# Limnology Problem Set 1

```Limnology Problem Set 1 2005
Geological, Physical and Chemical Limnology
The purpose of this problem set is three-fold –
(1) To give you some experience solving physical and chemical limnological problems.
In contrast, the exam (7 October) will concentrate more on concepts than on solving
equations for specific values (you will not need to memorize equations for the exam).
(2) To provide a few more practical examples of how limnologists actually use all of the
concepts and equations that you’ve been learning in the past few weeks.
(3) To help you integrate some of the physical, chemical and biological ideas that we’ve
learned so far.
Due in class Friday 30 September 2005
 Don’t panic! Most (all?) people find the problem sets tougher than the exam.
 You can work in groups, but I expect that you will each hand in answers separately.
 Show your work to receive partial credit. Write clearly so that we can read and decipher
what you’ve done 
 Feel free to see or email me or Jason (the TA) if you have questions.
1. You are hired to help manage three lakes in a large state park. Most of the lakes in the region
are kettle lakes, but you find a brochure on the geology of the park stating that the three lakes in
the park were formed by three different processes. One is a typical kettle lake, one is a plunge
pool lake, and one a reverse drainage basin. Unfortunately the brochure doesn’t specify which
lake is which! However, the brochure does list a few basic morphometric parameters for the
lakes:
Lake surface area (A0
in m2)
Length of shoreline
(m)
Trout Lake
245,280
Bass Lake
272,300
Sunny Lake
296,500
2,026
7,600
4,065
a. How can you use these morphometric parameters to determine how each lake was likely
formed?
b. Which lake is likely the kettle lake, which the plunge pool lake, and which the reverse
drainage basin? (Show any calculations and explain your reasoning).
c. What other parameter(s) might you want to measure to verify your above informed guess
on each lake’s origin?
2. One of lakes is much more transparent than the others, despite the close proximity of all three
lakes. Your first task as assistant lake manager is to compare the optical properties of the
clear lake with one of its neighbors, and determine why it is more transparent. You head to
the lakes with a light meter and find the following:
1
Depth (meters)
Trout Lake
Bass Lake
-2 -1
Light (moles quanta m s )
Light (moles quanta m-2 s-1)
PAR
PAR
0
650
1800
1
590
990
2
530
540
3
480
300
4
435
160
5
395
90
6
355
50
7
320
27
8
290
15
9
265
Bottom of lake
10
240
11
215
12
195
13
180
14
160
15
145
a. Plot light versus depth (using the typical limnological backwards graphs) for each lake.
b. Calculate the light attenuation coefficients for both lakes. Which lake is clearer?
c. Often limnologists calculate the depth at which 1% of incident (surface) light remains in
the lake. They do this because the 1% light level is thought to be the depth at which
phytoplankton no longer receive enough light energy for photosynthesis to exceed
respiration (this is considered the depth at which the ‘euphotic’ zone ends). Calculate the
depth at which 1% of surface light remains for both lakes. Which lake has a deeper
euphotic zone?
d. You are trying to determine what is attenuating light more in the less clear lake. You find
data that suggest the absorption of light at 600 nm does not differ significantly between
the two lakes, and that there is a lot of chlorophyll in the seston of the more turbid lake.
What do these observations tell you about the cause of the water clarity differences
between the two lakes? Which lake do you think is more productive?
e. Do you think you can manage the more turbid lake so that it has the same water clarity as
the clearer lake? Why or why not?
2
3. You graduate from ESF and become the limnologist for your local town (Homeville). The
town upriver from you, Beavertown, wants to build a dam to generate hydropower.
Beavertown is also dumping sewage (treated with secondary treatment) into the river, and
would continue to dump the sewage outflow into the bottom of the reservoir they are
constructing upstream of your town. Beavertown argues that the reservoir outlet will be at
the top of the dam, and so the sewage will be trapped in the reservoir below the thermocline,
where bacteria can break it down, causing you less trouble than if they dumped the sewage in
the river, as they do now.
You are skeptical of some of Beavertown’s claims, and worried that nutrient rich, potentially
anoxic water will run downstream, degrading your stream ecosystem as well as causing damage
to your tourism and fishing industries. Because you are such a good limnologist, you know that
many lakes have internal seiches that can cause the thermocline to oscillate, and can result in
upwellings. You first do a few calculations to see whether internal seiches in the reservoir may
bring hypolimnetic water (filled with Beavertown sewage) to the surface through upwelling
events, thus allowing it to flow downstream to Homeville.
The proposed reservoir is 5 km long in the direction of the wind and 25 m deep. Based on other
similarly sized local lakes, you believe the reservoir will stratifies with 22 degree C epilimnetic
water, and an epilimnion thickness of 5 m. The bottom water should be 8 degrees C throughout
the summer. The mean summer wind speeds in your region are about 4 m/sec. You look up the
acceleration of gravity (9.8 m s-2) and find a water density table (units of g cm-3; see last page of
problem set) to assist your calculations.
(a) Based on the parameters above, what is the height of the seiche during average winds
in summer?
(b) How big a sustained wind is necessary to get an upwelling in summer?
(c) Describe one other physical, chemical or biological occurrence that would happen if
there was upwelling and hypolimnetic water poured over the dam into the stream.
