The Titan Global The Titan Global Ionosphere-Ionosphere-

Thermosphere Model Thermosphere Model (1-D and 3-D)(1-D and 3-D)

The Titan Global The Titan Global Ionosphere-Ionosphere-

Thermosphere Model Thermosphere Model (1-D and 3-D)(1-D and 3-D)

Hunter Waite, Jared M. BellHunter Waite, Jared M. Bell

ISSI Bern Modeling WorkshopISSI Bern Modeling Workshop

March, 2009March, 2009

OutlineOutlineOutlineOutline

1.1. Titan Global Ionosphere-Thermosphere Model (T-Titan Global Ionosphere-Thermosphere Model (T-GITM)GITM)

a)a) FormulationFormulationb)b) Titan-Specific PhysicsTitan-Specific Physicsc)c) 1-D and a 3-D configuration1-D and a 3-D configuration

2.2. Current work on the Upper atmosphere of TitanCurrent work on the Upper atmosphere of Titan

3.3. 1-D Results1-D Results

4.4. ((unrefinedunrefined) 3-D Results) 3-D Results

5.5. Future Plans.Future Plans.

Previous Modeling Previous Modeling EffortsEfforts

Previous Modeling Previous Modeling EffortsEfforts• One-Dimensional (1-D)One-Dimensional (1-D)

– Photochemical (Photochemical (WilsonWilson, [2002]), [2002])– Thermal Structure (Thermal Structure (Friedson & YungFriedson & Yung, [1987]), [1987])– Coupled Chemical-Thermal-DiffusiveCoupled Chemical-Thermal-Diffusive

• De La Haye et. alDe La Haye et. al. [2007a, 2007b, 2008]. [2007a, 2007b, 2008]

• Three-Dimensional (3-D)Three-Dimensional (3-D)– Wodarg et alWodarg et al [2000, 2003] [2000, 2003]– Hydrostatic, pressure level modelHydrostatic, pressure level model– No true vertical transportNo true vertical transport– No chemistry, specification of speciesNo chemistry, specification of species– No magnetospheric inputsNo magnetospheric inputs

• This work builds upon these effortsThis work builds upon these efforts

Enter Titan-GITMEnter Titan-GITMEnter Titan-GITMEnter Titan-GITM• First Titan 3-D model that couples First Titan 3-D model that couples

dynamics, energetics, and composition dynamics, energetics, and composition calculationscalculations

• 3-D Spherical grid3-D Spherical grid– Altitude coordinatesAltitude coordinates– Gravity is a function of altitudeGravity is a function of altitude– True vertical transport can be calculatedTrue vertical transport can be calculated

• Carries 15 Neutral and 5 Ion Species.Carries 15 Neutral and 5 Ion Species.– Including NIncluding N22, CH, CH44, HCN, H, HCN, H22, , 1515N-N-1414N, N, 1313CHCH44

– And HCNHAnd HCNH++, C, C22HH55++

• Based on the Based on the Global Ionosphere-Thermosphere Global Ionosphere-Thermosphere Model (GITM)Model (GITM) framework ( framework (Ridley et alRidley et al [2006])[2006])

Titan-GITM HeritageTitan-GITM HeritageTitan-GITM HeritageTitan-GITM Heritage3-D Models 1-D Models

Lebonnois, Wilson and Atreya, Gan, Keller

NCAR TIE-GCM,Space Weather Modeling Framework

Global Ionosphere-Thermosphere Model

De La Haye

Titan-GITM

Basics of GITMBasics of GITMBasics of GITMBasics of GITM• First 3-D numerical framework that allowsFirst 3-D numerical framework that allows

– Altitude specification for key fieldsAltitude specification for key fields

– Directly calculate vertical transportDirectly calculate vertical transport• Other codes derive vertical winds by Other codes derive vertical winds by demandingdemanding

– Allows for coupling with magnetosphereAllows for coupling with magnetosphere

– Provides for topside fluxesProvides for topside fluxes

• Can function as a 1-D rotating modelCan function as a 1-D rotating model– Turn off the horizontal sources.Turn off the horizontal sources.

