modeling titans atmosphere with observational constraints claire e. newman kliegel planetary science...

Modeling Titan’s Modeling Titan’s Atmosphere with Atmosphere with

Observational ConstraintsObservational Constraints

Claire E. NewmanClaire E. Newman

Kliegel Planetary Science SeminarKliegel Planetary Science Seminar

February 24th 2009February 24th 2009

Overview of talkOverview of talk

Description of the TitanWRF modelDescription of the TitanWRF model

Horizontal diffusion and TitanWRF’s stratosphereHorizontal diffusion and TitanWRF’s stratosphere

TitanWRF surface winds and surface featuresTitanWRF surface winds and surface features

The observed and modeled methane cycleThe observed and modeled methane cycle

Ballooning on TitanBallooning on Titan

Method

Results

Applications

MethodMethod

Model description

General Circulation Models (GCMs)General Circulation Models (GCMs)

‘dynamics’ ‘physics’

Force = mass x accelerationin rotating frame + mass & energy conservation

Discretized equations of momentum, mass & energy conservation on finite # of grid points

Parameterizationsof everything acting at sub-grid scales

Includes:

1. Sub-grid scale eddies

2. Small scale turbulence

3. Friction at the surface

4. Absorption, emission and scattering of radiation

The TitanWRF GCMThe TitanWRF GCM TitanWRF is a version of PlanetWRF (TitanWRF is a version of PlanetWRF (www.planetwrf.comwww.planetwrf.com))

Uses Titan parameters (gravity, surface pressure, rotation…) Uses Titan parameters (gravity, surface pressure, rotation…)

Physical parameterizations include:Physical parameterizations include:

McKay et al. [1989] radiative transfer scheme with:McKay et al. [1989] radiative transfer scheme with:

IR : pressure-induced absorption and haze, CIR : pressure-induced absorption and haze, C22HH22 and C and C22HH66 emission emission

VIS:VIS: methane absorptionmethane absorption and haze absorption and scatteringand haze absorption and scattering

Surface/sub-surface scheme to update soil temperaturesSurface/sub-surface scheme to update soil temperatures

Vertical diffusion scheme to account for turbulent mixingVertical diffusion scheme to account for turbulent mixing

Horizontal diffusion scheme to account for sub-grid scale mixingHorizontal diffusion scheme to account for sub-grid scale mixing

Model description

One Titan year is ~ 30 Earth years, 1 Titan day ~ 16 Earth days

SunEmpty focus

x

Ls=270Northern

winter solstice

Ls = planetocentric solar longitude =0

Northern spring equinox

Ls=180

Northern autumn equinox

Ls=90Northern

summer solstice

Shortest distance

Perihelion(Ls~278)

Longest Sun-planet distanceAphelion 90

Includes seasonal (and daily) cycle in solar forcingModel description

Seasons on Titan

Also includes tidal forcing• Eccentric orbit around Saturn => time-varying gravity field (‘tides’)

• Tidal accelerations repeat every orbit (1 Titan day since tidally locked)

Model description

Diagram from Tokano [2005] showing time-dependent part of forcing:

Titan hour 0

Titan hour 6

Titan hour 12

Titan hour 18

Longitude (deg E)

Lat

itud

e (d

eg N

)

Tidal forcing repeats every orbit (Titan day): accelerations are:Tidal forcing repeats every orbit (Titan day): accelerations are:Titan hour 0 Titan hour 6

Titan hour 12 Titan hour 18

Model description

ResultsResults

Stratospheric resultsObservations of Titan’s Observations of Titan’s

stratosphere stratosphere Temperature profile at 15 S fromCassini 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

Stratospheric resultsA

ltit

ude

(km

)

Zonal wind speed (m/s)

Zonal winds > 100m/s in lower stratosphere

Huygens probe winds at ~10° S [Folkner et al. 2006]

Observations of Titan’s Observations of Titan’s stratosphere stratosphere

Stratospheric results

Observations of Titan’s Observations of Titan’s stratosphere stratosphere

Mean circulation transports angular Mean circulation transports angular momentum momentum away from equatoraway from equator

But equatorial stratosphere observed to But equatorial stratosphere observed to superrotatesuperrotate

How does it accumulate angular momentum? How does it accumulate angular momentum? Eddies!Eddies!

