# A Hexagon in Saturn’s Northern Stratosphere Surrounding the Emerging
Summertime Polar Vortex

L.N. Fletcher*1 G.S. Orton2 J.A. Sinclair2 S. Guerlet3 P.L. Read4 A. Antuñano1
R.K. Achterberg5 F.M. Flasar6 P.G.J. Irwin4 G.L. Bjoraker6 J. Hurley7 B.E.
Hesman8 M. Segura6 N. Gorius9 A. Mamoutkine6 & S.B. Calcutt4

###### Abstract

Saturn’s polar stratosphere exhibits the seasonal growth and dissipation of
broad, warm, vortices poleward of $\sim 75^{\circ}$ latitude, which are
strongest in the summer and absent in winter. The longevity of the exploration
of the Saturn system by Cassini allows the use of infrared spectroscopy to
trace the formation of the North Polar Stratospheric Vortex (NPSV), a region
of enhanced temperatures and elevated hydrocarbon abundances at millibar
pressures. We constrain the timescales of stratospheric vortex formation and
dissipation in both hemispheres. Although the NPSV formed during late northern
spring, by the end of Cassini’s reconnaissance (shortly after northern summer
solstice), it still did not display the contrasts in temperature and
composition that were evident at the south pole during southern summer. The
newly-formed NPSV was bounded by a strengthening stratospheric thermal
gradient near $78^{\circ}$N. The emergent boundary was hexagonal, suggesting
that the Rossby wave responsible for Saturn’s long-lived polar hexagon - which
was previously expected to be trapped in the troposphere - can influence the
stratospheric temperatures some 300 km above Saturn’s clouds.

Department of Physics & Astronomy, University of Leicester, University Road,
Leicester, LE1 7RH, UK (*Corresponding author leigh.fletcher@le.ac.uk).

Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove
Drive, Pasadena, CA, 91109, USA.

Laboratoire de Meteorologie Dynamique/IPSL, Sorbonne Université, École normale
supérieure, PSL Research University, École polytechnique, CNRS, F-75005 Paris,
France.

Department of Physics (Atmospheric, Oceanic and Planetary Physics), University
of Oxford, Parks Rd, Oxford, OX1 3PU, UK.

Department of Astronomy, University of Maryland, College Park, MD 20742, USA.

NASA/Goddard Space Flight Center, Greenbelt, Maryland, 20771, USA

STFC Rutherford Appleton Laboratory, Harwell Science and Innovation Campus,
Didcot, OX11 0QX, UK.

Space Telescope Science Institute (STScI), 3700 San Martin Drive Baltimore, MD
21218, USA.

Department of Physics, The Catholic University of America, Washington, DC
20064, USA.

## Introduction

Polar vortices are important features of planet-wide atmospheric circulation
systems on terrestrial worlds and giant planets alike, from Jupiter’s
turbulent polar environment[1], to Uranus’ seasonal polar hood[2], and
Neptune’s warm south polar vortex[3]. Saturn’s axial tilt of $26.7^{\circ}$
renders its seasonally-illuminated poles readily accessible from Earth,
providing the paradigm for testing our understanding of the interplay between
dynamics, chemistry, cloud formation and auroral processes in shaping giant
planet polar environments. Saturn’s stratosphere, some 200-300 km above the
clouds, exhibits the growth and dissipation of broad, warm polar vortices over
seasonal timescales (Saturn’s orbit spans 30 Earth years), which are strongest
in the summer and absent during winter[4, 5]. These vortices, which extend
$\sim 15^{\circ}$ latitude away from the pole, are bounded by a strong
latitudinal temperature gradient and are distinct from the compact,
seasonally-independent polar cyclones present in the troposphere[6, 5, 7, 8,
9, 10]. It has not been previously possible to constrain the formation
timescales of Saturn’s stratospheric vortices. By the time the Keck
observatory observed Saturn in February 2004 (a planetocentric solar longitude
of $L_{s}=287^{\circ}$), 16 months after southern summer solstice (October
2002), the warm South Polar Stratospheric Vortex (SPSV) was already well
established poleward of $70^{\circ}$S[4]. Half a Saturnian year earlier, when
the NASA Infrared Telescope Facility observed Saturn’s North Pole in March
1989 ($L_{s}=104.5^{\circ}$), 15 months after the northern summer solstice
(December 1987), the warm North Polar Stratospheric Vortex (NPSV) could
already be seen[11]. The longevity of Cassini’s exploration of Saturn
(2004-2017) now provides the first complete dataset to trace the growth of the
NPSV, as Saturn reached northern summer solstice ($L_{s}=90^{\circ}$) in May
2017.

Previous work used 7-16 $\mu$m infrared spectroscopy obtained by the Cassini
spacecraft[12] to trace the dissipation of the SPSV from northern winter (July
2004, $L_{s}=293^{\circ}$) to northern spring (June 2014, $L_{s}=56^{\circ}$).
However, the seasonal evolution in the northern hemisphere was less dramatic:
although the north had been warming, as expected from radiative and dynamical
climate models [13, 14, 15], there was no sign of the sharp latitudinal
thermal gradients (and hence vertical windshear) that had been associated with
the SPSV at the beginning of Cassini’s mission. This suggested[12] that the
NPSV might begin to form during the remaining years of the Cassini mission
(2014-2017, $L_{s}=56-93^{\circ}$), during late spring or early summer.

Theoretical expectations for the warming and cooling of Saturn’s stratosphere
are hampered by an incomplete knowledge of both the distribution of opacity
sources contributing to the radiative balance[16, 14, 13]; and of
contributions from dynamical upwelling and subsidence[17, 14]. In particular,
the primary stratospheric coolants (ethane and acetylene) are spatially and
temporally variable due to both photochemistry and atmospheric circulation[18,
19, 20, 21, 22, 23, 24], and the rarity of studies constraining the properties
of polar stratospheric aerosols prevents a comprehensive assessment of their
contribution to the radiative budget[13, 25, 26]. Whilst subsidence within the
vortices might be expected to cause heating by adiabatic compression, the
increased hydrocarbon and aerosol abundances could balance this by enhanced
radiative cooling, rendering this coupled radiative-dynamical-chemical balance
extremely complex.

Here we provide observational evidence for the development of localised
thermal and compositional gradients to understand the formation timescales of
the NPSV, and present the final status of Saturn’s polar stratosphere at the
end of the Cassini mission. Furthermore, the spatial resolution and
sensitivity provided by the Composite Infrared Spectrometer (CIRS)[27] reveal
a significant surprise: the NPSV exhibits a hexagonal boundary that mirrors
the well-studied hexagonal wave in Saturn’s troposphere[28, 29, 30]. The
meandering of the jet that forms the hexagon is believed to be a Rossby
wave[31] resulting from an instability of the eastward zonal jet near
$78^{\circ}$N[32, 33, 29, 34] and trapped within a waveguide formed by the
zonal jets and Saturn’s vertical static stability profile. We show here that
Saturn’s famous hexagon is not always restricted to the troposphere, but can
persist high in the stratosphere in the spring/summer, creating a hexagonal
structure that spans more than $\sim 300$ km in height from the clouds to the
stratospheric polar vortex.

## Results

###  0.1 Hexagonal boundary of the NPSV.

This study uses nadir-sounding spectroscopy from Cassini’s Composite Infrared
Spectrometer (CIRS)[27, 35], a 10-1400 cm-1 Fourier Transform Spectrometer
with programmable spectral resolution between 0.5-15.5 cm-1. We utilise the
mid-infrared Michelson interferometer (600-1400 cm-1), which featured two
arrays of $1\times 10$ HdCdTe detectors, each with an instantaneous field of
view of $0.27\times 0.27$ mrad. Spectra are inverted using an optimal
estimation retrieval algorithm[36, 37] to characterise the upper tropospheric
(80-300 mbar) and stratospheric (0.5-5.0 mbar) temperatures and
composition[38] as a function of time (see Methods). Before performing
spectral inversions, we begin with an investigation of the polar morphology
observed in the raw brightness temperatures.

