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
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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!
1
Methodology
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
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3.
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
1.
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3.
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:
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Vertical transport
Simple exponential attenuation in U.V.
Chemical processes found in database (estimations are limited)
Condensation
• Many processes are not included:
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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.
2
Details of the model
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:
ur
u
dyi Pi
div(i )
  yi Li 
dt
n
n
+ other processes
(condensation…)
+ boundary
conditions
Chemistry
Vertical
transport
 1 dni
 1 dni
1 1 dT 
1
1 dT 
i  ni Di 




  ni K 

n
dt
H
T
dz
n
dt
H
T
dz
 i

 i

i
a
No thermal diffusion
Matrix formulation
Time-dependant system to solve:
Finite difference method
Crank-Nicholson method:
r
r
dY
 f (Y )
dt
Y vector of dimension
Ncompounds  Nlevels
r
Y
  f (t  t)  (1   ) f (t)
t
With 
Matrix formulation
r r
r
 1
   J  Y  f (Y )
t
Jacobian matrix

Resolution using
the LU method
 0.501
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 conditions
Upper 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 conditions
Lower boundary
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y(CH4) = 1.41 10-2 (b)
1   yi
y(N2) = 98.47 10-2
i
-5
y(Ar) = 4.3 10 (a)
y(CO) = 5.2 10-5 (*)
= Wilson and Atreya, 2004
≠ Krasnopolsky, 2009
y(H2) = 1.1 10-3 (*)
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).
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.
if
yi  yisat , then f (yi )  0
Note: in the present version, K(z) has not been well constrained…
Chemical scheme
Hébrard et al. 2006
• Number of compounds: 127
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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 rates
are given by:
Ji (z) 

2
1
q( )s i ( )F( ,z)d
• 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
Model output
1000 km
Counts
Number of simulations: 500
log(mole fraction)
Counts
500 km
Hébrard et al. 2007
log(mole fraction)
• Nominal abundance profiles
• Histograms or set of profiles
Counts
200 km
(after uncertainty propagation study)
log(mole fraction)
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
kb CH 4 

ka
H 
Large
uncertainties
kb CH 4 

ka
H 
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:
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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:
vendor_id:
model name:
cpu MHz:
cache size:
4
GenuineIntel
Intel(R) Xeon(TM) CPU 3.06GHz
3056.539
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
log k  log k0  log Fk
k0 : nominal rate
(T ≈ 300 K)
Fk : uncertainty factor
The main limitation: huge computation time!