Table 2. Summary of sea ice radiative transfer models.
Spectral
Number
Solution
Output
Model
Streams range (nm)
of layers
scheme
parameters
Comments
Fd, Fu, α, T
Grenfell (1979)
2
4002150
3
Analytic
Examined thin ice, devel-
oped parameterizations
for α and T as a function
of thickness, isotropic
scattering
I(θ), Fd, Fu, α, T
Perovich and Grenfell (1982) 14
4001000
2
DOM*-analytic
Anistropic scattering, esti-
mate scattering param-
eters from observations
of α and T
I(θ), Fd, Fu, α, T
Grenfell (1983)
16
3502750
1
DOM-numerical
Detailed angular resolution,
optical and physical pro-
perties are related
I (θ,x)
Trodahl et al. (1987)
500, 700
multiple
Monte Carlo
Isotropic and anisotropic
scattering, treats beam
spread
Fd, Fu, α, T
Perovich (1990, 1993)
2
2501000
multiple
Analytic
Ultraviolet and visible wave-
lengths, computationally
simple, easy ice charac-
terization, isotropic scat-
tering
Arrigo et al. (1991)
1
400700
multiple
Exponential
Fd, T
Detailed treatment of im-
pact of biogenic material
on light transmission
I(θ), Fd, Fu, α, T
Grenfell (1992)
4
3502750
multiple
DOM-analytic
Tied closely to ice physical
properties, treats vertical
variability in ice
I(θ), Fd, Fu, α, T
Jin et al. (1994)
select
2504000
multiple
DOM-numerical
Coupled atmosphereice
ocean radiative transfer
absorption model, deter-
mines solar absorption in
each component
*Discrete ordinates method (Chandrasekhar 1960)
(1979) used this model to investigate the depen-
upwelling (Fu) and downwelling (Fd) irradiances
dence of albedo, transmittance, and i0 on thick-
are
ness and ice type. He then used the results to
Fd (z, λ) = A sinh (κ λ z) + B cosh (κ λ z)
derive simple parameterized formulae for αt and
Fu (z, λ) = C sinh (κ λ z) + B cosh (κ λ z)
i0 suitable for use in sea ice thermodynamic
models.
This two-stream formulation was expanded
where A, B, C and D are determined from the
into an n-layer model (Perovich 1990) and ex-
boundary conditions. For an optically thick me-
dium (z → ∞), this solution converges to the ex-
tended into the ultraviolet (Perovich 1993). The
focus of these studies was on the spatial and tem-
ponential decay law (eq 5). The major deficiency
poral variability of reflection, absorption, and
of the two-stream model is its treatment of scat-
transmission of solar radiation by sea ice. To il-
tering, in particular, the simplifying assumption
lustrate the utility of such models let us examine
of isotropic scattering. An important advantage
a particular problem of interest: the transmission
of this formulation is that it directly utilizes the
of visible and ultraviolet light through sea ice in
observations of light extinction in sea ice made
the Weddell Sea during spring. Spring is the pe-
by Grenfell and Maykut (1977) and Perovich and
riod when ozone depletion is the greatest, as is
Grenfell (1981). Because of this, only a qualitative
the consequent increase in incident ultraviolet ir-
description of the ice is needed; blue or white,
radiance and potential biological hazard. Physi-
melting or cold, snow-covered or bare. Grenfell
16
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