Line shape modeling and application to remote sensing

Transcription

1 Line shape modeling and application to remote sensing Dr. Ha Tran Senior Researcher at CNRS, Paris, France Laboratoire de Météorologie Dynamique Sorbonne Université, Ecole Polytechnique, Ecole Normale Supérieure de Paris

2 Dr. Ha TRAN Laboratoire de Météorologie Dynamique, CNRS, Sorbonne Université, Ecole Polytechnique, Ecole Normale Supérieure de Paris 4 Place Jussieu, Paris Cedex, France ha.tran@lmd.jussieu.fr Tel: 33 (0) Research interests Molecular Spectroscopy; Diode laser and FTS spectroscopy; Spectra modelling; Intermolecular Collisions and impact on the line shape; Molecular Dynamic Simulations Atmospheric spectra analysis; Green House Gases Remote Sensing Education and Professional Experience 2013 Habilitation thesis, senior researcher at National Center for Scientific Research (CNRS) Since 2007 Researcher at CNRS Postdoctoral research associate, Laboratoire de Physique Moléculaire et Application, Pierre and Marie Curie University Postdoctoral research associate, Laboratoire Interuniversitaire des Systèmes Atmosphériques, Université Paris Ph. D. Thesis, Université de Franche-Comté 2001 Master of Science in Physics, Université de Franche-Comté 2000 Bachelor of Science in Physics, Hanoi National University of Education 2

3 Outline Introduction: Atmospheric observation and spectral shape The Doppler, Lorentz and Voigt profiles The limits of the Voigt profile Widely-used non-voigt approaches A new line-shape model for spectroscopic databases and applications Line-mixing for closely spaced lines Conclusions 3

4 Introduction: atmospheric retrieval Measured spectra (satellite, balloon, ground, ) Radiative transfer Forward model Input spectroscopic data (Position, Intensity, spectral shape, ) - P, T profiles - Molecule mole fraction profiles - Cloud altitude, aerosol - etc. Spectral shapes Collisional (pressure) effects on the spectral shape 4

5 Introduction: Atmospheric observations - In situ measurements, generally using lasers. On ground, balloons, air planes Sounding a short (single T,P,vmr) path - Remote measurements, generally using Fourier Transform (FT) spectrometers ; ground, balloons, air planes, satellites Collecting the atmospheric emission or transmitted solar radiation (many T, P, vmr) Nadir Ground based Limb 5

6 6 6

7 Atmospheric observations example Emission Tangent height 36 km Tangent height 17 km Tangent height 12 km (cm -1 ) Atmospheric emissions by a CO 2 Q-branch as observed by the balloon-borne Smithsonian Astrophysical Observatory FT Experiment for various tangent altitudes 7

8 Atmospheric observations example IMG: Interferometric Monitor for Greenhouse gases IMG observation April 4, 1997, South Pacific 1.0 transmittance H2O CO2 O3 N2O CH4 CO HCFC-22 CFC-11 CFC-12 HNO3 NO2 NO OCS wavenumber (cm -1 ) 8

9 Absorption coefficient Gas sample Cell of base length L, I 0 (): input intensity I(): transmitted intensity dx Let s consider a small volume of thickness dx. I(,x): Light intensity at the entrance of this volume di(,x): its change due to absorption by the sample in this this volume. This change is: - negative - proportional to dx - proportional to the incident intensity I(,x) di(, x) (, x) I(, x) dx (cm -1 ) is the absorption coefficient 9

10 Absorption coefficient Homogeneous medium: absorption coefficient is independent of x t 0 L I I e Beer-Lambert s law () depends on the wavenumber since an absorption line (transition) is never strictly monochromatic Relative wavenumber (cm -1 ) 10

11 Absorption coefficient When line is isolated, its intensity is redistributed over a spectral range around the resonance wavenumber fi S I fi fi fi fi S fi is the integrated line intensity fi fi fi fi fi S d d I fi is the normalized line shape Relative wavenumber (cm -1 ) fi fi d I d I 1 11

12 Doppler broadening A molecule having a speed v#0, absorbs or emits at a wavenumber, which is different of 0 of this molecule at v=0. The corresponding Doppler shift is: = fi (1±v z /c) where v z the radiator velocity component along the wave propagation vector. The velocity distribution (1 dimension) is given by 12

13 Doppler broadening I 0 I 1/2 D fi D 13

14 Doppler broadening ln2 1 ID exp ln 2 fi fi D D 1 2 2k BT where D ln 2 2 mc fi 2 is the HWHM of the line. Determine the Determine the 14

