Potential vorticity of the south polar
vortex of Venus
I. Garate-Lopez
1
, R. Hueso
1
, A. Sánchez-Lavega
1
, and A. García Muñoz
2,3
1
Departamento de Física Aplicada I, E.T.S. Ingeniería, Universidad del País Vasco, Bilbao, Spain,
2
ESA/RSSD, ESTEC,
Noordwijk, Netherlands,
3
Zentrum für Astronomie und Astrophysik, Technische Universität Berlin, Berlin, Germany
Abstract Venus’atmosphere shows highly variable warm vortices over both of the planet’s poles. The nature
of the mechanism behind their formation and properties is still unknown. Potential vorticity is a conserved
quantity when advective processes dominate over friction and diabatic heating and is a quantity frequently used
to model balanced flows. As a step toward understanding the vortices’dynamics, we present maps of Ertel’s
potential vorticity (EPV) at Venus’south polar region. Weanalyzethreeconfigurations of the south polar vortex at
the upper cloud level (P~ 240 mbar; z~ 58 km), based on our previous analyses of cloud motions and thermal
structure from data acquired by the Visual and InfraRed Thermal Imaging Spectrometer instrument on board
Venus Express. Additionally, we tentatively estimate EPV at the lower cloud level (P~ 2200 mbar; z~43km),based
on our previous wind measurements and on static stability data from Pioneer Venus and the Venus International
Reference Atmosphere (VIRA) model. Values of EPV are on the order of 10
6
and 10
8
Km
2
kg
1
s
1
at the upper
and lower cloud levels, respectively, being 3 times larger than the estimated errors. The morphology observed in
EPV maps is mainly determined by the structures of the vertical component of the relative vorticity. This is in
contrast to the vortex’s morphology observed in 3.8 or 5 μm images which are related to the thermal structure of
the atmosphere at the cloud top. Some of the EPV maps point to a weak ringed structure in the upper cloud,
while a more homogenous EPV field is found in the lower cloud.
1. Introduction
During the nominal and part of its extended mission (from April 2006 to October 2008), the Venus Express
spacecraft obtained detailed images of the thermal structure in the south polar region of the planet, which
behaves as an atmospheric warm vortex at cloud top [Piccioni et al., 2007; Titov et al., 2012; Garate-Lopez
et al., 2015]. The south polar vortex (SPV) is similar to the circumpolar vortex of the north hemisphere
observed by previous missions at visual wavelengths [Suomi and Limaye, 1978] and in the thermal infrared
[Taylor et al., 1979, 1980; Schofield and Diner, 1983]. The SPV cloud morphology and its temporal evolution
and lifetime have been investigated with data from the VIRTIS (Visual and InfraRed Thermal Imaging
Spectrometer) and VMC (Venus Monitoring Camera) instruments. Luz et al. [2011] and Garate-Lopez et al.
[2013] presented detailed accounts of the vortex’s morphology and its cloud motions. The three-dimensional
thermal structure of the vortex was first investigated by Grassi et al. [2008] and has also been the subject of a
recent detailed study based on VIRTIS data for three specific vortex configurations [Garate-Lopez et al., 2015].
The combination of velocity and thermal structure determines the behavior of atmospheric structures
through its combination into potential vorticity in one of its many different formulations [Pedlosky, 1987;
Sánchez-Lavega, 2011]. Ertel’s potential vorticity (EPV) is a key atmospheric variable used in diagnostic and
prognostic models of geophysical fluids because, for an inviscid atmospheric flow (neglecting friction) and
in the absence of sinks or sources of potential vorticity from diabatic heating, EPV is a conserved quantity
and becomes a tracer of fluid motions [Sánchez-Lavega, 2011]. In fact, any dynamical field in a fluid can be
determined given the global distribution of isentropic potential vorticity (e.g., the EPV), the mass under each
isentropic surface, and appropriate boundary conditions [Hoskins et al., 1985; Vallis, 2006].
On Earth, potential vorticity maps are a tool commonly used to study the evolution of the stratospheric polar
vortices [Nash et al., 1996]. The jet stream and the cyclonic circulation around terrestrial polar vortices act as a
barrier to mixing and are responsible for the intensity of the ozone hole [Schoeberl et al., 1992]. Relatively low
values of total column ozone and cold temperatures in the lower stratosphere are found colocated with polar
vortices [Schoeberl and Hartmann, 1991]. Both polar vortices are strongly seasonally dependent, but the
winter southern polar vortex is larger, more intense, and longer lasting than its northern counterpart.
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 574
PUBLICATION
S
Journal of Geophysical Research: Planets
RESEARCH ARTICLE
10.1002/2015JE004885
Key Points:
•We present Ertel’s potential vorticity
(EPV) maps of Venus’south polar
vortex
•The relative vorticity dominates over
the thermal term in the EPV calculation
•EPV is ~2 × 10
6
and ~2 × 10
8
Km
2
kg
1
s
1
in the upper and
lower clouds, respectively
Correspondence to:
I. Garate-Lopez,
Citation:
Garate-Lopez, I., R. Hueso, A. Sánchez-
Lavega, and A. García Muñoz (2016),
Potential vorticity of the south polar
vortex of Venus, J. Geophys. Res. Planets,
121, 574–593, doi:10.1002/
2015JE004885.
Received 1 JUL 2015
Accepted 7 MAR 2016
Accepted article online 14 MAR 2016
Published online 7 APR 2016
©2016. American Geophysical Union.
All Rights Reserved.
Latitudinal confinement by a mixing barrier could be important in polar vortices present in other solar system
planets. Mitchell et al. [2014] used EPV to compare the polar vortices on Earth and Mars. Unlike on Earth, the
Martian polar vortices are annular and become dramatically smaller with height. Teanby et al. [2008] com-
pared EPV maps with measurements of five independent chemical tracers to study Titan’s winter polar vortex
and found that indeed the vortex circumpolar jet separates a tracer-enriched air mass in the north pole from
air at lower latitudes. Permanent, strong polar vortices confined by narrow jet streams exist also at the poles
of Saturn as observed in the cloud [Sánchez-Lavega et al., 2006; Dyudina et al., 2008; Antuñano et al., 2015] and
temperature fields [Fletcher et al., 2008]. Therefore, a comparative view of the dynamics of these vortices in
very different environments could help to understand the mechanisms behind their formation and
temporal variability.
The Venus atmosphere shows an enhancement of CO, a trace gas in Venus atmosphere, from the equator
to the south pole with a peak at ~60°S and 35 km altitude [Tsang et al., 2008]. The decrease of CO from
60°S to the pole could be an evidence of the existence of a latitudinal mixing barrier with the CO enhance-
ment at 35 km caused by the descending branch of a Hadley cell that may advect CO from the cloud top,
where CO is produced by photodissociation, to this lower altitude [Tsang et al., 2008]. Piccialli et al. [2012]
investigated this possibility by calculating the zonal mean of EPV from thermal vertical profiles at subpolar
latitudes obtained by the Venus Radio Science (VeRa) instrument. These data were used to compute zonal
mean thermal winds and EPV. The values of EPV from this study slightly increase from equator to pole, but
they do not show any mixing barrier or region of strong latitudinal gradient. However, they only studied
the zonal mean of the EPV and assumed cyclostrophic balance which constitutes a physical approximation
that fails in reproducing the winds obtained by cloud tracking close to the equator and the poles.
