1. Modeling Titan’s Atmosphere with Observational Constraints
Claire E. Newman
Kliegel Planetary Science Seminar
February 24th 2009

2. Overview of talk Method Results Applications
Description of the TitanWRF model
Horizontal diffusion and TitanWRF’s stratosphere
TitanWRF surface winds and surface features
The observed and modeled methane cycle
Ballooning on Titan
Results
Applications

3. Method

4. General Circulation Models (GCMs)
Model description
General Circulation Models (GCMs)
‘physics’
‘dynamics’
Force = mass x acceleration
in rotating frame + mass & energy conservation
Parameterizations
of everything acting at sub-grid scales
Discretized equations of momentum, mass & energy conservation on finite # of grid points
Includes:
Sub-grid scale eddies
Small scale turbulence
Friction at the surface
Absorption, emission and scattering of radiation

5. Model description
The TitanWRF GCM
TitanWRF is a version of PlanetWRF (
Uses Titan parameters (gravity, surface pressure, rotation…)
Physical parameterizations include:
McKay et al. [1989] radiative transfer scheme with:
IR : pressure-induced absorption and haze, C2H2 and C2H6 emission
VIS: methane absorption and haze absorption and scattering
Surface/sub-surface scheme to update soil temperatures
Vertical diffusion scheme to account for turbulent mixing
Horizontal diffusion scheme to account for sub-grid scale mixing

6. Northern summer solstice Ls=180 Northern autumn equinox
Model description
Includes seasonal (and daily) cycle in solar forcing
One Titan year is ~ 30 Earth years, 1 Titan day ~ 16 Earth days
Ls = planetocentric solar longitude =0
Northern spring equinox
Ls=90
Northern summer solstice
Seasons on Titan
Perihelion
(Ls~278)‏
Shortest distance
Sun
Empty focus x
Longest Sun-planet distance
Aphelion
90
Ls=270
Northern winter solstice
Ls=180 Northern autumn equinox

7. Also includes tidal forcing
Model description
Also includes tidal forcing
Eccentric orbit around Saturn => time-varying gravity field (‘tides’)
Tidal accelerations repeat every orbit (1 Titan day since tidally locked)
Diagram from Tokano [2005] showing time-dependent part of forcing:
Titan hour 18
Titan hour 0
Titan hour 12
Titan hour 6

8. Tidal forcing repeats every orbit (Titan day): accelerations are:
Model description
Tidal forcing repeats every orbit (Titan day): accelerations are:
Titan hour 0
Titan hour 6
Latitude (deg N)
Titan hour 12
Titan hour 18
Longitude (deg E)

9. Results

10. Observations of Titan’s stratosphere
Stratospheric results
Observations of Titan’s stratosphere
Temperature profile at 15 S from
Cassini CIRS [Flasar et al. 2005]
Zonal winds from Cassini CIRS
[Achterberg et al. 2008]
Latitude (deg N)
Peak zonal winds > 190m/s at this season

11. Observations of Titan’s stratosphere
Stratospheric results
Observations of Titan’s stratosphere
Huygens probe winds at ~10° S [Folkner et al. 2006]
Zonal winds
> 100m/s in lower stratosphere
Altitude (km)
Zonal wind speed (m/s)

12. Observations of Titan’s stratosphere
Stratospheric results
Observations of Titan’s stratosphere
Mean circulation transports angular momentum away from equator
But equatorial stratosphere observed to superrotate
How does it accumulate angular momentum? Eddies!
We wanted to investigate using TitanWRF

13. Poor early simulations of Titan’s stratosphere
Stratospheric results
Poor early simulations of Titan’s stratosphere
Northern winter (Ls~ ) observed by Cassini CIRS [Achterberg et al. 2008]
Zonal mean u
Zonal mean T
Pressure (mb)
The same time period in the original version of TitanWRF [Richardson et al. 2007]
Zonal mean T
Pressure (mb)
Peak wind < 30m/s
Zonal mean u
Latitude (deg N)

