.
There is no mistake. The variable x was misinterpreted by the reviewer.
We rewrote our equations in terms of planetographis latitudes and planet’s radii and added detailed description on how the formula is derived from the vorticity definition (see SOM, beginning of Section 2).
> Second, if this is the formula used to derive the continuous line in
> Fig. 2A, it seems to me that the contribution of the curvature term
> to the relative vorticity z (e.g. Holton 4th edition Appendix C, page
> 500) which important in the polar latitudes, has not been included in
> the calculations. To show its importance, take for example latitude
> -86.5 deg. Interpolating 0.5 deg around this latitude for the wind
> speed (from the measured profile presented in Figure 2A) I get that
> the wind shear term contributes to the relative vorticity with
> du/dy=-1.6x10-5 whereas the curvature term contributes with u
> tan(phi)/r=-4.2x10-5, which is 2.5 times the shear contribution. Here
> r is the planetary radius at the latitude of calculation.
The curvature term is included in our calculations (See SOM, Sec. 2)
> The authors should consider revising their vorticity calculations
> according to these comments and/or clarify all this in the text and
> SOM.
See new Section 2 of SOM.
> In addition it will be helpful to have vertical lines drawn in

> Figs. 2A and 2B to mark the latitude location of the inner and outer
> eyewall edges.
Thanks, we marked the eyewalls in those figures and in Fig $ of the new manuscript.
> (5) Finally, concerning the hurricane analog hypothesis stated by the
> authors, although I recognize there can be some similarities between
> both, I also see important differences that makes risky to use this
> term in the title. This is a list of some differences/problems I see:
> (a) This feature is probably long-lived (a dark small spot has been
> observed regularly from Earth under favourable viewing conditions),
> so long-term sustained moist convection would be required with
> continuous moisture supply to keep the engine working. It is not
> evident how this can be accomplished without a large water reservoir
> (an ocean as occurs for Earth hurricanes).
We rewrote our comparison with hurricane, and stress the differences with th hurricane on p.5, par 2 of the main manuscript.
> (b) An important ingredient of hurricane physics is the presence of a
> rigid lower boundary (the Earth surface) along which pressure
> gradients can be maintained and the moist air convergence toward the
> central eye occurs due to the low pressure centre. Not evident
> surface analog exists for a giant planet, being the vortex bounded
> below by an adiabatic atmosphere where horizontal pressure gradients
> are expected to be small.
We summarized the similarities and differences between vortices on Earth,
Jupiter, and Venus in main text, p. 5, last two paragraphs, and in the SOM,
Section 5, where we compare the presence of the rigid planet beneath the atmosphere.
> (c) There are important differences in the eye vorticity values
> between both features (at about the same altitude). Hurricanes on
> Earth have relative vorticities in the eyewall: z = 6x10-3 s-1 (for
> tangential speeds of 75 ms-1 and eye radius 25 km). The planetary
> vorticity is f=2W sin(20deg) = 5x10-5, implying that z =100 f. The
> centrifugal force is 100 times the Coriolis one. The Saturn polar
> vortex has in the eyewall z = 3x10-4 (Figure 2A) and f = 2W sin(89) =
> 3x10-4, implying z = f. The centrifugal force is 2 times the Coriolis
> one.
We included that comparison in Sec. 5 of SOM.
> (d) Saturn circulation is dominated at cloud level by a pattern of
> zonal jets alternating in direction with latitude. In this context,
> the peak speed between -87 and -88 deg that encloses the polar vortex
> can be viewed as the last jet of the system.
We agree, but as we do not discuss the driving forces for SPV in the new paper, we do not include this point.
> (e) At the terrestrial tropopause level the tropical cyclones are
> cold. On the contrary Saturn's polar vortex is warm at this level. In
> addition, on hurricanes the warm eye anomaly (of the order of 10-15

> K) extends the whole cyclone altitude but on Saturn's appears
> concentrated in a thin layer. If latent heat release is the power
> source for Saturn's cyclone, I would expect the thermal anomaly to
> extend deep in the atmosphere, not to be concentrated.
From our Fig 4 (former Fig. S5), the warm core is extended vertically to all elevations covered by the observations and not concentrated to the thin level.
> These and other problems could be obviously avoided only if one
> assumes add hoc hypothesis for Saturn's atmosphere below the upper
> ammonia cloud. At the state of knowledge of Saturn's deep atmosphere
> and without presenting dynamical modelling to test/support the
> observations, it is not clear for me how useful, if not confusing, is
> the terrestrial hurricane comparison.
Now we compare SPV with the wider range of vortices, which should solve the possible confusion.