Here we construct horizontal maps of the EPV field at the upper cloud level (about 58 km above the surface)
over the south polar region of Venus. For that purpose we combine simultaneously obtained maps of wind
and temperature that we derived previously from observations acquired by the VIRTIS instrument on board
Venus Express [Garate-Lopez et al., 2013, 2015]. Additionally, we tentatively estimate the EPV distribution at
the lower cloud level (about 43 km altitude) combining our previous wind measurements [Garate-Lopez
et al., 2013] and combined values of the static stability from Pioneer Venus North probe, Pioneer Venus radio
occultation experiment, and the VIRA model [Seiff et al., 1980, 1985] which we consider as representative of
Figure 1. Polar projected images showing the morphology of the south polar vortex of Venus at the (top row) upper and
(bottom row) lower cloud levels on orbits (left) 038, (middle) 310, and (right) 475. The upper cloud is observed at 3.8
or 5.1 μm VIRTIS-M-IR images and the lower cloud at 1.74 μm images. Latitude circles are plotted at 5° intervals from the
south pole (represented by a blue dot). Green stars have been added to stress the vertical consistency of the overall shape
of the vortex.
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 575
the possible thermal structure of the lower cloud level in the south polar atmosphere. We examine three
different configurations of the vortex in order to comprehend the relation of the vortex morphology with
its dynamical properties and its long-term behavior. Figure 1 shows images of the vortex’s upper and lower
clouds in the three configurations. The hourly evolution of the potential vorticity in the upper cloud is also
investigated for the last of these configurations, which was observed during orbit 475 when VIRTIS obtained
high-resolution observations of the vortex every 15 min over several hours.
Deriving EPV fields in the polar region of Venus’s atmosphere has been significantly challenging due to the
limitations of the actual data sets (mainly horizontal and vertical spatial resolutions) and the highly variable
nature of the vortex. However, they are likely to be the only available EPV estimates for some time to come,
since the Japanese Akatsuki mission will not be able to observe the polar latitudes from its equatorial orbit.
Section 2 summarizes the wind and temperature analyses. Section 3 describes the calculation of Ertel’spotential
vorticity. We present the results in section 4, and in section 5 we discuss the results and present our conclusions.
2. Wind Measurement and Temperature Retrieval
2.1. Wind Field Analysis
We measured wind motions at the southern pole of Venus [Garate-Lopez et al., 2013], from the analysis of
images obtained with the infrared channel of the VIRTIS-M instrument over the 1.0–5.1 μm spectral range
[Drossart et al., 2007]. The data consist of imaging qubes with two spatial dimensions of up to 256 × 256 pixels
and one spectral dimension. Nightside images at 1.74 μm are sensitive to the structure of the lower cloud
(at about 42 km altitude above the surface at polar latitudes [Barstow et al., 2012]) and constitute the main data
to study lower cloud dynamics [Sánchez-Lavega et al., 2008; Hueso et al., 2012, 2015]. Images at 3.8 and 5.1 μm
are sensitive to the thermal emission of the upper cloud (at about 63km altitude at polar latitudes [Ignatiev et al.,
2009; Peralta et al., 2012]). In some cases the characteristics of the VIRTIS hyperspectral images allowed the
retrieval of simultaneous wind field at both levels. This was done by analyzing images obtained when the space-
craft was close to the apocenter in near-nadir pointing, achieving a spatial resolution of ~16 km × 16km for each
individual pixel. Feature motions were extracted with an image correlation algorithm [Hueso et al., 2009] that
allows to manually filter spurious measurements on the fly. The selected image pairs were separated in time
by 1–2 h, and uncertainties in each individual wind measurement were estimated to be about 4 m/s. We here
revise this figure and increase it to 6 m/s to take into account the larger uncertainty of some tracked features.
Maps of the vertical component of the relative vorticity,
ζλ;φðÞ¼1
Rcos φ
∂v
∂λ1
R
∂u
∂φþu
Rtan φ;(1)
with uand vbeing the zonal and meridional wind velocities, φthe latitude, λthe longitude, and Rthe radius of
the planet, were obtained from the wind measurements for different vortex configurations [see Garate-Lopez
et al., 2013, Figure 2]. These derivatives were calculated using a coordinate transformation into a rectangular
x-y grid centered in the pole, and spatial derivatives were calculated with a spatial step of 5° (525 km) to
reduce errors associated with small irregularities in the wind field. In both cloud levels, the polar vortex is a
relatively weak vortex immersed in a cyclonic environment whose cloud and thermal morphology is not
directly related to the structures observed in the relative vorticity maps. Higher mean vorticity values about
ζ~ (6.0 ± 3.5) × 10
5
s
1
were found at polar latitudes (75°S–90°S) when compared with subpolar latitudes
(60°S–75°S) where ζ~ (2.5 ± 3.5) × 10
5
s
1
. The uncertainties here reflect the increased uncertainty in wind
measurements with respect to Garate-Lopez et al. [2013].
2.2. Temperature Field Analysis
VIRTIS infrared spectra from 4.2 to 5.1 μm contain enough information to retrieve temperatures from about
55 to 85 km altitudes [García Muñoz et al., 2013]. We used an inversion relaxation technique that tries to find
a best match between an observed spectrum and a modeled spectrum by iteratively correcting an initial
guess temperature profile to a final thermal profile. We used synthetic spectra generated from an atmo-
spheric model as described in García Muñoz et al. [2013]. The retrieval algorithm largely followed the meth-
odology by Grassi et al. [2008] with changes in the way clouds and aerosols are treated. Instead of considering
the cloud top altitude and the aerosol scale height as free parameters within the iteration algorithm, we
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 576
retrieved temperatures for a discrete set of fixed values of both parameters and then selected the cloud
parameters and thermal profile that showed a better fit of the modeled and observed spectra (in terms of
the root-mean-square deviation). The thermal retrievals are fully explained in Garate-Lopez et al. [2015].
We selected three of the orbits where we measured wind fields with enough spatial resolution and provided
high-quality spectral data over the 3–5μm range in most of the image area. These three cases show very
different morphologies of the vortex (see Figure 1) and correspond to Venus Express orbits 038 (28 May
2006), 310 (24 February 2007), and 475 (8 August 2007). Thermal maps at altitudes from 55 km (~360 mbar
pressure level) to 85 km (~1 mbar) are given in Figures 4 to 6 in Garate-Lopez et al. [2015].
In the Venusian atmosphere the temperature increases downward from 100 to ~40 km, except for an inver-
sion layer (at about 60–70 km) coincident with the cold collar [Taylor et al., 1980; Seiff, 1983; Piccialli et al.,
2008; Tellmann et al., 2009]. The cold collar is a ring of colder air that surrounds the vortex and is observed
as a darker area between 60° and 80° in Figure 1 (top row). Our retrieved thermal profiles agree well with
the mentioned trend and reproduce the inversion (a temperature decrease of up to 20 K in just 10 km
altitude) at locations where the cold collar is observed. On orbit 038 the cold collar is more pronounced show-
ing temperatures on the order of 220 K, while on orbit 475 the cold collar temperatures increase to 235 K. The
latter case also shows the highest temperature values for the warm vortex [Garate-Lopez et al., 2015]. At
~68 km altitude the collar is on average 13 K colder than the mean vortex temperature, but the difference
increases up to 30 K as we go downward in the atmosphere. These temperature differences between the
warm vortex and the cold collar are much larger than the associated errors, which were estimated to be
about 3 K on average at the whole altitude range (55–85 km) but increase up to 9 K in the lowest ~7 km.
