Journal of Geophysical Research: Planets
RESEARCH ARTICLE
10.1002/2016JE005146
Key Points:• Unprecedented 3-D resolved
convective layer of Venusian cloudlayer and induced gravity waves• Convection layer organized aspolygonal closed cells of several
kilometers wide
• Strong impact of the global
circulation on the convection
and its variability

Correspondence to:
M. Lefèvre,maxence.lefevre@lmd.jussieu.fr

Citation:
Lefèvre, M., A. Spiga, and S. Lebonnois(2017), Three-dimensional
turbulence-resolving modeling of
the Venusian cloud layer andinduced gravity waves, J. Geophys.
Res. Planets, 122, 134–149,
doi:10.1002/2016JE005146.

Received 29 JUL 2016
Accepted 16 NOV 2016
Accepted article online 23 NOV 2016
Published online 20 JAN 2017

Three-dimensional turbulence-resolving
modeling of the Venusian cloud layer
and induced gravity waves
Maxence Lefèvre1, Aymeric Spiga1, and Sébastien Lebonnois1

1 Laboratoire de Météorologie Dynamique, UMR CNRS 8539, Institut Pierre-Simon Laplace, Centre National de laRecherche Scientiﬁque, Sorbonne Universités, UPMC Univ Paris 06, Paris, France

Abstract The impact of the cloud convective layer of the atmosphere of Venus on the global circulation
remains unclear. The recent observations of gravity waves at the top of the cloud by the Venus Express
mission provided some answers. These waves are not resolved at the scale of global circulation models(GCM); therefore, we developed an unprecedented 3-D turbulence-resolving large-eddy simulations (LES)
Venusian model using the Weather Research and Forecast terrestrial model. The forcing consists of three
diﬀerent heating rates: two radiative ones for solar and infrared and one associated with the adiabatic
cooling/warming of the global circulation. The rates are extracted from the Laboratoire de Météorlogie
Dynamique Venus GCM using two diﬀerent cloud models. Thus, we are able to characterize the convection
and associated gravity waves in function of latitude and local time. To assess the impact of the global
circulation on the convective layer, we used rates from a 1-D radiative-convective model. The resolved
layer, taking place between 1.0 × 105 and 3.8 × 104 Pa (48–53 km), is organized as polygonal closed cells of
about 10 km wide with vertical wind of several meters per second. The convection emits gravity waves bothabove and below the convective layer leading to temperature perturbations of several tenths of kelvinwith vertical wavelength between 1 and 3 km and horizontal wavelength from 1 to 10 km. The thicknessof the convective layer and the amplitudes of waves are consistent with observations, though slightly
underestimated. The global dynamics heating greatly modify the convective layer.

1. Introduction
Venus hosts a global sulfuric acid cloud layer between 45 and 70 km which has been investigated in detailby the Venus Express mission. One of the main questions that remains unclear about the dynamics ofthe Venusian atmosphere, and its interaction with the photochemistry is how this convective cloud layer
mixes momentum, heat, and chemical species and generates gravity waves. Gravity waves emitted by theconvection have been proposed to promote a signiﬁcant contribution to the maintenance of the superrotation [Hou and Farrell, 1987]. However, these waves develop from regional to local scales and cannot
be resolved by global circulation models (GCM) developed so far to study Venus’ atmospheric dynamics.
Before a subgrid-scale parametrization of those convectively induced waves can be developed in existing
GCMs, small-scale (“mesoscale”) modeling is needed to explore the dynamics of convection and waves in the
Venusian cloud layer.

©2016. American Geophysical Union.
All Rights Reserved.

LEFÈVRE ET AL.

