A regression approach to estimating reactive solute uptake in advective and transient storage zones of stream ecosystems

A method is developed, the Regression Partitioning Method (RPM), for estimating the proportion of reactive solute uptake occurring within transient storage zones of streams. The RPM is a technique for analyzing solute addition data in which whole stream uptake (mg m^-2 d^-1) is determined from the longitudinal pattern in plateau tracer concentrations. At one location, a time series of samples are collected that define the 'rising limb' of the solute breakthrough curve. The y-intercept estimated by regressing a measure of reactive tracer availability (e.g. NO₃-¹⁵N:Cl ratio) and the percentage of tracer that has resided within, and returned from, the transient storage zone (i.e. hyporheic zone) was used to predict channel-specific NO₃ uptake rates. Uptake within the transient storage zone of stream-derived material is calculated by difference. Several numerical steps are developed that link uptake rate estimates to first-order reaction rate constants (λ_C and λ_S, min^-1) more commonly used to describe solute behavior in one-dimensional transport models. The RPM was used to analyze the results of 2 stable isotope additions performed in Snake Den Branch, a small headwater stream in western North Carolina, USA. Channel-specific uptake rates (U_C) ranged from 10.6 to 23.0 mg NO₃-N m^-2 d^-1 and slightly exceeded uptake in the transient storage zone (U_S), which varied from 10.1 to 18.2 mg NO₃-N m^-2 d^-1. Uptake within the transient storage zone accounted for 44-49% of the total uptake. λ_C and λ_S estimates ranged from 0.023 to 0.034 min^-1 and 0.011 to 0.024 min^-1, respectively. These processing rates correspond to solute residence times of 30-44 min and 41-90 min in the channel and storage zones, respectively. Finally, we assess the sensitivity of our approach to variation in the subsurface uptake coefficient and differing proportions of uptake occurring within the hyporheic zone.