3. Calculation of Ertel’s Potential Vorticity
The general definition of Ertel’s potential vorticity (EPV) under the hydrostatic approximation can be written
as [Pedlosky, 1987; Sánchez-Lavega, 2011]
q¼ωR
→þ2Ω
→
ρ∇θeζθþfðÞg∂θ
∂P
;(2)
with ωR
→¼∇U
→
being the vorticity of the wind vector U
→
,Ω
→
the angular rotation speed of the planet, ρthe
density, θthe potential temperature, f=2Ωsin ϕthe Coriolis parameter (with ϕbeing latitude), Pthe
pressure, and gthe gravitational acceleration. On Venus, the Coriolis parameter fcan be neglected, since it
is 2 orders of magnitude lower than ζ
θ
(for example, at ϕ=80°S, f~6 × 10
7
s
1
, while ζ
θ
~6×10
5
s
1
),
so that equation (2) becomes
qeζθg∂θ
∂P
;(3)
where the vertical component of the relative vorticity (ζ
θ
) is calculated on an isentropic surface (θ= constant).
This definition is valid for a vertically stable atmosphere, a condition that is globally fulfilled on Venus above
45 km according to the atmosphere’s thermal structure found from VeRa data [Tellmann et al., 2009]. The top-
most cloud layer and the atmosphere above are extremely stable to vertical motions. This high stability
decreases below the upper clouds, and the vertical lapse rate approaches to adiabatic at the middle cloud
altitudes (50–55 km) with the possibility of finding convective regions in shallow layers [Tellmann et al.,
2009]. Therefore, equation (3) should not be used to derive EPV fields at ~50–55 km.
In our detailed thermal study of the vortex [Garate-Lopez et al., 2015] we calculated the static stability distri-
bution at the upper cloud level and obtained values on the order of 8–14 K/km for the three vortex config-
urations under analysis. Accordingly, Piccialli et al. [2012], based on VeRa data, show large values of the
Richardson number at vertical levels that are in agreement with the cloud top altimetry and its latitudinal
profile independently derived from VMC and VIRTIS data sets [Ignatiev et al., 2009].
On the other hand, the static stability profiles from the Pioneer Venus radio occultation experiment and VIRA
model show another local maximum close to 43km [Seiff et al., 1985] where the lower cloud is located in the
polar regions. These vertical profiles display a decrease in the static stability toward the pole, also present on
VeRa static stability profiles [Tellmann et al., 2009]. Hence, we use equation (3) to tentatively estimate the EPV
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 577
distribution at the lower cloud level, even though at the highest latitudes it may not be a good approximation
since the static stability values are small.
In this paper, we will focus on the two regions of high static stability, the uppermost one located at the upper
cloud level and the lower cloud located close to 45 km altitude where the static stability increases again
[Tellmann et al., 2009].
3.1. Potential Temperature for an Atmosphere With Temperature-Dependent Specific Heat
The potential temperature θis the temperature that an air parcel would have if it were moved adiabatically
(no heating, cooling, or mixing) from a level with temperature Tand pressure Pto a reference level with pres-
sure P
0
[Sánchez-Lavega, 2011]:
θ¼TP0
P
k
;(4)
where k¼ðγ1Þ
γ¼R*
CPis the adiabatic index with γbeing the adiabatic coefficient, R* the specific gas
constant (R*¼R
MCO2
¼0:1889 J g1K1, where R= 8.3143 J mol
1
K
1
and MCO2¼44:01 g mol1),
and C
P
the specific heat capacity at constant pressure.
This definition is obtained after considering the perfect gas law and assuming C
P
is a temperature-independent
constant. However, for Venus’atmosphere, where temperatures extend over a large range, it is necessary to
consider an explicit dependence of C
P
on temperature. The specific heat at constant pressure of a gas essentially
constituted by linear molecules such as CO
2
(96.5% on Venus atmosphere) can be approximated as a series of
powers in T[Epele et al., 2007]:
CP=R*eAþBT þCT2;(5)
where the coefficients A, B, and C are empirically adjusted to models of the specific heat of linear molecules
from their translation and rotational and vibrational modes and result in A= 2.5223, B= 0.77101 × 10
2
K
1
,
and C=0.3981 × 10
5
K
2
[Epele et al., 2007].
The temperature dependency of the specific heat capacity leads to a more complex relation between the
potential temperature of the adiabatic trajectory and the pressure level of reference [see Epele et al., 2007,
equation 19], where the value of θhas to be computed numerically using an iterative algorithm. Nevertheless,
anewquantityτwith physical dimensions of temperature can be defined which verifies
CPT
ðÞ
δT
T¼C0
P
δτ
τ:(6)
This new variable allows to treat the problem in exactly the same way as in the case of the ideal perfect gas
but using the new “extended”potential temperature:
eτ¼τP0
P
k0
;(7)
where k0¼R*
C0
P
with C0
P¼CPT0
ðÞand T
0
=τ(T
0
). Thus, the relation between τand Tis given by [Epele et al., 2007]
ln τ
T0
¼A
C0
P
ln T
T0
exp B
ATT0
ðÞ
þC
2AT2T2
0
:(8)
In the current work, we use the reference values P
0
= 1 bar and T
0
= 350 K that correspond to an altitude of
~50 km in the Venusian atmosphere [Seiff et al., 1985].
According to the general definition of the potential vorticity, θin equation (3) could be any conserved
scalar quantity that (for a nonbarotropic fluid) is a function of density and pressure only. Therefore, the
“extended”potential temperature eτdefined by Epele et al. [2007] is a valid alternative to potential tem-
perature. Since the difference between θand eτcan be larger than the estimated error at the upper limit
of the isentropic surface over which we calculate the EPV at the upper cloud level (see below), we use eτ
instead of θ. Thus, equation (3) becomes
qeζeτg∂eτ
∂P
:(9)
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GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 578
3.2. EPV at the Upper and
Lower Clouds
The horizontal spatial structure of q(x,y)
depends on the wind velocity field
that determines ζeτx;yðÞand on the
three-dimensional temperature struc-
ture through ∂eτ
∂Px;yðÞ. Thus, from our
previous analyses, we can compute
maps of the instantaneous distribu-
tion of q(x,y) for the upper cloud
layer. Temperature retrievals from
VIRTIS infrared spectra (summarized in
section 2.2) do not allow us to obtain
temperatures below 55 km altitude in
the Venus atmosphere. Therefore, we
cannot derive information about the
thermal distribution at the lower cloud
level (at about 43 km altitude) in the
same way as at the upper cloud’s level.
However, the ∂eτ
∂Px;yðÞterm can be
estimated from measurements of the
atmosphere’s static stability, defined
as ST¼dT
dzΓ
with Γ=g/C
P
being
the adiabatic lapse rate
dθ
dP¼θ
TST
1
ρg;(10)
and where hydrostatic equilibrium
is assumed [Sánchez-Lavega, 2011].
Definitions of eτand θin equations
(4)–(6) and direct numerical compari-
son result in
dθ
dP
≈
∂eτ
∂P;(11)
so we can use equation (10) and an
approximate evaluation of the static
stability at the lower cloud layer (that
will be presented in section 4.2.) to esti-
mate the ∂eτ
∂Px;yðÞterm at the lower
cloud’s level.
