Abstract

Infrared extinction optical depth (500–5000 cm-1) has been measured with a Fourier transform infrared spectrometer for clouds produced with an ultrasonic nebulizer. Direct measurement of the cloud droplet size spectra agree with size spectra retrieved from inversion of the extinction measurements. Both indicate that the range of droplet sizes is 1–14 µm. The retrieval was accomplished with an iterative algorithm that simultaneously obtains water-vapor concentration. The basis set of droplet extinction functions are computed once by using numerical integration of the Lorenz–Mie theory over narrow size bins, and a measured water-vapor extinction curve was used. Extinction and size spectra are measured and computed for both steady-state and dissipating clouds. It is demonstrated that anomalous diffraction theory produces relatively poor droplet size and synthetic extinction spectra and that extinction measurements are helpful in assessing the validity of various theories. Calculations of cloud liquid-water content from retrieved size distributions agree with a parameterization based on optical-depth measurements at a wave number of 906 cm-1 for clouds that satisfy the size spectral range assumptions of the parameterization. Significance of droplet and vapor contribution to the total optical depth is used to evaluate the reliability of spectral inversions.

© 1997 Optical Society of America

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    [CrossRef]

1995

U. Amato, F. Esposito, C. Serio, G. Pavese, F. Romano, “Inverting high spectral resolution aerosol optical depth to determine the size distribution of atmospheric aerosols,” Aerosol Sci. Technol. 23, 591–602 (1995).
[CrossRef]

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

1994

1990

Z. S. Wu, K. F. Ren, Y. P. Wang, “10.6 micron wave propagation in cloud, fog, and haze,” Int. J. Infrared Millim. Waves 11, 499–504 (1990).
[CrossRef]

1989

1987

G. R. Markowski, “Improving Twomey’s algorithm for inversion of aerosol measurement data,” Aerosol Sci. Technol. 7, 127–141 (1987).
[CrossRef]

P. F. Nolan, S. G. Jennings, “Extinction and liquid water content measurements at CO2 laser wavelengths,” J. Atmos. Oceanic Technol. 4, 391–400 (1987).
[CrossRef]

P. R. Solomon, R. M. Carangelo, P. E. Best, J. R. Markham, D. G. Hamblen, “Analysis of particle emittance, composition, size and temperature by FT-i.r. emission/transmission spectroscopy,” Fuel 66, 897–908 (1987).
[CrossRef]

1984

1982

1981

1980

1979

A. L. Fymat, C. B. Smith, “Analytical inversions in remote sensing of particle size distributions. 4: comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation,” Appl. Opt. 18, 3595–3598 (1979).
[CrossRef] [PubMed]

R. G. Pinnick, S. G. Jennings, P. Chylek, H. J. Auvermann, “Verification of a linear relation between IR extinction, absorption, and liquid water content of fogs,” J. Atmos. Sci. 36, 1577–1586 (1979).
[CrossRef]

1978

1976

1975

H. D. Downing, D. Williams, “Optical constants of water in the infrared,” J. Geophys. Res. 80, 1656–1661 (1975).
[CrossRef]

1973

1969

V. M. Zolatarev, B. A. Mikhailov, L. I. Aperovich, S. I. Popov, “Dispersion and absorption of water in the infrared,” Opt. Spectrosc. 27, 430–432 (1969).

1966

R. G. Eldridge, “Haze and fog aerosol distributions,” J. Atmos. Sci. 23, 605–613 (1966).
[CrossRef]

1963

K. S. Shifrin, A. Ya. Perelman, “The determination of the spectrum of particles in a dispersed system from data on its transparency,” Opt. Spectrosc. 15, 285–289 (1963).

1960

D. Deirmendjian, “Atmospheric extinction of infrared radiation,” Q. J. R. Meteorol. Soc. 86, 371–381 (1960).
[CrossRef]

1957

R. Penndorf, “Comments on ‘Measurements of cloud drop-size distributions’,” J. Meteorol. 14, 573–574 (1957).
[CrossRef]

R. G. Eldridge, “Measurements of cloud drop-size distributions: reply,” J. Meteorol. 14, 575–577 (1957).

R. G. Eldridge, “Measurements of cloud drop-size distributions,” J. Meteorol. 14, 55–59 (1957).
[CrossRef]

A. Arnulf, J. Bricard, E. Curé, C. Véret, “Transmission by haze and fog in the spectral region 0.35 to 10 microns,” J. Opt. Soc. Am. 47, 491–498 (1957).
[CrossRef]

Amato, U.