14. Another way to show this
Stratospheric results
Stratospheric results
Stratospheric results
Another way to show this
Superrotation index = total angular momentum of an atmospheric layer
(S.I.) total angular momentum of layer at rest with respect to the surface
S.I. during ‘spin-up’ of TitanWRF
Peaks at ~ 3
Should be ~ 10
0-2mb
2-20mb
Superrotation index
TitanWRF was not doing well
20-200mb
1 Titan year
200mb-surface
Titan days

15. Angular momentum transport (I)
Stratospheric results
Angular momentum transport (I)
Equinox
Solstice
Momentum transported up and polewards
Momentum transported downwards
POLE EQ
POLE
SUMMER
WINTER
Strong easterlies at low latitude surface => lots of momentum gained there
Strong westerlies in winter hemisphere => lots of momentum lost at surface
Wind slows down surface (gains angular momentum from surface)
Wind speeds up surface (loses angular momentum to surface)

16. Zonal mean T in TitanWRF Zonal mean u in TitanWRF
Stratospheric results
What’s the problem?
Zonal mean T in TitanWRF
Zonal mean u in TitanWRF
Pressure (mb)
Winter pole
Latitude (deg N)
Summer pole
Latitude (deg N)
Very weak latitudinal temperature gradients towards winter pole
Very weak zonal wind jets
Almost no equatorial superrotation
We looked at radiative transfer, the dynamical core, model resolution, haze effects…
Finally we discovered the problem in our horizontal diffusion scheme

17. Less diffusion => more superrotation
Stratospheric results
Stratospheric results
Stratospheric results
Less diffusion => more superrotation
0-2mb
High diffusion
Default (deformation-dependent) diffusion (Smagorinsky parameter=0.25):
peak S.I. ~ 3 after ~3000 Titan days
2-20mb
20-200mb
200mb-surface
Superrotation index
Low diffusion
Constant diffusion (K=104 m2s-1):
peak S.I. ~ 8 after ~7000 Titan days
Zero diffusion
No diffusion:
peak S.I. ~ 11 after ~2700 Titan days
Titan days

18. Why didn’t we see this sooner?
Stratospheric results
Stratospheric results
Stratospheric results
Why didn’t we see this sooner?
Used default diffusion settings for a long time
The effects of changing diffusion weren’t immediately apparent
Default Smagorinsky (effectively high) diffusion
Constant diffusion (with low coefficient)
Zero horizontal diffusion
Superrotation index
2 Titan years
2 Titan years
2 Titan years
For the first two Titan years all cases look similar.

19. Improved simulations of Titan’s stratosphere
Stratospheric results
Improved simulations of Titan’s stratosphere
Northern winter (Ls~ ) observed by Cassini CIRS [Achterberg et al. 2008]
Zonal mean u
Pressure (mb)
Zonal mean T
Same period in the latest version of TitanWRF: no horizontal diffusion
Zonal mean T
Zonal mean u
Latitude (deg N)

20. The effect of changing horizontal diffusion
Stratospheric results
The effect of changing horizontal diffusion
Zonal mean T
Zonal mean u
Observed
Pressure (mb)
Old
TitanWRF
New
TitanWRF
Latitude (ºN)

21. Now we have a more realistic stratosphere:
Stratospheric results
Now we have a more realistic stratosphere:
We can compare TitanWRF results with those observed by Cassini, Huygens and Earth-based telescopes
We can make predictions (about the circulation, chemistry and haze distribution) for times of year not yet observed
And importantly:
We can look at the mechanism driving the equatorial superrotation in TitanWRF

22. Angular momentum transport in TitanWRF
Stratospheric results
Angular momentum transport in TitanWRF
Stratospheric annual mean northward transport of angular momentum
mean meridional circulation
transient eddies
total advection
poleward transport
equatorward transport
Mean meridional circulation transports momentum polewards
But eddies begin transporting significant momentum equatorwards at ~three Titan years (once the winter zonal wind jet has become strong)

23. Stratospheric results
Northern winter solstice
Northern spring equinox
Strongest mean transport poleward; strongest eddy transport equatorward
Weak equatorward eddy transport opposes poleward mean transport
mean meridional circulation
poleward transport
transient eddies
total advection
equatorward transport