Fig. 1 displays spatially resolved maps of CIRS brightness temperatures from
2013 to 2017. These are brightness temperatures averaged over the CH4 Q band
emission between 1280-1320 cm-1, and represent the kinetic temperatures over a
broad range of altitudes between 0.5-5.0 mbar[38]. For the purpose of these
observations, the CIRS focal plane was slowly scanned from north to south as
the planet rotated beneath over one or two rotations (10-20 hours).

Four features are immediately evident in the maps. Firstly, the brightness
temperature has increased by approximately 10 K during the four years shown in
this figure. Secondly, the compact polar cyclone[5] is evident in the centre
of each image, related to a strong negative vertical shear on the zonal jet at
$87\pm 1^{\circ}$N (see below). Thirdly, a boundary can be seen near 78∘N in
the later images, separating cooler low-latitude temperatures from warmer
polar temperatures and suggesting the strengthening of the temperature
gradient there. Finally, and most surprising, the boundary appears to have a
hexagonal appearance in many of these images. Cassini demonstrated that
Saturn’s famous hexagonal wave[28], observed at the cloud tops ($p\sim 500$
mbar) since the Voyager era, was related to hexagonal temperature contrasts
reaching as high as Saturn’s tropopause ($p\sim 80-100$ mbar)[5]. However, at
the conclusion of the 2004-2014 study[12], the north polar stratosphere did
not exhibit enough of a latitudinal temperature gradient
($\partial{T}/\partial{y}$, where $y$ is the north-south distance) to observe
any contrast associated with the jet at $78^{\circ}$N. This is therefore the
first evidence that Saturn’s hexagon extends far higher than previously
thought, into the stably-stratified middle atmosphere to the 0.5-5.0 mbar
level.

There are limitations to what the CIRS observations can tell us. An attempt to
provide a spatially-resolved temperature retrieval of the stratospheric
hexagon was unsuccessful, as the binned spectra did not have sufficient
signal-to-noise to constrain the hexagonal shape of the temperature field as a
function of altitude. We therefore cannot tell whether the hexagon is present
at 5 mbar or at 0.5 mbar, or a combination of both. However, data presented in
the next section indicates that Saturn’s banded structure is clearer at 5 mbar
than at lower pressures, raising the likelihood that the hexagon is only
detectable in the lower stratosphere ($p>1$ mbar). Furthermore, the low signal
in the pre-2014 data means that we cannot distinguish between scenarios where
the hexagon is always present in the stratosphere irrespective of season, or
the hexagon is allowed to extend upwards due to the seasonally-changing
temperatures as summer solstice approaches (to be discussed below).

Fig. 2 displays both a periodogram analysis and an attempt to fit a simple
sinusoidal shape to the hexagon brightness temperatures in 2014 and 2017. The
wavenumber-6 pattern is clearly detected in both the troposphere and
stratosphere, and we find that the hexagon vertices differ in position by no
more than $4^{\circ}$ longitude between the two altitudes, so there appears to
be no longitudinal translation in the pattern with height. Using the
tropospheric maps, we find a clockwise (westward) translation of the hexagon
pattern with time, equating to $((9.9\pm 1.3)\times 10^{-3})^{\circ}$/day
(using the System III West Longitude System). Performing the same calculation
in the stratosphere yields $((7.6\pm 1.9)\times 10^{-3})^{\circ}$/day, such
that the rotation rates are equivalent to within the uncertainties. Given that
precise identification of the vertex longitudes is limited by the low spatial
resolution and noise of the thermal maps, this drift rate is likely consistent
with the $((12.8\pm 1.3)\times 10^{-3})^{\circ}$/day estimate[29] from
tracking the hexagon at the cloud tops between 2008 and 2014. The hexagon is
therefore present in a least three altitude ranges separated by three decades
of pressure, from the deep 2-3 bar troposphere[8] to the tropopause[5] and
into the stratosphere; a vertical distance of $\sim 300$ km. Finally, we note
that the tropospheric hexagon vertices do not move with the $\sim 120$ ms-1
eastward cloud-top velocity of the jet at $78^{\circ}$N, so despite the strong
windshear from the troposphere to the stratosphere (next section), the
presence of a coherent wave in both altitude domains, with a coupled and very
slow rotation, is plausible irrespective of the winds. The long-term
temperature changes that allowed the hexagon to be visible in the stratosphere
after 2014 will be explored in the next section.

Figure 1: Brightness temperature maps of the north polar stratosphere from
2013 to 2017. Brightness temperatures were averaged over the 1280-1320 cm-1
range sensing 0.5-5.0 mbar, and each map has the same temperature scale. The
figure indicates the hexagonal boundary to the polar stratospheric hood. The
panels provide maps for (a) August 17, 2013, (b) October 18, 2014, (c) June 9,
2016, (d) September 20, 2016, (e) November 8, 2016, (f) February 12, 2017, (g)
April 17, 2017, (h) August 26, 2017. Maps with spectral resolutions of 2.5
cm-1 (REGMAPs) and 15.0 cm-1 (FIRMAPs) were used here, spanning Cassini’s
solstice mission and proximal orbits. These data were obtained from a
relatively high orbital inclination to facilitate views of the north pole.
Spectra have been averaged on an equal-area projection to reduce noise.
Regions of dark blue represent missing data and defects - in particular, the
central polar cyclone was partially obscured in the final FIRMAP of the
mission acquired in August 2017 (panel h). The hexagonal boundary near 78-80∘
latitude is clearest in the October 2014 (b), November 2016 (e) and February
2017 (f) data. The sinusoidal variation of temperature is shown in Fig. 2e-f
for two dates.

Figure 2: Detection of the hexagon in the troposphere and stratosphere. Panels
c-f show brightness temperatures and their uncertainties in the troposphere
(c-d, averaged over 600-620 cm-1) and stratosphere (e-f, averaged over
1280-1320 cm-1) extracted from $77-79^{\circ}$N in the June 25, 2014 and
February 12, 2017 REGMAP observations, and the October 18th 2014 FIRMAP
observation. As a guideline, a wavenumber-6 sinusoid has been fitted to each
observation (red curve), although the stratospheric map in 2014 is extremely
noisy. Panels a, b, g and h show the corresponding Lomb Scargle
periodograms[5], displayed as a function of latitude, showing the spectral
power contained in each longitudinally-resolved brightness temperature scan.
Black lines on the colour bars represent false-alarm probabilities (from top
to bottom) of 0.001, 0.01 and 0.1. A wavenumber-6 feature is clear in each
dataset near 78∘N (vertical red dashed line), although the 2014 stratospheric
hexagon is rather noisy (Fig. 1b). Using the sinusoidal fits, we detect a
westward shift in the tropospheric hexagon vertices of $8.5\pm 1.1^{\circ}$
over 963 days (the uncertainty comes from the quality of the sinusoidal fit).
Offsets between the tropospheric and stratospheric vertices were $<4^{\circ}$
in February 2017.

###  0.2 Long-term temperature trends.

Figure 3: Retrieved temperatures in the upper troposphere and stratosphere
from the entire Cassini mission. Temperatures are displayed at five pressure
levels: (a) 0.5 mbar, (b) 1.1 mbar, (c) 2.5 mbar, (d) 5.0 mbar, and (e) 110
mbar. Colours refer to dates given by the legend. Saturn’s equatorial
oscillation is observed at low latitudes[39], the effects of the Great
Northern Storm are visible at northern mid-latitudes[40], and the reversal of
the stratospheric temperature asymmetry is most evident at the poles (this
work).