4. Results
4.1. Upper Cloud Level
4.1.1. Extended Potential
Temperature From 55 to 85 km
Figure 2 shows zonally averaged results
of the extended potential temperature
eτðÞcalculated from the thermal fields
for the three dates analyzed. The latitu-
dinal and vertical structure of eτis very
Figure 2. Zonally averaged extended potential temperature between 55
and 85 km altitude, on orbits (top) 038, (middle) 310, and (bottom) 475.
Data were averaged in 1° bins.
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GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 579
Figure 3. (left column) Altitude variation of the 330 K isentropic surface (with respect to the original geometry of the
observations) on orbits (top) 038, (middle) 310, and (bottom) 475. The white pixels and vertical lines are due to the lack
of thermal information. A certain degree of pixilation of these maps come from the noise present in the maps and depends
on the cloud model parameters used in the temperature retrieval [Garate-Lopez et al., 2015]. (right column) Altitude
variation over the solid lines displayed in Figure 3 (left column). Dashed lines depict the altitude uncertainty range. The
spatial resolution is 1 pixel ~ 16 km.
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 580
similar in the three cases. eτincreases with altitude showing a statically stable atmosphere, at least at the alti-
tude range 55–85 km (1–360 mbar). eτdecreases toward the south pole, this effect being stronger below
~66 km (~50 mbar). The results above 60 km altitude agree with the analysis by Piccialli et al. [2012] who used
the usual potential temperature θinstead ofeτ. At this altitude range, the polar atmosphere is slightly vertically
depressed with the largest decrease of altitudes for isentropic surfaces eτ¼constantðÞbetween 70°S and 80°S
(the poleward limit of the cold collar is usually observed in this latitude range). This sinking of the isentropic
surfaces with altitude toward the pole is not so strong as the one that occurs with the isobaric surfaces
(P= constant) [Piccialli et al., 2012] or with the sinking of cloud top altitude [Garate-Lopez et al., 2015].
However, below 60 km, the isentropic surfaces seem to increase with altitude as shown by Piccialli et al.
[2012]. The remarkable “cold collar”, located typically between 60°S and 75°S at 62 km altitude in the
averaged T(z,ϕ) maps [Garate-Lopez et al., 2015], disappears in the averaged eτ(z,ϕ) maps because of the
combined dependence of temperature and pressure with altitude and latitude.
Figure 3 displays the altitude variation of the 330 K isentropic surface for the three dates. This is the deepest
isentropic surface that can be continuously computed for the three orbits in all the pixels of the VIRTIS
images. The white pixels and lines are due to the lack of thermal information and the rectilinear structures
visible in the images due to the spatial resolution of the retrieval of the cloud parameters as discussed in
Garate-Lopez et al. [2015]. Results for a horizontal single line in the original images are also shown for com-
parison. The overall shape of the vortex at the cloud top is clearly distinguishable in these isentropic altitude
images. The vortex constitutes a depressed area where bright narrow features in the 3.8 or 5.1 μm images
(see Figure 1) are located slightly deeper in the atmosphere. The best results in terms of less noise and spatial
resolution are obtained in orbit 475, where the 330 K isentropic surface reaches the 360 mbar pressure in a
region that corresponds to the local maxima of brightness emission. This pressure corresponds to an altitude
of ~55 km. In the three orbits, the pressure along the 330 K isentropic surface varies by about 160–180 mbar,
which corresponds to altitude differences of about 4–5 km at these atmospheric levels, comparable to the
vertical scale height at these altitudes (~5.6 km). Plots on the right of Figure 3 show altitude variations of
2–3 km over horizontal distances of 240–300 km (from regions out of the warm vortex to its center) and
resolve some degree of spatial structure within the vortex.
The horizontal distribution of eτat the deepest level of the thermal analysis (360 mbar, ~55 km) is shown in
Figure 4. The small-scale vortex’s structure characteristic of the original images (Figure 1) is also present here.
Just as in the thermal structure at this vertical level, the vortex stands out as a hot region with slightly blurred
warmer filaments and surrounded by colder air. Extended potential temperature differences at this pressure
level can be as large as ~50 K between the cold collar and the vortex on the three orbits, agreeing with
Figure 4. Polar maps displaying the extended potential temperature distribution at ~360 mbar (~55 km) on orbits (left)
038, (middle) 310, and (right) 475. The estimated error at this pressure level is ~33 K. Latitude circles are plotted at 5°
intervals from the south pole. Labels correspond to local time in hours. The white pixels and lines are due to the lack of
thermal information, and the presence of large square pixels present in the maps depend on the cloud model parameters
used in the temperature retrieval [Garate-Lopez et al., 2015].
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 581
atmospheric temperature differences previously found [Garate-Lopez et al., 2015]. This means that the cold
collar and the warm vortex are dynamically separated.
4.1.2. Vertical Gradient of the Extended Potential Temperature
The vertical gradient of the extended potential temperature, ∂eτ
∂P, is the quantity that incorporates the thermal
structure into the definition of EPV in equation (9). This magnitude can also be used to measure the stability
of the atmosphere with respect to convection and defines those regions that are stable to vertical motions
∂eτ
∂P<0
. In our previous temperature analysis [Garate-Lopez et al., 2015], we studied the static stability of
the atmosphere, S
T
, which is equivalent to this magnitude but can be interpreted more easily. Since S
T
depends on vertical derivatives of temperature, it was necessary to use an adequate vertical discretization
that minimized errors in the vertical derivatives while preserving the information on S
T
. We calculated
the static stability for seven atmospheric layers between 55 and 85 km considering relatively thick vertical
layers that allowed to maintain the estimated static stability errors below ~10% of the adiabatic lapse rate
(Γ~ 10.4 K/km on Venus’s atmosphere). The thickness for each layer from top (~85 km) to bottom
(~55 km) was equal to 4.0, 3.2, 3.3, 3.7, 3.2, 4.9, and 7.3 km. We here consider the same seven atmospheric
layers to compute the vertical gradient of the extended potential temperature.
The zonally averaged distribution of ∂eτ
∂P(not shown here) presents a stratified, statically stable atmosphere
in this altitude range for the three dates, with absolute values increasing with altitude and no remarkable
Figure 5. Polar maps of the vertical gradient of the extended potential temperature (bottom) between 360 and 100 mbar
and (top) between 100 and 35 mbar levels on orbits (left) 038, (middle) 310, and (right) 475. The estimated errors are
0.13 K/mbar and 0.14 K/mbar for Figure 5 (bottom) and Figure 5 (top), respectively. Latitude circles are plotted at 5° intervals
from the south pole. The white pixels and lines are due to the lack of thermal information, and the presence of large square
pixels in the maps depend on the cloud model parameters used in the temperature retrieval [Garate-Lopez et al., 2015].
