Visible and near-ultraviolet absorption spectrum of ice from transmission of solar radiation into snow

Stephen G. Warren; Richard E. Brandt; Thomas C. Grenfell

doi:10.1364/AO.45.005320

Visible and near-ultraviolet absorption spectrum of ice from transmission of solar radiation into snow

Stephen G. Warren, Richard E. Brandt, and Thomas C. Grenfell

Applied Optics
Vol. 45,
Issue 21,
pp. 5320-5334
(2006)
•https://doi.org/10.1364/AO.45.005320

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Stephen G. Warren, Richard E. Brandt, and Thomas C. Grenfell, "Visible and near-ultraviolet absorption spectrum of ice from transmission of solar radiation into snow," Appl. Opt. 45, 5320-5334 (2006)

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Related Topics
Table of Contents Category
- Atmospheric and Oceanic Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Ice crystal phenomena (010.2940)
- Optical properties (160.4760)
- Multiple scattering (290.4210)

About this Article
History
- Original Manuscript: November 23, 2005
- Revised Manuscript: February 14, 2006
- Manuscript Accepted: February 14, 2006
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Abstract

Snow is a scattering-dominated medium whose scattering is independent of wavelength at $350 - 600 nm$ . The attenuation of solar radiation in snow can be used to infer the spectral absorption coefficient of pure ice, by reference to a known value at $600 nm$ . The method is applied to clean Antarctic snow; the absorption minimum is at $390 nm$ , and the inferred absorption coefficient is lower than even the lowest values of the Antarctic Muon and Neutrino Detector Array (AMANDA) experiment on glacier ice: The absorption length is at least $700 m$ , by comparison with $240 m$ for AMANDA and $10 m$ from laboratory attenuation measurements.

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	Dependent On
Quantity	λ	r_i	C
σ_ext	No	Yes	No
σ_abs	Yes	No	Yes
$(1 - \bar{ω})$	Yes	Yes	Yes
$(1 - \bar{ω} g)$	No	No	No

