Abstract

An analytical expression for the variance of the radiance measured by Fourier-transform infrared (FTIR) emission spectrometers exists only in the limit of low noise. Outside this limit, the variance needs to be calculated numerically. In addition, a criterion for low noise is needed to identify properly calibrated radiances and optimize the instrument bandwidth. In this work, the variance and the magnitude of a noise-dependent spectral bias are calculated as a function of the system responsivity (r) and the noise level in its estimate (σr). The criterion σr /r <0.3, applied to downwelling and upwelling FTIR emission spectra, shows that the instrument bandwidth is specified properly for one instrument but needs to be restricted for another.

© 2011 OSA

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  1. H. E. Revercomb, H. Buijs, H. B. Howell, D. D. Laporte, W. L. Smith, and L. A. Sromovsky, “Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the High-Resolution Interferometer Sounder,” Appl. Opt. 27(15), 3210–3218 (1988).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  4. R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  10. P. Rowe, L. Miloshevich, D. Turner, and V. Walden, “Dry bias in Vaisala RS90 radiosonde humidity profiles over Antarctica,” J. Atmos. Ocean. Technol. 25(9), 1529–1541 (2008).
    [CrossRef]
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    [CrossRef]
  12. D. D. Turner, R. O. Knuteson, H. E. Revercomb, C. Lo, and R. G. Dedecker, “Noise reduction of Atmospheric Emitted Radiance Interferometer (AERI) observations using principal component analysis,” J. Atmos. Ocean. Technol. 23(9), 1223–1238 (2006).
    [CrossRef]
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2010

2009

G. Lesins, L. Bourdages, T. Duck, J. Drummond, E. Eloranta, and V. Walden, “Large surface radiative forcing from topographic blowing snow residuals measured in the High Arctic at Eureka,” Atmos. Chem. Phys. 9(6), 1847–1862 (2009).
[CrossRef]

2008

P. Rowe, L. Miloshevich, D. Turner, and V. Walden, “Dry bias in Vaisala RS90 radiosonde humidity profiles over Antarctica,” J. Atmos. Ocean. Technol. 25(9), 1529–1541 (2008).
[CrossRef]

2006

D. D. Turner, R. O. Knuteson, H. E. Revercomb, C. Lo, and R. G. Dedecker, “Noise reduction of Atmospheric Emitted Radiance Interferometer (AERI) observations using principal component analysis,” J. Atmos. Ocean. Technol. 23(9), 1223–1238 (2006).
[CrossRef]

2004

P. Antonelli, H. E. Revercomb, L. A. Sromovsky, W. L. Smith, R. O. Knuteson, D. C. Tobin, R. K. Garcia, H. B. Howell, H. L. Huang, and F. A. Best, “A principal component noise filter for high spectral resolution infrared measurements,” J. Geophys. Res. 109(D23), D23102 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

2003

1999

1988

Ackerman, S. A.

Antonelli, P.

P. Antonelli, H. E. Revercomb, L. A. Sromovsky, W. L. Smith, R. O. Knuteson, D. C. Tobin, R. K. Garcia, H. B. Howell, H. L. Huang, and F. A. Best, “A principal component noise filter for high spectral resolution infrared measurements,” J. Geophys. Res. 109(D23), D23102 (2004).
[CrossRef]

Best, F. A.

P. Antonelli, H. E. Revercomb, L. A. Sromovsky, W. L. Smith, R. O. Knuteson, D. C. Tobin, R. K. Garcia, H. B. Howell, H. L. Huang, and F. A. Best, “A principal component noise filter for high spectral resolution infrared measurements,” J. Geophys. Res. 109(D23), D23102 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

Bourdages, L.

G. Lesins, L. Bourdages, T. Duck, J. Drummond, E. Eloranta, and V. Walden, “Large surface radiative forcing from topographic blowing snow residuals measured in the High Arctic at Eureka,” Atmos. Chem. Phys. 9(6), 1847–1862 (2009).
[CrossRef]

Buijs, H.

