Geoscience Reference
In-Depth Information
The sampling was designed to capture complete and well-resolved concentra-
tion-time profiles at both sites. Experiment 1 was, in effect, a trial run designed to
discover the general solute transport features of the Murray Burn for the reach
between Sites 1 and 4. As such it was successful, but due to only a small amount of
tracer being used and to initial estimates of the travel time being incorrect, the
concentration-time profiles were rather noisy and incomplete. Experiment 2 was
much more successful, but the final parts of the profiles were not completely
captured. Experiments 3-6 were successful in giving complete profiles at both
observation sites. Experiments 4-6 yielded well-resolved profiles, but the profiles
from experiment 3 were not quite so well resolved. In the following sections,
experiments 3-5 are used to illustrate some concepts, and experiments 2 and 6
are used to validate an enhanced version of the method of moments.
3 Similarity of Tracer Profiles
The idea that tracer data might exhibit similarity was first proposed by Day and
Wood (
1976
). When they non-dimensionalised observed tracer concentration-time
profiles they found that profiles from different experiments had similar shapes.
Concentration is non-dimensionalised by dividing all observed concentrations by
the maximum observed concentration, or peak value (
c
p
): time is non-dimensiona-
lised by choosing two points on the profile as reference times. The choice is
arbitrary, but Day and Wood chose the two points on the profile when the concen-
tration was half of the peak value. One of these occurs on the rising limb or leading
edge of a profile, at time
t
L
, the other occurs on the falling limb or trailing edge of
the profile, at time
t
T
. Day and Wood's approach was used in this work. Thus, non-
dimensional profiles were constructed using the following two equations, where
c
and
t
are the observed concentration and time, and where
C
and
t
are the non-
dimensional concentration and time.
c
c
p
C
¼
(1)
t
t
L
t ¼
(2)
t
T
t
L
Since the times
t
L
and
t
T
did not correspond exactly with a time at which a
sample was collected, they were estimated by linear interpolation.
Figure
2
shows non-dimensional tracer concentration-time profiles from both
sites for experiments 3-5. It is clear that all six profiles have a similar shape,
showing that the concept of similarity applies not only over a range of flows at an
individual site but also at different sites. The small deviation (on the leading edge)
between the non-dimensional profile at Site 3 for experiment 3 and the other
profiles is caused by that profile not being as well resolved as the others.
