Reach-scale modeling of reaction cascades and spatially-dependent reactions in the hyporheic zone

Stream tracer injection experiments are widely used  to characterize reach-scale transport and reaction in rivers. Results from tracer injection experiments (i.e., concentration vs. time profiles, or breakthrough curves) are often used to estimate reach-averaged processes controlling solute fate. Advances in both tracer technology have greatly improved our ability to infer finer scale processes from the integrated, reach-scale result. However, to better meet the demands of improved tracer technology and the small-scale processes they elucidate, we need a model that incorporates process-based understanding of solute transport and reactivity. In brief, smarter tracers require smarter models. 

A noteworthy example of the disconnect between measurement and modeling capabilities is the resazurin-resorufin (Raz-Rru) tracer system. Raz is a fluorescent chemical that transforms irreversibly to Rru at a rate proportional to the local rate of aerobic metabolic activity. Co-injections of Raz and a conservative tracer provide experimentalists with a “smart tracer” system that is commonly used to estimate aerobic metabolic activity in streams, particularly within the hyporheic zone. At present, aerobic respiration rates are challenging to estimate from breakthrough curves for two reasons. First, multiple reaction pathways are possible beyond the target parent-to-daughter transformation of Raz to Rru. This implies that aerobic respiration rates inferred from breakthrough curve concentrations may be confounded by additional, zone-specific reactions such as the abiotic degradation of Rru after it is created. Second, field campaigns using the Raz-Rru system have demonstrated that aerobic respiration rates vary strongly with depth in the hyporheic zone. Nevertheless, existing reach-scale models assume uniform reaction rates throughout the hyporheic zone for analytical tractability. This assumption biases the rates of metabolic activity inferred from tracer injection experiments in streams where metabolic rates are spatially variable. 

Here, we present recent advances in reach-scale analytical modeling that address both challenges. We generalize a classic mobile-immobile model to account for multiple reaction pathways of Raz (e.g., via aerobic metabolic activity and abiotic decay) and Rru (e.g., via Raz transformation and abiotic decay). We then extend this framework to account for spatial variability in the hyporheic zone, and we validate semi-analytical model solutions against reach-scale simulations for reactive transport. Together, these advances provide a simple way to estimate reactivity of the benthic biolayer – a known hotspot of reach-scale ecosystem respiration – using established methods. The new framework also opens the door for modeling other chemical constituents transformed through reaction cascades in streams.