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Weather on strange new worlds: A troposphere benchmark model
for a tidally locked terrestrial planet
Ludmila Carone, KU LeuvenCenter for mathematical Plasma-Astrophysics
(CmPA), Institute of Astronomy (IvS)
+ KU Leuven IDO groupRony Keppens (CmPA),
Leen Decin , Olivia Venot, Pieter Degroote (IvS), Shaun Carl, Minh Tho Nguyen, Thi Huyen
Nguyen, Aysha Roshni Hashim (Chemistry)Vincent van Eylen (Aarhus),
Held &Suarez 1994: 'fruitfly' of climate research – Fluid Dynamics
• Navier-Stokes equation under hydrostatic equilibrium (HPE)
Dv⃗ hDt
+(2Ω⃗× v⃗ )h+1ρ ∇ h p=Fh
∂ p∂ z
+ρg=0
Horizontal momentum equation
Hydrostatic equilibrium
Continuity equation∇ h⋅v⃗h+
∂ w∂ z
=01ρDρDt
+
DDt
= ∂∂ t
+ v⃗h⋅∇ h+w∂∂ z
Held &Suarez 1994: 'fruitfly' of climate research – Thermal forcing
• Navier-Stokes equation (HPE)
• Newtonian relaxation towards equilibrium temperature
DTDt
=−[T−T eq ]
τ rad
40 d for Earth
Temperature forcing for Earth
200 K stratosphere
Held &Suarez 1994: 'fruitfly' of climate research – Surface <-> Atmosphere friction
• Navier-Stokes equation (HPE)
• Newtonian relaxation towards equilibrium temperature
• Rayleigh friction between surface and atmosphere
F⃗h=k v v⃗ h kv=1 day-1...0
p=1000-700 mbar
Temperature forcing for Earth
200 K stratosphere
Rayleigh friction
Adaptation for tidally locked dayside
x I 0 (1−α) determines Teff,P
Assuming leaky greenhouse model+skin layer concept
T s=(2
2−ϵ)
1 /4
T eff , P T tropopause=0.51 /4T eff , P
e.g. Pierrehumbert 2010
e.g. J. Marshall 2008
0.8 for Earth
At the nightside and terminator: Martian polar night scenario
• Equilibrium between condensation and IR-back radiation of atmosphere
T cond=T ref
1−RT refL
ln (ppref
)
Smith, 2008, Spacecraft Observationsof the Martian Atmosphere, Annu. Rev. Earth Planet. Sci. 2008. 36:191–219
Tref
=77 K @ pref
=1000 mbar for N2
Tidally locked dayside rad.-conv.-Teq
Earth-like atmosphere and insolation
α=0.3I 0=1368W /m2
T ( p)=max (T s(pps
)R / c p
,T tropopause)
τrad=cP psg 4σ T 3
=4d−813d
Put it on a Super-Earth
If it exists, it lies in the habitable zone of the M dwarf star
MGl581g=3.1M Earth→ R pl=1.45R Earth ; g=14.3m /s2
Prot
=Porb
=36.5, 10d,... days,
Dynamics on terrestrial Super-EarthsProt=10 d Prot=36 d
p=10
00 m
bar
p=52
5 m
bar
1000 d time average∇T p=525mb≈25 K ∇T p=525mb≈10K
Dynamics on terrestrial Super-EarthsProt=10 d Prot=36 d
p=10
00 m
bar
p=52
5 m
bar
1000 d time average cyclones
Cyclones are cloud/ precipitation generators
Cyclone near Iceland
Wiki commons
Dynamics on terrestrial Super-EarthsProt=10 d Prot=36 d
p=10
00 m
bar
p=52
5 m
bar
1000 d time average anticyclones
Anti-cyclones are cloud/precipitation dispersers
Anti-cyclone near South-Australia
Wiki-commons
Zalucha 2013
• H2O atmosphere, P
rot=1.5 d, Hot regime, ps=1000 mbar
KU Leuven Benchmark Prot=10 d
Prot
=10 days
Our benchmark P
rot=36.5 daysP
rot=10 days
Vertical temperature at anti-stellar point
36d10d
Thermal inversion-> Smog formation
BBC Weather
Conclusion
• A tidally locked terrestrial planet benchmark with the same conceptional simplicity than the Held&Suarez benchmarko Fast, versatile, good for parameter study
• On average, nightside temperature does not drop very low (280-290 K)
• Dayside temperatures allow for liquid water (350-300 K)
• Substellar point is upwelling region (cloud formation)
• For slow rotation (>30 d), Cyclones at mid-latitude in mid-troposphere (cloud formation, reduced horiz. diffusion)
• Thermal inversion at the surface (hinders vertical diffusion)
In preparation:
Carone et al., Connecting the dots: A versatile terrestrial planet benchmark for tidally locked Super-Earths with Earth-like atmospheres, MNRAS