sources have also been made. In particular, stud-
erties and changes in optical properties (Grenfell
ies were conducted examining the spreading of a
1983, 1991), analyzing the spread of a beam of
collimated beam as it passes through sea ice
light as it passes through ice (Trodahl et al. 1987),
(Trodahl et al. 1987, Gilbert and Schoonmaker
investigating bio-optical interactions (Arrigo et
1990, Voss and Schoonmaker 1992, Voss et al.
al. 1991), examining the transmission of visible
1992). In these experiments a collimated beam of
and ultraviolet light through sea ice (Perovich
light was incident on either the surface or bottom
1990, 1991, 1993) and assessing radiative interac-
of the ice and the spatial distribution of the emer-
tions between the atmosphere, ice and ocean (Jin
gent irradiance was measured. Examining the
et al. 1994).
peak magnitude and the spatial distribution of
These radiative transfer models for sea ice
irradiance provide information on scattering and
range in complexity from a simple wavelength-
absorption in the ice. Laboratory studies indicate
integrated parameterization of an exponential
that scattering in the ice is quite strong, with the
decay law to numerically intricate solutions of
radiation field quickly becoming diffuse, and that
the radiance field in the ice. There are several
there is increased attenuation and scattering for
different models with a variety of solution
colder ice (Gilbert and Schoonmaker 1990, Voss
schemes and different input and output param-
and Schoonmaker 1992). Beam spread measure-
eters; however, the same physics underlies all of
ments, when combined with radiative transfer
these models. They may use different techniques
models, show promise as a means of determining
but they all treat the basic physical properties of
scattering coefficients and phase functions from
absorption and scattering of light in the ice. Be-
multiply scattering sea ice.
cause of their diversity, these models all have
attributes that endorse them for some applica-
tions and restrict them for others. A sampling of
MODELS
sea ice radiative transfer models is presented in
Table 2.
It is evident from the observational data that
One of the distinguishing features of radiative
the optical properties of sea ice vary greatly. The
transfer models is the number of "streams" they
optical properties vary spatially over scales of
consider. The number of streams refers to the num-
only a few meters and they vary temporally as
ber of moments from which the radiance is calcu-
the ice cover melts in the summer and freezes in
lated. Quite common are two-stream models,
the fall. An analysis of optical observations has
where the upwelling and downwelling irradiances
demonstrated that the optical properties of sea
are computed. More streams means more angu-
ice are directly affected by the state and structure
lar detail in the calculated radiance field. The cost
of the ice. Models are essential in interpreting
of this additional detail is more complexity in the
observations and in progressing from a phenom-
computations and often a requirement for more
enological collection of observations to a physi-
detailed information on the optical properties of
cally based understanding of radiative transfer in
the ice.
sea ice.
The simplest sea ice radiative transfer model is
The variability in optical properties also cre-
the exponential decay relationship
ates difficulties in extrapolating observations. In-
F (z, λ) = (1 - α λ ) F0 (λ) e - λ z
κ
dividual observations provide information on the
(5)
optical properties at a particular location at a par-
where F0(λ) is the incident solar irradiance. This
ticular time, but for many problems more general
formulation has the advantage of being simple
information is needed on how the optical proper-
computationally. However, there is an implicit
ties of a region evolve with time. In principle, this
assumption that the medium is infinitely thick,
information can be obtained observationally, but
and consequently, the exponential decay law does
for a large-scale, long-term study this is not prac-
a poor job of representing radiative transfer in
tical. For such studies, models are an essential
thin ice (Grenfell 1979).
tool.
Grenfell (1979) developed a two-stream, three-
Radiative transfer models have been applied
layer model, based on the work of Dunkle and
to a wide range of problems, including estimat-
Bevans (1957), that improved the treatment of
ing the absorption of solar radiation in sea ice
thin ice with only a modest increase in computa-
(Maykut and Untersteiner 1971), studying the re-
tional complexity. The general solution for the
lationship between changes in ice physical prop-
15
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