U. Amato, F. Esposito, C. Serio, G. Pavese, F. Romano, “Inverting high spectral resolution aerosol optical depth to determine the size distribution of atmospheric aerosols,” Aerosol Sci. Technol. 23, 591–602 (1995).
[CrossRef]

Aperovich, L. I.

V. M. Zolatarev, B. A. Mikhailov, L. I. Aperovich, S. I. Popov, “Dispersion and absorption of water in the infrared,” Opt. Spectrosc. 27, 430–432 (1969).

Arnott, W. P.

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]

W. P. Arnott, C. Schmitt, Y. Liu, J. Hallett, “Laboratory FTIR measurements of ice crystal and water droplet clouds: particle size spectrum inversion,” in Proceedings of the Twelfth International Conference on Clouds and Precipitation (Page Bros., Norwich, 1996), pp. 990–992.

Arnulf, A.

Auvermann, H. J.

R. G. Pinnick, S. G. Jennings, P. Chylek, H. J. Auvermann, “Verification of a linear relation between IR extinction, absorption, and liquid water content of fogs,” J. Atmos. Sci. 36, 1577–1586 (1979).
[CrossRef]

Best, P. E.

P. R. Solomon, R. M. Carangelo, P. E. Best, J. R. Markham, D. G. Hamblen, “Analysis of particle emittance, composition, size and temperature by FT-i.r. emission/transmission spectroscopy,” Fuel 66, 897–908 (1987).
[CrossRef]

Bottiger, J. R.

J. R. Bottiger, “Intercomparison of some inversion methods on systems of spherical particles,” in Advances in Remote Sensing Retrieval Methods, A. Deepak, H. E. Fleming, M. T. Chahine, eds. (Deepak, Hampton, Virginia, 1985), p. 587.

Box, M. A.

Braun, C. J. M.

Bricard, J.

Bruce, C. W.

Bruce, D.

Burden, R. L.

R. L. Burden, J. D. Faires, Numerical Analysis, (PWS, Boston, 1993) 410–411.

Burket, H.

Businger, J. A.

R. G. Fleagle, J. A. Businger, An Introduction to Atmospheric Physics (Academic, New York, 1963), pp. 81–91.

Cahenzli, L.

Carangelo, R. M.

P. R. Solomon, R. M. Carangelo, P. E. Best, J. R. Markham, D. G. Hamblen, “Analysis of particle emittance, composition, size and temperature by FT-i.r. emission/transmission spectroscopy,” Fuel 66, 897–908 (1987).
[CrossRef]

Chimelis, V.

Chylek, P.

R. G. Pinnick, S. G. Jennings, P. Chylek, H. J. Auvermann, “Verification of a linear relation between IR extinction, absorption, and liquid water content of fogs,” J. Atmos. Sci. 36, 1577–1586 (1979).
[CrossRef]

P. Chylek, “Extinction and liquid water content of fogs and clouds,” J. Atmos. Sci. 35, 296–300 (1978).

Clapp, M. L.

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

Clay, M. R.

Curé, E.

Deirmendjian, D.

D. Deirmendjian, “Atmospheric extinction of infrared radiation,” Q. J. R. Meteorol. Soc. 86, 371–381 (1960).
[CrossRef]

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 114–119.

Dong, Y. Y.

Downing, H. D.

H. D. Downing, D. Williams, “Optical constants of water in the infrared,” J. Geophys. Res. 80, 1656–1661 (1975).
[CrossRef]

Eldridge, R. G.

R. G. Eldridge, “Haze and fog aerosol distributions,” J. Atmos. Sci. 23, 605–613 (1966).
[CrossRef]

R. G. Eldridge, “Measurements of cloud drop-size distributions: reply,” J. Meteorol. 14, 575–577 (1957).

R. G. Eldridge, “Measurements of cloud drop-size distributions,” J. Meteorol. 14, 55–59 (1957).
[CrossRef]

Esposito, F.

U. Amato, F. Esposito, C. Serio, G. Pavese, F. Romano, “Inverting high spectral resolution aerosol optical depth to determine the size distribution of atmospheric aerosols,” Aerosol Sci. Technol. 23, 591–602 (1995).
[CrossRef]

Essenwanger, O. M.

D. A. Stewart, O. M. Essenwanger, “A survey of fog and related optical propagation characteristics,” Rev. Geophys. Space Phys. 20, 481–495 (1982).
[CrossRef]

Faires, J. D.

