1. The Titan Global Ionosphere- Thermosphere Model (1-D and 3-D) Hunter Waite, Jared M. Bell ISSI Bern Modeling Workshop March, 2009

2. OutlineOutline 1.Titan Global Ionosphere-Thermosphere Model (T-GITM) a)Formulation b)Titan-Specific Physics c)1-D and a 3-D configuration 2.Current work on the Upper atmosphere of Titan 3.1-D Results 4.(unrefined) 3-D Results 5.Future Plans.

3. Previous Modeling Efforts One-Dimensional (1-D)One-Dimensional (1-D) –Photochemical ( Wilson, [2002]) –Thermal Structure ( Friedson & Yung, [1987]) –Coupled Chemical-Thermal-Diffusive De La Haye et. al. [2007a, 2007b, 2008] De La Haye et. al. [2007a, 2007b, 2008] Three-Dimensional (3-D)Three-Dimensional (3-D) – Wodarg et al [2000, 2003] –Hydrostatic, pressure level model –No true vertical transport –No chemistry, specification of species –No magnetospheric inputs This work builds upon these efforts This work builds upon these efforts

4. Enter Titan-GITM First Titan 3-D model that couples dynamics, energetics, and composition calculationsFirst Titan 3-D model that couples dynamics, energetics, and composition calculations 3-D Spherical grid3-D Spherical grid –Altitude coordinates –Gravity is a function of altitude –True vertical transport can be calculated Carries 15 Neutral and 5 Ion Species.Carries 15 Neutral and 5 Ion Species. –Including N 2, CH 4, HCN, H 2, 15 N- 14 N, 13 CH 4 –And HCNH +, C 2 H 5 + Based on the Global Ionosphere-Thermosphere Model (GITM) framework ( Ridley et al [2006])Based on the Global Ionosphere-Thermosphere Model (GITM) framework ( Ridley et al [2006])

5. Titan-GITM Heritage 3-D Models1-D Models Lebonnois, Wilson and Atreya, Gan, Keller NCAR TIE-GCM, Space Weather Modeling Framework Global Ionosphere- Thermosphere Model De La Haye Titan-GITM

6. Basics of GITM First 3-D numerical framework that allowsFirst 3-D numerical framework that allows –Altitude specification for key fields –Directly calculate vertical transport Other codes derive vertical winds by demandingOther codes derive vertical winds by demanding –Allows for coupling with magnetosphere –Provides for topside fluxes Can function as a 1-D rotating modelCan function as a 1-D rotating model –Turn off the horizontal sources.

7. Titan-Specific Physics Hydrogen Cyanide (HCN) rotational coolingHydrogen Cyanide (HCN) rotational cooling – Yelle [1991], Wodarg [2000] Solar EUV/UV absorption for N 2 & CH 4Solar EUV/UV absorption for N 2 & CH 4 –1.6 - 175.0 nm Planet Parameters:Planet Parameters: –Viscosity, Conduction, Eddy Diffusion, etc… –All generalized for a mixture of N 2 & CH 4 – De La Haye [2005, 2007a, 2007b] Chemistry ( Wilson and Atreya [2004], De La Haye [2007a, 2007b, 2008]):Chemistry ( Wilson and Atreya [2004], De La Haye [2007a, 2007b, 2008]): –Photo-dissociate N 2 and CH 4 –Subsequent neutral and ion chemistry

8. Titan Chemistry

9. HCN Rotational Cooling HCN a linear, asymmetric moleculeHCN a linear, asymmetric molecule –Rotational spectrum from dipole moment –Lines are well separated (unique) –Allows for a line-by-line treatment HCN Rotational Radiative Cooling RatesHCN Rotational Radiative Cooling Rates –Assumed to balance Solar EUV/UV Full line-by-line calculationFull line-by-line calculation –116 Rotational Lines –Local Thermodynamic Equilibrium (LTE) –Gaussian Quadrature integration of the Radiative Transfer Equation (RTE) – Yelle [1991], Wodarg [2000, 2003]

10. T-GITM Boundary Conditions Lower Boundary at 500 km:Lower Boundary at 500 km: –Set mixing ratios (GCMS/CIRS). –Set total density (poorly constrained). –Vertical Velocities = 0.0 –Take CIRS Temperatures. –Horizontal winds approximated from 2-D GCM of Crespin et al [2008] (approximately). Topside boundary at 1500 km:Topside boundary at 1500 km: –Set fluxes on key constituents. LatitudeLatitude Pressure (mbar) 50 50-500 50 -50 50 050 10.00 1.00 0.10 0.01 50 10.00 1.00 0.10 0.01 From Crespin et al [2008]

11. Recent Upper 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 ~4-5 * 10 28 amu/s (~66 - 80 kg/s). –Enceladus (~150 kg/s Hansen et al [2008] ). –Not yet corroborated by direct measurements in Saturn’s magnetosphere. Problems:Problems: –Yelle et al [2008] had to reduce mixing ratio of CH 4 deep in the atmosphere by 30% from GCMS values to match INMS data. –Strobel et al [2008] based upon HASI data above 1000 km. Retrievals possess appreciable errors in the upper atmosphere (Colombatti et al [2008]).Retrievals possess appreciable errors in the upper atmosphere (Colombatti et al [2008]).

