Collisional effects on spectral shapes
and remote sensing
H. Tran
LISA, CNRS UMR 7583,
Université Paris-Est Créteil and Université Paris Diderot
1
HiResMIR@CAES-Frejus-2013
Outline
• Introduction: Atmospheric observation and spectral shape
• Isolated line :
- The Doppler, Lorentzian and Voigt profiles
- Limits of the Voigt profile
- Laboratory studies
- Influence on atmospheric retrieval
• Line-mixing for closely spaced lines
- Line-mixing effects
- Laboratory studies
- Influence on spectroscopic data extraction
- Influence on atmospheric retrieval
• Conclusions
2
HiResMIR@CAES-Frejus-2013
Introduction: Atmospheric retrievals
Measured spectra (satellite, balloon, ground,…)
Input spectroscopic data
(Position, Intensity, spectral shape,…)
Radiative transfer
Forward model
- P, T profiles
- Molecule mole fraction profiles
- Cloud altitude, aerosol
- etc. …
Spectral shapes  Collisional (pressure) effects on the spectral shape
3
HiResMIR@CAES-Frejus-2013
Introduction: The Voigt profile
Gaussien
Doppler
Voigt
Lorentzian
Doppler+Collision Collisions
Pressure
Comparaison between the Gaussian, the
Lorentz and the Voigt profiles.
4
HiResMIR@CAES-Frejus-2013
Introduction: isolated lines and closely spaced lines
ACE spectra at different tangent altitudes
n3 R(9)
(1-0) R(0)
Bernath et al., GRL, 32, L15S01 (2005)
HiResMIR@CAES-Frejus-2013
5
Isolated lines
6
HiResMIR@CAES-Frejus-2013
Limits of the Voigt profile
H2O/N2, n3 band,
111,11101,10 110,11 100,10
0.30
300 Torr
250 Torr
200 Torr
150 Torr
100 Torr
50 Torr
0.15
1.0
-1
0.20
Coefficient d'élargissement (cm /atm)
Absorption
0.25
0.10
0.05
100x(observed-adjusted)
0.00
0.4
0.0
0.9
0.8
0.7
-0.4
0.6
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.0
Relative wave number (cm-1)
0.2
0.4
0.6
0.8
1.0
1.2
Pression (atm)
Measured and adjusted spectra using the Voigt profile.
7
HiResMIR@CAES-Frejus-2013
Limits of the Voigt profile
It neglects:
1. The velocity changes induced by collisions.
 




The detailed balance: f (v  v ' )  f MB (v )  f (v '  v )  f MB (v ' )
 change from v to v’ < v is more probable than that from v to v’ > v.
 reduction of the Doppler broadening  Dicke narrowing effect
2. The speed-dependences of the collisional width G(v) and shift D(v) of the
line.
This also (in general) leads to a narrowed line
8
HiResMIR@CAES-Frejus-2013
Simple and widely used non-Voigt approaches
- For the velocity changes effect: The Galatry (soft collisions) and Rautian (hard
collisions) line-shapes. Introducing a parameter nVC
(or b) - the velocity changing collisions frequency.
- For the speed dependences of the line-width and shift: The speed-dependent
Voigt profile, assuming a simple quadratic dependence on the absolute speed or
polynomial dependence on the relative speed
G(v)  G0  G2[(v / v)2  3/ 2] or G(vr )  A vr p
9
HiResMIR@CAES-Frejus-2013
Influence of non-Voigt effects on atmospheric retrievals
In situ absorption spectrum of tropospheric H2O recorded by balloonborne diode laser
and its fits using the Voit profile and the Hard Collision profile
Durry et al, JQSRT 94, 387,2005
10
HiResMIR@CAES-Frejus-2013
Influence of non-Voigt effects 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 profiles smoothed.
11
Barret et al, JQSRT 95, 499, 2005
HiResMIR@CAES-Frejus-2013
Influence of non-Voigt effects on line parameters determination
(Diode laser) Measured absorption of pure H2O (left) and H2O in air (right) and their
differences with those adjusted using the VP, HC, and SDVP
HC
HC
12
HiResMIR@CAES-Frejus-2013
Influence of non-Voigt effect on line parameters
Ratios of the self-broadening coefficients and intensity obtained by the HC (o) and SDVP
() to those obtained by the VP, for 13 H2O lines in the near-infrared.
13
HiResMIR@CAES-Frejus-2013
Remaining problems with these non-Voigt approaches
Dependence of nVC on pressure
Relaxation of the 317.2 GHz line of O3 in collision with O2 at 240 K.
nVC rate in red (SC)
Rohart et al, J Mol Spectrosc 251, 282, 2008
 Need to take into account both Dicke and speed dependence effects
HiResMIR@CAES-Frejus-2013
14
Velocity changing by the Keilson and Storer model
 