24. Conditions for barotropic eddies
Stratospheric results
Conditions for barotropic eddies
Barotropic instability criterion: the northward gradient of vorticity (d2u/dy2 - df/dy) must change sign in the flow
Year one average
Year three average
Zonal mean zonal wind
Pressure (Pa)
Zonal mean dq/dy (shown for dq/dy > 0)
Pressure (Pa)
Latitude (deg N)
Latitude (deg N)

25. Angular momentum transport (II)
Stratospheric results
Angular momentum transport (II)
Equinox
Solstice
Momentum transported up and polewards
Momentum transported downwards
Strong easterlies at low latitude surface => lots of momentum gained there
Strong westerlies in winter hemisphere => lots of momentum lost at surface
Barotropic eddies transport angular momentum:
weakly equatorwards in both hemispheres at equinox
strongly equatorwards from winter hemisphere at solstice

26. Angular momentum transport (II)
Stratospheric results
Angular momentum transport (II)
Equinox
Solstice
Momentum transported up and polewards
Momentum transported downwards
Strong easterlies at low latitude surface => lots of momentum gained there
Strong westerlies in winter hemisphere => lots of momentum lost at surface
Too much horizontal diffusion was over-mixing the atmospheric wind fields and impeding the development of the barotropic eddies

27. Summary of stratospheric results
Lower horizontal diffusion => more realistic stratosphere
Eddy momentum transport produces equatorial superrotation
Must tune diffusion coefficient by comparing TitanWRF’s circulation with observations of the actual circulation
Cannot just take diffusion coefficients from chemistry models

28. Surface winds and observed dune features
Surface results
Surface winds and observed dune features
Map of inferred dune directions (Lorenz, Radebaugh and the Cassini radar team)
Latitude (deg N) -
Longitude (deg W)
Cassini radar image
Dunes mostly within 30° of equator
Surface features suggest they formed in westerly (from the west) winds

29. But models / basic atmospheric dynamics predict easterlies here:
Surface results
But models / basic atmospheric dynamics predict easterlies here:
Annual mean surface winds (45S-45N) from TitanWRF (with tides included)
0.5 m/s
Latitude (deg N)
Longitude (deg E)
Latitude (deg N) -

30. What’s the problem with surface westerlies at the equator?
Surface results
What’s the problem with surface westerlies at the equator?
As wind moves towards equator
it becomes more easterly
As wind moves away from equator
it becomes more westerly

31. What’s the problem with surface westerlies at the equator?
Surface results
What’s the problem with surface westerlies at the equator?
But surface winds must be in balance:
Wind slows down surface (wind gains angular momentum from surface)
Wind speeds up surface (wind loses angular momentum to surface)
Surface westerlies at equator
=> Expect surface westerlies almost everywhere
In balance, have ~
Net imbalance => global atmosphere slows down, surface speeds up!

32. Could it be a seasonal effect?
Surface results
Could it be a seasonal effect?
Seasonal means:
Latitude (deg N)
Latitude (deg N)
Longitude (deg E)
Longitude (deg E)

33. Or a time of day (tide-related) effect?
Surface results
Or a time of day (tide-related) effect?
Snapshots:
Latitude (deg N)
Latitude (deg N)
Let’s look at the statistics…

34. Plots of dominant wind directions…
Surface results
Plots of dominant wind directions…
Dominant westerly winds
Easterlies
Dominant north-easterly winds
Latitude (deg N)
Westerlies
Dominant north-westerly winds
Direction wind blows towards
Percentage of time wind blows in given direction

35. Region where equatorial westerlies occur
Surface results
Plots of dominant wind directions…
Latitude (deg N)
Region where equatorial westerlies occur
Percentage of time wind blows in given direction

36. Dominant wind directions
Surface results
Dominant wind directions
Northern spring
Northern summer
Northern autumn
Northern winter

37. Mean wind in each direction
Surface results
Mean wind in each direction
Northern spring
Northern summer
Northern autumn
Northern winter

38. Occurrence of westerly winds from 30S-30N:
Surface results
Occurrence of westerly winds from 30S-30N:
30 N
15 N - -
15 S
30 S
Not close to pure westerlies
No bimodal westerlies (as required for longitudinal dunes) - at least not with an average westerly direction

