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only about a 2% reduction between non-dimensional times of 2 and 8. A velocity
reducing in this way is consistent with it accounting for the presence of transient
storage at large non-dimensional times because transient storage delays the passage
of the tracer through the reach.
Finally, the similarity of the non-dimensional concentration-time profiles offers a
means of predicting the velocity and the dispersion coefficient from tracer experi-
ments that, at first glance, might seem to have been unsatisfactory. For example, if
the trailing edge of a concentration-time profile is not observed it is clear that the
moments of that incomplete profile are of little use. However, because all non-
dimensional profiles have similar shapes, it is possible to use non-dimensional
properties derived from one or more other profiles instead, provided that these
profiles were completely observed. This method is termed the enhanced method
of moments (Wallis and Manson
2010
), and is illustrated here by estimating
U
and
D
for experiments 2 and 6, but using severely truncated profiles. Provided that the
profiles capture the peak and the 50% peak concentration reference points the
method can be used. For example, Fig.
6
shows the truncated profiles used for
experiment 2. If this data were analysed with the method of moments the results
would be very unreliable. However, using (
7
)-(
10
) with average values of
m
t
and
2
at each site (derived from experiments 3-5 at a non-dimensional time of 2) and
values of
t
L
and
t
T
derived from Fig.
6
, a velocity of 0.066 m/s and a dispersion
coefficient of 0.245 m
2
/s were found. These compare very favourably with values
obtained using the complete profiles for experiment 2 (0.066 m/s and 0.273 m
2
/s,
respectively). Figures
7
and
8
show the benefits of being able to use poor-quality
tracer data in this way, where the range of flow over which velocity and dispersion
can be estimated is significantly extended by including the analysis of truncated
profiles from experiments 2 and 6, compared to only using experiments 3-5. The
flow rates were estimated using dilution gauging with the complete profiles at Site 4.
s
t
Site 3
Site 4
2.0
1.6
1.2
0.8
0.4
0.0
0
50
100
150
Time since tracer injection (min)
Fig. 6 Truncated concentration-time profiles for experiment 2
