# Convective storms and atmospheric vertical structure in Uranus and Neptune

R. Hueso1, T. Guillot2 and A. Sánchez-Lavega1 1Física Aplicada I, Escuela de
Ingeniería de Bilbao, UPV/EHU, 48013 Bilbao, Spain
2Université Côte d’Azur, Laboratoire Lagrange, OCA, CNRS UMR 7293, Nice,
France

###### Abstract

The Ice Giants Uranus and Neptune have hydrogen-based atmospheres with several
constituents that condense in their cold upper atmospheres. A small number of
bright cloud systems observed in both planets are good candidates for moist
convective storms, but their observed properties (size, temporal scales and
cycles of activity) differ from moist convective storms in the Gas Giants.
These clouds and storms are possibly due to methane condensation and
observations also suggest deeper clouds of hydrogen sulfide (H2S) at depths of
a few bars. Even deeper, thermochemical models predict clouds of ammonia
hydrosulfide (NH4SH) and water at pressures of tens to hundreds of bars,
forming extended deep weather layers. Because of hydrogen’s small molecular
weight and the high abundance of volatiles, their condensation imposes a
strongly stabilizing vertical gradient of molecular weight larger than the
equivalent one in Jupiter and Saturn. The resulting inhibition of vertical
motions should lead to a moist convective regime that differs significantly
from the one occurring on nitrogen-based atmospheres like those of Earth or
Titan. As a consequence, the thermal structure of the deep atmospheres of
Uranus and Neptune is not well understood. Similar processes might occur at
the deep water cloud of Jupiter in Saturn, but the Ice Giants offer the
possibility to study these physical aspects in the upper methane cloud layer.
A combination of orbital and in situ data will be required to understand
convection and its role in atmospheric dynamics in the Ice Giants, and by
extension, in hydrogen atmospheres including Jupiter, Saturn and giant
exoplanets.

##  1 Introduction

Modern explorations of possible mission scenarios to the Ice Giants Uranus and
Neptune [1, 2, 3, 4] have motivated a revision of what we know about these
planets and their planetary systems. Recent reviews explore their atmospheric
dynamics [5], mean circulation patterns [6], and vertical structure [5, 7].
These atmospheric themes connect with their internal structure [8] and
formation mechanisms [9]. Knowledge of the properties of the Ice Giants can
guide us to understand the atmospheres of the growing population of exoplanets
with Neptune-size masses.

Additional insights to understand Uranus and Neptune come from the recent
exploration of Jupiter and Saturn by the Juno and Cassini missions [10]. Both
planets have zonal winds that extend a few thousand kilometers in the
atmosphere [11, 12]. For Jupiter, new questions arise on how meteorological
processes distribute condensables well bellow the upper clouds and through the
planet [13] and in both planets it is unknown how deep latitudinal variations
in the banded patterns of the planets extend. These new results and questions
from the detailed exploration of Gas Giants challenge our expectations on the
properties of the Ice giants Uranus and Neptune, and in particular in the
distribution of condensables, the characteristics of moist convection and how
these factors manifest in observable fields such as the dynamics of the cloud
fields.

In hydrogen-helium atmospheres, condensables are heavier than dry air,
imposing a fundamentally different dynamic regime to non-hydrogen based
atmospheres [14]. In the Gas and Ice Giants, above a critical abundance of the
condensing species, moist convection is inhibited by the weight of the
condensables rather than favored by latent heat release [14, 15, 16, 17]. This
inhibition requires a sufficiently high abundance of condensables, which might
be close to the water abundance in Jupiter [18] and might be found in the deep
water cloud in Saturn, thus providing a way to explain the observations of
episodic storms on this planet [19]. In the case of Uranus and Neptune,
methane, which condenses in the directly observable part of the atmosphere, is
abundant enough to lie in that regime. Uranus and Neptune are therefore
extremely interesting laboratories to understand convection in hydrogen
atmospheres and its overall effect on the global atmospheric dynamics.

Recent observations of Jupiter’s deep weather layer by Juno [13] and the Very
Large Array (VLA) [20, 21], and results from Cassini following the 2010-2011
Great Storm in Saturn [22, 23, 24] suggest that moist convection acts in both
planets to desiccate NH3 of the upper trospospheres below the ammonia
condensation level due to details in the thermodynamics of the water ammonia
system [25, 26]. But do other volatiles transport mechanisms occur in Uranus
and Neptune cloud layers? And how observations of their cloud activity
constrain the properties of moist convection in these colder atmospheres with
lower internal heat sources?

Uranus and Neptune have time variable cloud systems where storms are believed
to be fueled by methane condensation, but the frequency, spatial distribution
and strength of these storms including their size and temporal duration are
not well-known and most cloud activity observed so far is probably not
convective. Methane abundance is constrained from remote sensing to values in
the range of 80$\pm$20 times solar [27, 28, 29] (solar abundance is the
proportion of a given element to hydrogen in the Sun’s photosphere; the
standard values of solar abundances are given in [30]), which translate in
cloud bases close to 1 bar and consistent with observations of cloud systems
in both planets. Models of the formation of Uranus and Neptune [8] imply
similar high abundances of other condensables that would form a multi-layered
cloud structure with deep water clouds at pressures that can range 500-3,000
bar for water abundances in the range of 20-80 times solar [5, 7], i.e. well
above the limits to produce an inhibition of convection [14, 15, 16]. Both
planets receive weak amounts of energy from the Sun. The highest mean daily
solar irradiation received in Uranus is 3.7 Wm-2 in its polar regions during
summer, and 0.7 Wm-2 in Neptune, also near polar latitudes [5]. The annual
average solar insolation also varies strongly as a function of latitude, with
Uranus receiving the highest annual average insolation in their polar regions
and Neptune in the equator [31]. In addition, Neptune possesses an internal
energy source (it radiates $2.61\pm 0.28$ times as much energy as it absorbs
from the Sun), whereas the internal flux measured at Uranus appears to be at
least one order of magnitude smaller [32]. In terms of flux density, the
internal heat source in Uranus is negligible, and in Neptune it is about 20
and 7 times smaller than those of Jupiter and Saturn, respectively, resulting
in a much lower capacity to power internal convection.

