Environmental Engineering Reference
In-Depth Information
The water-budget equation, including chemical concentrations associated with each
term, can be written as a mass-balance equation:
Δ
ð
C
W
V
Þ=Δ
t
¼
C
P
P
þ
C
Si
S
i
þ
C
Gi
G
i
þ
C
Of
O
f
C
ET
ET
C
So
S
o
C
Go
G
o
ε
(3.40)
where
C
is the concentration of the chemical constituent,
is the total hydrologic
and chemical-measurement error, subscripts are related to the various components
of the water budget, and
W
refers to surface water in the wetland. In many settings,
surface water in the wetland is well mixed; therefore, it is reasonable to assume that
the concentration associated with
G
o
and
S
o
are the same as that of the wetland
surface water,
C
W
. Under this assumption, Eq.
3.39
is rearranged to isolate
G
o
and
this expression is substituted into Eq.
3.40
to obtain
ε
O
f
þ C
ET
C
W
V
Δ
C
w
Δ
t
þ C
W
C
P
ð
ÞP þ C
W
C
Si
ð
ÞS
i
þ C
W
C
Of
ð
ÞET
(3.41)
G
i
ε ¼
C
Gi
C
W
Note that the residual term
R
in Eq.
3.39
was omitted in this substitution because all
errors are now lumped into
ε
. Lastly,
G
i
can be inserted into Eq.
3.39
, which can be
rearranged to solve for
G
o
:
S
o
Δ
V
Δ
G
o
ε ¼
P
þ
S
i
þ
G
i
þ
O
f
ET
(3.42)
t
Another important assumption is that the chosen chemical constituent is conser-
vative, meaning that it is not altered by any chemical or biological process. Water
solutes are commonly used in this analysis and chloride is often considered
conservative in many settings. Stable isotopes of water, usually deuterium (
2
H) or
oxygen-18 (
18
O), are an excellent choice because they are not a dissolved solute but
part of the water molecule. If chloride or another solute is used, the equation is
simplified somewhat because the evaporation process distils the water and no solute
is lost with the evaporating water; therefore
C
ET
ET
is zero. If a stable isotope of
water is used, the isotopic value of the evaporating water needs to be determined.
This value is rarely available, is relatively difficult to obtain, and often is estimated
based on other studies conducted within the area or region (e.g., LaBaugh
et al.
1997
).
This method is not well suited for wetland water budgets dominated by ground-
water discharge. As
G
i
becomes large, the difference between the two terms in the
denominator of Eq.
3.41
,
C
Gi
C
W
, becomes small, at which point measurement
errors can greatly affect the solution. If water isotopes are used, the method is not
very robust when the water residence time of the wetland is short or seasonal
variation in isotopic composition is large (Krabbenhoft et al.
1994
). In such
instances, it is better to use a conservative major ion. Errors can be substantial for
some of the terms and in some cases the residual term,
, can approach or exceed
ɛ
