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

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Presentation on theme: "Modeling Titans Atmosphere with Observational Constraints Claire E. Newman Kliegel Planetary Science Seminar February 24th 2009."— Presentation transcript:

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

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

3 Method

4 Model description General Circulation Models (GCMs) dynamics physics Force = mass x acceleration in rotating frame + mass & energy conservation Discretized equations of momentum, mass & energy conservation on finite # of grid points Parameterizations of 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

5 The TitanWRF GCM TitanWRF is a version of PlanetWRF (www.planetwrf.com) TitanWRF is a version of PlanetWRF (www.planetwrf.com)www.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, C 2 H 2 and C 2 H 6 emission IR : pressure-induced absorption and haze, C 2 H 2 and C 2 H 6 emission VIS: methane absorption and haze absorption and scattering VIS: methane absorption and haze absorption and scattering Surface/sub-surface scheme to update soil temperatures Surface/sub-surface scheme to update soil temperatures Vertical diffusion scheme to account for turbulent mixing Vertical diffusion scheme to account for turbulent mixing Horizontal diffusion scheme to account for sub-grid scale mixing Horizontal diffusion scheme to account for sub-grid scale mixing Model description

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

7 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

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

9 Results

10 Stratospheric results Observations of Titans 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 Stratospheric results Altitude (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 Titans stratosphere

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

13 Poor early simulations of Titans stratosphere Stratospheric results Northern winter (Ls~ ) observed by Cassini CIRS [Achterberg et al. 2008] Zonal mean T Zonal mean u Pressure (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] Pressure (mb)

14 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 0-2mb 2-20mb mb 200mb-surface Superrotation index Titan days Another way to show this Peaks at ~ 3 Should be ~ 10 S.I. during spin-up of TitanWRF TitanWRF was not doing well 1 Titan year

15 Stratospheric results 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 (I) Wind slows down surface (gains angular momentum from surface) Wind speeds up surface (loses angular momentum to surface) EQ POLE SUMMERWINTER

16 Whats the problem? Stratospheric results Zonal mean T in TitanWRF Zonal mean u in TitanWRF Pressure (mb) Very weak latitudinal temperature gradients towards winter pole Winter pole Summer pole 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

17 Stratospheric results Default (deformation-dependent) diffusion ( Smagorinsky parameter =0.25): peak S.I. ~ 3 after ~3000 Titan days Constant diffusion (K=10 4 m 2 s -1 ): peak S.I. ~ 8 after ~7000 Titan days 0-2mb 2-20mb mb 200mb-surface No diffusion: peak S.I. ~ 11 after ~2700 Titan days Superrotation index Titan days Less diffusion => more superrotation High diffusion Low diffusion Zero diffusion

18 Stratospheric results Default Smagorinsky (effectively high) diffusion Constant diffusion (with low coefficient) Zero horizontal diffusion Superrotation index For the first two Titan years all cases look similar. 2 Titan years 1.Used default diffusion settings for a long time 2.The effects of changing diffusion werent immediately apparent Why didnt we see this sooner?

19 Stratospheric results Northern winter (Ls~ ) observed by Cassini CIRS [Achterberg et al. 2008] Zonal mean T Zonal mean u Improved simulations of Titans stratosphere Zonal mean T Zonal mean u Same period in the latest version of TitanWRF: no horizontal diffusion Pressure (mb) Latitude (deg N)

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

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

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

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

24 Stratospheric results Year one averageYear three average Barotropic instability criterion: the northward gradient of vorticity (d 2 u/dy 2 - df/dy) must change sign in the flow Zonal mean zonal wind Zonal mean dq/dy (shown for dq/dy > 0) Pressure (Pa) Latitude (deg N) Conditions for barotropic eddies

25 Stratospheric results 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 Barotropic eddies transport angular momentum: weakly equatorwards in both hemispheres at equinox strongly equatorwards from winter hemisphere at solstice Angular momentum transport (II)

26 Stratospheric results 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 Too much horizontal diffusion was over-mixing the atmospheric wind fields and impeding the development of the barotropic eddies Angular momentum transport (II)

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

28 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) Dunes mostly within 30° of equator Dunes mostly within 30° of equator Surface features suggest they formed in westerly (from the west) winds Surface features suggest they formed in westerly (from the west) winds Cassini radar image

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

30 Surface results Whats 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 Surface results Whats the problem with surface 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 ~

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

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

34 Latitude (deg 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

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

36 Northern spring Northern summer Northern autumnNorthern winter Dominant wind directions Surface results

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

38 Occurrence of westerly winds from 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

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

40 Surface results Predicted 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

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

42 Surface results Summary of surface results Low latitude winds in TitanWRF dont match directions inferred from surface features Low latitude winds in TitanWRF dont match directions inferred from surface features Including tides doesnt help Including tides doesnt help [Not shown: setting a threshold for particle motion didnt help either] [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 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) Look at correlations between westerlies and state of near-surface environment (e.g. static stability) Still to do

43 Methane cycle Simple methane cloud model Main controlling factors: 1.Near-surface temperatures (=> ability to hold methane) 2.Upwelling in atmosphere (=> cooling => clouds) Surface evaporation whenever near-surface is sub-saturated Condensation [binary or pure CH 4 ice] when saturation exceeds given ratio Falls immediately back to surface unless re- evaporates on way down

44 Missing from the scheme: latent heat effects and surface drying Missing from the scheme: latent heat effects and surface drying Current orbit => solar heating peaks in southern summer Current orbit => solar heating peaks in southern summer Methane cycle Simple methane cloud model Main controlling factors: 1.Near-surface temperatures (=> ability to hold methane) 2.Upwelling in atmosphere (=> cooling => clouds) Surface evaporation whenever near-surface is sub-saturated Condensation [binary or pure CH 4 ice] when saturation exceeds given ratio Falls immediately back to surface unless re- evaporates on way down

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

46 Methane cycle Upwelling in TitanWRFs troposphere Latitude (deg N) Planetocentric solar longitude (°L s ) 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 Pressure (mbar)

47 Methane cycle Controls on clouds and precipitation Maximum vertical velocity in troposphere Latitude (deg N) Cloud condensationSurface precipitation Planetocentric solar longitude (°L s ) =>

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

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

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

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

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

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

54 Methane cycle Summary of methane cycle results Clouds and precipitation track upwelling in Hadley cells Clouds and precipitation track upwelling in Hadley cells High CH 4, low T => clouds and precipitation at spring pole High CH 4, low T => clouds and precipitation at spring pole Simple argument for lake dichotomy: Simple argument for lake dichotomy: Perihelion during southern summer => warmer Perihelion 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

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 Titan 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!

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

59 Trajectory sensitivity to initial conditions Titan balloons Longitude (degrees east) Latitude (degrees north) 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

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

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

62 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 on Titan Altitude=1km Ls=0 t=0 t=8 Titan days Plots provided by Titan SURF student Han Bin Man

63 Expected time to goal Work 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

64 Launch date…? (hopefully before were all retired!) The Titan balloon mission


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