Abstract

A laboratory measurement of wavelength dependence in the real n(λ) and the imaginary k(λ) parts of a liquid’s complex refractive index is presented. A known heat flow through the liquid–gas interface is generated while a high-resolution infrared radiance spectrum is taken simultaneously. Wavelength variations of the absorption coefficient allow the emerging radiation to sense subsurface temperature gradients. This technique is valid only at intervals at which the absorption coefficient is sufficiently low to allow subsurface temperatures to be measured. Knowledge of a liquid’s thermal conductivity, specific heat, and light transmission speed is required. Measurement error depends on radiance measurement error and the minimization of atmospheric parameters.

© 1999 Optical Society of America

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References

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  1. W. L. Smith, “Future space-based sounding observations for weather analysis and forecasting,” Adv. Space Res. 12, 175–178 (1992).
    [CrossRef]
  2. H. E. Revercomb, H. Buijs, H. B. Howell, D. D. Laporte, W. L. Smith, L. A. Sromovsky, “Radiometric calibration of IR Fourier transform spectrometers: Solution to problems with the High-resolution Interferometer Sounder,” Appl. Opt. 27, 3210–3218 (1988).
    [CrossRef] [PubMed]
  3. P. Schluessel, W. Emery, H. Grassl, T. Mammen, “On the bulk-skin temperature difference and its impact on satellite remote sensing of sea surface temperature,” J. Geophys. Res. 95, 13,341–13,356 (1990).
    [CrossRef]
  4. K. Katsaros, “The aqueous thermal boundary layer,” Boundary-Layer Meteorol. 18, 107–127 (1980).
    [CrossRef]
  5. D. Plassl, G. F. Edwards, eds., Infrared Handbook (Springer-Verlag, Berlin, 1990).
  6. H. D. Downing, D. Williams, “Optical constants of water in the infrared,” J. Geophys. Res. 80, 1656–1661 (1975).
    [CrossRef]
  7. W. L. Smith, “Iterative solution of the radiative transfer equation for the temperature and absorbing gas profile of an atmosphere,” Appl. Opt. 9, 1993–1999 (1970).
    [CrossRef] [PubMed]
  8. W. F. Feltz, “Meteorological applications of the atmospheric emitted radiance interferometer,” M.S. thesis (Department of Oceanic and Atmospheric Sciences, University of Wisconsin-Madison, Madison, Wisc., 1994).
  9. W. McKeown, F. Bretherton, H. L. Huang, W. L. Smith, H. L. Revercomb, “Sounding the skin of water: sensing air/water interface temperature gradients with interferometry,” J. Atmos. Ocean. Technol. 12, 1313–1327 (1995).
    [CrossRef]

1995 (1)

W. McKeown, F. Bretherton, H. L. Huang, W. L. Smith, H. L. Revercomb, “Sounding the skin of water: sensing air/water interface temperature gradients with interferometry,” J. Atmos. Ocean. Technol. 12, 1313–1327 (1995).
[CrossRef]

1992 (1)

W. L. Smith, “Future space-based sounding observations for weather analysis and forecasting,” Adv. Space Res. 12, 175–178 (1992).
[CrossRef]

1990 (1)

P. Schluessel, W. Emery, H. Grassl, T. Mammen, “On the bulk-skin temperature difference and its impact on satellite remote sensing of sea surface temperature,” J. Geophys. Res. 95, 13,341–13,356 (1990).
[CrossRef]

1988 (1)

1980 (1)

K. Katsaros, “The aqueous thermal boundary layer,” Boundary-Layer Meteorol. 18, 107–127 (1980).
[CrossRef]

1975 (1)

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

1970 (1)

Bretherton, F.

W. McKeown, F. Bretherton, H. L. Huang, W. L. Smith, H. L. Revercomb, “Sounding the skin of water: sensing air/water interface temperature gradients with interferometry,” J. Atmos. Ocean. Technol. 12, 1313–1327 (1995).
[CrossRef]

Buijs, H.

Downing, H. D.

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

Emery, W.

