Hyporheic Reaction Potential: A Framework for Predicting Reach Scale Solute Fate and Transport

We develop a new framework, hyporheic reaction potential (HRP), to predict the influence of oxidation-reduction reactions on metal fate and transport in streams using data from tracer studies and geochemical sampling. HRP, with energy flux units [KJ m–2 s–1], is a metric calculated from both the physical and chemical properties of the hyporheic zone. We apply the HRP framework for iron reactions, using existing geochemical and geophysical data from two metal-impacted alpine streams at high and low flow. In these two systems, HRP delineates contrasting controls on iron fate and transport with biogeochemical controls in Mineral Creek and physical controls in Cement Creek. In both systems, HRP scales with discharge and hyporheic-zone extent as flows change seasonally, which demonstrates the ability of HRP to capture physical aspects of chemical reactions in the hyporheic zone. This paper provides a foundation on which HRP can be expanded to other solutes where chemical gradients in the hyporheic zone control reaction networks, making it broadly applicable to redox cycling in stream systems. This framework is useful in quantifying the role of the hyporheic zone in sourcing and storing metal(loid)s under varying hydrologic conditions with implications for water quality, mine remediation, and regional watershed management.


Figure SI-1:
Watershed maps of Mineral Creek and Cement Creek near Silverton, CO showing A) Mineral Creek and Cement Creek watershed map detailing hydrology, topography, and elevation at the HUC12 scale and B) regional extent of the Animas River headwaters in southwestern CO, USA.

Geochemical Sampling, Tracer Study, and Fe Speciation Methods
Groundwater samples were collected in three well nests in each stream.These well nests were installed 0.28, 0.44, and 0.58 m deep in Cement Creek 0.20, 0.40, and 0.68 m deep in Mineral Creek to measure redox properties and chemical concentrations across a vertical gradient in the hyporheic zone.Sampling was conducted at high flow and low flow in each stream, which were assumed to be hydrologic end members.Oxygen gradients were calculated using the difference in DO concentrations between surface water and the deepest groundwater well, and shallow groundwater chemistry (0.20-0.28 m bgs) was used to estimate thermodynamic potential of Fe dissolution and precipitation reactions in the hyporheic zone.
We defined the vertical extent of the hyporheic zone as the area around the stream with active exchange using tracer studies paired with electrical resistivity imaging from previous work 1,2 as well as a measurable DO gradient between surface water and nested groundwater wells.Shallow wells in both Mineral Creek and Cement Creek were within the redox front observed in the hyporheic zone based on nested-well DO concentrations.HRP represents a snapshot in time, so chemical parameters are all from the same sampling time for each calculation.While spatial heterogeneity of redox properties in the hyporheic zone exists, we are assuming that the radius of influence from sampling nested wells captures redox processes across a representative elementary volume that is appropriate to characterize local-scale hyporheic processes.However, we note that small-scale changes in oxygen gradients present at some sites may need to be captured by Minipoint sampling 4 , which is easier to install and interpret to measure in lowgradient, sandy streams.
Fe 2+ was measured directly in the field via colorimetry with a field spectrophotometer (HACH DR1900) using 1,10-phenanthroline reagent.However, in all but one sampling event (Cement Creek at high flow), the Fe 2+ was above the upper detection limit of the method (3 mg/L), indicating high concentrations of dissolved Fe 2+ .In samples where dissolved Fe 2+ was above the field spectrophotometry detection limit, we estimated the dissolved Fe 2+ concentration by calculating the equilibrium ratio of Fe 2+ and Fe 3+ from the total Fe concentration at an Eh of 0.70 V, the Eh calculated from the Fe 2+ /Fe 3+ concentration in the Cement Creek at high flow sample.Since the concentration of Fe 2+ was lowest in this sample, we assumed that Eh = 0.70 V represents a maximum Eh value for samples where Fe 2+ was at detectable concentrations.

Comparison of HRP to Existing Metrics
HRP compliments the familiar Damkohler number, a unitless parameter that describes the relative importance of transient storage and advective velocity 5 : where A is stream area, AS is storage area, L is reach length, and u is stream velocity.DaI predicts if streams will be transport limited (DaI > 1) or exchange limited (DaI < 1).These DaI formulations are broadly applicable and have been used to describe physical and chemical processes driving solute transformation in stream systems [6][7][8] .For example, Da was ~1 at high flow in Mineral Creek (Table 1), which supports a balance between exchange and advective time scales that enhances hyporheic zone capacity for biogeochemical reactions.
HRP expands beyond this idea by integrating thermodynamic favorability (ΔG), mixing efficiency (ε), and hyporheic zone area to estimate the hyporheic zone's potential to support redox transformations for a given solute.It delineates chemical and physical governing processes for solute exchange and geochemical reactions to estimate overall potential for a given geochemical reaction under specific hyporheic zone conditions.While DaI ~1 in Mineral Creek, there were biogeochemical favorability for initial Fe-oxidation, strong biogeochemical favorability for schwertmannite precipitation, and slight thermodynamic favorability for ferrihydrite oxidation that cannot be accounted for by DaI.During low flow, DaI shifted to transport-limited conditions, there was a redox reversal where Fe-reductive dissolution became favored, and mixing efficiency decreased by 30%, impeding the capacity of the hyporheic zone to support biogeochemical reactions and reversing source -sink dynamics.Cement Creek was exchange-limited in DaI, and had a low ε at both high and low flow, highlighting that solute interaction was limited even if sufficient chemical gradients as shown in HRP calculations (Table 1) were present to support biogeochemical reactions.
Another metric to assess the capacity of the hyporheic zone to support redox reactions is the Reaction Significance Factor 9 : This unitless term relates reaction timescales (λhz), hyporheic residence times (τhz), characteristic reach length (Lc), and storage zone flowpath length (Ls) to estimate the relative importance of the hyporheic zone in mediating redox reactions.Rs calculates the relative importance of reaction timescales and mass-transfer timescales, similar to the Damkohler number.Higher Rs values indicate greater capacity of the hyporheic zone to mediate redox reactions.For the hyporheic zone to be an important contributor to watershed-scale solute mass balances, Rs must be greater than 0.2 9 .Rs requires a combination of data from tracer studies and geochemical measurements, which is similar to our HRP term.HRP differs from Rs in that it explicitly parameterizes thermodynamic favorability and oxygen gradients in the hyporheic zone to estimate reaction favorability in energy units [KJ m -2 s -1 ].Rs requires an in-stream tracer test, and sampling of tracer concentrations in hyporheic water and groundwater during that tracer test to estimate reaction timescales 4 , which were not available for our dataset.