Abstract

The optical constants of water ice have been determined in the near infrared from 4000 to 7000 cm-1. Polycrystalline ice films with thickness as great as ∼1164 µm were formed by condensation of water vapor on a cold silicon substrate at temperatures of 166, 176, 186, and 196 K. The transmission of light through the ice films was measured during their growth from 0 to 1164 µm over the frequency range of approximately 500–7000 cm-1. The optical constants were extracted by means of simultaneously fitting the calculated transmission spectra of films of varying thickness to their respective measured transmission spectra with an iterative Kramers–Kronig technique. Equations are presented to account for reflection losses at the interfaces when the sample is held in a cell. These equations are used to reanalyze the transmission spectrum of water ice (358-µm sample at 247 K) recorded by Ockman in 1957 [Philos. Mag. Suppl. 7, 199 (1958)]. Our imaginary indices for water ice are compared with those of Gosse et al. [Appl. Opt. 34, 6582 (1995)], Kou et al. [Appl. Opt. 32, 3531 (1993)], Grundy and Schmitt [J. Geophys. Res. 103, 25809 (1998)], and Warren [Appl. Opt. 23, 1206 (1984)], and with the new indices from Ockman’s spectrum. The temperature dependence in the imaginary index of refraction observed by us between 166 and 196 K and that between our data at 196 K and the data of Gosse et al. at 250 K are compared with that predicted by the model of Grundy and Schmitt. On the basis of this comparison a linear interpolation of the imaginary indices of refraction between 196 and 250 K is proposed. We believe that the accuracy of this interpolation is better than 20%.

© 2001 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2000 (1)

P. Yang, K. N. Liou, K. Wyser, D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[CrossRef]

1999 (4)

G. M. McFarquhar, A. J. Heymsfield, A. Macke, J. Iaquinta, S. M. Aulenbach, “Use of observed ice crystal sizes and shapes to calculate mean-scattering properties and mutispectral radiances: CEPEX April 4, 1993, case study,” J. Geophys. Res. 104, 31763–31779 (1999).
[CrossRef]

W. H. Knap, M. Hess, P. Stammes, R. B. A. Koelemeijer, P. D. Watts, “Cirrus optical thickness and crystal size retrieval from ATSR-2 data using phase functions of imperfect hexagonal ice crystals,” J. Geophys. Res. 104, 31721–31730 (1999).
[CrossRef]

Y. Liu, W. P. Arnott, J. Hallett, “Particle size distribution retrieval from multispectral optical depth: influences of particle nonsphericity and refractive index,” J. Geophys. Res. 104, 31753–31762 (1999).
[CrossRef]

M. R. Poellot, W. P. Arnott, J. Hallett, “In situ observations of contrail microphysics and implications for their radiative impact,” J. Geophys. Res. 104, 12077–12084 (1999).
[CrossRef]

1998 (5)

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multi-spectral reflectance measurements during EUCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

W. M. Grundy, B. Schmitt, “The temperature-dependent near-infrared absorption spectrum of hexagonal H2O ice,” J. Geophys. Res. 103, 25809–25822 (1998).
[CrossRef]

R. T. Tisdale, D. L. Glandorf, M. A. Tolbert, O. B. Toon, “Infrared optical constants of low temperature H2SO4 solutions representative of stratospheric sulfate aerosols,” J. Geophys. Res. 103, 25353–25370 (1998).
[CrossRef]

K. Wyser, P. Yang, “Average ice crystal size and bulk short-wave single-scattering properties of cirrus clouds,” Atmos. Res. 49, 315–335 (1998).
[CrossRef]

A. Macke, P. N. Francis, G. M. McFarquhar, S. Kinne, “The role of ice particle shapes and size distributions in the single scattering properties of cirrus clouds,” J. Atmos. Sci. 55, 2874–2883 (1998).
[CrossRef]

1997 (2)

P. Yang, K. N. Liou, W. P. Arnott, “Extinction efficiency and single-scattering albedo for laboratory and natural cirrus clouds,” J. Geophys. Res. 102, 21825–21835 (1997).
[CrossRef]

B. Strauss, R. Meerkoetter, B. Wissinger, P. Wendling, M. Hess, “On the regional climatic impact of contrails: microphysical and radiative properties of contrails and natural cirrus clouds,” Ann. Geophys. 15, 1457–1467 (1997).
[CrossRef]

1996 (2)

U. Schumann, “On conditions for contrail formation from aircraft exhausts,” Meteorol. Zeitsc. 5, 4–23 (1996).

D. E. Brown, S. M. George, C. Huang, E. K. L. Wong, K. B. Rider, R. S. Smith, B. D. Kay, “H2O condensation coefficient and refractive index for vapor-deposited ice from molecular beam and optical interference measurements,” J. Phys. Chem. 100, 4988–4995 (1996).
[CrossRef]

1995 (3)

1994 (2)

