Erin Carter
7616892
Monday Lab
6 March, 2012
The heat content and process of thermal stratification in
northern dimictic lakes of varying morphometric parameters
INTRODUCTION
The temperate, dimictic lakes at the Fort Whyte Centre all experience thermal stratification in the
summer, where distinct and measurable layers form, differentiated by temperature (Hann (1),
2012). However, it is more correct to say that lakes stratify due to density, because of the unique
properties of water, where it the densest at 4 °C. This phenomenon is especially important when
moving into winter when inverse stratification occurs, after overturn and isothermal conditions in
the fall. The lake is said to be inversely stratified because the upper-epilimnotic layer contains
cooler 0 °C water, covered in less dense solid ice. Now, the warmer and most dense 4 °C water
resides in the bottom hypolimnion, resulting in a reverse thermal stratification column. After ice
off and spring mixing, the entire seasonal stratification process is complete. While each of the
five Fort Whyte lakes undergoes this process from year to year, the timing of each stage is
dependent on their individual morphological features, which were discussed in the previous lab.
The heat content is also an important factor in lake processes as it depends on temperature, the
total volume of water, and its heat capacity (Lab handout, Section 1). By knowing how much
heat a body of water can hold, inferences can be made about a lakes aquatic life, buffering
capacity, and heat budgets or incomes during the summer and winter seasons (Hann, (1) 2012).
The purpose of this lab is to determine how different morphometric parameters can affect the
process and timing of seasonal stratification, along with the heat content of a lake, which in itself
influences aquatic organisms and the local surrounding climate. Previous morphometric data
and calculations of summer heat income will allow for understanding of the stratification
process, along with useful information about the heat budget of a lake.
METHODS AND MATERIALS
To understand the seasonal stratification process, the temperature profiles provided in Table 1
were plotted. The data for Lake 2 and Lake 5 were graphed according to the approximate
seasonal period of spring turnover, summer stratification, and fall overturn, displayed as six
individual graphs in Figure 1. Each graph was plotted sequentially with common axis ranges to
better facilitate comparisons across the transitions into each seasonal period. Data was not
provided during the ice-on period or directly after ice-off, so the process of inverse stratification
is omitted from the graphs.
In the second part of the lab, summer heat income of Lake 5 was calculated using two
different methods. Both methods required the use of previous morphometric data found in
assignment #1, such as areas and volumes at each depth interval. For the first methods, summer
heat income was calculated by using the equation Θs = ∑ Δtz • Az • hz, (Lab handout, Section 2)
where the change in temperature represents the greatest temperature difference at each depth
interval (Table 2). Since Az • hz is equal to volume, the volume of each layer that was calculated
using the truncated cone method in assignment #1 was used instead in the equation for Θs (Lab
handout, Section 2). In order for the units to cancel out properly, each volume needed to be
converted from m3 to cm3. This was also useful in the calculation of heat content, which
provided the amount of heat in Lake 5 in the unit of calories. The planimeter was used again in
this assignment for the second method of calculating summer heat income. An area x ΔT-depth
hypsograph was created and the planimeter was traced along the curve. This gave a value for Θs
in planimeter units, which was then converted to units of heat with the help of the calibration
square.
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RESULTS
1. By comparing the temperature profiles listed in Table 1 and displayed as graphs in Figure 1,
the timing of seasonal transitions can be described in detail. Lake 2, show in the top row of
Figure 1, begins with isothermal conditions at a constant 4 °C, indicated by the straight line for
April 15th in the first graph. This graph ranges from the end of the ice-off period to when spring
mixing begins, due to increased solar radiation and mixing down of the less dense surface waters
(Hann (1), 2012). After April 15th, the epilimnotic layer continues to warm and the buoyant
water can no longer be mixed down, leading to the beginning of stratification around May 17th.
Moving into the summer months in the second graph, the surface layer (0-1m) of the lake
warms from 17.1-24.5°C and gradually declining down the water column, but no complete
stratification is present. The greatest temperature difference occurs around the 6-7m layer,
which could possibly be interpreted as a metalimnion. The third graph shows the transition from
summer to fall, where the epilimnion cools down to 15.5 °C around August 22nd. The epilimnion
continues to deepen to 6m between August 22nd and September 21st because the top of the
metalimnion is being mixed into the epilimnion. The fall turnover process completes the
breakdown of temperature differences around October 4th as the entire water column mixes to a
uniform 9.2 °C by October 21st. Isothermal conditions in the fall are driven by wind mixing and
loss of heat or heat conduction at the surface as solar radiation decreases (Hann (1), 2012).