Figure 4: North and South polar stratospheric temperature gradients as a
function of time throughout the whole Cassini mission, 2004-2017. We display
north polar temperatures (panels a-c), north polar windshears (panels d-f),
south polar windshears (panels g-i) and south polar temperatures (panels j-l)
at three different pressure levels (0.5, 1.0 and 5.0 mbar). These were derived
from averages of low-resolution CIRS spectra on a monthly temporal grid, and
interpolated using tensioned splines[41] to reconstruct a smoothed temperature
field. Horizontal dashed lines signify the peak of eastward zonal jets in the
troposphere[9]. The data are displayed as a function of time (years), but a
second horizontal axis provides the planetocentric solar longitude ($L_{s}$)
in degrees.

Fig. 3 displays the temperatures retrieved for each latitude (averaging
spectra over longitude, see Methods) for a selection of stratospheric
pressures as a function of time. These are interpolated in Fig. 4 to display
the reconstructed temperatures for the North Pole and the South Pole for three
altitudes (0.5, 1.0 and 5.0 mbar) in the stratosphere. Assuming geostrophic
balance (a valid assumption at polar latitudes with Rossby numbers less than
0.2[29]), meridional temperature gradients ($\partial{T}/\partial{y}$, where
$y$ is the north-south distance) are in thermal wind balance with the vertical
shear on the zonal winds[42] ($\partial{u}/\partial{z}$, where $u$ is the
zonal wind and $z$ is altitude). This allows us to estimate the windshear
$\partial{u}/\partial{z}=-(g/fT)\partial{T}/\partial{y}$, where $g$ is the
gravitational acceleration for each latitude and altitude, and $f$ is the
Coriolis parameter. This provides us with a means of expressing the changing
meridional gradients as a function of time, where the windshear can be
interpreted as enhancing eastward winds (positive shear) or westward winds
(negative shear) if a level-of-zero-motion exists somewhere in the lower
stratosphere. Tropospheric temperatures and windshear are shown in the
Supplementary Figure 1.

Fig. 4 allows us to compare the disappearance of the warm SPSV to the onset of
the NPSV. Warm stratospheric polar vortices become evident when strong
temperature gradients develop over time, strengthening negative windshear to
promote westward winds.. The zonal mean temperatures reveal latitudinal
gradients that are strongest at 5 mbar, reminiscent of the banded structure
that dominates in the troposphere. These contrasts are not as apparent at
0.5-1.0 mbar, where temperatures vary more smoothly with latitude and are
dominated by negative shear poleward of the prograde zonal jets at
$78^{\circ}$N and $74^{\circ}$S. At the start of the Cassini time series, the
SPSV had two primary structures: the negative $dT/dy$ near $88^{\circ}$S that
defines the edge of the compact polar cyclone[4], and the negative $dT/dy$
near $74^{\circ}$S that represents the edge of the SPSV[5] (Fig. 4j-l). In
2006 ($L_{s}=320^{\circ}$) temperatures increased towards the South Pole at
all altitudes, but in 2007-2008 a cool band began to form at 5 mbar centred on
$84^{\circ}$S, signified by the onset of the positive windshear in Fig. 4g-j.
By 2013-2014 ($L_{s}\approx 40^{\circ}$), the negative shear at the SPSV
boundary ($74^{\circ}$S) had weakened considerably and a cool band was
beginning to form near $80-85^{\circ}$S at 1 mbar, signifying the demise of
the SPSV. The cooling and dissipation of the SPSV started pre-equinox
($L_{s}\approx 340^{\circ}$), as measured from the timing of the most negative
windshear at $74^{\circ}$S.

The latitudinal structure of the vertical windshear in the northern hemisphere
(Fig. 4d-f) is remarkably similar to that in the south, with higher pressures
exhibiting banded temperature structures and lower pressures exhibiting smooth
latitudinal gradients. Negative windshear dominates poleward of $78^{\circ}$N
and $p<1$ mbar throughout the time series, because temperatures have always
increased towards $90^{\circ}$N despite the sequence starting in polar winter,
counter to the expectations of radiative climate models[13, 12, 43]. A 5-mbar
region of positive windshear (Fig. 4c,f, i.e., a cool band, mirroring the one
that formed in the SPSV) was centred on $83^{\circ}$N until 2017, when it had
weakened and was replaced by warmer temperatures (i.e., 5-mbar temperatures
increased everywhere poleward of $\sim 75^{\circ}$N by the end of the
mission). Similar positive windshear bands, centred over the broad westward
tropospheric jets, existed at $73\pm 1^{\circ}$N and $63\pm 1^{\circ}$N, but
these all weakened as Saturn approached solstice, indicating a positive
$dT/dy$ gradient throughout the north polar region. In particular, the
temperatures near the $78^{\circ}$N eastward jet in Fig. 4a exhibited a
strengthening $\partial{T}/\partial{y}$ gradient with time, signifying the
development of the NPSV boundary. The windshear on this jet transitioned from
weakly positive to negative at 5 mbar in 2012-13 ($L_{s}\approx 40^{\circ}$),
which would serve to promote westward winds surrounding the summertime vortex.

However, by the end of the mission near northern summer solstice
($L_{s}=93^{\circ}$), the NPSV boundary windshear was less than half of that
at the SPSV boundary in 2006-2008, and the 5-mbar temperature maximum ($\sim
140$ K at $90^{\circ}$N in Fig. 4c) was still cooler than that the maximum
temperature at the south pole ($\sim 150$ K at $90^{\circ}$S in Fig. 4l). So
although the NPSV had been developing a strong thermal gradient since the end
of the last CIRS study in northern spring[12], and positive windshear zones
had disappeared by northern summer, it still lacked the contrasts exhibited by
the SPSV during the later parts of southern summer. As the thermal maximum
lags behind the seasonal insolation maximum[12], we expect that the NPSV
continued to warm beyond northern summer solstice and the end of the Cassini
observations.

###  0.3 Composition of the NPSV and SPSV.

Although the NPSV was forming in the final years of Cassini’s mission, the
thermal gradients (and negative windshear) have not yet reached the extent of
those observed in the southern hemisphere surrounding the SPSV. This may not
be unexpected - northern summer occurred near aphelion (April 17, 2018)
whereas southern summer was closer to perihelion (July 26, 2003), implying a
difference in the rate of energy deposition in the upper atmosphere. However,
CIRS offers another technique for assessing the similarities and differences
between the NPSV and SPSV by studying the relative enhancements of different
chemical species within each vortex. This requires fitting high-spectral
resolution CIRS observations that stared directly at each vortex (see
Methods), as shown for the NPSV in Fig. 5.

Figure 5: Best-fitting brightness temperature spectrum for the 0.5-cm-1
resolution observation of the NPSV on March 27th 2017 (spanning
$84-87^{\circ}$N). The figure shows the model fit (red) to the data (black
points with grey uncertainties). The figure is split into the two spectral
ranges used in the inversions: (a) 600-870 cm-1 and (b) 1120-1370 cm-1. Key
gaseous features are labelled. Data between 870 and 1120 cm-1 were omitted
from the inversion. The measurement uncertainties (grey bars) depend on the
number of coadded CIRS spectra and the number of deep space reference spectra
used in the calibration.

