spectral shape modeling and remote sensing applications
TRANSCRIPT
13/06/2017 Ha Tran 1
Spectral shape modeling and remote sensing applications
H. TranLaboratoire de Météorologie Dynamique, CNRS UMR 8539,
Sorbonne Universités, UPMC Univ Paris 06
Date 13/06/2017 Ha Tran 2
Outline
• Introduction: Atmospheric observation and spectral shape
• The Voigt profile
• Line-mixing for closely spaced lines
• Isolated lines: limits of the Voigt profile
• Widely-used non-Voigt approaches
• A new line-shape model for spectroscopic databases and applications
• Conclusions
Date 13/06/2017 Ha Tran 3
Measured spectra (satellite, balloon, ground,…)
- P, T profiles- Molecule mole fraction profiles- Cloud altitude, aerosol- etc. …
Input spectroscopic data(Position, Intensity, spectral shape,…)
Spectral shapes Collisional (pressure) effects on the spectral shape
Radiative transferForward model
Introduction: Atmospheric retrievals
Date 13/06/2017 Ha Tran 4
The Voigt profile
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fi fi fi fiS I
fi
fi
fi fi fiS d d
fi fid I d I 1
The absorption coefficient is given by
Spectral shape of an isolated line
→ Line intensity is distributed around the line position
→ Normalized line profile Ifi()
Date 13/06/2017 Ha Tran 6
The 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+vz/c) where vz the radiator velocity component along the wave propagation vector.
The line profile is a Gaussian profile
2
fiD fi
D D
ln2 1I exp ln 2
1 2B
D fi2
2k Twhere ln 2mc
is the HWHM of the line.
Date 13/06/2017 Ha Tran 7
The Lorentz broadening and shifting
For an isolated transition, the main effects of intermolecular collisions (pressure) are the (Lorentz) broadening and shifting of the line
3038.4 3038.5 3038.6
3, R(1) line of CH4-N2 0.50 atm 0.24 atm
Abso
rptio
n
wavenumber
0
Abso
rptio
n
wavenumber
and proportional to the # of coll (dens or P)
E ne rg y (H 0+V )E upper
E L ow er
tim e
fi
L fi 2 2fi fi fi
1I ( )
Date 13/06/2017 Ha Tran 8
Let’s consider a speed class: [(vz) – (vz+dvz)]the corresponding spectral domain is [(’) – (’+d’)], with ’= 0(1+vz/c)
V fi D fi LI ( ) d ' I ' I '
The Voigt profile is thus a convolution of a Gaussian profile (Doppler effect) and a Lorentzian profile (collisional effect).
The Voigt profile
Due to collisions, the spectral intensity ID(’- fi)d’ is redistributed as a Lorentz profile centered at ’. The final contribution of this speed class at is thus:
ID(’- fi) d’ IL(- ’)
The resulting profile is then obtained by summing over all speed classes (or all ’) :
Date 13/06/2017 Ha Tran 9
The Gaussian, Lorentzian and Voigt profiles
Pressure
Doppler
Doppler+Collision
Collisions
Gaussien
Voigt
Lorentzian
Usual behavior of the line width
Date 13/06/2017 Ha Tran 10
Comparaison between the Gaussian, the Lorentz and the Voigt profiles.
-0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08
0
10
20
30
40
50
60
Nor
mal
ized
pro
file
(a.u
.)
W avenum ber (cm -1)
G aussian Voigt Lorentz
D=0.01 cm -1
L=0.01 cm -1
6364.0 6364.5 6365.0 6365.5 6366.0 6366.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
trans
mis
sion
nombre d'onde (cm-1)
FTS ground-based absorption spectrum (CO2)
The Gaussian, Lorentzian and Voigt profiles
Courtesy of S. Payan
Date 13/06/2017 Ha Tran 11
Bernath et al., GRL, 32, L15S01 (2005)
ACE spectra at different tangent altitudesIntroduction: isolated lines and closely spaced lines
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Non-isolated transitions: Line-mixing effects
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In some cases, for closely spaced lines, the Voigt profile fails when P increases. It predicts shapes that are too broad.
6076.6 6076.8 6077.0 6077.2 6077.4-0.2
0.0
0.2
0.4
0.6
0.8
1.0CH4/N2,R(6) manifold, P=900.5 hPa, T=296 K
A11F11
F22
A21
F21E1
Tran
smis
sion
Wavenumber (cm-1)
Collisions induce transfers of populations between the levels of the two lines that lead to transfers of intensity between the lines.