 
v
'v
2 3 / 2

f KS (v  v ' )  n VC  (1   )  f MB 
2
 1





: memory parameter
2 limits
 0 
 

f (v  v ' )  n VC f MB (v ' )
Hard collision model
 1 
 
 
f (v  v ' )  n VC (v , v ' )
Soft collision model
 KS more realistic than these two extreme cases and more suitable for intermediate cases
15
HiResMIR@CAES-Frejus-2013
Model-experiment comparison : pure H2O
With the model we compute the line shape. Then we fit the calculated spectra (as the
measured ones) by Voigt profiles and look at the residuals.
Pure H2O, 296K, 2n1+n2+n3 band:  measured,  calculated
0.4
0.1
0.2
0.0
0.0
-0.2
100 x residuals
-0.1 6 Torr
0.2 -0.4
0.2
0.0
0.0
-0.2 0.6
0.2
-0.4
0.0
-0.3
-0.2 10.1 Torr
0.4 -0.6
9 Torr
0.8
0.2
0.4
0.0
0.0
-0.2
12.3 Torr
-0.4 1.0
0.2
-0.4
12.1 Torr
-0.8
0.5
0.0
0.0
-0.2
-0.5
-0.4
-0.2
7 Torr
0.3
0.0
0.4
0.4
0.1
-0.1
8 Torr
6 Torr
14.1 Torr
-0.08
-1.0
-0.04
0.00
0.04
0.08
15.2 Torr
-0.08
-0.04
0.00
0.04
0.08
-1
606707
Relative wavenumber (cm )
HiResMIR@CAES-Frejus-2013
515414
16
Model-experiment comparison: H2O/air
H2O/N2, 296K, n3,
1111110110 , 1101110010 doublet
H2O/air, 296K, 2n1+n2+n3,
515414 line
Peak normalized absorption
 measured,  calculated
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
4
0.0
1
2
0
Peak absorption normalized residual (%)
0
-2
0.098 atm
-4
4
-1
0.132 atm
1
2
0
0
-2
0.197 atm
-4
4
-1
0.264 atm
1
2
0
0
-2
0.395 atm
-4
4
-1
0.526 atm
1
2
0
0
-2
0.592 atm
-4
-0.06
-0.03
0.00
0.03
0.06
-1
0.990 atm
-0.2
-0 (cm
-0.1
0.0
0.1
0.2
-1
)
HiResMIR@CAES-Frejus-2013
17
Model-experiment comparison: H2/N2
50
Collisional width
296 K, Q(1)
m = 0.92, 0 = 0.41
30
20
10
120
995 K, Q(1)
0
0
2
4
6
8
10
100
densité (amagat)
Gobs (10-3cm-1)
Gobs (10-3 cm-1)
40
m = 0.95, 0 = 0.50
80
60
40
20
0
Bonamy et al., Eur. Phys. J. D, 2004
0
2
4
6
densité (amagat)
HiResMIR@CAES-Frejus-2013
8
10
18
Non-isolated transitions: Line-mixing effects
19
HiResMIR@CAES-Frejus-2013
Line-mixing effects
CH4/N2,R(6) manifold, P=900.5 hPa, T=296 K
1.0
Transmission
0.8
0.6
In some cases, for closely spaced lines, the
Voigt profile fails when P increases. It predicts
shapes that are too broad.
0.4
0.2
A21
A11
F11
F21 F22
E1
0.0
E2
-0.2
6076.6
6076.8
6077.0
6077.2
6077.4
DE 
-1
Wavenumber (cm )
E1
Collisions induce transfers of populations
between the levels of the two lines that
lead to transfers of intensity between the
lines.
E2
DE 
E1
20
HiResMIR@CAES-Frejus-2013
Line-mixing effects: Absorption coefficient
α LM σ  

 ρ  d  d k k
 Σ  L 0  iPW 1

line  line k
rk
dk
, L0
W
populations
matrix element of radiation-matter coupling tensor
matrix of positions
relaxation operator. All effects of collisions. Independent of  within
the impact approximation (not too far in the wings)
Wlk0  Line coupling between |k> and |l>
Wlk=0  No line coupling (Lorentz)