The strong dynamical activity in the cloud layer has been known for a long time. The Mariner 10 mission[Belton et al., 1976] and the Pioneer Venus spacecraft [Rossow et al., 1980] used the UV marker to follow patterns
at the top of the cloud layer and evidenced cellular features with sizes between 200 and 1000 km. The Pioneer
Venus probes investigated the dynamics of the Venus atmosphere: a region of neutral stability between 50
and 55 km was detected [Seiﬀ et al., 1980] and small-scale waves with vertical wavelengths of about 7 km wereobserved [Seiﬀ et al., 1980; Counselman et al., 1980]. The VEGA missions sent two balloons in the convective
layer [Sagdeev et al., 1986], which ﬂoated at approximately 54 km at 7∘ N and 7∘ S. The balloons measured vertical winds ranging between −3.5 and 2 m s−1 inside the convective layer [Linkin et al., 1986] and encounteredconvective cells with an estimated width from several hundred meters to tens of kilometers [Kerzhanovich
et al., 1986].
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The Venus Express [Svedhem et al., 2007] mission has been able to investigate the dynamics of the atmosphereand detect small-scale waves at the top of the cloud layer with the help of the Venus Monitoring Camera (VMC)[Piccialli et al., 2014], the Visible and InfraRed Thermal Imaging Spectrometer (VIRTIS) [Peralta et al., 2008], andthe Venus Radio science device (VeRa) [Tellmann et al., 2009, 2012]. A strong variability of the convective layer
with latitude was observed [Tellmann et al., 2009] with a vertical extent between 49 and 59 km. The Venus
Express instruments also measured the wavelengths of the waves which range between about 2 and 3.5 km
along the vertical [Tellmann et al., 2012] and from 2 km to hundreds of kilometers in the horizontal [Peralta
et al., 2008; Piccialli et al., 2014]. The observations also provided the spatial variability of the waves, which aremainly observed at high latitudes, with a potential link with the topography [Bertaux et al., 2016]. The long
duration of the Venus Express mission, from 2006 to 2014, enabled a precise study of the top of the cloudover several Venus years [Markiewicz et al., 2007; Titov et al., 2012; Hueso et al., 2015]. The observations madewith VMC illustrated the diﬀerent morphologies of the cloud on the dayside, hinting at distinct dynamical
regimes. At low latitudes, mottled dark clouds dominate, suggesting convective activity. Around 50∘ latitude,
the clouds tend to be streaky, suggesting a horizontal laminar ﬂow. At higher latitude, the clouds are brightand almost featureless.
Several numerical models have been developed to investigate the dynamics of the convection layer and theassociated gravity waves. The pioneering models proposed in the 1980s [Schubert and Walterscheid, 1984;
Young et al., 1987] and the 1990s [Leroy and Ingersoll, 1995] were one-dimensional models focusing on thevertical wave propagation in an idealized Venusian atmosphere. Starting from the 2000s, two-dimensional
mesoscale models [Baker et al., 1998, 2000a, 2000b; McGouldrick and Toon, 2008; Imamura et al., 2014] weredeveloped to resolve the convective layer and the associated gravity waves.
The ﬁrst two-dimensional model of the Venusian cloud layer was built by Baker et al. [1998, 1999, 2000a,
2000b]. The model focuses on the convective layer between 47 and 55 km [Baker et al., 1998, 1999], and theinteraction of this layer with another convective layer between 18 and 30 km, either without [Baker et al.,2000a] or with [Baker et al., 2000b] wind shear. The forcing is similar in both studies, a solar heating model at
subsolar point. Baker et al. [1998] predicted the development between 47 and 55 km of alternating updrafts
and downdrafts over 15–30 km in the horizontal, with vertical wind increasing with the solar ﬂux from 2 to
7 m s−1 , and the emission below and above the cloud layer of gravity waves with horizontal wavelengths of
5–30 km. Baker et al. [2000a] discussed the emission of gravity waves in the stable layer between the two convective layers. The results obtained are two strong convective layers with maximum vertical wind of about
15 m s−1 . Baker et al. [2000b] suggested that the presence of a wind shear may create interaction between thetwo convective layers, resulting in the emission of stronger gravity waves.
The modeling study by McGouldrick and Toon [2008] focuses on microphysical processes in the cloud layer. The
dynamical forcing is produced by a vertical wind parametrization designed to mimic the eﬀect of convective
motions resolved by Baker et al. [2000b]. With this model, McGouldrick and Toon [2008] obtained gravity wave
perturbations of several kelvins, consistent with the VeRa observations [Tellmann et al., 2012], and associatedvariation of the optical depth.
The most recent two-dimensional model by Imamura et al. [2014] is forced with solar heating rates based onin situ measurements and infrared heating rates globally averaged over the planet. The main result of the
Imamura et al. [2014] modeling study is the inverse insolation dependence of the convection. The convectionin Venus’ cloud layer is stronger at high latitude, which is consistent with the VeRa observations [Tellmann
et al., 2012], and at night.
Despite past achievements, two-dimensional models have not been able, by design, to address thethree-dimensional organization of the convective layer and, in particular, the size, and shape of observed
convective cells. Moreover, the move toward three-dimensional modeling for the Venusian convective cloudlayer ensures a more complete prediction of the gravity waves emitted by convective motions. This has been
recently explored by Yamamoto [2014] through idealized three-dimensional numerical experiments usingprescribed lapse rate of the potential temperature and turbulent thermal ﬂux.
In this paper, we propose unprecedented three-dimensional turbulence-resolving simulations for the
Venusian convective cloud layer and the associated gravity waves. Our model is the ﬁrst to combine
three-dimensional dynamical integrations with realistic solar and infrared radiative forcing. This allows us to
improve on Yamamoto [2014] and revisit the questions raised by this work on the variability of convectiveLEFÈVRE ET AL.

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activity and emitted gravity waves with local time and latitude. Another novel aspect of our model of theVenus’ cloud layer is the inclusion of the thermal forcing induced by the large-scale circulation in addition to
the radiative forcing.
Our paper is organized as follows. The model is described in section 2. In section 3, we describe the results on
convective motions and gravity waves from a reference simulation. We then explore in section 4 the variabilityof this dynamical activity with latitude and local time. The impact of the global circulation, and the adopted
cloud model, on the convective activity is discussed in section 5. Our conclusions are summarized in section 6.