R. L. Burden, J. D. Faires, Numerical Analysis, (PWS, Boston, 1993) 410–411.

Fleagle, R. G.

R. G. Fleagle, J. A. Businger, An Introduction to Atmospheric Physics (Academic, New York, 1963), pp. 81–91.

Fymat, A. L.

Gertler, A. W.

A. W. Gertler, R. L. Steele, “Experimental verification of the linear relationship between IR extinction and liquid water content of clouds,” J. Appl. Meteorol. 19, 1314–1317 (1980).
[CrossRef]

Hale, G. M.

Hallett, J.

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]

W. P. Arnott, C. Schmitt, Y. Liu, J. Hallett, “Laboratory FTIR measurements of ice crystal and water droplet clouds: particle size spectrum inversion,” in Proceedings of the Twelfth International Conference on Clouds and Precipitation (Page Bros., Norwich, 1996), pp. 990–992.

Hamblen, D. G.

P. R. Solomon, R. M. Carangelo, P. E. Best, J. R. Markham, D. G. Hamblen, “Analysis of particle emittance, composition, size and temperature by FT-i.r. emission/transmission spectroscopy,” Fuel 66, 897–908 (1987).
[CrossRef]

Jennings, S. G.

P. F. Nolan, S. G. Jennings, “Extinction and liquid water content measurements at CO2 laser wavelengths,” J. Atmos. Oceanic Technol. 4, 391–400 (1987).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, H. J. Auvermann, “Verification of a linear relation between IR extinction, absorption, and liquid water content of fogs,” J. Atmos. Sci. 36, 1577–1586 (1979).
[CrossRef]

Klett, J. D.

Lenham, A. P.

Liu, Y.

W. P. Arnott, C. Schmitt, Y. Liu, J. Hallett, “Laboratory FTIR measurements of ice crystal and water droplet clouds: particle size spectrum inversion,” in Proceedings of the Twelfth International Conference on Clouds and Precipitation (Page Bros., Norwich, 1996), pp. 990–992.

Markham, J. R.

P. R. Solomon, R. M. Carangelo, P. E. Best, J. R. Markham, D. G. Hamblen, “Analysis of particle emittance, composition, size and temperature by FT-i.r. emission/transmission spectroscopy,” Fuel 66, 897–908 (1987).
[CrossRef]

Markowski, G. R.

G. R. Markowski, “Improving Twomey’s algorithm for inversion of aerosol measurement data,” Aerosol Sci. Technol. 7, 127–141 (1987).
[CrossRef]

Mason, B. J.

B. J. Mason, The Physics of Clouds (Clarendon, Oxford, 1971), pp. 93–94.

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere, Scattering by Molecules and Particles (Wiley, New York, 1976), pp. 133–142.

McKellar, B. H. J.

Mikhailov, B. A.

V. M. Zolatarev, B. A. Mikhailov, L. I. Aperovich, S. I. Popov, “Dispersion and absorption of water in the infrared,” Opt. Spectrosc. 27, 430–432 (1969).

Miller, R. E.

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

Nolan, P. F.

P. F. Nolan, S. G. Jennings, “Extinction and liquid water content measurements at CO2 laser wavelengths,” J. Atmos. Oceanic Technol. 4, 391–400 (1987).
[CrossRef]

Pavese, G.

U. Amato, F. Esposito, C. Serio, G. Pavese, F. Romano, “Inverting high spectral resolution aerosol optical depth to determine the size distribution of atmospheric aerosols,” Aerosol Sci. Technol. 23, 591–602 (1995).
[CrossRef]

Penndorf, R.

R. Penndorf, “Comments on ‘Measurements of cloud drop-size distributions’,” J. Meteorol. 14, 573–574 (1957).
[CrossRef]

Perelman, A. Ya.

A. Ya. Perelman, K. S. Shifrin, “Improvements to the spectral transparency method for determining particle-size distribution,” Appl. Opt. 19, 1787–1793 (1980).
[CrossRef] [PubMed]

K. S. Shifrin, A. Ya. Perelman, “The determination of the spectrum of particles in a dispersed system from data on its transparency,” Opt. Spectrosc. 15, 285–289 (1963).

Pinnick, R. G.

