Present status of numerical experiments onclimates of terrestrial exoplanets
by GFD-Dennou Club dcmodel project
M. Ishiwatari(1,2)
Collaborators: Y.O. Takahashi(2,3), K. Nakajima(4), S. Takehiro(5),S. Noda(5), Y.-Y. Hayashi(2,3)
and members of dcmodel project(1) Hokkaido University (2) Center of Planetary Science (CPS)(3) Kobe University (4) Kyushu University (5)Kyoto University
Japanese-French model studies of planetary atmospheres, May 15, 2015

Outline of this presentation• Introduction– Key words: Earth-like exoplanets, AGCM,
Climate regime diagram• Present status of our research– Target of experiment: Synchronously rotating planet– Planetary rotation rate dependence experiment(gray radiation, no cloud)– Planetary rotation rate dependence experiment(non-gray radiation, simple cloud model)– Solar constant dependence experiment(non-gray radiation, simple cloud model)• Concluding remarks

Introduction

Earth-like exoplanets• Many Earth-size planets havebeen discovered.
• They may have various climates,
since exoplanets are underconditions which are different
from solar system.

http://www.space.com/21708-images-habitable-alienplanets-gliese-667c.html– They provide new problems on existence conditionof Earth-like climate.

• Atmospheric component has been observable– Information on the climate can be obtained directly.

Previous GCM experiments• Some of previous studies with GCM– Oblique planet: Williams and Pollard (2003)– Eccentric planet: Williams and Pollard (2002)– Land planet: Abe et al. (2005) , Abe et al. (2011)– Synchronously rotating planet:
Joshi et al. (1997), Merlis and Schneider (2011),
Edson et al. (2013), Yang et al. (2014)

BAB• Most of previous studies discuss
whether exoplanets have habitableenvironments.
• However, neither existence condition ofequilibrium state nor parameter range ofappearance of each climate state are notinvestigated well.

AA
BAStarBPurpose of this study• Making climate regime diagrams• Determine existence ranges of equilibrium states, therunaway greenhouse state, snowball state
Snowball state
Budyko (1969), EBM

Runaway greenhouse state
Nakajima et al (1992), 1d model
σTs4
Pn0

Pn0
5=10 Pa=106 Pa

Komabayashi-Ingersoll
limit

Pn0=0 Pa(H2O atmosphere)• Systematic experiments (parameter sweep with asame model and various initial conditions) arenecessary.

• Numerical simulation with more realistic
configuration (in the next step)An example of climate regime diagram
Results of gray radiation model, Earth-like condition

GCM

runaway

Partially frozen

EBM(Ishiwatari et al., 2007)

runaway

Partiallyfrozen

Reversed Hadley

Snow ballSnow ball• Regime diagram makes existence ranges of regimes makes clear.
• Important points are (1) using multiple initial condition,(2) comparison with low order modelPresent statusof our research(in a way to goal)Target of experiment• Synchronously
rotating planets– Many have been
detected byexoplanet surveys– Planets near Mtype stars may behabitable

PeriodSolar Const.(Searth)
1day 10day 10 1 0.1
Exoplanetswith mass(Sun) lower than
10MearthVEM

J S

Tidal lockradiusSemi major axis (AU)
http://exoplanet.eu/catalog

Model• General circulation model: dcpam5– http:www.gfd-dennou.org/library/dcpam/– Takahashi et al. (talk on Monday)• For various experiments with a same framework
EarthZonal mean
zonal windMars

pressure

Venus (simpleradiative forcing)

90S

Eq.

latitude90N90SEq.

latitude90N90SEq.

90N

latitudeTone pattern differs among figures.

• Basic equations:3D primitive equation on a sphere• Discretization: spectrum method(horizontal),finite difference method(vertical)

Planetary rotation ratedependence experiment(gray radiation, no cloud)Planetary rotation rate dependence
experiment• Purpose– Examination on Ω*(planetary rotation ratenormalized by Earth’svalue) dependence of
day-night energy
transport– Circulation changes accordingto Ω*. Then, does day-night
energy transport also change
according to Ω*?