Ciganovich, N. C.

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

Cohen, D. L.

Dedecker, R. G.

D. D. Turner, R. O. Knuteson, H. E. Revercomb, C. Lo, and R. G. Dedecker, “Noise reduction of Atmospheric Emitted Radiance Interferometer (AERI) observations using principal component analysis,” J. Atmos. Ocean. Technol. 23(9), 1223–1238 (2006).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

Dirkx, T. P.

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

Drummond, J.

G. Lesins, L. Bourdages, T. Duck, J. Drummond, E. Eloranta, and V. Walden, “Large surface radiative forcing from topographic blowing snow residuals measured in the High Arctic at Eureka,” Atmos. Chem. Phys. 9(6), 1847–1862 (2009).
[CrossRef]

Duck, T.

G. Lesins, L. Bourdages, T. Duck, J. Drummond, E. Eloranta, and V. Walden, “Large surface radiative forcing from topographic blowing snow residuals measured in the High Arctic at Eureka,” Atmos. Chem. Phys. 9(6), 1847–1862 (2009).
[CrossRef]

Ellington, S. C.

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

Eloranta, E.

G. Lesins, L. Bourdages, T. Duck, J. Drummond, E. Eloranta, and V. Walden, “Large surface radiative forcing from topographic blowing snow residuals measured in the High Arctic at Eureka,” Atmos. Chem. Phys. 9(6), 1847–1862 (2009).
[CrossRef]

Feltz, W. F.

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

Garcia, R. K.

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

P. Antonelli, H. E. Revercomb, L. A. Sromovsky, W. L. Smith, R. O. Knuteson, D. C. Tobin, R. K. Garcia, H. B. Howell, H. L. Huang, and F. A. Best, “A principal component noise filter for high spectral resolution infrared measurements,” J. Geophys. Res. 109(D23), D23102 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

Howell, H. B.

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

P. Antonelli, H. E. Revercomb, L. A. Sromovsky, W. L. Smith, R. O. Knuteson, D. C. Tobin, R. K. Garcia, H. B. Howell, H. L. Huang, and F. A. Best, “A principal component noise filter for high spectral resolution infrared measurements,” J. Geophys. Res. 109(D23), D23102 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

H. E. Revercomb, H. Buijs, H. B. Howell, D. D. Laporte, W. L. Smith, and L. A. Sromovsky, “Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the High-Resolution Interferometer Sounder,” Appl. Opt. 27(15), 3210–3218 (1988).
[CrossRef] [PubMed]

Huang, H. L.

P. Antonelli, H. E. Revercomb, L. A. Sromovsky, W. L. Smith, R. O. Knuteson, D. C. Tobin, R. K. Garcia, H. B. Howell, H. L. Huang, and F. A. Best, “A principal component noise filter for high spectral resolution infrared measurements,” J. Geophys. Res. 109(D23), D23102 (2004).
[CrossRef]

Kadokura, S.

Knuteson, R. O.

D. D. Turner, R. O. Knuteson, H. E. Revercomb, C. Lo, and R. G. Dedecker, “Noise reduction of Atmospheric Emitted Radiance Interferometer (AERI) observations using principal component analysis,” J. Atmos. Ocean. Technol. 23(9), 1223–1238 (2006).
[CrossRef]

P. Antonelli, H. E. Revercomb, L. A. Sromovsky, W. L. Smith, R. O. Knuteson, D. C. Tobin, R. K. Garcia, H. B. Howell, H. L. Huang, and F. A. Best, “A principal component noise filter for high spectral resolution infrared measurements,” J. Geophys. Res. 109(D23), D23102 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

Kobayashi, H.

Laporte, D. D.

Lesins, G.

G. Lesins, L. Bourdages, T. Duck, J. Drummond, E. Eloranta, and V. Walden, “Large surface radiative forcing from topographic blowing snow residuals measured in the High Arctic at Eureka,” Atmos. Chem. Phys. 9(6), 1847–1862 (2009).
[CrossRef]

Lo, C.

