2.2 Flume Data Analysis
Tracer tests are commonly interpreted for transient storage residence
times using solute breakthrough curves from stream sensors
(e.g., Wörman
et al., 2002, Anderson et al.,
2005, Lautz et al.,
2006, Wondzell,
2006, Tonina and Buffington, 2007). We
plotted in-stream fluid conductivity data against time as breakthrough
curves for each flume run. To examine differences in breakthrough curves
across discharge and logjam characteristics, we analyzed the following
information based on the temporal moments of breakthrough curves: mass,
mean arrival time, variance, and skew
(Harvey & Gorelick, 1995; Gupta &
Cvetkovic, 2000). The mean arrival time of the injected tracer at the
point of observation is commonly used to describe advection patterns;
variance is used to describe dispersion and diffusion characteristics.
The statistical moment of skewness represents the asymmetry of the
breakthrough curve based on solute retention and can be used as a proxy
for the amount of transient storage (Nordin & Troutman, 1980). We
interpret skewness here as an indicator of transient storage in both the
channel and in underlying aquifer materials (e.g., Lees et al., 2000;
Doughty et al., 2020), though it is likely most sensitive to the
shortest timescales of transient storage in the channel (Harvey et al.,
1996). Higher values of skew indicate more tailing behavior exhibited in
the breakthrough curve, and therefore, more transient
storage. We calculated all
temporal moments in Matlab (MATLAB, 2020). A full calculation of the
temporal moments is included in the Supplemental Information; here, we
focus our analysis on mean arrival time and skew. The former reveals
changes in travel times through the mobile zone in the channel, and the
latter reveals changes in the interaction of mobile zones with transient
storage zones. Flume run times were truncated to include one minute of
background data prior to the pulse NaCl injection and a total time of 30
minutes to provide comparable skew values between runs. Fluid
conductivity readings in the flume return to background levels in under
10 minutes, so truncation does not affect estimates of tailing in the
breakthrough curves.
Statistical analyses were
performed in R Studio (R Core Team, 2020). We statistically assessed how
dependent variables (skew and mean arrival time) changed with
independent variables describing logjam characteristics and discharge.
The independent variables were the number of logjams (single or
multiple), discharge (high or low), and permeability (high or low). We
fit multiple two-way ANOVA models based on our hypotheses (Supplemental
Table 3). Tukey adjusted pairwise comparisons were calculated
using emmeans R package (Lenth, 2020). A significance level alpha
of 0.05 was used in all statistical analyses.