R. G. Pinnick, S. G. Jennings, P. Chylek, H. J. Auvermann, “Verification of a linear relation between IR extinction, absorption, and liquid water content of fogs,” J. Atmos. Sci. 36, 1577–1586 (1979).
[CrossRef]

Popov, S. I.

V. M. Zolatarev, B. A. Mikhailov, L. I. Aperovich, S. I. Popov, “Dispersion and absorption of water in the infrared,” Opt. Spectrosc. 27, 430–432 (1969).

Querry, M. R.

Ren, K. F.

Z. S. Wu, K. F. Ren, Y. P. Wang, “10.6 micron wave propagation in cloud, fog, and haze,” Int. J. Infrared Millim. Waves 11, 499–504 (1990).
[CrossRef]

Romano, F.

U. Amato, F. Esposito, C. Serio, G. Pavese, F. Romano, “Inverting high spectral resolution aerosol optical depth to determine the size distribution of atmospheric aerosols,” Aerosol Sci. Technol. 23, 591–602 (1995).
[CrossRef]

Schmitt, C.

W. P. Arnott, C. Schmitt, Y. Liu, J. Hallett, “Laboratory FTIR measurements of ice crystal and water droplet clouds: particle size spectrum inversion,” in Proceedings of the Twelfth International Conference on Clouds and Precipitation (Page Bros., Norwich, 1996), pp. 990–992.

Serio, C.

U. Amato, F. Esposito, C. Serio, G. Pavese, F. Romano, “Inverting high spectral resolution aerosol optical depth to determine the size distribution of atmospheric aerosols,” Aerosol Sci. Technol. 23, 591–602 (1995).
[CrossRef]

Shifrin, K. S.

A. Ya. Perelman, K. S. Shifrin, “Improvements to the spectral transparency method for determining particle-size distribution,” Appl. Opt. 19, 1787–1793 (1980).
[CrossRef] [PubMed]

K. S. Shifrin, A. Ya. Perelman, “The determination of the spectrum of particles in a dispersed system from data on its transparency,” Opt. Spectrosc. 15, 285–289 (1963).

Smith, C. B.

Smolders, H. J.

Snoeijs, C. A. M.

Solomon, P. R.

P. R. Solomon, R. M. Carangelo, P. E. Best, J. R. Markham, D. G. Hamblen, “Analysis of particle emittance, composition, size and temperature by FT-i.r. emission/transmission spectroscopy,” Fuel 66, 897–908 (1987).
[CrossRef]

Steele, R. L.

A. W. Gertler, R. L. Steele, “Experimental verification of the linear relationship between IR extinction and liquid water content of clouds,” J. Appl. Meteorol. 19, 1314–1317 (1980).
[CrossRef]

Stewart, D. A.

D. A. Stewart, O. M. Essenwanger, “A survey of fog and related optical propagation characteristics,” Rev. Geophys. Space Phys. 20, 481–495 (1982).
[CrossRef]

Tampieri, F.

Tomasi, C.

Twomey, S.

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977), Chap. 5 and 6.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 172–183.

van Dongen, M. E. H.

Véret, C.

Walters, P. T.

Wang, Y. P.

Z. S. Wu, K. F. Ren, Y. P. Wang, “10.6 micron wave propagation in cloud, fog, and haze,” Int. J. Infrared Millim. Waves 11, 499–504 (1990).
[CrossRef]

Weng, S.

Wieliczka, D. M.

Willems, J. F. H.

Williams, D.

H. D. Downing, D. Williams, “Optical constants of water in the infrared,” J. Geophys. Res. 80, 1656–1661 (1975).
[CrossRef]

Worsnop, D. R.

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

Wu, Z. S.

Z. S. Wu, K. F. Ren, Y. P. Wang, “10.6 micron wave propagation in cloud, fog, and haze,” Int. J. Infrared Millim. Waves 11, 499–504 (1990).
[CrossRef]

Yee, Y. P.

Zolatarev, V. M.

V. M. Zolatarev, B. A. Mikhailov, L. I. Aperovich, S. I. Popov, “Dispersion and absorption of water in the infrared,” Opt. Spectrosc. 27, 430–432 (1969).

Zuev, V. E.

V. E. Zuev, Laser Beams in the Atmosphere (Plenum, New York, 1982), pp. 133–137.

V. E. Zuev, “Laser-light transmission through the atmosphere,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, New York, 1976), pp. 55–56.

V. E. Zuev, Atmospheric Transparency in the Visible and Infrared (Israel Program for Scientific Translations, Jerusalem, 1970), pp. 92–124.

