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Modeling the Annual Temperature Cycle of a Temperate Zone Lake
Introduction
In this laboratory exercise, you will examine the physical characteristics of one type of lake using an aquarium as a model
of a temperate zone lake. You will work in groups. You each will prepare a report of this exercise and calculations.
The exercise outlined below is based on a simple and rather naive model of a lake. The following apparatus is required.
a. an aquarium, representing a lake basin.
b. a heat source (a Sylvania infrared 250 watt 115 volt heat lamp, the same kind that keeps your french fries soggy
at the golden arches).
c. a hair drier to be used as a wind source.
d. ice, to facilitate seasonal cooling.
f. methylene blue crystals, to make the results visible.
In this exercise always remember that you are studying a model, and not a lake. The two virtues of models are:
1. complexity is reduced to such an extent that mechanisms and processes can be quickly appreciated and intuitively
understood;
2. you can experiment with the model, whereas this is usually more difficult if not impossible with the natural
phenomenon itself.
On the other hand, unjustifiable extrapolations can be made from the model to nature if the observer is not careful to
distinguish between the two. In the experiment outlined here, for example, no attempt has been made to insulate the sides
and bottom of the aquarium, hence there is a more rapid heat exchange between the model "lake" and its surroundings than
would ever be the case in nature. Likewise, the heat supplied by the heat lamp in relation to the depth of water below is
much higher than in natural situations. The reason for the modification is, of course, to speed the process.
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The Temperate Zone Lake
Apparatus and Supplies
a. An aquarium containing cold tap water with sufficient ice to cool the water to 4°C leaving some ice still on top.
b. A heat lamp located directly over the middle of the aquarium, 9 inches above the water surface. Caution: Take care
not to splash water on the I.R. lamp, otherwise--explosion! Also needed are a ringstand and clamps to support the
lamp.
c. Seven thermometers (-20 to 110°C) attached by rubber bands to two plastic rulers. The rulers are cut to 23 cm and
thermometers are positioned at depths of 1, 3, 5, 9, 13, 17, & 21 cm. The string of thermometers is held to the front of
the aquarium with a bent paper clip (see me for a demonstration). In this manner, temperatures can be read directly and
quickly at the stated depths. An additional thermometer is used to read temperatures at intermediate depths as required,
inserting the thermometer into the water with as little turbulence as possible.
d. Methylene blue crystals. Before use, the dry crystals should be placed in the fold of a small piece of paper and gently
crushed by pressing the two sides together. In this way the crystals will be small enough so that most will dissolve
completely in the upper quarter of the water column.
e. your wind source.
f. standard graph paper.
Purpose
To illustrate thermal and temperature-dependent density stratification in a moderately deep lake in north temperate
latitudes, proceeding from spring through summer to autumn and back to winter again.
It is instructive in this
demonstration to try to separate the actions of sun and wind, and to that extent the model is unnatural. The demonstration
also illustrates the phenomena of internal seiches and convection cells sinking from the surface to the bottom during night or
autumnal cooling.
Procedure
1. Prepare a chart with columns for time, minutes elapsed, and temperatures at the depths at which you have thermometers.
Leave spaces at the extreme right for inserting temperatures at other (variable) depths.
2. Fill the aquarium with cold tap water and add excess ice to cool the water to 4° C with mixing. Allow the system to come
to rest (about 3-5 minutes). Now introduce a moderate wind on the top blowing from one side and then the other. After a
minute or two you will notice that the temperature at 1 cm has dropped to below 4° C. Why? Stop the wind and record
the temperature at the surface and on the thermometers at fixed depths. Next, remove the excess ice as gently as possible
and turn on the I. R. lamp. Record this as the beginning of the experiment (time zero). With the light on and no wind,
record temperatures at approximately 5 minutes, 12 min., 30 min., 45 min. and 60 min., taking special care to get
additional temperature readings in regions where temperature changes rapidly with depth (the upper 5 cm where the
thermocline is forming). Plot temperature as a function of depth on a piece of normal graph paper as they are recorded.
Connect isotherms in the same manner in which you drew isopleths on your contour maps in the map exercise. See the
demonstration chart for assistance. You will observe an exponential decrease in temperature with depth. Why?
3. With the lamp still on drop some crystals of methylene blue more or less randomly (and thinly) on the surface. Allow
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them sufficient time to sink so that most of the descending trails are in the upper third of the aquarium with a few
extending into the middle third and still fewer to the bottom. Observe the positions of the trails and the complexities of
the water motion, particularly near the surface. What can you infer about the currents in the water?
