Undiscovered errors of Voigt profile beyond tiny Wshaped residuals
Georg Wagner, Manfred Birk
Remote Sensing Technology Institute (IMF)
Deutsches Zentrum für Luft- und Raumfahrt (DLR)
Shepard A. Clough
Clough Radiation Associates
Introduction (I)
• HITRAN, GEISA databases contain only parameters for Voigt lineshape
• Codes for atmospheric trace gas retrieval use Voigt lineshape, too
• But Voigt lineshape is known to be an approximation
 Better: Speed-dependent Voigt, Galatry, etc. containing Dicke and speeddependent narrowing
• Why then Voigt?
• Fit of typical line with narrowing with Voigt  % level W-shaped residuals +
effective Lorentzian width L, area nearly maintained
T
Ptot
PH2O
Abs. path
Spectrometer
MOPD
317 K
50.43 mb
0.2159 mb
7862.7 cm
Bruker IFS 120HR
187.5 cm
0.4
0.2
0.0
obs-calc
Example with extremely large residuals,
typically only noise visible (p-p S/N ca. 20-60)
Absorptance
0.6
0.02
0.01
0.00
-0.01
-0.02
1344.00
1344.05
Wavenumber/cm
1344.10
-1
Introduction (II)
• Remote sensing: Typically coarse spectral resolution
 W-shaped residuals smeared out
• Exception: Water profiling from high resolution ground-based FT
measurements
 Agreement with radio sonde water profile when using speed-dependent
Voigt, but residuals similar to Voigt fit [1]
• There seems not to have been an urgent need to use more sophisticated
line profiles than Voigt (regarding narrowing)
BUT…
[1] M. Schneider, F. Hase, Improving spectroscopic line parameters by means of atmospheric
spectra: Theory and example for water vapor and solar absorption spectra, Journal of
Quantitative Spectroscopy & Radiative Transfer 110, 1825–1839 (2009).
• Measurements of water 2 carried out at DLR
• Numerous measurements covering 4 orders of magnitude of column
amount
 Many transitions with lines ranging from optically thin to very opaque
• Voigt fit of micro windows within single spectra  line positions, line
intensities, line broadenings for each measurement
• Lines with optical depth >4 (transmittance <1.8%) excluded from further
analysis (line intensity, pressure broadening, …).
• Reasons: 1. High correlation between line intensity and line broadening.
2. Susceptibility of line parameters to systematic errors
• Further data reduction: Determine transition dependent parameters from
single spectrum results for spectroscopic database (e.g. HITRAN)
• Test of new spectroscopic database: Can we reproduce measured spectra
within noise level?
• Only for spectral windows of measurements used in the analysis? What
about opaque lines?
• If opaque lines were not modeled within noise level, this would be ignored,
for the same reasons they are not used in the analysis
• What are the requirements for opaque lines to be included in the test?
• Accurate line intensities AND broadening
parameters with defined uncertainties
(correlation!)
• Good knowledge of instrumental
line shape function
• Assessment of self broadening
contribution to line width
• Why take this effort?
Transmittance
• Good knowledge of 0% and 100% level,
e.g. good reference spectra, no
channeling, non-linearity correction
if necessary
1.0
0.8
0.6
-2
Column density/cm
17
#22 1.93x10
18
#23 1.09x10
18
#24 4.62x10
19
#25 1.03x10
19
#26 3.89x10
20
#27 1.28x10
20
#28 2.56x10
0.4
0.2
0.0
1418
1419
1421
1420
-1
Wavenumber/cm
1422
• The answer: Whereas non-opaque lines are mostly predicted within the
noise level (beside tiny W-shaped residuals) with the new spectroscopic
database there are significant systematic differences for opaque lines
• Lines are modeled too narrow – red residuals: L fitted 3-4% smaller than in
database
• The area of the line is affected
• Residuals appear in line wings
• The effect should show up in remote sensing measurements due to opacity
broadening of the lines as was observed in IASI spectra
All spectra modeled with Voigt profiles have systematic errors for
opaque lines if these differences appear generally!