D. D. Turner, R. O. Knuteson, H. E. Revercomb, C. Lo, and R. G. Dedecker, “Noise reduction of Atmospheric Emitted Radiance Interferometer (AERI) observations using principal component analysis,” J. Atmos. Ocean. Technol. 23(9), 1223–1238 (2006).
[CrossRef]

Miloshevich, L.

P. Rowe, L. Miloshevich, D. Turner, and V. Walden, “Dry bias in Vaisala RS90 radiosonde humidity profiles over Antarctica,” J. Atmos. Ocean. Technol. 25(9), 1529–1541 (2008).
[CrossRef]

Revercomb, H. E.

V. P. Walden, R. L. Tanamachi, P. M. Rowe, H. E. Revercomb, D. C. Tobin, and S. A. Ackerman, “Improvements in the data quality of the Interferometric Monitor for greenhouse Gases,” Appl. Opt. 49(3), 520–528 (2010).
[CrossRef] [PubMed]

D. D. Turner, R. O. Knuteson, H. E. Revercomb, C. Lo, and R. G. Dedecker, “Noise reduction of Atmospheric Emitted Radiance Interferometer (AERI) observations using principal component analysis,” J. Atmos. Ocean. Technol. 23(9), 1223–1238 (2006).
[CrossRef]

P. Antonelli, H. E. Revercomb, L. A. Sromovsky, W. L. Smith, R. O. Knuteson, D. C. Tobin, R. K. Garcia, H. B. Howell, H. L. Huang, and F. A. Best, “A principal component noise filter for high spectral resolution infrared measurements,” J. Geophys. Res. 109(D23), D23102 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

H. E. Revercomb, H. Buijs, H. B. Howell, D. D. Laporte, W. L. Smith, and L. A. Sromovsky, “Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the High-Resolution Interferometer Sounder,” Appl. Opt. 27(15), 3210–3218 (1988).
[CrossRef] [PubMed]

Rowe, P.

P. Rowe, L. Miloshevich, D. Turner, and V. Walden, “Dry bias in Vaisala RS90 radiosonde humidity profiles over Antarctica,” J. Atmos. Ocean. Technol. 25(9), 1529–1541 (2008).
[CrossRef]

Rowe, P. M.

Shimota, A.

Short, J. F.

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

Smith, W. L.

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

P. Antonelli, H. E. Revercomb, L. A. Sromovsky, W. L. Smith, R. O. Knuteson, D. C. Tobin, R. K. Garcia, H. B. Howell, H. L. Huang, and F. A. Best, “A principal component noise filter for high spectral resolution infrared measurements,” J. Geophys. Res. 109(D23), D23102 (2004).
[CrossRef]

H. E. Revercomb, H. Buijs, H. B. Howell, D. D. Laporte, W. L. Smith, and L. A. Sromovsky, “Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the High-Resolution Interferometer Sounder,” Appl. Opt. 27(15), 3210–3218 (1988).
[CrossRef] [PubMed]

Sromovsky, L. A.

Tanamachi, R. L.

Tobin, D. C.

V. P. Walden, R. L. Tanamachi, P. M. Rowe, H. E. Revercomb, D. C. Tobin, and S. A. Ackerman, “Improvements in the data quality of the Interferometric Monitor for greenhouse Gases,” Appl. Opt. 49(3), 520–528 (2010).
[CrossRef] [PubMed]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

P. Antonelli, H. E. Revercomb, L. A. Sromovsky, W. L. Smith, R. O. Knuteson, D. C. Tobin, R. K. Garcia, H. B. Howell, H. L. Huang, and F. A. Best, “A principal component noise filter for high spectral resolution infrared measurements,” J. Geophys. Res. 109(D23), D23102 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

Turner, D.

P. Rowe, L. Miloshevich, D. Turner, and V. Walden, “Dry bias in Vaisala RS90 radiosonde humidity profiles over Antarctica,” J. Atmos. Ocean. Technol. 25(9), 1529–1541 (2008).
[CrossRef]

Turner, D. D.