39. E.g. look at dominant wind directions for 10-20 N:
Surface results
But DO find bimodal winds with an average easterly direction:
E.g. look at dominant wind directions for N:
Northern spring
Northern summer
Northern fall
Northern winter
=> Bimodal wind direction with easterly average, ~

40. Predicted dune statistics using TitanWRF Resultant Drift Direction
Surface results
Predicted dune statistics using TitanWRF
Drift Potential
~25S to 25N: highest drift potential, but for dunes forming towards the west:
Resultant Drift Direction
(° clockwise from N) N N N
Latitude (deg N)

41. The surface wind conundrum
Surface results
The surface wind conundrum
Dunes seem to have formed in westerly winds
Other equatorial features (streaks etc.) also seem to have been formed by westerly winds
But:
TitanWRF predicts mostly easterlies here
So do other Titan models (Tokano, LMD)
We expect easterlies here from dynamical arguments
=> unknown geophysical or dynamical process!?!

42. Summary of surface results
Low latitude winds in TitanWRF don’t match directions inferred from surface features
Including tides doesn’t help
[Not shown: setting a threshold for particle motion didn’t help either]
Look at effect of topography and surface properties (could not explain all observations, however)
Look at correlations between westerlies and state of near-surface environment (e.g. static stability)
Still to do

43. Simple methane cloud model
Methane cycle
Simple methane cloud model
Falls immediately back to surface unless re-evaporates on way down
Surface evaporation whenever near-surface is sub-saturated
Condensation
[binary or pure CH4 ice] when saturation exceeds given ratio
Main controlling factors:
Near-surface temperatures (=> ability to hold methane)
Upwelling in atmosphere (=> cooling => clouds)

44. Simple methane cloud model
Methane cycle
Simple methane cloud model
Falls immediately back to surface unless re-evaporates on way down
Surface evaporation whenever near-surface is sub-saturated
Condensation
[binary or pure CH4 ice] when saturation exceeds given ratio
Main controlling factors:
Near-surface temperatures (=> ability to hold methane)
Upwelling in atmosphere (=> cooling => clouds)
Missing from the scheme: latent heat effects and surface drying
Current orbit => solar heating peaks in southern summer

45. Controls on evaporation
Methane cycle
Controls on evaporation
Solar heating of troposphere
=>
Near-surface air temperature
Latitude (deg N)
Time of peak solar heating
Near-surface methane needed for saturation
=>
Actual near-surface methane
Latitude (deg N) +
=>
Amount needed to saturate near-surface air
=>
Evaporation
Latitude (deg N)
Time of year (°Ls)
Time of year (°Ls)

46. Upwelling in TitanWRF’s troposphere
Methane cycle
Upwelling in TitanWRF’s troposphere
Northern summer solstice (1 pole-to-pole cell)
Plot the upwelling region by plotting the maximum vertical velocity (in the troposphere) through one Titan year:
Equinox (2 ~symmetric cells)
Single, persistent pole-to-pole Hadley cells around the solstices
Pressure (mbar)
Latitude (deg N)
Southern summer solstice (1 pole-to-pole cell)
Double Hadley cell; upwelling region moves rapidly
Planetocentric solar longitude (°Ls)
Latitude

47. Controls on clouds and precipitation
Methane cycle
Controls on clouds and precipitation
Maximum vertical velocity in troposphere
=>
Cloud condensation
Surface precipitation
=>
Latitude (deg N)
Planetocentric solar longitude (°Ls)

48. Lake dichotomy on Titan
Methane cycle
Lake dichotomy on Titan
Many north polar lakes
Fewer south polar lakes
Currently perihelion occurs during southern summer
Simple argument => net transport from south to north
Might help to explain lake dichotomy

49. Argument for net south-north transport
Methane cycle
Argument for net south-north transport
1. Warmer southern summer (since perihelion occurs here)
=> Atmosphere can hold more methane
South pole
North pole

50. Argument for net south-north transport
Methane cycle
Argument for net south-north transport
2. Stronger circulation and more methane in atmosphere
=> More methane accumulates in northern high latitudes over winter/spring
South pole
North pole