D. P. Wylie, W. P. Menzel, H. M. Woolfand, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
[CrossRef]

O. B. Toon, M. A. Tolbert, B. G. Koehler, A. M. Middlebrook, J. Jordan, “Infrared optical constants of water ice, amorphous nitric acid solutions, and nitric acid hydrates,” J. Geophys. Res. 99, 25631–25654 (1994).
[CrossRef]

1993 (2)

J. Marti, K. Mauersberger, “A survey and new measurements of ice vapor pressure at temperatures between 170 and 250 K,” Geophys. Res. Lett. 20, 363–366 (1993).
[CrossRef]

L. Kou, D. Labrie, P. Chylek, “Refractive indices of water and ice in the 0.65–2.5 µm spectral range,” Appl. Opt. 32, 3531–3540 (1993).
[CrossRef] [PubMed]

1990 (1)

G. L. Stephens, S.-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

1986 (1)

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

1984 (1)

1983 (1)

O. Mishima, D. D. Klug, E. Whalley, “The far-infrared spectrum of ice Ih in the range 8–25 cm-1: sound waves and difference bands, with application to Saturn’s rings,” J. Chem. Phys. 78, 6399–6404 (1983).
[CrossRef]

1981 (1)

G. P. Johari, “The spectrum of ice,” Contemp. Phys. 22, 613–642 (1981).
[CrossRef]

1973 (1)

1958 (1)

N. Ockman, “The infrared spectra and raman-spectra of ice,” Phil. Mag. Suppl. 7, 199–220 (1958).

Arnott, W. P.

M. R. Poellot, W. P. Arnott, J. Hallett, “In situ observations of contrail microphysics and implications for their radiative impact,” J. Geophys. Res. 104, 12077–12084 (1999).
[CrossRef]

Y. Liu, W. P. Arnott, J. Hallett, “Particle size distribution retrieval from multispectral optical depth: influences of particle nonsphericity and refractive index,” J. Geophys. Res. 104, 31753–31762 (1999).
[CrossRef]

P. Yang, K. N. Liou, W. P. Arnott, “Extinction efficiency and single-scattering albedo for laboratory and natural cirrus clouds,” J. Geophys. Res. 102, 21825–21835 (1997).
[CrossRef]

W. P. Arnott, Y. Y. Dong, J. Hallett, “Extinction efficiency in the infrared (2–18 µm) of laboratory ice clouds: observations of scattering minima in the Christiansen bands of ice,” Appl. Opt. 34, 541–551 (1995).
[CrossRef] [PubMed]

Aulenbach, S. M.

G. M. McFarquhar, A. J. Heymsfield, A. Macke, J. Iaquinta, S. M. Aulenbach, “Use of observed ice crystal sizes and shapes to calculate mean-scattering properties and mutispectral radiances: CEPEX April 4, 1993, case study,” J. Geophys. Res. 104, 31763–31779 (1999).
[CrossRef]

Brown, D. E.

D. E. Brown, S. M. George, C. Huang, E. K. L. Wong, K. B. Rider, R. S. Smith, B. D. Kay, “H2O condensation coefficient and refractive index for vapor-deposited ice from molecular beam and optical interference measurements,” J. Phys. Chem. 100, 4988–4995 (1996).
[CrossRef]

Chylek, P.

Clapp, M. L.

M. L. Clapp, R. E. Miller, D. R. Worsnop, “Frequency-dependent optical constants of water ice obtained directly from aerosol extinction spectra,” J. Phys. Chem. 99, 6317–6326 (1995).
[CrossRef]

Dong, Y. Y.

Flatau, P. J.

G. L. Stephens, S.-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Francis, P. N.

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multi-spectral reflectance measurements during EUCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

A. Macke, P. N. Francis, G. M. McFarquhar, S. Kinne, “The role of ice particle shapes and size distributions in the single scattering properties of cirrus clouds,” J. Atmos. Sci. 55, 2874–2883 (1998).
[CrossRef]

George, S. M.

D. E. Brown, S. M. George, C. Huang, E. K. L. Wong, K. B. Rider, R. S. Smith, B. D. Kay, “H2O condensation coefficient and refractive index for vapor-deposited ice from molecular beam and optical interference measurements,” J. Phys. Chem. 100, 4988–4995 (1996).
[CrossRef]

Glandorf, D. L.

R. T. Tisdale, D. L. Glandorf, M. A. Tolbert, O. B. Toon, “Infrared optical constants of low temperature H2SO4 solutions representative of stratospheric sulfate aerosols,” J. Geophys. Res. 103, 25353–25370 (1998).
[CrossRef]

Gosse, S.

Grundy, W. M.

W. M. Grundy, B. Schmitt, “The temperature-dependent near-infrared absorption spectrum of hexagonal H2O ice,” J. Geophys. Res. 103, 25809–25822 (1998).
[CrossRef]

Hallett, J.