Vertical profiles of temperature, ethane, and acetylene were derived starting
from a broad ensemble of priors (see Methods), and are displayed in Fig. 6 for
both the NPSV ($L_{s}=88^{\circ}$) and the SPSV ($L_{s}=346^{\circ}$). The
temperature profiles are compared with the predictions of a radiative climate
model[13] for the same season, which assumed a time-invariant low-latitude
mean of the stratospheric coolants ethane and acetylene derived from CIRS limb
observations between 2005 and 2008[20]. Whilst the northern $T(p)$ is
consistent with these predictions for 2-100 mbar, the southern $T(p)$ is
always warmer, even though the maximum stratospheric temperatures ($T\sim 160$
K at 0.3-0.5 mbar) are similar at both poles. This hints at a missing source
of heat in the radiative model for the lower stratosphere during southern
summer that was not required in the north at $L_{s}=88^{\circ}$, maybe due to
stratospheric aerosols (radiative) or stronger polar subsidence (adiabatic
heating)[13, 12, 25], the latter being supported by the excess C2H2 observed
in the SPSV compared to the NPSV in Table LABEL:tab:compsit_abundance,
discussed below. At lower pressures, both the NPSV and SPSV inversions suggest
a weak stratopause, with temperatures declining from 160 K at 0.3 mbar to
$\sim 150$ K at 0.01 mbar, again consistent with the radiative model with and
without the presence of polar aerosols[25]. Although this is dependent on the
prior and hampered by the nadir viewing geometry, it is worth noting that this
decrease in temperature occurs even with an isothermal 170-K prior.
Intriguingly, the presence of a mesosphere overlying a warmer stratosphere was
also inferred from ground-based IRTF observations of Saturn’s southern
hemisphere[44] at $L_{s}=268^{\circ}$, before Cassini’s arrival.

The vertical hydrocarbon profiles in Fig. 6 are less well constrained than the
temperatures, but they show that CIRS 0.5 cm-1 spectral resolution data can
constrain the acetylene gradient between 0.05 and 5 mbar and the ethane
gradient between 0.5 and 5 mbar. Outside of these ranges, the profiles diverge
and tend back to their respective priors. For this reason, abundances at low
pressures ($p<0.1$ mbar) should be treated with caution, but there is a trend
for the south polar data to exhibit well-mixed hydrocarbons with altitude
(i.e., no deviation from the uniform prior at low pressures), whereas north
polar ethane shows a slight decline with altitude, and north polar acetylene
shows a high-altitude peak near 0.01 mbar. Ethane is enhanced in the 0.5-5
mbar range compared to the expectations of photochemical models[19, 45, 43]
for both poles, and exhibits a somewhat shallower vertical gradient than
predicted. This is qualitatively consistent with the idea of a long-lived
photochemical product being advected downwards over the pole. Conversely, the
acetylene gradient is steeper than expected from the photochemical model,
suggesting photochemical depletion at a rate that is faster than the downward
advection. The 1-mbar acetylene abundance is well-matched at the south pole,
but somewhat depleted at the north pole compared to predictions.

Figure 6: Vertical distributions of temperature, acetylene and ethane derived
from 0.5-cm-1 spectral resolution data of both poles. The panels show COMPSITs
targeting the north pole in March 2017 (panels a-c, $84-87^{\circ}$N) and the
south pole in July 2008 (panels d-f, $83-88^{\circ}$S). A grid of 2000 a
priori atmospheres (varying the temperature and hydrocarbon distributions) was
employed as starting point. Red lines indicate profiles fitting the spectrum
within $1\sigma$ of the best fit, blue lines are for $2\sigma$, turquoise
lines are for $3\sigma$ and grey lines are for optimal estimates that do not
fit within the $3\sigma$ envelope. We have confidence in retrieved profiles in
altitude ranges where the profiles converge, irrespective of the a priori
starting points. The hydrocarbon profiles are compared to the output of a
diffusive photochemistry model[19] at $\pm 72^{\circ}$ latitude for
$L_{s}=88^{\circ}$ (dashed black line) and $L_{s}=346^{\circ}$ (solid black
line). The temperature profiles are compared to the predictions or a radiative
climate model[13] in the absence of stratospheric aerosols for $\pm
85^{\circ}$ latitude and for $L_{s}=88^{\circ}$ (dashed black line) and
$L_{s}=346^{\circ}$ (solid black line).

###  0.4 Minor hydrocarbons.

Adopting the best-fitting (i.e., minimum $\chi^{2}$) temperature, ethane and
acetylene profiles from Fig. 6, the 0.5-cm-1 spectra were used to search for
evidence of minor species in both the NPSV and SPSV by scaling the model
profiles[19] of each species during the spectral inversion. Fig. 7 shows the
effect on the spectra of removing a gas species or doubling its best-fitting
abundance, compared to the uncertainty on the coadded CIRS spectrum. The
change in $\chi^{2}$, evaluated over the spectral range shown in each figure,
is given beneath each brightness temperature spectrum. Methyl-acetylene and
diacetylene are both clearly detected at both poles, whereas detections of
propane, CO2 and benzene are more marginal, particularly in the NPSV.

The retrieved abundances are recorded in Table LABEL:tab:compsit_abundance,
and show that the ratio of the NPSV and SPSV abundances are always smaller
than one, contrary to the expectations of a photochemical model[19] for the
same season. This provides another indication that the NPSV was not as mature
as the SPSV when viewed at northern summer solstice. Only ethane and benzene
have abundances that are consistent between both poles (although with the
largest uncertainties), whereas all other species are less abundant by 20-60%
in the north compared to the south. The uncertainties on the mole fractions in
Table LABEL:tab:compsit_abundance are the uncertainties on the scale factor
for the prior abundance - propane and diacetylene exceed the expectations of
the photochemical model[19], methyl-acetylene is close to expectations, and
CO2 and benzene are smaller than expectations. That benzene is $0.6-0.8\times$
less than 1-mbar photochemical predictions at the poles is consistent with
previous findings using limb-sounding CIRS spectra[25]. Nevertheless, the
measured ratio deviates from the model ratio[19] substantially for all but
ethane and benzene.

There may be a weak trend with the longevity of the photochemical species[18],
with longer-lived ethane and propane showing the most similarity between the
poles (ratios of 0.7-1.0), and the shorter-lived acetylene, diacetylene and
methyl-acetylene showing greater contrasts (0.2-0.6). This makes sense if the
shorter-lived species are more sensitive to the dynamical and chemical changes
associated with the polar vortex formation, although this qualitative view
ignores any potential feedbacks between dynamics, chemistry and radiative
cooling in the vortices. The challenge to future seasonal photochemistry
models is to reproduce the observed gradients by better constraining the
vertical and horizontal mixing rates.

Table 1: Abundances of gases in NPSV and SPSV at 1 mbar [ppbv] compared to the expected ratio from a photochemical model[19] for the same season. With the exception of ethane and acetylene, these values were derived by scaling the a priori profiles from Moses et al.[19]. Gas | NPSV | SPSV | Ratio (N/S) | Model Ratio
---|---|---|---|---
Acetylene C2H2 | $225\pm 65$ | $423\pm 132$ | $0.53\pm 0.23$ | $1.04$
Ethane C2H6 | $8000\pm 1841$ | $8214\pm 4585$ | $0.97\pm 0.58$ | $0.98$
Methyl-Acetylene C3H4 | $2.0\pm 0.2$ | $3.3\pm 0.5$ | $0.62\pm 0.11$ | $0.91$
Propane C3H8 | $100\pm 16$ | $147\pm 20$ | $0.68\pm 0.14$ | $0.96$
Diacetylene C4H2 | $0.11\pm 0.03$ | $0.53\pm 0.07$ | $0.20\pm 0.06$ | $1.10$
Benzene C6H6 | $0.26\pm 0.10$ | $0.33\pm 0.14$ | $0.80\pm 0.45$ | $0.95$
Carbon Dioxide CO2 | $0.2\pm 0.1$ | $0.5\pm 0.2$ | $0.37\pm 0.26$ | $1.02$

Figure 7: Detection of minor species within Saturn’s northern and southern
polar vortices. The NPSV was observed in March 2017 (panels a-e), the SPSV was
observed in July 2008 (panels f-j), using the same data as in Fig. 6. Five
minor species are shown: propane (panels a and f), diacetylene (panels b and
g), methyl acetylene (panels c and h), carbon dioxide (panels d and i), and
benzene (panels e and j). Once the best-fitting atmospheric profiles
(temperatures and hydrocarbons) had been established, we scaled the abundance
of five minor species by 0.0 (black), 1.0 (red) and 2.0 (blue) times to show
their detectability in the spectrum. For each panel and gaseous species, we
show the brightness temperature spectrum and its uncertainty, as well as the
difference spectrum between the data and the model. The goodness-of-fit is
reported for each model, with a $\Delta\chi^{2}>1$ signifying a $1\sigma$
detection.