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∇• u = 0

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∇• u = 0

Titan-Specific PhysicsTitan-Specific PhysicsTitan-Specific PhysicsTitan-Specific Physics• Hydrogen Cyanide (HCN) rotational coolingHydrogen Cyanide (HCN) rotational cooling

– YelleYelle [1991], [1991], Wodarg Wodarg [2000][2000]

• Solar EUV/UV absorption for NSolar EUV/UV absorption for N22 & CH & CH44

– 1.6 - 175.0 nm1.6 - 175.0 nm

• Planet Parameters:Planet Parameters:– Viscosity, Conduction, Eddy Diffusion, etc…Viscosity, Conduction, Eddy Diffusion, etc…– All generalized for a mixture of NAll generalized for a mixture of N22 & CH & CH44

– De La HayeDe La Haye [2005, 2007a, 2007b] [2005, 2007a, 2007b]

• Chemistry (Chemistry (Wilson and Atreya Wilson and Atreya [2004], [2004], De La HayeDe La Haye [2007a, 2007b, 2008]):[2007a, 2007b, 2008]):– Photo-dissociate NPhoto-dissociate N22 and CH and CH44

– Subsequent neutral and ion chemistrySubsequent neutral and ion chemistry

Titan ChemistryTitan ChemistryTitan ChemistryTitan Chemistry

HCN Rotational CoolingHCN Rotational CoolingHCN Rotational CoolingHCN Rotational Cooling• HCN a linear, asymmetric moleculeHCN a linear, asymmetric molecule

– Rotational spectrum from dipole momentRotational spectrum from dipole moment– Lines are well separated (Lines are well separated (uniqueunique))– Allows for a line-by-line treatmentAllows for a line-by-line treatment

• HCN Rotational Radiative Cooling RatesHCN Rotational Radiative Cooling Rates– Assumed to balance Solar EUV/UVAssumed to balance Solar EUV/UV

• Full line-by-line calculationFull line-by-line calculation– 116 Rotational Lines116 Rotational Lines– Local Thermodynamic Equilibrium (LTE)Local Thermodynamic Equilibrium (LTE)– Gaussian Quadrature integration of the Gaussian Quadrature integration of the Radiative Transfer Equation (RTE)Radiative Transfer Equation (RTE)

– YelleYelle [1991], [1991], WodargWodarg [2000, 2003] [2000, 2003]

T-GITM Boundary T-GITM Boundary ConditionsConditions

T-GITM Boundary T-GITM Boundary ConditionsConditions• Lower Boundary at Lower Boundary at 500 km500 km::

– Set mixing ratios Set mixing ratios (GCMS/CIRS).(GCMS/CIRS).

– Set total density (poorly Set total density (poorly constrained).constrained).

– Vertical Velocities = 0.0Vertical Velocities = 0.0– Take CIRS Temperatures.Take CIRS Temperatures.– Horizontal winds Horizontal winds approximated from 2-D GCM approximated from 2-D GCM of Crespin et al [2008] of Crespin et al [2008] (approximately).(approximately).

• Topside boundary at Topside boundary at 1500 km1500 km::– Set fluxes on key Set fluxes on key constituents.constituents.

LatitudeLatitudeLatitudeLatitude

Pressure (mbar)

Pressure (mbar)

Pressure (mbar)

Pressure (mbar)

5050 5050-50-50 00

5050-50-50

5050

00 505010.010.000

1.00

0.10

0.01

5050

10.00

1.00

0.10

0.01

From Crespin et al From Crespin et al [2008][2008]

From Crespin et al From Crespin et al [2008][2008]

Recent Upper Recent Upper Atmosphere Work (1-D)Atmosphere Work (1-D)

Recent Upper Recent Upper Atmosphere Work (1-D)Atmosphere Work (1-D)

• Yelle et al [2008], Strobel [2008], and Cui et al [2008]Yelle et al [2008], Strobel [2008], and Cui et al [2008]– Predict global outflows Predict global outflows ~4-5 * 10~4-5 * 102828 amu/s amu/s (~66 - 80 (~66 - 80 kg/s). kg/s).

