Abstract

Monitoring the amount of gaseous species in the atmosphere and exhaust gases by remote infrared spectroscopic methods calls for the use of a compilation of spectral data, which can be used to match spectra measured in a practical application. Model spectra are based on time-consuming line-by-line calculations of absorption cross sections in databases by use of temperature as input combined with path length and partial and total pressure. It is demonstrated that principal component analysis (PCA) can be used to compress the spectrum of absorption cross sections, which depend strongly on temperature, into a reduced representation of score values and loading vectors. The temperature range from 300 to 1000 K is studied. This range is divided into two subranges (300–650 K and 650–1000 K), and separate PCA models are constructed for each. The relationship between the scores and the temperature values is highly nonlinear. It is shown, however, that because the score-temperature relationships are smooth and continuous, they can be modeled by polynomials of varying degrees. The accuracy of the data compression method is validated with line-by-line-calculated absorption data of carbon monoxide and water vapor. Relative deviations between the absorption cross sections reconstructed from the PCA model parameters and the line-by-line-calculated values are found to be smaller than 0.15% for cross sections exceeding 1.27 × 10-21 cm-1 atm-1 (CO) and 0.20% for cross sections exceeding 4.03 × 10-21 cm-1 atm-1 (H2O). The computing time is reduced by a factor of 104.

© 2002 Optical Society of America

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References

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  1. M. Hilton, A. H. Lettington, I. M. Mills, “Quantitative analysis of remote gas temperature and concentration from their infrared emission spectra” Meas. Sci. Technol. 6, 1236–1241 (1995).
    [CrossRef]
  2. P. Haschberger, E. Lindermeir, “Spectroscopic inflight measurements of aircraft exhaust emissions: first results of the June 1995 campaign,” J. Geophys. Res. 101, 25995–25006 (1996).
    [CrossRef]
  3. J. Heland, K. Schaefer, “Analysis of aircraft exhaust with Fourier-transform infrared spectroscopy,” Appl. Opt. 36, 4922–4931 (1997).
    [CrossRef] [PubMed]
  4. J. Workman, “A comparison of methods of calculating optical absorption cross sections for various gases,” Report JS14211 (Bae Systems, Advanced Technology Centres—Sowerby, Filton, Bristol, U.K., 2000).
  5. S. Clausen, J. Bak, E. Lindermeir, “Laboratory investigations of the AEROPROFILE FT-IR instrumentation and gas data analysis,” submitted to Meas. Sci. Technol.
  6. L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
    [CrossRef]
  7. H. Martens, T. Næs, Multivariate Calibration (Wiley, New York, 1993).

1997

1996

P. Haschberger, E. Lindermeir, “Spectroscopic inflight measurements of aircraft exhaust emissions: first results of the June 1995 campaign,” J. Geophys. Res. 101, 25995–25006 (1996).
[CrossRef]

1995

M. Hilton, A. H. Lettington, I. M. Mills, “Quantitative analysis of remote gas temperature and concentration from their infrared emission spectra” Meas. Sci. Technol. 6, 1236–1241 (1995).
[CrossRef]

1992

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Bak, J.

S. Clausen, J. Bak, E. Lindermeir, “Laboratory investigations of the AEROPROFILE FT-IR instrumentation and gas data analysis,” submitted to Meas. Sci. Technol.

Benner, D. C.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Brown, L. R.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Camy-Peyret, C.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Clausen, S.

S. Clausen, J. Bak, E. Lindermeir, “Laboratory investigations of the AEROPROFILE FT-IR instrumentation and gas data analysis,” submitted to Meas. Sci. Technol.

Flaud, J. M.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Gamache, R. R.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Goldman, A.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Haschberger, P.

P. Haschberger, E. Lindermeir, “Spectroscopic inflight measurements of aircraft exhaust emissions: first results of the June 1995 campaign,” J. Geophys. Res. 101, 25995–25006 (1996).
[CrossRef]

Heland, J.

Hilton, M.

