Evaluating the reliability of the stream tracer approach to characterize stream-subsurface water exchange

Harvey et al., 1996

Two Approaches to Characterize Hyporheic Exchange

• Hydrometric approach– Sub-reach-scale measurement of hydraulic heads

and hydraulic conductivity to compute streambed fluxes

• Stream tracer approach– Reach-scale modeling of in-stream solute tracer

injections to determine characteristic length and time scales of exchange with storage zones

Steps Taken in Study1. Conduct stream tracer experiment during both low and high base

flow and simultaneously measure hydraulic gradients and tracer movement in the subsurface.

2. Use the transient storage model and statistical methods to identify storage characteristics.

3. Compare detailed subsurface measurements with model storage characteristics.

4. Assess the reliability of the stream tracer approach to characterize hyporheic exchange under variable flow conditions.

St. Kevin Gulch, Colorado• Third order channel: smaller, headwater, upper

reaches of watershed (Strahler, 1952)

• Average slope: 0.07 (varies from 1% to >20%)

• Stream flow: sustained by inflow of groundwater from permanently saturated areas of the lower hill slope.

• Channel sediment: well-sorted sand and gravel, distributed in patches that range from fine sand to coarse sand to gravel.

• Alluvial sediment: poorly sorted fine and coarse sand, gravel and cobbles ~2 m thick and extends ~5 m on either side of stream.

Acid burn. AMD seeps from St. Kevin Gulch near Leadville, Colorado, an area mined for gold, silver, lead, and zinc. Image credit: Carol Russell/EPA

Methods• 60 wells, piezometers, staff gauges

emplaced along a 36-m study reach.

• LiCl tracer injected into stream at a steady rate for four days.– low base flow- 10 L/s (August

1990)– high base flow-120 L/s (June 1991)

• During tracer injections stream water samples were collected at both endpoints and from a subset of wells along the reach.

• Hydraulic heads were measured in all wells and at all staff gauges during the injections.

Subsurface Measurements of Hyporheic Exchange• Using Water Balance Approach 12 m sub-reach

– Well-sorted gravel bar deposits adjacent to channel (6 wells)– Poorly sorted alluvium at sides and beneath stream (8 wells)

• Reach-averaged streambed flux measured by closely spaced hydraulic head measurements and divided into:– Stream-hyporheic exchange- flow paths are short, concentric-shaped, and

enter and return from the subsurface within the stream reach.– Stream-groundwater exchange - flow paths much longer and leave or enter

study reach once.

• % stream water at wells was calculated using standard mixing models.– Measuring the distribution of tracers in the stream and subsurface.

• Travel time for stream water to reach wells was determined by observing the arrival of the chloride tracer.

Stream Tracer Experimentation and Modeling

• 1D model where storage of solute is simulated as a mass transfer between the channel and a decoupled storage reservoirs in which mixing is complete and instantaneous (Figure B)

• Stream Tracer Model Equation:

– t and x = time and direction along the stream– C, Cs, CL = concentrations in the stream, storage zones, & groundwater– Q = in-stream volumetric flow rate– qL = groundwater in flow– D = longitudinal dispersion coefficient in the stream– A and As = stream and storage zone cross-sectional areas– α = stream water exchange rate with storage zones

Stream Tracer Experimentation and Modeling

• Stream flow discharge (Q)- determined by the dilution gaging method.

• Groundwater inflow (qL)- estimated as the difference in stream flow at endpoints divided by the reach length.

• Other parameters (A, D, α, and As) were determined by inverse methods using the nonlinear, least squares regression approach.

• Simulations were fit to measured data in order to select the best-fit values for the parameters.

Stream Tracer Experimentation and Modeling

During the four day injections of cl tracer, concentrations were measured at upstream (1329 m) and downstream (1382 m) endpoints.

After cutoff of the tracer, concentrations:• initially decreased rapidly in the

stream• followed by a longer period

where tracer concentration remained elevated above background concentration levels

Assumptions Underlying the Use of the Stream Tracer Approach to Simulate Hyporheic Exchange

The downstream change in stream flow in a channel without tributaries that is closely connected with shallow ground water is

Q = stream flow dischargeX = downstream directionqin

L & qoutL = reach-averaged groundwater flux into and out of stream

qins &qout

s = reach-averaged fluxes of stream water out or into hyporheic flow paths

Assumptions Underlying the Use of the Stream Tracer Approach to Simulate Hyporheic Exchange

• Groundwater flow paths are determined by “Seepage runs” estimate the net groundwater flux across the streambed (qin

L – q out

L), and is determined by the difference in streamflow at upstream and downstream reach ends.

• Hyporheic exchange fluxes are estimated by a series of equations and substitutions that include the previous set of equations.