###  0.5 Chemical distributions within the NPSV.

Despite the strong constraints on abundances provided by the 0.5-cm-1 CIRS
spectra, they lack the spatial coverage to track the latitudinal variation of
these species. A compromise is to consider the variations of only temperature,
ethane and acetylene using the 2.5-cm-1 resolution REGMAP observations. The
north polar priors (Fig. 6a-c) were used as the starting point for
latitudinally-resolved retrievals between 2013 and 2017 shown in Fig. 8. These
figures reinforce the warming trends described above, and show the difference
between $p<1$ mbar, where the $\partial{T}/\partial{y}$ gradients are
relatively smooth with latitude, and $p>2$ mbar, where the banded structure
that typifies the troposphere can be seen. The north polar cyclone is easily
observed on all dates as the sharp temperature rise within $3^{\circ}$ of the
pole for $p>1$ mbar, but is not evident for $p<1$ mbar. The 2.5-, 5- and
10-mbar temperature gradients are particularly strong across the latitude of
the hexagonal jet at $78^{\circ}$N, which is why the stratospheric hexagon
appears readily in Fig. 1.

Figure 8: Zonal-mean north polar temperatures for three REGMAP datasets
showing the warming of the polar stratosphere. Temperatures are displayed at
six pressure levels: (a) 0.5 mbar, (b) 1.1 mbar, (c) 2.5 mbar, (d) 5.0 mbar,
(e) 11 mbar, and (f) 110 mbar. Three dates are included in each panel: August
17th 2013 (black, REGMAP $196\\_001$), June 25th 2014 (blue, REGMAP
$205\\_001$) and February 12th 2017 (red, REGMAP $261\\_003$). Vertical dotted
lines show the locations of prograde jet peaks[9] for comparison with the
meridional temperature gradients. Error bars represent the formal retrieval
uncertainty. Note that the June 2014 dataset utilised 15-cm-1 resolution
spectra, whereas the 2013 and 2017 datasets are better constrained by 2.5-cm-1
resolution spectra.

The 1-mbar distributions of acetylene and ethane at the North Pole for the
same three dates are shown in Fig. 9a-b, and were generated by scaling the
best-fitting vertical profiles in Fig. 6. We caution the reader that these
simple scalings of the a priori gas abundances would omit any changes in the
vertical hydrocarbon gradients, which are assumed to be invariant in the
present study. These are compared to the 1-mbar abundances at both poles
derived from the low-resolution inversions, which have been smoothed and
interpolated via a tensioned spline[41, 12]. C2H2 shows a minimum near
$75^{\circ}$N and increases towards the poles by a factor of $\sim 2$ (Fig.
9c), similar to that seen poleward of $75^{\circ}$S when the SPSV was present
(Fig. 9e). However, whilst there was little change between 2013-2014, there
has been a surprising drop in C2H2 by 2017 which is counter to the pre-2014
trend[12]. This reduction is seen in both the 2.5-cm-1 and 15-cm-1 inversions,
suggesting that the C2H2 abundance peaked before summer solstice. However, the
comparison with the SPSV suggests that the NPSV has not reached the same
elevated abundance during this time series, as suggested in Table
LABEL:tab:compsit_abundance.

The distribution of C2H6 is different, showing an overall increase in the
northern hemisphere and a potential spike in the abundance poleward of
$86^{\circ}$N (Fig. 9b), although this is not seen in the low-resolution time
series (Fig. 9d). A similar high-latitude peak in ethane may have been present
in the centre of the SPSV early in the Cassini mission (Fig. 9f). In summary,
both C2H2 and C2H6 increase poleward of the NPSV boundary at $78^{\circ}$N,
similar to chemical enhancements observed in the SPSV at the start of the
Cassini mission. Such an increase is not seen in photochemical models that
lack meridional motions[19, 45], and is further evidence that subsidence is
occurring throughout the NPSV to generate the warming and elevated chemical
abundances[30]. Based on the record of the SPSV, we would expect these polar
enhancements to start to decline after the summer solstice
($L_{s}=90^{\circ}$). However, we caution that ion chemistry in the auroral
regions, which could also be modulating the hydrocarbon abundances, remains to
be explored in detail.

Figure 9: Temporal evolution of polar ethane and acetylene. Latitudinal
distributions of (a) acetylene and (b) ethane at 1 mbar as derived from
spectra on August 17th 2013 (black, REGMAP $196\\_001$), June 25th 2014 (blue,
REGMAP $205\\_001$) and February 12th 2017 (red, REGMAP $261\\_003$). These
results come from scaling of the hydrocarbon profiles derived for the north
pole from the 0.5-cm-1 resolution observations, at the same time as retrieving
the temperature profiles in Fig. 8. Uncertainties on these retrieved scale
factors are shown for each data point. The four contour plots show the spline-
interpolated results for (c) north polar aceylene, (d) north polar ethane, (e)
south polar acetylene, and (f) south polar ethane from the low-resolution time
series in Fig. 4. Dotted/dashed lines show the locations of prograde jet
peaks[9] in all six panels.

## Discussion

Our results indicate that Saturn’s long-awaited NPSV started to develop during
late northern spring ($L_{s}>40^{\circ}$), but that temperature gradients only
became positive poleward of $78^{\circ}$N at 5 mbar in 2017, around northern
summer solstice ($L_{s}=90^{\circ}$). Even so, neither the temperature
gradients, nor the peak temperatures, nor the stratospheric molecular
abundances, were able to match those observed in the SPSV in late southern
summer. Either the NPSV will never reach the same contrasts as those of the
SPSV, or the NPSV will continue to develop through early northern summer.

Most surprisingly, the boundary of the NPSV exhibited a hexagonal shape
mirroring that observed in the clouds $\sim 300$ km below. Saturn’s polar
hexagon was discovered by Voyager[28], re-observed during Saturn’s last
northern summer in the early 1990s by Hubble[46] and ground-based
facilities[47], and re-detected by Cassini in the thermal-infrared[5, 12],
near-infrared[8] and visible[29, 9, 10, 48, 49]. The meandering of the
jetstream that forms the hexagon is believed to be a Rossby wave[31] resulting
from an instability of the eastward zonal jet near $78^{\circ}$N[32, 33, 29,
34] and trapped within a waveguide formed by the zonal jets.

Fig. 10 shows how the 2D temperatures and winds derived from the CIRS time
series can be used to explore the nature of the wave and its vertical
propagation. Mean zonal winds $u$ are calculated via the thermal wind
equation[42], using the latitudinal temperature gradients of Fig. 4 to
integrate the cloud-top winds[9] (assumed to reside at 500 mbar). Gradients in
temperatures, winds, and vorticity provide a valuable diagnostic tool for
understanding wave propagation, and we follow previous work[50] in estimating
the latitudinal gradient of quasi-geostrophic potential vorticity
($\beta_{e}=\partial{q_{G}}\partial{y}$), where $y$ is the north-south
distance and $q_{G}$ is the potential vorticity[51]. $\beta_{e}$ is the sum of
three terms: (1) $\beta=\partial{f}/\partial{y}$, the northward gradient of
planetary vorticity (i.e., the Coriolis parameter $f$); (2)
$\beta_{y}=-\partial^{2}u/\partial{y^{2}}$, the meridional curvature of the
zonal wind field; and (3) $\beta_{z}$, related to the vertical curvature of
the wind field and the static stability. This reduces to[50]:

$\displaystyle\beta_{e}=\beta+\beta_{y}+\beta_{z}$ (1)
$\displaystyle\beta_{e}=\beta-\frac{\partial^{2}u}{\partial
y^{2}}-\frac{1}{\rho}\frac{\partial}{\partial
z}\left(\rho\frac{f^{2}}{N^{2}}\frac{\partial u}{\partial z}\right)$ (2)

Here, $\rho$ is the density and $N$ is the Brunt Väisälä frequency:

$N^{2}=\frac{g}{T}\left(\frac{\partial T}{\partial z}+\frac{g}{c_{p}}\right)$
(3)

The latitudinal and vertical distribution of $N$ is shown in Fig. 10c,
calculated using the spatial distribution of gravitational acceleration $g$
assuming an oblate spheroid; and the specific heat capacity $c_{p}$ based on
an equilibrium ratio of ortho-to-para-hydrogen for all dates in the time
series, and including contributions from helium and methane.