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 582
structure in any of the orbits. In contrast, the horizontal distribution does show structure, mainly in the low-
ermost layers. Figure 5 plots the spatial structure of ∂eτ
∂Pat the two lowermost layers which cover the altitude
range reported in the literature for the upper cloud (55–67 km). At the 55–62 km altitude range the fine-scale
structures show slightly smaller absolute values (less negative) than their immediate surroundings, implying
that the highly variable structures present within the vortex and seen as bright at ~5 μm images are slightly
less stable than any other region in the vortex. This is better appreciated in the case of orbit 475 where the
filament inside the vortex is completely recovered in the ∂eτ
∂Pmap. At 62–67 km layer, the vortex is clearly
distinguishable with a smaller absolute gradient than the area covered by the cold collar. In fact, the cold col-
lar shows the most negative values of ∂eτ
∂Pbeing, therefore, the most stable region in the polar area. These
results are fully consistent and equivalent to those obtained in our previous analysis of S
T
[Garate-Lopez
et al., 2015] and are here reiterated due to the role played by the ∂eτ
∂Pterm in the definition of EPV.
4.1.3. Ertel’s Potential Vorticity
We assume that the winds derived over the ~5 μm images are representative of the motions at theeτ¼330 K
isentropic surface which varies in the range 120–360 mbar or 55–61.5 km in different regions of the polar
area and dates (see Figure 3). This assumption is supported by the similarity of air temperature maps at
the eτ¼330 K isentropic surface (see Figure 6) with the spatial structure in the ~5 μm images (Figure 1).
Even if the motions are not exactly retrieved at a constant isentropic level, this assumption is still valid pro-
vided there is a small altitude difference between the isentropic surface and the vertical level where the
observed motions occur or a small vertical wind shear at this altitude level as found by Hueso et al. [2015].
Ertel’s potential vorticity (EPV) can then be calculated over the 330 K isentropic surface on the three
orbits. Figure 7 shows the horizontal distribution of EPV and separates the effects from the two terms
of equation (9) that define EPV (vertical component of the relative vorticity, ζeτ, and vertical gradient of
the potential temperature multiplied by gravity, g∂eτ
∂P). The white areas within the maps represent
regions where we do not have an adequate sampling of wind measurements to retrieve the relative
vorticity. We notice that the EPV does not retain the structure seen in the radiance image or in eτand
∂eτ
∂Pmaps, but it mostly resembles the distribution of the relative vorticity ζeτ.
We found previously that peaks of relative vorticity are generally surrounded by bright features as seen
in ~5 μm images [Garate-Lopez et al., 2013] and that these bright features are due to higher atmospheric
temperatures [Garate-Lopez et al., 2015]. Consequently, we now find that the warmest structures are located
coincident with local minima of EPV. The relation between high absolute potential vorticity values and colder
Figure 6. Polar projected maps of retrieved temperature over the 330 K isentropic surface on orbits (left) 038, (middle) 310,
and (right) 475. The estimated error is about 9 K on average. Latitude circles are plotted at 5° intervals from the south
pole. The white pixels and lines are due to the lack of thermal information, and the large square pixels present in the maps
depend on the cloud model parameters used in the temperature retrieval [Garate-Lopez et al., 2015].
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 583
temperatures is also seen on Earth’s stratospheric polar vortices at large spatial scales when the whole
stratospheric vortex (that can extend from the pole to latitudes lower than 60°) is observed [Schoeberl and
Hartmann, 1991].
The global EPV structure of the SPV of Venus at the upper cloud’s level does not show any strong latitudinal
gradient that could act as a mixing barrier to transported compounds. Interestingly, the structure of EPV map
of orbit 310 suggests the presence of a weak ring of potential vorticity that is not related to the morphology
of the vortex or to the temperature field (cold collar or warm vortex). However, the limited number of orbits
analyzed hinders the assessment of the significance of this feature.
Local minima and maxima of the EPV are found close to each other with differences of up to 4 PVU (potential
vorticity units; PVU ≡10
6
Km
2
kg
1
s
1
). The local maxima close to the south pole on orbits 310 and 475 are
probably due to numerical artifacts in the EPV derivations and should not be taken into account. Recall that
we have derived EPV in the region where we have simultaneous measurements of winds and temperatures,
resulting in a range of barely 20° in latitude around the pole and only on the nightside of the planet (due
to constraints imposed by the thermal retrieval). Thus, it is possible that our field of view of the SPV is not
large enough to distinguish the entire high EPV area and that we only see small-scale structures within a
larger vortex.
Figure 7. Polar maps of the vertical component of the (left) relative vorticity, (middle) g∂eτ
∂Pterm, and (right) potential
vorticity distribution at the 330 K isentropic surface on orbits (top) 038, (middle) 310, and (bottom) 475. Latitude circles
are plotted at 5° intervals from the south pole. The large white areas within the maps have been eliminated due to
the scarcity of wind measurements there. The white pixels and lines are due to the lack of thermal information, and
the large square pixels present in the maps depend on the cloud model parameters used in the temperature retrieval
[Garate-Lopez et al., 2015]. Units: 1 PVU = 10
6
Km
2
kg
1
s
1
.
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 584
4.2. Lower Cloud Level
On many dates, we obtained cloud
motion measurements for the deeper
cloud at ~ 43 km observed in nighttime
at 1.74 μm that are simultaneous to
those of the upper cloud [Garate-Lopez
et al., 2013]. However, temperature
retrievals of VIRTIS spectra do not sound
this deeper layer. In order to estimate
the potential vorticity of the lower
atmosphere, its thermal structure must
be inferred from other data sets.
Although temporal changes can be
expected, the temperature structure
of the Venus atmosphere at this alti-
tudelevelinbothpolarregionsas
derived from different experiments in
different epochs seems to be quite
steady [Seiff et al., 1985; Tellmann
et al., 2009]. Additionally, Yamamoto
and Takahashi [2015] showed results
from a Venusian middle atmosphere
general circulation model that predicts zonally uniform temperatures at this altitude. This is our working
hypothesis for the temperature structure at this altitude level.
Vertical profiles of static stability are available from in situ measurements performed by the Pioneer Venus
probes [Seiff et al., 1980] and from Pioneer Venus radio occultation measurements [Seiff et al., 1985].
Besides, the VIRA model [Seiff et al., 1985] integrates much of the practical knowledge of the Venusian
atmosphere prior to Venus Express. Profiles of static stability of the atmosphere at the four Pioneer Venus
probe entry sites show a stability peak at about 43 km altitude [see Seiff et al., 1980, Figure 17]. On the other
hand, the Pioneer Venus radio occultation data and the VIRA model present a smooth decrease of the atmo-
sphere’s static stability toward the pole [Seiff et al., 1985]. We have constructed a latitude-dependent distribu-
tion of S
T
at the lower cloud altitude based on a quadratic fit of the Pioneer Venus North probe that fell at
~60°N, Pioneer Venus radio occultation results at latitudes higher than 55°, and VIRA data between 60° and
90° (see Figure 8):
ST¼0:0045φ20:7853φþ34:8912:(12)
The global stability decay toward the pole agrees with experimental results from Tellmann et al. [2009], who
analyzed the VeRa radio occultation data from Venus Express and found that the stable layer below the upper
cloud does not appear in all their high latitude S
T
profiles, meaning that static stability values close to zero are
possible there. Imamura et al. [2014] used theoretical arguments to state that lower cloud convection and less
stability are caused by the lower solar irradiation on the upper cloud at high latitudes.
The low values of the static stability at high latitudes and the fit to several S
T
data sets represented by
Figure 8 means that our EPV results at the lower cloud levelshouldbeviewedcriticallyandconsideredonly
as a first-order assessment.