2E
2E
1E
1E E
E
Line-mixing effects
Date 13/06/2017 Ha Tran 14
line kline
10k
LM iPW LΣ kddρσα
Line-mixing effects: Absorption coefficient
rk populationsdk matrix element of radiation-matter coupling tensor, L0 matrix of positionsW relaxation operator. All effects of collisions. Independent of within
the impact approximation (not too far in the wings)
Wlk0 Line coupling between |k> and |l>
Wlk=0 No line coupling (Lorentz)
k kkk
kkk
Lo d
1
222
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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
σσdd2Y
k
k
k kk
W
Line-mixing effects: Relaxation matrix
kkiW k k
llines lSum rule: d l W k 0
k W l l W k : Balance Dkl
rr.et
Relations for W
Date 13/06/2017 Ha Tran 16
Nadir looking instruments onboard satellitesGreenhouse 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- CO2 from 1.6 mm (weak) and 2.1 mm (strong) bands- Air mass from O2 A band (0.76 mm)- CH4 from 23 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)
Line-mixing and remote sensing: Monitoring Greenhouse Gases from space
Date 13/06/2017 Ha Tran 17
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26376
378
380
382
384
386
388
390
392
394
396
398
400
Tota
l CO
2/to
tal a
ir (p
pm)
Time
4820 4840 4860 4880
0.0
0.2
0.4
0.6
0.8
1.0
Observed Fitted Residuals
Tran
smis
sion
wavenumber (cm-1)
Sza 79.9°, Park Falls, region 2.1 mmWrong air-mass (and time) dependences
6180 6200 6220 6240 6260
0,0
0,2
0,4
0,6
0,8
1,0
wavenumber
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26376
378
380
382
384
386
388
390
392
394
396
398
400
Tota
l CO
2/to
tal a
ir (p
pm)
Time
CO2 retrievedSza 79.9°, Park Falls, region 1.6 mm
CO2: ground-based measurements
Date 13/06/2017 Ha Tran 18
7770 7800 7830 7860 7890 7920 7950 7980 8010
0,0
0,2
0,4
0,6
0,8
1,0
trans
mis
sion
wavenumber
Sza 79.9°, Park Falls, 1.27 mm band
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 260,211
0,212
0,213
0,214
0,215
0,216
0,217
0,218
0,219
0,220
0,221
0,222
Tota
l O2/
tota
l air
time
12990 13020 13050 13080 13110 13140 13170
-0.2
0.0
0.2
0.4
0.6
0.8
1.0 Observed Fitted Residuals
Tran
smis
sion
wavenumber (cm-1)
Sza 79.9°, Park Falls, A bandWrong time (and air-mass) dependences
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 260,211
0,212
0,213
0,214
0,215
0,216
0,217
0,218
0,219
0,220
0,221
0,222
Tota
l O2/
tota
l air
time
O2: Ground-based measurements
Date 13/06/2017 Ha Tran 19
Modeling of line-mixing effectW: Scaling laws, from the basic collisional rates. For O2:
Q – Basic collisional rates, modeled by
λ1)L(LTTAQ(L)
N
0
A, N, are adjusted from the mesured line widths using the sum rule
- adiabatic factor
Q(L)1)L(2T)Ω(L,T),Ω(N
JJ
JJ
nL
NJ
NJ
SL
NJ
NJ
SL
0L
0N
0N
0L
0N
0N
JNJNWJNJN
i
f
i'
f'
i
f
f'
f'
f
f
i
i'
i'
i
i
ff'ii'iiffi'i'f'f'
L
Date 13/06/2017 Ha Tran 20
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016 DTot
=106 amagatsT = 194K
12900 13000 13100 13200 13300 13400
-0.001
0.000
0.001
0.002
0.003
(cm -1)
O2/N2 A band
___ measurement, ___ Line-mixing ___ Lorentz
4900 4920 4940 4960 4980 5000 5020 50400.0
0.2
0.4
0.6
0.8
(cm -1)
0.00.20.40.60.81.01.2
Abs.
