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

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.

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.

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.

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)

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 Density Temperature Top & Bottom Gradient Conductive Heat Flow Thermal Conductivity Ice Thickness

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

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?

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

Four Thought Experiments 1. 2. 3. 4. Four Thought Experiments What is the conductive heat flow?

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: 0.058 W m-1 K-1 0.058 W m-1 K-1 Fa: -9.3 W m-2 -5.2 W m-2

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: 0.126 W m-1 K-1 0.058 W m-1 K-1 Fa: -10.1 W m-2 -5.2 W m-2

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: 0. 058 W m-1 K-1 0. 058 W m-1 K-1 Fa: -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? Thin, Dense Thick, Less Snow Dense Snow Tgrad: -320°C m-1 -170°C m-1 keff: 0. 126 W m-1 K-1 0. 058 W m-1 K-1 Fa: -40.3 W m-2 -9.8 W m-2

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