Modeling Lakes?
Center for Watershed Science & Education
UW- Stevens Point
Lake Leaders 2010
What’s a model
One definition: A mathematical description to
help visualize something
What’s a model
One definition: A mathematical description to
help visualize something
80 lb
Phosphorus/yr
325 million
gallons/year
A model for
the
phosphorus
concentration
in a lake
Amount of
Phosphorus
= ------------------------
Amount of
Water
80 lb
Phosphorus/yr
325 million
gallons/year
= 80 lb/ 325 million gallons =
80 lb
Phosphorus/yr
325 million
gallons/year
= 80 lb/ 3 billion lbs water=
80 lb
Phosphorus/yr
325 million
gallons/year
= 80 lb/ 3 billion lbs water= 27 ppb
Why Model?
• Groundwater flow– where water is coming
from?
• Lake concentration —what if we change the
amount added?
• Watershed modeling– can watershed
changes help and by how much?
• In-Lake Restoration – “experiment” with
treatment, diversions etc.
Rule #1
“All models are wrong but some are useful”
George Box
32”
Watershed
Models
10”
22”
300,000
microgram
/liter
40
microgram
/liter
Land is a concentrated nutrient source
Simple Model:
Assign annual
transfer rate to
different land
uses
Complex Model:
Simulate every storm,
interaction with ground,
conveyance to channel,
transport to lake
Rule #2
“Make everything as simple as possible, but not
simpler”
A. Einstein
Lake Models
Water
Quality
FISH
Zooplankton
Bacteria
Algae
NUTRIENTS
WATER
Lake Models
Phosphorus
Concentration
(mg/l)
Productivity
10
Low (Oligotrophic)
10-20
Medium (Mesotrophic)
Greater than 20
High (Eutrophic)
Annual
Phosphorus
Input
Simpler Models…
--completely mixed
-- steady with time
Annual Water
Input
Complex Models…
--segments in lake
--vary with time
--biology!
Annual
Phosphorus
Settling
Lake Response Model?
Phosphorus
Concentration
Algae
Concentration
Application to Portage County
J a Be
cq ar
So uel
ut ine
h
Tw
in
W
Se o l
ve f
rs
Su on
n
Th set
om
as
Li
on
Sk s
u
Fo n k
un
ta
O in
nl
an
Sp d
rin
Co g
llin
Bo s
el
t
Ad er
am
s
Em
Ri ily
ne
Am
he P har
rs ick t
tM e
ill rel
Po
nd
Eb
er
t
Be
nt Tre
ly
e
Po
Ro nd
sh
o
J o lt
rd
an
Li
m
e
Jo
na
M s
Sp cD
rin ill
gv
ille
He
le
n
Chloide (mg/L)
T
Fo re e
un
ta
R in
os
ho
l
B Jor t
en d
t ly a n
P
on
d
M
A
cD
m
he
i
rs Sp ll
t M ri
ill ng
P
on
d
E
b
S
pr er t
in
gv
ill
e
J a Be
cq ar
ue
S line
ev
er
s
S on
un
se
t
W
o
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S oel
ou te
th r
Tw
in
Li
on
O s
nl
an
S d
ku
Th n k
om
a
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na
s
Li
m
e
H
el
R en
in
eh
P ar t
ic
ke
re
l
E
m
i
A ly
da
m
C s
ol
lin
s
NO2+NO3-N (mg/L)
Median Nitrate
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
Median Chloride
25.00
20.00
15.00
10.00
5.00
0.00
Th
om
Am
a
he
rs On s
t M la
ill nd
Po
Ri nd
ne
ha
r
Eb t
Fo er
un t
ta
in
Jo
na
Pi
s
ck
er
el
Em
i
S u ly
ns
Ad et
am
s
Li
on
s
W
Se o l
ve f
rs
o
Sk n
un
Jo k
rd
an
Be He
nt
l
ly en
Ja Pon
cq d
ue
lin
e
Be
a
Co r
llin
s
Tr
Ro e e
sh
ol
t
Li
m
Sp e
rin
g
M
So cD
ut
i
h ll
Sp Tw
rin in
gv
i
B o lle
el
te
r
Chlor a (mg/L)
Ad
am
O s
nl
an
d
Jo
na
s
Eb
er
Em t
ily
Li
on
Ri
ne s
h
Fo ar
un t
ta
i
Sk n
un
Su k
ns
Pi et
ck
Se ere
ve l
r
Th son
om
as
W
ol
f
Be
a
H r
Ja e l
cq en
ue
lin
e
Tr
ee
Co
llin
s
So Lim
ut
h e
Sp Tw
rin in
Am
gv
ill
he
rs
M e
t M cD
ill ill
Po
nd
Jo
rd
Ro a n
sh
ol
Be Sp t
nt rin
ly g
Po
n
Bo d
el
te
r
TP (μg/L)
Median Total Phosphorus
70
60
50
40
30
20
10
0
Median Chlorophyll A
20
18
16
14
12
10
8
6
4
2
0
ou
th
B
Tw
in
o
Ja elt
cq er
ue
lin
e
B
e
C ar
ol
S lin s
e
B ve
en rs
tly on
P
o
R nd
os
ho
lt
Li
m
e
S
pr
in
A g
da
m
s
A
E
m
be
he
r
rs Jo t
t M rd
ill a n
P
on
S d
un
se
t
Tr
Fo e e
un
ta
i
M n
cD
S ill
ku
nk
Jo
S na
pr
in s
gv
R ille
in
eh
ar
Li t
o
Th n s
om
a
O s
nl
an
d
E
m
ily
H
el
en
W
P o lf
ic
ke
re
l
S
pH
Ja
So cqu
u l e li
th n e
T
Bo win
e
C lter
ol
lin
Be s
Jo a r
Th an
om is
O as
n
Pi lan
ck d
e
Li rel
Su ons
ns
e
Em t
H ily
el
e
M
cd W n
il l o lf
P
J o R on
rd os d
a n ho
Po lt
n
Tr d
Sk e e
un
Se Li k
v e me
Fo rso
un n
t
Be ai n
nt
ly
E
R be
Sp in eh rt
ri n ar
gv t
Sp i ll e
Am ri n
he g
Ad rs t
am
s
mg/L as CaCO 3
Average Total Hardness in Portage Co. Lakes
250
225
200
175
150
125
100
75
50
25
0
Median pH
10.00
9.50
9.00
8.50
8.00
7.50
7.00
6.50
6.00
5.50
5.00
• Groundwater Inputs (based on groundwater
modeling)
• Surface watershed inputs (two categories:
developed and undeveloped)
• In-lake – mixed and steady-state
Portage County Model
Groundwater Flow System
Used Actual Lake Data to
Determine Watershed Export
Coefficients
Current Condition
Questions