12. Recent Upper Atmosphere Work (3-D) Mueller-Wodarg [2008].Mueller-Wodarg [2008]. –Developed an empirical model using retrieved INMS densities. –Use characterized densities to extract temperatures –Use these derived temperatures as a constraint in a zonally- symmetric simulation using the model of Mueller-Wodarg [2000]. Potential Problems:Potential Problems: –Temperatures derived from mass densities notoriously difficult to get correct (well known in the Mars aerobraking community [Gerald Keating, private communication]. –Not a truly self-consistent simulation of the Titan upper atmosphere.

13. T-GITM 1-D Model Results

14. Two Configurations of GITM Hydrodynamic Scenario:Hydrodynamic Scenario: –Fluxes of CH 4 consistent with Yelle [2008] and Strobel [2008] at 1500 km (top of the model). Aerosol Trapping Scenario:Aerosol Trapping Scenario: –Aerosols trap material (Jacovi et al [2008], Icarus ).(Jacovi et al [2008], Icarus ). Adopt experimental trapping efficienciesAdopt experimental trapping efficiencies –Similar to amorphous ice (e.g. Bar-Nun et al [2007], Icarus). Set vertical distribution of aerosols according to Bar-Nun et al [2008], JGR.Set vertical distribution of aerosols according to Bar-Nun et al [2008], JGR. Species N2N2N2N2 CH 4 H2H2H2H2 40 Ar Efficiency (%) ~0.00011.500.01

15. 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 Magee et al [2009] (PSS Special Issue). –Average over all prime flyby passes. –Place into 10 km vertical bins. –Horizontal “Error” bars contain two components Counting statistics ( 40 Ar only).Counting statistics ( 40 Ar only). Global variations (latitude, longitude).Global variations (latitude, longitude). –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). –Squared correlation coefficients (trend capturing). Method of Comparison

16. INMS Flyby Data Comparison

17. INMS Flyby Data 40 Ar Note : Errors here have a larger counting statistics component

18. T-GITM 3-D Model Results

19. INMS Flyby Data Comparison Use 15 flyby datasetsUse 15 flyby datasets –T5 - T40 –Span several Earth years –Sample both northern and southern hemispheres –Each flyby covers a significant range of latitudes and altitudes. All flybys occur at nearly the same season and solar flux level at Titan.All flybys occur at nearly the same season and solar flux level at Titan. –Thus, a single simulation is used for comparison –Fly Cassini through the model along each flyby trajectory for a direct comparison –Local differences among the flybys may be responsible for some data/model mismatch e.g. localized wave forcinge.g. localized wave forcing

20. Sample Flyby Trajectory: T21 Black = Ingress White = egress

21. Flyby Comparison I

22. Flyby Comparison II

23. Flyby Comparison III

24. Flyby Comparison IV

25. Argon Scatter At 500 km, Ar Mixing = 4.32 x 10 -5

26. 15 N- 14 N Isotope Scatter At 500 km, 14 N/ 15 N = 130.0

27. 13 CH 4 Isotope Scatter At 500 km, 12 C/ 13 C = 80.0

28. Summary of Flyby Results Quantity N2N2N2N2 CH 4 Ar 15 N- 14 N 13 CH 4 NRMSE(%)22.827.340.514.710.0 CorrelationCoefficient0.96.97.61.74.55 T-GITM is a viable theoretical tool for Titan’s upper atmosphere.T-GITM is a viable theoretical tool for Titan’s upper atmosphere. We know of no other 3-D model has been compared with data in this manner at Titan.We know of no other 3-D model has been compared with data in this manner at Titan.

29. Future Work Construct a 3-D first principles model for Titan’s upper atmosphere.Construct a 3-D first principles model for Titan’s upper atmosphere. –validate against INMS in-situ data. Couple with lower atmosphere modelsCouple with lower atmosphere models –Both 1-D, 2-D, 3-D –Incorporate better chemistry, heterogeneous reactions (aerosols) Extend into the exosphere using 13-moment corrections suggested by Boqueho and Blelly [2005].Extend into the exosphere using 13-moment corrections suggested by Boqueho and Blelly [2005]. –Compare results with other published work in Titan’s exosphere (c.f. Cui et al [2009]). Improve Chemistry and Ion treatments.Improve Chemistry and Ion treatments.

30. GITM Formulation GITM is a spherical, non-hydrostatic, Navier-Stokes modelGITM is a spherical, non-hydrostatic, Navier-Stokes model Finite Volume CodeFinite Volume Code –Lax-Wendroff solver (Rusanov Solver) with Upwind bias 2nd order calculations over the physical domain2nd order calculations over the physical domain –Explicit time evolution Useful for real-time simulations (studies of Earth during storm-time events)Useful for real-time simulations (studies of Earth during storm-time events) –Resolve acoustic waves and can resolve shock waves in the model –Inherits the solver sets and capabilities from the Space Weather Modeling Framework (SWMF) Michigan coding families

31. ContinuityContinuity Neutral Density (m -3 ) Species Velocity (m/s) Chemical Production (m -3 /s) Chemical Loss (m -3 /s)

32. MomentumMomentum Coriolis and Curvature terms Ion and Neutral Momentum Coupling Turbulent Contribution (Boqueho and Blelly [2005])

33. EnergyEnergy Unlike Continuity and Momentum, GITM assumes a single bulk temperature for all species External Source Terms Conduction