The goals of this paper are to review the observational evidences in favor of
moist convection in Uranus and Neptune, explore how moist convection may
operate in the Ice Giants from a comparison with moist convection in the Gast
Giants and inspect the effects that storms may produce in the vertical
properties of the atmosphere. We also aim to address which measurements a
mission to these planets should perform, in addition to the fundamental
determination of a vertical profile of temperature and condensables abundances
that could be obtained by an atmospheric probe [33].

##  2 Observations of convective activity in Uranus and Neptune

Here we review the observational evidences in favor of moist convective storms
in Uranus and Neptune (i.e. clouds formed by vertical ascending motions
powered by buoyancy differences and vertically transporting heat). These
evidences come from two sources: (a) Observations of the cloud activity; (b):
The inferred abundance of atmospheric methane above the tropopause for Neptune
[34]. Both are incomplete sources of information and show remarkable
differences with what we know about convective storms in Jupiter and Saturn.
The observations of the possible cloud activity in Uranus and Neptune either
lack the spatial resolution, or the temporal sequences required to study their
dynamics, or the spectral coverage to properly model the vertical cloud
structure of candidate storms. The high methane abundance above the tropopause
was historically the main argument in favor of moist convection in Neptune.
This argument does not apply to Uranus (because of a low methane abundance
above the tropopause) and Jupiter and Saturn (although they are convective,
they do not show high ammonia abundances above the tropopause). In addition,
this high abundance in Neptune’s lower stratosphere can be explained by other
ideas (leakage of methane at the lower stratosphere from warm polar regions)
without requiring moist convection [35, 36]. Thus, in this section we will
discuss candidates to moist convective storms and not cloud systems completely
proven to have a convective origin.

Observations of moist convective storms in the Gas Giants show divergent
clouds on short time-scales of hours to a few days, elevated clouds above
their environment and close to the tropopause, and in some cases large
disturbances evolving over months. Clouds with strong divergences, as updrafts
expand in the stable part of the troposphere, are a key signature of
convective storms, but the observational record of such activity in Uranus and
Neptune is almost inexistent because it requires frequent observation at very
high-spatial resolution. In Jupiter and Saturn features with irregular cloud
morphologies that show rapid changes tend to be convective, as opposed to
compact ovals (closed vortices), regularly spaced spots and long filamentary
wavy structures (waves). Intense convective storms large enough to be observed
from Earth are frequent in Jupiter [37] and rare in Saturn [22, 38]. In both
planets radio emissions emitted from lightning have been observed by different
spacecraft [39], and lightning flashes have been observed in some of the most
intense storms [40, 41], including Jupiter locations with no evident storms in
the observed cloud field [42, 43], but lightning in Uranus and Neptune has
only been inferred from radio signals [44, 45, 46].

Juno observations of Jupiter show small-scale storms at many latitudes. Storms
big enough to be observed from Earth are more rare [47], and strong convective
eruptions able to change the visual aspect of entire bands (like in the North
Temperate Belt or in the South Equatorial Belt) [48, 49, 50] only happen every
few years [51]. Saturn storms occur also on different scales, with small puffy
clouds in the polar regions, seasonal storms at mid-latitudes, and the much
more rare Great White Spots [38]. In both planets the mechanisms underlying
the spatial distribution of storms, their cyclic nature in Jupiter, and their
seasonal distribution in Saturn, are not known.

Due to the difficulties to study cloud motions in images of Uranus and
Neptune, the fundamental criterion for selecting candidates of convective
storms is their morphology as irregular features or elongated plume-shaped
clouds, with rapid temporal evolution in their size and shape and their high
brightness in images at methane absorption bands indicative of high cloud
tops. Besides convection, bright clouds are also observed accompanying dark
anticyclones in Neptune [52]. These ”companion clouds” are suggested to be
formed by similar processes to those occurring on orographic clouds on Earth.
Numerical simulations indicate that methane humid air forced by the vortex
circulation can rise a few kilometers and condense close to the tropopause as
the vortex interacts with the environment flow [53]. These bright clouds are
produced through a dynamic interaction that does not require buoyancy produced
by condensation as in convective storms and are separated from the moist
convective storm candidates we discuss here.

###  2.1 Convective activity in Uranus

The first spatially resolved images of Uranus were obtained by the Voyager 2
in 1986 and showed a planet with a homogeneous cloud cover with no bright
features [54]. Voyager observations of the atmospheric lapse rate and ortho to
para hydrogen were used to suggest thin-layered convection with sub-saturated
methane [55]. Those observations inspired the idea of a planet with low cloud
activity, and slow variability. Figure 1 shows cloud features in Uranus that
reveal that that early view of Uranus is incorrect. There are several cases of
discrete bright clouds that could be caused by moist convective storms. Some
of them were short-lived and others were active for years.