M. Hilton, A. H. Lettington, I. M. Mills, “Quantitative analysis of remote gas temperature and concentration from their infrared emission spectra” Meas. Sci. Technol. 6, 1236–1241 (1995).
[CrossRef]

Lettington, A. H.

M. Hilton, A. H. Lettington, I. M. Mills, “Quantitative analysis of remote gas temperature and concentration from their infrared emission spectra” Meas. Sci. Technol. 6, 1236–1241 (1995).
[CrossRef]

Lindermeir, E.

P. Haschberger, E. Lindermeir, “Spectroscopic inflight measurements of aircraft exhaust emissions: first results of the June 1995 campaign,” J. Geophys. Res. 101, 25995–25006 (1996).
[CrossRef]

S. Clausen, J. Bak, E. Lindermeir, “Laboratory investigations of the AEROPROFILE FT-IR instrumentation and gas data analysis,” submitted to Meas. Sci. Technol.

Malathy Devi, V.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Martens, H.

H. Martens, T. Næs, Multivariate Calibration (Wiley, New York, 1993).

Massie, S. T.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Mills, I. M.

M. Hilton, A. H. Lettington, I. M. Mills, “Quantitative analysis of remote gas temperature and concentration from their infrared emission spectra” Meas. Sci. Technol. 6, 1236–1241 (1995).
[CrossRef]

Næs, T.

H. Martens, T. Næs, Multivariate Calibration (Wiley, New York, 1993).

Perrin, A.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Rinsland, C. P.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Rothmann, L. S.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Schaefer, K.

Smith, M. A. H.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Tipping, R. H.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Toth, R. A.

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Workman, J.

J. Workman, “A comparison of methods of calculating optical absorption cross sections for various gases,” Report JS14211 (Bae Systems, Advanced Technology Centres—Sowerby, Filton, Bristol, U.K., 2000).

Appl. Opt.

J. Geophys. Res.

P. Haschberger, E. Lindermeir, “Spectroscopic inflight measurements of aircraft exhaust emissions: first results of the June 1995 campaign,” J. Geophys. Res. 101, 25995–25006 (1996).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

L. S. Rothmann, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Meas. Sci. Technol.

M. Hilton, A. H. Lettington, I. M. Mills, “Quantitative analysis of remote gas temperature and concentration from their infrared emission spectra” Meas. Sci. Technol. 6, 1236–1241 (1995).
[CrossRef]

Other

H. Martens, T. Næs, Multivariate Calibration (Wiley, New York, 1993).

J. Workman, “A comparison of methods of calculating optical absorption cross sections for various gases,” Report JS14211 (Bae Systems, Advanced Technology Centres—Sowerby, Filton, Bristol, U.K., 2000).

S. Clausen, J. Bak, E. Lindermeir, “Laboratory investigations of the AEROPROFILE FT-IR instrumentation and gas data analysis,” submitted to Meas. Sci. Technol.

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Figures (5)

Fig. 1
Fig. 1

Low-temperature model shows (a) loading vector number 3 and (b) the corresponding score plot with the best fit.

Fig. 2
Fig. 2

Percentage deviation between PCA-reconstructed absorption cross sections and lbl-calculated values for a (a) and (b) low-temperature case (375 K) and (c) and (d) high-temperature case (980 K). The lbl-calculated cross sections multiplied by the constant are shown by the thick curves.

Fig. 3
Fig. 3

Example of the difference in shape between the 300 K (lower spectrum) and the 650 K (upper spectrum) H2O absorption cross sections.

Fig. 4
Fig. 4

(a) Loading vector number 3 and (b) the corresponding score plot with the best fit.

Fig. 5
Fig. 5

Percentage deviation between the PCA-reconstructed absorption cross sections and lbl-calculated (a) and (b) low-temperature case (560 K) and (c) and (d) high-temperature case (840 K).

Tables (1)

Tables Icon

Table 1 Parameters Used as Input to the HITRAN Program for Calculating Absorption Cross Values (CO and H2O)

Equations (4)

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OD=STggTg, p NLpAL=STggTg, pconst.=σTg, pconst.
A=TB+E.
tT=k0+k1T+k2T2+k3T3+k4T4+ 
a=tTB.

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