D. D. Turner, R. O. Knuteson, H. E. Revercomb, C. Lo, and R. G. Dedecker, “Noise reduction of Atmospheric Emitted Radiance Interferometer (AERI) observations using principal component analysis,” J. Atmos. Ocean. Technol. 23(9), 1223–1238 (2006).
[CrossRef]

Walden, V.

G. Lesins, L. Bourdages, T. Duck, J. Drummond, E. Eloranta, and V. Walden, “Large surface radiative forcing from topographic blowing snow residuals measured in the High Arctic at Eureka,” Atmos. Chem. Phys. 9(6), 1847–1862 (2009).
[CrossRef]

P. Rowe, L. Miloshevich, D. Turner, and V. Walden, “Dry bias in Vaisala RS90 radiosonde humidity profiles over Antarctica,” J. Atmos. Ocean. Technol. 25(9), 1529–1541 (2008).
[CrossRef]

Walden, V. P.

Appl. Opt.

Atmos. Chem. Phys.

G. Lesins, L. Bourdages, T. Duck, J. Drummond, E. Eloranta, and V. Walden, “Large surface radiative forcing from topographic blowing snow residuals measured in the High Arctic at Eureka,” Atmos. Chem. Phys. 9(6), 1847–1862 (2009).
[CrossRef]

J. Atmos. Ocean. Technol.

D. D. Turner, R. O. Knuteson, H. E. Revercomb, C. Lo, and R. G. Dedecker, “Noise reduction of Atmospheric Emitted Radiance Interferometer (AERI) observations using principal component analysis,” J. Atmos. Ocean. Technol. 23(9), 1223–1238 (2006).
[CrossRef]

P. Rowe, L. Miloshevich, D. Turner, and V. Walden, “Dry bias in Vaisala RS90 radiosonde humidity profiles over Antarctica,” J. Atmos. Ocean. Technol. 25(9), 1529–1541 (2008).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part I: instrument design,” J. Atmos. Ocean. Technol. 21(12), 1763–1776 (2004).
[CrossRef]

R. O. Knuteson, H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short, and D. C. Tobin, “Atmospheric Emitted Radiance Interferometer (AERI) Part II: instrument performance,” J. Atmos. Ocean. Technol. 21(12), 1777–1789 (2004).
[CrossRef]

J. Geophys. Res.

P. Antonelli, H. E. Revercomb, L. A. Sromovsky, W. L. Smith, R. O. Knuteson, D. C. Tobin, R. K. Garcia, H. B. Howell, H. L. Huang, and F. A. Best, “A principal component noise filter for high spectral resolution infrared measurements,” J. Geophys. Res. 109(D23), D23102 (2004).
[CrossRef]

Other

M. Jackson, Mathematics Department, University of Puget Sound, 1500 N. Warner, Tacoma, WA 98416 (personal communication, 2010).

P. M. Rowe, Department of Geography, University of Idaho, 875 Perimeter Drive, Moscow, Idaho 83844, S. P. Neshyba, C. J. Cox, and V. P. Walden are preparing a manuscript to be called, “A responsivity-based criterion for accurate calibration of FTIR emission spectra: identification of in-band low-responsivity wavenumbers.”

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Figures (6)

Fig. 1
Fig. 1

Measurements of the instrument response (rm ) and its standard deviation (σ r ) for (a) the Atmospheric Emitted Radiance Interferometer (AERI) and (b) band 1 of the Interferometric Monitor for Greenhouse Gases (IMG).

Fig. 2
Fig. 2

The mean of fr (described in the text) as a function of the uncertainty in the measured instrument response relative to the true instrument response (σ r /r) with a) the x-axis on a log scale and b) both axes on log scales.