Voyager 2 only found a plume like feature at 35∘S whose morphology and
brightness in methane band filters were suggestive of a convective origin [54]
(Fig. 1a). Later observations with ground-based telescopes and the Hubble
Space Telescope (HST) captured this feature between 1994 and 2009 [56, 57, 58]
(Fig. 1b). This feature was nicknamed the ”Berg”, it showed oscillations in
longitude and a latitude migration that eventually caused its disintegration
when it reached 5∘S. The Berg extended $\sim 5,000-10,000$ km and had smaller
clouds whose brightness changes suggested convective sources. Although most of
the clouds in the Berg could be “companion clouds” as those occurring on
Neptune’s dark vortices (i.e., generated by an unobserved deep anticyclone)
intense brigtening events in 2004 and 2007 suggest convective storms [58].

As the northern hemisphere turned into view in the mid-90s, a large number of
discrete features were captured in a latitude band centered at 30∘N [59].
Because that latitude received the first rays of the Sun after a long winter,
this activity was proposed to be seasonal convection triggered by the
increasing insolation. However, observations made to date suggest that the
band between 28∘N and 42∘N is an intrinsically active region in generating
discrete bright spots with typical sizes of 2,000-4,000 km and sometimes
developing in series [60] (Fig. 1c). The cloud tops of the brightest features
(Fig. 1d) were estimated to be at 300-500 mbar. New outbreaks of activity
occurred in 2004-2006 at this latitude and were named ”Bright Complex” [61].
This high level of activity lasted until Uranus’ equinox in December 2007
[57].

Another bright feature was observed in 2011 and was active for several months
[62]. The brightest spot in Uranus so far recorded was observed in 2014 close
to the equator at 15∘N [63] (Fig. 1e). Its reflectivity in the deep methane
band K’ (2.2 $\mu$m) reached 30% of Uranus disk brightness implying that cloud
tops were above the 330 mbar altitude level. The feature extended $\sim$
17,000 km in longitude and 4,300 km in latitude and its texture was complex
and formed by smaller spots of $\sim$ 2,000 km (Fig. 1e, upper inset). A
second cloud system at 32∘N, less bright and deeper in the atmosphere at
approximately 2 bar (Fig. 1e, lower inset), developed over months forming an
elongated tail-like structure similar to large-scale convective storms in
Jupiter and Saturn [49, 22]. Because of these characteristics, these systems
are probably the best candidates for moist convective storms in Uranus.
However, detailed radiative transfer analysis suggest that although the clouds
reached levels close to the tropopause, their optical depth (around 1 at 0.467
nm) was not as large as it would be expected for convective features where
near infinite optical depths are expected at all wavelengths. The elongated
tail-like structure was found to lay around 1-2 bar not reaching the top
altitudes of the main bright feature [64].

Finally, a different type of convective activity could occur in Uranus’s North
Pole, above latitude 60∘N, where a cluster of bright spots were observed [65]
(Fig. 1f). These spots have sizes of $\sim$ 500 km and are mutually separated
by $\sim$ 1,000-3,000 km. The pattern strongly reminds that seen in Saturn’s
North Pole [66], so the dynamical mechanisms responsible of their formation
could be similar.

From the point of view of seasonal variations, there is a global indication of
enhanced cloud activity and convective candidates as the planet was reaching
its equinox in 2007 and afterwards until reaching a peak in 2014. Since 2014
(corresponding to 1/12th of the Uranus year after equinox) there has not been
any strong indication of convective activity, although since 2015, an
occasional bright cloud system appears in the boundary of the North polar
hood.

Figure 1: Candidate features to moist convection in Uranus: (a) A plume-like
feature observed by Voyager 2 in 1986 in Uranus’ southern hemisphere [54, 67].
The arrow signals the direction of rotation and the inset shows details from
[54]; (b) The Berg feature observed in 2007 (arrow) [57] with details in the
inset; (c) The active northern band with multiple spots observed in 2004 [60,
61]; (d) Bright spot observed in 2005 [60]; (e) The brightest spot in Uranus
as observed in 2014 [63] with the elongated cloud system with insets showing
details; (f) Cloud cluster in the North Pole observed in 2012 with details
shown in the inset [65]. North is up in all the images. Panels (a-d) show
color composite images based in visible to near infrared wavelengths below 1
$\mu$m with bright features in wide methane absorption bands. Panel (e) from
images in band H (1.6 $\mu$m) with insets using a combination of near infrared
images in bands H (blue), a CH4S filter (1.53-1.66 $\mu$m, green) and K’ (2.2
$\mu$m, red), being the latter the most sensitive to high clouds. Panel (f)
shows observations in band H.

###  2.2 Convective activity in Neptune

Figure 2: Candidate features to moist convection in Neptune: (a-e) Variable
activity at the center of the anticyclone DS2 in 1989 from Voyager 2 [71]; (f)
Details at the center of DS2 [52, 71]; (g) The ”scooter” imaged by Voyager 2
[52]; (h) Details of the SPF observed by Voyager 2 [76]; (i) Bright equatorial
cloud complex in 2017 at near infrared wavelengths [77]. Panels (a-g) in
Voyager 2 clear filters (a-b), orange (c), violet (d), green (e), blue (f) and
green (g). Panel (h) is a false color composite with red, green and blue from
observations in yellow, blue and ultraviolet light respectively. Panel (i)
show images on moderate to strong methane absorption wavelengths in band H
(1.63 $\mu$m), CH4 (1.59 $mu$m) and K’ (2.12 $\mu$m).

