Model
derivations
for
nutrient diversion
on
lakes
A.
Akkoyunlu
Bogaziqi
University,
Engineering
Faculty,
Civil
Engineering
Department,
80815
Bebek,
Instanbul,
Turkey
Email:
akkoyun@boun.
edu.
tr
Abstract
Lakes
are
frequently subjected
to
wastewater
discharges.
If
nutrients
like
nitrogen,
phosphorus
and
carbon
are
present
in
sufficiently
large
amounts,
the
water
body
will
be
polluted
and
eutrophication
can
take place. Eutrophication
of
a
lake induced
by
municipal wastes
can be
retarded
by
removing
the
source
of
plant
nutrients, notably
phosphorus.
This
is
accomplished
by
diversion
of the
effluent
around
the
lake,
or by
treatment
of the
wastewater
employing
advanced
treatment processes.
In
this
study,
first a
mathematical
model
with different
assumptions
about
nutrient
exchange
processes
is
introduced, then
the
mass
balance considering
input,
output,
net
loss
to the
sediments
was
used
to
predict
the
lake nutrient
concentration
as a
function
of
nutrient residence time.
Lake
Iznik located
in the
southern part
of the
Marmara
region
of
Turkey
is
subjected
to
three different
levels
of
nutrient loadings, with
a
certain
amount
of
diversions each time
to
study
the
response
of the
lake.
1
Introduction
Eutrophication
is the
enrichment
of
water bodies with nutrients such
as
nitrogen
and
phosphorus.
One of the
methods
for
controlling
or
minimizing
lake
eutrophication
is to
reduce
the
rate
of
nutrient flux
into
lakes.
Regulatory
agencies require predictions
of the
impact
of
present
and
future nutrient inputs
on
lake
quality.
Those
who are
concerned
with lake
management
need
to
know
Transactions on Ecology and the Environment vol 27 © 1999 WIT Press, www.witpress.com, ISSN 1743-3541
264
Ecosystems
and
Sustainable Development
the
rate
of
improvement
which
might
be
expected
as a
result
of
reduced nutrient
discharge into
a
lake.
It is
important
to
know
how
fast
and to
what
extent
will
a
lake
respond
to a
change
in the
nutrient
influx.
*
Diversion
of
wastewaters
away
from a
lake
has
various degrees
of
success
in
decelerating
or
reversing
the
process
of
eutrophication.^
A
simple
model
is
presented
in
this
paper
to
predict
the
response
of
lakes
to
changes
in
nutrient influx.
The
model
give
a
good
solution
of the
problem
for
the
purpose
of
watershed
planning
and
management.
2
Lake
Iznik
Lake
Iznik
is
located
in the
southern part
of
Marmara
region within
the
province
of
Bursa
(see
Figure
1). It has an
average surface area
of
304.30 km^,
and a
mean
volume
of
12.12
billion
mV
Drainage
area
of
the
lake
is 626
knf. Lake
Iznik
was
formed
by a
tectonic depression
which
took
place during geological
ages.
Figure
1:
Drainage
area
of
lake Iznik
Transactions on Ecology and the Environment vol 27 © 1999 WIT Press, www.witpress.com, ISSN 1743-3541
Ecosystems
and
Sustainable
Development
265
3 A
Simple
Model
for
nutrient
exchange
processes
in
Lakes
In
this
paper
a
model
is
derived
taking
into
consideration
different
assumptions
about
nutrient
exchange
processes/
Assuming
that
long term
effects
can be
approximated
by
average annual
values
in a
well-mixed
lake,
a
mass
balance
can be
written
on the
nutrient
of
interest.
A
diagrammatic
representation
of
this
case
is
shown
below.
Q,C,
Q,C
KC
Figure
2:
Diagrammatic
representation
of
the
model
The
rate
of
change
in
concentration with time
is
given
by
dc
M CQ KCA
dt
" V ~ V V
where
M =
mass
flow in from
all
sources, g/yr
C =
average
annual
nutrient
concentration, g/m^
k = net
specific
rate
of
loss
to
sediments, m/yr
Q =
average annual outflow, m^/yr
V =
lake
volume,
m^
A =
surface area
Co =
nutrient
concentration
at
time zero, g/m^
t
=
time,
yrs
Integration
of
Equation
1 from Co at
time zero
to C at
time
t
yields
(1)
Transactions on Ecology and the Environment vol 27 © 1999 WIT Press, www.witpress.com, ISSN 1743-3541
266
Ecosystems
and
Sustainable
Development
M
Q+KA
Q+KA
c = -
-(1-e
(2)
Equation
2
describes
the
concentration
of
nutrient
in the
water
as a
function
of
time
as a
result
of
changing
the
nutrient input rate,
M.
The
model
can be
incorporating
the
nutrient fluxes into
and out of the
sediments independently
as
shown
in
Figure
3.
M ->
CQ
k:C,
Figure
3:
Diagrammatic
representation
of the
Model
For
cases
in
which
the
nutrient concentration
in the
sediments
does
not
change
significantly over time,
mass
balance
yields
dc
dt
M
k,C,A k^CA
CQ
V
V
V
V
(3)
in
which
M, C, Q, V, A, Co are as
previously defined
ki
=
specific rate
of
nutrient
transfer
to
sediment,
m/yr
k%
=
specific
rate
of
nutrient transfer
from
sediment,
m/yr
Cs=
nutrient
concentration
in
sediment,
g/m^
The
solution
to
Equation
3 is
(4)
Transactions on Ecology and the Environment vol 27 © 1999 WIT Press, www.witpress.com, ISSN 1743-3541
Ecosystems
and
Sustainable
Development
267
In
this
case
the
specific rates
ki and k%
must
be
determined independently.
Thirdly
we can
take
into
account
the
possibility that
nutrients
may be
depleted
from
the
sediments
when
nutrient
input
to the
water
is
decreased.
In
this
case
the
value
ofC,
is
variable.
The
diagrammatic
representation
of
this
model
is
shown
in
Figure
4.
Notice
that
here
we
have
a set of
coupled
differential
equations representing
the
nutrient
concentration
in
water
(C) and
sediment
(C,).
M
CO
Figure
4:
Diagrammatic
representation
of
the
Model
dc
M
k,C,A k,CA
CQ
dt
" V
"^
V " V "" V
k,CA
k,C A
dt
V.
V.
(5)
(6)
in
which
M, C, Q, V, A, Co,
ki,
k%, C, are as
previously defined
and V,
volume
of
sediment.
The
solution
to the
coupled
set of
Equations
5 and 6 is
somewhat
more
complicated
and the
solution procedure
is
outlined
in
detailed
in the
reference/
3.1
First
form
of the
model
presented
in
this
study
The
last
form
of the
model
presented above require information
about
the k%, k:
rates,
Cs
nutrient
concentration
in
sediment
and V,
volume
of
sediment.
Therefore
at
first
step
the
simple
model
represented
in
Equation
1 was
studied.
Transactions on Ecology and the Environment vol 27 © 1999 WIT Press, www.witpress.com, ISSN 1743-3541