Y. Liu, W. P. Arnott, J. Hallett, “Particle size distribution retrieval from multispectral optical depth: influences of particle nonsphericity and refractive index,” J. Geophys. Res. 104, 31753–31762 (1999).
[CrossRef]

M. R. Poellot, W. P. Arnott, J. Hallett, “In situ observations of contrail microphysics and implications for their radiative impact,” J. Geophys. Res. 104, 12077–12084 (1999).
[CrossRef]

W. P. Arnott, Y. Y. Dong, J. Hallett, “Extinction efficiency in the infrared (2–18 µm) of laboratory ice clouds: observations of scattering minima in the Christiansen bands of ice,” Appl. Opt. 34, 541–551 (1995).
[CrossRef] [PubMed]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1991).

Hess, M.

W. H. Knap, M. Hess, P. Stammes, R. B. A. Koelemeijer, P. D. Watts, “Cirrus optical thickness and crystal size retrieval from ATSR-2 data using phase functions of imperfect hexagonal ice crystals,” J. Geophys. Res. 104, 31721–31730 (1999).
[CrossRef]

B. Strauss, R. Meerkoetter, B. Wissinger, P. Wendling, M. Hess, “On the regional climatic impact of contrails: microphysical and radiative properties of contrails and natural cirrus clouds,” Ann. Geophys. 15, 1457–1467 (1997).
[CrossRef]

Heymsfield, A. J.

G. M. McFarquhar, A. J. Heymsfield, A. Macke, J. Iaquinta, S. M. Aulenbach, “Use of observed ice crystal sizes and shapes to calculate mean-scattering properties and mutispectral radiances: CEPEX April 4, 1993, case study,” J. Geophys. Res. 104, 31763–31779 (1999).
[CrossRef]

Hignett, P.

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multi-spectral reflectance measurements during EUCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

Huang, C.

D. E. Brown, S. M. George, C. Huang, E. K. L. Wong, K. B. Rider, R. S. Smith, B. D. Kay, “H2O condensation coefficient and refractive index for vapor-deposited ice from molecular beam and optical interference measurements,” J. Phys. Chem. 100, 4988–4995 (1996).
[CrossRef]

Iaquinta, J.

G. M. McFarquhar, A. J. Heymsfield, A. Macke, J. Iaquinta, S. M. Aulenbach, “Use of observed ice crystal sizes and shapes to calculate mean-scattering properties and mutispectral radiances: CEPEX April 4, 1993, case study,” J. Geophys. Res. 104, 31763–31779 (1999).
[CrossRef]

Johari, G. P.

G. P. Johari, “The spectrum of ice,” Contemp. Phys. 22, 613–642 (1981).
[CrossRef]

Jordan, J.

O. B. Toon, M. A. Tolbert, B. G. Koehler, A. M. Middlebrook, J. Jordan, “Infrared optical constants of water ice, amorphous nitric acid solutions, and nitric acid hydrates,” J. Geophys. Res. 99, 25631–25654 (1994).
[CrossRef]

Kay, B. D.

D. E. Brown, S. M. George, C. Huang, E. K. L. Wong, K. B. Rider, R. S. Smith, B. D. Kay, “H2O condensation coefficient and refractive index for vapor-deposited ice from molecular beam and optical interference measurements,” J. Phys. Chem. 100, 4988–4995 (1996).
[CrossRef]

Kinne, S.

A. Macke, P. N. Francis, G. M. McFarquhar, S. Kinne, “The role of ice particle shapes and size distributions in the single scattering properties of cirrus clouds,” J. Atmos. Sci. 55, 2874–2883 (1998).
[CrossRef]

Klett, J. D.

H. R. Pruppacher, J. D. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1980).

Klug, D. D.

O. Mishima, D. D. Klug, E. Whalley, “The far-infrared spectrum of ice Ih in the range 8–25 cm-1: sound waves and difference bands, with application to Saturn’s rings,” J. Chem. Phys. 78, 6399–6404 (1983).
[CrossRef]

Knap, W. H.

W. H. Knap, M. Hess, P. Stammes, R. B. A. Koelemeijer, P. D. Watts, “Cirrus optical thickness and crystal size retrieval from ATSR-2 data using phase functions of imperfect hexagonal ice crystals,” J. Geophys. Res. 104, 31721–31730 (1999).
[CrossRef]

Koehler, B. G.

O. B. Toon, M. A. Tolbert, B. G. Koehler, A. M. Middlebrook, J. Jordan, “Infrared optical constants of water ice, amorphous nitric acid solutions, and nitric acid hydrates,” J. Geophys. Res. 99, 25631–25654 (1994).
[CrossRef]

Koelemeijer, R. B. A.

W. H. Knap, M. Hess, P. Stammes, R. B. A. Koelemeijer, P. D. Watts, “Cirrus optical thickness and crystal size retrieval from ATSR-2 data using phase functions of imperfect hexagonal ice crystals,” J. Geophys. Res. 104, 31721–31730 (1999).
[CrossRef]

Kou, L.

Labrie, D.

Liou, K. N.

P. Yang, K. N. Liou, K. Wyser, D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[CrossRef]

P. Yang, K. N. Liou, W. P. Arnott, “Extinction efficiency and single-scattering albedo for laboratory and natural cirrus clouds,” J. Geophys. Res. 102, 21825–21835 (1997).
[CrossRef]

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

Liu, Y.