Using equations (10)–(12), the extended potential temperature definition and the same reference values of
P
0
= 1 bar and T
0
= 350 K as at the upper cloud’s level, it is possible to calculate the g∂eτ
∂Pterm appearing
in the definition of potential vorticity. The calculation is done for an average pressure level for the lower
cloud. We have used P= 2.2 bar and T= 378.5 K, based on the measurements of Pioneer Venus at ~43 km
altitude and between 55° and 90° [Seiff et al., 1985].
Combining this result with our previous measurements of the relative vorticity from the tracking of features
seen at 1.74 μm images [Garate-Lopez et al., 2013] and using equation (9), we have tentatively estimated the
Figure 8. Pioneer Venus’radio occultation (triangles) and VIRA (squares)
data between 60° and 90° have been used together with the measure-
ment of the Pioneer Venus North probe (dot) in order to describe the
static stability of the atmosphere at the 43 km altitude. The continuous
black line shows a 2° fit to all data. Dashed lines show the ± 1σcurves.
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 585
EPV distribution at the lower cloud’s level. Figure 9 shows the EPV maps, together with the two terms appear-
ing in equation (9), for orbits 038 and 310. Data from orbit 475 could not be used since the VIRTIS-M-IR images
at 1.74 μm were not good enough to provide cloud motion measurements. The white areas within the maps
represent regions where the lack of enough wind measurements prevents obtaining meaningful results.
Typical values of EPV at the lower cloud layer are on the order of 2.0 × 10
2
PVU.
A direct comparison of EPV at both cloud layers is not immediate. There is a difference of two orders of magnitude
in the potential vorticity, being higher at the upper cloud’s level (Figure 7) than at the lower cloud’s level (Figure 9).
This is due to two effects: on the one hand, the large variation of the g∂eτ
∂Pterm, which contains high values of
static stability in the upper cloud and much lower values in the lower cloud; and on the other hand, there is an
inverse variation with pressure in the definition of potential temperature. Note that the range at which g∂eτ
∂P
varies at 55–62 km is not enough to have a significant effect on the spatial distribution of potential vorticity, as
previously discussed. At the upper cloud the vorticity term dominates with respect to the thermal contribution
and determines most of the appearance of potential vorticity map. Contrarily, in the lower cloud level the slowly
varying values of g∂eτ
∂Pbetween 75°S and the south pole tend to homogenize the distribution of potential
vorticity, thereby smoothing the structure present in the relative vorticity map and impeding us from
characterizing the details of the potential vorticity at this lower depth.
In order to compare the values of EPV at both cloud layers, we have normalized q(x,y) in each layer by the
horizontal mean value of g∂eτ
∂P(not shown here). This technique has been used previously by Read et al.
[2009] and Piccialli et al. [2012] in global estimations of EPV at different altitudes in Saturn and Venus, respec-
tively. The normalized potential vorticity values at the upper cloud’s level (from 3.6 to 15.9 × 10
5
s
1
) are
3–4 times those at the lower cloud level (from 0.9 to 5.2 × 10
5
s
1
) meaning that the vortex strength is
higher at the upper cloud but extends toward the lower atmosphere. The spatial structure remains similar
to the not normalized EPV maps.
Figure 9. Polar maps of the vertical component of the (left) relative vorticity, (middle) g∂eτ
∂Pterm, and (right) potential
vorticity distribution at the lower cloud’s level on orbits (top) 038 and (bottom) 310 (bottom). Latitude circles are plotted
at 5° intervals from the south pole. The large white areas within the maps have been eliminated due to the scarcity of
wind measurements there. Units: 1 PVU = 10
6
Km
2
kg
1
s
1
.
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 586
4.3. Error Analysis
Combining the estimated errors of the thermal retrieval and the estimation of 3.5 × 10
5
s
1
error asso-
ciated to the maps of the vertical component of the vorticity, the error propagation from equation (9) results
in an average value of ~1.6 PVU for the Ertel’s potential vorticity at the upper cloud’s level for the three orbits.
Although there are many unknowns that complicate the EPV analysis and may enlarge the uncertainty of the
results, we consider this a good global estimation of errors. The main unknowns are (1) The analysis is
restricted to the nightside of the planet (we can obtain motions in the nightside and dayside but tempera-
tures are only available in the nightside). (2) The motions are obtained from the displacements of features
in ~3.8 or 5 μm thermal images that in fact correspond to a range of vertical altitudes that is difficult to
precisely constrain. Our calculation of EPV over an isentropic surface assumes that the vertical gradient of
Figure 10. Polar maps showing the short-term evolution of the (first and second rows) atmospheric temperature and
(third and fourth rows) g∂eτ
∂Pfields over the 330 K isentropic surface during orbit 475. From left to right and top to
bottom, data qubes correspond to VI0475_04, VI0475_08, VI0475_12, VI0475_16, VI0475_20, and VI0475_24 and are
separated by intervals of ~60 min with a total time of ~ 6 h (~1/9 of the rotation period of the vortex). The white pixels and
lines are due to the lack of thermal information, and the large square pixels present in the maps depend on the cloud
model parameters used in the temperature retrieval [Garate-Lopez et al., 2015].
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 587
motions is small enough to use the winds derived over the thermal images as representative of the motions
at the 330 K isentropic surface. (3) The limited vertical resolution in the thermal retrieval impedes investigat-
ing thermal variations at vertical scales lower than ~7 km in the layer between 55 and 62 km altitude (which is
of the order of the gas scale height).
At the lower cloud the error propagation results in an average uncertainty of ~2 × 10
2
PVU, when consider-
ing the ± 1σstandard deviation curves of the quadratic fit of Pioneer Venus and VIRA data as the S
T
error (see
Figure 8). At this level, we do not know the precise horizontal thermal structure and the static stability of the
atmosphere is estimated from data that come mainly from the northern hemisphere and previous missions
(not coinciding in time with our wind analysis). We assume that the wind measured using 1.74 μm images are
representative of the motions at the altitude where the static stability observed by Pioneer Venus and mod-
eled by VIRA shows a peak below 50 km. Nevertheless, we consider that these factors may have a limited
impact in the EPV calculation and that the EPV errors given above are large enough to encompass variations
associated to these factors.
All in all, the significance of the structures visible in EPV maps derived here can be estimated from the range
of variation in EPV that is 3 times larger than the uncertainties at both cloud levels. Although this is not an
optimal S/Nratio, EPV fields from VIRTIS data are likely to be the only available ones for the study of the vortex
because the Akatsuki spacecraft cannot observe the polar areas from its equatorial orbit.
4.4. Short-Term Evolution
In some of the Venus Express orbits, several high-resolution observations of the vortex were obtained every
15 min providing an excellent data set for short-term dynamics. We have extensively analyzed Venus EXpress
(VEX) orbit 475 grouping the data into six image pairs separated by 1 h. The total time covered is ~ 6 h (about
one ninth of the rotation period of the vortex). Each image pair has been used to obtain accurate wind
measurements and each VIRTIS qube to retrieve thermal profiles (as explained in section 2).
Figure 10 depicts the retrieved atmospheric temperatures and the term g∂eτ
∂Pover the 330 K isentropic
surface for six VIRTIS data qubes on orbit 475. Since the fine-scale features seen in 5 μm radiance images
are recovered in the temperature maps, radiance images are not shown. Some bins in boxes of 6 × 6 pixels,
as well as a few white bins, appear in the data. The former is due to the cloud parameters’analysis and the
latter because the temperature retrieval did not provide good results there [Garate-Lopez et al., 2015].