Neptune is much more active in producing new cloud systems and cloud
variations than Uranus, with large-scale changes occuring regularly [75]. The
stratosphere of Neptune has a higher abundance of CH4 than the saturated
abundance at the cold tropopause [34], and the stratospheric abundance of CH4
in Neptune is nearly 3 orders of magnitude larger than in Uranus. Early
attempts to understand these high stratospheric abundances in Neptune relied
on moist convection as a mechanism able to transport methane to the
stratosphere [68, 69]. Another possibility is that methane could leak out to
the stratosphere through warm regions like the hot south polar region [35]
without the need for strong convection. However, this scenario is in conflict
with circulation patterns that could explain the thermal structure observed in
the planet’s stratosphere [70, 36, 6]. Here we review observations of Neptune
that suggest vigorous methane moist convection on discrete cloud systems.

Since the Voyager 2 flyby in 1989, Neptune has exhibited a rich variety of
bright and dark spots with their related ”orographic” cloud companions [52,
71]. Clouds with some characteristics of convective storms were observed by
Voyager 2 in at least two features. One was in the interior of the so-called
DS2 anticyclone at 55∘S, where bright and high altitude clouds developed
displaying rapidly changing morphology (Fig. 2a-f). The relation with the
vortex dynamics is a challenging issue. This vortex was an anticyclone, but
convective storms in Jupiter and Saturn that resemble the possible convection
inside DS2 develop in cyclones [72, 47, 38]. Furthermore, two transient bright
spots, suggestive of convective activity were also observed in 2007 in
Neptune’s South Pole [73], where the wind profile shows cyclonic vorticity.

Voyager 2 images also showed a complex system of narrow streaks stacked in
latitude and forming the so-called ”scooter” at 40∘S, extending about $\sim$
3,000 km (Fig. 2g). Their clouds were deeper than its surroundings but their
plume-like structure was interpreted as formed by updrafts in a region with
vertical wind shear [71]. In fact, the latitude band $\sim$37-47∘S has also
been very active in bright spot activity during the last 20 years, as recorded
by a variety of telescopes [74], including amateur observers [75]. These spots
with sizes in the range 4,000 – 8,000 km stand out in red and near infrared
wavelengths, where methane absorptions occurs, therefore implying cloud tops
high in the atmosphere, but their convective origin can not be proven with the
existing data.

Bright clouds are also found in the South Polar Feature (SPF) (Fig. 2g) and
South Polar Waves (SPW), apparently permanent cloud systems since the Voyager
2 flyby and located at sub-polar latitudes (60-70∘S) [76]. Both are formed by
elongated clouds that display a very stable motion that has been suggested to
represent Neptune’s rotation period. The clouds have been proposed to be
related to a Rossby wave, but where localized convection could occur regularly
forming the small bright spots embedded on it (Fig. 2h).

The brightest spot observed in Neptune was a large bright spot centered at 2∘N
that lasted 7 months in 2017 [77] (Fig. 2i). It developed two equatorial
bright cloud systems with the largest one showing a variable zonal extension
$\sim$ 8,500-12,000 km and $\sim$ 6,000-9,000 km of meridional size and
reaching the altitude level of 300-600 mbar. This cloud system was proposed as
a good candidate for methane moist convection. No dark vortices that could
explain the formation of these cloud systems were expected or found at the
equatorial latitude of the bright spots.

We stress that, while most of the features shown in Figures 1 and 2 are very
good convective storm candidates, we cannot make a definite statement on their
convective nature. According to what we know on Jupiter and Saturn, convective
storms can reach horizontal sizes $L$ in the range $L/R\sim 0.01-0.1$, where
$R$ is the planetary radius. These are sizes comparable to most cloud systems
described above. These convective storms should be formed by clusters of
updrafts with horizontal sizes comparable to the scale height $H\sim 30-50$ km
(depending on the temperature). Resolving these elements is currently
impossible with ground based telescopes, HST or the future JWST, but will be
in the limit of the ELT. Observations that could determine the convective
nature of a particular cloud system require high-spatial resolution over
multiple wavelengths from the continuum to the near IR methane absorption
bands together with the time evolution of the global cloud fields. The
apparent low frequency of convective candidates makes unlikely that such
observations will be obtained from a combination of ground-based AO
observations and HST or JWST observations, and the short flybys by Voyager 2
did not produce a dataset large enough to characterize convective candidates.
Only observations from an orbiter mission seem able to provide such data [1].

##  3 Vertical structure of the atmosphere

The cloud systems described in the previous section are observed at levels
compatible with methane condensation. In Jupiter and Saturn, thermal infrared
(typically at 5 $\mu$m) sensitive to 2-4 bar and radio observations allow to
glimpse in the dynamics of the clouds below. In Uranus and Neptune, the colder
temperatures of the atmosphere imply that observations in the microwave to
milimiter wavelengths are needed to peer below the upper clouds. Such
observations using radio interferometers result in a banded structure of the
planets down to 50-80 bar [78, 79]. This deep structure is interpreted as a
signature of the latitudinal distribution of condensables such as H2S, and is
interpreted as caused by a deep global circulation [6]. We here describe the
expected multi-cloud layer structure of Uranus and Neptune and show caveats in
the classical description of the vertical cloud structure.

