Geology Reference
In-Depth Information
incorporate multiple layers of ice and snow as well as
reflection and refraction of radiation at all layer bounda-
ries. It is well known that refraction at the snow‐ice inter-
face causes the incident radiation to be redirected in a
direction closer to the normal to the interface, allowing
deeper penetration into the ice. Model results indicate
that ignoring refraction can lead to a significant overesti-
mation of surface albedo, especially when the solar radia-
tion is incident on bare ice surface at large zenith angles.
Results from
Grenfell
[1983] show how the evolution of ice
thickness affects the albedo (Figure 8.25). The ice thick-
ness range (1-300 cm) in the figure represents a transition
from the gray/black surface of a Nila ice sheet to the
brighter surface of fully grown thick FYI. The model
results confirm the increase of albedo with ice thickness
and its saturation beyond 1 m thick. Note that these
results are of snow‐free ice surface. Albedo attains a
maximum value between approximately 400-550
μ
m
wavelength followed by a rapid decrease beyond 600
μ
m
wavelength. In the NIR spectrum, albedo levels off to a
constant low value (≅0.06) and therefore becomes largely
insensitive to ice thickness [
Allison et al
., 1993;
Light
et al.
, 1998;
Perovich
, 1996]. The albedo of thick ice (≥1 m
thickness) is about eightfold its value for 1 cm ice thick-
ness in the VIS range, but it has the same low value in
the NIR range. The rate of increase of albedo in the VIS
range is higher during the early growth stage (for thickness
<25 cm). Another model to determine albedo from sea ice
in the presence of melt ponds is presented in
Pedersen
et al
. [2009] to support the fifth generation of atmospheric
general circulation model.
As for modeling the spectral albedo of snow
Wiscombe
and Warren
[1980] presented a model that can estimate
albedo at any wavelength in the solar spectrum. It accounts
for direct and diffuse incident radiation. The only adjust-
able parameter in the case of deep snow is the snow grain
size. A second parameter, the liquid‐equivalent depth,
is required for relatively thin snow. Spectral variation of
albedo, calculated for a few values of snow grain radius, is
shown in Figure 8.26a. It can be seen that albedo decreases
at all wavelengths as the grain radius (or snow age)
increases. Albedo in the NIR is more sensitive to grain size
where it may decrease by a factor of 3 or more between
snow grain radii of 50 and 1000
μ
m. By comparison, the
decrease of albedo in the visible range never exceeds
10-15%. The peaks near the wavelengths 0.4, 1.1, 1.3,
1.85, and 2.3
μ
m correspond to minima in absorption
coefficient. The sensitivity of the albedo to the snow grain
1. 0
1 m
3 m
0.8
50 cm
0.6
25 cm
0.4
10 cm
0.2
1 cm
0.0
400
600
800
1000
1200
1500
2000
2500
Wavelength (nm)
Figure 8.25
Modeled spectral albedo from bare sea ice sur-
face with density 0.88 g/cm
3
, salinity 11‰, and temperature
−2.8°C, for different ice thickness [
Grenfell
, 1983, Fig. 4a,
with permission from AGU].
(a)
(b)
1. 0
1. 0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Calculated :
0.9
Solar Zenith = 60°
Diffuse/Direct = 0
A = 200
μ
m
B = 400
μ
m
Grain Radius
0.8
0.7
0.6
0.5
50
μ
m
Depth = semi-infinite
A
Observed :
Dry old snow
Wet melting
Refrozen
100
μ
m
200
μ
m
0.4
0.3
0.2
0.1
0.0
0.2
B
R = 500
μ
m
R = 1000
μ
m
0.4 0.6 0.8 1. 0 .2
1. 4
1. 6 .8
2.0
2.2 2.4 2.6
2.8
0.6
0.8
1. 0 .2
1. 4 .6
1. 8
2.0
2.2
2.4
Wavelength (
μ
m)
Wavelength (
μ
m)
Figure 8.26
Calculated spectral albedo of snow showing (a) the effect of the snow grain radii and (b) the liquid
water content. Comparison of the calculated albedo against laboratory measurements is shown also in (b).
[
Wiscombe and Warren
, 1980, Figure 8, with permission from the American Meteorological Society].