λ (nm)	k _ice (m⁻¹)	k _ice ⁻ (m⁻¹)	k _ice ⁺ (m⁻¹)
350	1.78 × 10⁻³	8.38 × 10⁻⁴	3.08 × 10⁻³
355	1.45 × 10⁻³	6.48 × 10⁻⁴	2.60 × 10⁻³
360	1.25 × 10⁻³	5.12 × 10⁻⁴	2.33 × 10⁻³
365	1.08 × 10⁻³	4.02 × 10⁻⁴	2.08 × 10⁻³
370	9.21 × 10⁻⁴	3.11 × 10⁻⁴	1.86 × 10⁻³
375	8.11 × 10⁻⁴	2.49 × 10⁻⁴	1.70 × 10⁻³
380	7.31 × 10⁻⁴	2.06 × 10⁻⁴	1.59 × 10⁻³
385	6.60 × 10⁻⁴	1.71 × 10⁻⁴	1.47 × 10⁻³
390	6.38 × 10⁻⁴	1.63 × 10⁻⁴	1.43 × 10⁻³
395	6.79 × 10⁻⁴	1.83 × 10⁻⁴	1.50 × 10⁻³
400	7.43 × 10⁻⁴	2.17 × 10⁻⁴	1.59 × 10⁻³
405	7.82 × 10⁻⁴	2.40 × 10⁻⁴	1.64 × 10⁻³
410	8.18 × 10⁻⁴	2.61 × 10⁻⁴	1.69 × 10⁻³
415	8.62 × 10⁻⁴	2.86 × 10⁻⁴	1.75 × 10⁻³
420	9.38 × 10⁻⁴	3.31 × 10⁻⁴	1.86 × 10⁻³
425	1.04 × 10⁻³	3.96 × 10⁻⁴	2.01 × 10⁻³
430	1.21 × 10⁻³	5.04 × 10⁻⁴	2.24 × 10⁻³
435	1.47 × 10⁻³	6.76 × 10⁻⁴	2.59 × 10⁻³
440	1.79 × 10⁻³	8.95 × 10⁻⁴	3.00 × 10⁻³
445	2.15 × 10⁻³	1.16 × 10⁻³	3.47 × 10⁻³
450	2.58 × 10⁻³	1.48 × 10⁻³	4.01 × 10⁻³
455	3.05 × 10⁻³	1.84 × 10⁻³	4.59 × 10⁻³
460	3.62 × 10⁻³	2.28 × 10⁻³	5.28 × 10⁻³
465	4.33 × 10⁻³	2.85 × 10⁻³	6.13 × 10⁻³
470	5.23 × 10⁻³	3.59 × 10⁻³	7.21 × 10⁻³
475	6.29 × 10⁻³	4.47 × 10⁻³	8.46 × 10⁻³
480	7.49 × 10⁻³	5.48 × 10⁻³	9.84 × 10⁻³
485	8.91 × 10⁻³	6.71 × 10⁻³	1.15 × 10⁻²
490	1.07 × 10⁻²	8.25 × 10⁻³	1.35 × 10⁻²
495	1.27 × 10⁻²	9.99 × 10⁻³	1.57 × 10⁻²
500	1.48 × 10⁻²	1.18 × 10⁻²	1.82 × 10⁻²
505	1.72 × 10⁻²	1.39 × 10⁻²	2.09 × 10⁻²
510	1.98 × 10⁻²	1.62 × 10⁻²	2.39 × 10⁻²
515	2.28 × 10⁻²	1.89 × 10⁻²	2.71 × 10⁻²
520	2.60 × 10⁻²	2.18 × 10⁻²	3.07 × 10⁻²
525	2.96 × 10⁻²	2.51 × 10⁻²	3.45 × 10⁻²
530	3.34 × 10⁻²	2.87 × 10⁻²	3.87 × 10⁻²
535	3.76 × 10⁻²	3.26 × 10⁻²	4.32 × 10⁻²
540	4.22 × 10⁻²	3.69 × 10⁻²	4.80 × 10⁻²
545	4.71 × 10⁻²	4.16 × 10⁻²	5.31 × 10⁻²
550	5.23 × 10⁻²	4.67 × 10⁻²	5.84 × 10⁻²
555	5.78 × 10⁻²	5.21 × 10⁻²	6.40 × 10⁻²
560	6.37 × 10⁻²	5.80 × 10⁻²	6.99 × 10⁻²
565	6.99 × 10⁻²	6.43 × 10⁻²	7.59 × 10⁻²
570	7.63 × 10⁻²	7.10 × 10⁻²	8.21 × 10⁻²
575	8.31 × 10⁻²	7.81 × 10⁻²	8.84 × 10⁻²
580	9.01 × 10⁻²	8.56 × 10⁻²	9.48 × 10⁻²
585	9.73 × 10⁻²	9.36 × 10⁻²	1.01 × 10⁻¹
590	1.05 × 10⁻¹	1.02 × 10⁻¹	1.08 × 10⁻¹
595	1.12 × 10⁻¹	1.11 × 10⁻¹	1.14 × 10⁻¹
600	1.20 × 10⁻¹	1.20 × 10⁻¹	1.20 × 10⁻¹

	Dependent On
Quantity	λ	r_i	C
σ_ext	No	Yes	No
σ_abs	Yes	No	Yes
$(1 - \bar{ω})$	Yes	Yes	Yes
$(1 - \bar{ω} g)$	No	No	No