Y. Liu, W. P. Arnott, J. Hallett, “Particle size distribution retrieval from multispectral optical depth: influences of particle nonsphericity and refractive index,” J. Geophys. Res. 104, 31753–31762 (1999).
[CrossRef]

Macke, A.

G. M. McFarquhar, A. J. Heymsfield, A. Macke, J. Iaquinta, S. M. Aulenbach, “Use of observed ice crystal sizes and shapes to calculate mean-scattering properties and mutispectral radiances: CEPEX April 4, 1993, case study,” J. Geophys. Res. 104, 31763–31779 (1999).
[CrossRef]

A. Macke, P. N. Francis, G. M. McFarquhar, S. Kinne, “The role of ice particle shapes and size distributions in the single scattering properties of cirrus clouds,” J. Atmos. Sci. 55, 2874–2883 (1998).
[CrossRef]

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multi-spectral reflectance measurements during EUCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

Marti, J.

J. Marti, K. Mauersberger, “A survey and new measurements of ice vapor pressure at temperatures between 170 and 250 K,” Geophys. Res. Lett. 20, 363–366 (1993).
[CrossRef]

Mauersberger, K.

J. Marti, K. Mauersberger, “A survey and new measurements of ice vapor pressure at temperatures between 170 and 250 K,” Geophys. Res. Lett. 20, 363–366 (1993).
[CrossRef]

McFarquhar, G. M.

G. M. McFarquhar, A. J. Heymsfield, A. Macke, J. Iaquinta, S. M. Aulenbach, “Use of observed ice crystal sizes and shapes to calculate mean-scattering properties and mutispectral radiances: CEPEX April 4, 1993, case study,” J. Geophys. Res. 104, 31763–31779 (1999).
[CrossRef]

A. Macke, P. N. Francis, G. M. McFarquhar, S. Kinne, “The role of ice particle shapes and size distributions in the single scattering properties of cirrus clouds,” J. Atmos. Sci. 55, 2874–2883 (1998).
[CrossRef]

Meerkoetter, R.

B. Strauss, R. Meerkoetter, B. Wissinger, P. Wendling, M. Hess, “On the regional climatic impact of contrails: microphysical and radiative properties of contrails and natural cirrus clouds,” Ann. Geophys. 15, 1457–1467 (1997).
[CrossRef]

Menzel, W. P.

D. P. Wylie, W. P. Menzel, H. M. Woolfand, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
[CrossRef]

Middlebrook, A. M.

O. B. Toon, M. A. Tolbert, B. G. Koehler, A. M. Middlebrook, J. Jordan, “Infrared optical constants of water ice, amorphous nitric acid solutions, and nitric acid hydrates,” J. Geophys. Res. 99, 25631–25654 (1994).
[CrossRef]

Miller, R. E.

M. L. Clapp, R. E. Miller, D. R. Worsnop, “Frequency-dependent optical constants of water ice obtained directly from aerosol extinction spectra,” J. Phys. Chem. 99, 6317–6326 (1995).
[CrossRef]

Mishima, O.

O. Mishima, D. D. Klug, E. Whalley, “The far-infrared spectrum of ice Ih in the range 8–25 cm-1: sound waves and difference bands, with application to Saturn’s rings,” J. Chem. Phys. 78, 6399–6404 (1983).
[CrossRef]

Mitchell, D.

P. Yang, K. N. Liou, K. Wyser, D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[CrossRef]

Montieth, J. L.

J. L. Montieth, M. H. Unsworth, Principles of Environmental Physics, 2nd ed. (Arnold, London, 1990), pp. 36–57.

Ockman, N.

N. Ockman, “The infrared spectra and raman-spectra of ice,” Phil. Mag. Suppl. 7, 199–220 (1958).

Philipp, H. R.

H. R. Philipp, “Silicon dioxide (SiO2) glass,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, San Diego, Calif., 1985), Vol. 1, pp. 749–763.
[CrossRef]

Poellot, M. R.

M. R. Poellot, W. P. Arnott, J. Hallett, “In situ observations of contrail microphysics and implications for their radiative impact,” J. Geophys. Res. 104, 12077–12084 (1999).
[CrossRef]

Pruppacher, H. R.

H. R. Pruppacher, J. D. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1980).

Reding, F. P.

F. P. Reding, “The vibrational spectrum and structure of several molecular crystals at low temperature,” Ph.D. dissertation (Brown University, Providence, R.I., 1951).

Rider, K. B.

D. E. Brown, S. M. George, C. Huang, E. K. L. Wong, K. B. Rider, R. S. Smith, B. D. Kay, “H2O condensation coefficient and refractive index for vapor-deposited ice from molecular beam and optical interference measurements,” J. Phys. Chem. 100, 4988–4995 (1996).
[CrossRef]

Schaaf, J. W.

Schmitt, B.