Aerosol Sci. Technol.

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Figures (14)

Fig. 1
Fig. 1

Typical reference spectrum taken with no cloud present.

Fig. 2
Fig. 2

Measured water-vapor spectrum at 32-cm-1 resolution for a vapor-density increase of 5.2 g/m3. Arrows indicate wave numbers of the comparison in Fig. 6.

Fig. 3
Fig. 3

Refractive index of water as a function of wave number. Solid, long-dashed, dotted, and short-dashed curves are from Refs. 32, 33, 34, and 35, respectively.

Fig. 4
Fig. 4

(a) Optical depth for two settings of the ultrasonic nebulizer as a function of wave number measured (solid curves) and modeled (dotted curves) by means of Lorenz–Mie theory. (b) Water droplet measured counts (solid binned curve) and concentration retrieved by inversion of the greater and lesser optical depths of a) (thin solid and dotted curves, respectively).

Fig. 5
Fig. 5

(a) Optical depth [curves as in Fig. 4(a)] and (b) retrieved droplet spectra for a dissipating fog. The time elapsed between adjacent spectra was 6 s. Arrows in (a) indicate wave numbers of the comparison in Fig. 6.

Fig. 6
Fig. 6

Measured optical depth as a function of time at a strong absorption wave number of water vapor (3747.69 cm-1) and at a nearby less absorbing wave number (4102.87 cm-1). The strongest influence of water-vapor-density changes is seen as a dip before 30 s in the 3747.69-cm-1 curve. Curves are guides to the eye.

Fig. 7
Fig. 7

Water-vapor-density-change as a function of time retrieved from the measured optical depth in Fig. 5(a). The curve is a guide to the eye.

Fig. 8
Fig. 8

Cloud liquid-water content as a function of time computed from droplet size spectra (filled circles) shown in Fig. 5(b) and from Chylek’s parameterization given in Eq. (1) as computed from the measured IR spectra (filled squares). Curves are guides to the eye.

Fig. 9
Fig. 9

Total number concentration (filled squares, left axis) and mean diameter (filled circles, right axis) as a function of time for the dissipating fog as computed from the size spectra of Fig. 5(b). Curves are guides to the eye.

Fig. 10
Fig. 10

Comparison of varying amounts of smoothing applied in the droplet-retrieval algorithm with the measured size spectrum to illustrate the nonuniqueness of size retrieval from a measured optical spectrum [lesser optical-depth curve in Fig. 4(a)]. Smoothing parameters of α = 0 (no smoothing), α = 0.25 (semi-smooth), and α = 0.5 (smooth) were applied in the lower, middle, and upper panels, respectively. The directly measured size spectrum of Fig. 4(b) is shown to aid comparison.

Fig. 11
Fig. 11

(a) Optical depth as a function of wave number measured [solid curve, same as lesser optical-depth curve in Fig. 4(a)] and modeled (dotted curve) with anomalous diffraction theory. (b) Water droplet measured counts (solid curve) and concentration retrieved by inversion of the optical depth (dotted curve). The directly measured size spectrum of Fig. 4(b) is shown to aid comparison.

Fig. 12
Fig. 12

Optical depth during fog evaporation [curves as in Fig. 4(a)].

Fig. 13
Fig. 13

Time-resolved droplet spectra retrieved from optical-depth measurements (upper panel) and normalized significance of droplet contribution to optical depth (lower panel) for an evaporating fog. Water-vapor normalized significance is unity.

Fig. 14
Fig. 14

Microphysical properties of the evaporating fog. The upper panel is vapor-density change, middle panel symbols are the same as in Fig. 8, and the lower panel symbols are the same as in Fig. 9. Curves are guides to the eye.

Tables (1)

Tables Icon

Table 1 Cloud Microphysical Properties and Error between Measured and Synthetic Optical-Depth

Equations (6)

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w=3.91τν=906 cm-1,
τν=Li=1N nDiσDi, ν+i=1Ngngiσgiν,
σDi, ν=1ΔDDi-ΔD/2Di+ΔD/2 σD, νdD
nknew=j=1Nν σSk, νjτmνjL-i=1k-1nioldσSi, νj-i=k+1Nt ninewσSi, νjj=1NνσSk, νj2,
nknew=α2 nk-1old+1-αnknew+α2 nk+1new,
SigSk=nkj=1NνσSk, νj2j=1NνσSk, νjτmνj.

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