P. Schluessel, W. Emery, H. Grassl, T. Mammen, “On the bulk-skin temperature difference and its impact on satellite remote sensing of sea surface temperature,” J. Geophys. Res. 95, 13,341–13,356 (1990).
[CrossRef]

Feltz, W. F.

W. F. Feltz, “Meteorological applications of the atmospheric emitted radiance interferometer,” M.S. thesis (Department of Oceanic and Atmospheric Sciences, University of Wisconsin-Madison, Madison, Wisc., 1994).

Grassl, H.

P. Schluessel, W. Emery, H. Grassl, T. Mammen, “On the bulk-skin temperature difference and its impact on satellite remote sensing of sea surface temperature,” J. Geophys. Res. 95, 13,341–13,356 (1990).
[CrossRef]

Howell, H. B.

Huang, H. L.

W. McKeown, F. Bretherton, H. L. Huang, W. L. Smith, H. L. Revercomb, “Sounding the skin of water: sensing air/water interface temperature gradients with interferometry,” J. Atmos. Ocean. Technol. 12, 1313–1327 (1995).
[CrossRef]

Katsaros, K.

K. Katsaros, “The aqueous thermal boundary layer,” Boundary-Layer Meteorol. 18, 107–127 (1980).
[CrossRef]

Laporte, D. D.

Mammen, T.

P. Schluessel, W. Emery, H. Grassl, T. Mammen, “On the bulk-skin temperature difference and its impact on satellite remote sensing of sea surface temperature,” J. Geophys. Res. 95, 13,341–13,356 (1990).
[CrossRef]

McKeown, W.

W. McKeown, F. Bretherton, H. L. Huang, W. L. Smith, H. L. Revercomb, “Sounding the skin of water: sensing air/water interface temperature gradients with interferometry,” J. Atmos. Ocean. Technol. 12, 1313–1327 (1995).
[CrossRef]

Revercomb, H. E.

Revercomb, H. L.

W. McKeown, F. Bretherton, H. L. Huang, W. L. Smith, H. L. Revercomb, “Sounding the skin of water: sensing air/water interface temperature gradients with interferometry,” J. Atmos. Ocean. Technol. 12, 1313–1327 (1995).
[CrossRef]

Schluessel, P.

P. Schluessel, W. Emery, H. Grassl, T. Mammen, “On the bulk-skin temperature difference and its impact on satellite remote sensing of sea surface temperature,” J. Geophys. Res. 95, 13,341–13,356 (1990).
[CrossRef]

Smith, W. L.

W. McKeown, F. Bretherton, H. L. Huang, W. L. Smith, H. L. Revercomb, “Sounding the skin of water: sensing air/water interface temperature gradients with interferometry,” J. Atmos. Ocean. Technol. 12, 1313–1327 (1995).
[CrossRef]

W. L. Smith, “Future space-based sounding observations for weather analysis and forecasting,” Adv. Space Res. 12, 175–178 (1992).
[CrossRef]

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

W. L. Smith, “Iterative solution of the radiative transfer equation for the temperature and absorbing gas profile of an atmosphere,” Appl. Opt. 9, 1993–1999 (1970).
[CrossRef] [PubMed]

Sromovsky, L. A.

Williams, D.

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

Adv. Space Res. (1)

W. L. Smith, “Future space-based sounding observations for weather analysis and forecasting,” Adv. Space Res. 12, 175–178 (1992).
[CrossRef]

Appl. Opt. (2)

Boundary-Layer Meteorol. (1)

K. Katsaros, “The aqueous thermal boundary layer,” Boundary-Layer Meteorol. 18, 107–127 (1980).
[CrossRef]

J. Atmos. Ocean. Technol. (1)

W. McKeown, F. Bretherton, H. L. Huang, W. L. Smith, H. L. Revercomb, “Sounding the skin of water: sensing air/water interface temperature gradients with interferometry,” J. Atmos. Ocean. Technol. 12, 1313–1327 (1995).
[CrossRef]

J. Geophys. Res. (2)

P. Schluessel, W. Emery, H. Grassl, T. Mammen, “On the bulk-skin temperature difference and its impact on satellite remote sensing of sea surface temperature,” J. Geophys. Res. 95, 13,341–13,356 (1990).
[CrossRef]

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

Other (2)

D. Plassl, G. F. Edwards, eds., Infrared Handbook (Springer-Verlag, Berlin, 1990).

W. F. Feltz, “Meteorological applications of the atmospheric emitted radiance interferometer,” M.S. thesis (Department of Oceanic and Atmospheric Sciences, University of Wisconsin-Madison, Madison, Wisc., 1994).

