Stephen G. Warren,1
Richard E. Brandt,1
and Thomas C. Grenfell1
1The authors are with the Department of Atmospheric Sciences, University of Washington, Seattle, Washington 98195. The e-mail address for S. G. Warren is sgw@atmos.washington.edu.
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)
Snow is a scattering-dominated medium whose scattering is independent of
wavelength at
. 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
.
The method is applied to clean Antarctic snow; the absorption minimum is at
,
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
, by
comparison with
for AMANDA and
from laboratory attenuation
measurements.
Per Askebjer, Steven W. Barwick, Lars Bergström, Adam Bouchta, Staffan Carius, Eva Dalberg, Kevin Engel, Bengt Erlandsson, Ariel Goobar, Lori Gray, Allan Hallgren, Francis Halzen, Hans Heukenkamp, Per Olof Hulth, Stephan Hundertmark, John Jacobsen, Albrecht Karle, Vijaya Kandhadai, Igor Liubarsky, Doug Lowder, Tim Miller, Pat Mock, Robert M. Morse, Rodin Porrata, P. Buford Price, Austin Richards, Hector Rubinstein, Eric Schneider, Christian Spiering, Ole Streicher, et al. Appl. Opt. 36(18) 4168-4180 (1997)
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Dependences of Radiative Transfer Quantities within the Domains of 350–600 nm for Wavelength λ, 20–200 μm for Snow Grain Radius ri, and 0–100 ppb for Soot Concentration C
Dependent On
Quantity
λ
ri
C
σext
No
Yes
No
σabs
Yes
No
Yes
Yes
Yes
Yes
No
No
No
Table 2
Upper Limit for Absorption Coefficient of Pure Ice, Obtained from Snow Transmission Measurements in Layer Ca
λ (nm)
kice (m−1)
kice− (m−1)
kice+ (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
The values are a smoothed version of the plot in Fig. 7(b) (also shown in Fig. 5). This upper limit is obtained by assuming that all the absorption at all wavelengths is due to ice. The central estimate of this upper limit is kice, a smoothed version of the upper-limit line in Fig. 7(b). Uncertainty in the linear slopes in Fig. 3 propagates to a range of values from to , corresponding to 1 standard deviation of the slope estimate. The values of and listed here are smoothed boundaries of the shaded region in Fig. 7(b).
Tables (2)
Table 1
Dependences of Radiative Transfer Quantities within the Domains of 350–600 nm for Wavelength λ, 20–200 μm for Snow Grain Radius ri, and 0–100 ppb for Soot Concentration C
Dependent On
Quantity
λ
ri
C
σext
No
Yes
No
σabs
Yes
No
Yes
Yes
Yes
Yes
No
No
No
Table 2
Upper Limit for Absorption Coefficient of Pure Ice, Obtained from Snow Transmission Measurements in Layer Ca
λ (nm)
kice (m−1)
kice− (m−1)
kice+ (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
The values are a smoothed version of the plot in Fig. 7(b) (also shown in Fig. 5). This upper limit is obtained by assuming that all the absorption at all wavelengths is due to ice. The central estimate of this upper limit is kice, a smoothed version of the upper-limit line in Fig. 7(b). Uncertainty in the linear slopes in Fig. 3 propagates to a range of values from to , corresponding to 1 standard deviation of the slope estimate. The values of and listed here are smoothed boundaries of the shaded region in Fig. 7(b).