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The “Bordeaux” 1D photochemical model of Titan. Michel Dobrijevic Laboratoire d’Astrophysique de Bordeaux. In collaboration with Eric Hébrard, Nathalie Carrasco and Pascal Pernot. A brief history. First version: 1D Titan model (Toublanc et al. 1995) in Fortran77
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The “Bordeaux” 1D photochemical model of Titan Michel Dobrijevic Laboratoire d’Astrophysique de Bordeaux In collaboration with Eric Hébrard, Nathalie Carrasco and Pascal Pernot
A brief history • First version: 1D Titan model (Toublanc et al. 1995) in Fortran77 • Following versions: giant planets, telluric planets and Titan • Dobrijevic, 1996 (Neptune) • Lefloechmoen, 1997 (Jupiter) • Ollivier et al. 2000 (Saturn) • Selsis et al. 2002 (Earth and Mars, exoplanets) • Dobrijevic et al. 2003 (New: Fortran90+uncertainty - giant planets) • Hébrard et al. 2007 & Dobrijevic et al. 2008 (Titan(*)) Notes: A second version, in C, has been written by Toublanc and developed by Lebonnois (see Carrasco talk). (*)Our Titan model is not the “best model” we have developed!
Methodology 1 Methodology controls the complexity of the models
Photochemical model: main objectives Compute compounds abundances: • to validate our understanding of physical and chemical processes occurring in the atmosphere (by comparison with observational data), • to predict the abundances of undetected trace species, • to predict the chemical evolution in time of major and/or minor compounds. Different objectives can generate different codes, and consequently different results
The common methodology • We assume that the chemical scheme is “quite well known”. • Then, we try to constrain the physical parameters. • (Sometimes, some chemical processes are considered as free parameters). Our methodology • We identify and quantify all the sources of uncertainties (especially in chemistry). • We study the uncertainty propagation to quantify the model output uncertainties. • We aim to identify the key input by sensitivity methods to lower output uncertainties. This changes the way we develop our model!
Characteristics of the model • Only the main processes are included in the model: • Vertical transport • Simple exponential attenuation in U.V. • Chemical processes found in database (estimations are limited) • Condensation • Many processes are not included: • Multiple scattering • Mie scattering (spherical or fractal aerosols) • Heterogeneous reactions • Coupling with ions (effects are studied with Pernot, Carrasco et al.) • 2D or 3D geometry • Chemical processes with no measurements • Coupling with I.R. radiative transfer, haze microphysics… • Etc.
Details of the model 2 Technical characteristics of the photochemical model
What are the causes of the differences in the different code results ? • Physical processes • List of processes • How they are implemented in the code • Chemical processes • Cross sections and quantum yields • Reaction rates • Chemical network (number of reactions and compounds) • Output • Numerical aspects • Spatial discretization (geometry) • Numerical method (time dependant or not,…) • Convergence criteria • Initial conditions • Boundary conditions • Background atmosphere • Scientific objectives of the model • We need to identify all these points (and others…) • We need benchmark (simple) models
The continuity equation (1D model) For each compound i, at each altitude level: + other processes (condensation…) + boundary conditions Chemistry Vertical transport No thermal diffusion
Matrix formulation vector of dimensionNcompounds Nlevels Time-dependant system to solve: Finite difference method Crank-Nicholson method: With Matrix formulation Resolution using the LU method Jacobian matrix
Initial conditions • Major compounds have constant abundances with altitude given by boundary conditions: CH4 ; N2 ; Ar ; CO ; H2 • All other compounds: y(t=0) = 0 • Photodissociation rates are computed with these initial profiles • T(z), P(z) and n(z) are constant with time
Geometry • Altitudinal grid: constant z = 5 km • Atmospheric boundary: min = 0 km, max = 1300 km Number of altitude levels: 260 • Location: latitude = 0°, declination = 0° (corresponding to mean diurnal conditions with zenithal angle: 30°)
Boundary conditionsUpper boundary • Jeans escape for H and H2 • v(H) = 2.54 104 cm s-1 • v(H2) = 5.90 103 cm s-1 • External input for H2O • (H2O) = 5.0 106 cm-2s-1(Wilson and Atreya, 2005) • Zero flux for all other compounds
Boundary conditionsLower boundary • y(CH4) = 1.41 10-2 (b) • y(N2) = 98.47 10-2 • y(Ar) = 4.3 10-5(a) • y(CO) = 5.2 10-5 (*) • y(H2) = 1.1 10-3 (*) • Zero flux for all other compounds = Wilson and Atreya, 2004 ≠ Krasnopolsky, 2009 Notes: abundances of these compounds are fixed at the lower boundary Ref: (a) INMS data (Yelle et al. 2008)(b) GCMS data (Niemann et al. 2005).
