A numerical study on convectionof a condensing CO2 atmosphere
under an early Mars like condition
Tatsuya YAMASHITA1, Masatsugu ODAKA2,Ko-Ichiro SUGIYAMA3, Kensuke NAKAJIMA4,Masaki ISHIWATARI2, Seiya NISHIZAWA5,
Yoshiyuki O. Takahashi6, Yoshi-Yuki HAYASHI6
odakker@gfd-dennou.org
1 Geospatial Information Authority of Japan, 2 Hokkaido University, Japan,
3 Institute of Space and Astronautical Science, Japan,
4 Kyushu University, Japan, 5RIKEN AICS, 6 Kobe University, Japan

Warm climate and CO2 ice cloud in Early Mars
• Major atmospheric component, CO2, condenses, and theice clouds are widely distributed.
• In Early Martian climate study, stratiform cloud is assumed.
– The nature of convective CO2 cloud is not studied well.
(km)
100

Temprature by 1D model(kasting 1991)

80

CO2 cloud distribution by GCM(Forget et al. 2013)

(km)
40

Deep CO2
saturation layer

60

2040

200 0

CO2 cloud exists
wide region

0200

300

(K)

90S

EQ

90N

Condensation convection of CO2 and cloud type(Colaprete et al. 2003)• Whether supersaturation is allowed or not is key point.
– No: Stratiform cloudP×Yes: Convective cloud

NearlyneutralAir
parcelPCan obtainbuoyancy

AirparcelTT• However, circulation features and cloud distribution due
to condesation convection of CO2 are not examined.
– Results of Colaprete et al.(2003) is based on 1D cloud model.

The purpose of this study• We investigate circulation features and cloud
distribution associated with condensation convectionof CO2 under Early Mars condition– Use 2D cloud resolving numerical model, implemented CO2
ice cloud physics considering supersaturation– Perform long-term numerical simulations until statisticalequilibrium states are reached.

• In this presentation…
– We show dependencies of critical saturation ratio(Scr)on the circulation features and cloud distribution.
• Scr is the saturation ratio for the onset of condensation.

Outline of numerical model• Dynamics: 2D Quasi-compressible fluid– Pure CO2 atmosphere and its condensation is considered• CO2 ice cloud microphysics (Tobie et al. 2003)– Diffusional growth, gravitational settling of cloud particles– Number density of condensation nuclei is constant• Radiation– Only IR is considered, given as a horizontal uniform cooling• Surface flux (Louis, 1979)– Estimated from bulk formula with fixed surface temperature• Subgrid scale turbulence (Klemp and Wilhelmson, 1978)– Turbulent flux is calculated by using urbulent kinetic energy.

Governing equations• Quasi-compressible equations(Klemp and Wilhelmson, 1978) andconservation equation for CO2 ice
Momentumequation:uR  u  u  C p   Du  g 
sg
cv / Rt
p0 Pressure
equation:

csc Lc    u   2 s 2 M cond  s M cond2t
C p C p C p  Thermodynamic
equation: 
 1  LM cond u     w Qdis  Qrad   Dtz   C p Conservation
equation for CO2ice: s    s u   M fall  M cond  D st2

2Condensation/evaporationterm

2u  (u , w) : Velocity ,  : Potential temperature, : The Exner function,  : Density of vapor, s : Density of cloud, T : Temperature,
cs : Sound speed,
C p : Specific heat at constant pressure,
L : Latent heat , M cond : Condensation rate,
Qdis : Dissipative heating rate,
Qrad : Radiative heating rate,
Du  ( Du , Dw ), D , D s : Turbulent diffusion term,g  (0, g ) : Gravitational accerelati on

