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ERROR PROPAGATION FROM LINE PARAMETERS TO SPECTRA SIMULATIONS

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.

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ERROR PROPAGATION FROM LINE PARAMETERS TO SPECTRA SIMULATIONS

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  1. 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 16-18 June 2010 1 / 49

  2. 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

  3. Methane at high-temperature A typical illustration 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 3 / 49

  4. STDS prediction - extrapolation 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 4 / 49

  5. 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

  6. What to do with the 126 inacurrate hot lines ? 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 6 / 49

  7. Simply ignore inaccurate lines ! 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 7 / 49

  8. Low-resolution information Useful ? 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 8 / 49

  9. 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

  10. 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

  11. Titan | Cassini - Huygens 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 11 / 49

  12. Huygens DISR data 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 12 / 49

  13. High temperature 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 13 / 49

  14. Methane polyads and rovibrational energy levels 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 14 / 49

  15. 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 16-18 June 2010 15 / 49

  16. 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 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 16 / 49

  17. Propagation of information within the polyads Influence of various «ab initio» results Significant discrepancies @ low resolution - 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) 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 17 / 49

  18. 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

  19. Propagation of information within the polyads from Octad, Tetradecad, [ ] data … … into «Octad» effective parameters 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 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 19 / 49

  20. 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 16-18 June 2010 20 / 49

  21. Multi-resolution modeling road map High resolution spectra PES / DMS Line parameter reduction Convolution Variational calculation High resolution (10-4 cm-1) Medium to low resolution / precision (1 to 10 cm-1) Band profiles Energy levels Transition moments Frequencies Intensities Global Effective Polyad Hamiltonian « Dual Core » STDS Global Effective Polyad Dipole Moment 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 21 / 49

  22. Multi-resolution modeling road map High resolution spectra PES / DMS Line parameter reduction Convolution Variational calculation High resolution (10-4 cm-1) Medium to low resolution / precision (1 to 10 cm-1) Band profiles Energy levels Transition moments Frequencies Intensities Global Effective Polyad Hamiltonian « Dual Core » STDS Global Effective Polyad Dipole Moment 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 21 / 49

  23. Multi-resolution modeling road map • Several sets of model parameters • Orders of approximation depending on vibrational and rotational excitation • Exhaustive use of external information @ relevant resolutions 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 22 / 49

  24. Multi-resolution modeling road map High resolution spectra PES / DMS Irreducible tensor form Explicite contact transformation Band profiles Energy levels Transition moments Frequencies Intensities Global Effective Polyad Hamiltonian « Dual Core » STDS Global Effective Polyad Dipole Moment Promissing works about XY3 pyramidal molecules (Tyuterev et al Reims) 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 23 / 49

  25. 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 16-18 June 2010 24 / 49

  26. Absorption coefficient @ resolutionD 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 25 / 49

  27. Methane R(3) n3 region – High temperature 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 26 / 49

  28. Absorption coefficient : Accuracy @ various resolutions ? Resolution = 0.003 cm-1 Resolution = 0.020 cm-1 Resolution = 0.100 cm-1 ? 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 27 / 49

  29. Typical Results 90 % confidence bands @ 3 typical resolutions 0.003 ; 0.020 ; 0.100 cm-1 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 28 / 49

  30. Absorption coefficient 90 % confidence band @ res = 0.100 cm-1 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 29 / 49

  31. Absorption coefficient 90 % confidence band @ res = 0.020 cm-1 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 30 / 49

  32. Absorption coefficient 90 % confidence band @ res = 0.003 cm-1 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 31 / 49

  33. 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 16-18 June 2010 32 / 49

  34. 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 16-18 June 2010 33 / 49

  35. Statistical properties Zoom @ 3058.204 cm-1 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 34 / 49

  36. Procedure • Numerical determination of the confidence intervals 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 35 / 49

  37. Histogram 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 36 / 49

  38. Histogram 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 37 / 49

  39. Histogram 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 38 / 49

  40. Confidence band @ different levels 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 39 / 49

  41. Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 40 / 49

  42. Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 40 / 49

  43. Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 40 / 49

  44. Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 40 / 49

  45. Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 40 / 49

  46. Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 40 / 49

  47. Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 40 / 49

  48. Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 40 / 49

  49. Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 40 / 49

  50. Predicted signal in black 90% Confidence Band : Sup in red & Inf in blue 11th HITRAN Conference Harvard-Smithsonian Center forAstrophysics Cambridge 16-18 June 2010 40 / 49

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