Lake 5, shown in the bottom row of Figure 1 displays relatively the same seasonal patterns as
Lake 2 but with differences in timing between stages. Again, the lake initially has an isothermal
column at 4 °C after ice-off and during spring mixing on April 15th.
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Continuing into the spring period, the epilimnion slowly warms to 13.8 °C by May 17, with little
addition of heat into the now forming stratified hypolimnion and metalimnion. By the beginning
of summer in the second graph (June 13), the lake is fully stratified as the epilimnion extends to
a depth of 3 m around 15 °C and the temperature rapidly drops to under 10 °C in and below the
metalimnion. The top 1 m layer of water quickly warms to 24 °C in the next week (June 20) due
to increasing solar radiation, and displays an even greater change in temperature in the
metalimnion (between 3-4 m).
Thermal stratification is the most defined around July 18th where the epilimnion warms to a
constant temperature of 25 °C in the top 3 m, and the metalimnion has its maximum temperature
change of 10 °C/m. In the late summer, between August 22nd and September 21st, Lake 5 still
displays a stratification pattern, but mixing of the top of the metalimnion into the epilimnion is
visible, as the epilimnion deepens to 4 m and then 5 m in each month. Stratification finally
breaks down around October 4th when wind mixing and decreased solar radiation allow for
cooling of the epilimnion and entire water column to 9 °C in the middle of October.
1. Calculating Summer Heat Income:
Method 1: Using the equation 
Θs = ∑ Δtz • Az • hz
Volumes from the truncated cone method as used in place of Az • hz, to create the equation:
Θs = ∑ Δtz • Vz
The volume of the 0-2 m layer was calculated as 104 720.4 m3 in assignment #1, which is
converted to cm3 in this sample calculation:
1 m3 = 1 000 000 cm3  x cm3/104 720.4 m3 x 1 000 000 cm3/1 m3  1.05 x 1011 cm3
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Next, this newly converted figure was incorporated into the equation for summer heat income
Θs = Δtz • Vz
= 21.5 °C • 1.05 x 1011 cm3
Θs = 2.25 x 1012 cm3• °C
After these values were found for each depth layer of Lake 5, they were summed to give a final
value for total summer heat income:
Θs = ∑ Δtz • Vz
Θs = ∑ (2.25 x 1012 + ...)
Θs = 5.44 x 1012 cm3• °C
Therefore, the summer heat income of Lake Cargill (Lake 5) using method 1 is 5.44 x 1012 cm3•
°C. Note: this is similar to the value found in Table 2 (except that it is in m2 • °C) since it was
calculated using areas in m2 and height in m instead of volumes in cm3.
Method 1 also used a modification of the heat income equation to calculate the heat content of
the lake, showing how the units cancelled to get calories. The heat content was calculated by:
Heat content = Volume x Density x Temperature x Specific Heat
(calories) = (cm3) x (gm/cm3) x (°C) x (calories/gram-°C)
Where, we assume the density of water is 1 gm per cm3 for all temperatures (Lab handout).
For the 0-2 depth interval, a sample calculation is given by:
Heat content = (1.05 x 1011 cm3) x (1.0 g/cm3) x (21.5 °C) x (1 calorie/g-°C)
Heat content = 2.25 x 1012 calories
Therefore, the total heat content for Lake Cargill (Lake 5) after summing each individual layer is
5.44 x 1012 calories. This modification gives us the same value as heat income, but with different
units.
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Method 2:
Total heat income measured with the planimeter = 71.4 PU (Figure 2).
The calibration square drawn on the curve in Figure 2 represents 1 600 000 m3 • °C for 25.4 PU,
traced with the planimeter.
Summer Heat Income = x m3 • °C/ 71.4 PU = 1600 000 m3/ 25.4 PU 4 497 637.8 m3 • °C
Therefore, the summer heat income of Lake Cargill (Lake 5) using method 2 is
4 497 637.8 m3 • °C or 4.50 x 1012 cm3 • °C when converted.
Table 1. Temperature profiles for Lake 2 and 5 at the Fort Whyte Centre.
