Table 1. Values of i0 and κt
rather than air bubbles, and the amount of scat-
(Grenfell and Maykut 1977).
tering is less and extinction coefficients are re-
duced. The much smaller values of extinction co-
κt (m1)
Case
i0
efficient for bubble-free ice and clear Arctic water
illustrate how significant scattering is in sea ice.
Clear
Blue ice
0.43
1.5
The importance of scattering is illustrated by the
White ice
0.18
1.6
rough rule of thumb that extinction through 1 cm
of snow is approximately the same as through 10
Cloudy
Blue ice
0.63
1.4
cm of ice or 100 cm of water.
White ice
0.35
1.5
As was the case for albedo (Fig. 11), extinction
coefficients also depend on the internal structure
of the ice (Zaneveld 1966, Grenfell and Maykut
spectral albedo and the spectral extinction coeffi-
1977, Perovich and Grenfell 1981, Gilbert and
cient. Since all of these quantities vary with wave-
Buntzen 1986). Extinction coefficients decrease
length, the total extinction coefficient does not
during warming as the brine volume increases
depend entirely on the properties of the ice. As
and the number of inclusions decrease. Also, at a
was the case for total albedo, the total extinction
given brine volume extinction coefficients are
coefficient depends on sky conditions. On sunny
larger for faster grown ice, which has more inclu-
days the incident irradiance has a larger longwave
sions. In these experiments the ice was changing
component, which is absorbed rapidly in the ice,
internally, but the only change in surface condi-
resulting in higher values of κt. More significantly,
tions was a slight wetting as the air temperature
approached 0C. The results would be quite dif-
surface. Observations have shown that the spec-
ferent if there were brine drainage from the sur-
tral transmittance changes greatly near the sur-
face layer of the ice as a result of the warming. In
face of the ice due to the rapid extinction of the
that case the resulting air voids would form a
highly scattering surface layer, and albedos and
near the ice surface and decreases by more than
extinction coefficients would increase. This would
an order of magnitude in the top 0.1 m of the ice
be expected in thicker ice with more freeboard.
(Grenfell and Maykut 1977). Below 0.1 m, only
Such an effect has been observed in the Antarctic,
visible light remains, where the spectral depen-
where low humidities keep the ice surface free of
dence of κλ is weaker, and changes in κt with
water during melt (Andreas and Ackley 1981).
depth are small. Total extinction coefficients have
Observations made in McMurdo Sound, Antarc-
been used in sea ice thermodynamic models
tica (Trodahl et al. 1987, Buckley and Trodahl 1987,
(Maykut and Untersteiner 1971) to calculate the
Trodahl and Buckley 1990), have shown that as
surface heat balance and solar heating in the ice
the ice warms, a drained surface layer forms re-
interior. To do this Maykut and Untersteiner (1971)
sulting in an increase in backscatter and a de-
modified the exponential decay law to the form:
crease in transmittance.
Fd (z) = i0 Fd (0) e -κ t z for z > 0.1 m
Observations of total light transmission have
been used to determine wavelength-integrated,
or total, extinction coefficients (κt). Values for sea
ice are in the 1.1 to 1.5 m1 range (Untersteiner
grated incident irradiance transmitted through the
top 0.1 m of the ice and κt is the total extinction
1961, Chernogovskiy 1963, Thomas 1963, Weller
coefficient in the ice below 0.1 m. Values of κt
and Schwerdtfeger 1967). Extinction coefficients
for snow are much larger, varying from 4.3 m1
below 0.1 m and i0 determined from field obser-
for dense Antarctic snow (Weller and Schwerdt-
vations (Grenfell and Maykut 1977) are summa-
feger 1967) to as high as 40 m1 in freshly fallen
rized in Table 1. There is more scattering in white
snow (Thomas 1963). Though total extinction co-
ice than blue ice, resulting in a smaller i0 and a
larger κt.
efficients are simpler to measure and simpler to
use computationally than spectral values, they
are severely limited. The total extinction coeffi-
Beam spread
cient combines contributions from different wave-
While much of the observational emphasis has
lengths and therefore depends on the spectral dis-
been on measurements of transmitted solar irra-
tribution of transmitted irradiance, which in turn
diance to determine transmittance and extinction
depends on the spectral incident irradiance, the
coefficient, measurements using artificial light
14
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