The volatiles in Uranus and Neptune are methane (CH4), ammonia (NH3), hydrogen
sulfide (H2S), water (H2O) and a mixed cloud of ammonium hydrosulfide (NH4SH).
The formation of ammonium hydrosulfide requires one molecule of NH3 and one of
H2S and desiccates the atmosphere of the less abundant volatile. NH3 is highly
depleted in both planets at pressures lower than 40 bar. This is known from
observations at cm wavelengths where both planets are too bright to allow for
high abundances of ammonia [80, 81]. In addition, H2S has been detected
spectroscopically in both planets [82, 83]. This implies that the S/N ratio in
their tropospheres must be higher than 1, at least down to the NH4SH cloud
base, which is close to the transition from the water ice to the water liquid
level. Given sulfur’s lower abundance in a solar-composition mixture, this
means that sulphur should be enriched at least 5 times more than nitrogen
compared to solar abundance. It also implies the absence of an NH3 cloud.
Potential atmospheric sinks for NH3 and also H2S complicate the
interpretations that can be extracted from the absence of NH3 in the upper
troposphere. These sinks are a suspected liquid water ocean at pressures of 10
kilobar or higher and a ionic/superionic ocean at pressures of hundreds of
kilobars [7].

Most models of the vertical structure of Uranus and Neptune assume
thermochemical equilibrium to describe the vertical location and extent of
cloud layers [84, 85]. Although the complexity of cloud systems on Earth,
Jupiter and Saturn [86, 87, 88] shows that the thermochemical equilibrium
assumption is not realistic, in the current absence of in situ or remote
sensing data below the methane cloud, these models are generally used to
anticipate what to expect below the methane cloud.

Figures 3 and 4 show the thermal, density and volatile vertical structure of
Uranus and Neptune. Thermal profiles obtained from the Voyager 2 radio
occultation experiments [89, 90] ended at pressures of 2.3 bar in Uranus and
6.3 bar in Neptune (highlighted with stars in figure 3a). These levels
correspond to the regions where CH4 and H2S condense, and future atmospheric
occultation measurements that could be obtained by an orbiter could sense the
thermal structure of the atmosphere over different latitudes sampling both
cloud condensing regions. Below those pressures we examine the planets’ deep
tropospheres, considering abundances of 20 and 80 times solar for all
volatiles except for ammonia, which is assumed to be less abundant than H2S,
to be consistent with the spectroscopic detections of H2S vapor in the
tropospheres of both planets.

Figure 3: Temperature pressure profiles measured by radio occultation in
Uranus (green) and Neptune (blue) extended in the deep atmosphere following
wet adiabats with different abundances of condensables. Stars in panel a show
the bottom pressure layer sensed in radio occultation experiments performed by
Voyager 2 in Uranus (green) and Neptune (blue). (a and b): Dashed horizontal
lines represent the cloud base level for different condensates and abundances.
Red profiles indicate possible thermal profiles in the case that moist
convection is fully inhibited producing sharp discontinuities in temperature.
These discontinuities would be found at critical abundances of methane and
water but for simplicity only the one from high water abundance is shown based
in [15]. c: Density profiles as a function of altitude above the 1 bar level
except for the convectively inhibited profile. The kink in the 80 times solar
abundance profile at 550 km is caused by the critical point of water at 647 K.
Pink dotted lines in b and c show the extrapolation of Neptune’s thermal
profile following an adiabat without latent heat release but considering
volatiles with a deep abundance of 80 times solar and relative humidities of
99%.

Other physical processes, including the inhibition of moist convection at high
abundances of methane [14, 15, 16] and water or layered convection [55] can
affect the vertical structure producing small and large thermal and mean
molecular weight discontinuities in the vertical thermal profile. Figure 3b
sketches possible effects caused by the vertical distribution of water and is
based in [15]. It must be noted that these large thermal discontinuities can
be produced in combination with a discontinuity in the mean molecular weight
of the atmosphere and the volatiles concentration without neccesarily
resulting in a large discontinuity in density. Such discontinuities would be
readily found by a descending atmospheric probe, but could be different at
different locations of the planet requiring a characterization of the
descending region from remote sensing observations by an orbiter. Figure 3c
examines the atmospheric density profile for a range of possible deep
abundances of condensables (dry atmosphere, 20 and 80 times solar). The
density profile depends on the thermal structure, the local gravity and local
winds (we here considered the equator and Voyager 2 winds constant in depth).
Because of water’s potential high abundance in the deep tropospheres of the
Ice Giants, it probably dominates the overall mean molecular weight and
controls the density profile.

Figure 4: Thermochemical models of the atmosphere of Uranus and Neptune for 20
times solar abundance of condensables (a), and 80 times solar abundances (b).
Volatiles mixing ratio (colored lines, lower axis) and maximum cloud density
(black lines with shaded regions, upper axis). Horizontal dashed black lines
represent the transition between water ice and liquid water plus ammonia
cloud. The dark red line shows the vertical temperature profile of the
atmosphere (bottom axis). Maximum cloud densities can be calculated following
[85] and are given in g/l (upper axis) assuming an updraft length scale equal
to the atmospheric scale height and following [91] (colored dotted lines) in
g/l per meter (top blue axis) without assuming an explicit updraft length
scale. Panels (c) and (d) show parameters related with the stability of the
atmosphere for 20 and 80 times solar abundances respectively. Green lines show
the vertical distribution of molecular weight (lower axis). Grey lines are the
static stability of the atmosphere (upper axis). Dark red lines are Brunt-
Väisällä frequencies including effects of the vertical gradient of molecular
weight (bottom axis). Red line represents the atmospheric density profile (top
axis). Note the sharp discontinuity for the model with 80 times solar
abundance at the critical point of water.

Figure 4 shows the vertical distribution of volatiles and clouds compatible
with the thermal structure described above. This figure does not take into
account super adiabatic effects or thermal discontinuities associated to the
inhibition of moist convection and can be considered as highly ideal. The
densities associated to the cloud content should be considered as
illustrative, as the real properties of a cloud depend on microphysical
processes including the density of condensation nucleii and precipitation,
which are neglected in these simple models. Properties of real clouds depend
also on the history of the cloud formation and the vertical motions through
the clouds. Densities in Figure 3c do not include contributions from the
clouds.