4. Now introduce a light-to moderate-wind blowing first from one side and then the other so as to mix up the surface water
into one homogeneous mass. Avoid too strong of a wind which could destroy the thermocline that you are now creating.
The epilimnion (with homogeneous distribution of color) should now be about 5-7 cm thick. Turn off the light. Allow
the currents to settle down and record the depth of the homogeneous blue layer and (summer) temperatures as a function
of depth.
5. Turn on the light. Using the same wind speed, create a slope of 10-15° to the thermocline by blowing from one side only.
You are stacking up the epilimnetic waters at the opposite end of the lake. This can best be achieved in stages, allowing
successive winds with intervening periods of quiescence to build up an internal seiche. When there is the desired slope to
the thermocline, stop the wind and measure the periods of the internal seiche (average approximately 5 measurements).
This is easiest to do if you concentrate on the oscillations that occur at one corner, counting the time it takes the layer to
rise, fall, and rise again to its initial level. Allow the system to come to rest, record the temperatures and measure the
depth of the homogeneous blue layer.
6. To simulate the cool nights of fall when the warm lake loses heat to the cooler air, carefully add a layer of ice cubes to the
surface with minimal disturbance of the water. It will be necessary to cover about 3/4 of the surface if small cubes from
the ice machine are used. Observe the descending convection cells sinking through the thermocline region causing the
thermocline to descend. When the thermocline has descended to about halfway down the tank, carefully remove the
remaining ice with a slotted spoon with as little turbulence as possible. Record temperatures and the depth of the
homogeneous blue layer.
7. Allow the system to come to rest and now simulate the strong storms of autumn which will be strong enough to turn over
our destabilizing lake. (Do not get splashing water on the lamp!) When mixing is complete record the temperatures. As
far as the lake is concerned, winter is beginning.
8. Although we cannot simulate these conditions, what kind of stratification occurs under the ice of a frozen lake?
Where is the water coldest? Where is it densest?
Calculations
1.
Density vs. temperature. Using the data on water density as a function of temperature (appended to this handout)
and a single sheet of graph paper, plot densities vs. depth, and temperature vs. depth. Note and explain the
differences.
2.
Heat Budget. There are various ways of expressing heat budgets. The one that we shall use here corresponds to the
heat gained by a lake between the time of its lowest and highest heat content (usually late winter to midsummer).
The simplest method of calculating the heat budget is to plot depth (Z) on the vertical axis vs. the products of
[Az x (Tsz - Twz)] on the horizontal axis, where
Az = Area of the stratum at depth Z, and
Tsz and Twz are the summer and winter temperatures.
The integral is measured either planimetrically or by counting squares, and the sum thus arrived at is divided by Ao
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(surface area of the lake). Since the area at all depths in the simplified case of the aquarium is the same as the
surface area, the heat budget will be given directly as the integral from Z = 0 to Z = max of (T sz - Twz)dz. If the
measurements of depth are recorded in cm and the heat capacity of water at all temperatures is taken as 1 gramcalorie per cm3 the integral will, with small error, be given in gram calories/cm2, the usual units in which heat
budgets are expressed. What then is the "annual" heat budget for the aquarium lake?
3.
Thermal resistance to mixing. This concept, invented by Birge, is a function of the density difference between the
top and bottom of a defined thickness of water relative to the difference in density between water at 4 oC and that at
5oC (0.000008). In our case, it is convenient to separate the lake into layers of 1 cm thickness.
On a sheet of graph paper, plot temperature as a continuous curve vs. depth using your data (a) for the aquarium
'lake' just prior to the first wind (i.e., when only the "sun" was shining) and (b) for the "lake” after the first wind
when a good thermocline had developed. Construct a table as follows:
Depth Interval (cm)
T2
D2
T1
D1
106(D2-D1)
[106 (D2-D1)]/8
0-1
1-2, etc
In this table, T2 and T1 are the temperatures at the bottom and top, respectively of the 0-1 cm layer, etc.; and D2 and
D1 are the corresponding densities for pure water at temperatures T 2 and T1. We are, of course, not dealing with
distilled water here, but so long as the water is homogeneous in total dissolved solids the difference in density (D2D1) will be solely determined by temperature. Finally, plot the results in graphic form. Note the pronounced
difference between the two situations of no wind and wind. What do you infer about turbulence and vertical
currents in the thermocline region? Recall the dye trails you saw near the surface when methylene blue crystals
were first added, before the wind was introduced. How do you now explain them?