The resulting $q_{G}$ gradient is shown in Fig. 10d, revealing that the
hexagon is co-located with a narrow lane of positive $\beta_{e}$ in both the
troposphere and stratosphere, and resides between two latitudes where
$\beta_{e}$ changes sign. This reinforces the idea that the vorticity gradient
serves as a waveguide for the propagating Rossby wave[29], suggestive of an
atmospheric ‘duct’ where the hexagon is observed. The $\beta_{e}$ sign
reversal suggests that the atmosphere violates both the neutral-stability
criterion relative to Arnol’d’s second theorem[32], and the Charney-Stern[52]
and Rayleigh-Kuo necessary conditions for baroclinic and barotropic stability,
respectively. Although the possibility of instability is not sufficient to
explain the hexagon’s origins, waves and large-scale eddies are often found in
such locations[32].

The ability of a Rossby wave to propagate is related to the index of
refraction ($\nu^{2}$) of the background medium[53], which is the sum of the
squares of the vertical $m$, meridional $l$, and zonal $k$ wavenumbers[54,
50]:

$\nu^{2}\equiv k^{2}+l^{2}+\left(\frac{f^{2}}{N^{2}}\right)m^{2}$ (4)

This can be related to the dispersion relationship for a 3D Rossby wave in a
baroclinic atmosphere[55]:

$\nu^{2}=\frac{\beta_{e}}{u-c_{x}}-\frac{f^{2}n^{2}}{N^{2}}$ (5)

where $n^{2}$ includes the higher-order vertical derivatives of the buoyancy
frequency[54, 50]. This index depends only on the phase speed of the wave
($c_{x}$) and the properties of the background medium ($u$, $N^{2}$, scale
height $H$, $f$ and $\beta_{e}$). With known values of $k$ and $l$, this can
be rearranged to estimate the vertical wavenumber $m$: $m^{2}>0$ implies that
Rossby waves are permitted to propagate in the vertical, whereas regions of
$m^{2}<0$ imply evanescent waves that decay exponentially with altitude.

To investigate whether changing atmospheric conditions have permitted the
tropospheric hexagon to propagate into the stratosphere, Fig. 10e shows the
subtle changes in $\nu^{2}$ since spring equinox, calculated assuming the
measured phase speed of the tropospheric hexagon $c_{x}=-0.036$ ms-1[29], and
confirms that regions of positive $\nu^{2}$ are confined to low pressures by
the static stability (the $\beta_{z}$ term, which changed with time), and
confined latitudinally by the curvature of the windfield (the $\beta_{y}$
term, which was relatively constant over time). The hexagon latitude is
characterised by a vertically-extended region of positive $\nu^{2}$ in the
stratosphere coincident with a region of positive vorticity gradient
$\beta_{e}$ between $77-80^{\circ}$N, which is suggestive of a wave duct that
can be seen to extend downwards as northern solstice approached (i.e., the
static stability changed with season), but never quite reached the tropopause.
These distributions are subject to large uncertainties[50], most notably
because the temperatures and winds in the 5-80 mbar range are poorly
constrained by the CIRS inversions (see Methods), such that quantitative
values should be treated with caution.

However, taking values of $k=2\pi/L_{x}$ (where $L_{x}=$14,500 km is the
length of the hexagon’s side[29]) and $l=2\pi/L_{y}$ (where $L_{y}=3150$ km,
estimated as the distance between the two $\beta_{e}$ sign changes at
$77-80^{\circ}$N in Fig. 10d, which could demarcate the latitudinal boundaries
of the wave), we searched for regions where vertical propagation is possible
for a hexagon-like Rossby wave (i.e., where $m^{2}>0$). Although a region of
positive $m^{2}$ does exist for the hexagon at $p>600$ mbar (i.e., near the
cloud tops), we found $m^{2}<0$ throughout the upper troposphere and
stratosphere, supporting the ‘trapped-wave’ concept. This poses a problem for
the hexagon observed in both the upper troposphere ($p\sim 100$ mbar) and
stratosphere ($p\sim 1$ mbar).

Figure 10: Derived dynamical products based on the reconstructed north polar
time series. Annual averages for 2009, 2011, 2013, 2015 and 2017 are shown in
the five rows. We show (a) the temperatures $T$, (b) zonal winds $u$, (c)
Brunt Väisälä buoyancy frequency $N$, (d) effective vorticity gradient
$\beta_{e}$, and (e) the index of refraction $\nu^{2}$. Negative values are
shown as dotted contours, positive values as solid contours. In panel (e),
regions of real refractive index are shown as grey. In panel (d), the scale
for $\beta_{e}$ ranges from $\pm 80\times 10^{-12}$ m-1s-1 in steps of
$8\times 10^{-12}$ m-1s-1. Contour lines in panel (e) for $\nu^{2}$ are drawn
for $\pm 0.5\times 10^{-12}$ m-2, $\pm 0.25\times 10^{-12}$ m-2 and 0 m-2.
Given the uncertainties in the thermal winds (see Methods), these panels
should be considered as qualitative trends rather than quantitative values.

At least two possibilities should therefore be considered. Firstly, if the
magnitude of the imaginary $m$ were sufficiently small, any vertically-
propagating wave could travel by evanescence (tunnelling) over a limited
altitude range from the troposphere into the stratosphere. Although the
coupling of these two altitude ranges may be weak, the amplitude of a Rossby
wave will still tend to increase with height because of the decreasing density
of the air. The fact that we do not see any zonal phase shift of the hexagon
vertices between the upper troposphere and stratosphere (Fig. 2) is consistent
with the idea that the wave is not formally propagating. Secondly, the
$\beta_{e}$ sign reversal in Fig. 10d shows that the atmosphere exhibits the
necessary conditions for instability in the stratosphere, irrespective of what
is happening in the troposphere. However, if such a pattern were excited
independently, one would need to explain why it retains the same wavenumber,
meridional amplitude, and phase speed as its tropospheric counterpart. Such a
stable phase alignment would require some form of dynamical coupling between
these two altitude ranges. Distinguishing between these cases will require
investigation via more detailed middle atmosphere modelling. Finally, we note
that we found no evidence of stratospheric polygonal waves surrounding the
SPSV during southern summer, consistent with their absence in the troposphere,
and confirming the differences in dynamical stability of Saturn’s northernmost
($78^{\circ}$N) and southernmost ($74^{\circ}$S) eastward jets.

