smaller platelets, higher salinity, and more
1.0
brine inclusions (Weeks and Ackley 1982).
A
B
This is consistent with our premise that
a
more inclusions means more scattering
0.8
b
and higher albedos.
The Monte Carlo method is another
c
approach to radiative transfer modeling.
a
d
0.6
As the name implies, Monte Carlo models
b
e
c
take a statistical approach to solving the
equation of radiative transfer (eq 2). In
d
short, the absorption coefficient, the scat-
0.4
tering coefficient and the phase function
are transformed into the probability that
over a given distance a photon is absorbed
0.2
or scattered, and if scattered, in what di-
rection. With these probabilities known,
enormous numbers of photons are numeri-
cally "shot" into the medium. The fate of
0
400 600 800 1000 1200 1400 400 600 800 1000 1200 1400
each photon is decided by the roll of the
Wavelength (nm)
dice, or more precisely, the whim of the
Figure 18. Calculated estimates of spectral albedo as a function of
random number generator. Radiative
ice density and growth rate (from Grenfell 1983). The ice was 3
transfer in the medium is described by
m thick. The air volume was zero for the growth rate simulation.
the cumulative result of all the photons.
Figure 18a shows albedo as a function of ice density (ρ): a) ρ =
Because of the large number of photons
0.86 g cm3, b) ρ=0.88 g cm3, c) ρ = 0.90 g cm3, d) ρ = 0.91 g
needed, Monte Carlo models are very in-
cm3 and e) ρ = 0.94 g cm3. Figure 18 shows albedo as a func-
efficient computationally. They are, how-
tion of growth rate (f) for a) f = 8 105 cm s1, b) f = 4 105
ever, simple conceptually, simple to pro-
cm s1, c) f = 2 105 cm s1 and d) f = 8 106 cm s1 .
gram, and widely applicable (Mobley
1994). This method is particularly well
suited for complex geometries or boundary con-
ficients depended explicitly on the amount and
ditions, where other solutions to the equation of
size distribution of air bubbles and brine pockets.
radiative transfer are difficult or impossible.
These values in turn depended on the ice growth
Trodahl et al. (1987) and Trodahl and Buckley
conditions, thermal history, temperature, salinity
(1989) effectively used Monte Carlo solutions in
and density. With this formulation, it was pos-
beam spread studies, both to model observations
sible to theoretically explore the impact of growth
and infer information on the scattering proper-
conditions and thermal history on spectral albe-
ties of sea ice. They found that scattering in the
dos and extinction coefficients. For example, Fig-
surface layer of the ice was greater than in the
ure 18 shows calculated estimates of spectral al-
interior and that the scattering was anisotropic.
bedo for different ice densities and ice growth
An exciting new modeling development has
rates. The ice was 3 m thick in these cases. The
been the inclusion of biological effects in sea ice
large impact of air bubbles on scattering and ice
optical models. Sea ice is the habitat of a rich
optical properties is demonstrated in Figure 18a.
microbial community (Palmisano and Sullivan
There is an increase in albedo as the ice density
1983, Garrison et al. 1986). Ice biota both affect
decreases and the number of air bubbles increases.
and are affected by the spectral irradiance within
This increase is most pronounced at 470 nm, where
the ice. Arrigo et al. (1991) developed a bio-opti-
absorption is smallest. The albedo at 470 nm was
about 0.57 for bubble-free ice (ρ = 0.94) and in-
cal model to investigate the interdependence be-
tween biology and transmitted light. They used a
creased to 0.84 for bubbly ice with an air volume
of 8% (ρ = 0.86). Calculations also indicated that
simple exponential decay law to model irradi-
ance within the ice, but they coupled this with a
faster growth rates result in larger albedos (Fig.
sophisticated treatment of the extinction coeffi-
18b). For these calculations the air volume was
cients (κ). They formulated polynomial relation-
assumed to be zero, so changes in albedo resulted
ships defining spectral extinction coefficients for
from changes in the platelet spacing and the num-
dry snow, wet snow, congelation ice, platelet ice,
ber of brine inclusions. Faster grown ice has
18
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