Snow, Ice & Polar Environmental Change for K-12 Classrooms Conductive Heat Flow through Snow and Ice Dr. Martin Jeffries, University of Alaska Fairbanks.

Snow, Ice & Polar Environmental Change for K-12 Classrooms

Conductive Heat Flow through Snow and IceDr. Martin Jeffries,

University of Alaska FairbanksGeophysical 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.

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.

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.

Snow

Ice

WaterLevel

-40°C

-6°C

0°C

2. That latent heat is released as water freezes and ice forms.

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 CalculateConductive Heat Flow?

Yes, and you only need information about the snow.

SnowTemperature

Gradient(°C m-1)

SnowThermal

Conductivity(W m-1 K-1)

Snow Depth(m)

ConductiveHeat Flux

(W m-2)

MeasuredVariable

DerivedVariable

Simple Measurements and DataAnalysis Yield GeophysicallyUseful Information

Snow SurfaceTemperature

(°C)

Snow BottomTemperature

(°C)

Snow Density(kg m-3)

Ice Thickness(m)

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 temperatureTb: snow bottom temperatureZs: snow depthkeff: 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.

(Source: Sturm et al., 1997)

And there are two simple equations that allow you to convert snow density to thermal conductivity.

Calculating Conductive Heat Flow V

Two simple equations:

• If snow density () is < 0.156 g cm-3, then

keff = 0.023 + 0.234

• If 0.156 ≤ ≤ 0.6 g cm-3 , then

keff = 0.138 - 1.01+ 3.233

Calculating Conductive Heat Flow VI

Calculating the snow temperature gradient

Ts-Tb/Zs

where

Ts: snow surface temperatureTb: snow bottom temperatureZs: 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

ThermalConductivity

TemperatureTop & Bottom

TemperatureGradient

ConductiveHeat Flow

IceThickness

Heat Flow Through Snow:Thought Experiment, I

The heat flow is greater through which snow block?

-20°C

-20°C

-4°C -2°C10 cm

20 cm

150 kg m-3 150 kg m-3

Heat Flow Through Snow:Thought Experiment, II


-20°C-20°C

-2°C-4°C

20 cm 20 cm

300 kg m-3 150 kg m-3

Heat Flow Through Snow:Thought Experiment, III


20 cm 20 cm

150 kg m-3 150 kg m-3

-20°C-40°C

-2°C-6°C

Heat Flow Through Snow:Thought Experiment, IV


-40°C

-6°C10 cm

20 cm

300 kg cm-3 150 kg cm-3

-40°C

-8°C

-20°C

-20°C

-4°C -2°C

-20°C

-4°C

-40°C

-6°C

-40°C

-8°C

What is the conductive heat flow through these snow blocks?

Start your calculators

Four Thought Experiments

-20°C

-20°C

-4°C -2°C10 cm

20 cm

150 kg m-3 150 kg m-3

1.

-20°C-20°C

-2°C-4°C

20 cm 20 cm

300 kg m-3 150 kg m-3

2.

20 cm 20 cm

150 kg m-3 150 kg m-3

-20°C-40°C

-2°C-6°C

3.

-40°C

-6°C10 cm

20 cm

300 kg cm-3 150 kg cm-3

-40°C

-8°C

4.

What is the conductive heat flow?

Snow Insulation Thought Experiment, I

What is the conductive heat flow through each snow block?

Thin Snow Thick SnowTgrad: -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

-20°C

-20°C

-4°C -2°C10 cm

20 cm

150 kg m-3 150 kg m-3

Snow Insulation Thought Experiment, II


High Low 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

-20°C-20°C

-2°C-4°C

20 cm 20 cm

300 kg m-3 150 kg m-3

Snow Insulation Thought Experiment, III


Very Cold Snow Cold SnowTgrad: -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

20 cm 20 cm

150 kg m-3 150 kg m-3

-20°C-40°C

-2°C-6°C

Snow Insulation Thought Experiment, IV


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

-40°C

-6°C10 cm

20 cm

300 kg cm-3 150 kg cm-3

-40°C

-8°C

Which Snow Block Provides TheMost Insulation For The Conditions?

*

-20°C

-20°C

-4°C -2°C

-20°C

-4°C

-40°C

-6°C

-40°C

-8°C

-9.3 W m-2 -5.2 W m-2 -10.1 W m-2 -9.8 W m-2-40.3 W m-2

Snow, Ice & Polar Environmental Change for K-12 Classrooms Conductive Heat Flow through Snow and Ice Dr. Martin Jeffries, University of Alaska Fairbanks.

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