Finally, we discuss potential sources of the heating responsible for the
formation of the NPSV. Supplementary Figure 2 compares the CIRS temperatures
at 1 mbar to the results of radiative models from several different studies.
Although they differ in the details, each model qualitatively reproduces the
amplitude of the temperature changes and the timing of the temperature
minima/maxima. However, none of the models successfully reproduces the
formation of $\partial{T}/\partial{y}$ gradients associated with the edges of
the compact polar cyclones or the broad stratospheric vortices. All models
account for the radiative balance between heating (methane and H2 absorption)
and cooling (from C2H2, C2H6 and, to a much smaller extent, CH4 and the H2
continuum), but they treat the distribution of the stratospheric coolants
differently - some using mean abundances that are uniform with latitude and
time[13, 14]; some using meridional distributions that are fixed with
time[15]; and one[43] using temporally- and spatially-variable abundances
predicted by iterating between their seasonal photochemistry model[45] and a
radiative model[15]. None of these adequately represent the spike in
hydrocarbon abundances in the NPSV and SPSV (Fig. 9), nor their temporal
variation. To date, only one model[14] includes circulation resulting from
seasonal forcings (Supplementary Fig. 2c), making some progress in introducing
sharper $\partial{T}/\partial{y}$ gradients, but this model was not designed
with polar circulations in mind and does not generate gradients in the right
locations.

Warming by polar subsidence of order 1 mm s-1 at 1 mbar has been invoked to
close the gap between the CIRS measurements and radiative models[12]. However,
aerosols also constitute a significant part of the radiative budget[13], which
can introduce a 5-6 K warming effect in the stratosphere[25]. Aerosols are a
challenge to include in a time-resolved seasonal model, primarily because the
latitudinal distribution and temporal variability of upper tropospheric and
stratospheric hazes remain poorly understood. A recent study of Saturn’s
reflectivity by Cassini’s Imaging Science Subsystem[49] observed that the
tropospheric hazes moved deeper and became optically thinner poleward of the
hexagon. This provides further evidence that subsidence is occurring within
the hexagon, and that it extends from the cloud-forming region into the mid-
stratosphere. In addition, the polar region exhibits an increased optical
thickness of stratospheric hazes[56, 49] that is potentially related to
aerosol production associated with Saturn’s aurora. Saturn’s main auroral
oval, associated with the boundary between open and closed magnetic field
lines, occurs at an average latitude of $76.5^{\circ}$N[57] and therefore
completely encompasses the area of the NPSV, sitting $\sim 1^{\circ}$ south of
the hexagon latitude ($78^{\circ}$N). Stratospheric aerosols, irrespective of
how they are formed, may be localised within the NPSV and SPSV and contribute
to the sharp rise in stratospheric heating across the vortex boundaries.
Currently it is not possible to disentangle the complementary effects of
radiative warming and atmospheric subsidence, although the elevated polar
hydrocarbon abundances in Fig. 9 indicate that polar downwelling occurs within
both vortices.

At nanobar pressures, far above the stratosphere, Saturn’s exospheric
temperatures increase to $\sim 400$ K[58], but this value also shows
latitudinal and seasonal fluctuations, being warmer in summer (with increased
insolation increasing ionospheric conductivity and, therefore, Joule heating
rates) than winter. On Jupiter, stratospheric temperatures are elevated within
the auroral oval, both by Joule heating and particulate absorption[59]. Future
work could address whether the processes heating the atmosphere at nanobar
pressures could also influence the temperatures of Saturn’s polar stratosphere
at millibar levels, but would require a close coupling of thermospheric and
stratospheric circulation, chemistry, and radiative models that include the
influences of aerosols.

That the formation and strengthening of the NPSV should be occurring right at
the end of Cassini’s unprecedented 13-year mission is frustrating.
Nevertheless, ground-based and space-based (James Webb Space Telescope)
observations will continue to track its evolving temperature, composition, and
aerosol field, as well as the hexagonal boundary, whenever possible. This
northern-summer survey will include searches for any inter-annual variability
between the NPSV observations in 1989[11] and those in 2018, one Saturnian
year later.

###  0.6 Low-resolution CIRS time series.

To track the evolving stratospheric temperature gradients as a function of
latitude and time, we adopt a similar technique to previous work[12, 39],
truncating all CIRS interferograms so that they are all treated at the lowest
possible spectral resolution of 15 cm-1. This means that all CIRS Saturn
observations, including those that rode along with other Cassini instruments,
are considered. These are binned onto a monthly time grid on a $2^{\circ}$
latitude grid (with a $1^{\circ}$ step size) for all latitudes, retaining only
observations within $\pm 10^{\circ}$ emission angle of the mean for each bin,
and ensuring that this emission angle was smaller than $60^{\circ}$. Data were
also filtered for smearing due to fast motion of the focal plane across the
disc; (known interferences; instances of negative radiances introduced by
shifting instrument temperatures; and examples where fewer than ten spectra
were available at a particular latitude and time. This produced approximately
13,000 spectra for inversion over the 2004-2017 timeline. At the spatial
resolution and sensitivity of the CIRS data, Saturn’s thermal structure is
largely axisymmetric in the absence of large-scale storms and waves[12], so
the coadded spectra are a good approximation of the zonal mean.

###  0.7 Spectral Retrieval.

Spectral inversions use the NEMESIS optimal estimation retrieval
algorithm[37]. The latitude-independent atmospheric prior and weighting
between measurement and a priori uncertainty are described by Fletcher et
al.[12], whereas the sources of spectroscopic line data have been updated to
those given in Supplementary Table 1 and the H2-H2 collision induced opacities
are from the compilation of free-free and dimeric contributions[60]. The
vertical temperature profile is retrieved alongside a scaling of the a priori
ethane and acetylene abundances (additional hydrocarbon species are not
visible at low spectral resolution, but are considered only at high spectral
resolution). Aerosols are omitted, and we assume the equilibrium distribution
of para-hydrogen. The results for every latitude and month are shown in Fig.
3. Temperature uncertainties range from $\sim 3$ K at the tropopause, to
1.5-2.0 K near 200 mbar (the peak of the tropospheric contribution), 3.5-4.5 K
at 1-5 mbar (the peak of the stratospheric contribution).

The resulting time series contains numerous outliers related to problems with
calibration, incomplete longitude sampling, differences in spatial resolution,
etc[12]. Although a quadratic fit to every latitude and altitude was
previously used to interpolate and smooth the 10-year time series[12], we find
that a quadratic was inadequate for the 14-year time series, and instead adopt
the tensioned-spline fitting technique[41] as a better representation of the
expected sinusoidal variation of temperatures with season. Splines are best
constrained near the middle of the time series and show divergence at the
start and end, but are still within the uncertainties of the earliest and
latest CIRS measurements available.

###  0.8 Thermal Winds.

Integration of the thermal wind equation to estimate the zonal winds as a
function of latitude and altitude is hampered by several factors[39]: the
vertical resolution of nadir spectra is limited to approximately a scale
height, implying that regions of strong $\partial{u}/\partial{z}$ are smoothed
with altitude; nadir spectra do not sense $\partial{T}/\partial{y}$ gradients
between 5-80 mbar, such that we have no knowledge of the windshear in the
lower stratosphere; and the boundary conditions for the integration (namely,
the altitude of the cloud-top winds) remains poorly constrained, and it likely
to vary significantly with location on the planet. By the time the integration
reaches millibar pressures, this can lead to uncertainties in the absolute
values of the winds of hundreds of metres per second. Thus we caution the
reader that the stratospheric winds derived from nadir remote sounding, in
this study and all others, should be considered as only a qualitative
guideline for the zonal motions of the middle atmosphere.

###  0.9 Composition from high-resolution CIRS data.

The spectral resolution of the CIRS data used so far is insufficient for the
identification of species beyond CH4, C2H2 and C2H6, so we instead utilise
observations acquired at 0.5 cm-1 by sitting and staring at a particular
latitude (an observation design known as a COMPSIT). Observation $267\\_002$
targeted the NPSV at $85^{\circ}$N for 8 hours (1200 spectra) with a mean
emission angle of $70^{\circ}$ on March 27th 2017 ($L_{s}=88.2^{\circ}$). This
is compared to observation $076\\_001$, which targeted the SPSV at
$85^{\circ}$S for 8 hours on July 15th 2008 ($L_{s}=346^{\circ}$). Although
the latter was closer to equinox than southern solstice, this was one of the
first COMPSITs to target the south polar region, capturing the SPSV in its
later stages. The NPSV spectrum is shown in Fig. 5, with key hydrocarbons
labelled.

