Geology Reference
In-Depth Information
10.4.1. Thermal Infrared Observations
Table 10.4 Values of ice surface albedo ( α s ) and transmittance
( i 0 ) for four intervals of ice thickness ( H ).
H
In this approach, the term ice thickness is used to
refer to the thermodynamically grown ice (referred to as
thermal ice thickness in some studies) as opposed to
mechanically accumulated ice (forms of deformed ice).
TIR observations were the first remote sensing data used
to calculate ice thickness. However, the calculations are
limited to ice of thickness less than 50. The premise is
the relations between surface temperature and ice thick-
ness within this range. The approach, however, is adversely
affected by clouds (even thin clouds) or fog. The assump-
tions involved in this approach are: (1) the temperature
profile in ice and snow is linear, (2) ice thickness is uni-
form across the sensor's footprint, and (3) the observed
ice is in a state of thermal equilibrium with a constant
seawater temperature.
A one‐dimensional surface energy balance model is
used to derive the ice thickness distribution. Heat flux
through the ice is balanced by the atmospheric heat and
radiation fluxes. A simple linear approximation of this
balance is described by the following equation [ Yu and
Rothrock, 1996] assuming a constant value of surface
temperature (whether snow or ice), i.e., the surface is in a
state of thermal equilibrium:
i 0
α s
≤ 5 cm
0.091571
0.641808
5 cm ≤ H < 20 cm
0.663315
0.604537
20 cm ≤ H < 40 cm
0.777930
0.254103
H ≥ 40 cm
0.799825
0.094115
Source : Rudjord et al. [2011].
on solving equation (10.63) when other parameters are
specified. This  can be achieved after substituting each
term with its appropriate parameterization. Details of
the method are presented in Yu and Rothrock [1996] and
used by several authors including Rudjord et  al. [2011].
It is summarized in the following.
To calculate F r , three terms in equation (10.65) have to
be determined: α s , i 0 , and F sw . AVHRR visible channels
can be used to derive α s [ Lindsay and Rothrock , 1993].
The value of i 0 can be determined as a function of ice
and snow thickness [ Grenfell, 1979]. However, it would
be better to use constant (mean) values of α s and i 0 within
four intervals of ice thickness H as given in Rudjord et al.
[2011]. Table 10.4 includes these values. F sw can be esti-
mated using an expression presented in Bisht et al. [2005]
based on a parameterization by Zillman [1972]:
up
dn
FF FFFF
r
0
(10.63)
l
l
s
e
c
2
FS d
sw
cos
/
(10.66)
0
where F r is the net solar radiation absorbed by the snow
and ice media, F l up and F l dn are the upwelling and down-
welling longwave radiation (the blackbody radiation of
the ice surface and the atmosphere, respectively); F s , F e ,
and F c are the sensible (turbulent), latent, and conductive
heat fluxes, respectively. In the night passes F r should be
neglected. It is also possible to assume F s = F e = 0 as a
first approximation. This assumption is in line with the
finding by Maykut [1978] that these two terms are much
smaller than the incoming longwave radiation. The term
F r can be decomposed into components: the penetrated
shortwave radiation minus the transmitted radiation flux
I 0 through the ice and snow:
where S 0 is the solar constant at the TOA (=136 W/m 2 ),
θ   is the solar zenith angle, and d is a function of θ and
the surface water vapor pressure e a :
3
(10.67)
d
1 085
. os
e a
(. cos)
27
10
01
.
Here e a = fe sa , where f is the relative humidity, which can
be assumed to be 90%, and e sa is the saturation vapor
pressure in hectopascals (hPa), which is estimated by
Maykut [1982] as a fourth‐order polynomial of the air
temperature T a :
(10.64)
F
(
1
)
F
I
64
33
e
2 780 10
.
T
2 691 10
.
T
r
s
sw
0
sa
a
a
0 979
.
T
2
158 638
.
T
9653 19
.2
(10.68)
a
a
where α s is the surface albedo and F sw is the incoming
shortwave radiation. The transmitted radiation through
the ice volume is given by
The second to the fifth terms in equation (10.63) can be
determined as follows. The upward and downward long-
wave radiations are given by the blackbody radiation
(section  7.3.3) from the ice surface and atmosphere,
respectively:
sw
(10.65)
Ii
0 (
)
F
0
s
where i 0 is the transmittance (the term T λ in equation
7.13) ). The method of deriving the ice thickness is based
F
up
T
4
(10.69)
l
i
s
 
Search WWH ::




Custom Search