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![Page 1: ERROR PROPAGATION FROM LINE PARAMETERS TO SPECTRA SIMULATIONS Illustration on High Temperature Methane. Jean Paul Champion & Christian Wenger Laboratoire.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d4a5503460f94a26a90/html5/thumbnails/1.jpg)
ERROR PROPAGATION FROM LINE PARAMETERS TO SPECTRA SIMULATIONS
Illustration on High Temperature Methane.
Jean Paul Champion & Christian Wenger
Laboratoire Interdisciplinaire Carnot de BourgogneUMR 5209 CNRS - Université de Bourgogne
Dijon - France
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 1 / 49
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What to do when high-resolution spectroscopic information
is missing ?
Simply ignore missing data !
Are lower-resolution studies useless ?
What about error bars !
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 2 / 49
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Methane at high-temperature
A typical illustration
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3057.6 3057.8 3058.0 3058.2 3058.4 3058.6
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
Methane | Trot : 296 K | Tvib : 2000 K | Doppler regime
3 cold lines form "Pentad - GS" : 0.65 cm-2.atm-1
27 hot lines from "Octad - Dyad" : 0.30 cm-2.atm-1
126 hot lines from "Tetradecad - Pentad" : 0.43 cm-2.atm-1
Abs
orpt
ion
Coe
ffici
ent /
cm
-1
Wavenumber / cm-1
STDS prediction - extrapolation
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 4 / 49
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Hot methane statistics (3057 - 3059 cm-1) STDS Tvib = 2000 K | Trot = 296 K
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 5 / 49
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3057.6 3057.8 3058.0 3058.2 3058.4 3058.6
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
Methane | Trot : 296 K | Tvib : 2000 K | Doppler regime
3 cold lines form "Pentad - GS" : 0.65 cm-2.atm-1
27 hot lines from "Octad - Dyad" : 0.30 cm-2.atm-1
126 hot lines from "Tetradecad - Pentad" : 0.43 cm-2.atm-1
Abs
orpt
ion
Coe
ffici
ent /
cm
-1
Wavenumber / cm-1
What to do with the 126 inacurrate hot lines ?
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 6 / 49
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3057.6 3057.8 3058.0 3058.2 3058.4 3058.6
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
Methane | Trot : 296 K | Tvib : 2000 K | Doppler regime
3 cold lines form "Pentad - GS" : 0.65 cm-2.atm-1
27 hot lines from "Octad - Dyad" : 0.30 cm-2.atm-1
126 hot lines from "Tetradecad - Pentad" ignored
Abs
orpt
ion
Coe
ffici
ent /
cm
-1
Wavenumber / cm-1
Simply ignore inaccurate lines !
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 7 / 49
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3057.6 3057.8 3058.0 3058.2 3058.4 3058.6
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
0.0030
0.0035
0.0040
0.0045
0.0050
Methane | Trot : 296 K | Tvib : 2000 K | Res = 0.1 cm-1
"Tetradecad - Pentad" included : 1.38 cm-2.atm-1
"Tetradecad - Pentad" ignored : 0.95 cm-2.atm-1
Abs
orpt
ion
Coe
ffici
ent /
cm
-1
Wavenumber / cm-1
Low-resolution informationUseful ?
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 8 / 49
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The scope of this presentation
How to provide completeness and confidence needed for astrophysical applications?
How to combine« high and low-resolution » information ?
How to provide rigorous estimates of the accuracy of spectrum predictions ?
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 9 / 49
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Methane
present in the atmosphere of many astrophysical objects
specific energy structure due to symmetry
adapted for polyad simultaneous modeling
challenging ab initio approaches
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 10 / 49
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Titan | Cassini - Huygens
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 11 / 49
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Huygens DISR data
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High temperature
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 13 / 49
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Methane polyads and rovibrational energy levels
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
Statisticaldescription ...
