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.