In both Uranus and Neptune the base of the water cloud lies at pressures of
several hundred to a few thousand bars and their study would require the use
of non-ideal gas laws. Most of the water cloud particles would be in liquid
phase with the potential to dissolve ammonia, desiccating the upper atmosphere
from this volatile. For the models with higher enhancement of volatiles (80
times solar) the water cloud base deepens until reaching temperatures close to
the critical point of water at 647 K at pressures of $\sim 3,000$ bar at a
depth of about 550 km bellow the 1 bar level. The right panels in this figure
show different variables related with the stability of the atmosphere. The
most relevant of this is the vertical gradient of the molecular weight of the
atmosphere. As a result of the increase in methane abundance, the mean
molecular weight in the upper troposphere varies from 2.3 g mol-1 in the
tropopause to 2.5-2.9 g mol-1 at the methane cloud base for 20-80 times solar
abundances, respectively. The mean molecular weight continues to increase in
the lower atmosphere and can reach 2.8-4.2 g mol-1 at the water condensation
level for the range of abundances here explored. For 80 times solar abundances
the water cloud base occurs at the water critical level, an effect expected in
many exoplanets with Neptune-like masses [92].

High values of the deep water abundance result in a combination of high
molecular weight (Figure 4b-d) and lower deep temperatures for profiles where
moist convection is operating (Figure 3b). The high molecular weight
determines a high density at depth expected for high water abundances
suggesting that gravity measurements could be used to uncover the deep
abundance of volatiles.

##  4 Moist Convection in the Ice Giants

Because of the higher stratospheric methane on Neptune than in Uranus [34],
moist convective models have been traditionally developed for Neptune without
additional work to address Uranus convective systems. Different authors [68,
69] have used one-dimensional models of moist convection of methane, or simple
estimations of the maximum Convective Available Potential Energy (CAPE) [77]
that predicted powerful updrafts capable to reach vertical velocities of $\sim
200-250$ ms-1. These updrafts would be able to ascend to the tropopause and
transport methane to the lower stratosphere. However these storms need strong
perturbations of the environment to be initiated (initial vertical velocities
$>40$ ms-1) to counteract the static stability of the atmosphere, very
favourable environments with high humidity to counter-act the weight of
methane gas in the saturated updraft, and very efficient rain-out . These pre-
Voyager predictions of such powerful methane moist convection storms have not
been verified observationally.

An additional complication is that Uranus and Neptune abundances of methane
imply an inhibition of moist convection at pressure levels just below those
directly observed [14]. The moist convection inhibition criteria also applies
in the pressence of double-diffusive convection [15, 16] and it is yet unclear
how heat is transported in such a situation.

In order to get a simplified grasp of the inhibition of convection we will
calculate a few numbers that will help us to show the regions of the
atmosphere where convective inhibition plays a role and we extend this
discussion to the deep clouds that determine the vertical structure of the
atmosphere. We closely follow [17] in this discussion, and ignore the negative
buoyancy effect of the weight of condensates, assuming precipitation is
efficient. There are a number of quantities important to examine the potential
to drive moist convection. One of them is the capacity to produce increases in
temperature by the release of latent heat. The increase of temperature by
latent heat from a condensable $i$ reaching its vapor saturation, $\Delta
T_{Li}$, can be calculated as:

$\Delta T_{L_{i}}=\frac{q_{vi}L_{Vi}}{C_{p}},$ (1)

where $q_{vi}$ is the maximum mass mixing ratio of the condensate $i$,
$L_{Vi}$ is the latent heat per unit mass and $C_{p}$ is the atmospheric heat
capacity per mass.

A second important quantity is the temperature increase required to compensate
for the weight of the volatiles in a wet parcel, $\Delta T_{\mu i}$. This
quantity can be calculated as:

$\Delta T_{\mu i}=-\left[ln(1-\varpi q_{v})\right]T,$ (2)

where $T$ is temperature and $\varpi=(M_{vi}-M_{a})/M_{vi}$ is the reduced
mean molar mass difference calculated from the molar masses of the vapor $i$,
$M_{vi}$, and the dry air, $M_{a}$.

The third quantity is the moist convection inhibition factor $\xi_{i}$ [14,
15, 17], which predicts that moist convection for condensable $i$ is not
possible when $\xi_{i}>1$. This inhibition factor is defined as:

$\xi_{i}=\frac{\varpi M_{vi}L_{vi}}{RT}q_{vi},$ (3)

where $R$ is the ideal gas constant.

For models shown in Figure 4 these quantities are given in Table 1. For
ammonia we assume a slightly different atmosphere with equal ammonia and
hydrogen sulfide resulting in an ammonia cloud with no hydrogen sulfide cloud.
For those condensables where $\xi_{i}>1$ at the cloud base there is always a
level above where $\xi_{i}=1$. This level constitutes the deepest level where
moist convection can be powered for each condensable and is also given in
Table 1 as $P_{c}$. This can be compared with the cloud base $P_{b}$ at the
deepest layer where saturation is reached. So, although moist convection is
inhibited at the base of different clouds, convection is possible in the upper
atmosphere in a range of altitudes, possibly resulting in a complex thermal
and compositional structure of the atmosphere. Adding the mass-loading of
precipitation would complicate further the problem and numerical models will
have to be designed to answer these questions. In addition, dry convection
without latent heat release could be activated by differences in condensable
abundances below their saturation values with moist air sinking and dry air
ascending, an effect that could also be observable in the methane condensation
layer at low optical depth.