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Figures (6)

Fig. 1
Fig. 1

Variation in the absorption coefficient of water in the 3–5-µm region. Data from Ref. 5.

Fig. 2
Fig. 2

Brightness temperature spectrum of radiance that emerges from cooled water. Area of interest shows an upward bulge, indicating a variation of absorption with wavelength.

Fig. 3
Fig. 3

Section of the brightness temperature spectrum from Fig. 2 used in the example.8

Fig. 4
Fig. 4

Comparison of measured and modeled temperature gradients in an air–water interface.8

Fig. 5
Fig. 5

Difference in the known and the measured alpha as calculated with Eq. (3).

Fig. 6
Fig. 6

Percent error in measured alpha as calculated by Eq. (3).

Tables (1)

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Table 1 Radiometric Performance of MAERI at NIST

Equations (31)

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Robs=τatmosεRfluid+τatmosτatmos1-εRatmos+τatmosRatmos,
=z-zsfc Bλ, Tfluiddτfluiddzdz,
=zsfc0 Bλ, Tairpdτatmoszsfc, zdzdz;
=0zsfc Bλ, Tairzdτatmos0, zdzdz;
τatmos=Aτ=Bτ.
ε=Robs-Ratmos-RatmosτatmosRfluid-Ratmosτatmos.
εvλ=1-nλ-12+kλ2nλ+12+kλ2.
1-nλ-12+kλ2nλ+12+kλ2=Robs-Ratmos-RatmosτatmosRfluid-Ratmosτatmos.
Qtot=ΔTfluid/ΔtCpVρA-Cor,
Qtotκ=ΔTΔz,
τfluidλ=exp-αλz,
αλ=ccfluidλ4π kλ;
ζλ=1αλ.
Rfluidλ, z=Tbλ2, Rfluidz-Tbλ1, Rfluidzζλ2-ζλ1=ΔTbλ, RfluidΔζλ  ΔTfluidΔz=Qtotκ,
Δζλ=κQtot ΔTbλ, Rfluid=κQtot ΔTfluid.
Tz=Tbζ=Tsfc+Qtotκ.
αcalculated=BλmeasuredBλcalculated αknown+αknown, αerror=αcalculatedαknown 100,
ε=fRobs, Ratmos, Ratmos, Rfluid, τatmos.
σε2=σRobs2δεδRobs2+σRatmos2δεδRatmos2+σRatmos2δεδRatmos2+σRfluid2δεδRfluid2+στatmosτ2δεδτatmos2+2σRobsτatmosδεδRobsδεδτatmos+2σRatmosτatmosδεδRatmosδεδτatmos+2σRatmosτatmosδεδRatmosδεδτatmos+2σRfluidτatmosδεδRfluidδεδτatmos.
σRatmos, τatmos2=0, σRfluid,τatmos2=0, σRatmos,τatmos2=0.
σε2=σRobs2+σRatmos2+σRatmos2+σRfluid2+στatmosτ2+2σRobsτatmos=7σRobs2=1.575×10-7.
n-12+k2n+12+k20.017.
n2-2n+1+k2n2+2n+1+k2,
σn22n4=2 σnn, σ-2n2-2n=σnn, σ+2n2+2n=σnn, σk22k4=σkk,
σk2=kk, σ2n=n, σ-2n=-2n, σn2=2nn,
σε2ε2=4n+1σn+2kσk=1.575×10-7.
σΔζ2ζ2=σΔTb2ΔTb2+σQtot2Qtot2-2 σQtotΔTb2QtotΔTb.
σΔζ2=0.01ζ2.
σα2=0.01α2.
σα2=0.01 ccfluidλkλ4π2,
σε2=1.57510-7nλ-12+kλ2nλ+12+kλ22.

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