These polar projections show a counterclockwise cyclonic rotation of the vortex with only minor changes
in the fine-scale filamentary structure inside the vortex.
Figure 11 shows the short-term evolution of the vertical component of the relative vorticity field at the upper
cloud’s level and of Ertel’s potential vorticity distribution over theeτ¼330 K isentropic surface. Both variables
show essentially the same spatial variation. Local minima and maxima, which apparently extend over time,
are found in all the six qubes, but we do not see any clear rotation of the structures appearing in the EPV
maps as we do in the evolution of the temperature (and radiance) field. This result is surprising since the
EPV is expected to be a conserved quantity and, therefore, a tracer of fluid motions for atmospheric flows.
Taking into account the unpredictable and highly variable nature of the vortex, we could speculate about
possible sinks and sources of potential vorticity at the polar region of Venus’s atmosphere, but the lack of
correlation between the behavior of the thermal and EPV structures is more likely related to the large errors
(about one third of the EPV) and the reduced spatial resolution of about 525 km (due to the spatial derivatives
in the relative vorticity) in our analysis. Interestingly, the anticorrelation between warm features at 360 mbar
(~55 km) and high values of EPV remains.
The mean structure observed in the EPV maps in this sequence points to a weak ring of potential vorticity
which is particularly clear in the second map in the sequence (VI0475_08 data qube) or when averaging all
six panels. This structure is also present in the EPV map corresponding to orbit 310 at the upper cloud’s level
(Figure 7). This feature, the weak vorticity ring, not centered in the pole, appears in approximately half of the
EPV maps of the upper cloud. However, the low number of orbits analyzed and the limited spatial coverage
inhibit us from infering conclusions about the significance of this ring. If confirmed, the ringed structure of vor-
ticity would be a trait in common with Mars’polar vortices [Mitchell et al., 2014], while the extended structure of
the vortex along large vertical scales (it extends vertically at least 20 km) is similar to Earth’s polar vortices.
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 588
Hence, Venus’SPV apparently shares features with Mars’and Earth’s polar vortices and may therefore be an
intermediate case between both atmospheres.
5. Discussion
The SPV has been continuously observed during the VEX mission (from 2006 till 2008 by VIRTIS and VMC
instruments and from 2008 till 2014 by VMC showing only the external part of the vortex), so it can be
considered as a long-lived feature of Venus’atmospheric dynamics. Because of the hemispheric symmetry
of the general circulation of Venus at cloud level [Limaye, 2007; Peralta et al., 2007], and the similarities of
thermal structures found by the Venus Express VeRa and VIRTIS-H instruments on both hemispheres
Figure 11. Polar maps showing the short-term evolution of the vertical component of the (first and second rows) relative
vorticity field and (third and fourth rows) Ertel’s potential vorticity distribution over the 330 K isentropic surface during orbit
475. From left to right and top to bottom, data qubes correspond to VI0475_04, VI0475_08, VI0475_12, VI0475_16,
VI0475_20, and VI0475_24 and are separated by intervals of ~60 min with a total time of ~ 6 h (~1/9 of the rotation period
of the vortex). The large white areas within the maps have been eliminated due to the scarcity of wind measurements there.
The white pixels and lines are due to the lack of thermal information, and the large square pixels present in the maps
depend on the cloud model parameters used in the temperature retrieval [Garate-Lopez et al., 2015].
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 589
[Tellmann et al., 2009; Migliorini et al., 2012], we conjecture that the same conclusion is valid for the northern
polar vortex observed in the Mariner 10 and Pioneer Venus epochs. This is in contrast to Earth and Mars
vortices that show an annual trend of formation and destruction linked to the seasonal insolation cycle
[Schoeberl and Hartmann, 1991; Kieffer et al., 2000]. The vortices on these two planets are related to their sur-
face structure and icy polar caps, which is not the case of Venus. Venus polar vortices are embedded within
the clouds, at ~10 scale heights above the surface, whereas Earth’s polar vortex is located at ~2 scale heights
from the surface and essentially no clouds form on them. On Venus heat deposition at the polar cloud level is
probably a basic ingredient in driving the formation of the warm polar vortices, a mechanism that does not
play any role on Earth and Mars. Apparently, Venus’polar vortices are free, high-altitude atmospheric features
not linked to Venus’polar topography. In all three planets, the vortices extend meridionally from the pole to
latitudes close to ~60° [Garate-Lopez et al., 2013; Mitchell et al., 2014] or down to even lower latitudes in the
case of the Earth [Waugh and Polvani, 2010].
On Earth, the polar vortices extend vertically from the tropopause (~10 km) up to ~50 km [Schoeberl and
Hartmann, 1991], but they intensify their circulation at ~35 km in the stratosphere (in particular during winter
time over Antarctica). Earth’s polar vortices are highly variable with velocities up to 90 m/s at the stratospheric
polar jet [Schoeberl and Hartmann, 1991; Waugh and Polvani, 2010]. On Mars, polar vortices have been traced
at about 40 km altitude by Mitchell et al. [2014], who found that the mean strength of the jet maximum is
~70 m/s in the southern hemisphere winter and ~130 m/s in the northern hemisphere winter. On Venus,
the polar vortices have been observed to exist from ~43 km to 80 km, intensifying at the upper cloud level
about 63 km altitude [Garate-Lopez et al., 2015]. Contrarily to what happens on Earth and Mars, Venus’s
SPV does not seem to be related to a polar jet since we did not see any localized jet in the instantaneous
[Garate-Lopez et al., 2013] or mean wind fields [Hueso et al., 2015].
The comparison of polar maps of the EPV in the three planets shows similarities and differences. On Venus
and Earth, the EPV field shows typical concentration of vorticity patches with maximum values of about
5 PVU at 55–62 km on Venus (Figure 7) and 1200 PVU at ~35 km on Earth [Clough et al., 1985]. Zonal wave
numbers 1 and 2 are typically observed on Earth, but on Venus more variability is found. On both planets
the EPV is of the same order of magnitude (0–10 PVU) close to the tropopause (at ~60 km on Venus, see
Figure 7, and at ~10 km on Earth [Kunz et al., 2011]). The EPV decrease by 2 orders of magnitude in approxi-
mately 20 km altitude variation is also a common characteristic of Venus’(Figures 7 and 9) and Earth’s polar
vortices [Clough et al., 1985; Kunz et al., 2011; Harvey et al., 2009].
On Mars, the vortex has a ring-like structure with EPV values of ~10
3
–10
4
PVU at ~35 km altitude [Mitchell
et al., 2014; Montabone et al., 2014]. Some of the Venusian EPV maps presented in this paper hint at a weak
ringed structure around the vortex in the upper cloud region. We do not find a correlation between the
ringed structure and the vortex morphology or temperature field (cold collar or warm vortex). On orbits
310 and 475 the weak ring is observed in those regions where the zonal wind decreases more rapidly toward
the pole (in agreement with the second term of equation (1)). On orbit 038 the zonal wind shows a similar
decrease toward the pole, but the vorticity ring is not seen in the EPV maps. Hence, the weak vorticity ring
seems to grow from the combination of the three terms in equation (1). Importantly, we must recall that
we have analyzed a limited number of dates and that the EPV maps have been derived in the region where
we have simultaneous measurements of winds and temperatures resulting in a range of barely 20° in latitude
around the pole and only on the nightside of the planet. Thus, it is possible that our limited perspective of the
south polar region impedes us from distinguishing the entire high EPV area and that we only see small-scale
structures within a larger vortex.
