Geoscience Reference
In-Depth Information
in DO concentration. Minimum values of DO usually occur in the early morning,
predawn hours, and maximum values occur in the early afternoon. The likely mag-
nitude can be measured via light- and dark-bottle BOD tests, and simulated using
simple cosine source/sink functions (Dresnack and Dobbins, 1968) or a more compli-
cated model coupled with phytoplankton (or algae) growth and mortality. The latter
simulation approach is used in recent water quality models, such as QUAL2E (Brown
and Barnwell, 1987) and WASP (Wool
et al
., 1995). This is demonstrated below.
In the 1-D and depth-averaged 2-D models,
the phytoplankton population is
governed by
DC
phy
Dt
K
M
C
Phy
−
ω
Phy
h
=
K
Phy
C
Phy
−
C
Phy
(12.62)
where
C
Phy
is the biomass concentration of phytoplankton, defined in carbon
(gC
m
−
3
, i.e., gram of carbon per cubic meter) or chlorophyll;
K
Phy
is the growth
rate coefficient of phytoplankton (day
−
1
);
K
M
is the mortality rate coefficient of phy-
toplankton (day
−
1
), which is affected by temperature, as described in Eq. (12.51); and
ω
Phy
is the settling velocity of phytoplankton (m
·
day
−
1
).
In the 3-D and width-averaged 2-D models, the settling term has a different
formulation, and thus the phytoplankton population equation is
·
DC
phy
Dt
K
M
C
Phy
−
∂(ω
Phy
C
Phy
)
∂
=
K
Phy
C
Phy
−
(12.63)
z
The growth of phytoplankton is affected by temperature, solar radiation (light), and
nutrient availability. Thus, the growth rate coefficient is assumed as
T
−
20
K
Phy
=
K
Phy
,
m
θ
f
N
f
L
(12.64)
Phy
where
K
Phy
,
m
is the optimal growth rate coefficient of phytoplankton at 20
◦
C,
θ
Phy
is the temperature coefficient for phytoplankton growth,
f
N
is the nutrient limitation
factor, and
f
L
is the light limitation factor.
An initial estimate of the optimal growth rate
K
Phy
,
m
can be obtained from studies
of phytoplankton dynamics and refined through calibration. Low concentration of
either inorganic nitrogen or phosphorus would affect the growth of phytoplankton,
so the nutrient limitation factor is determined by
min
,
C
NH
3
+
C
NO
3
C
PO
4
k
P
,1
/
2
f
N
=
(12.65)
k
N
,1
/
2
+
C
NH
3
+
C
NO
3
+
C
PO
4
or
C
NH
3
+
C
NO
3
C
PO
4
k
P
,1
/
2
+
f
N
=
·
(12.66)
k
N
,1
/
2
+
C
NH
3
+
C
NO
3
C
PO
4
m
−
3
, i.e., gram of nitrogen
per cubic meter);
C
NO
3
is the nitrate nitrogen concentration (gN
where
C
NH
3
is the ammonia nitrogen concentration (gN
·
m
−
3
);
C
PO
4
is the
·