CO2 ice cloud microphysics• Condensation/Evaporation rate (Tobie et al., 2003)– For 1<S<Scr, condensation does not occur if cloud density is lessthan a threshold value– We assume the value of threshold as 1.0-6 kg/m3• Gravitational settling rateSp: Saturation ratio
p*p : Pressure

p* : Saturation vapor pressure : Gas density  : viscosity coefficien t
N * : Number density of condensation nucleir : Radius of cloud particle  I : CO2 ice density
Kn : Knudsen number for cloud particle
k : Thermal diffusion coefficien t R : Gas constantSetup of experiments• Domain size:– 100km in horizontal direction(grid spacing: 500m)– 80km in vertical direction(grid spacing: 400m)• Initial temperature and cooling profile– Based on Kasting (1991)• Critical saturation ratio (Scr): 1.0, 1.35
(Glandorf et al., 2002)

Initial temperature andcooling profile(x10 km)Iso-thermal

Newtoniancooling

Uniformcooling(-0.1 K/day)

Ts = 273K
Ps = 2.0x105 Pa• Number density of condensation nuclei (N*): 5.0x104, 5.0x106,
5.0x108 /kg(Tobie et al.,2003: Forget et al., 2013)

Results

Parameter dependence:time evolution of total cloud mass
Large

Large

Scr = 1.0

Scr = 1.35

Quasi steady

Small

Total cloud mass

N*

Small

PeriodicParameter dependence:time evolotion of total kinetic energy
Large

Scr = 1.0

Quasi steadyN*
PeriodicSmallCirculation features and cloud distribution: Scr=1.0
Vertical velocity(km)（100 days)(km) Potential temperature(θ-Θ(z))

4040

2020000204060800(km)20406080(km)Clouds are generated by gravity wave

Cloud density

(km)
40

40

202000020

4060

Saturation ratio(km)

80(km)

020406080(km)Circulation features and cloud distribution: Scr=1.35
Vertical velocity(km)(143 days)(km) Potential temperature(θ-Θ(z))

4040202000020406080

020406080 (km)(km)
Buoyancy flow occurs above condensetion region

The dry convection is activated due to evaporation cooling of dropped cloud particle

Cloud density(km)
40402020000204060

Saturation ratio(km)

80(km)

020406080(km)Dependency of number density of condensation nuclei:
Scr=1.35
Large

N*

Small

Clouds develop upward
Clouds develop downwardEstimation of radius of cloud particles
and cloud optical depth• Suitable combination of cloud particle radius andoptical depth for “scattering green house effect” does
not occur.
– The estimation of optical depth is following to Petty (2006)– The scattering green house effect is effective when cloudparticle radius is 10 μm and its optical depth is about 10.

Concluding remarks• Circulation features and cloud distributions associatedwith condensation convection of CO2 vary greatly with thevalues of Scr.
• Scr=1.0: No supersaturation case– Condensation occurs continuously– Stratiform clouds is generated by gravity wave

• Scr=1.35: Supersaturation case
– Non-condensation and condensation periods occur alternately– In condensation periods, convective clouds forms• Note: In any cases, suitable combination of cloud particle
radius and optical depth for scattering green house effectdoes not occur.
This study is submitted to Journal of the Atmospheric Sciences.

AppendicesHorizontal mean cloud distribution
Large

N*

Dependency of number density of condensation nuclei:
Scr=1.0
Large

N*

Small

Total cloud mass
Large

N*

Small

Total kinetic energy
Large

N*

Small

Total kinetic enregy and cloud mass
(x1010J)
20

Scr = 1.0

Ke 101000(x105Kg)
420406080 (day)

Cloud
2mass
0

Scr = 1.35(x1010J)
2000(x106Kg)
44080

120160 (day)4080120160 (day)2020406080 (day)Total energy and cloud mass
are quasi-steady00

non-condensation andcondensation periods
occur alternately

Vertical profiles of cloud mass density
in no supersaturation caseN* = 5.0 x 108 kg-1

(x10-3 kg m-3)

N* = 5.0 x 106 kg-1

N* = 5.0 x 104 kg-1

(x10-4 kg m-4)

(x10-5 kg m-5)

• Vertical profiles of cloud mass density is determined by– In the Uppper part: balances between radiative cooling andcondensation heating, and condensation rate and gravitational
setteling (red dot line)– In the lower part: conservation of liquid water static energy (blue dushline)