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

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

Method

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

Model description The TitanWRF GCM 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

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

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

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)

Results

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

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)

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

Poor early simulations of Titan’s stratosphere Stratospheric results Poor early simulations of Titan’s stratosphere Northern winter (Ls~293-323) 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 < 30m/s Zonal mean u Latitude (deg N)

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

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)

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

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

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.

Improved simulations of Titan’s stratosphere Stratospheric results Improved simulations of Titan’s stratosphere Northern winter (Ls~293-323) 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)

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)

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

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)

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

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)

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

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

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

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) -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

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 0 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

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!

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)

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…

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

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

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

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

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

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 10-20 N: Northern spring Northern summer Northern fall Northern winter => Bimodal wind direction with easterly average, ~

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)

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!?!

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

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)

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

Controls on evaporation Methane cycle Controls on evaporation Solar heating of troposphere => Near-surface air temperature Latitude (deg N) Time of peak solar heating -60 -30 0 30 60 Near-surface methane needed for saturation => Actual near-surface methane Latitude (deg N) -60 -30 0 30 60 + => Amount needed to saturate near-surface air => Evaporation 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)

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) -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

Controls on clouds and precipitation Methane cycle Controls on clouds and precipitation Maximum vertical velocity in troposphere => Cloud condensation Surface precipitation => -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)

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

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

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

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

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

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

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

Applications

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

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:

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

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

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

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

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

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)

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