2. Large-Eddy Simulations for Venus
2.1. Dynamical Integrations
Our three-dimensional simulations are based on the Weather Research and Forecast (WRF) terrestrial model[Skamarock and Klemp, 2008]. The WRF dynamical core integrates the fully compressible nonhydrostaticNavier-Stokes equations on a chosen area of the planet. The mass, momentum, and entropy conservation are ensured by an explicitly conservative ﬂux-form formulation of the fundamental equations, basedon mass-coupled meteorological variables (winds and potential temperature). To simulate the convective
motions, and associated gravity waves, in the Venusian cloud layer, we use the WRF dynamical core as aturbulence-resolving model in so-called large-eddy simulations (LES): the mesh spacing is set to a few hundred meters to resolve the largest turbulent eddies (i.e., plumes) responsible for the majority of energy
transport and mixing processes by buoyant convection [Lilly, 1962; Sullivan and Patton, 2011]. The remainderof turbulent mixing exerted by small, unresolved, eddies is accounted for by a subgrid-scale “prognostic Turbulent Kinetic Energy” closure [Deardorﬀ , 1972], similar to what is done in WRF LES for the Earth [Moeng et al.,2007] and Mars [Spiga et al., 2010].
We focus in this study on both the Venusian cloud layer and the gravity waves emitted above this convective
layer, so we chose domain settings and resolutions compliant with existing two-dimensional studies [Baker
et al., 1998, 2000a, 2000b; McGouldrick and Toon, 2008; Imamura et al., 2014]. The vertical domain ranges from40 to 70 km. The chosen horizontal resolution is 200 m, and the vertical resolution follows an exponential law
with a mean value of 145 m. We set 181 grid points in the three spatial dimensions, so the domain extent
is 36 × 36 × 30 km. This choice of spatial resolution requires a temporal resolution of 1.2 s, as a trade-oﬀ
between numerical stability and computational eﬃciency and small enough to provide high temporal resolution over the lifetime of a convective cell. The horizontal boundary conditions are periodical, and at the topof the domain a free relaxation condition sets vertical velocity to zero. In this study, no background wind shear
is imposed (i.e., no atmospheric superrotation).
2.2. Radiative and Dynamical Forcing
Our Venus LES model couples the WRF dynamical integrations with an oﬀ-line radiative and (large-scale)dynamical forcing based on heating rates extracted from simulations with the Laboratoire de Météorologie
Dynamique (LMD) Venus GCM [Lebonnois et al., 2010]. We use the most up-to-date LMD Venus GCM run whichreached superrotation (similar to the ones described in Lebonnois et al. [2016]). The solar ﬂux scheme is basedon Crisp [1986]. The IR transfer [Lebonnois et al., 2015] is based on Eymet et al. [2009], in an updated version
that uses the cloud model of Haus et al., 2013 [2013, 2014]. Figure 1 details the three distinct heating rates
coupled with our dynamical integrations: two radiative ones for short wave (solar) and long wave (IR) and theadiabatic cooling/warming due to the global dynamics of the atmosphere (mainly the Hadley cell, Lebonnois
et al. [2016]). Heating rates in this paper are expressed in kelvin per Earth day (K/Ed) to compare with previous works. Those heating rates are applied at each dynamical time steps in our model and remain constantthroughout the LES integrations.
Figure 1 shows that the behavior of each heating rate is diﬀerent. The solar heating rate is strictly positiveand increases up to 7.0 × 103 Pa, decreases, and then increases again above 3.0 × 103 Pa. The IR radiativeand dynamics rates add up to mirror the solar rate. These two rates generally decrease with the altitude up
to 7.0 × 103 Pa, increase, and then decrease above 3.0 × 103 Pa. For the IR radiative rate there are also twoareas of increase below 7.0 × 103 Pa: above (4.0 × 104 Pa) and below (1.0 × 105 Pa) the convective layer. The
IR rate signiﬁcantly increases and even become positive below the convective layer. The increase below theconvective layer has no variability with latitude nor local time, while the one above the convective layer has astrong variability with the position on the planet. The dynamical heating rate decrease with altitude is causedLEFÈVRE ET AL.

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Figure 1. The three types of heating rates in kelvin per Earth day (K/Ed) extracted from LMD Venus GCM and used forthe forcing: (a) over the whole vertical extent and (b) more speciﬁcally in the convective layer. Conditions: equator, LT
12 h (noon). Symbols indicate the vertical resolution of the GCM. dTsw stands for the short-wave rate (solar), dTlw for
the long-wave rate (IR), and dTdyn for the global dynamics rate.

by the rising branch of the Hadley cell and associated adiabatic cooling (this is described in further details in
section 4.2 and Figure 16). We could therefore expect a signiﬁcant variability of the convective motions withlatitude.
The initial state of the LES model is interpolated from a temperature proﬁle predicted by the same GCM run as
the one from which heating rates are extracted. The WRF dynamical core uses potential temperature insteadof temperature. In Venusian conditions, caution must be exerted when converting the initial proﬁle and theheating rates from temperature to potential temperature. Following Lebonnois et al. [2010], we use a speciﬁcheat capacity Cp varying with temperature following the formulation[ ]𝜈
T
Cp (T) = Cp0(1)
T0
with Cp0 = 1000.0 J kg−1 K−1 , T0 = 460.0 K and 𝜈 = 0.35. The potential temperature formulation then can be
written]𝜅 0[P𝜃 𝜈 = T 𝜈 + 𝜈T0𝜈 ln reﬀ(2)
P
with Preﬀ = 92.0 × 106 Pa and 𝜅0 =R∕Cp0 , and the static stability S can be written
S=

g
dT
+
dz Cp (T)(3)

where dT∕dz is the variation of temperature with altitude and g the acceleration of gravity. The value of theBrunt-Väisälä frequency N is computed from N2 = Tg S. Figure 2 shows the initial state of the domain (verticalstatic stability proﬁle). The convective layer is clearly seen in the proﬁle as a neutral stability layer extending(for this conﬁguration: equatorial location and local time noon) from 5.0 to 7.0 × 104 Pa.
Our simulations are run long enough so that the combination of radiative and (large-scale) dynamical heating
rates act to destabilize the initial atmospheric proﬁle and to cause convective instability, thereby triggering vertical motions resolved by our LES dynamical integrations which act to mix heat and momentum inthe cloud layer. After several Venusian hours, the system reaches a steady state. Hence, the mixed proﬁleobtained in the cloud layer stems from the plumes resolved by LES integrations, in complete independence
from the initial mixed proﬁle from the GCM (which was generated by a subgrid-scale parameterization inthis model).