Line by line in progress
Line by line close to experimental precision
Heptacontad
Pentacontakaipentad
Tetracontad
Triacontad
P9
P8
P7
P6P5 : Icosad
P4 : Tetradecad
P3 : Octad
P2 : Pentad
P1 : Dyad
Ene
rgy
/ cm
-1
J Quantum Number
P0 : Ground State
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 14 / 49
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Starting point : Position and Intensity predictionswith individual standard deviations
Global / simultaneous analyses
Polyads
Effective hamiltonians
Variational / Ab initio calculations
(High resolution – highly sensitive lab. experiments)
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 15 / 49
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Propagation of information within the polyads« Vibrational extrapolation schema »
Simultaneous fit of 5 sets of energies taken from higher order fits and / or « ab initio » results
58 adjustable parameters only for all polyads up to 2nd order …… with an accuracy of the order of 1 cm-1 !
Nb Jmax Wtd SD Bands Weight RMS Input Data 1 919 20 0.529 P1-P0 1.0 0.5 calc energies (order 6) 2 3492 20 0.693 P2-P0 1.0 O.6 calc energies (order 6) 3 2774 10 0.929 P3-P0 1.0 0.9 calc energies (order 4) 4 18 0 15.2 P4-P0 0.1 1.5 «observed» band centers 5 60 0 13.1 P4-P0 0.2 2.6 «ab initio» predictions cm-1 7263 Data fitted : Weighted Standard Deviation 1.617
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Propagation of information within the polyads
Influence of various «ab initio» results
5800 5900 6000 6100 6200
- Simple extrapolation from P0 – P3 - Including P4 band centers predicted by Georges et al. J. Mol. Spectrosc. (1998) - Including P4 band centers predicted by Schwenke et al. Spec Chemica Acta (2001)- Including P4 band centers predicted by Wang et al. J. Chem. Phys. (2003)
Significant discrepancies
@ low resolution
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 17 / 49
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Propagation of information within the polyads
from Dyad, Pentad, Octad, Tetradecad, [ ] data …… into «Dyad» effective parameters
Relative weights of Data from Parameter Value(St.Dev) Dyad Pentad Octad Tetradecad obs ab initio
11 0(0,0A1) 0100E 0100E 1534.002(72) 2.5 21.7 32.2 12.2 31.4 12 2(0,0A1) 0100E 0100E -6.79(84)x10-3 9.4 81.3 9.3 0.0 0.0 13 2(2,0E ) 0100E 0100E -2.909(76)x10-2 13.7 77.9 8.4 0.0 0.0 26 1(1,0F1) 0100E 0001F2 -9.144(42) 11.5 77.4 10.1 0.0 0.0 27 2(2,0F2) 0100E 0001F2 -5.735(87)x10-2 14.2 83.5 2.3 0.0 0.0 46 0(0,0A1) 0001F2 0001F2 1309.969(57) 2.4 23.4 35.8 8.2 30.2 47 1(1,0F1) 0001F2 0001F2 10.2468(83) 10.8 65.7 23.6 0.0 0.0 48 2(0,0A1) 0001F2 0001F2 -6.3(5.5)x10-4 8.4 82.0 9.6 0.0 0.0 49 2(2,0E ) 0001F2 0001F2 -7.50(88)x10-3 14.8 79.3 5.9 0.0 0.0 50 2(2,0F2) 0001F2 0001F2 -2.731(65)x10-2 13.8 80.1 6.1 0.0 0.0
from covariance matrix
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 18 / 49
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Propagation of information within the polyads
Relative weights of Data from Parameter Value(St.Dev) Dyad Pentad Octad Tetradecad obs ab initio
207 0(0,0A1) 1100 E 1100 E -1.12(28) 0.0 0.0 8.8 38.5 52.7 217 0(0,0A1) 1100 E 0011 E -2.62(73) 0.0 0.0 5.6 41.4 53.0 235 0(0,0A1) 1001F2 1001F2 -10.94(26) 0.0 0.0 26.6 3.6 69.7 243 0(0,0A1) 1001F2 0110F2 7.04(88) 0.0 0.0 15.4 36.9 47.7 254 0(0,0A1) 1001F2 0011F2 -22.41(34) 0.0 0.0 17.5 41.9 39.6 277 0(0,0A1) 0110F1 0110F1 -18.93(15) 0.0 0.0 14.6 58.6 26.8 285 0(0,0A1) 0110F2 0110F2 -24.36(20) 0.0 0.0 15.0 55.1 29.8 293 0(0,0A1) 0110F1 0011F1 13.21(52) 0.0 0.0 20.0 48.5 31.5 307 0(0,0A1) 0110F2 0011F2 23.03(27) 0.0 0.0 11.7 29.6 57.7 347 0(0,0A1) 0011A1 0011A1 -37.20(48) 0.0 0.0 10.1 58.9 31.0 352 0(0,0A1) 0011 E 0011 E -12.03(30) 0.0 0.0 11.5 42.5 46.0 359 0(0,0A1) 0011F1 0011F1 -22.51(30) 0.0 0.0 23.2 40.2 36.6 367 0(0,0A1) 0011F2 0011F2 -11.63(27) 0.0 0.0 18.6 36.9 44.5 460 0(0,0A1) 2000A1 2000A1 -48.82(52) 0.0 0.0 0.0 50.0 50.0
from covariance matrix
from Octad, Tetradecad, [ ] data …… into «Octad» effective parameters
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 19 / 49
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When high-resolution is not possible …
Band profile fitting
Degrading high-resolution experimental spectra !
