Thermodynamics of Atmospheres and Oceans
Sea Ice
1. Circle all true statements about the salinity of sea ice (section 10.3):
a) Sea ice has a greater salinity than sea water from which it is formed, because brine
pockets concentrate the salt in sea ice
b) Thin ice has a higher salinity than thick ice
c) Meltwater flushing is the primary mechanism for decreasing salinity in multiyear ice
2. Circle all of the following characteristics of sea ice that influence the sea ice density
(section 10.4):
a) specific heat capacity
b) temperature
c) salinity
d) snow cover
e) air bubble volume
3. The specific heat capacity of sea ice will be largest under the following conditions
(section 10.4):
a) -2C, 14 psu
b) -2C, 5 psu
c) -10C, 14 psu
d) -10C, 5 psu
4. Rank the following sea ice surface types by albedo, with 1 for the lowest albedo and 4
for the highest albedo (section 10.5)
_____3_______ bare sea ice
_____4_______ snow-covered sea ice
_____1_______ open water in leads
_____2_______ ponded melting sea ice
Consider the following application of Beer's law to sea ice. Since the density of the
absorber is constant with depth and the absorption coefficient is constant with depth,
Beer's law can be written in the following simplified form using fluxes (section 10.5):
F z = F 0 1  0  exp  k 
v,ext
z
where k is the volume absorption coefficient.
5. What are the units of the volume absorption coefficient??
m-1
6. The penetration depth, d, is defined as d=1/k. The penetration depth can be
interpreted as the depth to which the incoming beam of radiation is diminished by 1/e
owing to absorption. The volume absorption coefficients of sea ice in two different
spectral intervals (visible and near infrared) are given in the table below. Calculate the
penetration depth in sea ice for these two spectral bands.
visible
near infrared
wavelength
0.25-0.7 m
0.7 -1.2 m
absorption coefficient (m-1)
1.4
17.6
penetration depth (m)
d=1/k
1/1.4=0.41 visible
1/17.6 = .0568 near infrared
7. In which spectral band (visible or near infrared) is radiation more likely to penetrate
through the sea ice and into the ocean? Visible has the greater penetration depth between
the two.
8. During winter, the surface temperature of thin (10 cm) sea ice is (warmer, cooler, the
same as) thick multi-year ice (3 m). (section 10.6) Warmer. As indicated by figure 10.9
multiyear ice is colder than first year ice.
9. During winter, the surface sensible heat flux of thin (10 cm) sea ice is (greater than,
less than, equal to) that for thick multi-year ice (3 m). (section 10.6)
greater than
The sensible heat flux from the sea ice to the adjacent air layer will be greater for the
conditions of larger temp gradient. Since the surface temp of thin ice is always warmer
than that of the air, the SH flux from thin ice is always greater than it is for multiyear ice.
10. The wintertime growth rate for thin ice (10 cm) is (greater than, less than, equal to)
that for multi-year ice. (section 10.7.1)
greater than
11. Compare the conductive heat flux, Fc, for a slab of snow with thickness 10 cm thick
and a temperature gradient of 5°C across this distance for snow of the following
characteristics:
According to 10.21
κs=aρ2 using a=2.8456x10^-6
a) new snow,  = 100 kg m-3
3 2
Fc= κs *(dT/dz) = 2.8456x10-6*(100 kg m- ) *(5ºC/.1m)1.4 W/m2
b) settled snow,  = 250 kg m-3
8.9 W/m2
c) wind packed snow,  = 400 kg m-3
22.8 W/m2
d) firn,  = 550 kg m-3
43.0 W/m2
e) very wet snow and firn,  = 700 kg m-3
69.7 W/m2
f) glacier ice,  = 900 kg m-3
115.2 W/m2
Consider during wintertime (i.e. no solar radiation) a 2-layer system consisting of a slab
of snow with depth hs and a constant thermal conductivity ks overlying a thin slab of sea
ice with depth hi and constant thermal conductivity ki. (See section 10.7.1). The
temperature at the bottom of the sea ice is at the freezing temperature of the mixed layer
(Tf) and the temperature at the top of the snow layer is T0.
12. Write an expression for the steady state conductive flux through the snow
K
Fcs  s (T0  T ')
hs
13. Write an expression for the steady-state conduction through the ice.
K
Fci  i (T ' T f )
hi
14. At the snow-ice interface, the conductive flux in the snow must equal the conductive
flux in the ice. Derive an expression for the steady-state (diffusive) values of the
temperature at the ice/snow interface, T’.
Fcs  Fci
Ki
K
(T ' T f )  s (T ' TI )
hi
hs
T'
K s hT
i 0  K i hsT f
K i hs  K s hi