3. Simulated Convection and Gravity Waves
We will now focus on a Venus LES run using heating rates for the equator at noon (LT 12 h) to study ﬁrst theconvective behavior, then the induced gravity waves.
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Figure 2. Initial static stability (K/km) vertical proﬁle extracted from the LMD Venus GCM, for the equator at noon.
Symbols indicates the vertical resolution of the GCM.

3.1. The Convective Layer
Figure 3 represents the average static stability and the average potential temperature vertical proﬁles.
Averages are computed the following way: when the simulation has reached the steady state, the average
proﬁle is calculated by taking the average at each vertical level over the entire horizontal domain. The perturbation of a quantity X is X ′ = X − X with X the average vertical proﬁle (or value at the vertical level of interest)of the quantity.
The zero value of the static stability and the constant value of the potential temperature indicates that theconvection takes place between 6.0 × 104 and 3.8 × 104 Pa (50.1 and 53.3 km) with low static stability down
to 1.0 × 105 Pa (48 km). In the radio occultation measurements of VeRa [Tellmann et al., 2009] the convective
layer at the equator was located between approximately 49 and 59 km. The bottom of the resolved convective
layer is consistent in altitude with the observations, although the convection is thinner. The values of the static
stability in the model, up to 15 K/km, are also weaker than in the observations (25 K/km). The small-scale
structures above and below the convective layer are inherited from the vertical linear interpolation from theGCM vertical resolution, from the vertical cloud structures and also from the resolved motions.
Figure 4 shows two snapshots of the convective motions: a vertical cross section in the middle of the domain
and a horizontal cross section in the middle of the convective layer, at 4.7 × 104 Pa. Values of vertical wind
weaker than observations are predicted by the model: between −1.6 and 1.2 m s−1 against −3.5 to 2 m s−1 forthe measurements made by the VEGA balloons [Linkin et al., 1986]. Figure 4b delivers information about theorganization of the convection. The convective layer develops as closed hexagonal-like type of cells, i.e., withbroad updrafts in the center of the cells and narrow downdrafts at the edge. This indicates that radiative cooling in the middle cloud drives the convection [Agee et al., 1973] and leads to downdrafts being stronger thanFigure 3. (a) Average static stability (K/km) vertical proﬁle and (b) average potential temperature (K) vertical proﬁle, forequator, noon. Here and after the symbols indicate the vertical resolution of the LES model, except when it is indicated.

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Figure 4. Snapshots of the convective vertical motions: (a) vertical cross section at y = 18 km and (b) horizontal crosssection at 4.7 × 104 Pa of the vertical wind (m s−1 ), for Equator, noon. The black line in Figure 4a represents the locationof the horizontal cross section in Figure 4b. The green circles represent location discussed in the text.

updrafts. These cells are about 6 km wide, which is consistent with, but, again slightly lower than the VEGA
measurements [Kerzhanovich et al., 1986], whereas the downdrafts are only a couple kilometers thick. The
width
is then approximately 3, while on the Earth the value for closed cell is between
aspect ratio of the cells height
3 and 28 due to much wider cells [Atkinson and Zhang, 1996].
The vertical eddy heat ﬂux deﬁned as Cp 𝜌w′ 𝜃 ′ (in W m−2 , with Cp the speciﬁc heat calculated from equation (3),𝜌 the density calculated with the ideal gas law, 𝜃 ′ the potential temperature perturbation, and w′ the verticalwind perturbation) is shown in Figure 5. The heating rate (in kelvin per Earth day) associated with resolved
convective motions is, to ﬁrst order, equal to the negative of the vertical gradient of w′ 𝜃 ′ . The ﬂux is increasingin the bottom half of the convective layer (from 6.0 × 104 to approximately 5.0 × 104 Pa) and decreasing in
the top half. Thus, convection acts to cool down the bottom half of the convective layer and warm up the top
half. This heat transport, in conditions where 𝜃 ′ w′ > 0, is exerted mostly by warm updrafts (𝜃 ′ > 0 and w′ > 0)and cold downdrafts (𝜃 ′ < 0 and w′ < 0). By analogy with planetary boundary layer (PBL) convection on the
Earth and Mars, we could deﬁne this core layer of convective motions as the mixing layer. This mixing layer iscapped by a thin layer where w′ 𝜃 ′ is both increasing (i.e., convection cools down this layer) and negative (i.e.,heat transport exerted by cold updrafts and warm downdrafts): the action of updrafts thus dominates in thislayer, which we identify as an updraft-induced entrainment layer by analogy with terrestrial and Martian PBL
convection (an interpretation that diﬀers from Baker et al. [1998]). The mixing layer is also overlying a thin layer
where 𝜃 ′ w′ is both decreasing (i.e., convection warms up this layer) and negative (i.e., heat transport exerted
by warm updrafts and cold downdrafts): the action of downdrafts thus dominates in this layer, which we
identify as a downdraft-induced entrainment layer (which has no counterpart in terrestrial and Martian PBL,

Figure 5. Vertical proﬁle of the turbulent heat ﬂux (W m−2 ), for Equator, noon.