4.
Periods of internal seiches. The periodic time of a seiche is the time required for an oscillation to complete one
cycle of up and down motion. You have determined such periods for two separate situations, one with a high
thermocline and the other with a lower thermocline. Were the periodic times identical?
The period of a uninodal internal seiche in a rectangular basin of uniform depth when the two layers have thickness
of Ze and Zh (e=epilimnion and h=hypolimnion) and mean densities of D e and Dh is given by
T  2L / ( g ( Dh  De) /[ Dh / zh  De / Ze)]
where L=length of the basin in the direction of the wind and g is the acceleration due to gravity (980cm/sec 2). Using
your data for the two internal seiches whose periods you measured, calculate the periods on the above theoretical
basis. Do the values agree? Explain in words why the periods for the two different seiches differed.
5.
The stability of a lake. Schmidt defined the stability of a lake as the amount of work needed to mix an entire lake to
a uniform temperature without the addition or subtraction of heat. Measuring the wok in g-cm/cm2, the stability, S,
is defined as
s  (1/ Ao) 
Zm
o
( Z  Zg )( Az )(1  Dz )(dz)
where Ao = surface area of the lake (cm2)
Az = area at depth z (cm2)
Z = depth under consideration (cm)
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Zg =
(1/ v)
Zm
o
(ZxAzdz ) =depth of the center of gravity of the unstratified lake (cm)
Zm = mean depth
Dz = density at depth Z
In our case, Az=Ao and Zg = mean depth (i.e., midway from top to bottom).
Note: The Schmidt stability equation is defined for the lake which has a period of isothermy at 4 oC in winter, hence
the "one" in the (1-Dz) term. For our purposes, it is preferable to substitute (D w,z - Ds,z) for this term. Dw,z is the
density of water at depth Z before you turned on the lamp ("winter" conditions). Ds,z is the density of water at depth
Z under summer conditions at the time of maximum heat content. The entire calculation is equivalent to raising the
entire lake by a distance equal to the difference between the center of gravity during stratification and the center of
gravity for homothermy.
For your report, derive a value for the Stability (S) of your lake using temperature data recorded before you
turned on the lamp, and the data recorded after you applied the wind (Step 4). The value of S is most easily
determined by plotting Z on the vertical axis and (Z-Zg) (Dw,z - Ds,z) on the horizontal axis. The area under the curve
is measured planimetrically or by counting squares, giving the stability in g-cm/cm2 (providing c-g-s units have
been used throughout).
Be sure that you have answered all questions that have been asked throughout this exercise!
Additional Models
There are other effects that may be studied if time permits.
These might include
1.
Simultaneous action of wind and sun on the thermal properties of lakes.
2.
Production of multiple thermoclines.
3.
The effects of irregular bottoms (sand bars, rock outcroppings, etc.) on water movements during mixing.
4.
Determination of eddy conductivity coefficients from temperature measurements with continuous wind in the
absence of light from the I.R. lamp.
5.
Determination of eddy diffusivity coefficients from dye concentrations with wind in the absence and presence of
light from the I.R. lamp.
6.
Determine the effects of colored water (simulating the humic staining that occurs in bogs and lakes with much leaf
litter input). Dense tea solutions can be used here.
7.
The effects of varying the angle of the "sun's" rays on the lake, simulating seasonal movements. (In our original
model, we always had the sun directly overhead--this would only happen in the tropics.)
8.
Calcium carbonate precipitation with high surface temperatures from an initially saturated solution (of cold water).
This simulates 'whiting'.
9.
Differences of thermal activities in a tropical lake, i.e., one that never cools to less than 20 oC.
10. The effects of identical sun and wind conditions on lakes of different depths.
11. Effect of the earth's rotation on the motion of internal seiches (e.g., hitch up a stirrer motor to an aquarium system
on a rotatable laboratory stool.)
Note: These laboratory exercises are modified slightly from those written by Dr. J. Vallentyne, and used by Dr. David
Culver of The Ohio State University. For additional information, see: Vallentyne, J. R. 1967. A Simplified Model of a Lake
for Instructional Use. J. Fish. Res. Bd. Canada 24 (11): 2473-79.