A numerical study on atmospheric general circulationsof synchronously rotating aqua-planets:
Dependence on planetary rotation rateand Solar Constant
S. Noda(1,6), M. Ishiwatari(2,3), K. Nakajima(4), Y. O. Takahashi(1,3),
S. Nishizawa(7), M. Onisi(1,3), G. L. Hashimoto(5) ,K. Kuramoto(2,3), Y.-Y. Hayashi(1,3)(1) Kobe University, Kobe, (2) Hokkaido University, Sapporo,(3) Center for Planetary Science, Kobe, (4) Kyushu University, Fukuoka,(5) Okayama University, Okayama, (6) Meteorological Research Institute, Tsukuba,(7) RIKEN Advanced Institute for Computational Science, Kobe
WTK, 14 Mar. 2013

Synchronously rotating planets• Some terrestrial exoplanets are expected
to be tidally locked and synchronously rotating.
– fixed dayside and nightside

B• Climates of synchronously rotatingaqua-planets?
– With solar constant of present Earth,day-side is in runaway greenhouse
BconditionAA

StarA

B

AB

Previous aqua-planet experiments• GCM experiment with changing rotation rate.
– Joshi (2003):
Ω/ΩE=1– Merlis and Schneider (2010): Ω/ΩE=1/365～1– Edson et al. (2011):
Ω/ΩE=1/100～1• Equilibrium states are obtained in all cases.
Surface temperature(Merlis and Schneider, 2010)Ω = ΩE /365

Ω = ΩE

Slowly rotating regime

Rapidly rotating regime

Aims of this study• Parameter study with various planetary rotation
rate (Ω) and solar constant (S)– Parameter dependences of circulation and energy
transports ?
• In previous works, cases with Ω～0,ΩE are focused on.

– Occurrence condition of the runaway greenhousestate?
• The dependence on solar constant has not been examinedin previous works.

Model• Atmospheric General Circulation model：dcpam(http://www.gfd-dennou.org/library/dcpam/index.htm.en)• Dynamical part：３-d primitive equation on sphere
Hydrostaticequation
Equation ofmotion

Continuity
equation
Equation ofheat
Conservationof water vapor

Boundary Condition
Φ = 0 at σ = 1.
σ = 0 at σ = 0,1(λ, ϕ):longitude, latitude
π = ln ps
σ = p / psσ. = dσ/dt
p: pressure
ps: surface pressure
a: planetary radius
u: zonal wind
v: meridional windvH: horizontal velocity
T: temperature
Tv: virtual temperatureΦ: goepotential
f: Coliorils parameter
Rd: gas constant of dry air
Cpd: specific heat of dry air
q: specific humidity
Q*: external Heating
Sq: Source of water vapor
Fλ, Fϕ: external forcin

Physical Processes
Atmospheric composition“Water vapor” and “dry gas”

Radiation process

Water vapor : gray to IR radiation
Dry gas: transparent
Convective adjustment(Manabe et al., 1965)
condensed water is removed fromsystem immediately (no cloud)
Mellor and Yamada (1972) Level 2Cumulus process

Turbulent vertical mixing
Surface condition

Aqua-planet, flat surfaceZero heat capacity, no sea ice

Experimental setup
Day-sideNight-side

latitude• Radius of planets, mean surfacepressure, gravitational
acceleration, and so on are
Earth’s values• Obliquity is 0

Incoming radiation flux

longitude
Ω dependence exp.

S dependence exp.

Rotation rate Ω(ΩE: Earth’s value)

0 - ΩE (16 cases)

0, 0.15 ΩE, 0.5 ΩE, ΩE

Solar constant S(global mean flux)

1380 W/m2(345 W/2)

1380 - 1700 W/m2 (24 cases)(345 - 425 W/m2)

Resolution

T21L16 (64 x 32 x 16)

T21L32 (64 x 32 x 32)

Integration time2000 day(last 1000 days areanalyzed)

Over 2000 days
(last 500 days are analyzed)

Time step

20 min10 min or less

Dependence on rotation rate
• Experiment– Various Ω, fixed solar constant• Results– In all cases, the runaway greenhouse states do notoccur: statistically equilibrium state or oscillatingstate– Day-night energy transport is independent of Ω.
Circulation pattern depends on Ω.

