Geoscience Reference
In-Depth Information
m
−
3
, i.e., gramof phosphorus per
cubic meter); and
k
N
,1
/
2
and
k
P
,1
/
2
are the Michaelis-Menten half-saturation nitrogen
and phosphorus concentrations for phytoplankton growth, respectively.
C
NH
3
,
C
NO
3
,
and
C
PO
4
are determined using Eqs. (12.78), (12.79), and (12.86), respectively.
Phytoplankton growth is a function of light intensity, until an optimal value is
reached. The light limitation factor can be determined by Smith's (1936), Steele's
(1962), or the half-saturation approach. The half-saturation approach gives
inorganic (dissolved) phosphorus concentration (gP
·
I
z
k
L
,1
/
2
f
L
=
(12.67)
+
I
z
where
k
L
,1
/
2
is the Michaelis-Menten half-saturation light intensity for phytoplankton
growth; and
I
z
is the light intensity at a given height
z
and varies with
z
according to
Beer's law:
I
z
=
I
0
exp
[−
λ(
z
s
−
z
)
]
(12.68)
where
I
0
is the light intensity at the water surface, and
is the light extinction
coefficient. Note that the energy source for photosynthesis is the light in the range
of 400- to 700-nanometer wavelengths. It is called the photosynthetically active radi-
ation (PAR). PAR is different from the insolation
J
Tsw
in Eq. (12.27), which is in the
entire spectrum of wavelengths (see Rounds
et al
., 1999).
The light extinction coefficient
λ
is affected by phytoplankton, suspended sediments,
etc., in the water column. The following linear relation between
λ
λ
and
C
Phy
is often
used:
λ
=
λ
+
k
r
a
CChl
C
Phy
(12.69)
0
where
0
is the light extinction coefficient without phytoplankton,
k
r
is a coefficient
for light attenuation by phytoplankton, and
a
CChl
is the conversion factor of carbon
to chlorophyll of phytoplankton.
To consider the effects of both phytoplankton and suspended sediments on light
attenuation, Stefan
et al
. (1983) suggested the following relation:
λ
λ
=
λ
+
0.025
a
CChl
C
Phy
+
0.043
C
s
(12.70)
0
m
−
1
,
C
Phy
is in mgC
m
−
3
, and
C
s
is the suspended sediment
λ
λ
0
are in l
·
·
where
and
m
−
3
.
The depth-averaged light limitation factor is obtained by integrating Eq. (12.67)
over the flow depth as
concentration in g
·
h
ln
k
L
,1
/
2
+
I
0
1
λ
f
L
,
av
=
(12.71)
I
0
e
−
λ
h
k
L
,1
/
2
+
A byproduct of phytoplankton growth is dissolved oxygen. An additional source
of oxygen from phytoplankton growth occurs when the available ammonia nutrient