Table 1: Convective parameters for different condensables for models of Uranus and Neptune for 20 times solar abundances (1; left columns) and 80 times solar abundances (2; right columns). (*) Ammonia clouds are explored considering a 20 times solar abundance of all condensates (1) or 80 times solar abundance (2). Vapor | $\Delta T_{L1}$ | $\Delta T_{\mu 1}$ | $\xi_{1}$ | $P_{c1}$ | $P_{b1}$ | $\Delta T_{L2}$ | $\Delta T_{\mu 2}$ | $\xi_{2}$ | $P_{c2}$ | $P_{b2}$
---|---|---|---|---|---|---|---|---|---|---
| (K) | (K) |  | (bar) | (bar) | (K) | (K) |  | (bar) | (bar)
CH4 | 4.0 | 5.8 | 1.05 | 1.1 | 1.1 | 18.8 | 33.8 | 3.1 | 1.5 | 1.8
H2S | 0.3 | 0.6 | 0.08 | 7.0 | 7.0 | 1.0 | 25 | 0.2 | 9.4 | 9.4
NH${}_{3}(*)$ | 3.0 | 3.0 | 0.3 | 20 | 20 | 14.5 | 13.9 | 1.1 | 34 | 37
H2O | 34 | 73 | 1.5 | 334 | 490 | 112 | 454 | 2.7 | 415 | 3000

##  5 A complex weather layer

Given current unknowns in the abundances of volatiles in Uranus and Neptune,
their impact in the vertical structure of the atmosphere, and the complexities
of moist convection previously examined, a large range of possible structures
could form below the upper methane clouds in Uranus and Neptune. Which
measurements would provide the most data to solve open questions? We turn to
Jupiter and its better known atmosphere and later examine the measurements
needed for Uranus and Neptune.

###  5.1 Lessons from the Galileo Probe and Juno

In 1995 the Galileo probe entered Jupiter’s atmosphere obtaining measurements
of its composition and vertical structure down to 22 bars [93]. Measurements
of ammonia and water abundances increased in depth but were separated from
saturated profiles. While a deep value of ammonia was found, water was still
highly subsolar and was still rising at the 22 bar level [94]. Explanations of
these measurements required the probe to have descended in a dry location in
the planet caused by local meteorology [95]. The Galileo probe did not find
the deep value of oxygen, which, given the paramount importance of water for
planet formation, also motivated the Juno mission.

Recent measurements of the ammonia latitudinal and vertical distribution
obtained by the Juno MWR instrument resulted in another puzzle. Ammonia is not
uniformly distributed in Jupiter’s atmosphere below the clouds, but depleted
to around 30 bar at all latitudes except at the equator [13]. A viable model
to explain this global desiccation is that water-powered moist convective
storms could trap ammonia in hailstones that would precipitate and deplete the
upper atmosphere of ammonia [25, 26], making water-powered moist convective
storms an essential piece of the jovian meteorology. This mechanism is in
agreement with the ammonia and lower clouds aerosol depletion observed in
Saturn after the development of the large Great White Storm of 2010-2011 [22,
23, 24] and could be a general drying mechanism affecting also the atmospheres
of Uranus and Neptune in case moist convection from a lower cloud could reach
the condensation region of a volatile of the upper atmosphere. The recent
determination of water abundance in Jupiter ($2.7^{+2.4}_{-1.7}$ times solar,
representative of the equatorial region and possibly of the deep atmosphere)
[18] seems to exclude inhibition of water moist convection in Jupiter, which
requires a water abundance of 9.9 times solar [15].

The atmospheres of Uranus and Neptune have the potential to be more complex
than those of Jupiter and Saturn due to the larger values of condensable
abundances, higher number of cloud layers, and the potential transition of
liquid water to vapor at the water critical point for water abundances close
to 80 times solar. The higher abundance of H2S than NH3 in the upper
troposphere requires ammonia depletion mechanisms that could be similar or
different to those proposed in Jupiter and could include dissolution of
ammonia in the liquid water cloud layer or in the interior below the hydrogen-
helium atmosphere.

An exploration of the atmospheres or Uranus or Neptune by an atmospheric probe
[33, 7] would be limited to the first few tens of bars. Radio interferometric
measurements performed by ALMA show the structure of Neptune down to 80 bar at
low spatial resolution, and we have seen that the deep abundance of water
plays a critical aspect in the overall density profile that could be
investigated from a gravity experiment. Measurements from an in situ probe
would require a global characterization by an orbiter [1] sensitive to the
deep structure of the atmosphere through a combination of gravity measurements
and microwave radiation. Such an orbiter could also obtain detailed
observations of the methane clouds and convective storms and could determine
through occultation experiments thermal profiles at several locations of the
planet to depths of a few bars. In Jupiter, the combination of results from
the Galileo Probe, the Juno mission and the detailed observations of jovian
meteorology at the upper ammonia clouds show that such a combination of global
and detailed local measurements is needed to understand its atmosphere. The
alternative to send a secondary or multiple probes at other planet locations
would also highly enhance the capability to study these questions [96], but
would also benefit from a characterization from orbit studying also changes in
the upper atmosphere.

