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 (Saturn) –Selsis et al (Earth and Mars, exoplanets) –Dobrijevic et al (New: Fortran90+uncertainty - giant planets) –Hébrard et al & Dobrijevic et al (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 1.We assume that the chemical scheme is “quite well known”. 2.Then, we try to constrain the physical parameters. 3.(Sometimes, some chemical processes are considered as free parameters). Our methodology 1.We identify and quantify all the sources of uncertainties (especially in chemistry). 2.We study the uncertainty propagation to quantify the model output uncertainties. 3.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 ? Numerical aspects –Spatial discretization (geometry) –Numerical method (time dependant or not,…) –Convergence criteria –Initial conditions –Boundary conditions –Background atmosphere Scientific objectives of the model 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 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: Chemistry Vertical transport + other processes (condensation…) + boundary conditions No thermal diffusion

Matrix formulation vector of dimension N compounds  N levels Crank-Nicholson method: With Jacobian matrix  Resolution using the LU method Time-dependant system to solve: Finite difference method Matrix formulation

Initial conditions Major compounds have constant abundances with altitude given by boundary conditions: CH 4 ; N 2 ; Ar ; CO ; H 2 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 conditions Upper boundary Jeans escape for H and H 2 –v(H) = cm s -1 –v(H 2 ) = cm s -1 External input for H 2 O –  (H 2 O) = cm -2 s -1 (Wilson and Atreya, 2005) Zero flux for all other compounds

Boundary conditions Lower boundary y(CH 4 ) = (b) y(N 2 ) = y(Ar) = (a) y(CO) = (*) y(H 2 ) = (*) Zero flux for all other compounds 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). = Wilson and Atreya, 2004 ≠ Krasnopolsky, 2009

Steady state Total integration time: ~ 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: ~ 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 (~ 10 9 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 (N 2, CH 4 ). 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 scheme Hébrard et al 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 N 2 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 q : quantum yield F : actinic flux  : absorption cross section For each compound i, at each altitude z, photodissociation rates are given by: 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 Floyd et al bin = 1 nm

Model output Nominal abundance profiles Histograms or set of profiles (after uncertainty propagation study) Hébrard et al log(mole fraction) Counts log(mole fraction) 1000 km 500 km 200 km Number of simulations: 500

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. Hébrard et al D model CH + H  C + H 2 (k b ) CH + CH 4  C 2 H 4 + H (k a ) Dobrijevic et al Epistemic bimodality Large uncertainties

Planetologists need a chemical database that has been validated by chemists! This database is under construction!

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

Thank you

Computer specifications Number of bi-processors: 4 vendor_id: GenuineIntel model name: Intel(R) Xeon(TM) CPU 3.06GHz cpu MHz: cache size: 512 KB Computation time by run: about 1 hour. (initial conditions: nominal steady state concentrations, maximal integration time: 10 9 s). Computation time to reach a steady state: few hours.

Uncertainty propagation k 0 : nominal rate (T ≈ 300 K) F k : uncertainty factor The main limitation: huge computation time!