Modeling Titans Atmosphere with Observational Constraints

1
Modeling Titans Atmosphere with Observational
Constraints

• Claire E. Newman
• Kliegel Planetary Science Seminar
• February 24th 2009

2
Overview of talk
Method

• Description of the TitanWRF model
• Horizontal diffusion and TitanWRFs 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
physics
dynamics
Parameterizations of everything acting at
sub-grid scales
Force mass x acceleration in rotating frame
mass energy conservation
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
The TitanWRF GCM
Model description

• TitanWRF is a version of PlanetWRF
  (www.planetwrf.com)
• 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
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
Ls90 Northern summer solstice
Seasons on Titan
Perihelion (Ls278)?
Shortest distance
Sun
Empty focus
x
Longest Sun-planet distance
Aphelion
90?
Ls270 Northern winter solstice
Ls180 Northern autumn equinox
7
Model description
Also includes tidal forcing

• Eccentric orbit around Saturn gt 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
Model description
Tidal forcing repeats every orbit (Titan day)
accelerations are
Titan hour 6
Titan hour 0
Latitude (deg N)
Titan hour 12
Titan hour 18
Longitude (deg E)
9
Results
10
Observations of Titans stratosphere
Stratospheric results
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 gt 190m/s at this season
11
Observations of Titans stratosphere
Stratospheric results
Huygens probe winds at 10 S Folkner et al.
2006
Zonal winds gt 100m/s in lower stratosphere
Altitude (km)
Zonal wind speed (m/s)
12
Observations of Titans stratosphere
Stratospheric results

• 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 Titans stratosphere
Stratospheric results
Northern winter (Ls293-323) 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 lt 30m/s
Zonal mean u
Latitude (deg N)
14
Another way to show this
Stratospheric results
Stratospheric results
Stratospheric results
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
200mb-surface
1 Titan year
Titan days
15
Angular momentum transport (I)
Stratospheric results
Equinox
Solstice
Momentum transported up and polewards
Momentum transported downwards
EQ
POLE
POLE
SUMMER
WINTER
Strong easterlies at low latitude surface gt lots
of momentum gained there
Strong westerlies in winter hemisphere gt 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
Whats the problem?
Stratospheric results
Zonal mean T in TitanWRF
Zonal mean u in TitanWRF
Pressure (mb)
Winter pole
Summer pole
Latitude (deg N)
Latitude (deg N)
Almost no equatorial superrotation
Very weak latitudinal temperature gradients
towards winter pole
Very weak zonal wind jets
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 gt more superrotation
Stratospheric results
Stratospheric results
Stratospheric results
0-2mb
High diffusion
Default (deformation-dependent) diffusion
(Smagorinsky parameter0.25) peak S.I. 3 after
3000 Titan days
2-20mb
20-200mb
200mb-surface
Low diffusion
Superrotation index
Constant diffusion (K104 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 didnt we see this sooner?
Stratospheric results
Stratospheric results
Stratospheric results

• Used default diffusion settings for a long time
• The effects of changing diffusion werent
  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 Titans stratosphere
Stratospheric results
Northern winter (Ls293-323) observed by Cassini
CIRS Achterberg et al. 2008
Zonal mean u
Zonal mean T
Pressure (mb)
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
Zonal mean T
Zonal mean u
Observed
Pressure (mb)
Old TitanWRF
New TitanWRF
Latitude (ºN)
21
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

• 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
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 gt 0)
Pressure (Pa)
Latitude (deg N)
Latitude (deg N)
25
Angular momentum transport (II)
Stratospheric results
Equinox
Solstice
Momentum transported up and polewards
Momentum transported downwards
Strong easterlies at low latitude surface gt lots
of momentum gained there
Strong westerlies in winter hemisphere gt 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
Equinox
Solstice
Momentum transported up and polewards
Momentum transported downwards
Strong easterlies at low latitude surface gt lots
of momentum gained there
Strong westerlies in winter hemisphere gt 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
Stratospheric results

• Lower horizontal diffusion gt more realistic
  stratosphere
• Eddy momentum transport produces equatorial
  superrotation
• Must tune diffusion coefficient by comparing
  TitanWRFs circulation with observations of the
  actual circulation
• Cannot just take diffusion coefficients from
  chemistry models

28
Surface winds and observed dune features
Surface results
Map of inferred dune directions (Lorenz,
Radebaugh and the Cassini radar team)
Latitude (deg N)
-60 -30 0 30
60
-
Longitude (deg W)
Cassini radar image

• Dunes mostly within 30 of equator
• Surface features suggest they formed in westerly
  (from the west) winds

29
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 0 30
-
30
Whats the problem with surface westerlies at the
equator?
Surface results
As wind moves towards equator it becomes more
easterly
As wind moves away from equator it becomes more
westerly
31
Whats the problem with surface westerlies at the
equator?
Surface results
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 gt Expect surface
westerlies almost everywhere
In balance, have
Net imbalance gt global atmosphere slows down,
surface speeds up!
32
Could it be a seasonal effect?
Surface results
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
Snapshots
Latitude (deg N)
Latitude (deg N)
Lets look at the statistics
34
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
Surface results
Plots of dominant wind directions
Latitude (deg N)
Region where equatorial westerlies occur
Percentage of time wind blows in given direction
36
Surface results
Dominant wind directions
Northern spring
Northern summer
Northern autumn
Northern winter
37
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
30 N
15 N
-
0
-
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
Surface results

• But DO find bimodal winds with an average
  easterly direction

E.g. look at dominant wind directions for 10-20 N
Northern spring
Northern summer
Northern fall
Northern winter
gt Bimodal wind direction with easterly average,

40
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
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
• gt unknown geophysical or dynamical process!?!