Variational | ab initio approaches
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« Dual Core »STDS
Frequencies IntensitiesEnergy levels
Global Effective Polyad Hamiltonian
Global Effective Polyad Dipole Moment
High resolution spectra PES / DMS
Line parameter reduction Variational calculationConvolutionHigh resolution (10-4 cm-1) Medium to low resolution / precision (1 to 10 cm-1)
Band profiles
Transition moments
Multi-resolution modeling road map
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« Dual Core »STDS
Frequencies IntensitiesEnergy levels
Global Effective Polyad Hamiltonian
Global Effective Polyad Dipole Moment
High resolution spectra PES / DMS
Line parameter reduction Variational calculationConvolutionHigh resolution (10-4 cm-1) Medium to low resolution / precision (1 to 10 cm-1)
Band profiles
Transition moments
Multi-resolution modeling road map
11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 21 / 49
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Several sets of model parameters
Orders of approximation depending on vibrational and rotational excitation
Exhaustive use of external information @ relevant resolutions
Multi-resolution modeling road map
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« Dual Core »STDS
Frequencies IntensitiesEnergy levels
Global Effective Polyad Hamiltonian
Global Effective Polyad Dipole Moment
High resolution spectra PES / DMS
Band profiles
Transition moments
Multi-resolution modeling road map
Irreducible tensor formExplicite contact transformation
Promissing works about XY3 pyramidal molecules (Tyuterev et al Reims)
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Multi-resolution investigations
How to provide rigorous estimates of the precision of spectrum predictions ?
Propagation of line parameter uncertaintiesinto absorption coefficient uncertainty
Statistical simulations + Analytical modeling
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Absorption coefficient
@ resolution
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Methane R(3) 3 region – High temperature
3057.6 3057.8 3058.0 3058.2 3058.4 3058.6 3058.80.0
0.1
0.2
0.3
: 0.200S : 50%
: 0.010S : 10%
: 0.001S : 3%
Trot : 296 K | Tvib : 2000 KIntensity threshold : 0.025
Pentad - GS linesOctad - Dyad lines
Tetradecad - Pentad lines
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Absorption coefficient : Accuracy @ various resolutions ?
Resolution = 0.003 cm-1
Resolution = 0.020 cm-1
Resolution = 0.100 cm-1
?