– Enceladus (~150 kg/s Hansen et al [2008] ).Enceladus (~150 kg/s Hansen et al [2008] ).– Not Not yetyet corroborated by direct measurements in Saturn’s corroborated by direct measurements in Saturn’s magnetosphere.magnetosphere.

• Problems:Problems:– Yelle et al [2008] had to reduce mixing ratio of CHYelle et al [2008] had to reduce mixing ratio of CH44 deep in the atmosphere by 30% from GCMS values to match deep in the atmosphere by 30% from GCMS values to match INMS data.INMS data.

– Strobel et al [2008] based upon HASI data above 1000 Strobel et al [2008] based upon HASI data above 1000 km.km.• Retrievals possess appreciable errors in the upper Retrievals possess appreciable errors in the upper atmosphere (Colombatti et al [2008]).atmosphere (Colombatti et al [2008]).

Recent Upper Recent Upper Atmosphere Work (3-D)Atmosphere Work (3-D)

Recent Upper Recent Upper Atmosphere Work (3-D)Atmosphere Work (3-D)

• Mueller-Wodarg [2008].Mueller-Wodarg [2008].– Developed an empirical model using retrieved INMS Developed an empirical model using retrieved INMS

densities.densities.– Use characterized densities to extract temperaturesUse characterized densities to extract temperatures– Use these derived temperatures as a constraint in a Use these derived temperatures as a constraint in a

zonally-symmetric simulation using the model of zonally-symmetric simulation using the model of Mueller-Wodarg [2000].Mueller-Wodarg [2000].

• Potential Problems:Potential Problems:– Temperatures derived from mass densities notoriously Temperatures derived from mass densities notoriously

difficult to get correct (well known in the Mars difficult to get correct (well known in the Mars aerobraking community [Gerald Keating, private aerobraking community [Gerald Keating, private communication].communication].

– Not a truly self-consistent simulation of the Titan Not a truly self-consistent simulation of the Titan upper atmosphere.upper atmosphere.

T-GITM 1-D Model T-GITM 1-D Model ResultsResults

T-GITM 1-D Model T-GITM 1-D Model ResultsResults

Two Configurations of Two Configurations of GITMGITM

Two Configurations of Two Configurations of GITMGITM

• Hydrodynamic ScenarioHydrodynamic Scenario:: – Fluxes of CHFluxes of CH44 consistent with Yelle consistent with Yelle [2008] and Strobel [2008] at 1500 km (top [2008] and Strobel [2008] at 1500 km (top of the model).of the model).

• Aerosol Trapping Scenario:Aerosol Trapping Scenario:– Aerosols trap material Aerosols trap material

• (Jacovi et al [2008], Icarus ). (Jacovi et al [2008], Icarus ). • Adopt experimental trapping Adopt experimental trapping efficiencies efficiencies – Similar to amorphous ice (e.g. Bar-Similar to amorphous ice (e.g. Bar-Nun et al [2007], Icarus).Nun et al [2007], Icarus).

• Set vertical distribution of aerosols Set vertical distribution of aerosols according to Bar-Nun et al [2008], according to Bar-Nun et al [2008], JGR.JGR.