51. Argument for net south-north transport
Methane cycle
Argument for net south-north transport
3. Colder temperatures and more polar methane
=> More high latitude precipitation of methane
in northern spring
South pole
North pole

52. Argument for net south-north transport
Methane cycle
Argument for net south-north transport
2. Methane accumulates at northern high latitudes
1. Atmosphere can hold more methane in southern summer
3. More precipitation of methane in northern spring
South pole
North pole

53. Net transfer from south to north in TitanWRF
Methane cycle
Net transfer from south to north in TitanWRF
Evaporation
Column mass of methane
More accumulation at N high latitudes
Latitude (deg N)
More evaporation during S summer
Precipitation
Net increase in surface methane since start
More precip in N spring
North pole gains more than south
Latitude (deg N)
Planetocentric solar longitude (°Ls)
Planetocentric solar longitude (°Ls)

54. Summary of methane cycle results
Clouds and precipitation track upwelling in Hadley cells
High CH4, low T => clouds and precipitation at spring pole
Simple argument for lake dichotomy:
Perihelion during southern summer => warmer
=> more methane held in atmosphere
=> more transported out of southern hemisphere
=> net transport from south to north
Cannot verify using TitanWRF until:
include latent heat effects
allow areas with evaporation >> precipitation to dry out

55. Applications

56. Ballooning on Titan Titan balloons
Simple ‘Montgolfiere’ filled with heated ambient air
Vertical control easy, horizontal control possible
Low temperature, high pressure environment is ideal
Floats in troposphere => can image below the haze layer
In situ sampling of boundary layer
Surface sampling a possibility
From the NASA/ESA TSSM joint summary report

57. Ballooning on Titan Questions a perfect model could help answer:
Titan balloons
Ballooning on Titan
Questions a perfect model could help answer:
Where will the balloon travel?
Can it hover in place using vertical control only?
How can it get from point A to point B for the least time / power?
What will the basic circulation look like at this time of year?
How much horizontal control is the balloon likely to need?
Are there entry latitudes we should avoid?
Fundamental predictability limits in a chaotic system =>
No model will ever give exact answers!
Questions an imperfect model can help answer:

58. Trajectory sensitivity to initial conditions
Titan balloons
Trajectory sensitivity to initial conditions
Time varying zonal wind field before tides
Tidal accelerations at t=0…
Latitude (degrees north)
…or at t=6 Titan hrs
Longitude (degrees east)
speed of background flow
+ position relative to tides (time of day)
=> trajectory

59. Trajectory sensitivity to initial conditions
Titan balloons
Trajectory sensitivity to initial conditions
Balloons all started at 4km altitude and at (0E, 45S) [shown by ]
Each color has a local start time differing by just two Titan hours
Start time and background wind determines whether you ‘surf’ around the planet or stay nearly in one place
Latitude (degrees north)
Longitude (degrees east)
Work by Alexei Pankine

60. Trajectories movie Titan balloons
Trajectories produced using TitanWRF output with tides included
Provided by Philip DuToit

61. Looking for transport barriers on Titan
Titan balloons
Looking for transport barriers on Titan
Trajectories produced using TitanWRF output with tides included
Drifters are colored by starting latitude
Plots provided by Titan SURF student Han Bin Man
t=0
t=8 Titan days
t=16 Titan days

62. Looking for transport barriers on Titan
Titan balloons
Looking for transport barriers on Titan
Trajectories used to produce maps of Finite Time Lyapunov Exponent
Red shows ridges separating regions of different mechanical behavior
These ‘Lagrangian Coherent Structures’ vary with time
t=0
t=8 Titan days
Altitude=1km
Ls=0
Plots provided by Titan SURF student Han Bin Man

63. Comparison of cell reachability % for different actuations
Titan balloons
Expected time to goal
Unpropelled
Gray indicates 1+ years
Work by Michael Wolf and JPLballoon navigation team using TitanWRF output
Comparison of cell reachability % for different actuations
# of days to reach target
Propelled (1 m/s)
Goal (Ontario Lacus)

64. Launch date…? (hopefully before we’re all retired!)
The Titan balloon mission
Launch date…? (hopefully before we’re all retired!)