control volume inputs mass balance modeling outflows

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.