We wanted to investigate using TitanWRFWe wanted to investigate using TitanWRF

Poor early simulations of Titan’s stratosphere Poor early simulations of Titan’s stratosphere Stratospheric results

Northern winter (Ls~293-323) observed by Cassini CIRS [Achterberg et al. 2008]

Zonal mean T

Zonal mean u

Pre

ssu

re (

mb

)

Latitude (deg N)

Zonal mean T

Zonal mean u

Peak wind < 30m/s

The same time period in the original version of TitanWRF [Richardson et al. 2007]

Pre

ssu

re (

mb

)

Stratospheric resultsStratospheric resultsStratospheric results

Superrotation index = total angular momentum of an atmospheric layer

(S.I.) total angular momentum of layer at rest with respect to the surface

0-2mb

2-20mb

20-200mb

200mb-surfaceSu

per

rota

tion

ind

ex

Titan days

Another way to show thisAnother way to show this

Peaks at ~ 3

Should be ~ 10

S.I. during ‘spin-up’ of TitanWRF

TitanWRF was not doing well1 Titan year


Equinox

Strong easterlies at low latitude surface => lots of momentum gained there

Momentum transported up and polewards

Solstice

Strong westerlies in winter hemisphere => lots of momentum lost at surface

Momentum transported downwards

Angular momentum transport Angular momentum transport (I)(I)

Wind slows down surface (gains angular

momentum from surface)

Wind speeds up surface (loses angular momentum

to surface)

EQPOLE POLE SUMMER WINTER

What’s the problem?What’s the problem?Stratospheric results

Zonal mean T in TitanWRF Zonal mean u in TitanWRF

Pre

ssur

e (m

b)

Very weak latitudinal temperature gradients towards winter pole

Winter pole

Summer pole

Latitude (deg N) Latitude (deg N)

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


Default (deformation-dependent) diffusion (Smagorinsky parameter=0.25):peak S.I. ~ 3 after ~3000 Titan days

Constant diffusion (K=104 m2s-1):peak S.I. ~ 8 after ~7000 Titan days

0-2mb

2-20mb 20-200mb200mb-surface

No diffusion: peak S.I. ~ 11 after ~2700 Titan days

Su

per

rota

tion

ind

ex

Titan days

Less diffusion => more Less diffusion => more superrotationsuperrotation

High diffusion

Low diffusion

Zero diffusion


Default Smagorinsky (effectively high) diffusion

Constant diffusion (with low coefficient)

Zero horizontal diffusion

Supe

rrot

atio

n in

dex

For the first two Titan years all cases look similar.

2 Titan years 2 Titan years 2 Titan years

1. Used default diffusion settings for a long time

2. The effects of changing diffusion weren’t immediately apparent

Why didn’t we see this Why didn’t we see this sooner?sooner?


Northern winter (Ls~293-323) observed by Cassini CIRS [Achterberg et al. 2008]

Zonal mean T

Zonal mean u

Improved simulations of Titan’s stratosphere Improved simulations of Titan’s stratosphere

Zonal mean T Zonal

mean u

Same period in the latest version of TitanWRF: no horizontal diffusion

Pre

ssu

re (

mb

)

Latitude (deg N)


Observed

OldTitanWRF

NewTitanWRF

Pre

ssu

re (

mb

)

Latitude (ºN)

The effect of changing horizontal The effect of changing horizontal diffusiondiffusionZonal mean T Zonal mean u


Now we have a more realistic stratosphere:Now we have a more realistic stratosphere:

We can compare TitanWRF results with those observed by We can compare TitanWRF results with those observed by Cassini, Huygens and Earth-based telescopesCassini, Huygens and Earth-based telescopes

We can make predictions (about the circulation, chemistry We can make predictions (about the circulation, chemistry and haze distribution) for times of year not yet observedand haze distribution) for times of year not yet observed

And importantly:And importantly:

We can look at the mechanism driving the equatorial We can look at the mechanism driving the equatorial superrotation in TitanWRFsuperrotation in TitanWRF


mean meridional circulation

Angular momentum transport in TitanWRFAngular momentum transport in TitanWRF

total advection

transient eddies

poleward transport

equatorward transport

Mean meridional circulation transports momentum polewardsMean meridional circulation transports momentum polewards

But But eddieseddies begin transporting significant momentum equatorwards at begin transporting significant momentum equatorwards at ~three Titan years (once the winter zonal wind jet has become strong)~three Titan years (once the winter zonal wind jet has become strong)

Stratospheric annual mean Stratospheric annual mean northwardnorthward transport of angular momentum transport of angular momentum


mean meridional circulation

total advectiontransient eddies

Northern winter solstice Northern spring equinox

poleward transport

equatorward transport

Strongest mean transport poleward; strongest eddy transport equatorward

Weak equatorward eddy transport opposes poleward mean transport


Year one average Year three average

Barotropic instability criterion: the northward gradient of vorticity (d2u/dy2 - df/dy) must change sign in the flow