SpeciesSpecies NN22 CHCH44 HH224040ArAr

Efficiency Efficiency (%)(%)

~0.0001~0.0001 1.5 1.5 0 0 0.010.01

• Focus on global mean structures produced by T-GITMFocus on global mean structures produced by T-GITM

• Create global average INMS dataCreate global average INMS data– Method of Method of Magee et al [2009] (PSS Special Issue).Magee et al [2009] (PSS Special Issue).– Average over all prime flyby passes.Average over all prime flyby passes.– Place into 10 km vertical bins.Place into 10 km vertical bins.– Horizontal “Error” bars contain two componentsHorizontal “Error” bars contain two components

• Counting statistics (Counting statistics (4040Ar only).Ar only).• Global variations (latitude, longitude).Global variations (latitude, longitude).

– Show a least-squares fit to the data (calibration).Show a least-squares fit to the data (calibration).

• Overplot the T-GITM results.Overplot the T-GITM results.– Calculate model-to-data % deviations (how far off).Calculate model-to-data % deviations (how far off).– Squared correlation coefficients (trend capturing).Squared correlation coefficients (trend capturing).

Method of ComparisonMethod of ComparisonMethod of ComparisonMethod of Comparison

INMS Flyby Data INMS Flyby Data ComparisonComparison

INMS Flyby Data INMS Flyby Data ComparisonComparison

INMS Flyby Data INMS Flyby Data 4040ArArINMS Flyby Data INMS Flyby Data 4040ArAr

Note : Errors here have a larger counting Note : Errors here have a larger counting statistics componentstatistics component

Note : Errors here have a larger counting Note : Errors here have a larger counting statistics componentstatistics component

T-GITM 3-D Model T-GITM 3-D Model ResultsResults

T-GITM 3-D Model T-GITM 3-D Model ResultsResults

INMS Flyby Data INMS Flyby Data ComparisonComparison

INMS Flyby Data INMS Flyby Data ComparisonComparison• Use 15 flyby datasetsUse 15 flyby datasets

– T5 - T40T5 - T40– Span several Earth yearsSpan several Earth years– Sample both northern and southern Sample both northern and southern hemispheres hemispheres

– Each flyby covers a significant range of Each flyby covers a significant range of latitudes and altitudes.latitudes and altitudes.

• All flybys occur at nearly the same season and All flybys occur at nearly the same season and solar flux level at Titan.solar flux level at Titan.– Thus, a single simulation is used for Thus, a single simulation is used for comparisoncomparison

– Fly Cassini through the model along each Fly Cassini through the model along each flyby trajectory for a direct comparisonflyby trajectory for a direct comparison

– Local differences among the flybys may be Local differences among the flybys may be responsible for some data/model mismatchresponsible for some data/model mismatch• e.g. localized wave forcinge.g. localized wave forcing

Sample Flyby Sample Flyby Trajectory: T21Trajectory: T21Sample Flyby Sample Flyby

Trajectory: T21Trajectory: T21Black = IngressBlack = Ingress

White = egressWhite = egress

Flyby Comparison IFlyby Comparison IFlyby Comparison IFlyby Comparison I

Flyby Comparison IIFlyby Comparison IIFlyby Comparison IIFlyby Comparison II

Flyby Comparison IIIFlyby Comparison IIIFlyby Comparison IIIFlyby Comparison III

Flyby Comparison IVFlyby Comparison IVFlyby Comparison IVFlyby Comparison IV

Argon ScatterArgon ScatterArgon ScatterArgon Scatter

At 500 km, Ar Mixing = 4.32 x 10-5

At 500 km, Ar Mixing = 4.32 x 10-5

1515N-N-1414N Isotope ScatterN Isotope Scatter1515N-N-1414N Isotope ScatterN Isotope Scatter

At 500 km, 14N/15N = 130.0At 500 km, 14N/15N = 130.0

1313CHCH44 Isotope Scatter Isotope Scatter1313CHCH44 Isotope Scatter Isotope Scatter

At 500 km, 12C/13C = 80.0At 500 km, 12C/13C = 80.0

Summary of Flyby Summary of Flyby ResultsResults

Summary of Flyby Summary of Flyby ResultsResults

QuantityQuantity NN22 CHCH44 ArAr 1515N-N-1414N N 1313CHCH44

NRMSENRMSE

(%)(%)22.22.88

27.27.33

40.40.55

14.714.7 10.010.0

CorrelatiCorrelationon

CoefficieCoefficientnt

0.90.966

.97.97 .61.61 .74.74 .55.55

• T-GITM is a viable theoretical tool for T-GITM is a viable theoretical tool for Titan’s upper atmosphere.Titan’s upper atmosphere.