Coe
f (10
-2 c
m-1)
0.0
0.5
1.0
1.5
2.0
CO2/N2
Line-mixing effects: Laboratory studies
Date 13/06/2017 Ha Tran 21
12990 13020 13050 13080 13110 13140 13170
-0.05
0.00
0.05
0.10
0.15
observed-(LM+CIA)Res
idua
l
wavenumber (cm-1)
-0.05
0.00
0.05
0.10
0.15
observed-Voigt
0.0
0.2
0.4
0.6
0.8
1.0
Tran
smis
sion
10 12 14 16 18 20 22 24 260.211
0.212
0.213
0.214
0.215
0.216
0.217
0.218
0.219
0.220
0.221
0.222
0.223
0.224
1.27 micron O2 band O2 A band no LM no CIA O2 A band LM and CIA
Tota
l O2/
tota
l air
UT (hour)
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
Date 13/06/2017 Ha Tran 22
Fits of a ground based transmission spectra in the region of the 2 1+ 3 band of CO2
Significant errors on the CO2atmospheric amount.Sinks and sources !!!
Influence on retrievals: CO2 ground-based measurements
4820 4840 4860 4880
-0.02
0.00
0.02
observed-LM
Res
idua
ls
wavenumber (cm-1)
-0.02
0.00
0.02
observed-Voigt
0.0
0.2
0.4
0.6
0.8
1.0
Tran
smis
sion
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26376
378
380
382
384
386
388
390
392
394
396
398
400
Tota
l CO
2/to
tal a
ir (p
pm)
UT (hour)
2.1 mm band, no LM 2.1 mm band, with LM 1.6 mm band
Date 13/06/2017 Ha Tran 23
Other systems
1000 1100 1200 1300 1400 1500
-5
0
5 Exp-notre m odèleRadi
ance
et R
ésid
us [m
W/(m
2 cm-1sr
)]
(cm -1)
-5
0
5
10
15Exp-Voigt
0
5
10
15
20
25
30
35Expérience
ISO/SWS spectrum of Jupiter, 4 band region of CH4
CH4/H2
920 940 960 980 1000-0.10
-0.05
0.00
0.05
0.10 Exp-notre modèle
Obs
- C
alc
wavenumber (cm-1)
-0.10
-0.05
0.00
0.05
0.10 Exp-Voigt
Obs
- C
alc
0.0
0.2
0.4
0.6
0.8
1.0
ExpérienceTran
smis
sion
500 hPa, 234 K, 6 band
Date 13/06/2017 Ha Tran 24
Isolated line
Date 13/06/2017 Ha Tran 25
Measured and adjusted spectra using the Voigt profile.
0.0 0.2 0.4 0.6 0.8 1.0 1.20.6
0.7
0.8
0.9
1.0
Pression (atm)
Coe
ffici
ent d
'éla
rgis
sem
ent (
cm-1/a
tm)
H2O/N2, 3 band, 111,11101,10 110,11 100,10
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Abs
orpt
ion
300 Torr 250 Torr 200 Torr 150 Torr 100 Torr 50 Torr
-0.3 -0.2 -0.1 0.0 0.1 0.2
-0.4
0.0
0.4
Relative wave number (cm-1)
100
x(ob
serv
ed-a
djus
ted)
Limits of the Voigt profile
Date 13/06/2017 Ha Tran 26
1. The velocity changes induced by collisions.
The detailed balance:
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 (v) and shift (v) of the line.This also (in general) leads to a narrowing of the line
Limits of the Voigt profile
The Voigt profile neglects:
0 200 400 600 800 1000 1200 1400 16000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
H2O, 296 K
Rel
ativ
e de
nsity
Molecule speed (m/s)
Date 13/06/2017 Ha Tran 27
Widely used non-Voigt approaches
Date 13/06/2017 Ha Tran 28
The Galatry (soft collisions, SC) profile:- Assumes that radiators undergo only a very small changes per collision- Introduces a velocity changing rate b or Diff related to the diffusion coefficient
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
Simple non-Voigt approaches: the velocity changes effect
We can show that the Galatry profile is more appropriate for systems for which the radiator molecule is much heavier than the perturber.
However, experiences show that the Galatry profile and the Nelkin-Ghatak profile lead to similar quality in term of residual fit of measured spectra
Date 13/06/2017 Ha Tran 29
Simple non-Voigt approaches: the velocity changes effect
Date 13/06/2017 Ha Tran 30
Limits of the Voigt profile: atmospheric retrieval In situ absorption spectrum of tropospheric H2O recorded by balloonborne diode laser and its fit using the Voigt profile
Durry et al, JQSRT 94, 387,2005
Date 13/06/2017 Ha Tran 31
Limits of the Voigt profile: Influence on atmospheric retrievals
Barret et al, JQSRT 95, 499, 2005
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.
