Dr. Martin T. Auer MTU Department of Civil & Environmental Engineering ENVE5504 Surface Water...
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Dr. Martin T. Auer MTU Department of Civil & Environmental Engineering ENVE5504 Surface Water Quality Modeling Lab 4. One-Dimensional Models Vertical Mass Transport in Dollar Bay, Michigan
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Transcript of Dr. Martin T. Auer MTU Department of Civil & Environmental Engineering ENVE5504 Surface Water...
Dr. Martin T. AuerMTU Department of Civil & Environmental Engineering
ENVE5504Surface Water Quality
ModelingLab 4. One-Dimensional Models
Vertical Mass Transport in Dollar Bay, Michigan
8
8
Lake Superior – 8/25/00
Vertical Resolution: Lake Superior
Temperature and the Density of Water
1.0000
0.9995
0.9990
0.9985
0.9980
0.9975
0.9970
0.9965
0.9960
0.99550.9950
Den
sity
(g∙
cm3 )
0 5 10 15 20 25 30
Temperature (°C)
MaximumDensity3.94 °C
Thermal Stratification
spring summer
Temperature (°C)
Thermal Stratification
Seasonality in Stratification and Mixing
= °C
Dollar Bay - Temperature
0
1
2
3
4
5
6
7 8
Dep
th (
m)
0 5 10 15 20
Temperature (°C)
0
1
2
3
4
5
6
7
8
Dep
th (
m)
M A M J J A S O N D
Productivity and Oxygen
Trophic State and Oxygen Profiles
Orthograde
0
2
4
6
8
10
12
14
16
18
20
0 5 10 15 20 25
De
pth
(m
)
Clinograde
0
2
4
6
8
10
12
14
16
18
20
0 5 10 15 20 25
De
pth
(m
)
Oligotrophic Lake Eutrophic Lake
Temperature (°C) Temperature (°C)
Dollar Bay - Temperature
0
1
2
3
4
5
6
7 8
0 5 10 15 20
Temperature (°C)
0
1
2
3
4
5
6
7
8
Dep
th (
m)
M A M J J A S O N D
Dollar Bay – Dissolved Oxygen
Dep
th (
m)
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10 12
Dissolved Oxygen (mg∙L-1)
M A M J J A S O N D
Onondaga Lake – Dissolved Oxygen
Oneida Lake – Dissolved Oxygen
Lake Erie – Dissolved Oxygen
Gulf of Mexico – Dissolved Oxygen
8
8
Lake Superior – 8/25/00
Vertical Resolution - Stratification
Vertical Mass Transport
11 2 1' ( )dC
V E C Cdt
' cE AE
l
Application to Vertical Mass Transport
11 2 1
33
3 3
' ( )dC
V E C Cdt
g m gm
m d d m
g g
d d
11 2 1
3 23 3
( )t t
dCV v A C C
dt
g m gm m
m d d m
g g
d d
turbulent diffusion coefficient thermocline heat transfer coefficient
Calculation of the Thermocline Heat Transfer Coefficient
Epilimnion Heat Balance
3 33 2 2
3 3 3 2 3
( ) ( )ee p p in p e s t p t h e
dTV C Q C T t Q C T J A v C A T T
dt
g cal C m g cal m g cal cal m g calm C C m m C
m g C d d m g C d m g C m d d m g C
cal cal cal cal cal
d d d d d
changein heat
tributaryheat in
dischargeheat out
surfaceheat flux
thermoclineheat exchange
Calculation of the Thermocline Heat Transfer Coefficient
Hypolimnion Heat Balance
3 23 3
( )hh p t p t e h
dTV C v C A T T
dt
g cal C m g calm m C
m g C d d m g C
cal cal
d d
changein heat
thermoclineheat exchange
assumes no direct heating ofhypolimnion or sediments
upper mixed layer(~epilimnion)
lower mixed layer(~hypolimnion)
thermocline vt∙As
Calculation of the Thermocline Heat Transfer Coefficient
( )hh p t p t e h
dTV C v C A T T
dt
h t t t te e
h h
dT v A v AT T
dt V V
t th
h
v A
V
Canceling the and Cp terms, dividing by Vh and expanding …
And defining …
Yields …
hh e h h
dTT T
dt
uml
lml
Calculation of the Thermocline Heat Transfer Coefficient
, (1 )h ht th h i eT T e T e
,
,
ln e h iht
t s e h s
T TVv
A t T T
and re-arranging, yields …
Which, for Th at the beginning of the calculation = Thi, yields …
,
,
1ln e h ih
st t e h s
T TVt
v A T T
further re-arranging, yields …
where a plot of ts versus termyields 1/vt as the slope
term
Application to Dollar Bay
Dollar Bay - Temperature
0
1
2
3
4
5
6
7 8
0 5 10 15 20
Temperature (°C)
0
1
2
3
4
5
6
7
8
Dep
th (
m)
M A M J J A S O N D
Dollar Bay – Dissolved Oxygen
Dep
th (
m)
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10 12
Dissolved Oxygen (mg∙L-1)
M A M J J A S O N D
0
2
4
6
8
10
12
14
16
18
20
0 50 100 150 200 250 300 350
For diffusion calculation, need to choose an interval where Te is stable and Th is warming.
Dollar Bay – Temperature Calculations
,
,
1ln e h ih
st t e h s
T TVt
v A T T
( )h t te h
h
dT v AT T
dt V
Hypolimnion temperature mass balance.
Sediment oxygen demand reflects the diffusion of oxygen into the sediment to meet the metabolic needs of microorganisms participating in the aerobic decomposition of organic matter. SOD is also exerted through the aerobic oxidation of reduced species byproducts of anaerobic respiration.
The mass balance, for SOD alone is …
Sediment Oxygen Demand
uml
lml
2 12,SOD gO m d
2sed
dOV SOD A
dt
0
2
4
6
8
10
12
0 50 100 150 200 250 300 350
For the SOD calculation, we need to choose the interval of oxygen depletion.
Dollar Bay – Oxygen Calculations
22, 2,
t t sede h
h h
v A SOD AdOO O
dt V V
Time-Variable vt
Values for Onondaga Lake (Doerr et al. 1996)