To reproduce these spectra, $k$-distributions were generated from the gases
listed in Supplementary Table 1, and vertical profiles of stratospheric
hydrocarbons were extracted from a 2D seasonal photochemistry model[19]. Given
that this model includes an estimate for the vertical diffusion ($K_{zz}$) but
assumes no meridional motion ($K_{yy}=0$), we elected to take average polar
compositions for $72^{\circ}$N and $72^{\circ}$S (the maximum poleward extent
of the model) over the $L_{s}=280-90^{\circ}$ range representing Cassini’s
mission. The profiles of methylacetylene (C3H4), diacetylene (C4H2), carbon
dioxide (CO2), propane (C3H8) and benzene (C6H6) were simply scaled during the
retrievals of full vertical profiles for temperature, ethane and acetylene. To
test the sensitivity of the retrievals to the priors, we set up a grid of 2000
separate inversions for each pole, each with a different profiles for
temperature, ethane and acetylene. The temperature priors merged tropospheric
temperatures[61] with stratospheric isotherms from 130-170 K. The acetylene
profile was parameterised as a uniform abundance (ranging from 0.5-5.0 ppm)
for $1<p<300$ $\mu$bar and a decreasing abundance (linear in log-pressure)
into the deeper stratosphere. The ethane profile was similar, with abundances
of 2-20 ppm for $1<p<300$ $\mu$bar and a declining abundance for $p>300$
$\mu$bar. These values were broadly representative of those extracted from the
photochemical model [19].

The retrieved profiles, based on this grid of priors, are shown in Fig. 6 for
both the NPSV ($L_{s}=88^{\circ}$) and the SPSV ($L_{s}=346^{\circ}$). Some
inversions fit the CIRS spectra better than others, but where multiple
profiles overlap, we can be confident that it is the data (rather than the
prior) that is driving the inversion. For example, temperatures only begin to
diverge for $p<1$ mbar, whereas the gas profiles are best constrained in the
0.5-5.0 mbar range, approximately. The goodness-of-fit for the acetylene and
ethane spectra were calculated from the 710-750 cm-1 and 800-840 cm-1 ranges
respectively, whereas the goodness-of-fit for temperature uses the full
spectrum (600-900 cm-1 and 1120-1370 cm-1).

## Data availability statement

All data can be obtained from the primary author (LNF, email:
<EMAIL_ADDRESS>upon request, or can be accessed from the
following GitHub repository doi:10.5281/zenodo.1286856, which contains the
temporally and latitudinally averaged spectra used in this study. Raw and
calibrated Cassini Composite Infrared Spectrometer observations are available
from NASA’s Planetary Data System (PDS). The entire CIRS database was used in
this study, but we provide unique data identifiers where data subsets were
used in our figures. The NEMESIS spectral retrieval tool is available upon
reasonable request from P.G.J. Irwin (patrick.irwin@physics.ox.ac.uk). The
reconstructed temperature and hydrocarbon fields are also available at the DOI
listed above.

## Supplementary Material

Figure 11: Supplementary Fig. 1: North and South polar tropospheric temperature gradients as a function of time throughout the whole Cassini mission, 2004-2017. We display north polar temperatures (panels a-c), north polar windshears (panels d-f), south polar windshears (panels g-i) and south polar temperatures (panels j-l) at three different pressure levels (110, 220 and 330 mbar). These were derived from averages of low-resolution CIRS spectra on a monthly temporal grid, and interpolated using tensioned splines[41] to reconstruct a smoothed temperature field. Horizontal dashed lines signify the peak of eastward zonal jets in the troposphere[9]. The data are displayed as a function of time (years), but a second horizontal axis provides the planetocentric solar longitude ($L_{s}$) in degrees. Figure 12: Supplementary Fig. 2: Comparison of the 1-mbar temperature field to the predictions of radiative models. We compare (a) the CIRS low-resolution measurements to predictions of (b) the radiative model of Greathouse et al.[15]; (c) the radiative-dynamical model of Friedson and Moses[14]; (d) the radiative-convective model of Guerlet et al.[13]; and (e) the combined radiative-photochemical model of Hue et al.[43]. Results for the north pole are shown on the left, and the south pole are shown on the right. Although the predicted temperatures are close to those observed, none of the models include the warming of the North Pole, and none of them predict the appearance of the strong $\partial{T}/\partial{y}$ gradients associated with the polar vortices. Table 2: Supplementary Table 1: Sources of spectroscopic linedata and foreign broadening assumptions. Exponents for temperature dependence $T^{n}$ given in the final column. Gas |  Line Intensities |  Broadening Half Width |  Temperature Dependence
---|---|---|---
CH4, CH3D |  Brown et al.[62] |  H2 broadened using a half-width of 0.059 cm-1atm-1 at 296 K |  $n=0.44$ Margolis et al.[63]
C2H6 |  Vander-Auwera et al.[64] |  0.11 cm-1atm-1 at 296 K Blass et al.[65] |  $n=0.94$ Halsey et al.[66]
C2H2 |  GEISA’03[67] |  Fits to data in Varanasi et al.[68] |  Varanasi et al.[68]
PH3 |  Kleiner et al.[69] |  Broadened by both H2 and He using $\gamma_{H_{2}}=0.1078-0.0014J$ cm-1atm-1 and $\gamma_{He}=0.0618-0.0012J$ cm-1atm-1 Levy et al.[70], Bouanich et al.[71] |  $n=0.702-0.01J$ ($J$ is the rotational quantum number) Salem et al.[72]
NH3 |  Kleiner et al.[69] |  Empirical model of Brown et al.[73] |  Brown et al.[73]
C2H4 |  GEISA’03[67] |  Polynomial fits to data from Bouanich et al.[74, 75] |  $n=0.73$, Bouanich et al.[75]
C3H4 |  GEISA’09[76] |  0.075 cm-1atm-1 for all lines |  $n=0.50$ assumed
C4H2 |  GEISA’09[76] |  0.1 cm-1atm-1 for all lines |  $n=0.75$ assumed
C3H8 |  GEISA’09[76] |  0.08 cm-1atm-1 for all lines |  $n=0.75$ assumed.
C6H6 |  GEISA’09[76] |  Linear fit to N2-broadening of Waschull et al.[77] |  $n=0.75$ assumed

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Requests for materials should be addressed to L.N.F.
(leigh.fletcher@le.ac.uk).

This work is based on data acquired by the Cassini Composite Infrared
Spectrometer, and would not have been possible without the tireless efforts of
the instrument design, operations, and calibration team over more than two
decades. LNF was supported by a Royal Society Research Fellowship and European
Research Council Consolidator Grant (under the European Union’s Horizon 2020
research and innovation programme, grant agreement No 723890) at the
University of Leicester. The UK authors acknowledge the support of the Science
and Technology Facilities Council (STFC). A portion of this work was performed
by GSO at the Jet Propulsion Laboratory, California Institute of Technology,
under a contract with NASA. JAS was supported by the NASA Postdoctoral and
Caltech programs as well as by a contract with NASA. SG was supported by the
Centre National d’Etudes Spatiales (CNES). This research used the ALICE High
Performance Computing Facility at the University of Leicester. We are
extremely grateful to S. Guerlet, V. Hue. A.J. Friedson, T. Greathouse and
J.I. Moses for sharing the outputs of their Saturn simulations.

The authors declare that they have no competing interests.

LNF wrote the manuscript and performed the analysis. GSO, JAS, SG, AA
participated in the data analysis; PLR, RKA, FMF aided in dynamical
interpretations; PGJI and SBC developed the software for spectral modelling;
GLB, JH, BEH, MS designed and implemented the CIRS observations; NG and AM
developed the calibration software. All of the authors discussed the results
and commented on the manuscript.