###  5.2 Non-homogeneous weather layers

The standard picture of Uranus and Neptune used during decades assumes well-
defined cloud decks and a temperature profile that follows a moist adiabat
accounting for the condensation of the different species. Meridional
circulation may affect the abundances of condensables and the thermal
properties, producing contrasts in the band pattern of the planet at a variety
of depths [6, 78, 79]. An alternative and more complex picture can be build by
assuming non-homogeneous weather layers where cold dry air could coexist with
warm humid air at the same level, and where convective storms could shape the
characteristics of the atmosphere [17]. The vertical structure of the
atmosphere could have a combination of the following characteristics. For each
one we briefly suggest measurements that could help to advance in each of
these cases.

  * 1.

Variable temperature profile from moist adiabatic to superadiabatic. An
orbiter capable to obtain occultation measurements could investigate the
thermal profile on different locations at least to the methane cloud base.

  * 2.

No ubiquitous methane cloud deck but regular formation of methane clouds
including possible convective storms. These storms could combine strong
updrafts powered by latent heat release and downdrafts powered by the weight
of the condensates and evaporative cooling. Observations obtained from an
orbiter could determine which of the active cloud systems are actually
convective storms and the characteristics of such storms. The risk here is
that we do not know the frequency and time scales of convective events in
Uranus or Neptune.

  * 3.

Deep H2S stable clouds with little impact in the thermal structure. Depending
on the abundance of CH4 and H2S, thermal profiles from occultation
measurements could investigate this question. Observations in the thermal
infrared from thermal emissions emitted from the lower atmosphere above the
NH4SH cloud level could also reveal the dynamics of this cloud layer.

  * 4.

Complex dynamics at the NH4SH cloud layer. This cloud layer could be complex
due to the combination of a large heat release (comparable to the water latent
heat release) and the high molecular weight of its components. This cloud
region can be investigated by thermal emissions in the milimeter and microwave
regime and a Juno-like MWR instrument could investigate the physical processes
in this cloud layer through the planet. Current interferometer telescopes like
VLA and ALMA are currently able to latitudinally map Uranus [79] and Neptune
[78] down to 50-80 bar.

  * 5.

Strong vertical transport at the water condensation layers. The dynamics here
could be an extreme version of the dynamics produced at the methane
condensation region but these deep layers are hidden to observations using
radiation or measurements from an atmospheric probe. Gravity measurements by
an orbiter could investigate the deep abundance of water and a detailed model-
observations comparison may be required to interpret gravity data.

  * 6.

Vertical motions driven by compositional differences and not latent heat
release. In atmospheres with large horizontal compositional gradientes
vertical motions could be driven by compositional differences and not latent
heat release. Updrafts of dry air in a more wet environment could be possible
at any of the condensation regions. Detailed observations of these processes
at the upper CH4 layer could be obtained by observations in the visible and
near infrared.

  * 7.

Ammonia powered storms in exo-Neptunes. Cold exo-Neptunes are likely very
common planets [97], and they may be very diverse in terms of the abundances
of volatiles. In those planets with higher tropospheric abundances of NH3 than
H2S ammonia moist convective storms could have similar strength to methane
storms in Uranus and Neptune. The lack of observed NH3 in Uranus and Neptune
upper tropospheres implies that the best candidates to study ammonia-driven
moist convective storms are Jupiter and Saturn, where ammonia storms seem to
play a minor role compared with water powered storms.

##  6 Conclusions

The mechanisms responsible for the structure, dynamics and energy balance of
the atmospheres of Gas and Ice Giants are complex and poorly known. In
particular, the role of moist convection and precipitation, its importance to
determine the vertical structure of temperature, condensables and density, and
the interplay of moist convection with the large-scale circulation are yet to
be understood. Adding to this complexity, multiple cloud layers and sources of
storms are present in these planets, most of them too deep to be probed
directly. This is for example the case of water, thought to be fueling most of
Jupiter’s and Saturn’s storms, but whose abundance in both planets is poorly
constrained because of its condensation at relatively high pressures and high
optical depths. Owing to their larger distance to the Sun, Uranus and Neptune
possess colder atmospheres with abundant methane cloud activity that could be
interpreted as convective, but the existing data does not allow to determine
which of the possible storm candidates observed are actually moist convective
events. This methane condensation region is at a relatively low optical depth,
and can be probed relatively easily. We thus believe that Uranus and Neptune
are laboratories to understand the underlying physics of atmospheric dynamics
in hydrogen atmospheres. The hidden cloud layers below the upper methane
clouds have a key importance in the global vertical structure of the planets.
Understanding these cloud layers has applications to understand and constrain
the atmospheres, interior structure and evolution of not only Uranus and
Neptune, but also Ice Giants and Gas Giants in general.

Uranus and Neptune remain the only planets in the Solar System that have not
been visited by an orbiting spacecraft. A mission to at least one of them
would bring an essential piece of the puzzle to complete the inventory of our
Solar System, understand the structure and atmosphere dynamics of Ice Giants
and Gas Giants in the Universe. Such a mission should include an orbiter to
fully map and characterize the planet’s atmosphere and its time-variability
[1], and an atmospheric probe [33], or multiprobe system [96], to measure with
high precision the thermal structure and volatile abundance profiles at a
well-defined location, or set of locations. An instrumentation suite similar
to the one carried by Juno would be the most efficient to provide spatial
context to the measurements obtained by a descending probe. The combination of
this information would provide unique data to understand planetary
atmospheres.

Acknowledgements. RH and ASL were supported by the Spanish MINECO project
AYA2015-65041-P and PID2019-109467GB-I00 (MINECO/FEDER, UE) and Grupos
Gobierno Vasco IT1366-19. We are thankful to the Royal Astronomical Society
for hosting the Ice Giant Systems workshop on January 2020 and to Leigh N.
Fletcher for organizing this event.

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