Zonal mean zonal wind

Zonal mean dq/dy (shown for dq/dy > 0)

Pre

ssur

e (P

a)P

ress

ure

(Pa)

Latitude (deg N) Latitude (deg N)

Conditions for barotropic Conditions for barotropic eddieseddies


Equinox



Solstice



Barotropic eddies transport angular momentum:

• weakly equatorwards in both hemispheres at equinox• strongly equatorwards from winter hemisphere at solstice

Angular momentum transport Angular momentum transport (II)(II)


Equinox



Solstice



Too much horizontal diffusion was over-mixing the atmospheric wind fields and impeding the development of the barotropic eddies

Angular momentum transport Angular momentum transport (II)(II)

Stratospheric resultsSummary of stratospheric Summary of stratospheric

resultsresults

Lower horizontal diffusion => more realistic stratosphereLower horizontal diffusion => more realistic stratosphere

Eddy momentum transport produces equatorial superrotationEddy momentum transport produces equatorial superrotation

MustMust tunetune diffusion coefficient by comparing TitanWRF’s diffusion coefficient by comparing TitanWRF’s circulation with observations of the actual circulationcirculation with observations of the actual circulation

CannotCannot just take diffusion coefficients from chemistry models just take diffusion coefficients from chemistry models

Surface results

Surface winds and observed dune featuresSurface winds and observed dune featuresMap of inferred dune directions (Lorenz, Radebaugh and the Cassini radar team)

Lat

itud

e (d

eg N

)

-

Longitude (deg W)

Dunes mostly within 30° of equatorDunes mostly within 30° of equator

Surface features suggest they formed Surface features suggest they formed in in westerlywesterly (from the west)(from the west) winds winds

-60

-3

0

0

30

60

Cassini radar image

But models / basic atmospheric dynamics predict But models / basic atmospheric dynamics predict easterlieseasterlies here:here:

Surface results

0.5 m/s

Annual mean surface winds (45S-45N) from TitanWRF (with tides included)

Longitude (deg E)

Lat

itu

de

(deg

N)

-

-30

0

30

Lat

itu

de

(deg

N)

Surface results

What’s the problem with surface What’s the problem with surface westerlies at the equator?westerlies at the equator?

As wind moves towards equatorit becomes more easterly

As wind moves away from equatorit becomes more westerly

Surface results

What’s the problem with surface What’s the problem with surface westerlies at the equator?westerlies at the equator?

Net imbalance => global atmosphere slows down, surface speeds up!

Wind speeds up surface (wind loses angular momentum to surface)

Wind slows down surface (wind gains angular momentum from surface)

Surface westerlies at equator

=> Expect surface westerlies almost everywhere

But surface winds must be in balance:

In balance, have ~

Surface results

Could it be a seasonal effect?Could it be a seasonal effect?

Longitude (deg E) Longitude (deg E)

Lat

itud

e (d

eg N

)L

atit

ude

(deg

N)

Seasonal means:

Surface results

Or a time of day (tide-related) effect?Or a time of day (tide-related) effect?

Let’s look at the statistics…

Lat

itud

e (d

eg N

)L

atit

ude

(deg

N)

Snapshots:

Lat

itud

e (d

eg N

)

Direction wind blows towards

Percentage of time wind blows in given direction

Dominant north-

easterly winds

Dominant westerly

winds

Dominant north-

westerly winds

Plots of dominant wind directions…

Easterlies

Westerlies

Surface results

Lat

itud

e (d

eg N

)

Percentage of time wind blows in given direction

Plots of dominant wind directions…

Region where equatorial westerlies occur

Surface results

Northern spring Northern summer

Northern autumn Northern winter

Dominant wind directionsSurface results


Northern autumn Northern winter

Mean wind in each directionSurface results

Surface resultsOccurrence of westerly winds from Occurrence of westerly winds from

30S-30N:30S-30N:

30 S

0

30 N

15 N

15 S

-

-

• Not close to pure westerlies

• No bimodal westerlies (as required for longitudinal dunes) - at least not with an average westerly direction


Northern fall Northern winter

E.g. look at dominant wind directions for 10-20 N:

Surface results

=> Bimodal wind direction with easterly average, ~

• But DO find bimodal winds with an average easterly direction:

Surface results

PredictedPredicted dune statistics using TitanWRF dune statistics using TitanWRF

N

N

~25S to 25N: highest drift potential, but for dunes forming towards the west:

Resultant Drift Direction

(° clockwise from N)

Latitude (deg N)

N

Drift Potential

Surface results

The surface wind conundrumThe surface wind conundrum

Dunes seem to have formed in westerly windsDunes seem to have formed in westerly winds

Other equatorial features (streaks etc.) Other equatorial features (streaks etc.) alsoalso seem to have seem to have been formed by westerly windsbeen formed by westerly winds

But:But: TitanWRF predicts mostly easterlies hereTitanWRF predicts mostly easterlies here

So do other Titan models (Tokano, LMD)So do other Titan models (Tokano, LMD)

We expect easterlies here from dynamical argumentsWe expect easterlies here from dynamical arguments

=> unknown geophysical or dynamical process!?!=> unknown geophysical or dynamical process!?!

Surface results

Summary of surface resultsSummary of surface results

Low latitude winds in TitanWRF don’t match directions inferred from Low latitude winds in TitanWRF don’t match directions inferred from surface featuressurface features

Including tides doesn’t helpIncluding tides doesn’t help

[Not shown: setting a threshold for particle motion didn’t help either][Not shown: setting a threshold for particle motion didn’t help either]

Look at effect of topography and surface properties (could not explain Look at effect of topography and surface properties (could not explain all observations, however)all observations, however)

Look at correlations between westerlies and state of near-surface Look at correlations between westerlies and state of near-surface environment (e.g. static stability)environment (e.g. static stability)

Still to do

Methane cycle

Simple methane cloud modelSimple methane cloud model

Main controlling factors:

1. Near-surface temperatures (=> ability to hold methane)

2. Upwelling in atmosphere (=> cooling => clouds)

Surface evaporationSurface evaporation whenever near-surface whenever near-surface

is sub-saturatedis sub-saturated CondensationCondensation

[binary or pure CH[binary or pure CH44 ice] ice] when saturation exceeds when saturation exceeds

given ratiogiven ratio

Falls Falls immediatelyimmediately back back to surfaceto surface unless re- unless re-

evaporates on way downevaporates on way down

Missing from the schemeMissing from the scheme: latent heat effects and surface drying: latent heat effects and surface drying

Current orbit =>Current orbit => solar heating peaks in solar heating peaks in southern summersouthern summer

Methane cycle

Simple methane cloud modelSimple methane cloud model

Main controlling factors:

1. Near-surface temperatures (=> ability to hold methane)

2. Upwelling in atmosphere (=> cooling => clouds)

Surface evaporationSurface evaporation whenever near-surface whenever near-surface

is sub-saturatedis sub-saturated CondensationCondensation

[binary or pure CH[binary or pure CH44 ice] ice] when saturation exceeds when saturation exceeds

given ratiogiven ratio

Falls Falls immediatelyimmediately back back to surfaceto surface unless re- unless re-

evaporates on way downevaporates on way down

Methane cycleControls on evaporationControls on evaporation

Time of year (°Ls) 330 0 30 60 90 120 150 180 210 240 270 300

=>

=>

+

=>

=>

Time of year (°Ls)

Lat

itud

e (d

eg N

) -

60

-30

0

3

0

60

-60

-

30

0

3

0

60

-60

-

30

0

3

0

60

Lat

itud

e (d

eg N

)L

atit

ude

(deg

N) Solar heating of troposphere Near-surface air temperature

Near-surface methane needed for saturation Actual near-surface methane

Amount needed to saturate near-surface air Evaporation

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

Time of peak solar heating

Methane cycle

Upwelling in TitanWRF’s troposphereUpwelling in TitanWRF’s troposphere

Lat

itud

e (d

eg N

) -

60

-

30

0

30

60

Planetocentric solar longitude (°Ls) 330 0 30 60 90 120 150 180 210 240 270 300 330

Double Hadley cell; upwelling region

moves rapidly

Single, persistent pole-to-pole Hadley cells around the solstices

Equinox (2 ~symmetric cells)

Northern summer solstice (1 pole-to-pole cell)

Southern summer solstice (1 pole-to-pole cell)

Plot the upwelling region by plotting the

maximum vertical velocity (in the troposphere) through one Titan year:

Latitude

Pre

ssur

e (m

bar)

Methane cycleControls on clouds and precipitationControls on clouds and precipitation

Maximum vertical velocity in troposphere

Lat

itud

e (d

eg N

)