λ (nm)	k _ice (m⁻¹)	k _ice ⁻ (m⁻¹)	k _ice ⁺ (m⁻¹)
350	1.78 × 10⁻³	8.38 × 10⁻⁴	3.08 × 10⁻³
355	1.45 × 10⁻³	6.48 × 10⁻⁴	2.60 × 10⁻³
360	1.25 × 10⁻³	5.12 × 10⁻⁴	2.33 × 10⁻³
365	1.08 × 10⁻³	4.02 × 10⁻⁴	2.08 × 10⁻³
370	9.21 × 10⁻⁴	3.11 × 10⁻⁴	1.86 × 10⁻³
375	8.11 × 10⁻⁴	2.49 × 10⁻⁴	1.70 × 10⁻³
380	7.31 × 10⁻⁴	2.06 × 10⁻⁴	1.59 × 10⁻³
385	6.60 × 10⁻⁴	1.71 × 10⁻⁴	1.47 × 10⁻³
390	6.38 × 10⁻⁴	1.63 × 10⁻⁴	1.43 × 10⁻³
395	6.79 × 10⁻⁴	1.83 × 10⁻⁴	1.50 × 10⁻³
400	7.43 × 10⁻⁴	2.17 × 10⁻⁴	1.59 × 10⁻³
405	7.82 × 10⁻⁴	2.40 × 10⁻⁴	1.64 × 10⁻³
410	8.18 × 10⁻⁴	2.61 × 10⁻⁴	1.69 × 10⁻³
415	8.62 × 10⁻⁴	2.86 × 10⁻⁴	1.75 × 10⁻³
420	9.38 × 10⁻⁴	3.31 × 10⁻⁴	1.86 × 10⁻³
425	1.04 × 10⁻³	3.96 × 10⁻⁴	2.01 × 10⁻³
430	1.21 × 10⁻³	5.04 × 10⁻⁴	2.24 × 10⁻³
435	1.47 × 10⁻³	6.76 × 10⁻⁴	2.59 × 10⁻³
440	1.79 × 10⁻³	8.95 × 10⁻⁴	3.00 × 10⁻³
445	2.15 × 10⁻³	1.16 × 10⁻³	3.47 × 10⁻³
450	2.58 × 10⁻³	1.48 × 10⁻³	4.01 × 10⁻³
455	3.05 × 10⁻³	1.84 × 10⁻³	4.59 × 10⁻³
460	3.62 × 10⁻³	2.28 × 10⁻³	5.28 × 10⁻³
465	4.33 × 10⁻³	2.85 × 10⁻³	6.13 × 10⁻³
470	5.23 × 10⁻³	3.59 × 10⁻³	7.21 × 10⁻³
475	6.29 × 10⁻³	4.47 × 10⁻³	8.46 × 10⁻³
480	7.49 × 10⁻³	5.48 × 10⁻³	9.84 × 10⁻³
485	8.91 × 10⁻³	6.71 × 10⁻³	1.15 × 10⁻²
490	1.07 × 10⁻²	8.25 × 10⁻³	1.35 × 10⁻²
495	1.27 × 10⁻²	9.99 × 10⁻³	1.57 × 10⁻²
500	1.48 × 10⁻²	1.18 × 10⁻²	1.82 × 10⁻²
505	1.72 × 10⁻²	1.39 × 10⁻²	2.09 × 10⁻²
510	1.98 × 10⁻²	1.62 × 10⁻²	2.39 × 10⁻²
515	2.28 × 10⁻²	1.89 × 10⁻²	2.71 × 10⁻²
520	2.60 × 10⁻²	2.18 × 10⁻²	3.07 × 10⁻²
525	2.96 × 10⁻²	2.51 × 10⁻²	3.45 × 10⁻²
530	3.34 × 10⁻²	2.87 × 10⁻²	3.87 × 10⁻²
535	3.76 × 10⁻²	3.26 × 10⁻²	4.32 × 10⁻²
540	4.22 × 10⁻²	3.69 × 10⁻²	4.80 × 10⁻²
545	4.71 × 10⁻²	4.16 × 10⁻²	5.31 × 10⁻²
550	5.23 × 10⁻²	4.67 × 10⁻²	5.84 × 10⁻²
555	5.78 × 10⁻²	5.21 × 10⁻²	6.40 × 10⁻²
560	6.37 × 10⁻²	5.80 × 10⁻²	6.99 × 10⁻²
565	6.99 × 10⁻²	6.43 × 10⁻²	7.59 × 10⁻²
570	7.63 × 10⁻²	7.10 × 10⁻²	8.21 × 10⁻²
575	8.31 × 10⁻²	7.81 × 10⁻²	8.84 × 10⁻²
580	9.01 × 10⁻²	8.56 × 10⁻²	9.48 × 10⁻²
585	9.73 × 10⁻²	9.36 × 10⁻²	1.01 × 10⁻¹
590	1.05 × 10⁻¹	1.02 × 10⁻¹	1.08 × 10⁻¹
595	1.12 × 10⁻¹	1.11 × 10⁻¹	1.14 × 10⁻¹
600	1.20 × 10⁻¹	1.20 × 10⁻¹	1.20 × 10⁻¹

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