Date 13/06/2017 Ha Tran 32
Velocity changes effects: Remaining problems
Pressure dependence of the frequency optical collisions obtained for the R(24) line of CO2 in air from the NGP, GP and single-spectrum fits. The green line is the frequency of optical collisions calculatedfrom the mass diffusion coefficient
The collisional narrowing parameter is non linear with pressure
Date 13/06/2017 Ha Tran 33
Velocity changes effects: Remaining problems
Only Dicke narrowing is insufficient
404-303 3 band of H2O in N2: multi-spectrum fitting technique99, 197, 294, 398, 499, 600, 797, 1000, 1200 hPa
Lisak et al, JQSRT, 2015
Date 13/06/2017 Ha Tran 34
Simple non-Voigt approaches: the speed dependences
- The quadratic dependence of Rohart
a
2a 0 2 a 0 a v
(v ) [(v / v) 3 / 2] with (v )
pr r(v ) v
- The polynomial dependence of Berman-Pickett
va < < vr # vb
G(va) # Ctea
b
mactive > > mbuffer
Weak speed dependence
va # vr > > vb
G(va) # G(vr)b
a
mactive << mbuffer
Strong speed dependence
a r r a r(v ) (v ). f (v v )dv
Courtesy of F. Rohart
Date 13/06/2017 Ha Tran 35
Simple non-Voigt approaches: the speed dependences707<-606 and 717<-616 lines (at 0,83nm) of pure H2O (left) and H2O/air (right)
Ngo et al, JQSRT, 113, 870, 2012
Date 13/06/2017 Ha Tran 36
Speed dependent Voigt profile: Remaining problems
Larcher et al, JQSRT, 2015
2/0 non constant vs pressure!
R(20) line of pure CO2 at 1,6 mm
Date 13/06/2017 Ha Tran 37
Speed dependent Voigt profile: Remaining problems
→ Speed dependence only is not sufficient
R(9) line of the fundamental band of HCl perturbed by Ar
Date 13/06/2017 Ha Tran 38
Dicke narrowing+Speed dependences effect: Which line-shape?
An isolated line of CO2 in air An isolated line of pure H2O
De Vizia et al, PRA, 83, 052506, 2011Long et al, J Chem Phys, 135, 064308, 2011
Date 13/06/2017 Ha Tran 39
“Today” situation for line-shape study
1- Thanks to the development of high resolution and S/N laboratory techniques (egCEAS, CRDS) and spectra analysis techniques (multispectrum fits) the vast majority of experimental studies now clearly evidence the limits of the Voigt. Various fitting line shapes are used, chosen according to ad hoc criteria, so that the available data are inconsistent with no consensus.
2- Very ambitious and precision-demanding remote sensing experiments are operational, under study or being developed (GOSAT, OCO-2, TCCON, MERLIN, Micro Carb…) which require an accuracy of spectra simulations (<0.3%) that prohibits the use of the Voigt profile
Date 13/06/2017 Ha Tran 40
A functional form for non-Voigt line shapesfor spectroscopic databases and applications
Date 13/06/2017 Ha Tran 41
Urgent need for a better isolated line shape model and associated data to fit experimental/calculated spectra and feed databases used for remote sensing. This line shape should fulfill various constraints:
1- Take into account the various processes that affect the line profile (Doppler, molecule velocity changes, speed dependences of broadening and shifting) and be sufficiently physically-based to describe the (experimental) line profiles of various transitions of various gases with an accuracy (<0.1%) fulfilling the remote sensing accuracy needs
2- Be based on well identified line-by-line parameters with known and physically based pressure dependences for storage in databases
3- Contain simpler models as limiting cases in order to maximize the possibility to use previously published results obtained using simpler profiles
4- Require CPU time compatible with a use in atmospheric spectra calculations (many lines and layers).
