SNOW HYDROLOGY (GEOG 4321): HOMEWORK ASSIGNMENT 7

Instuctor: Mark Williams
Telephone: 492-8830

Homework 7

• Assigned 28 March.
• Due 1 April at 4pm.
• There are 40 possible points.

1. Calculate LE using the Bowen ratio. Make sure that you keep track of positives and negatives (5 points)!
   • Net radiation is 100 W/m2
   • Ground heat flux is 5 W/m2
   • q_a is 0.001
   • q_s is 0.006
   • T_a is 2 deg C
   • T_s is 0 deg C
2. Calculate the "cold content" of the snowpack, in J/m2, using the following information. The cold content of the snowpack is the amount of energy needed to bring the snowpack to an average temperature of 0 deg C (5 points).
   • density of snow = 340 kg/m3
   • T_snow = -5 deg C
   • Snow Depth = 1 m
3. Calculate the heat advected by rain, in kJ/m2-day and W/m2. Assume the snowpack is at zero degrees C and the rain does not freeze. (5 points).
   • Temperature of the rain is +1 degree C.
   • 30 mm/day of rain.
4. Calculate the heat advected by rain, in kJ/m2-day and W/m2. Assume the snowpack is below zero and the rain freezes. (5 points).
   • Temperature of the rain is 0 degree C.
   • 30 mm of rain.
5. Calculate the following (20 points):
   1. net radiation;
   2. net energy balance;
   3. amount of snowmelt in mm for a 4 hr interval, assuming the energy flux from (b) is constant for 4 hrs.

   from these measurements:

   • K_in(shortwave) = 500 W / m2
   • L_in(longwave) = 200 W / m2
   • shortwave integrated snow albedo = 0.60
   • longwave integrated snow emissivity = 0.98
   • snow temperature = 0 deg C
   • at z₂ = 2 m, T₂ = 2 deg C
   • at z₂ = 2 m, q₂ = 0.0055
   • at z₂ = 2 m, u₂ = 10 m/s
   • at z₁ = 0.5 m, T₁ = 0 deg C
   • at z₁ = 0.5 m, q₁ = 0.006
   • at z₁ = 0.5 m, u₁ = 5 m/s
   • heat flux from soil = 6 W / m2
   • density of snow = 550 kg / m3

   hint 1: remember that the amount of melt = amt of energy available divided by the latent heat of fusion times the density of liquid water, if the snowpack is isothermal.

   hint 2: 1 Watt = 1 Joule/second