42
Summary of surface results
Surface results

• Low latitude winds in TitanWRF dont match
  directions inferred from surface features
• Including tides doesnt help
• Not shown setting a threshold for particle
  motion didnt 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
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 (gt ability to hold
  methane)
• Upwelling in atmosphere (gt cooling gt clouds)

44
Simple methane cloud model
Methane cycle
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 (gt ability to hold
  methane)
• Upwelling in atmosphere (gt cooling gt clouds)

• Missing from the scheme latent heat effects and
  surface drying
• Current orbit gt solar heating peaks in southern
  summer

45
Controls on evaporation
Methane cycle
gt
Solar heating of troposphere
Near-surface air temperature
Time of peak solar heating
Latitude (deg N)
-60 -30 0 30 60
gt
Near-surface methane needed for saturation
Actual near-surface methane
Latitude (deg N)

-60 -30 0 30 60
gt
Evaporation
gt
Amount needed to saturate near-surface air
Latitude (deg N)
-60 -30 0 30 60
330 0 30 60 90 120
150 180 210 240 270 300

330 0 30 60 90 120
150 180 210 240 270 300

Time of year (Ls)
Time of year (Ls)
46
Upwelling in TitanWRFs troposphere
Methane cycle
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)
-60 -30 0 30 60
Southern summer solstice (1 pole-to-pole cell)
Double Hadley cell upwelling region moves rapidly
330 0 30 60 90
120 150 180 210 240 270
300 330
Planetocentric solar longitude (Ls)
Latitude
47
Controls on clouds and precipitation
Methane cycle
Maximum vertical velocity in troposphere
gt
Cloud condensation
Surface precipitation
gt
-60 -30 0 30 60
Latitude (deg N)
330 0 30 60 90
120 150 180 210 240 270
300
330 0 30 60 90
120 150 180 210 240 270
300
Planetocentric solar longitude (Ls)
48
Lake dichotomy on Titan
Methane cycle
Many north polar lakes
Fewer south polar lakes

• Currently perihelion occurs during southern
  summer
• Simple argument gt net transport from south to
  north
• Might help to explain lake dichotomy

49
Argument for net south-north transport
Methane cycle
1. Warmer southern summer (since perihelion
occurs here) gt Atmosphere can hold more methane
South pole
North pole
50
Argument for net south-north transport
Methane cycle

• 2. Stronger circulation and more methane in
  atmosphere
• gt More methane accumulates in northern high
  latitudes over winter/spring

South pole
North pole
51
Argument for net south-north transport
Methane cycle

• 3. Colder temperatures and more polar methane
• gt More high latitude precipitation of methane
• in northern spring

South pole
North pole
52
Argument for net south-north transport
Methane cycle
2. Methane accumulates at northern high latitudes
3. More precipitation of methane in northern
spring
1. Atmosphere can hold more methane in southern
summer
South pole
North pole
53
Net transfer from south to north in TitanWRF
Methane cycle
Evaporation
Column mass of methane
More accumulation at N high latitudes
Latitude (deg N)
-60 -30 0 30 60
More evaporation during S summer
Net increase in surface methane since start
Precipitation
More precip in N spring
North pole gains more than south
Latitude (deg N)
-60 -30 0 30 60
330 0 30 60 90 120
150 180 210 240 270 300
330
330 0 30 60 90 120
150 180 210 240 270 300
Planetocentric solar longitude (Ls)
Planetocentric solar longitude (Ls)
54
Summary of methane cycle results
Methane cycle

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

55
Applications
56
Titan balloons
Ballooning on Titan

• Simple Montgolfiere filled with heated ambient
  air
• Vertical control easy, horizontal control
  possible
• Low temperature, high pressure environment is
  ideal
• Floats in troposphere gt 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
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 gt No model will ever give exact answers!
Questions an imperfect model can help answer
58
Titan balloons
Trajectory sensitivity to initial conditions
Time varying zonal wind field before tides
Tidal accelerations at t0
Latitude (degrees north)
or at t6 Titan hrs
Longitude (degrees east)
speed of background flow position
relative to tides (time of day) gt
trajectory
59
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
Trajectories produced using TitanWRF output with
tides included Drifters are colored by starting
latitude
Plots provided by Titan SURF student Han Bin Man
t0
t8 Titan days
t16 Titan days
62
Looking for transport barriers on Titan
Titan balloons

• 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

t8 Titan days
t0
Altitude1km Ls0
Plots provided by Titan SURF student Han Bin Man
63
Expected time to goal
Titan balloons
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
The Titan balloon mission
Launch date?(hopefully before were all
retired!)