W. M. Grundy, B. Schmitt, “The temperature-dependent near-infrared absorption spectrum of hexagonal H2O ice,” J. Geophys. Res. 103, 25809–25822 (1998).
[CrossRef]

Schumann, U.

U. Schumann, “On conditions for contrail formation from aircraft exhausts,” Meteorol. Zeitsc. 5, 4–23 (1996).

Smith, R. S.

D. E. Brown, S. M. George, C. Huang, E. K. L. Wong, K. B. Rider, R. S. Smith, B. D. Kay, “H2O condensation coefficient and refractive index for vapor-deposited ice from molecular beam and optical interference measurements,” J. Phys. Chem. 100, 4988–4995 (1996).
[CrossRef]

Stackhouse, P. W.

G. L. Stephens, S.-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Stammes, P.

W. H. Knap, M. Hess, P. Stammes, R. B. A. Koelemeijer, P. D. Watts, “Cirrus optical thickness and crystal size retrieval from ATSR-2 data using phase functions of imperfect hexagonal ice crystals,” J. Geophys. Res. 104, 31721–31730 (1999).
[CrossRef]

Stephens, G. L.

G. L. Stephens, S.-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Strabal, K. L.

D. P. Wylie, W. P. Menzel, H. M. Woolfand, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
[CrossRef]

Strauss, B.

B. Strauss, R. Meerkoetter, B. Wissinger, P. Wendling, M. Hess, “On the regional climatic impact of contrails: microphysical and radiative properties of contrails and natural cirrus clouds,” Ann. Geophys. 15, 1457–1467 (1997).
[CrossRef]

Tisdale, R. T.

R. T. Tisdale, D. L. Glandorf, M. A. Tolbert, O. B. Toon, “Infrared optical constants of low temperature H2SO4 solutions representative of stratospheric sulfate aerosols,” J. Geophys. Res. 103, 25353–25370 (1998).
[CrossRef]

Tolbert, M. A.

R. T. Tisdale, D. L. Glandorf, M. A. Tolbert, O. B. Toon, “Infrared optical constants of low temperature H2SO4 solutions representative of stratospheric sulfate aerosols,” J. Geophys. Res. 103, 25353–25370 (1998).
[CrossRef]

O. B. Toon, M. A. Tolbert, B. G. Koehler, A. M. Middlebrook, J. Jordan, “Infrared optical constants of water ice, amorphous nitric acid solutions, and nitric acid hydrates,” J. Geophys. Res. 99, 25631–25654 (1994).
[CrossRef]

Toon, O. B.

R. T. Tisdale, D. L. Glandorf, M. A. Tolbert, O. B. Toon, “Infrared optical constants of low temperature H2SO4 solutions representative of stratospheric sulfate aerosols,” J. Geophys. Res. 103, 25353–25370 (1998).
[CrossRef]

O. B. Toon, M. A. Tolbert, B. G. Koehler, A. M. Middlebrook, J. Jordan, “Infrared optical constants of water ice, amorphous nitric acid solutions, and nitric acid hydrates,” J. Geophys. Res. 99, 25631–25654 (1994).
[CrossRef]

Tsay, S.-C.

G. L. Stephens, S.-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Unsworth, M. H.

J. L. Montieth, M. H. Unsworth, Principles of Environmental Physics, 2nd ed. (Arnold, London, 1990), pp. 36–57.

Warren, S. G.

S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
[CrossRef] [PubMed]

S. G. Warren, Department of Atmospheric Sciences and Geophysics, 524 ATG Bldg., Box 351640, University of Washington, Seattle, Washington 98195-1640, sgw@atmos.washington.edu (personal communication, 1999).

Watts, P. D.

W. H. Knap, M. Hess, P. Stammes, R. B. A. Koelemeijer, P. D. Watts, “Cirrus optical thickness and crystal size retrieval from ATSR-2 data using phase functions of imperfect hexagonal ice crystals,” J. Geophys. Res. 104, 31721–31730 (1999).
[CrossRef]

Wendling, P.

B. Strauss, R. Meerkoetter, B. Wissinger, P. Wendling, M. Hess, “On the regional climatic impact of contrails: microphysical and radiative properties of contrails and natural cirrus clouds,” Ann. Geophys. 15, 1457–1467 (1997).
[CrossRef]

Whalley, E.

O. Mishima, D. D. Klug, E. Whalley, “The far-infrared spectrum of ice Ih in the range 8–25 cm-1: sound waves and difference bands, with application to Saturn’s rings,” J. Chem. Phys. 78, 6399–6404 (1983).
[CrossRef]

Williams, D.

Wissinger, B.

B. Strauss, R. Meerkoetter, B. Wissinger, P. Wendling, M. Hess, “On the regional climatic impact of contrails: microphysical and radiative properties of contrails and natural cirrus clouds,” Ann. Geophys. 15, 1457–1467 (1997).
[CrossRef]

Wong, E. K. L.

