Extracting information about solute uptake kinetics in advective-dispersive transport based on instantaneous-release tracer experiments in streams

A common approach to studying whole-stream biogeochemical reaction kinetics in the context of one-dimensional, advective-dispersive transport is an upstream release of reactive artificial tracers concurrent with time-series measurement of downstream solute concentrations. These experiments provide information about the balance between physical transport processes and the biogeochemical consequences of ecosystem metabolic processes, at a scale of 100s to 1000s of meters of stream length. Saturating kinetics (e.g., Michaelis Menten kinetics, MM) are commonly observed in whole-system behavior of streams at this scale, which provides a useful context for understanding the elemental resources limiting metabolic function of stream biota. Despite the importance of saturating kinetic models to understanding biological limitation in streams, the theory underlying field methods based on MM kinetics has not been explored as thoroughly as that based on first-order kinetics (e.g. resource spiraling theory). We present a relatively simple Lagrangian analysis with a one-dimensional, advection-dispersion model to clarify the dynamics of whole-system MM kinetics occurring during an instantaneous-release solute tracer experiment. We use the results from two streams with published MM-based analyses to illustrate the conditions experienced by a parcel of water traveling from the instant and location of tracer release to that parcel's moment of arrival at the location of solute concentration measurement. We found that a dynamic, quasi-Lagrangian perspective was important to establishing theoretical context behind inference of MM kinetic parameters. Based on our results, we suggest that a consistent foundational theory of whole-system MM kinetics in streams requires assumption of higher effective concentrations in transport than those used in previous publications regarding instantaneous-release experiments.