On Earth, if we compare the shape of the polar vortex (defined by an ellipse covering the whole vortex), we
see that it rotates with height in the Northern Hemisphere [Mitchell et al., 2014]. On Mars, the orientation of
the polar vortex can change strongly from one day to another during certain times of the season, but it
remains remarkably coherent with height at all times. However, the horizontal projection of the Martian
vortices decreases dramatically with height. In terms of cloud morphology, the SPV of Venus preserves its glo-
bal shape (oval, circular, or irregular shape seen as a bright region at the upper cloud level) throughout 20 km
in the vertical, but the fine-scale structure is different at the lower and upper cloud levels (see Figure 1).
However, it is difficult to study the vertical coherence of its EPV distribution since the area where motions
can be retrieved at the upper and lower cloud levels is not exactly the same, we cannot retrieve the exact
thermal field in the lower cloud level, and because of the limited number of orbits analyzed.
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 590
The comparison between the three planets shows that the Venus polar vortices are weaker in terms of the
EPV by 3 to 4 orders of magnitude relative to those of Earth and Mars. However, they are permanent, which
is not the case for Earth and Mars. This reflects the differences between the three planets in the ingredients
involved in the recipe of their formation: planetary rotation (fast and similar on Earth and Mars; slow in
Venus), seasonality (fundamental in Earth and Mars; lacking on Venus), role played by the surface (fundamen-
tal in Earth and probably Mars; not apparent on Venus), and heat deposition on clouds (essential for Venus;
absent in Earth and Mars). Titan’s polar vortex [Teanby et al., 2008; de Kok et al., 2014; West et al., 2015] could
represent an interesting case for future studies since the polar clouds show the emergence of a seasonal
cloud similar in shape to Venus SPV. Additionally, Titan’s intermediate rotation rate between Venus and
Earth-Mars and the presence of strong seasonal effects like Earth and Mars add intriguing properties to the
polar vortices puzzle.
So far, there have been few attempts to model the structure and dynamics of Venus’polar vortices. On the
one hand, Limaye et al. [2009] tried to simulate the S-shape feature observed in VIRTIS images during the early
stage of the Venus Express mission by means of a two-dimensional nonlinear, nondivergent barotropic
model. On the other hand, Lee et al. [2010] investigated the cloud structures produced by the circulation
and eddy transport by implementing a passive cloud condensation scheme into a Venus general circulation
model with a superrotating middle atmosphere. However, these two works fail to reproduce the highly vari-
able morphology of the vortex. Yamamoto and Takahashi [2015] have investigated the polar vortex in the
presence of a thermal tide with a Venus middle atmosphere general circulation model. In that model the
warm polar air mass at the cloud top is maintained by the thermal wind associated with a high-latitude jet,
and the cold collar is enhanced by a polar diurnal tide. Interestingly, the geometric center of their warm oval
is displaced from the pole about 10° by the diurnal tide, and transient dipole and tripole structures appear as
a consequence of the superposition of a transient baroclinic wave and a diurnal thermal tide. However, the
model implied thermal tides that are stronger than those so far measured in the Venus polar atmosphere
[Peralta et al., 2012].
To date no study has established a link between the cloud morphology of the Venus’polar vortex, its motions,
and its relation with the overall atmospheric dynamics. Therefore, extending the study of long- and short-
term evolution of the Ertel’s potential vorticity will help understand the dynamics of the vortex. Further
studies would also include the calculation of EPV at higher altitude levels by estimating the thermal winds
by an appropriate cyclostrophic wind equation for polar latitudes.
6. Summary
Venus’south polar vortex (SPV) is a long-lived, highly variable structure of Venus’atmosphere subject to strong
changes and erratic motions around the south pole [Piccioni et al., 2007; Luz et al., 2011; Garate-Lopez et al.,
2013]. This is related to the fact that the motions defining the vortex are weak when compared to the envir-
onmental winds in its surrounding region. From the point of view of relative vorticity the vortex is a weak
cyclone. However, the thermal imprint of the vortex is strong with large differences of temperature at the
same pressure level.
We summarize the main conclusions from this study in the following:
1. The vortex is a highly vertically depressed structure when observed in isentropic surfaces from 55 to
85 km, at least in the three dates analyzed here. The 330 K isentropic surface (the deepest we have access
to in all the pixels of the VIRTIS images) varies from 62 km altitude at the cold collar region to 55 km inside
the vortex. The vortex itself experiences a strong altitude variation of 2–3 km in horizontal distances of
240–300 km between regions out of the warm vortex and its center over the 330 K isentropic surface.
This is most probably related to the global atmospheric circulation formed by a meridional Hadley cell
that transports air from higher altitudes downward at the polar region, heating the air and forming the
vertically depressed structure [Read, 2013].
2. Ertel’s potential vorticity’s horizontal distribution at the upper cloud’s level does not retain the structure
seen in the radiance image or in the temperature maps but resembles the distribution of the relative
vorticity. The kinetic component dominates with respect to the thermal structure at the upper cloud’s
level, while in the lower cloud’s level the low g∂eτ
∂Pvalues tend to homogenize the EPV distribution
between 75° and 90°S with respect to ζeτdistribution.
Journal of Geophysical Research: Planets 10.1002/2015JE004885
GARATE-LOPEZ ET AL. VENUS POLAR VORTEX’S POTENTIAL VORTICITY 591
3. The warm highly variable fine-scale features seen in the ~5 μm images that define the SPV of Venus are
located in regions where the EPV over the 330 K isentropic surface is locally minimum. This is remarkable
since the relation between high absolute potential vorticity values and colder temperatures is also seen
on Earth’s stratospheric polar vortices.
4. Although a clear rotation of the general EPV distribution is not appreciated in the short-term evolution, as
it is in radiance and temperature maps, the anticorrelation between warm features at 55–62 km and high
values of EPV over the 330 K isentropic surface (located at the same altitude range) remains.
5. The structure observed in many of the EPV maps at the upper cloud’s level point to a weak ring of poten-
tial vorticity without any strong latitudinal gradient of EPV, as should be expected in the presence of a
mixing barrier. However, the limited number of orbits analyzed does not allow us to draw a clear conclu-
sion about the significance of this feature. Nevertheless, local minima and maxima of EPV are found close
to each other with differences of up to ~4.0 ± 1.6 PVU.
6. Values of EPV at the lower cloud are only tentative and represent the mean EPV at this layer (2 × 10
2
PVU)
and the range of variation expected due to the vortex (2 × 10
2
PVU).
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Acknowledgments
The data for this paper are available at
ESA’s Planetary Science Archive in
Venus Express/VIRTIS instrument’s data
set (ftp://psa.esac.esa.int/pub/mirror/
VENUS-EXPRESS/VIRTIS/). The data sup-
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requested from Itziar Garate-Lopez
thank ESA for supporting the Venus
Express mission, ASI (by the contract
I/050/10/0), CNES, and the other
national space agencies supporting the
VIRTIS instrument on board Venus
Express and their principal investigators
G. Piccioni and P. Drossart. This work
was supported by the Spanish project
AYA2012-36666 with FEDER support,
Grupos Gobierno Vasco IT-765-13, and
Universidad País Vasco UPV/EHU
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