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Figure 6. Schematic representation of the link between the convective cells with associated convection heat ﬂux andlayers. (left) The vertical proﬁle of w′ 𝜃 ′ with its sign. Next to it is the sign of the vertical gradient of w′ 𝜃 ′ with color
representing warming for red and cooling for blue. Then is represented several plumes with color representing warm
(𝜃 ′ > 0) for red and cool for blue (𝜃 ′ < 0).

an interpretation similar to Baker et al. [1998] and Imamura et al. [2014] although, in contrast to Baker et al.
[1998], we also name this layer an entrainment layer). Thus, according to our simulations, the convective cloudlayer on Venus is made of a mixing layer that is underlain and overlain by two entrainment layers, the one
above where the action of updraft overshoots dominate and the one below where the action of downdraft
overshoots dominate (making the two sides propitious to the emission of gravity waves). Figure 6 sums up
the link between the convection cells and associated convective heat ﬂux. This results from the convection
being forced from below by net warming and above by net cooling, as a result of the infrared, visible, andlarge-scale dynamical contributions detailed in Figure 1.
3.2. The Induced Gravity Waves
Here and after we use the Cartesian system as coordinate system with the vertical axis as z axis, and the twohorizontal axis as x axis and y axis.
Figure 7 displays a snapshot of a vertical cross section of the temperature perturbation at y = 18 km and an
instantaneous vertical proﬁle of the temperature perturbation at x = 18 km. The induced gravity waves arevisible as alternating positive and negative perturbations of temperature. The gravity waves are emitted both
below and above the convective layer. The perturbations are between −0.13 and 0.16 K, while VeRa measured
the temperature perturbations between −1.7 and 1.7 K at 19.6∘ of latitude [Tellmann et al., 2012]. The gravity
waves obtained are weak compared with the observations but as is mentioned above, this is directly linked
to the modeled convective layer being weaker than observed.
The peak-to-peak amplitude of temperature perturbations above the convective layer is quite constant up to
2.0 × 104 Pa, while it strongly decreases above this level (at approximately 104 Pa, around 59 km, the inten-

Figure 7. Snapshots of the gravity waves: (a) temperature perturbation (K) vertical cross section and (b) instantaneousvertical proﬁle at the center (x = 18 km and y = 18 km) of the domain, for equator, noon.

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Figure 8. Snapshot of the gravity waves: the horizontal cross section of the vertical wind (m s−1 ) perturbation at
3.0 × 104 Pa, for equator, noon. The green circles represent location discussed in the text.

sity of the waves becomes too weak and no wavefront is discernible). A similar decrease is observed in theradio occultation carried out using the Magellan [Hinson and Jenkins, 1995] spacecraft and the Venus Express[Tellmann et al., 2012] missions. At ﬁrst glance, this phenomenon is counterintuitive, since the decrease of density with altitude usually causes an increase in the amplitude of the waves [Frits and Alexander, 2003]. However,in a very similar way to the static stability (Figure 3a), above the convective layer the Brunt-Väisälä frequency
decreases between 2.0 × 104 Pa and 5.0 × 103 Pa (this decrease may be linked to the radiative damping of
the atmosphere [Hinson and Jenkins, 1995]). Such variation with altitude of the Brunt-Väisälä frequency could
imply a variation with altitude of the energy of the waves [VanZandt and Fritts, 1989], namely, when the frequency decreases the energy decreases. The fact that the amplitude of the waves decreases with altitude
would indicate that the impact of the decrease of the Brunt-Väisälä frequency is stronger than the impactof the decrease of the density. This is further suggested by the emitted gravity waves being high-frequency
gravity waves (see below), which makes them particularly sensitive to changes in background Brunt-Väisälä
frequency.
In the horizontal plane, the wavefront of the gravity waves is circular as illustrated in Figure 8 with the vertical wind perturbation, 1 km above the convection at 3.0 × 104 Pa (see, e.g., the green circles at x = 6 km andy = 20 km or x = 18 km and y = 24 km). These structures are correlated with the position of the updrafts(see the green circles in Figure 4): when the plumes reach the top of the convective layer, they encounter andperturb the stable layer above. This leads to the emission of gravity waves [Fovell et al., 1992], which propagate vertically and horizontally with no preferred axis (i.e., with circular wave fronts, note that the eﬀect of abackground wind shear on the propagation of those waves will be investigated in another study). Therefore,
stronger plumes lead to stronger waves.
To characterize the waves, we use a continuous wavelet transform with the Morlet wavelet deﬁned in Torrence
and Compo [1998] (Python software by Evgeniya Predybaylo, available in this URL http://paos.colorado.edu/
research/wavelets). In Figure 9, we obtain through this wavelet transform that the horizontal wavelength
ranges from 1 to 5 km. The multiplicity of the wavelengths suggests possible interference between the waves.
The values of the wavelengths are consistent with the observations, between 2 and 30 km for VMC [Piccialli
et al., 2014], but still on the lower side of the spectrum. This can be attributed to the weak convection, butalso to the size of the domain: with a wider one, larger wavelengths should be able to develop. We applied
the same methodology for vertical wavelengths, it ranges between 1 and almost 3 km below the convective
layer, the same order of magnitude of the VeRa observations, between 2 and 3.5 km [Tellmann et al., 2012].
̂ (theUsing the horizontal and vertical wavelengths of the gravity waves, the intrinsic angular frequency 𝜔angular frequency 𝜔 with respect to the background wind) can be estimated. Since the background wind
shear is set to zero, the intrinsic frequency is equal to the frequency. Given that the Coriolis parameter,f = 2Ωsin(𝜙), is negligible because of the weak rotation Ω of the solid body, and considering that the squareLEFÈVRE ET AL.

