The Heat Budget of Lakes
47
Sample data sheet for the heat storage calculation
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(
~ (
Average J (t Average )
!hickness
are~ of
temperature of
In cm
layer III cm~
stratum
= °C-cm 3 /layer = cal/layer
(1 )
Depth in
lake (m)
0-0.5
0.5-1.5
1.5-2.5
etc.
Notes
(2) [hJ
(3) [AJ
Layer
A verage area
thickness
for layer
(cm)
(cm 2 )
(4)
(5) [tJ
(6)
Layer
Average
Weighted
volume
temperature
calorie
(cm 3 )
for stratum
content per
[columns
(0C)
layer
2 x 3J
(OC_cm 3 )
[columns
4 x 5J
1. Partition the lake into layers of appropriate thickness according to the thermal
profile, i.e., use thinner layers where the temperature change is rapid, use thicker
layers where the temperature is constant or nearly so. Use common sense and
remember that you are integrating the area under a curve.
2. Sum the values in column 6 and divide by the surface area of the lake in cm 2 to
obtain the caloric content of the entire lake in cal/cm 2 .
HEAT BUDGET
The difference in heat content over some time interval, as calculated above, is
referred to as a heat budget. An alternate method of approximating the change in heat
content with time is to construct a plot with depth z on the Y axis and the products A z
(Tzo - Tz1 ) on the X axis [Tzo and Tzl are the temperatures at the beginning and end of
the period, respectively, at depth z; note that (T zmax - T zmin ) is the formulation for the
Birgean heat budget]. The integral is measured either with a digitizer, planimetrically,
or by counting squares, and the sum thus produced is divided by Ao.
SPECIAL CONSIDERATIONS FOR SNOW AND ICE
Since specific heat and latent heat are related to mass rather than volume (for water the
unit values for mass and volume are conveniently equal!), it is important to determine
the density of snow or ice. For example,
Latent heat of ice (calories) = thickness (cm) x area (cm 2 )
x density (g/cm 3 ) x latent heat of fusion (cal/g)