– Investigating thechange of atmosphericcirculation fields
according to Ω*

Period1day 10day

Solar Const.
10 1 0.1

Tidallockradius

Semi major axis (AU)Physical parameterizations• Radiation– Water vapor is gray to IR radiation– Dry gas is transparent• Cumulus convection– Convective adjustment (Manabe et al., 1965)• Surface flux: Louis et al. (1982)• Vertical turbulent mixing:
Mellor and Yamada (1974) level2.5• Planetary surface：flat surface,ocean with zero heat capacity (swamp condition),no horizontal heat transport• No cloudExperimental configuration

latitude• Solar radiation flux is given only to dayside
Day-side Night-side• Planetary rotation rate Ω*:0 – 1.0 (18 cases)• Planetary radius: 6.371 x 106 m• Solar constant: 1380 W m-2• gravitational acceleration: 9.8 m s-2• Averaged surface pressure: 105 Pa
longitude• surface albedo: 0• Resolution: T21L16• Initial condition: isothermal (280K) rest state(10 runswith different noise)• Integration time: 2000 days
(last 1000 days is used for analysis)

Surface temperature for various Ω*
W * = 0.05

W * = 0.15

W * = 0.25

W * = 0.33

W * = 0.5

Repeated reverseof N-S. asymmetry
W * = 0.67

Repeated reverseof N-S. asymmetry
W * = 0.8

Repeated reverseof N-S. asymmetry
W * = 1.0

latitude

W* = 0longitude

Repeated reverseof N-S. asymmetry

Time mean over
1000-2000day

Horizontal wind and geopotential*W = 0.0

σ=0.17 (upper troposphere)

Vectors : (u,v)
Color: geopotential

Time mean over
1000-2000day

Horizontal wind and geopotential*
W = 0.15

σ=0.17 (upper troposphere)

Vectors : (u,v)
Color: geopotential

Time mean over
1000-2000day

Horizontal wind and geopotential*
W = 0.5

σ=0.17 (upper troposphere)

Vectors : (u,v)
Color: geopotential

Time mean over
1000-2000day

North-south asymmetric state• Significant north-south asymmetric states appear in 0.2 ≤Ω∗ ≤ 0.8• The pattern reverses repeatedly.

Ω* =0.5

latitudeSurfacepressuret = 1750 – 1800 [day]t = 1400 – 1450 [day]zonal meansurface pressure96000

latitudelongitude

Time (day)104000Horizontal wind and geopotential*
W = 1.0

σ=0.17 (upper troposphere)

Vectors : (u,v)
Color: geopotential

Time mean over
1000-2000day

*
Dependence of energy transport on Ω
Energy transport
OLR of night side

Averaged Surf Temp.
Day-side

Sensible energy transport
globalLatent energy transport

Night-side

Rotation rate (normalized by Earth’s value)• Total energy transport (summation of sensible andlatent energy transports) is almost independent of Ω*The radiation limit constraints
energy transport
1d model:Outgoinginfraredradiation[W/m2]
Ω*=0.0Ω*=0.15 (GCM 120[deg]x12g[deg] region
Ω*=0.5around subsolar point)*Ω =1.0Surface Temperature[K]• Day-side infrared radiation is bounded by radiation limit of
1-dim model.
• Radiation limit: Nakajima et al. (1992), Ishiwatari et al. (2002)• (Total energy transport) = (Incident flux) – (radiation limit):
independent of Ω*Ω dependence experiment(non-gray radiation,simple cloud model)Ω* dependence experiment(non-gray, cloud)• Purpose– Examination of Ω* dependence of day-night
energy transport in more realistic configuration

