1. 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

2. Conductive heat flow through snow and ice
Why do scientists study snow and ice ?
Conductive heat flow through snow and ice
provides data about global climate change.

3. What is Conductive Heat Flow?
Lake ice and snow offer a good way to explain conductive heat flow
Water holds a tremendous
amount of heat.
That latent heat is released as water freezes and ice forms.
The latent heat (crystallization) is conducted away from the water-ice interface to the atmosphere along the temperature gradients in the snow and ice.
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.

4. 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.

5. Is It Easy to Calculate Conductive Heat Flow?
Yes, and you only need information about the snow.

6. 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).
Ts: snow surface temperature
Tb: snow bottom temperature
Zs: snow depth
keff: snow thermal conductivity
2. Snow thermal conductivity
is a function of snow density.
(Source: Sturm et al., 1997)

7. 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

8. 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?

9. 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)

10. Calculating Conductive Heat Flow V
Two simple equations:
• If snow density (r) is < g cm-3, then
keff = r
• If ≤ r ≤ 0.6 g cm-3 , then
keff = r r

11. 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

12. 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

13. What Determines The Conductive Heat Flow Through Snow, And Thus The Ice Thickness?
Depth
Density
Temperature
Top & Bottom
Gradient
Conductive
Heat Flow
Thermal
Conductivity
Ice
Thickness

14. Heat Flow Through Snow: Thought Experiment, I
The heat flow is greater
through which snow block?

15. Heat Flow Through Snow: Thought Experiment, II
The heat flow is greater
through which snow block?

16. Heat Flow Through Snow: Thought Experiment, III
The heat flow is greater
through which snow block?

17. Heat Flow Through Snow: Thought Experiment, IV
The heat flow is greater
through which snow block?

18. What is the conductive heat flow through these snow blocks?
Start your calculators

19. Four Thought Experiments1. 2. 3. 4.
Four Thought Experiments
What is the conductive heat flow?

20. Snow Insulation Thought Experiment, I
What is the conductive heat flow
through each snow block?
Thin Snow Thick Snow
Tgrad: -160°C m-1 -90°C m-1
keff: W m-1 K W m-1 K-1 Fa: -9.3 W m W m-2

21. Snow Insulation Thought Experiment, II
What is the conductive heat flow
through each snow block?
High r Low r
Tgrad: -80°C m-1 -90°C m-1
keff: W m-1 K W m-1 K-1 Fa: W m W m-2

22. Snow Insulation Thought Experiment, III
What is the conductive heat flow
through each snow block?
Very Cold Snow Cold Snow
Tgrad: -170°C m-1 -90°C m-1
keff: W m-1 K W m-1 K-1 Fa: -9.8 W m W m-2

23. Snow Insulation Thought Experiment, IV
What is the conductive heat flow
through each snow block?
Thin, Dense Thick, Less
Snow Dense Snow
Tgrad: -320°C m °C m-1
keff: W m-1 K W m-1 K-1
Fa: W m W m-2

24. Which Snow Block Provides The
Most Insulation For The Conditions? *