Lo
   
k

k
1
rk d  
 
2
2
    k   k    k  
2
k
21
HiResMIR@CAES-Frejus-2013
Line-mixing effects: Relaxation matrix
Relations for W
k W k  G  iD
k
k
Det. Balance: r k W l  r l W k
k
l
Sum rule:

lines l
l W k 0
d
l
For moderate line overlapping, a first order perturbation approach is possible. Then we
only need to know one coupling parameter (Y, related to the W matrix elements) per
line
d  W k
 k d k σ k  σ 
Yk  2
22
HiResMIR@CAES-Frejus-2013
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)
MicroCarb (CNES, under study), CarbonSat
(ESA, under study)
Spectral regions and aims
- CO2 from 1.6 mm (weak) and 2.1 mm (strong) bands
- Air mass from O2 A band (0.76 mm)
- CH4 from 2n3 band (near 1.7 mm)
- aerosols from CO2 and O2 bands
Detection/quantifying sinks and sources (1 ppm for xCO2, 0.3 %)
→ Extreme accuracy of spectra modelling. Huge constraints on the spectroscopic data and
the prediction of pressure effects (collisions and spectral-shape)
23
HiResMIR@CAES-Frejus-2013
CO2: ground-based measurements
Sza 79.9°, Park Falls, region 2.1 mm
Wrong air-mass (and time) dependences
400
1.0
398
Observed
Fitted
Residuals
396
0.8
392
390
0.6
388
Transmission
Total CO2/total air (ppm)
394
386
384
382
0.4
380
0.2
378
376
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
0.0
Time
4820
Sza 79.9°, Park Falls, region 1.6 mm
4840
-1
4880
CO2 retrieved
400
1,0
4860
wavenumber (cm )
398
396
0,8
Total CO2/total air (ppm)
394
0,6
0,4
0,2
392
390
388
386
384
382
380
378
0,0
376
6180
6200
6220
6240
6260
10
11
12
13
wavenumber
HiResMIR@CAES-Frejus-2013
14
15
16
17
18
Time
19
20
21
22
23
24
25
26
24
O2: Ground-based measurements
Sza 79.9°, Park Falls, A band
Wrong time (and air-mass) dependences
Observed
Fitted
Residuals
1.0
0.8
0,222
0,221
0,220
0,219
Total O2/total air
0.4
0.2
0,218
0,217
0,216
0,215
0,214
0,213
0.0
0,212
-0.2
0,211
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
time
12990
13020
13050
13080
13110
13140
-1
13170
wavenumber (cm )
Sza 79.9°, Park Falls, 1.27 mm band
0,222
1,0
0,221
0,220
0,8
0,219
0,218
transmission
Total O2/total air
Transmission
0.6
0,217
0,216
0,215
0,214
0,6
0,4
0,2
0,213
0,0
0,212
0,211
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
7770
7800
time
7830
7860
7890
wavenumber
HiResMIR@CAES-Frejus-2013
7920
7950
7980
8010
25
CH4: Ground-based atmospheric solar absorption
Wrong time and airmass
dependences
Spectra: air mass 5.7, Park Falls
airmass=5.7 November 11 2004
1.0
Transmittance
0.8
measured
CH4
CO2
H2O
others
solar
0.6
0.4
0.2
% Residual
0.0
4
2
0
-2
-4
5900
5910
5920
5930
5940
5950
5960
5970
5980
5990
-1
Frequency (cm )
→ Largely erroneous conclusions on sinks and sources
26
HiResMIR@CAES-Frejus-2013
Modeling of line-mixing effect
CO2 bands: Scaling model, self consistent model for all bands. Adjustment of model in
720 cm-1 Q branch. No use of present NIR bands
CH4 : Semi-classical model. Self consistent model for n3, n4 and 2n3 bands. Adjustment
of model in n3 band at high pressure. No use of present 2n3 band
O2 A-band: Scaling model. Model developed from O2 A band at elevated pressure. No
use of low pressure spectra
Collision induced absorption: From analysis of O2 A band at elevated pressures
27
HiResMIR@CAES-Frejus-2013
Line-mixing effects: Laboratory studies
O2/N2 A band
CO2/N2
___ measurement, ___ Line-mixing ___ Lorentz
2.0
0.016
1.5
0.014
1.0
0.5
0.012
76.0 atm
0.010
0.0
-2
-1
Abs. Coef (10 cm )
DTot=106 amagats
T = 194K
0.008
1.2
0.006
1.0
0.004
0.8
0.6
0.4
47.6 atm
0.002
0.2
0.000
0.0
0.003
0.8
0.002
0.001
0.6
0.4
0.000
28.1 atm
-0.001
0.2
12900
0.0
4900
13000
13100
13200
13300
13400
-1
4920
4940
4960
4980
5000
5020
5040
 (cm )
-1
 (cm )
28
HiResMIR@CAES-Frejus-2013
Line-mixing effects: Influence on spectroscopic parameters retrieval
LM
CH4/N2, 2n3, R(6), 296 K
Voigt
N2(cm /atm)
0.08
-1
1.0
Transmitance
0.8
0.6
0.06
0.05
0.04
0.4
1.6
1.4
1.2
1.0
0.8
0.6
0.2
0.0
2
0
-2
-8
-6
-4
-2
0
LM
0.000
2
4
6
8
10
6
8
10
Voigt
-0.005
-0.010
-1
2
0
-2
2
0
-2
6076.0
Voigt/LM
-10
2
0
-2
N2 (cm /atm)
Residuals (%)
0.07
6076.5
6077.0
6077.5
-1
Wavenumber (cm )
-0.015
-0.020
6078.0
-0.025
-10
-8
-6
-4
-2
0
m
HiResMIR@CAES-Frejus-2013
2
4
29
Influence on retrievals: O2 ground-based measurements
Spectra: Sza 79.9°, Park Falls
O2 A band region
O2 A band:
Relative errors on surface pressures
retrieved from atmospheric spectra
1.0
Transmission
0.8
0.6
0.224
0.223
0.4
1.27 micron O2 band
O2 A band no LM no CIA
O2 A band LM and CIA
0.222
0.2
0.221
0.220
Total O2/total air
0.0
0.15
observed-Voigt
0.10
0.05
0.218
0.217
0.216
0.215
0.00
Residual
0.219
0.214
-0.05
0.213
0.15
0.212
observed-(LM+CIA)
0.10
0.211
10
0.05
12
14
16
18
20
22
24
UT (hour)
0.00
-0.05
12990
13020
13050
13080
13110
13140
-1
13170
wavenumber (cm )
30
HiResMIR@CAES-Frejus-2013
26
Influence on retrievals: CO2 ground-based measurements
1.0
Transmission
0.8
0.6
 Fits of a ground based transmission
spectra in the region of the 2 n1+ n3 band of
CO2
0.4
0.2
0.0
0.00
-0.02
observed-Voigt
0.02
0.00
-0.02
observed-LM
4820
400
4840
4860
-1
398
4880
wavenumber (cm )
2.1 mm band, no LM
2.1 mm band, with LM
1.6 mm band
396
394
Significant errors (10%) on
the CO2 atmospheric amount.
Sinks and sources !!!