Fig. 3
Fig. 3

Averaged calibrated radiance, <Ls + εL > and the limit approached at high noise, 0.5(Lh + Lc ). Panel (a) shows the average of 1816 downwelling radiance spectra taken over a 24-hour period on 01 July 2008 with the Atmospheric Emitted Radiance Interferometer (AERI), while (b) shows the average of 3 upwelling radiance spectra measured by the Interferometric Monitor for Greenhouse Gases (IMG) at −68.8° latitude and 93.4° longitude.

Fig. 4
Fig. 4

(a)-(d). The means of four functions, described in the text, each excluding a small region of the probability space about a singularity [see legend in (a)]. The position of the singularity depends on the values of two random, complex variables with combined standard deviation σ r /r. For small σ r /r, the mean is proportional to (σ r /r)2, as shown (low-noise).

Fig. 5
Fig. 5

The relative uncertainty in the system responsivity (σ r /r) for measurements using a) an Atmospheric Emitted Radiance Interferometer (AERI) and (b) band 1 of the Interferometric Monitor for Greenhouse Gases (IMG).

Fig. 6
Fig. 6

The standard deviation (√<ε L 2>) and mean bias (<ε L >) of calibrated Atmospheric Emitted Radiance Interferometer (AERI) spectra, where ε L is the error due to noise. The standard deviation is calculated numerically excluding 0.001% of probability about a singularity in <ε L 2>, and in the low-noise limit. The vertical dotted line indicates the wavenumber where σ r /r = 0.3.

Equations (24)

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V x = 0.5 η R d t A I L x exp ( i ϕ ) + R d O ,
V x = r L x exp ( i ϕ ) + R d O + n x exp ( i ϕ ) .
L s + ε L = Re [ V s V c V h V c ] [ L h L c ] + L c ,
ε L = Re ( r ( L s L c ) + ( n s n c ) r ( L h L c ) + ( n h n c ) ) [ L h L c ] + L c L s .
ε L Re [ n s n c r ] ( L s L c L h L c ) Re [ n h n c r ] ,  for  n h - n c r ( L h - L c ) 1 ,
ε L 2 σ n s 2 r 2 + ( σ n c 2 r 2 ) ( L h L s L h L c ) 2 + ( σ n h 2 r 2 ) ( L c L s L h L c ) 2 ,  for  n h - n c r ( L h - L c ) 1 ,
V h V c = r [ L h L c ] exp ( i ϕ ) + ( n h n c ) exp ( i ϕ ) .
r m ( V h V c ) / ( L h L c ) = ( r + e r ) exp ( i ϕ ) ,
e r ( n h n c ) / ( L h L c ) .
σ r 2 = ( r m r m ) ( r m r m ) ,
σ r 2 [ ( e r e r ) exp ( i ϕ ) ] [ ( e r e r ) exp ( i ϕ ) ] = e r 2 ,
σ r / r 1.
ε L = ( L h L c ) Re ( ( n s n c ) / [ r ( L h L c ) ] 1 + e r / r ) + ( L c L s ) Re ( e r / r 1 + e r / r ) .
f r Re [ e r / r 1 + ( e r / r ) ] ,
f c Re [ e c / r 1 + ( e r / r ) ] ,
f s Re [ e s / r 1 + ( e r / r ) ] ,
ε L = ( s f s f c ) ( L h L c ) + ( f r ) ( L c L s ) .
ε L = s f s ( L h L c ) f c ( L h L c ) + f r ( L c L s ) .
f s = Re [ e s / r 1 + e r / r ] P e s d e s P e r d e r ,
ε L = f c ( L h L c ) + f r ( L c L s ) .
ε L = f r ( 0.5 L h + 0.5 L c L s ) .
ε L 0.5 L h + 0.5 L c L s , as  σ r / r .
ε L 2 = ( s f s f c ) 2 ( L h L c ) 2 + f r 2 ( L c L s ) 2 + 2 ( s f s f c ) f r ( L h L c ) ( L c L s ) .
ε L 2 = ( s 2 f s 2 + f c 2 ) ( L h L c ) 2 + f r 2 ( L c L s ) 2 2 f c f r ( L h L c ) ( L c L s ) .

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