Geoscience Reference
In-Depth Information
m
−
3
day
−
1
);
C
CBOD
is the
concentration of carbonaceous biochemical oxygen demand (CBOD) (gO
2
R
is the rate of DO loss due to respiration (gO
2
·
m
−
3
);
K
d
is the deoxygenation coefficient (day
−
1
);
C
NBOD
is the concentration of nitrogenous
biochemical oxygen demand (NBOD) (gO
2
·
m
−
3
);
K
N
is the rate coefficient for NBOD
(day
−
1
);
S
SOD
is the sediment oxygen demand (SOD), defined as the rate of DO loss
per unit (horizontal) bed area (gO
2
·
m
−
2
day
−
1
); and
h
is the flow depth (m).
The terms on the right-hand side of Eq. (12.53) represent atmospheric reaeration,
phytoplankton photosynthesis (
P
), respiration (
R
), CBOD oxidation, NBOD oxi-
dation, and sediment oxygen demand, respectively. Note that the exchanges fluxes
K
L
·
and
S
SOD
at the water and bed surfaces are considered through
boundary conditions in the 3-D and width-averaged 2-D models; thus, the 3-D or
width-integrated DO balance equation is
(
C
sDO
−
C
DO
)
DC
DO
Dt
=
P
−
R
−
K
d
C
CBOD
−
K
N
C
NBOD
(12.54)
The determination of all terms in Eqs. (12.53) and (12.54) is discussed in the
following subsections.
Atmospheric reaeration
The exchange of oxygen across the water surface is affected by temperature, flow
conditions, and atmospheric conditions. The effect of temperature can be accounted
for using Eq. (12.51), with a value of about 1.024 for the coefficient
.
In the absence of wind, O'Connor and Dobbins (1958) suggested the reaeration
coefficient of oxygen (day
−
1
)as
θ
3.9
U
1
/
2
h
3
/
2
K
L
h
K
a
=
=
(12.55)
s
−
1
), and
h
is the average flow depth (m).
O'Connor and Dobbins's relation may underestimate the reaeration coefficient for
small streams. Two equations that performed well in a comparison between predicted
and measured reaeration rates (Rathbun, 1977) are those by Padden and Gloyna
(1971):
where
U
is the average flow velocity (m
·
4.55
U
0.703
h
1.054
K
a
=
(12.56)
and by Tsivoglou and Wallace (1972):
K
a
=
13648
US
(12.57)
where
K
a
is in day
−
1
at 20
◦
C,
U
is in m
s
−
1
,
h
is in m, and
S
is the stream slope
·
(unitless).