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Figure 9. (a) Vertical wind perturbations (m s−1 ) cross section at 3.0 × 104 Pa and x = 18 km and (b) the associatedwavelet power spectrum, for equator, noon. The areas circled in green are the areas with at least 95% of conﬁdence level.

of the vertical wave number m2 ≫ 1∕4H2 with H the Venus scale height (equals to 7 km in the cloud), thedispersion relation [Frits and Alexander, 2003] then reads( )()
N2 kh2N2 k 2 + l 2
𝜔2 = 2 2== N2 cos2 𝛼(4)
k + l + m2
kh2 + m2
where N is the Brunt-Väisälä frequency, k, l, and m, respectively, are the wave number in the x axis, y axis, andz axis, and 𝛼 is the angle between the line of constant phase and the vertical axis. From the circular wavefront√
we can assume that k and l are equal and so we deﬁne kh as the horizontal wave number equal to k2 + l2 .
The order of magnitude of N2 above the convective layer (10−4 s−2 ) is consistent with observations by the
Pioneer Venus probes [Gierasch et al., 1997]. With a vertical wavelength of 1.5 km and horizontal wavelengthsof 1 and 5 km, the angular frequencies are 9 × 10−3 and 3.9 × 10−3 s−1 , i.e., the high-frequency regime close
to N. The associated angle 𝛼 are 25.23∘ and 67.01∘ .
With the same assumptions as the ones made for the dispersion relation, the group velocity (cgh , cgz ) deﬁned
as 𝜕𝜔∕𝜕k simpliﬁes as(cgh , cgh ) = (uh , 0) +(m, −kh )(m, −kh )
Nm
Nm
= 2
(
)
(
)
kh2 + m2 k2 + m2 1∕2
kh + m2 k2 + m2 1∕2
h

(5)

h

with cgh and cgh , respectively, the horizontal group velocity and the vertical group velocity. The group velocities with the diﬀerent horizontal wave numbers vary from −0.39 to −0.79 m s−1 for the vertical component
and from 0.18 to 1.8 m s−1 for the horizontal component. The horizontal phase velocity, deﬁned as 𝜔k , ranges
from 1.43 to 3.1 m s−1 for horizontal wavelengths of 1 and 5 km. These values are the same order of magnitude (from 5 to 10 m s−1 ) that the VeRa observations [Tellmann et al., 2012] and the ones in Baker et al. [2000a].
The measured meridional wind reaches several meters per second [Hueso et al., 2012; Khatuntsev et al., 2013];
thus, the wave packets propagating in the right meridional direction would reach critical level and eventually
break. It appears less probable that this would occur in the zonal direction given the amplitude of superrotating winds [Sánchez-Lavega et al., 2008]. A full LES study of the waves with a background wind shear isnecessary and is considered as future work.
To summarize, the model predicts a convective layer too thin, though with realistic vertical winds, and provides insight on the cellular organization of the convection. The amplitude of the gravity waves is impacted
by the weak convection; they are of lower amplitude than the observations and with wavelengths in the orderof magnitude of the smallest observed.

4. Variability With Local Time and Latitude
Observations of the gravity waves on Venus [Peralta et al., 2008; Tellmann et al., 2012; Piccialli et al., 2014]
showed a strong variability with latitude (with a preference for higher latitudes). In the VeRa observations[Tellmann et al., 2009], the convective layer is thicker at high latitude but exhibits no clear variability with local
time, which is at odds with the model predictions of Imamura et al. [2014]. In what follows, we discuss thevariability of the modeled convective layer with local time and latitude.
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Figure 10. Comparison of the average static stability vertical proﬁle (K/km) at the equator, for noon (LT 12 h) andmidnight (LT 00 h).

4.1. Variability With Local Time
Figure 10 shows the average static stability at the equator compared between noon and midnight. The convection is thicker at midnight; it extends from 1.0 × 105 to 3.8 × 104 Pa (from 48 to 53.3 km). At midnight(Figure 11) the vertical wind ranges from −2.9 at 2.2 m.s−1 in the middle of the convective layer. The cells arealso larger, with typical width of 15 km. With a vertical extent of 5 km and, the aspect ratio is equal to 3, very
similar to the one at noon. The temperature perturbations are also stronger (Figure 12a) at midnight comparedat noon, typical values are between −0.35 and 0.5 K with circular wavefront (Figure 12b). Horizontal wavelengths are similar to the noon simulation, except for some very localized areas with horizontal wavelengthof almost 10 km, while vertical wavelengths reach 3 km.
The equator showing a stronger convection at midnight is not observed: the VeRa proﬁles exhibit very low
variability with local time. However, the behavior of our model is consistent with the simulations of Imamura
et al. [2014]. The stronger convection at midnight is interpreted as a stabilization of the convection by thesolar heating of the cloud top. The IR heating rates are similar in the convective layer (between 1.0 × 105 and
4.0 × 104 Pa) for the two conﬁgurations, but the heating rates associated with the global circulation are diﬀerent (Figure 13): negative at noon, no clear trend at midnight. At noon the dynamical heating rate compensates
the solar rate, which results in a weaker convection than at midnight.
At 60∘ of latitude, the convection at noon and midnight are very similar (Figure 14). The convective layers
extend from 5.8 × 104 Pa and 5.5 × 104 Pa for, respectively, noon and midnight to both 3.8 × 104 Pa. The

Figure 11. Snapshots of the convective vertical motions: (a) vertical cross section and (b) horizontal cross section at
6.4 × 104 Pa of the vertical wind (m s−1 ), for the equator, midnight. The black line in Figure 11a represents the locationof the horizontal cross section in Figure 11b.

