Georg Wagner, Manfred Birk

Remote Sensing Technology Institute (IMF) Deutsches Zentrum für Luft- und Raumfahrt (DLR)

Shepard A. Clough

Clough Radiation Associates

Undiscovered errors of Voigt profile beyond tiny W-shaped residuals

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 speed-dependent narrowing

• Why then Voigt?

• Fit of typical line with narrowing with Voigt % level W-shaped residuals + effective Lorentzian width L, area nearly maintained

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Example with extremely large residuals, typically only noise visible (p-p S/N ca. 20-60)

T 317 K Ptot 50.43 mbPH2O 0.2159 mbAbs. path 7862.7 cmSpectrometer Bruker IFS 120HRMOPD 187.5 cm

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 0% and 100% level, e.g. good reference spectra, no channeling, non-linearity correction if necessary

• Good knowledge of instrumental line shape function

• Assessment of self broadening contribution to line width

• Why take this effort?1418 1419 1420 1421 1422

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#22 1.93x1017

#23 1.09x1018

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#27 1.28x1020

#28 2.56x1020

• 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!

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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

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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

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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

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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

•Narrowing parameters have reasonable values

•Good agreement of narrowing parameters from different measurements

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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