Primary assumptions associated with stream tracer approach

• Mass Transfer Process- Solute holding times in the hyporheic zone are assumed to be distributed exponentially (the bulk response of all hyporheic flow paths can be modeled as a simple first-order mass transfer between channel and well mixed reservoir).

• Exchange parameters uniquely characterize hyporheic exchange rather than mixing between the central channel and surface water storage zones (bottom pools, recirculating eddies).– Surface water storage processes are assumed to be accounted for by

the longitudinal dispersion coefficient.

Primary assumptions associated with stream tracer approach

• Required channel length must be met for proper mixing to occur in the stream and allow the surface water storage to be properly accounted for by the longitudinal dispersion coefficient.

• Lengths have been established and require:– Transverse dispersion coefficient– Channel depth– Shear velocity– Proportionality coefficient

Subsurface Results• Hyporheic exchange 40 - 80% of total streambed water flux• Hyporheic exchange greatest at low base flow• Groundwater inflow to the stream increased at high base flow.• 30% decrease in hyporheic exchange relative to low base flow.• Decrease in hyporheic exchange attributed to higher inflow from

groundwater increasing the resistance of stream water to recharge in the hyporheic zone.

Subsurface ResultsWater table contours were used to map individual hyporheic flow paths that ranged in length from cm to m in the 12-m sub-reach.

High base flow compared to Low

• Length and distance of penetration of individual hyporheic flow paths reduced

• Percent stream water composition in hyporheic flow paths less

• Finding consistent with the slight reduction of hyporheic exchange at higher base flows determined by water balance

Subsurface ResultsSolute tracer arrival times indicated that timescales of hyporheic exchanged ranged between minutes and tens of hours.

• Well-sorted gravel sediment averaged 6 hour exchange times

• Poorly sorted alluvial sediment averaged 84 hour exchange times

Stream Tracer Results• Stream tracer modeling provided simulations that were a good

match to measured tracer concentrations in the stream.• Best fit model results were similar to measurements for both high

and low base flow.• Parameter uncertainty estimates were mostly below 20%.

Comparison of Stream Tracer Modeling Parameters with Subsurface MeasurementsLow base flow• Best fit storage zone cross section area twice as large as best fit

stream cross sectional area which is similar to hydrometric exchange measurements.

• Best fit storage zone residence time of 6 hours at low base flow was consistent with hydrometric exchange measurements of travel time to reach gravel bars.

Comparison of Stream Tracer Modeling Parameters with Subsurface MeasurementsHigh base flow• Stream tracer and hydrometric exchange approaches were not

consistent.• Stream tracer approach indicated orders of magnitude decreases in

storage zone area, while measurements suggested only a modest reduction in storage zone area.

• Stream tracer approach indicated orders of magnitude decrease in storage zone residence time, measurements showed a 30% reduction in hyporheic flux.

Sensitivity of the Stream Tracer Model to Subsurface Storage Processes

• Sensitivity is the partial derivative of modeled stream tracer concentration with respect to a change in the value of a parameter.

• Model less sensitive at high base flow

Comparison of Stream Tracer Modeling Parameters with Subsurface Measurements• No objective means to assess whether the stream tracer approach

could uniquely distinguish surface and subsurface water storage processes, but calculations indicated that the equilibrium phase for mixing was not met in the study reach, which means mixing in the stream could not be accounted for by adjusting the longitudinal dispersion coefficient and that some overlap of surface and subsurface storage was expected in the tracer signals.

• The tracer experiment at high base flow was likely more sensitive to surface water storage processes, because measured hyporheic flow paths were affected little by the change.

Stream tracer approach could not detect all timescales of stream-hyporheic exchange fluxes.• Model exhibited maximum sensitivity to exchange processes that occurred

quickly following the cut-off of the tracer.• Window of time .2-2 best fit residence times.• Same window of time when normalized travel times are plotted against

distance from the stream and linear trends are placed.• Model sensitivity did not account for the longer deeper alluvium

timescale.

Stream tracer method compared to “Hydrometric-Based” Simulation.

• Models were compared against an independent low flow dataset.

Summary• Advantage of stream tracer approach to detect hyporheic exchange is

the simplicity and efficiency at large scales compared to subsurface observations.

• Hyporheic exchange persisted through two seasons of low and high base flow.

• Differences is magnitude of hyporheic exchange accounted for by groundwater inflow opposition of localized recharge of stream water to hyporheic flow.

• Stream tracer approach estimated exchange with greater reliability at low base flow.

Summary• Greater sensitivity at low base flow resulted from interaction with a larger

proportion of the tracer with flow paths and a higher plateau concentration.

• At high base flow the stream tracer approach is likely more sensitive to surface water storage processes than to hyporheic exchange.

• Regardless of base flow, stream tracer approach only accurately characterized the fastest exchange times (between streams and gravel bars).

• Without modification, (addition of multirate/multiclass storage) the approach may not be sensitive to longer timescale interactions with deeper alluvium.