ERROR PROPAGATION FROM LINE PARAMETERS TO SPECTRA SIMULATIONS Illustration on High Temperature Methane. Jean Paul Champion & Christian Wenger Laboratoire Interdisciplinaire Carnot de Bourgogne UMR 5209 CNRS - Université de Bourgogne Dijon - France 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
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 June / 49
Methane at high-temperature A typical illustration 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
STDS prediction - extrapolation 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Hot methane statistics ( cm -1 ) STDS T vib = 2000 K | T rot = 296 K 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
What to do with the 126 inacurrate hot lines ? 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Simply ignore inaccurate lines ! 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Low-resolution information Useful ? 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
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 June / 49
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 June / 49
Titan | Cassini - Huygens 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Huygens DISR data 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
High temperature 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Methane polyads and rovibrational energy levels 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Starting point : Position and Intensity predictions with 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 June / 49
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 P1-P calc energies (order 6) P2-P0 1.0 O.6 calc energies (order 6) P3-P calc energies (order 4) P4-P «observed» band centers P4-P «ab initio» predictions cm Data fitted : Weighted Standard Deviation th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Propagation of information within the polyads Influence of various «ab initio» results - 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 low resolution 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
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 (72) (0,0A1) 0100E 0100E -6.79(84)x (2,0E ) 0100E 0100E (76)x (1,0F1) 0100E 0001F (42) (2,0F2) 0100E 0001F (87)x (0,0A1) 0001F2 0001F (57) (1,0F1) 0001F2 0001F (83) (0,0A1) 0001F2 0001F2 -6.3(5.5)x (2,0E ) 0001F2 0001F (88)x (2,0F2) 0001F2 0001F (65)x from covariance matrix 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
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) (0,0A1) 1100 E 0011 E -2.62(73) (0,0A1) 1001F2 1001F (26) (0,0A1) 1001F2 0110F2 7.04(88) (0,0A1) 1001F2 0011F (34) (0,0A1) 0110F1 0110F (15) (0,0A1) 0110F2 0110F (20) (0,0A1) 0110F1 0011F (52) (0,0A1) 0110F2 0011F (27) (0,0A1) 0011A1 0011A (48) (0,0A1) 0011 E 0011 E (30) (0,0A1) 0011F1 0011F (30) (0,0A1) 0011F2 0011F (27) (0,0A1) 2000A1 2000A (52) from covariance matrix from Octad, Tetradecad, [ ] data … … into «Octad» effective parameters 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
When high-resolution is not possible … Band profile fitting Degrading high-resolution experimental spectra ! Variational | ab initio approaches 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
« Dual Core » STDS FrequenciesIntensities Energy levels Global Effective Polyad Hamiltonian Global Effective Polyad Dipole Moment High resolution spectraPES / DMS Line parameter reductionVariational calculationConvolution High 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 June / 49
« Dual Core » STDS FrequenciesIntensities Energy levels Global Effective Polyad Hamiltonian Global Effective Polyad Dipole Moment High resolution spectraPES / DMS Line parameter reductionVariational calculationConvolution High 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 June / 49
Several sets of model parameters Orders of approximation depending on vibrational and rotational excitation Exhaustive use of external relevant resolutions Multi-resolution modeling road map 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
« Dual Core » STDS FrequenciesIntensities Energy levels Global Effective Polyad Hamiltonian Global Effective Polyad Dipole Moment High resolution spectraPES / DMS Band profiles Transition moments Multi-resolution modeling road map Irreducible tensor form Explicite contact transformation Promissing works about XY 3 pyramidal molecules (Tyuterev et al Reims) 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Multi-resolution investigations How to provide rigorous estimates of the precision of spectrum predictions ? Propagation of line parameter uncertainties into absorption coefficient uncertainty Statistical simulations + Analytical modeling 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Absorption resolution 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Methane R(3) 3 region – High temperature 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Absorption coefficient : various resolutions ? Resolution = cm -1 Resolution = cm -1 Resolution = cm -1 ? 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Typical Results 90 % confidence 3 typical resolutions ; ; cm -1 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Absorption coefficient 90 % confidence res = cm -1 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Absorption coefficient 90 % confidence res = cm -1 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Absorption coefficient 90 % confidence res = cm -1 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Procedure Relationship between absorption coefficient and line parameters highly non-linear ! Numerical statistical simulations Pseudo random generator 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
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 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
cm -1 Statistical properties 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Procedure Numerical determination of the confidence intervals 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Histogram 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Histogram 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Histogram 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Confidence different levels 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
« Warnings » for astrophysicists and others … Predicted signal inside confidence band and baseline outside. Idem but … baseline inside Predicted signal outside confidence band 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
« Warnings » for astrophysicists and others … Prediction exploitable without restriction Exploitable with caution Exploitable with circumspection ! 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Transmission Confidence band Simulated Exp. Cond. Resolution cm -1 Pressure 1 Torr Path length 1 km T vib 2000 K ; T rot 296 K 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Summary Multi-resolution investigations relevant for astrophysical applications Completeness All sources of relevant resolutions line by line | band profile | ab initio Reliability Confidence relevant resolutions 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Prospects Accounting for correlations among predicted line parameters Line shape uncertainties … Computer implementation : « expert system » User input : spectral range | pressure | temperature Output : confidence various resolutions 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Computer implementations Open access … In project 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Connected work about multi-resolution investigations Open access … Partition function already available 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
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 J ø rgensen … Brown dwarfs LEFE-CHAT National Program CNRS (France) ANR : (France) GDRI : SAMIA Tomsk (Russia), Hefei (China), CNRS (France) 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49
Thank You for attention 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge June / 49