• We know of no other 3-D model has been We know of no other 3-D model has been compared with data in this manner at Titan.compared with data in this manner at Titan.

Future WorkFuture WorkFuture WorkFuture Work• Construct a 3-D first principles model for Construct a 3-D first principles model for

Titan’s upper atmosphere.Titan’s upper atmosphere.– validate against INMS in-situ data.validate against INMS in-situ data.

• Couple with lower atmosphere modelsCouple with lower atmosphere models– Both 1-D, 2-D, 3-DBoth 1-D, 2-D, 3-D– Incorporate better chemistry, Incorporate better chemistry, heterogeneous reactions (aerosols) heterogeneous reactions (aerosols)

• Extend into the exosphere using 13-moment Extend into the exosphere using 13-moment corrections suggested by Boqueho and Blelly corrections suggested by Boqueho and Blelly [2005].[2005].– Compare results with other published work Compare results with other published work in Titan’s exosphere (c.f. Cui et al in Titan’s exosphere (c.f. Cui et al [2009]).[2009]).

• Improve Chemistry and Ion treatments.Improve Chemistry and Ion treatments.

GITM FormulationGITM FormulationGITM FormulationGITM Formulation• GITM is a spherical, non-hydrostatic, Navier-GITM is a spherical, non-hydrostatic, Navier-

Stokes modelStokes model• Finite Volume CodeFinite Volume Code

– Lax-Wendroff solver (Rusanov Solver) with Lax-Wendroff solver (Rusanov Solver) with Upwind biasUpwind bias• 2nd order calculations over the physical 2nd order calculations over the physical domaindomain

– Explicit time evolutionExplicit time evolution• Useful for real-time simulations (studies Useful for real-time simulations (studies of Earth during storm-time events)of Earth during storm-time events)

– Resolve acoustic waves and can resolve shock Resolve acoustic waves and can resolve shock waves in the modelwaves in the model

– Inherits the solver sets and capabilities from Inherits the solver sets and capabilities from the Space Weather Modeling Framework (SWMF) the Space Weather Modeling Framework (SWMF) Michigan coding familiesMichigan coding families

ContinuityContinuityContinuityContinuity

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∂ns∂t

+∇ • (nsus) = Ps − Ls

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ns

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us

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Ps

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Ls

Neutral Density (m-3)

Species Velocity (m/s)

Chemical Production (m-3/s)

Chemical Loss (m-3/s)

MomentumMomentumMomentumMomentum

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ρs

DusDt

+∇Ps − ρ sg−∇ • τ =Ψs + Fsturb +Φs

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Ψs = ρ iν is vi −us( ) + PsnqNDst

ut −us( )t≠s

∑

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F turbs =

PsN

ntDst

Kmsg

kT−m_

g

kT

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟

⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥

t≠s

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Φ s = (Ω× (Ω× r)) + 2(Ω×us) +CurvatureCoriolis and Curvature terms

Ion and Neutral Momentum Coupling

Turbulent Contribution (Boqueho and Blelly [2005])

EnergyEnergyEnergyEnergy

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ρcv∂T

∂t+ ρcv u • ∇T( ) + (γ −1)P ∇ • u( ) + τ :∇u =Qext +∇ • q

Unlike Continuity and Momentum, GITM assumes a single bulk temperature for all species

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Qext =QHCN +QEUV ,UV +QMagnetosphereExternal Source Terms

Conduction

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q = -λ∇T