Total CO2/total air (ppm)
Residuals
0.02
392
390
388
386
384
382
380
378
376
10
11
12
13
14
15
16
17
18
UT (hour)
HiResMIR@CAES-Frejus-2013
19
20
21
22
23
24
25
31
26
Influence on retrievals: CH4 ground-based measurements
airmass=5.7 November 11 2004
1.0
measured
CH4
CO2
H2O
others
solar
Transmittance
0.8
0.6
Methane amounts retrieved
from atmospheric spectra
0.4
6.
4.
Air mass
2.25
3.
3.
4.
6. 9.
15
16
1.79
0.2
1.78
% Residual
0.0
Voigt
4
2
0
-2
-4
5900
ppmv
1.77
4
2
0
-2
-4
1.76
1.75
1.74
1.73
with line-mixing
Voigt
1.72
8
Line-mixing
5920
5940
5960
9
10
11
12
13
14
Local solar time (hour)
5980
-1
Frequency (cm )
32
HiResMIR@CAES-Frejus-2013
Influence on planetary spectra
2
-1
Radiance and Residuals [mW/(m cm sr)]
Jupiter ISO/SWS spectrum in the n4 band region of CH4
35.
30.
25.
20.
15.
10.
5.
0.
15.
Measured
Meas-Lorentz
10.
5.
0.
-5.
5.
0.
-5.
1000.
Meas-our model
1100.
1200.
1300.
1400.
-1
 (cm )
HiResMIR@CAES-Frejus-2013
1500.
33
Summary
• Spectral shape has become a key issue for high precision soundings (OCO, ACE, …)
• When line is isolated:
- The Voigt profile fails to model isolated line-shape -> need to take
into account Dicke narrowing and speed dependence effects (velocity
effects)
- Influence of velocity effects on atmospheric retrieval is quite small
(but few studies available)
• When lines are closely spaced (especially at high pressure):
- line-mixing can be observed
- Increasing evidences of influence of line-mixing for remote sensing
- Need to take into account both line-mixing and velocity effects
34
HiResMIR@CAES-Frejus-2013
-General Equations
-Isolated Lines
-Line-mixing
-Far wings
-Collision Induced processes
-Consequences for applications
-Remaining problems
35
HiResMIR@CAES-Frejus-2013