D. E. Brown, S. M. George, C. Huang, E. K. L. Wong, K. B. Rider, R. S. Smith, B. D. Kay, “H2O condensation coefficient and refractive index for vapor-deposited ice from molecular beam and optical interference measurements,” J. Phys. Chem. 100, 4988–4995 (1996).
[CrossRef]

Woolfand, H. M.

D. P. Wylie, W. P. Menzel, H. M. Woolfand, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
[CrossRef]

Worsnop, D. R.

M. L. Clapp, R. E. Miller, D. R. Worsnop, “Frequency-dependent optical constants of water ice obtained directly from aerosol extinction spectra,” J. Phys. Chem. 99, 6317–6326 (1995).
[CrossRef]

Wylie, D. P.

D. P. Wylie, W. P. Menzel, H. M. Woolfand, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
[CrossRef]

Wyser, K.

P. Yang, K. N. Liou, K. Wyser, D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[CrossRef]

K. Wyser, P. Yang, “Average ice crystal size and bulk short-wave single-scattering properties of cirrus clouds,” Atmos. Res. 49, 315–335 (1998).
[CrossRef]

Yang, P.

P. Yang, K. N. Liou, K. Wyser, D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[CrossRef]

K. Wyser, P. Yang, “Average ice crystal size and bulk short-wave single-scattering properties of cirrus clouds,” Atmos. Res. 49, 315–335 (1998).
[CrossRef]

P. Yang, K. N. Liou, W. P. Arnott, “Extinction efficiency and single-scattering albedo for laboratory and natural cirrus clouds,” J. Geophys. Res. 102, 21825–21835 (1997).
[CrossRef]

Ann. Geophys. (1)

B. Strauss, R. Meerkoetter, B. Wissinger, P. Wendling, M. Hess, “On the regional climatic impact of contrails: microphysical and radiative properties of contrails and natural cirrus clouds,” Ann. Geophys. 15, 1457–1467 (1997).
[CrossRef]

Appl. Opt. (4)

Atmos. Res. (1)

K. Wyser, P. Yang, “Average ice crystal size and bulk short-wave single-scattering properties of cirrus clouds,” Atmos. Res. 49, 315–335 (1998).
[CrossRef]

Contemp. Phys. (1)

G. P. Johari, “The spectrum of ice,” Contemp. Phys. 22, 613–642 (1981).
[CrossRef]

Geophys. Res. Lett. (1)

J. Marti, K. Mauersberger, “A survey and new measurements of ice vapor pressure at temperatures between 170 and 250 K,” Geophys. Res. Lett. 20, 363–366 (1993).
[CrossRef]

J. Atmos. Sci. (2)

A. Macke, P. N. Francis, G. M. McFarquhar, S. Kinne, “The role of ice particle shapes and size distributions in the single scattering properties of cirrus clouds,” J. Atmos. Sci. 55, 2874–2883 (1998).
[CrossRef]

G. L. Stephens, S.-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

J. Chem. Phys. (1)

O. Mishima, D. D. Klug, E. Whalley, “The far-infrared spectrum of ice Ih in the range 8–25 cm-1: sound waves and difference bands, with application to Saturn’s rings,” J. Chem. Phys. 78, 6399–6404 (1983).
[CrossRef]

J. Clim. (1)

D. P. Wylie, W. P. Menzel, H. M. Woolfand, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 1972–1986 (1994).
[CrossRef]

J. Geophys. Res. (9)

P. Yang, K. N. Liou, W. P. Arnott, “Extinction efficiency and single-scattering albedo for laboratory and natural cirrus clouds,” J. Geophys. Res. 102, 21825–21835 (1997).
[CrossRef]

W. H. Knap, M. Hess, P. Stammes, R. B. A. Koelemeijer, P. D. Watts, “Cirrus optical thickness and crystal size retrieval from ATSR-2 data using phase functions of imperfect hexagonal ice crystals,” J. Geophys. Res. 104, 31721–31730 (1999).
[CrossRef]

Y. Liu, W. P. Arnott, J. Hallett, “Particle size distribution retrieval from multispectral optical depth: influences of particle nonsphericity and refractive index,” J. Geophys. Res. 104, 31753–31762 (1999).
[CrossRef]

P. Yang, K. N. Liou, K. Wyser, D. Mitchell, “Parameterization of the scattering and absorption properties of individual ice crystals,” J. Geophys. Res. 105, 4699–4718 (2000).
[CrossRef]

G. M. McFarquhar, A. J. Heymsfield, A. Macke, J. Iaquinta, S. M. Aulenbach, “Use of observed ice crystal sizes and shapes to calculate mean-scattering properties and mutispectral radiances: CEPEX April 4, 1993, case study,” J. Geophys. Res. 104, 31763–31779 (1999).
[CrossRef]

W. M. Grundy, B. Schmitt, “The temperature-dependent near-infrared absorption spectrum of hexagonal H2O ice,” J. Geophys. Res. 103, 25809–25822 (1998).
[CrossRef]

M. R. Poellot, W. P. Arnott, J. Hallett, “In situ observations of contrail microphysics and implications for their radiative impact,” J. Geophys. Res. 104, 12077–12084 (1999).
[CrossRef]

