HEAT
AND O2 BUDGETS FOR ICE LAKE
The RUSS
data from Ice Lake is summarized to show the lake's average heat and
oxygen content on each day. These are calculated by averaging the amount
of heat and oxygen contained in each 1 meter thick layer of the lake
over the course of the day and then adding them up from 0-3 m, 3-8 m
and 8 meters to bottom. Therefore, the sum of the values for the 3 layers
is the total amount in the whole lake on that day. - Limnologists say
that these values are morphometrically, or volume-weighted.
Charts of
heat and oxygen content are provided below. These are "stacked-area"
charts - showing the contribution of each layer to the total. Below
each chart you will find a more detailed description of the calculations
involved for determining the heat content and oxygen content. You can
also download the Excel spreadsheet
(it's about 90 Kbytes) containing this data and the charts for Ice Lake.
These data
should be considered "provisional" until otherwise indicated. The data
are undergoing several rounds of QA/QC review and some may be modified
at a subsequent date. We chose to leave the data hose on full blast
whenever possible to familiarize ourselves with the operation and maintenance
requirements of the RUSS units and to generate real data for use in
developing curricula and lesson plans. Data gaps were associated with
various RUSS system upgrades and occasional gremlins.
HEAT
CONTENT
Click
image for a larger version
The ability
of a body of water to store heat is due primarily to the heat capacity
of its water. Water has a specific heat of 1.0 calories per gram per
degree Celsius. This means that it takes 1 calorie of heat energy to
raise the temperature of a gram of water by 1°C. For example, using
the data from Ice Lake on May 29, 1998 at 6 a.m. we can calculate the
heat content of the upper layer, where
heat content
= mass x specific heat x temperature (m * C * deltaT )
= (grams)
x (calories/gram/degree) x (degrees°C)
And since
Mass of water = density x volume and density = 1 gram/milliliter which
= 1 kg/Liter,
Heat content
= volume x density x specific heat x temperature
(m * C *
deltaT ) = (liters x kg/Liter) x (calories/gram/degree) x (degrees°C)
|
Layer
|
Volume
(x 105 m3)
|
Temperature
(average of layer)
|
Heat
(calories per layer)
|
| 0-1
meters |
1.60 |
20.80 |
3.33
x 1012 |
| 1-2
meters |
1.48 |
20.75 |
3.07
x 1012 |
| 2-3
meters |
1.36 |
19.55 |
2.66
x 1012 |
| Total
(0-3 m) |
4.44 |
|
9.06
x 1012
|
Large bodies
of water can modify the weather in their region by their ability to
store heat energy during warm periods and release it during cooler times.
For instance in Duluth, Minnesota, the weather forecasts typically say
"cooler by the lake" in summer because the average surface
temperature of the lake is only about 10°C (50°F) then, and
"warmer by the lake" in winter because its average temperature
is about 4°C (39°F) which is much warmer than the air.
We can follow
trends in the lake's "heat budget" by computing the heat content
of its layers relative to their minimum values at 0°C. This is
the subject of a specific Studying
Heat Budgets Lesson and the Investigating
Heat Budgets Lesson. Further discussion of the heat balances of
lakes can be found in standard limnology and geosciences texts (e.g.
Horne, A.J. and C.R. Goldman 1994. Limnology, 2nd
edition. McGraw-hill, Inc.).
OXYGEN CONTENT
Click
image for a larger version
We plot
the dissolved oxygen content of the top (0-3 m), middle (3-8 m) and
bottom (8 m - bottom) layers for use in a number of specific lab lessons
and for generating hypotheses to explain changes in these values over
time. As for heat, the total amount of oxygen in a layer is calculated
as the sum of individual layer volumes multiplied by their respective
dissolved oxygen concentrations. This yields a mass of oxygen. Using
the data set again taken from 6 a.m. on May 29, 1998:
Note: remember
that 1 mg/L = 1 g/m3
|
Layer
|
Volume
(x 105 m3)
|
Dissolved
O2
(mg/L average for layer)
|
Total
O2 mass
(kilograms)
|
| 0-1
meters |
1.60 |
9.40 |
1504
|
| 1-2
meters |
1.48 |
9.40 |
1391
|
| 2-3
meters |
1.36 |
9.90 |
1346 |
| Total
(0-3 m) |
4.44 |
|
4241 |
That's
more than 4 metric tons of oxygen gas !
|
