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Control Volume
Inputs
Mass Balance Modeling
Outflows
The “Check-book” Analogy.
Balance = deposits – withdraws
Is a $50 account balance a large amount?
The answer depends in part upon a couple factors.
Is there a difference between :
In: $200 $2000Out: $150 $1950Net: $50 $50
The “Check-book” Analogy.
Account Balance = deposits – withdraws
Relative importance of inflows and outflows depends upon how much $ you’ve got in the account and the size of both inputs and outflows relative to this amount.
Mean Summer Circulation
Population Around the Great Lakes
0 40 80
km
85
Chicago
South Haven
86oo
87o
88o
46 o
45 o
44 o
43 o
42 o
Green Bay
LAKE MICHIGAN
LAKE MICHIGAN FACTS
Lake Michigan is the third largest Great Lake by surface area and the sixth largest freshwater lake in the world. Many rivers and streams flow into Lake Michigan, and the major tributaries are the Fox-Wolf, the Grand and the Kalamazoo. There is a diversion from the lake into the Mississippi River basin through the Illinois Waterway at the Chicago River. Small lunar tidal effects have been documented for Lake Michigan1. Internal waves (upwellings) can produce a 15 degree C. water temperature decrease along the coast in only a few hours, requiring drastic alterations in fishing strategy1. The northern part of the Lake Michigan watershed is covered with forests, sparsely populated, and economically dependent on natural resources and tourism, while the southern portion is heavily populated with intensive industrial development and rich agricultural areas along the shore. The world's largest freshwater dunes line the lakeshore.
1. Ayers, John C. "Great Lakes Waters, Their Circulation and Physical and Chemical Characteristics," in Great Lakes Basin: A symposium presented at the Chicago Meeting of the American Association for the Advancement of Science, 29-30 December, 1959. ed. Howard J. Fincus. 1962. Washington, D.C. American Association for the Advancement of Science.
LAKE MICHIGAN
LENGTH: 307 miles / 494 km. BREADTH: 118 miles / 190 km. AVERAGE DEPTH: 279 ft. / 85 m MAXIMUM DEPTH: 925 ft. / 282 m. VOLUME: 1,180 cubic miles / 4,920 cubic km. WATER SURFACE AREA: 22,300 sq. miles / 57,800 sq. km. TOTAL DRAINAGE BASIN AREA: 45,600 sq. miles / 118,000 sq. km.SHORELINE LENGTH (including islands): 1,638 miles / 2,633 km. ELEVATION: 577 ft. / 176 m. OUTLET: Straits of Mackinac to Lake Huron RETENTION/REPLACEMENT TIME: 99 years
North Carolina
SURFACE AREA: 53821 sq. miles or 48718 sq miles of land
WATER SURFACE AREA:5103 square miles
SHORELINE LENGTH (including islands): 3375 miles
2.41 times larger surface area than Lake Michigan
Riverine
Water-Sediment
Exchange
Exchange
Accumulation
Air-Water
Exchange
Wet & Dry
Deposition
Water
Exchange
Exchange
SHELF
SEDIMENT
DEEP SEDIMENT
Generic Model of Mass Budget Pathwaysfor POPs in Limnic and Marine Systems
Inputs
Mixing
Water
Exchange
Mass Budget for Lake Michigan
Burial ? kg/yr
Atmos. DepositionWet ? kg/yr
Dry kg/yr
Outflow ? kg/yr
Gross Gas Volatilization
? kg/yr
Riverine ? kg/yr
Green Bay ? kg/yr
Water Column ? kg
in Sediment ~ ? kg
?+ ? kg/yr
net loss from lake? kg/yr (est.)
Gross Gas Absorption? kg/yr
Lake Michigan PCB mass budget .
Decline in [PCB] over time
R2 = 0.98
0.0
0.5
1.0
1.5
2.0
2.5
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
Con
cen
trat
ion
(n
g/L
) 19
9
6
20
24
5
[PCB]year = [PCB]1980 - 0.12 ( year - 1980)
R2 = 0.88
-2
-1.5
-1
-0.5
0
0.5
1
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
Ln
Con
cen
trat
ion
Mass Budgets for Lake MichiganMass budgets for PCBs in Lake Michigan: 1991, 1994 and 1994 with urbanatmospheric loadings.
1991 1994 1994-Urban
Total PCB Mass inWater Column (kg)
2280 965 965
Inputs (kg/year)
Riverine 110 45 45
from Green Bay 115 115 115
Atmospheric Deposition Wet 90 50 100
Dry Aerosol 20 50 1090
Gas Absorption 330 280 510Total Loadings 665 540 1860
Outflows (kg/year)
to Lake Huron 25 10 10
Burial 1530 730 730
Net Loss 170 440 440Volatilization 1025 640 640Total Losses 2750 1820 1820
Loadings - Losses = -2085 -1280 40
91% of inventory
-132% of inventory
4% ofinventory
Inflows in kg / year
Wet Deposition1005%
Dry Deposition109059%
Gross Gas Absorption51027%
Riverine452%
from Green Bay1156%
Inflows
Outflowsin kg / year
to L.Huron101%
Gross Gas Volatilization64035%
Net Sedimentation73040%
Net loss44024%
Outflows
Mass Budget for Lake Michigan
Burial 730 kg/yr
Atmos. DepositionWet 100 kg/yr
Dry 1090 kg/yr
Outflow 10 kg/yr
Gross Gas Volatilization
640 kg/yr
Riverine 45 kg/yr
Green Bay 115 kg/yr
Water Column 965 kg
in Sediment ~75000 kg
?+ 40 kg/yr
net loss from lake440 kg/yr (est.)
Gross Gas Absorption510 kg/yr
Lake Michigan PCB mass budget in 1994 including influence of urban areas.