15 The Lorentz broadening and shifting For an isolated transition, the main effects of intermolecular collisions (pressure) are the broadening and shifting of the line E upper E L ow er Absorption E ne rg y (H 0 + V ) 0 fi L L tim e wavenumber When a molecule A is in collision with another molecule, its lower and upper energy levels (E lower, E upper ) will be modified due to collision. This modification depends on the distance and the relative orientation between the two molecules. The life time of the molecule on its energy levels is thus modified. Therefore, this leads to a broadening of the line. In general, the modification of E lower is different of that of E upper, this difference thus leads to a line shifting. The profile is a Lorentz function 1 I ( ) L L fi 2 2 fi L L L is the HWHM L is the line shift 15

16 The Lorentz broadening and shifting Absorption 3, R(1) line of CH 4 -N atm 0.24 atm L (HWHM) and L (shift) proportional to the # of coll (dens or P) In spectroscopy, we also use the pressurenormalized width and shift: L L /P and L L /P wavenumber line broadening and line shifting coefficients show that the Lorentz profile is normalized to 1 What is the main broadening mechanism for a transition of CO 2, located at 6000 cm -1 at room temperature (25 C) and 1000 mbar giving that its Lorentz broadening coefficient is 0.05 cm -1 /atm 16

17 The Lorentz broadening and shifting: The case of a mixture The active molecule The collision-partner A B L = A-A P A + A-B P B A-A : self-broadening coefficient A-B : broadening coefficient due to collision with molecules B In the atmosphere, the two main perturbators are N 2 and O 2. However, sometimes we need to consider also self-broadening: for H 2 O for instance, its partial pressure is relatively small with respect to that of N 2 and O 2 but its collision efficiency is about 5 times larger than that of N 2 and O 2. For a species A in the atmosphere, one can write: L = A-N2 P N2 + A-O2 P O2 + P N2 = P P O2 = P L = A-air P P Ar = P 17

18 The Lorentz broadening and shifting: Temperature dependence For the Earth atmosphere, we need to know also the temperature dependence of the broadening coefficients. This temperature dependence is usually given by with T ref = 296 K and n the temperature exponent of the broadening coefficient, n depends on the active molecule and on the collision-partner as well as on the considered line. A-air and n are given in (atmospheric) spectroscopic databases such as HITRAN, GEISA Application: Calculate the Lorentz HWHM, L of a water vapor transition which has L,H2O-N2 (296 K) = cm -1 /atm, L,H2O-O2 (296 K) = cm -1 /atm, n=0.64 for the following atmospheric conditions: 1. At an altitude of 24 km of Polar Arctic Winter: T=300K, P=0.02 atm 2. At the surface: T = 300K, P=1 atm 18

19 The Voigt profile When the pressure increases from the pure Doppler regime (zero pressure) to the pure collisional regime (Doppler effect negligible) : -There is an intermediate regime in which collisions will change the molecule velocities which will thus change the Doppler effect. In the same time, these collisions will also modify the internal state of the line and then broaden the line -In this intermediate regime, the Doppler effect is not completely vanished and collisional broadenings occur. These two effects thus have to be taken into account The Voigt profile 19

20 The Voigt profile Let s consider a speed class: [(v z ) (v z +dv z )] the corresponding spectral domain is [( ) ( +d )], with = 0 (1+v z /c) Due to collisions, the spectral intensity I D ( - fi )d is redistributed as a Lorentz profile centered at. The final contribution of this speed class at is thus: I D ( - fi ) d I L (- ) The resulting profile is then obtained by summing over all speed classes (or all ) : I ( ) d ' I ' I ' V fi D fi L The Voigt profile is thus a convolution of a Gaussian profile (Doppler effect) and a Lorentzian profile (collisional effect). 20

21 The Voigt profile The Voigt profile with : and ln2 1 ID exp ln 2 fi fi D D 1 I ( ) L L fi 2 2 fi L I ( ) d 'I ' I ' V fi D fi L 2 Using fi x ln 2 D y ln 2 L D We have : 1 ln 2 I ( ) K x, y V fi D with K the error function t y e K(x, y) dt y (x t)

22 The Voigt profile Application: - Determine the Doppler and Lorentz broadenings for the H 2 O transition considered above (position = cm -1 ). Compare the two broadenings and conclude about the type of line profile which should be used for the two situations (polar stratosphere and tropical troposphere) 22

23 The Doppler, Lorentzian and Voigt profiles Pressure Usual behavior of an absorption line width Lorentzian Doppler+Collision Doppler 23