Steady state • Total integration time: ~ 5 109 s (time required for most compounds to go through the atmosphere) • Control of the time step to prevent strong variation of abundances • If y > 10%, then t decrease • If y < 10%, then t increase (depend on y) • Maximum time step: ~ 5 105 s (for a better behavior of the model) Note: control of time step is not performed for species with low abundances
Iterative procedure • Several runs are performed (~ 109 s each). • Photodissociation rates, diffusion coefficients (…) are re-computed at each run. • This iterative procedure is stopped when abundance profiles are stable (from one run to another).
Some precisions about physical processes • Molecular diffusion (Fuller formulation cf. Reid et al. 1988). Diffusion in binary mixture (N2, CH4). • Eddy diffusion K(z): free parameter. Should be constrained from comparison with observations. • Condensation: 16 compounds. • Vapor pressures found in literature. • No sursaturation. Note: in the present version, K(z) has not been well constrained…
Chemical schemeHébrard et al. 2006 • Number of compounds: 127 • Hydrocarbons up to C8-compounds: 70 • Nitrogen compounds: 37 • Oxygen compounds: 16 • Others: 4 • Number of photodissociations: 67 • Number of reactions: 676 • Dissociation of N2 by GCR (Lellouch et al. 1992) Notes: • Cross sections, quantum yield and reaction rates at low temperature are preferred. • The number of estimated rates are low. • An compound called “SOOT” is introduced for heavy compounds with no chemical sink.
UV radiative transfer For each compound i, at each altitude z, photodissociation ratesare given by: • q : quantum yield• F : actinic flux• s : absorption cross section Simple exponential attenuation: - absorption by gas - attenuation by Rayleigh scattering - absorption by aerosols (Yung et al. 1984)
Solar flux • Minimum wavelength: 5 nm • Resolution: = 1 nm • Mean solar irradiance bin = 1 nm Floyd et al. 1998
1000 km Counts log(mole fraction) 500 km Counts log(mole fraction) 200 km Counts log(mole fraction) Model output Number of simulations: 500 • Nominal abundance profiles • Histograms or set of profiles (after uncertainty propagation study) Hébrard et al. 2007
Hébrard et al. 2007 Conclusion of our recent results • It is crucial to take uncertainties of input into account. • Uncertainties of model output are essentially due to our poor knowledge of the chemistry. • It is of limited use to add second-order physical processes. 0D model Large uncertainties Epistemic bimodality Dobrijevic et al. 2008 • CH + H C + H2 (kb) • CH + CH4 C2H4 + H (ka)
Planetologists need a chemical database that has been validated by chemists! This database is under construction! http://kida.obs.u-bordeaux1.fr/
Comparison study is very important! • This should help us to: • Understand the origins of the discrepancies • Determine what are the second-order processes • Determine the limits of the models • Propose a roadmap to improve the predictability of photochemical models
Computer specifications Number of bi-processors: 4 vendor_id: GenuineIntel model name: Intel(R) Xeon(TM) CPU 3.06GHz cpu MHz: 3056.539 cache size: 512 KB Computation time by run: about 1 hour. (initial conditions: nominal steady state concentrations,maximal integration time: 109 s). Computation time to reach a steady state: few hours.
Uncertainty propagation k0 : nominal rate (T ≈ 300 K) Fk : uncertainty factor The main limitation: huge computation time!