Atmospheric structure for various Ω
SurfaceTemperatureΩ = 0.67 ΩΕΩ = ΩΕlatitudeΩ = 0.05 ΩΕlongitudeHorizontal velocity
at sigma=0.2
100 m/s
100 m/s

Surfacepressure

93000 Pa

107000 Pa

Time mean over
1000-2000day

Zonal mean zonal wind for various ΩΩ = 0.05 ΩΕΩ = 0.15 ΩΕΩ = 0.25 ΩΕΩ = 0.33 ΩΕΩ = 0.5 ΩΕΩ = 0.67 ΩΕΩ = 0.8 ΩΕΩ = ΩΕ

sigmaΩ=0latitude-100 m/s

100 m/sTime mean over
1000-2000day

Asymmetric state: 0.2ΩΕ −0.67ΩΕSurface pressure for 0.5ΩENorth-south
AsymmetricStatet = 1400 – 1450 [day]96000

104000zonal mean surface pressure
latitude• Oscillation– Non-periodicfor large Ω– “period”:
10day – 1000day– also in high reso.
experimentst = 1750 – 1800 [day]Time (day)Dependence of heat budget on Ω
Night-side heat budget

heat transport from day to nightcondensation heating
Planetary radiation

Averaged Surf Temp.
Surface Temp.

Integrated heat flux.

×1015WDay-side
globalNight-side

Rotation rate (normalized by Earth’s value)• Small dependence of summation ofsensible/latent heat transports on Ω• Total heat transport may be determined by(Incident solar flux) – (radiation limit)• Radiation limit: Nakajima et al. (1992), Ishiwatari et al. (2002)

Comparison with 1-d model
Ω=0 (GCM Day Side)
Ω=0.15ΩE
Ω=0.5ΩE
Ω=ΩE

1d model:50% (Relative humidity)
60%
70% 80%90%
100%• Outgoing Longwave Radiation does not exceed
radiation limit obtained by 1-dim radiative
convective equilibrium model.

Dependence on solar constant• Experiment– Various solar constant, Ω=0, 0.15 ΩE, 0.5 ΩE, ΩE• Aims– Does runaway condition corresponds to the radiation
limit obtained by 1-dim model?
– In non-synchronous rotating cases, runaway
condition corresponds to the radiation limit.
392.5 W/m2

○equilibrium×runaway

300 W/m2
Equilibrium solution obtained by
1-dim model given fixed RH

Ishiwatari et al. (2002)

Occurrence of Runaway greenhouse states
425

Non-equilibrium

Non-equilibrium

latitude

Global mean
incoming flux(W/m2)

longitude375

3450ΩErotationrateResults with various solar constant●: equilibrium●: runaway●: not yet
determinedΩThe runaway greenhouse states occur when mean
incident solar flux exceeds 400 W/m2

OLR difference between day and night
Planetary radiation averaged
over latitude

dashed line: present Earth S
solid line：just below
runawayΩ=0Ω = 0.15 ΩE
Ω = 0.5 ΩE
Ω = ΩE

longitude・day-side OLR：almost constant against increasing S・night-sde OLR：increase with increasing S

Summary• Amount of day-night energy transport isindependent of planetary rotation rate.
– Day-side planetary radiation is constrained by radiation
limit obtained by vertical 1-d radiative-convective model.

• It seems that occurrence condition of the runaway
greenhouse state is described by the radiation limit.
– Difference of planetary radiation between day-side andnight-side decreases with increased solar constant.

• Circulation patterns does not depend on solar
constant but on planetary rotation rate.
– Day-night direct circulation, super rotation, oscillating
asymmetric states