R. T. Tisdale, D. L. Glandorf, M. A. Tolbert, O. B. Toon, “Infrared optical constants of low temperature H2SO4 solutions representative of stratospheric sulfate aerosols,” J. Geophys. Res. 103, 25353–25370 (1998).
[CrossRef]

O. B. Toon, M. A. Tolbert, B. G. Koehler, A. M. Middlebrook, J. Jordan, “Infrared optical constants of water ice, amorphous nitric acid solutions, and nitric acid hydrates,” J. Geophys. Res. 99, 25631–25654 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Chem. (2)

M. L. Clapp, R. E. Miller, D. R. Worsnop, “Frequency-dependent optical constants of water ice obtained directly from aerosol extinction spectra,” J. Phys. Chem. 99, 6317–6326 (1995).
[CrossRef]

D. E. Brown, S. M. George, C. Huang, E. K. L. Wong, K. B. Rider, R. S. Smith, B. D. Kay, “H2O condensation coefficient and refractive index for vapor-deposited ice from molecular beam and optical interference measurements,” J. Phys. Chem. 100, 4988–4995 (1996).
[CrossRef]

Meteorol. Zeitsc. (1)

U. Schumann, “On conditions for contrail formation from aircraft exhausts,” Meteorol. Zeitsc. 5, 4–23 (1996).

Mon. Weather Rev. (1)

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

Phil. Mag. Suppl. (1)

N. Ockman, “The infrared spectra and raman-spectra of ice,” Phil. Mag. Suppl. 7, 199–220 (1958).

Q. J. R. Meteorol. Soc. (1)

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multi-spectral reflectance measurements during EUCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

Other (7)

J. L. Montieth, M. H. Unsworth, Principles of Environmental Physics, 2nd ed. (Arnold, London, 1990), pp. 36–57.

F. P. Reding, “The vibrational spectrum and structure of several molecular crystals at low temperature,” Ph.D. dissertation (Brown University, Providence, R.I., 1951).

S. G. Warren, Department of Atmospheric Sciences and Geophysics, 524 ATG Bldg., Box 351640, University of Washington, Seattle, Washington 98195-1640, sgw@atmos.washington.edu (personal communication, 1999).

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1991).

H. R. Pruppacher, J. D. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1980).

These data can be accessed from the following web address: http://cires.colorado.edu/people/tolbert.group/data/data.html .

H. R. Philipp, “Silicon dioxide (SiO2) glass,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, San Diego, Calif., 1985), Vol. 1, pp. 749–763.
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Near-infrared absorption spectrum of a ∼100-µm-thick film of water ice along with some satellite instruments that have channels in this region (CERES, Clouds and the Earth’s Radiant Energy System; MODIS, Moderate-Resolution Imaging Spectroradiometer; ETM-plus, Enhanced Thematic Mapper Plus; ASTER, Advanced Spaceborne Thermal Emission and Reflection Radiometer; VIRS, Visible Infrared Scanner; and EOSP, Earth Observing Scanning Polarimeter). Also summarized are the principal applications of the instruments. More information about these instruments can be obtained from the following website: http://spsosun.gsfc.nasa.gov/cgi-bin/eos-ksh/eosinstru.ksh/.

Fig. 2
Fig. 2

(a) Comparison of the frequency-dependent imaginary indices of refraction of Grundy and Schmitt22 at 270 K with those in the compilation of Warren16 at 266 K (1984). (b) Variation of the percentage difference (relative to the values of Grundy and Schmitt22) between the two data sets, plotted as a function of frequency.

Fig. 3
Fig. 3

(a) Comparison of the frequency-dependent imaginary indices of refraction of Grundy and Schmitt22 at 250 K with those obtained by Kou et al.,20 Gosse et al.,21 and the reanalyzed Ockman result.23 (b) Variation of the percentage difference (relative to Ockman) of the data sets mentioned in (a), plotted as a function of frequency. (c) Frequency regions where the agreement with the new Ockman result23 is within 10% (black diamonds) and where it is within 20% (gray diamonds), overlaid on the new Ockman23 imaginary index spectrum (solid curve).

Fig. 4
Fig. 4

(a) Near-infrared absorption spectrum of water ice showing the criterion used to determine the thickness of the films. The difference in the absorbance, [A(ν 0) - A′(ν 0)], at frequency ν 0 is used as a measure of the film thickness as explained in the text (ν 0 is ∼3960cm-1, ν 1 is ∼3825cm-1, and ν 2 is ∼4438cm-1). (b) Ice film thickness plotted as a function of [A(ν 0) -A′(ν 0)] for films at temperatures of 166, 176, 186, and 196 K.