24 The Gaussian, Lorentzian and Voigt profiles G au ssian V oig t Lo re n tz D = 0.01 cm -1 L = cm -1 FTS ground-based absorption spectrum (CO 2 ) Normalized profile (a.u.) transmission W aven u m b er (cm -1 ) Comparaison between the Doppler, Lorentz and Voigt profiles nombre d'onde (cm-1) 24

25 The Gaussian, Lorentzian and Voigt profiles Application: Absorption spectra of a CO line at room temperature and three pressures 25 25

26 The Gaussian, Lorentzian and Voigt profiles Application: Absorption spectra of a CO line at room temperature and three pressures - Determine the Doppler broadening - Use the executable to fit these spectra using the Voigt profile In this fitting code the following parameters are adjusted: 1.The position of the maximum absorption 2.The half-width at half-maximum of the line 3.The area of the line 4.Two parameters describing a linear base line - Compare the Lorentz and Doppler half width for each spectrum - From the adjusted parameters, calculate the line position, line broadening coefficient and line shifting coefficient 26

27 Non-Voigt effects on the line-shape 27

28 Limits of the Voigt profile 100x(observed-adjusted) Absorption Torr 250 Torr 200 Torr 150 Torr 100 Torr 50 Torr Coefficient d'élargissement (cm -1 /atm) H 2 O/N 2, 3 band, 11 1, , , , Relative wave number (cm-1) Measured and adjusted spectra using the Voigt profile. Ngo et al, JQSRT, Pression (atm) 28

29 Limits of the Voigt profile The Voigt profile neglects: 29 29

30 Limits of the Voigt profile: atmospheric retrieval In situ absorption spectrum of tropospheric H 2 O recorded by balloonborne diode laser and its fit using the Voigt profile Durry et al, JQSRT 94, 387,

31 Limits of the Voigt profile: Influence on atmospheric retrievals HF profile retrieved from ground-based absorption FTIR measurements (Jungfraujoch station) in the (1-0) R(1) micro-window by using the Voigt profile and the Soft Collision model, compared with the HALOE (Halogen Occultation Experiment) profiles smoothed. Barret et al, JQSRT 95, 499,

32 Widely used non-voigt approaches 32

33 Simple non-voigt approaches: the velocity changes effect The Galatry (soft collisions, SC) profile: - Assumes that radiators undergo only a very small changes per collision - Introduces a velocity changing rate The Nelkin-Ghatak (hard collisions, HC) profile: - Assumes that velocity memory is lost after each collision - Introduces a velocity changing rate VC also related to the diffusion coefficient Experiences show that the Galatry profile and the Nelkin-Ghatak profile lead to similar quality in term of residual fit of measured spectra 33 33

34 Simple non-voigt approaches: the velocity changes effect Application: Absorption spectra of a CO line at room temperature and three pressures 34 34

35 Simple non-voigt approaches: the velocity changes effect Application: Absorption spectra of a CO line at room temperature and three pressures -Use the executable to fit the two first spectra using the Hard Collision profile In this fitting code the following parameters are adjusted: 1.The position of the maximum absorption 2.The half-width at half-maximum of the line 3.The velocity changing rate (the Dicke narrowing parameter VC =/P) 4.The area of the line 5.Two parameters describing a linear base line -From the adjusted parameters, determine the line position, line broadening, line shifting coefficients and the Dicke narrowing parameters -Compare the fit residuals obtained with the HC and the Voigt profiles, compare the obtained parameters in the two cases 35

36 Simple non-voigt approaches: the velocity changes effect Claveau et al, JQSRT 68, 273,

37 Velocity changes effects: Remaining problems Bui et al, J. Chem. Phys., 141, , 2014 Pressure dependence of the frequency optical collisions obtained for the R(24) line of CO 2 in air from the NGP, GP and single-spectrum fits. The green line is the frequency of optical collisions calculated from the mass diffusion coefficient The collisional narrowing parameter is non linear with pressure 37

38 Velocity changes effects: Remaining problems band of H 2 O in N 2 : multi-spectrum fitting technique 99, 197, 294, 398, 499, 600, 797, 1000, 1200 hpa Lisak et al, JQSRT, 2015, accepted Only Dicke narrowing is insufficient 38

39 Simple non-voigt approaches: the speed dependences - The polynomial dependence of Berman-Pickett (v ) v r p r (v ) (v ). f (v v )dv a r r a r - The quadratic dependence of Rohart (v ) [(v / v) 3/ 2] with (v ) 2 a 0 2 a 0 a v a m active > > m buffer m active << m buffer Weak speed dependence v a < < v r # v b (v a ) # Cte a b Strong speed dependence v a # v r > > v b (v a ) # (v r ) b a Courtesy of F. Rohart 39