5- Be compatible with a treatment of line-mixing
Requirements for the proposed line-shape
Date 13/06/2017 Ha Tran 42
The (complex) area normalized spectral profile for an isolated line centered at w0 isgiven by:
t,vdvivv.ki'vdt,'vd'v,vFt,vd'vdv,'vFt,vdt
Velocity changes Speed dependent width and shift
w
ww
0
ti )t(dedtRe1I 0
vd)t,v(d)t(d
Theoretical background
where d(t) is the time autocorrelation function of the tensor (dipole, polarizability) for the considered optical transition. The latter results from the integration over all molecular velocities , i.e.:
If we assume no correlation (in time) between collisional changes of the moleculevelocity and rotational state, one can write:
Date 13/06/2017 Ha Tran 43
Limit cases: - No velocity changes nor speed dependence ↔ Voigt
- No velocity changes but speed dependence ↔ SD Voigt
- Velocity changes but no speed dependence ↔ Dicke narrowed profiles
Various combinaisons, e.g.: speed dependent Nelkin-Ghatak profile, speed dependent Galatry profile, etc etc, with or without the inclusion of a time-correlation between velocity and rotational state changing collisions
Theoretical background
t,vdvivv.ki'vdt,'vd'v,vFt,vd'vdv,'vFt,vdt
Velocity changes Speed dependent width and shift
Date 13/06/2017 Ha Tran 44
1- Speed dependence: quadratic dependences of (v) and (v) (Rohart et al) on absolute speed v
2- Velocity changes: hard collision model (HC)
3- Correlation between velocity and rotational state changes:
Replace VC by:
Four P and T dependent parameters: 0 and 2 for broadening, 0 and 2for spectral shift
One P and T dependent parameters parameter: VC
Four T dependent parameter : h
( ' ) ( ')VC MBf v v f v
( ) ( )VC VC v i v h
20 0 2 2(v) i (v) ( i ) ( i )[(v / v) 3/ 2]
Proposed model
Date 13/06/2017 Ha Tran 45
For each transition of a given absorbing species colliding with a given “perturber” (eg H2O-H2O, H2O-O2, etc) we have
Hence: pressure dependence known → compatible with databases if Temperature dependence parameterized.
1- For Speed Dependence (0 , 2, 0 and 2 ) : X(P,T)=PX0(T)
For absorbing molecule in mixture: combination of values for absorber-pertuber pairs
2- For Velocity changes : VC(P,T)=PVC0(T)
3- For Correlation : h (P,T)=h (T)
iVC i VC
i
i ii
i
i i ii
i
x ,
(v) i (v) x (v) i (v) ,
(v) i (v) x (v) i (v) ,
h h
Fulfilling the needs: 1- Database
Date 13/06/2017 Ha Tran 46
Some simpler models are directly obtained from the pCqSDHC
For Soft collisions (Galatry) and hypergeometric SD relations have been derived (see Ngo et al, JQSRT 129, 89, 2013)
Profile parameters Limit of the pCqSDHC profile
VP 0 0, VC 2 2 0 h
RP VC 0 0, , 2 2 0h
qSDVP 0 0 2 2, , , VC 0 h
qSDRP VC 0 0 2 2, , , , 0h
Hence: The simpler models can be cast onto the pCqSDHC so that published data can be used
Fulfilling the needs: 2- Simpler models
Date 13/06/2017 Ha Tran 47
Fulfilling the needs: 3- Quality, H2O/N2
Lisak et al, JQSRT, 2015
Date 13/06/2017 Ha Tran 48
With the proposed SD and VC models, the line shape becomes analytical and can be expressed in terms of two (complex) Voigt (or complex probability) functionsw(z)
for which a plethora of efficient Fortran routines have been proposed
Using the CPF routine by Humlicek [JQSRT 1979;21:309-313. ], a Fortran routine was built [Tran et al, JQSRT 129, 199-203 (2013)] and numerical tests showed that
- The relative accuracy is always better than 10-5
- The CPU time is, at most 5 times larger than for the computation of a Voigt profile
22
tzi e dtw(z) e erfc( iz)
z t
Fulfilling the needs: 4- CPU
Date 13/06/2017 Ha Tran 49
Line Mixing can be easily included, provided that two approximations can be made:
1- One can use the so-called (Rosenkranz) first order approximation, one can simply use the expression
2- One can neglect the speed dependence of line-mixing
In this case one has:
( ) ( ) 1pCqSDHC LM pCqSDHC LMI I iY w w
Fulfilling the needs: 5- line-mixing
Date 13/06/2017 Ha Tran 50
Spectroscopy for MERLIN: 0,2% accuracy required!
Voigt Profile
Accuracy: About 1-2%
Date 13/06/2017 Ha Tran 51
0,1-0,2% around λon
Spectroscopy for MERLIN: 0,2% accuracy required!
Delahaye et al, 2015
Date 13/06/2017 Ha Tran 52
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, velocity effects should be taken into account
• When lines are closely spaced, line-mixing should be taken into account
• Increasing evidences of influence of refined spectral shape effects for remote sensing
• Need to take into account both line-mixing and velocity effects; through the HT profile -> profile recommended by IUPAC and adopted by the HITRAN spectroscopic database