Friday, December 9, 2016

Winter Weather Insulation

I am currently in a ecology class where I learn about the exchanges of energy in the atmosphere. We learned about radiation and how that effects the earth and soil. We also learned that snow reflects a lot of the radiation thus keeps the grass below cool, but it also keeps the grass insulated because snow is mainly air and air is a good insulator. What I want to determine is whether the albedo effect of the snow offsets the insulative effect of air gaps inside snow.

Snow forms when it is 0 degrees C.
Assume there is 0.5m of snow.
Assume also that the area of the measured plot is 0.2m by 0.3m.
Thermal conductivity of snow is 0.05- 0.7 WK-1m-1
Assume that soil temperature is 39.7 degrees F (4.28 degrees C) in December (when it begins to snow)

Thus, using the lower scale of thermal conductivity,
Q/T = (k * A * (T2 - T1)) / l
Q/T = (0.05 * 0.2 * 0.3 * (4.28 - 0)) / 0.5
Q/T = 0.02568

Using the higher scale of thermal conductivity,

Q/T = (k * A * (T2 - T1)) / l
Q/T = (0.7 * 0.2 * 0.3 * (4.28 - 0)) / 0.5
Q/T = 0.35952

Emissivity constant of snow is 0.969 - 0.997.
Boltzman Constant is 5.67 X 10^-8
T1 = 273K
T2 = 312.7K

Now, looking at albedo effects, (using the lower end of emissivity constant)
Q/T = eoA(T1^4 - T2^4)
Q/T = (0.969)(5.67 X 10^-8)(0.2 X 0.3)(273^4 - 312.7^4)
Q/T = -13.21

Using the higher end of emissivity constant,
Q/T = eoA(T1^4 - T2^4)
Q/T = (0.997)(5.67 X 10^-8)(0.2 X 0.3)(273^4 - 312.7^4)
Q/T = -13.59

From this, we can see that the heat flow due to radiation is greater than the heat flow due to insulation (which is true because although snow has a lot of air, it is still very cold and cannot insulate the soil as much since the soil temperature is much higher).

References
https://nsidc.org/cryosphere/snow/science/formation.html
http://www.cnyweather.com/wxsoil.php