Environmental Engineering Reference
In-Depth Information
3.10.1 Evaluation of Water and Mass Balance Equations
An ideal tracer for the mass-balance method is chemically and biologically conservative
(no reaction, absorption, release or uptake), is readily measureable, and is harmless to
the observer and aquatic life. Chloride and bromide are commonly used as tracers (e.g.,
Choi and Harvey 2000 ; Parsons et al. 2004 ). For relatively shallow and small wetland
ponds, water is often assumed well mixed so that tracer concentration is uniform within
the pond. When this assumption is justified based on field data, for example by the
analysis of samples from multiple points and depths in a pond, Eq. 3.40 is simplified to
Δ
ð
C W V
Þ=Δ
t
¼
C P P
þ
C Si S i
C W S o þ
ð
G o
Þ þ
C Gi G i þ
C of O f
(3.49)
(note that C W V is equal to mass and that C E E has been neglected as it is assumed
that no tracer mass is lost through evaporation or transpiration). If the assumption is
not justified, C So and C Go need to be measured for each stratified layer, or for each
isolated embayment of the pond, and mass needs to be determined based on the
concentration and volume of each separate entity of the pond (e.g., Choi and Harvey
2000 ). Further simplification to Eq. 3.49 can be made in some settings. For
example, if chloride is used in a region that receives very small amounts of chloride
in precipitation relative to other components, then C P is assumed negligible.
Tracers also can be applied to an entire wetland in some cases. If bromide is used
as an artificial tracer in a system that has very low natural bromide concentrations,
then C P , C Si , C Gi , and C Of are all assumed negligible.
Mass balance calculation requires measurements or estimates of all “known”
terms in the water balance equation and all concentrations in the mass-balance
equation. Specialized monitoring devices, such as ion-specific electrodes, are
available for continuous monitoring of tracer concentration, but these devices
are prone to instrument drift and calibration issues. Therefore, best results are
obtained by collecting water samples and analyzing them in the laboratory. This
process can be conducted as part of a routine sampling program for water-quality
monitoring (see Chap. 6 on water quality). Using automated water samplers
(Fig. 3.32 ), concentrations can be determined daily or even hourly and the mass
balance calculated on a fine temporal resolution. When a longer sampling interval,
such as weekly or monthly, is used the water and mass balance equations need to be
evaluated using average values. The equations can be written as:
ð
V 2 V 1
Þ
ð
t 2 t 1
Þ <P> <E> þ <S i > <S o > þ <G i > <G o > þ <O f >
(3.50)
ð
C w 2 V 2
C w 1 V 1
Þ
ð
t 2
t 1
Þ <
C P P
> þ <
C Si S i > <
C w S o þ
ð
G o
Þ> þ <
C Gi G i > þ <
C Of O f >
(3.51)
where subscripts 2 and 1 indicate sampling dates 2 and 1, respectively, and
<>
indicates an average value for
the time interval. Definition of average is
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