Cloud condensation Surface precipitation

-60

-30

0

30

6

0

Planetocentric solar longitude (°Ls) 330 0 30 60 90 120 150 180 210 240 270 300 330 0 30 60 90 120 150 180 210 240 270 300

=>=>

Methane cycle

Many north polar lakes Fewer south polar lakesLake dichotomy on TitanLake dichotomy on Titan

Currently perihelion occurs during southern summerCurrently perihelion occurs during southern summer

Simple argument => net transport from south to northSimple argument => net transport from south to north

Might help to explain lake dichotomyMight help to explain lake dichotomy

Methane cycle

Argument for net south-north transportArgument for net south-north transport

South pole

1. Warmer southern summer (since perihelion occurs here)

=> Atmosphere can hold more methane

North pole

Methane cycle


South pole North pole

2. Stronger circulation and more methane in atmosphere

=> More methane accumulates in northern high latitudes over winter/spring

Methane cycle



3. Colder temperatures and more polar methane

=> More high latitude precipitation of methane

in northern spring

Methane cycle



3. More precipitation of methane in northern spring

2. Methane accumulates at northern high latitudes

1. Atmosphere can hold more methane in southern summer

Methane cycle

Net transfer from south to north in TitanWRFNet transfer from south to north in TitanWRF

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

Planetocentric solar longitude (°Ls)

Lat

itud

e (d

eg N

)

Net increase in surface methane since start

Evaporation

Precipitation

More evaporation

during S summer

More precip in N

spring

Column mass of methane

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

-60

-

30

0

30

6

0

Lat

itud

e (d

eg N

)

Planetocentric solar longitude (°Ls)

North pole gains more than south

-60

-

30

0

30

6

0

More accumulation at N high latitudes

Methane cycleSummary of methane cycle Summary of methane cycle

resultsresults Clouds and precipitation track upwelling in Hadley cellsClouds and precipitation track upwelling in Hadley cells

High CHHigh CH44, low T => clouds and precipitation at spring pole, low T => clouds and precipitation at spring pole

Simple argument for lake dichotomy:Simple argument for lake dichotomy: Perihelion during southern summer => warmerPerihelion during southern summer => warmer => more methane held in atmosphere=> more methane held in atmosphere => more transported out of southern hemisphere=> more transported out of southern hemisphere => net transport from south to north=> net transport from south to north

Cannot verify using Cannot verify using TitanWRF until: include latent heat effects allow areas with evaporation >> precipitation to dry out

ApplicationsApplications

Ballooning on TitanTitan 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

Ballooning on TitanTitan balloons

• 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?

Questions a perfect model could help answer:

Questions an imperfect model can help answer:

Fundamental predictability limits in a chaotic system => No model will ever give exact answers!

Trajectory sensitivity to initial conditions

Titan balloons

Longitude (degrees east)

Lat

itud

e (d

egre

es n

orth

)

Time varying zonal wind field before tides Tidal accelerations at t=0…

…or at t=6 Titan hrs

speed of background flow

+ position relative to tides (time of day)

=> trajectory

Trajectory sensitivity to initial conditions

Titan balloons

Longitude (degrees east)

Lat

itud

e (d

egre

es n

orth

)

• 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

Work by Alexei Pankine

Start time and background wind determines whether you ‘surf’ around the planet or stay nearly in one place

Titan balloons

Trajectories produced using

TitanWRF output with

tides included

QuickTime™ and aH.264 decompressor

are needed to see this picture.

Trajectories movieTrajectories movie

Provided by Philip DuToit

Titan balloons

Trajectories produced using TitanWRF output with tides included

Drifters are colored by starting latitude

Looking for transport barriers Looking for transport barriers on Titanon Titan

Plots provided by Titan SURF student

Han Bin Man

t=0

t=8 Titan days

t=16 Titan days

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

Looking for transport barriers Looking for transport barriers on Titanon Titan

Altitude=1km

Ls=0

t=0 t=8 Titan days

Plots provided by Titan SURF student Han Bin Man

Expected time to goalExpected time to goalWork by Michael Wolf and

JPLballoon navigation team using TitanWRF output

Gray indicates 1+ years

Unpropelled

Propelled (1 m/s)

Goal (Ontario Lacus)

Comparison of cell reachability % for different actuations

# of days to reach target

Titan balloons

Launch date…?(hopefully before we’re

all retired!)

The Titan balloon mission

modeling titans atmosphere with observational constraints claire e. newman kliegel planetary science...

Documents

titan slide

surface momentum

titanwrf slide

titan hour

titanwrf titanwrf

titan year slide

surface pressure

titan ballooning