radiance, I (z, λ), are even more pronounced,
tegral over angle is equal to one. The second term
provides the contribution of scattered light from
being exponentially greater than the changes in
the attenuated direct beam E0(λ). This term is
absorption coefficient.
needed only if there is direct incident irradiance
Examining the e-folding length gives a better
as well as a diffuse component.
understanding of the absorption coefficients. The
e-folding length is the amount of ice needed to
reduce the incident light (I (0, λ)) by 1/e (i.e., the
Absorption
transmitted light is 37% of the incident). e-folding
It is time to examine absorption and scattering
lengths for ice decrease sharply from 24 m at 470
in sea ice in detail, starting with absorption be-
nm, to 8 m at 600 nm, to 2 m at 700 nm, to 0.05 m
cause it is the simpler of the two processes. Con-
at 1000 nm, to 0.006 m at 1400 nm. This indicates
sider the case of absorption only for a direct beam
that ice is quite transparent in the blue, while it
of light normally incident on a medium. Since
there is no scattering, S = 0 and σ = 0. For normal
takes only a few centimeters of ice to absorb most
incidence, θ = 0, which means = 1. Equation 2
of the light beyond 1000 nm.
As Figure 5 indicates, absorption coefficients
then reduces to
for clean Arctic water are similar in magnitude
-dI (z, λ)
and spectral shape to values for pure ice. An ab-
= I (z, λ)
k (λ) dz
sorption coefficient for sea ice ksi is determined
by combining the absorption coefficients for the
constituent components of brine and ice using
which, when solved, gives the familiar exponen-
tial decay law
ksi = νi ki + νb kb
(4)
I (z, λ) = I (0, λ) e -kz
where νi and νb represent the volume fraction of
(3)
ice and brine, and ki and kb are the absorption
also known as Beer 's law or the Bouguer-Lam-
bert law. Radiative transfer in a purely absorbing
10 3
medium is quite simple to describe. The radiance
decreases exponentially with depth in the me-
dium, with the rate of decrease dependent on the
absorption coefficient. What needs to be known
are the absorption coefficients for the primary
10 2
components of sea ice: ice, brine and air. Equa-
tion 3 implies that absorption coefficients can be
determined by measuring the incident radiance,
Clear
the transmitted radiance, and the thickness of a
Seawater
1
10
Pure, Bubble-free
homogeneous sample that is free of scatterers
Ice
(Grenfell and Perovich 1981).
Absorption in the air inclusions in sea ice is
negligible, so absorption coefficients for air are
10 0
assumed to be zero. Spectral absorption coeffi-
cients from the ultraviolet to the near-infrared
for ice and seawater are shown in Figure 5. Ab-
sorption coefficients for ice were determined
using pure, bubble-free, fresh ice (Grenfell and
10 1
Perovich 1984, Perovich and Govoni 1991), and
absorption coefficients for brine taken from mea-
surements of clear Arctic water (Tyler and Smith
1970, Smith and Baker 1981). The minimum ab-
2
10
sorption and therefore maximum transmission
200
400
600
800
1000
1200
1400
Wavelength (nm)
for ice is in the blue part of the electromagnetic
spectrum at 470 nm. Spectral changes in ab-
Figure 5. Absorption coefficients of pure, bubble-free
sorption coefficient are extremely large, span-
ice (Grenfell and Perovich 1981, Perovich and Govoni
ning several orders of magnitude from 250 to
1991) and clear sea water (Tyler and Smith 1970, Smith
1400 nm. Spectral differences in the transmitted
and Baker 1981).
5
Previous Page
