Snow, Ice & Polar Environmental Change
for K-12 Classrooms
Conductive Heat Flow through Snow and Ice
Dr. Martin Jeffries,
University of Alaska Fairbanks
Geophysical Institute
Why do scientists study snow and ice ?
Conductive heat flow through snow and ice
provides data about global climate change.
What is Conductive Heat Flow?
Lake ice and snow offer a good way to explain conductive heat flow
1. Water holds a tremendous
amount of heat.
-40°C
2. That latent heat is released as
water freezes and ice forms.
3. The latent heat (crystallization) is
conducted away from the water-ice
interface to the atmosphere along
the temperature gradients in the
snow and ice.
Snow
-6°C
Water
Level
Ice
0°C
4. The rate at which the latent heat is
conducted from the water to the atmosphere, and thus the rate of ice
growth and the thickness of the ice, is a function of,
(a) snow depth, temperature and density,
(b) ice thickness, temperature and density.
Why Do We Want To Know The Conductive
Heat Flow Through Snow and Ice?
Because it dominates the energy balance of the
ice and snow and is the major source of heat
transfer through floating ice and snow in winter.
Consequently, it plays a role in weather and
climate.
The magnitude and variability of conductive heat
flow is quite well known for sea ice, but not for
freshwater ice.
Is It Easy to Calculate
Conductive Heat Flow?
Yes, and you only need information about the snow.
Snow De pth
(m )
Snow Sur face
Te m pe r atur e
(°C)
Me as ur e d
Var iable
Snow
Te m pe r atur e
Gr adie nt
(°C m-1)
Snow Bottom
Te m pe r atur e
(°C)
Ice Thick ne s s
(m )
De r ive d
Var iable
Simple Measurements and Data
Analysis Yield Geophysically
Useful Information
Conductive
He at Flux
(W m-2)
Snow De ns ity
(kg m-3)
Snow
The rm al
Conductivity
(W m-1 K-1)
Calculating Conductive Heat Flow I
1. Conductive heat flow (Fa) is a function of:
(a) snow temperature gradient (Ts-Tb/Zs); and
(b) snow thermal conductivity (keff).
2. Snow thermal conductivity
is a function of snow
density.
Ts: snow surface temperature
Tb: snow bottom temperature
Zs: snow depth
keff: snow thermal conductivity
(Source: Sturm et al., 1997)
Calculating Conductive Heat Flow II
Calculating Snow Density
What is density?
Mass per unit volume.
What is the unit of density?
kg m-3 (g cm-3)
We have snow mass.
We need snow volume.
What is the volume of the snow sample?
What is the volume of a cylinder?
r2 h,
where r: radius
h: height
Calculating Conductive Heat Flow III
Calculating Snow Thermal Conductivity
What is thermal conductivity?
It’s a measure of the ability of a material to
conduct heat, its ability to keep heat in (out),
its effectiveness as an insulator.
What is the unit of thermal conductivity?
W m-1 K-1
How do we find a value for Watts per meter per °Kelvin?
Calculating Conductive Heat Flow IV
Remember, snow thermal
conductivity (keff) is a
function of snow density.
And there are two simple
equations that allow you to
convert snow density to
thermal conductivity.
(Source: Sturm et al., 1997)
Calculating Conductive Heat Flow V
Two simple equations:
• If snow density (r) is < 0.156 g cm-3, then
keff = 0.023 + 0.234 r
• If 0.156 ≤ r ≤ 0.6 g cm-3 , then
keff = 0.138 - 1.01r + 3.233 r
Calculating Conductive Heat Flow VI
Calculating the snow temperature gradient
Ts-Tb/Zs
where
Ts: snow surface temperature
Tb: snow bottom temperature
Zs: snow depth
Calculating Conductive Heat Flow VII
Calculate the conductive heat flow, Fa (at last)
Fa = (Ts-Tb /Zs ) x keff
that is,
Snow temperature gradient
x snow thermal conductivity
What Determines The Conductive Heat Flow
Through Snow, And Thus The Ice Thickness?
Depth
Temperature
Top & Bottom
Temperature
Gradient
Thermal
Conductivity
Conductive
Heat Flow
Ice
Thickness
Density
Heat Flow Through Snow:
Thought Experiment, I
The heat flow is greater
through which snow block?
-20°C
-20°C
20 cm
10 cm
-4°C
150 kg m -3
-2°C
150 kg m -3
Heat Flow Through Snow:
Thought Experiment, II
The heat flow is greater
through which snow block?
Heat Flow Through Snow:
Thought Experiment, III
The heat flow is greater
through which snow block?
-40°C
-20°C
20 cm
20 cm
-6°C
150 kg m -3
-2°C
150 kg m -3
Heat Flow Through Snow:
Thought Experiment, IV
The heat flow is greater
through which snow block?
What is the conductive heat flow
through these snow blocks?
Start your calculators
-20°C
1.
-20°C
20 cm
10 cm
150 kg m -3
-40°C
3.
2.
-2°C
-4°C
150 kg m -3
-20°C
20 cm
20 cm
-6°C
150 kg m -3
-2°C
150 kg m -3
Four Thought
Experiments
What is the conductive heat flow?
4.
Snow Insulation Thought Experiment, I
What is the conductive heat flow
through each snow block?
-20°C
-20°C
20 cm
10 cm
-2°C
-4°C
150 kg m -3
Tgrad:
keff:
Fa:
150 kg m -3
Thin Snow
-160°C m-1
0.058 W m-1 K-1
-9.3 W m-2
Thick Snow
-90°C m-1
0.058 W m-1 K-1
-5.2 W m-2
Snow Insulation Thought Experiment, II
What is the conductive heat flow
through each snow block?
Tgrad:
keff:
Fa:
High r
-80°C m-1
0.126 W m-1 K-1
-10.1 W m-2
Low r
-90°C m-1
0.058 W m-1 K-1
-5.2 W m-2
Snow Insulation Thought Experiment, III
What is the conductive heat flow
through each snow block?
-40°C
-20°C
20 cm
20 cm
-6°C
150 kg m -3
Tgrad:
keff:
Fa:
-2°C
150 kg m -3
Very Cold Snow Cold Snow
-170°C m-1
-90°C m-1
0. 058 W m-1 K-1 0. 058 W m-1 K-1
-9.8 W m-2
-5.2 W m-2
Snow Insulation Thought Experiment, IV
What is the conductive heat flow
through each snow block?
Tgrad:
keff:
Fa:
Thin, Dense
Snow
-320°C m-1
0. 126 W m-1 K-1
-40.3 W m-2
Thick, Less
Dense Snow
-170°C m-1
0. 058 W m-1 K-1
-9.8 W m-2
Which Snow Block Provides The
Most Insulation For The Conditions?
-9.3 W m -2
-40.3 W m -2
-5.2 W m -2
-20°C
-20°C
-10.1 W m -2
-20°C
-9.8 W m -2
-40°C
-40°C
-4°C
-8°C
-2°C
*
-4°C
-6°C