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Figure 12. Snapshots of the gravity waves: (a) temperature perturbation (K) vertical cross section and (b) horizontal
cross section of the vertical wind perturbation (m s−1 ) at 3.0 × 104 Pa, for equator, midnight. The black line in Figure 12a
represents the location of the horizontal cross section in Figure 12b.

vertical winds are between −1.5 and 1.2 m s−1 at noon and between −1.0 and 0.75 m s−1 at midnight. The
temperature perturbations at noon are about ± 0.15 K against ± 0.10 K at midnight. The wavelengths of theassociated waves are similar to the equator noon case. The IR heating rates are extremely similar, while theheating rates associated with the global circulation have two diﬀerent behaviors (Figure 13). The dynamical
heating rate at noon oscillates between positive and negative values below 2.8 × 104 Pa while being 1 orderof magnitude less than the radiative heating rates at the top of the cloud. Conversely, the dynamical heating
rate at midnight has a behavior similar to the solar heating rate at noon: positive and increasing with altitudein the same order of magnitude. Thus, at night, the adiabatic warming by the global circulation compensates
the absence of solar heating, resulting in the convective layer at midnight and noon being of similar extent.
4.2. Variability With Latitude
At noon (Figure 15) there is very low meridional variability in the vertical extent of the convective layer
between the equator and 60∘ of latitude. This behavior is not consistent neither with the VeRa proﬁles nor
with the model of Imamura et al. [2014] which both exhibit a signiﬁcant variability with latitude. Nevertheless,the predictions of our model are consistent with the imposed radiative and large-scale dynamical heating
rates. In the convective layer region, the IR heating rate is exactly similar in our model for both latitudes. The
solar heating rate is approximately 3 times stronger at the equator. The dynamics heating rate (see Figure 13)
at the equator is negative and about the same order as the IR heating rate and follow a behavior symmetrical to the solar heating rate. At 60∘ the dynamics heating rate is weak, about 1 order of magnitude lower.

Figure 13. Global dynamics heating rates in Kelvin per Earth day (K/Ed) extracted from the LMD Venus GCM: (a) over thewhole LES vertical domain and (b) in the convective layer. The four proﬁles represent the four conﬁgurations studied.
The symbols represent here the vertical resolution of the GCM.

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Figure 14. Comparison of the average static stability vertical (K/km) proﬁle at 60∘ latitude, for noon and midnight.

Thus, at the equator the solar rate and the global circulation rate compensate each other, which results in a
weak convection; at 60∘ the situation is similar (although with weaker rates), which results in a similarly weak
convection than that close to the equator. Our model also predicts that contrary to noon at midnight, theconvection is stronger at the equator. This is due to a strong heating rate of the global dynamics at 60∘ thatcompensates the IR heating rate, while at the equator the weak global dynamics heating rate leads to a thickconvective layer.
Figure 16 illustrates the link between the convective layer and the global circulation of the GCM. The global
dynamics is clearly diﬀerent between day and night. At 60∘ of latitude, the convective layer is within a descending branch at midnight and within a rising branch at noon. In contrast, at the equator, it is within the uprisingbranch of the Hadley cell both at noon and midnight. This is in agreement with the imposed dynamical heating rates (Figure 13), showing an adiabatic warming at 60∘ at midnight, and an adiabatic cooling at the equator
at noon.
These discrepancies between observations and our model deserve further comments. The global geographical coverage of the VeRa retrievals [Tellmann et al., 2009] would have allowed to detect variations withlocal time. The absence of observations of gravity waves at low latitude (inferior to 40∘ ), due to a lack ofbrightness contrast [Piccialli et al., 2014], could be something very interesting to investigate further withthe ongoing Akatsuki mission or the future missions. The simplicity of the forcing used, completely dependant of the GCM simulations and especially on the low vertical resolution of the convective layer heating
rates may lead to some approximations on the heating rates. The temporal and horizontal homogeneity of
the forcing could as well have a signiﬁcant impact on the convective layer: with such spatial resolution theradiative-photochemical-dynamical feedbacks could be very important. We are therefore currently developing a mesoscale model coupled to the full radiative scheme to better resolve this kind of mechanism.

Figure 15. Comparison of the average static stability (K/km) vertical proﬁle at noon, between equator and 60∘ latitude.

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Figure 16. LMD Venus GCM vertical wind: (a) at noon and (b) midnight in the cloud convective layer altitudes. The blacklines represent the convective layer of the four spatial conﬁguration. The units is in Pa/s; therefore, positive value means
negative (downward) vertical wind in m s−1 and conversely.

Furthermore, the GCM uses a cloud model uniform in latitude; this may have an impact on the variability withlatitude. The variability of the cloud model with latitude will be implemented in future studies.

5. Impact of the Global Circulation and the Cloud Model
5.1. Global Circulation Dynamics
As it is described above, the global circulation plays an important role on the convective layer by warming
and cooling the atmosphere. To assess in a more quantitative fashion the impact of this circulation, we carried
out Venus LES with heating rates calculated from a one-dimensional version of the LMD Venus GCM. In otherwords, the heating rates correspond to a purely radiative-convective model devoid of large-scale dynamics:
the solar heating rate is similar to our reference Venus LES and the IR heating rates too (up to the top of theconvective layer), while the dynamical heating rate is zero.
Figure 17 is a comparison of the static stability at the equator at midnight between the reference Venus LES
and the one using forcing from one-dimensional radiative-convective computations. The convection is thicker
when the large-scale dynamical heating rate is not included: it extends from 1.1 × 105 to 2.5 × 104 Pa (47.5
to 56.4 km) with vertical wind between −4.7 and 2.8 m s−1 and typical values of gravity wave temperature
perturbations of ± 0.6 K (which horizontal wavelengths are similar to the reference Venus LES including the
dynamical heating rate).
The convection in the cloud layer at 60∘ and midnight is stronger in the no-dynamics case. It extends from
1.0 × 105 to 2.5 × 104 Pa (48.0 to 56.4 km). In contrast, at the equator at noon the convection is very weak

Figure 17. Comparison of the average static stability (K/km) vertical proﬁle with and without dynamics, for equator,
midnight.

