3.2 Analytical Representations of the Empirical RTD.
Because the RTD becomes progressively heavy tailed with increasing streambed depth, no single analytical distribution represents the RTD over the full range of \(d_{b}^{*}\) tested here (Table S\(1\), Supplemental Material). Instead, the RTD is best approximated by different analytical distributions over different depth ranges, including: (1) GAM for shallow streambeds (\({0\leq d}_{b}^{*}\leq\ 1.2\), Figure 2); (2) LN for streambeds of intermediate depth (\({1.2<d}_{b}^{*}\leq 3.1\), Figure 3); and (3) FR for deep streambeds (\(d_{b}^{*}\) \(>3.1\), Figure 4). Contrary to previous reports (e.g., Zaramella et al., 2003), the EXP distribution appears to be a poor representation of the empirical RTD across all streambed depths tested in this study. LN has been recommended as a surrogate for the hyporheic zone RTD in many studies (e.g., Cardenas et al., 2008; Alessandra Marzadri et al., 2016). Our results demonstrate that LN is a good representation for an intermediate range of\(d_{b}^{*}\), consistent with Wörman et al. (2002) who reported that the RTD is well fit by LN at \(\frac{d_{b}}{\lambda}=0.25\).