0.8
A
0.6
0.4
0.2
Transmittance
1.0
0.8
0.4
0.2
0.0
0.02
0.02
0.00
0.00
-0.02
1258.4
1258.6
Wavenumber/cm
1258.8
-1
B
0.6
0.0
OMC
OMC
Transmittance
1.0
-0.02
1393
1394
1395
Wavenumber/cm
-1
1396
There is another route to these differences:
• Valleys are modeled notoriously too deep in atmospheric spectra in vicinity
of strong lines (the Clough experience)
• These differences were tentatively attributed to non-Voigt line profiles but
without clear understanding:
Tony Clough at HITRAN conference 2010: „Manfred, there is some
problem associated with strong lines. Do you have lab measurements
of strong lines and can take a look?“
• This sentence motivated us to have a closer look at opaque lines in our
measurements
The explanation (I)
• Ratio of speed-dependent Voigt and Voigt profiles for same L
 in line wings the effect of narrowing vanishes and profiles become similar
• Line center is masked in opaque lines
• Thus, with increasing opacity speed-dependent Voigt and Voigt are getting
more similar
1.05
1.04
1.03
SDV/V
1.02
1.01
1.00
0.99
0.98
0.97
1257.8
1257.9
1258.0
Wavenumber/cm
1258.1
-1
1258.2
The explanation (II)
Speed-dependent Voigt modeled for optically thin (A+C) and thick (B+D) cases
A+B: Voigt profile modeled with same pressure broadening parameter as SDV
C+D: Voigt pressure broadening parameter fitted: C L 4.5% smaller than in
model, D L 0.6% smaller
1.0
A
0.9
0.8
Transmittance
Transmittance
1.0
0.8
B
0.6
0.4
0.2
1257.95
1258.00
Wavenumber/cm
1258.05
(SDV-V)/Amax
(SDV-V)/Amax
0.0
0.04
0.02
0.00
-0.02
-0.04
0.04
0.02
0.00
-0.02
-0.04
-1
Transmittance
Transmittance
1257.6
C
0.8
1257.8
1258.0
1258.2
Wavenumber/cm
1.0
1.0
0.9
1257.4
1258.4
1258.6
-1
0.8
D
0.6
0.4
0.2
0.04
0.02
0.00
-0.02
-0.04
1257.95
OMC/Amax
(OMC)/Amax
0.0
1258.00
Wavenumber/cm
1258.05
-1
0.04
0.02
0.00
-0.02
-0.04
1257.4
1257.6
1257.8
1258.0
1258.2
Wavenumber/cm
-1
1258.4
1258.6
The Voigt dilemma
• Lab spectroscopy fits Voigt with effective L from non-opaque lines
• This L is too small due to line narrowing
• Modeling opaque lines requires Voigt with correct L
• This can only be obtained from line profile including narrowing
The proof (I)
• Fit L with line intensities fixed for entire spectrum (2.5 mb H2O,
200 mb air+H2O, abs. path 21 m, T 296 K, MOPD 187.5 cm)
• Similar results for measurement with 5 mb H2O
 no self broadening problem – self broadening taken from HITRAN 2008
0.02
(orig-new)/orig
0.00
orig = database*
new = L fitted
-0.02
-0.04
-0.06
*from opt. thin lines
0
2
4
6
Optical depth
8
10
The proof (II)
• Fitted L for opaque lines (optical depth >4) are the correct values for profile
including narrowing
• Narrowing parameter for speed-dependent Voigt profile fitted from
measurements with 12.5 (black) and 28 (red) times less H2O column
amount with optically thin lines and L fixed to results above
• Residuals noise only
0.030
• Narrowing parameters have
reasonable values
0.025
0.020
-1
2air/(cm /atm)
• Good agreement of narrowing
parameters from different
measurements
0.015
0.010
0.005
0.000
0.00
0.02
0.04
0.06
-1
air/(cm /atm)
0.08
0.10
Conclusion/Outlook (I)
• Usually non-opaque lines from laboratory measurements feed the
spectroscopic database applying the Voigt profile, leading to too narrow
modeled opaque lines
• In case of H2O 2 at 200 mb opaque lines were too narrow by 3-4%
• The effect was overlooked in the past since opaque lines are difficult to
assess and normally excluded in analysis of laboratory spectra
The findings have significant consequences for radiative transfer and
thus remote sensing and to less extent to the calculation of the
continuum and radiative forcing.
Conclusion/Outlook (II)
• Since narrowing data are very sparse, the magnitude of the effect for other
molecules and spectral regions is unknown. Errors caused in remote sensing
are also unknown but may be significant.
• Multispectrum fitting of opaque + non-opaque lines is a source for high
accuracy narrowing parameters without relying on the W-shaped residuals
which require large signal-to-noise together with high spectral resolution
• Future: Narrowing parameters must be determined for key atmospheric
species, entered into spectroscopic databases. Remote sensing
groups should use narrowing profiles (equivalent to that for laboratory
analysis) and redo analysis