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Figure 18. Comparison of the average static stability (K/km) vertical proﬁle at the equator at midnight between forcing
using heating rates calculated from Haus et al. [2014] and Zasova et al. [2007] cloud models.

when the large-scale dynamical heating rate is neglected. At the altitude of 9.0 × 104 Pa, an area with much
weaker plumes is visible, with a lack of organization as clear polygonal cells. The variabilities with latitude andlocal time of the case without dynamics are very similar to the ones of Imamura et al. [2014].
Our exploration in this section thus reinforces the conclusion from section 4 that the global dynamics plays aimportant part in the variability of the convective layer with latitude and local time.
5.2. Cloud ModelIn the modeling of the chemical and microphysical processes being a work in progress in the LMD Venus GCM,
the formation of clouds is not yet implemented in our simulations: a cloud radiative model is simply derived
from the observations. In the results presented so far, the cloud model of Haus et al. [2014] was used. To test
the sensitivity of our predictions to the cloud model, we carried out Venus LES using heating rates derived
from LMD Venus GCM runs with the cloud model of Zasova et al. [2007] [see Lebonnois et al., 2016]. Retrievalsof the cloud properties in Haus et al. [2014] (hereafter H14) are based on VIRTIS/VEX spectra, while Zasova et al.
[2007] (hereafter Z07) used data set from Venera 15/Venera 16 and Vega 1/Vega 2 missions. In Figure 18 wecompare the results of Venus LES using the two distinct cloud models.
The convective layers obtained with the two cloud models clearly exhibit diﬀerences, which make the choiceof cloud model a key aspect in modeling the convection in the Venusian cloud layer. With the Z07 cloudmodel, the convection extends from 1.2 × 105 Pa to 5.5 × 104 Pa with vertical wind between −1.7 and 1.7 m s−1
and temperature perturbations with typical values of ± 0.2 K. Hence, the convective layer is both thicker andhigher (thus more consistent with the VeRa proﬁles) when using the H14 cloud model than when using theZ07 model. There is no predicted diﬀerence, however, in the wavelengths of the emitted gravity waves andthe variability of the cloud layer convection in latitude and local time. This preliminary analysis remains to becomplemented in future work coupling our Venus LES model with a representation of microphysical processes
as in McGouldrick and Toon [2008].

6. Conclusion
We performed unprecedented three-dimensional LES simulations of the convective cloud layer of Venus andthe induced gravity waves, with a radiative forcing consisting of IR and solar heating rates and an additional
heating rate associated with the global circulation extracted from the LMD Venus GCM.
The resolved convective layer is several kilometers thick, with vertical winds up to several meters per second,and organized horizontally as polygonal closed cells of about 10 km wide. The gravity waves emitted by theconvection (both above and below the convective layer) drive temperature perturbations of several tenths ofkelvins with vertical wavelengths from 1 to 3 km and horizontal wavelengths from 1 to about 10 km. These
results are in good agreement with the observations though our Venus LES is underestimating the thicknessof the convective layer and the amplitude of the gravity waves. As expected, the convective layer is stronglyLEFÈVRE ET AL.

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dependent on the cloud model used to calculate the heating rates, with the latest cloud model of Haus et al.
[2014] providing better comparison with observations.
The variability of the model with latitude and local time is diﬀerent from previous modeling. The additionof the heating rate associated with the global circulation provides an estimate of the impact of the global
circulation on the convective layer and proves to be a crucial inclusion to Venus LES for the cloud layer. By
warming up and cooling down the convective layer, the global dynamics tends to mitigate the convection.
The simplicity of the adopted forcing may be responsible for the diﬀerences between our model predictions
and the observations. Indeed, a complete radiative-photochemical-dynamical coupling in our Venus LES may
be key to understand the convective cloud layer of Venus. The follow-up to this work is thus to develop a Venus
LES model capable to couple the WRF dynamical integrations with the complete physical parameterizations
for Venus by Lebonnois et al. [2016], in a broader project to build a complete mesoscale model for Venus ina similar fashion to what was done on Mars by Spiga and Forget [2009]. Another area of improvement is toimplement an extension of the domain in the vertical (from 0 to about 90 km) to resolve the planetary boundary layer and the two convective layers (18–30 km and 50–60 km altitudes) and in the horizontal over 100 km
wide to study the full spectrum of emitted gravity waves, and their possible link with topography [Blamont
et al., 1986; Sagdeyev et al., 1992; Titov et al., 2012; Piccialli et al., 2014; Bertaux et al., 2016]. Further applicationsof our Venus mesoscale model will undoubtedly arise in the near future from the upcoming observations of
Akatsuki and future Venus missions.
Acknowledgments
The authors acknowledge support
from CNES and thank the tworeviewers for their constructive
comments which helped to
improve the paper. Results from thesimulations performed in this paper
are available upon request (contact:maxence.lefevre@lmd.jussieu.fr).

LEFÈVRE ET AL.

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