Physical parameterizations• Radiation– Absorption and emission by water vapor, CO2, cloud water
Chou and Lee (1996), Chou et al (2001)– Solar radiation is assumed to be same as that of Sun• Cumulus convection••••– Relaxed Arakawa-Schubert (Moorthi and Suarez, 1992)
Surface flux: Beljaars and Holtslag (1991)
Vertical turbulent mixing: Mellor and Yamada (1974) level2.5
Planetary surface：ocean with zero heat capacity,
no horizontal heat transport
Simple cloud model– considering its advection, turbulent mixing, generation andextinction𝜕𝑞𝑐𝜕𝑞𝑐
𝑞𝑐= −𝑣 ∙ 𝛻𝑣 − 𝜎+ 𝐹𝑡𝑢𝑟𝑏 + 𝑆𝑐 +𝜕𝑡𝜕𝜎𝜏𝐿𝑇𝑆𝑐 : Source of cloud water–Condensation in large scale condensation scheme–Detrain from could top in RAS scheme𝑞𝑐: extinction of cloud water𝜏𝐿𝑇

tuned as 𝜏𝐿𝑇 = 1500sec
under Earth condition(T42L26)

Experimental configuration• Rotation rate:Ω*=0.0, 0.5, 1.0• Solar constant is fixed: S=1366 W/m2
• Cloud extinction time:𝝉𝑳𝑻 =0,1.5×103 sec (tuned value under Earth condition),
1.5×106sec• Resolution: T42L26• Integration period: 3 Earth yearDay-night energy transport
Energy transport to the night side（365day mean）
S=1366W/m2
𝜏𝐿𝑇 = 0sec

𝜏𝐿𝑇 = 1.5 × 103 sec

𝜏𝐿𝑇 = 1.5 × 106 sec○：ＯＬＲ (= day-night total energy transport)▼：(sensible energy transport)/2𝜋𝑅2★：(latent energy transport)/2𝜋𝑅2• Again, the amount of day-night total energy
transport is almost independent of Ω*Surface temperature & cloud water
w/o cloud

Ω=0.0

Ω=0.5

S=1366W/m2
Ω=1Surface
Tepm.

w/ cloud 3(𝜏𝐿𝑇 = 1.5×10 sec)

Surface
Tepm.

Total
cloudwater
longitude

365 day mean

Solar constantdependence experiment(non-gray radiation,simple cloud model)

Solar constant dependence experiment（ongoing）• Purpose– Examination on theoccurrence conditionof the runaway
greenhouse state– Comparison of cases withclouds and cases without
clouds– Comparison ofsynchronously rotating
planet configuration andEarth configuration

Period1day 10day

Solar Const.
10 1 0.1

Tidal
lock
radiusSemi major axis (AU)Experimental configuration• Rotation rate: Ω*=1.0• Cloud extinction time:𝝉𝑳𝑻 =0, 1.5×103 sec• Solar constant: S=1366-2200W/m2• Two kinds of distributions of incident
solar flux
– Synchronously rotating planet configuration– Earth configuration• Resolution: T42L26• Integration period: 3 Earth year

Runaway threshold• Results of runs with increased solar constantWithout Cloud
SyncRot

S=1366
S=1600
S=1800
S=2000
S=2200○○×With cloud

No-SyncRot SyncRot

○
○×

○
○
○
○
×

No-SyncRot○○×?

○：equilibrium states, ×:runaway greenhouse states

Concluding remarks

TODO list (very long…)• Experiments with more realistic configuration– Stellar spectrum type, Ocean, Sea ice, ….
– Model development is also ongoing:radiation scheme (Onishi’s talk in today’s afternoon)• Understanding variety of climate with climateregime
diagram– Examination of occurrence conditions of runaway
greenhouse and snowball state– Making climate regime diagrams– We have not been able to draw
regime diagram even for synchronously
rotating planet.

– Consideration on other configuration:
land planet,very hot planet (runaway planet), etc.

runaway

Partially frozen
Reversed Hadley
Snow ballSummary• We are performing numerical experiments andmodel development in order to make climate
regime diagrams.
• Experiments on synchronously rotating planets– Day-night energy transport is almost independent of Ω*.
– Examination on the occurrence condition of
the runaway greenhouse is ongoing.
Is runaway threshold also independent of Ω*?

• On going (or near future) subjects– Model development for more realistic simulation– Examination of climate regimes in parameter spaces
not only for synchronously rotating planet but also
for land planet etc.