LAKE 2 Apr-15 May-02 May-17 Jun-13 Jun-20 Jul-18 Aug-22 Sep-21 Oct-04 Oct-21
Depth (m)
0
1
2
3
4
5
6
7
8
3.5
4
4
4
4
4
4
4
4
12
11
10.5
9
8.5
6
4
4
4
19
19
18.8
18.7
13.5
13.5
10
9
6.5
17.1
16.5
16.3
16
15.8
15.6
15
10
9.8
21
19
19
19
19
18
16.5
14
13
24.5
22.5
21.5
20.5
20
19
18
15.5
15
15.5
15.5
15.5
15.3
15.2
15.1
15
10.1
10
15.5
15.2
15.2
15.2
14.5
14.2
14
10
9.8
10.5
10.4
10.3
10.3
10.3
10.4
9.8
10.1
9.8
9.2
9.2
9.2
9.2
9.2
9.2
9.2
9.2
9.2
3.5
4
4
4
4
4
4
4
4
4
4
10
9.5
9
8
6
4
4
4
4
4
4
13.8
13.2
13
10
9
9
8
7
6
6
6
15.5
15.5
15
15
12
9
8
7
6
6
6
24
23
22
21
14
12
10
9
8
7
7
25
25
25
24
14
13
10
9
8
7
7
19
19
19
19
19
12
10
9
8
7
7
17
16
16
15
15
15
11
9
8
7
7
11
11
10
10
10
10
9.5
9
9
8
8
9
9
9
9
9
9
9
9
9
9
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LAKE 5
0
1
2
3
4
5
6
7
8
9
10
6
Temperature (°C)
0
5
10
15
20
25
0
Depth (m)
1
2
Apr-15
3
May-02
4
May-17
5
6
7
8
Temperature (°C)
0
5
10
15
20
25
0
Depth (m)
1
2
Jun-13
3
Jun-20
4
Jul-18
5
6
7
8
Temperature (°C)
0
5
10
15
20
25
0
1
Depth (m)
2
3
4
5
Aug-22
Sep-21
Oct-04
Oct-21
6
7
8
7
Temperature (°C)
Depth (m)
0
5
10
15
20
25
0
1
2
3
4
5
6
7
8
9
10
Apr-15
May-02
May-17
Temperature (°C)
Depth (m)
0
5
10
15
20
25
0
1
2
3
4
5
6
7
8
9
10
Jun-13
Jun-20
Jul-18
Temperature (°C)
Depth (m)
0
0
1
2
3
4
5
6
7
8
9
10
5
10
15
20
Aug-22
Sep-21
Oct-04
Oct-21
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Area x ∆ Temperature (cm2 ∙ °C)
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0
2
4
Calibration
Square =
4000 cm2 •
°C x
6 cm =
6
Depth (cm)
8
24 000
cm3 • °C
10
12
14
16
18
20
22
Figure 2. Area by change in temperature-depth hypsograph of a rectangular model lake basin.
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Table 2. Calculation of summer heat income for Lake 5 (method 1).
Depth Layer
(m)
0-2
2-4
4-6
6-8
8-10
Area
(m2)
61804.1
43453.6
33762.9
22835.1
11701.0
Lowest
Temperature
3.5
4.0
4.0
4.0
4.0
Highest
Temperature
25.0
25.0
19.0
11.0
9.0
Temperature Range Product (area x h x
(ΔT)
ΔT)
21.5
2 657 576.3
21.0
1 825 051.2
15.0
1 012 887.0
7.0
319 691.4
5.0
117 010.0
Total =
5 932 215.9
DISCUSSION
1 & 2. Lake 5 shows a dimictic annual mixing pattern, with turnover in the spring and fall. The
annual mixing pattern for Lake 2 is not as clear as in Lake 5, and seems to be classified as being
between a dimictic and cold monomictic lake. Lake 2 may appear to be dimictic due to the
isothermal conditions on April 15th and October 21st and the slight stratification pattern between
May 17th and June 13th. However, due to the lack of stratification throughout the rest of the
summer season, it may be classified as a cold monomictic lake with mixing in the summer. If it
were to be classified with a monomictic pattern, the gradual changes down the temperature
profiles could be explained not as stratification, but with the Beer-Lambert Law (Hann (1),
2012). Since the light intensity or heat decreases exponentially with depth, the water at the
surface of the lake would be heated more when compared to the bottom layer. The depth of Lake
2 may be a factor for its mixing pattern, as it may indicate a smaller volume of water when
compared to Lake 5. This would result in a reduced heat capacity, which explains the earlier
warming in May and return to cooler, isothermal conditions earlier in the fall.
