The Heat Budget of Lakes
Table 4.4. Thermal properties of ice and snow. a
Latent heat
Thermal conductivity (ice)
Thermal conductivity (snow)
Attenuation coefficient (ice)
Attenuation coefficient (snow)
Specific heat (ice)
Linear coefficient of expansion (ice)
Volume coefficient of expansion (ice)
79.8 cal/g (or 334 x 10 4 J/g)
2.3W/m-'C
0.31 W/m-'C
1.5/m visible band; 20/m infrared band
6/m visible band; 20/m infrared band
0.506 cal/C-g b
52.7 x 1O- 6 ;oC'
153 x 1O- 6 ;oC'
a Modified from Meier (1964), Patterson and Hamblin (1988).
bAt O°c.
'At melting temperature.
OPTION 3. LABORATORY EXERCISE
51
Combine this exercise with Exercise 3 as an elaboration of the section on heat contents of the
model systems. Calculate heat budgets based on data from the model systems and compare them
with calculations based on data from Mirror Lake (Tables 4.2 and 4.3; Fig. 4.3).
Questions
1. Compare graphically the temperature profiles for Mirror Lake during 1970 (Table 4.2). Plot
isolines oftemperature using coordinates of depth and time and also plot temperatures using
coordinates of depth and temperature (see Exercise 1 for details on how to make these plots).
2. Construct a hypsograph for Mirror Lake. Use the data in Table 4.3. If you want, you can
planimeter the basin contours for Mirror Lake (Fig. 4.3) and compare your values with those
in Table 4.3 (see Chapter 1 for an explanation of hypsographic curve).
3. Calculate the change in heat stored in Mirror Lake from January 25 to February 21.
Contrast this with the value for the period May 17 to June 24,1970. Compute the values in
terms of cal/cm 2 -day.*
4. Discuss the effects of an ice and snow cover on the heat budget of a lake.
5. Assume that one-half of the net solar energy flux affects the water and that one-half affects the
ice during winter. What would have been the thickness of the ice 10 days after January 25,
1970, in Mirror Lake? (Assume an average OR value during this period of - O.Olly/min.)
6. What was the density of the ice on Mirror Lake on January 25, 1970?
7. What could be the reason for the increasing water temperatures near the bottom in icecovered Mirror Lake during 1970 (Table 4.2)?
8. How would you explain the increase in water temperature near the bottom in Mirror Lake
during the summer (Table 4.2)?
9. In Antarctic lakes the water level is often depressed as much as 35 cm in a hole drilled
through the ice. Assuming a density of 0.917 g/cm 3 , what would be the thickness of the ice
cover?
10. If the temperature were to rise from - 40 to ODC overnight at Mirror Lake, theoretically how
far might the ice push onto the shore (see Table 4.5)?
11. How would you predict the ice-out date for a lake? List the evidence you would use as a basis
for this "guestimate."
* Assume that Pi = 0.91 g/cm 3 and Ps (density of snow) = 0.07 g/cm 3 on February 21, 1970.
Table 4.4. Thermal properties of ice and snow. a
Latent heat
Thermal conductivity (ice)
Thermal conductivity (snow)
Attenuation coefficient (ice)
Attenuation coefficient (snow)
Specific heat (ice)
Linear coefficient of expansion (ice)
Volume coefficient of expansion (ice)
79.8 cal/g (or 334 x 10 4 J/g)
2.3W/m-'C
0.31 W/m-'C
1.5/m visible band; 20/m infrared band
6/m visible band; 20/m infrared band
0.506 cal/C-g b
52.7 x 1O- 6 ;oC'
153 x 1O- 6 ;oC'
a Modified from Meier (1964), Patterson and Hamblin (1988).
bAt O°c.
'At melting temperature.
OPTION 3. LABORATORY EXERCISE
51
Combine this exercise with Exercise 3 as an elaboration of the section on heat contents of the
model systems. Calculate heat budgets based on data from the model systems and compare them
with calculations based on data from Mirror Lake (Tables 4.2 and 4.3; Fig. 4.3).
Questions
1. Compare graphically the temperature profiles for Mirror Lake during 1970 (Table 4.2). Plot
isolines oftemperature using coordinates of depth and time and also plot temperatures using
coordinates of depth and temperature (see Exercise 1 for details on how to make these plots).
2. Construct a hypsograph for Mirror Lake. Use the data in Table 4.3. If you want, you can
planimeter the basin contours for Mirror Lake (Fig. 4.3) and compare your values with those
in Table 4.3 (see Chapter 1 for an explanation of hypsographic curve).
3. Calculate the change in heat stored in Mirror Lake from January 25 to February 21.
Contrast this with the value for the period May 17 to June 24,1970. Compute the values in
terms of cal/cm 2 -day.*
4. Discuss the effects of an ice and snow cover on the heat budget of a lake.
5. Assume that one-half of the net solar energy flux affects the water and that one-half affects the
ice during winter. What would have been the thickness of the ice 10 days after January 25,
1970, in Mirror Lake? (Assume an average OR value during this period of - O.Olly/min.)
6. What was the density of the ice on Mirror Lake on January 25, 1970?
7. What could be the reason for the increasing water temperatures near the bottom in icecovered Mirror Lake during 1970 (Table 4.2)?
8. How would you explain the increase in water temperature near the bottom in Mirror Lake
during the summer (Table 4.2)?
9. In Antarctic lakes the water level is often depressed as much as 35 cm in a hole drilled
through the ice. Assuming a density of 0.917 g/cm 3 , what would be the thickness of the ice
cover?
10. If the temperature were to rise from - 40 to ODC overnight at Mirror Lake, theoretically how
far might the ice push onto the shore (see Table 4.5)?
11. How would you predict the ice-out date for a lake? List the evidence you would use as a basis
for this "guestimate."
* Assume that Pi = 0.91 g/cm 3 and Ps (density of snow) = 0.07 g/cm 3 on February 21, 1970.