(d) In addition to potential upwelling, are there any other problems that you believe
should be investigated before this project is permitted to continue?
4. Lake source cooling is a method by which cool hypolimnetic water from deep lakes is used to
cool buildings. The water is piped from the lake to buildings. The cool lake water cools the
buildings and gets warmer through exchange of heat with the air of the buildings. In many places
this method is thought to be ‘green’ (environmentally friendly) because it does not use ozonedestroying or untested chemicals for cooling. The energy expenditure is also greatly reduced,
although there is, of course, fuel burned by the pumps that bring the water to the buildings.
Recently, Cornell University developed a lake source cooling plant using the bottom waters of
Cayuga Lake. The water used in the cooling is then returned to the epilimnion. This plan was
controversial, because many people in the town (Ithaca) were concerned that the returning water
would (1) add excess heat to the lake, and (2) add excess phosphorus to the lake (because the
water was originally from the nutrient-rich hypolimnion).
3
The annual heat budget for Cayuga Lake is ~1.5*109 J/m2, and the lake source cooling project
will return the following amounts of heat to the lake compared with the monthly lake heat
storage:
Month
January
February
March
April
May
June
July
August
September
October
November
December
Lake Source Cooling Heat
(J/m2)
1.87 * 105
1.55 * 105
1.82 * 105
2.91 * 105
4.11 * 105
1.11 * 106
1.16 * 106
1.16 * 106
1.13 * 106
4.45 * 105
2.90 * 105
1.93 * 105
Minimum Cayuga Lake
Heat Storage (J/m2)
5.82*108
4.74*108
4.16*108
5.28*108
9.48*108
1.37*109
1.68*109
1.81*109
1.85*109
1.64*109
1.31*109
8.82*108
(a) Calculate the percentage of heat added each month due to the return of warm water from
the lake source cooling project. Calculate the percentage of added heat by lake source
cooling relative to the overall annual heat budget of the lake.
(b) Will this lake source cooling project substantially affect Cayuga Lake’s thermal regime or
stability? Why or why not?
(c) There is currently a proposal to have a similar project in Syracuse, where cool hypolimnetic
water from Lake Ontario would be piped to Syracuse for cooling, and the warm water
would be returned to Onondaga Lake. Some morphometric parameters for the two lakes
are listed below.
Parameter
Cayuga
Onondaga
172
Surface area [km2] 172
12
9.4
0.13
Volume [km3]
Maximum depth [m]
Mean depth [m]
132.6
54.5
19.5
10.9
4
(1)Do you think that this project would have greater or lesser effects on the heat budget of
Onondaga Lake than the Cornell project had on Cayuga Lake? Why?
(2)How would you go about assessing the potential thermal effects of this project on
Onondaga Lake?
(3)How might you minimize thermal effects on the lake?
(d) Might either of these projects (the Cayuga lake source cooling project already being
implemented, or the proposed Syracuse project) have other effects (in addition to thermal
effects)? Describe two ways you would evaluate the impact of one of these projects on its
lake.
5. “Liming” is one method by which people attempt to remediate the effects of acid precipitation.
When a lake management group decides to lime a lake or a watershed, they add CaCO3 or
Ca(OH)2 to the lake to increase the pH.
(a) Why would adding CaCO3 help to increase a lake’s pH and remediate acid precipitation
problems?
(b) You are hired by a lake association that is worried about acid precipitation. Their lake
currently has a pH of 5.8, but had a pH of 6.8 historically. If the pH is reduced much further,
the lake will become inhospitable to valued sports fish. First, the lake association wants to
know what the alkalinity of their water is.
You remember that alkalinity is determined by titration of buffering capacity with an acid.
You titrate a 200 mL lake water sample with 0.1 N HCl (N=Normality) and find that it takes
2.5 mL of acid to convert all of the carbonate species to CO2 and neutralize all and OH- and
anions of weak acids.
(1) What is the alkalinity of the water in units of mequivalents per liter?
(2) If you assume that all of the alkalinity in the lake is due to inorganic carbon and OH-,
what were the concentrations of CO2, HCO3- and CO32- in the sample before titration?
(c) The association is interested in liming the lake annually to counter future additions of
acidity and prevent further declines in pH. They have learned from United States Geological
Survey data that the average daily rainfall brings 3,000 mol of H+ per m2 of lake surface
(including watershed input). The lake itself is 450,000 m2 in surface area (4,500,000 m3 in
volume).
(1) How much CaCO3 will the lake association need to add to their lake annually to
counter this acidity? (you can report your answer either in equivalents or grams)
(2) If CaCO3 costs \$30 per ton (1 ton=2000 pounds; don’t forget to convert to metric),
how much will it cost annually to purchase lime to buffer this small lake? (hint: you will
need to convert your answer from the previous question from equivalents to weight to
complete this if you haven’t done so already)
5
The values in this table are water densities. To find the water density at 4.7 degrees, for example,
you would go down the first column to find 4 degrees, and then move columns over to the right
until you were at the 0.7 degree column. That value would be the water density at 4.7 degrees in
units of g/cm3. Water density values for integer temperatures are therefore in the first column of
density values.
6
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