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The main difference between the two lakes is in the timing and duration of each seasonal
period and the transitions between them. For example, both lakes display completely isothermal
conditions in the spring turnover period (April 15th) but the epilimnotic layer seems to warm and
deepen faster in Lake 2 than in Lake 5. Throughout the summer period, Lake 5 displays
stratification patterns and reaches its maximum stratification by July 18th whereas the epilimnotic
layer only seems to deepen to a constant 6 m with only gradual temperature differences down the
column in Lake 2. By late summer, Lake 2 no longer displays any stratification pattern and
quickly returns to near isothermal conditions in the top 6 m by August 22nd. Lake 5, on the other
hand, maintains its heat at a higher temperature of 19 °C in the epilimnion during the end of
August, when compared to 15 °C shown in Lake 2. Overall, stratification builds up and breaks
down much slower in Lake 5 than Lake 2, where stratification never completely forms.
3. Using the equation in method 1, a value of 5.44 x 1012 cm3 • °C was calculated for summer
heat income whereas method 2 gave a value of 4.50 x 1012 cm3 • °C. While the two values are
relatively similar, the difference leads to some form of discrepancy. The values differ by an
amount of 9.40 x 1011 cm3 • °C or around 17%. This discrepancy may have occurred as an error
at the state of measurement when using the planimeter. Instrument function may have been a
source of error for method 2 because the planimeter readings could have slightly smaller or
underestimated values when compared to the real world. This could be the case since actual
measurements of the lake itself would be made directly in units of heat when compared to
planimeter units. Also, the planimeter values are somewhat difference from real world
measurements, as estimations make on artificial paper representations are never as realistic as the
lake itself.
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You would expect this because map projections always have some degree of distortion when
versus the actual object being projected. Because of this, measurements made from a bathymetric
map and then converted onto a hypsograph will have some sort of discrepancy. Additionally, the
first method used the volumes from the truncated cone calculations, which may account for the
slightly larger Θs value of 5.44 x 10 12 cm3 • °C. This is because the truncated cone method
calculated each volume layer as a series of stacked rectangles, where a lake looks more like a
smooth gradual decline in reality. The extra edges of each rectangular volume layer may have led
to an overestimation of summer heat income when incorporated into the equation.
4. Information on summer heat income or heat budgets might be useful to limnologists because
the heat content of a water body can help to explain or predict a number of things. Aquatic
organisms and their growth, distribution, physiology, and behaviour can be heavily influenced by
the amount of heat in a lake (Lab handout, Section 1). Also, if a limnologist knows the heat
budget of two lakes, they can infer which lake as a larger volume and thus, greater heat capacity
available to moderate the local climate. By understanding the head budget of a lake, the timing of
seasonal processes such as transitions from ice-off to ice-on can be estimated,
5. The trend of global warming would influence the summer heat income of lakes by a gradual,
but not continuous increase in the amount of heat uptake. This would be expected as earlier ice
thaw and later freeze-up dates create a longer ice-free season, which allows for solar radiation to
penetrate the water for a longer time period. The amount of heat that would actually be able to be
absorbed by lakes would depend on their individual volumes, and would not be continuously
increasing since a volume of water can only absorb a certain maximum amount of heat.
Instead, it might be expected that a lake would simply warm faster after ice-off with the
increased amount and intensity of heat.
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The warming itself, leads to increased solar radiation in the summer stratification season, making
fall turnover conditions later than usual (more heat needed to be conducted away). Another
possibility is that water may evaporate at a higher rate with increased temperatures and drying
climate changes, leading to a reduction in the volume and therefore heat capacity of a lake. In
this case, summer heat income may actually decrease slightly since less water would need to be
heated to its maximum temperature. The maximum temperature would then be cooler since less
heat would be able to be absorbed by a smaller volume of water.
6. As stated above, summer heat income of lakes would most likely increase, as a water body
would absorb more heat over a longer ice-free period (with the exception of excessive
evaporation). Winter heat income, on the other hand, would likely decrease because ice cover
would be at a smaller extent over a shorter winter season, so less heat would be needed to melt
ice and warm the lake from 0-4 °C. In general, winter heat income would only decrease slightly
since the same amount of energy (calories of heat) are needed to convert 0 °C to 4 °C water, with
differences only in the spatial extent or mass of ice. With global warming, more intense heat will
be available for water body uptake, so annual heat budgets may end up increasing over a period
of time.
REFERENCES
Hann, B.J. 2012. Lecture Notes - January 31, 2012 and February 14, 2012. BIOL 3370
Limnology (1).
Hann, B.J. 2012. Thermal Stratification and Heat Budgets - Lab Handout. BIOL 3370
Limnology (2).
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