40 Simple non-voigt approaches: the speed dependences 707<-606 and 717<-616 lines (at 0,83nm) of pure H 2 O (left) and H 2 O/air (right) Ngo et al, JQSRT, 113, 870,

41 Speed dependent Voigt profile: Remaining problems R(9) line of the fundamental band of HCl perturbed by Ar Speed dependence only is not sufficient 41

42 Toward a new model: both speed dependences and Dicke narrowing Lisak et al, JQSRT,

43 Non-isolated transitions: Line-mixing effects 43

44 Line-mixing effects CH 4 /N 2,R(6) manifold, P=900.5 hpa, T=296 K 1.0 Transmission A21 A11 In some cases, for closely spaced lines, the Voigt profile fails when P increases. It predicts shapes that are too broad. 0.0 F21 E1 F11 F E 2 Wavenumber (cm -1 ) E E 1 Collisions induce transfers of populations between the levels of the two lines that lead to transfers of intensity between the lines. E E 2 E 1 44

45 Line-mixing and remote sensing: Monitoring GreenHouse Gases from space Nadir looking instruments onboard satellites Greenhouse gases Observation SATellite (GOSAT, JAXA-NIES, in orbit) Orbiting Carbon Observatory (OCO 2, NASA, in orbit) MicroCarb (CNES, under study), CarbonSat (ESA, under study) Spectral regions and aims - CO 2 from 1.6 m (weak) and 2.1 m (strong) bands - Air mass from O 2 A band (0.76 m) - CH 4 from 2 3 band (near 1.7 m) - aerosols from CO 2 and O 2 bands Detection/quantifying sinks and sources (1 ppm for x CO2, 0.3 %) Extreme accuracy of spectra modelling. Huge constraints on the spectroscopic data and the prediction of pressure effects (collisions and spectral-shape) 45

46 CO 2 : ground-based measurements Wrong air-mass (and time) dependences Sza 79.9, Park Falls, region 2.1 m O bserved Fitted Residuals Total CO2/total air (ppm) Tim e Transmission wavenum ber (cm -1 ) 1,0 0,8 Sza 79.9, Park Falls, region 1.6 m CO 2 retrieved 0,6 0,4 0,2 0, wavenumber Total CO2/total air (ppm) Time 46

47 O 2 : Ground-based measurements Sza 79.9, Park Falls, A band Wrong time (and air-mass) dependences Transmission 1.0 Observed Fitted Residuals Total O2/total air 0,222 0,221 0,220 0,219 0,218 0,217 0,216 0,215 0,214 0, ,222 0,221 0,220 0, wavenumber (cm -1 ) 0,212 0, time 1,0 0,8 Sza 79.9, Park Falls, 1.27 m band Total O2/total air 0,218 0,217 0,216 0,215 0,214 0,213 0,212 transmission 0,6 0,4 0,2 0,0 0, time wavenumber 47

48 Line-mixing effects: Laboratory studies CO 2 /N 2 O 2 /N 2 A band measurement, Line-mixing Lorentz Abs. Coef (10-2 cm -1 ) atm 47.6 atm 28.1 atm (cm -1 ) D T ot =106 amagats T = 194K (cm -1 ) 48

49 Influence on retrievals: O 2 ground-based measurements Spectra: Sza 79.9, Park Falls O 2 A band region O 2 A band: Relative errors on surface pressures retrieved from atmospheric spectra Transmission Residual observed-voigt observed-(lm+cia) wavenumber (cm -1 ) Total O2/total air micron O2 band O2 A band no LM no CIA O2 A band LM and CIA UT (hour) 49

50 Influence on retrievals: CO 2 ground-based measurements Transmission Residuals observed-voigt observed-lm Fits of a ground based transmission spectra in the region of the band of CO wavenumber (cm -1 ) m band, no LM 2.1 m band, with LM 1.6 m band Significant errors (10%) on the CO 2 atmospheric amount. Sinks and sources!!! Total CO2/total air (ppm) UT (hour) 50

51 Spectroscopy for MERLIN: 0.2% accuracy required! Voigt Profile Accuracy: About 1-2% 51

52 Spectroscopy for MERLIN: 0,2% accuracy required! Speed dependence + Dicke narrowing + Line-Mixing 0,1-0,2% around λ on Delahaye et al,