A New Titan GCM and Stratospheric
Superrotation
Yuan Lian, Claire Newman, Mark
Richardson and Chris Lee
Work funded through the OPR program,
and simulations performed on the
NASA Ames High End Computing cluster
Goals of this work
• To reproduce key aspects of Titan’s circulation in a
3-dimensional general circulation model (GCM)
• To form a robust understanding of the dynamical
mechanisms responsible
• To produce robust predictions of seasonal changes
in Titan’s circulation
Comparing the TitanWRF GCM with observations
In previous work, we simulated strong, realistic stratospheric
superrotation and seasonal change similar to that observed --
Pressure (mbar)
Zonal winds in northern summer
Zonal winds in southern summer
1e-3
TitanWRF predictions for same times
1e-2
1e-1
1e0
1e1
-90
1e2
1e3
-60
-30
0
30
Latitude (deg N)
60
90
Zonal winds from CIRS in 2005
(Ls~293-323°)
1e-3
1e-2
1e-1
1e0
1e1
-60
1e2
1e3
-30
0
30
Latitude (deg N)
60
Zonal winds from CIRS in 2011 (Ls~2026°) [from Achterberg et al.]
-90
-60
-30
0
30
Latitude (deg N)
60
90
Discrepancies between TitanWRF and observations
Zonal wind peaks at a lower altitude than observed (likely due to
the ‘low’ model top and/or the lack of active haze advection)
Pressure (mbar)
CIRS zonal winds for Ls~293-323°
Also, no lower stratosphere
zonal wind minimum as
seen by Huygens and also
Cassini (Flasar, 2012)
TitanWRF zonal winds for same period
Stratospheric superrotation in TitanWRF
d(angular momentum)/dt in kg m2/s2
We find superrotation is produced by episodic ‘transfer events’
Equatorial dM/dt
(22.5°S to 22.5°N)
Northern dM/dt
(Pole to 22.5°N)
Southern dM/dt
(Pole to 22.5°S)
Planetocentric solar longitude (in ° Ls)
Rate of change of angular momentum in 3 regions over a Titan year
Stratospheric superrotation in TitanWRF
Angular momentum ‘transfer events’ between northern/southern
hemisphere and equatorial region, in northern/southern late fall-spring
Planetocentric solar longitude (in ° Ls)
Momentum transport during a ‘transfer event’
Unstable region develops
on low-latitude flank of
~winter zonal jet
Waves carry westward
angular momentum -> jet
=> accelerate low latitudes
Waves break depositing
westward angular
momentum => decelerate
high latitudes
In TitanWRF we found too much atmospheric mixing disrupts these
delicate wave processes, leading to weak stratospheric circulations
Questions we wanted to answer
Question 1: Does another GCM using identical
radiative forcing produce a similar circulation?
- This is actually a well-known problem in Titan modeling
Question 2: Do we see episodic ‘transfer events’ in a
different Titan GCM?
- How robust is our proposed superrotation mechanism?
Question 3: How delicate are the wave interactions
involved in driving Titan’s equatorial superrotation?
- Was the need to minimize mixing limited to TitanWRF?
We examined two GCMs and four setups.
Setups 1 & 2 used our first Titan GCM, TitanWRF…
1. TitanWRF [Newman et al., Icarus, 2011]
• Lat-lon grid, finite-difference solver
2. TitanWRF with a ‘rotated pole’
• Numerical pole and ‘polar’ filtering now at the equator
Filtering to avoid
instabilities where
grid spacing is small
Grid rotated through 90°
…while setups 3 & 4 used our new second Titan
model, the Titan MITgcm
3. Titan MITgcm [Mars version
described in Lian et al., Icarus, 2012]
• Lat-lon grid, finite-volume solver
4. Titan MITgcm using ‘cubedsphere’ grid
• No singularities at poles
• ‘Special points’ at cube corners
Which produced realistic superrotation?
1. TitanWRF with a standard lat-lon grid
2. Titan MITgcm with a standard lat-lon grid
Which had problems?
2. TitanWRF with rotated pole
4. MITgcm with cubed-sphere grid
What do the problem set-ups have in common?
TitanWRF with rotated pole
Titan MITgcm with cubed-sphere grid
Has filtered
regions at both
numerical poles
Has 6
special
‘corner’
points
In both cases, we’re ‘messing with’ the low- to midlatitudes where the waves are produced that are
crucial to driving superrotation
Superrotation index for the MITgcm lat-lon grid
Superrotation index = mass-weighted angular momentum of layer
that of same layer at rest wrt the solid surface
Superrotation index for the MIT cubed-sphere grid
Far weaker superrotation is achieved with the cubed-sphere grid
Questions we wanted to answer
Question 3: How delicate are the wave interactions
involved in driving Titan’s equatorial superrotation?
- Was the need to minimize mixing limited to TitanWRF?
Answer from this work: The dynamics of the low- to
mid-latitudes should be treated very carefully to avoid
disrupting vital wave-mean flow interactions
- This does not seem to be limited to TitanWRF
dM/dt in kg m2/s2
TitanWRF
dM/dt in kg m2/s2
Another year of TitanWRF
Planetocentric solar longitude (in ° Ls)
dM/dt in kg m2/s2
TitanWRF
dM/dt in kg m2/s2
Titan MITgcm
Planetocentric solar longitude (in ° Ls)
Questions we wanted to answer
Question 2: Do we see episodic ‘transfer events’ in a
different Titan GCM?
- How robust is our proposed superrotation mechanism?
Answer from this work: Momentum transport in the
Titan MITgcm is remarkably close to that in TitanWRF
despite big differences in dynamical core / numerics
- The mechanism appears to be quite robust
The circulation in TitanWRF and the MITgcm
Comparing winds at Ls = 270°: TitanWRF has larger peak wind
speeds, but Titan MITgcm simulates a strong zonal wind minimum
Pressure (mbar)
TitanWRF
Titan MITgcm
The circulation in TitanWRF and the MITgcm
Comparing temperatures at Ls = 270°: largely look very similar, but
slight variations can have a big impact on dynamics
Pressure (mbar)
TitanWRF
Titan MITgcm
Questions we wanted to answer
Question 1: Does another GCM using identical
radiative forcing produce a similar circulation?
- This is actually a well-known problem in Titan modeling
Answer: Many similarities, but differences in detail:
e.g. superrotation strength; sharper vertical gradients
- Much more to investigate here!
Conclusions
• At Ashima we now have two superrotating Titan GCMs with
similarly realistic circulations: TitanWRF and Titan MITgcm
• Our proposed mechanism for the production of equatorial
stratospheric superrotation in TitanWRF – via ‘episodic
transfer events’ – is supported by Titan MITgcm results
• As found before, GCM set-ups that disrupt the low- to midlatitudes (e.g. too much diffusion, filtering, etc.) disrupt the
delicate wave momentum transports responsible
• Titan MITgcm also captures far more of the observed zonal
wind minimum above the tropopause than TitanWRF
– Could be due to improved accuracy of temperature advection
– However, tropospheric wind speeds in Titan MITgcm are too small
Future work
• Raise the model top for both models to cover more of the
haze production zone
• Turn on radiatively active advection of haze particles to
enable feedbacks between haze distribution, heating and
circulation
• These changes should allow a stronger circulation to
develop and reduce interference by the model top, thus
improving the match to observations
Tropospheric methane ice cloud predicted by TitanWRF
More future work: study the CH4 cycle in the MITgcm!