3057.6 3057.8 3058.0 3058.2 3058.4 3058.6
0.000
0.005
0.010
0.015
0.020
0.025
0.030
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Typical Results
90 % confidence bands @
3 typical resolutions
0.003 ; 0.020 ; 0.100 cm-1
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3057.6 3057.8 3058.0 3058.2 3058.4 3058.6
0.000
0.001
0.002
0.003
0.004
0.005
Wavenumber / cm-1
Ab
sorp
tion
Co
effi
cie
nt /
cm
-1
Absorption coefficient90 % confidence band
@ res = 0.100 cm-1
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3057.6 3057.8 3058.0 3058.2 3058.4 3058.6
0.000
0.002
0.004
0.006
0.008
0.010
Wavenumber / cm-1
Abs
orp
tion
Coe
ffici
ent /
cm
-1
Absorption coefficient90 % confidence band
@ res = 0.020 cm-1
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3057.6 3057.8 3058.0 3058.2 3058.4 3058.6
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035 A
bsor
ptio
n C
oeffi
cien
t / c
m-1
Wavenumber / cm-1
Absorption coefficient90 % confidence band
@ res = 0.003 cm-1
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Procedure
Relationship between absorption coefficient and line parameters highly non-linear !
Numerical statistical simulationsPseudo random generator
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Procedure
Normal random variables are associated to line parameters (and numerically simulated)
Statistical properties of the corresponding random function associated to the absorption coefficient are
deduced from the (numerical) analysis of histograms built at each spectral elements of the window
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3058.18 3058.19 3058.20 3058.21 3058.22
0.000
0.002
0.004
0.006
0.008
0.010
Wing
max prob
mean
min
max
Side Center
Wavenumber / cm-1
Abs
orpt
ion
Coe
ffici
ent /
cm
-1
Zoom @ 3058.204 cm-1
Statistical properties
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Procedure
Numerical determination of the confidence intervals
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3058.18 3058.19 3058.20 3058.21 3058.22
0.000
0.002
0.004
0.006
0.008
0.010
Wing
max prob
mean
min
max
Side Center
Wavenumber / cm-1
Abs
orpt
ion
Coe
ffici
ent /
cm
-1
Histogram
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3058.18 3058.19 3058.20 3058.21 3058.22
0.000
0.002
0.004
0.006
0.008
0.010
Wing
max prob
mean
min
max
Side Center
Wavenumber / cm-1
Abs
orpt
ion
Coe
ffici
ent /
cm
-1
Histogram
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3058.18 3058.19 3058.20 3058.21 3058.22
0.000
0.002
0.004
0.006
0.008
0.010
Wing
max prob
mean
min
max
Side Center
Wavenumber / cm-1
Abs
orpt
ion
Coe
ffici
ent /
cm
-1
Histogram
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Confidence band@
different levels
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue
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« Warnings » for astrophysicists and others …
Predicted signal inside confidence bandand baseline outside.
Idem but …baseline inside
Predicted signal outside confidence band
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« Warnings » for astrophysicists and others …
Prediction exploitable without restriction
Exploitable with caution
Exploitable with circumspection !
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Transmission Confidence band
Simulated Exp. Cond.Resolution 0.050 cm-1
Pressure 1 TorrPath length 1 km
Tvib 2000 K ; Trot 296 K
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Summary
Multi-resolution investigations relevant for astrophysical applications
Completeness All sources of information @ relevant resolutions
line by line | band profile | ab initio
ReliabilityConfidence band @ relevant resolutions
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Prospects
Accounting for correlations among predicted line parameters
Line shape uncertainties …
Computer implementation : « expert system »
User input : spectral range | pressure | temperature Output : confidence band @ various resolutions
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Computer implementations
Open access
…
In project
http://hal.archives-ouvertes.fr/JP-CHAMPION
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Connected work
about multi-resolution investigations
Open access…
Partition function
already available
http://hal.archives-ouvertes.fr/JP-CHAMPION
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Acknowledgments
Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB) Dijon (France)
Christian Wenger, Vincent Boudon … Methane
Jet Propulsion Laboratory (JPL) Pasadena (USA)Linda Brown … FTIR spectra
Institut of Atmospheric Optics (IAO) Tomsk (Russia)Andrei Nikitin, Vladimir Tyuterev … MIRS … octad …
Institut de Physique de Rennes (France)Robert Georges … High temperature emission
Niels Bohr Institut Copenhagen (Denmark)Uffe Jørgensen … Brown dwarfs
LEFE-CHAT National Program CNRS (France) ANR : CH4@Titan (France)
GDRI : SAMIA Tomsk (Russia), Hefei (China), CNRS (France)11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 48 / 49
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Thank You for attention
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