Fig. 5
Fig. 5

(a) Diamonds represent the points used to define the baseline of the spectrum. The thin black curve passing through the three points is obtained by fitting the points with a polynomial (order ≤2). To correct for scattering, this baseline is first subtracted from the original spectrum (black trace) to yield the dark gray curve. (b) Thickness dependence of the absorbances at the frequencies corresponding to the three diamonds in (a), observed in the case of the spectra recorded at 176 K (chosen because these spectra showed the least effects of scattering). The squares represent the measured absorbances, and the solid line is the result of fitting the measured absorbances to a straight line. The correct absorbances at the three frequencies for each of the spectra at all the other temperatures are calculated by use of the equations for the straight lines shown, along with the thickness of the films. (c) The thin black curve represents the correct baseline to be added on to the original-background-subtracted spectra [e.g., gray curve in (a) and (c)]. We obtain it by again fitting a smooth curve through the three new points calculated as described in (b). The final spectrum (black trace) used in the extraction of the optical constants is obtained by means of adding this new baseline (thin black curve) to the gray curve.

Fig. 6
Fig. 6

Typical fits between the measured (black trace) and the calculated (gray trace) absorption spectrum obtained. The spectra shown correspond to a temperature of 166 K.

Fig. 7
Fig. 7

Real indices of refraction of water ice at the temperatures of 166, 176, 186, and 196 K, plotted as a function of frequency.

Fig. 8
Fig. 8

(a) Comparison of the real indices of refraction (n) obtained in this study (186 K) with the values obtained by Toon et al. 28 (166 K) and the values from Warren’s compilation16 at 266 K (not temperature adjusted). (b) Variation of the percentage difference in the real indices of refraction (relative to the values in Warren’s compilation16) obtained in this study (186 K) and those from Warren’s compilation temperature adjusted with the Lorentz–Lorenz realtion to 186 K.

Fig. 9
Fig. 9

(a) Imaginary indices of refraction (k) at the temperatures of 166, 176, 186, and 196 K, plotted as a function of frequency. (b) Variation of the absolute change in the imaginary indices (k) at 196 K relative to the values at 166 K, as a function of frequency. The dashed curve represents our experimental observation, and the solid curve shows the absolute change predicted by the 17-Gaussian model of Grundy and Schmitt22 (c) Variation of the absolute change in the imaginary indices (k) at 250 K relative to the values at 196 K, as a function of frequency. The dashed curve is the difference between the results of Gosse et al. at 250 K and our experimental observation at 196 K. The solid curve is the absolute change predicted by the 17-Gaussian model of Grundy and Schmitt.22

Fig. 10
Fig. 10

(a) Comparison of the frequency-dependent imaginary indices of refraction (k) obtained in this study with those of Grundy and Schmitt22 at 250 K, Gosse et al. 21 at ∼250 K, the new values from the reanalysis of Ockman’s spectrum23 at 247 K, and Warren’s compilation16 at 266 K. Data shown here are at their respective temperatures. (b) Temperature-adjusted percentage difference [defined in Eq. (4)] between these sets of data. (c) Frequency regions where the agreement between the various other data and our results are within 10% (black diamonds) and where the agreement is within 20% (gray diamonds), overlaid on our k spectrum at 186 K (thick black curve).

Fig. 11
Fig. 11

Schematic of the transmission of light through a cell

Tables (3)

Tables Icon

Table 1 Summary of Recent Experimental Measurements of the Optical Constants of Water Ice in the Near Infrareda

Tables Icon

Table 2 Optical Constants of Water Ice at 166, 176, 186, and 196 K in the 3721–6981-cm-1 Spectral Range

Tables Icon

Table 3 Sample Calculation with the Cell Model

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

R=nvisT2-1/ρTnvisT2+2,
ρT=0.9167-1.75×10-4T-5.0×10-7T2,
kT=k196 K+dkdTT-196.
% difference =k(other) - kours×100/k(ours) - (% difference due to ΔT),
T=t1t2t3t4t1*t2*t3*t4*aa*,
r1=1-n11+n1  here after referred to as g1,
r2=g2+ih2,
g2=n12-n22-k22n1+n22+k22,  h2=2n1k2n1+n22+k22.
t1t2t3t4t1*t2*t3*t4*=l142+m142,
l14=1-g121-g22+h22, m14=-2g2h21-g12.
a=p14+iq14,
p14=p13-g1r13,  q14=q13-g1s13.
p13=p12p3-q12q3+r12t3-s12u3, p13=p12q3+q12p3+r12u3+s12t3, r13=p12r3-q12s3+r12v3-s12w3, s13=p12s3+q12r3+r12w3+s12v3.
p12=1+g1g2, q12=g1h2, r12=g1+g2, s12=h2.
α2=2πk2d2λ,  γ2=2πn2d2λ,
p3=expα2cos γ2, q3=expα2sin γ2, r3=-g2 expα2cos γ2+h2 expα2sin γ2, s3=-h2 expα2cos γ2-g2 expα2 sin γ2, t3=g2 exp-α2cos γ2-h2 exp-α2)sin γ2, u3=g2 exp-α2sin γ2-h2 exp-α2cos γ2, v3=exp-α2cos γ2, w3=-exp(-α2sin γ2.
g2=-g1, h2=0, α2=0, γ2=2πd2/λ.

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