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Explicit Modeling of Radon-222 inHydroGeoSphere During Steady Stateand Dynamic Transient Storageby B.S. Gilfedder1,2, I. Cartwright3, H. Hofmann4, and S. Frei5

AbstractTransient storage zones (TSZs) are located at the interface of rivers and their abutting aquifers and play an important role in

hydrological and biogeochemical functioning of rivers. The natural radioactive tracer 222Rn is a particularly well-suited tracer forstudying TSZ water exchange and age. Although 222Rn measurement techniques have developed rapidly, there has been less progressin modeling 222Rn activities. Here, we combine field measurements with the numerical model HydroGeoSphere (HGS) to simulate222Rn emanation, decay and transport during steady state (riffle-pool sequence) and transient (bank storage) conditions. Comparingthe HGS mean water ages with the conventional 222Rn apparent ages during steady state showed a systemic underestimation ofapparent age with increasing dispersion and especially where large concentration gradients exist within the subsurface. A largeunderestimation of apparent water age was also observed at the advective front during bank storage where regional high 222Rngroundwater mixes with newly infiltrated surface water. The explicit modeling of radiogenic tracers such as 222Rn offers a physicalinterpretation of this data as well as a useful way to test simplified apparent age models.

IntroductionSubsurface transient storage zones (TSZs) are areas

of active water exchange at the interface between streams,rivers, and the aquifer system. They are an impor-tant component of river corridor science and influencethe chemistry, hydrology, biology, and physics of water

1Limnological Research Station University of Bayreuth,Department of Hydrology, Bayreuth Center of Ecology andEnvironmental Research (Bayceer) Universitatsstrasse 30, 95447,Bayreuth, Germany.

2Corresponding author: Limnological Research StationUniversity of Bayreuth, Department of Hydrology, BayreuthCenter of Ecology and Environmental Research (Bayceer)Universitatsstrasse 30, 95447 Bayreuth, Germany; (49) 92155 2223; fax: (49) (0)921 55 2366; benjamin-silas.gilfedder@uni-bayreuth.de

3School of Geosciences Building 28, Monash University,Clayton, Victoria, Australia 3800; ian.cartwright@monash.edu

4School of Earth Sciences, The University of Queensland, St.Lucia, QLD, 4072, Australia; h.hofmann@uq.edu.au

5Department of Hydrology, Bayreuth Center of Ecologyand Environmental Research (Bayceer) University of Bayreuth,Universitatsstrasse 30, 95447, Bayreuth, Germany; Sven.Frei@uni-bayreuth.de

Article impact statement: This work couples a physically basedmodel (HydroGeoSphere) with radon measurements to understandwater ages in transient storage zones during steady and nonsteadystates.

Received March 2018, accepted November 2018.© 2018, National Ground Water Association.doi: 10.1111/gwat.12847

ways (Harvey and Gooseff 2015). Examples of subsurfacetransient storage include hyporheic flow, parafluvial flow,bank storage, and flood recharge (Boano et al. 2014). Dis-persive mixing between groundwater and surface water inTSZs is responsible for an array of chemical and biolog-ical processes that are ecologically significant (Cardenas2016). For example, the hyporheic zone often facilitatesa redox gradient important for both the production andreduction of nitrate, for carbon turnover and oxygen con-sumption due to microbial respiration (Zarnetske et al.2011b; Kessler et al. 2012). Hyporheic areas in particu-lar provide an important spawning ground for fish speciesand a vital habitat for stream invertebrates (Boulton 1993;Boulton et al. 1998; Marzadri et al. 2012; Cardenas et al.2016). The larger TSZs (e.g., bank storage) can also beresponsible for buffering and delaying storm flow, sup-plying rivers with water during base flow and regulatingstream temperatures (Todd 1955; Arrigoni et al. 2008;McCallum et al. 2010).

A fundamental distinction can be made betweenTSZs that are active under both steady and nonsteadystreamflow (e.g., hyporheic exchange) and those that areonly activated during transient hydrological events such asstorm flow (e.g., bank storage). Applying this distinctionto TSZ biogeochemistry has led to the concepts of “hotspots” which are usually associated with TSZs in thestreambed that are active at all times (Zarnetske et al.2011a) and “hot moments” that are initiated by transient

36 Vol. 57, No. 1–Groundwater–January-February 2019 (pages 36–47) NGWA.org

hydrological events (e.g., high river stage) and are onlysporadically present (Gu et al. 2012; Frei and Peiffer2016).

Both hydrological quantities (e.g., storage volume,water flux) and chemistry (e.g., kinetic redox processes)of TZSs are dependent on surface water residence times,or “age” (τ ) of water since infiltration (Boano et al. 2014).However, deriving water age from field data is nontrivial(Worman and Wachniew 2007), especially when time-series measurements during transient hydrological eventsare needed (Ward et al. 2013). Natural tracers are a usefulway to estimate τ during steady state and dynamic waterexchange. Some common examples include temperature(τ resolution ∼1 day; Rau et al. 2014), electrical conduc-tivity (EC) (τ resolution ∼1 day; Cirpka et al. 2007), and222Rn activities (τ resolution few hours; Lamontagne andCook 2007). Estimating meaningful τ and water fluxesfrom natural tracers requires some form of calculation toinvert tracer concentrations to time-scale data. These mod-els generally simplify the complex flowpaths and bound-ary conditions of natural systems (Suckow 2014). Therehas been a large effort to increase the mathematical rigorof the models that use temperature and EC as τ trac-ers in TSZs (Cirpka et al. 2007; Vogt et al. 2010, 2012;Rau et al. 2012; Schmidt et al. 2012; Vieweg et al. 2016),especially related to uncertainty analysis and dynamicboundary conditions (Rau et al. 2015; Vandersteen et al.2015). This effort is due in part to the low cost of temper-ature sensors, but also to the complexity of the heat trans-port equation when used for hyporheic sediments withvariable boundary conditions (one- to three-dimensional(1-3D) flow, variable upper boundary, variably saturatedflow (Cuthbert and Mackay 2013; Rau et al. 2017). Incontrast, the quantification of τ using 222Rn has not sig-nificantly evolved since Hoehn and von Gunten (1989),a model which is conceptually similar to many “apparentage” models used in the groundwater age dating literature(Ekwurzel et al. 1994; Sanford 2010). The Hoehn and vonGunten (1989) model was originally developed to quan-tify the steady-state flow velocity away from a losing riverin Switzerland and assumed 1D piston flow. For apparentRn age calculations (τ app.) there are no assumptions aboutflowpath geometry, but it does not allow for dispersivemixing of flow lines or complex boundary conditions suchas upwelling of regional groundwater, with errors likely tobe similar to that observed for other apparent age tracers(Bethke and Johnson 2002; Weissmann et al. 2002). Mod-ifications by Bertin and Bourg (1994) allowed correctionfor linear endmember mixing using chloride (or anotherconservative tracer), while Xie et al. (2016) used a 1Dnumerical solution to interpret 222Rn profiles. However,current methods still do not resolve complex flowpathsin more than 1D which is seldom the case in hyporheicflow (a fact that has plagued temperature models, see, e.g.,Cuthbert and Mackay [2013]). This is especially importantduring dynamic hydrological events such as bank returnflow where water changes direction, over-bank recharge,and subsequent return flow, or mixing of flow lines bydispersion in complex 2D and 3D flow fields. There is

also still very little information on the uncertainty thatsystem complexity creates in τ app. when using the Hoehnand von Gunten (1989) model, especially the dispersivemixing of water with different ages. The development ofnovel continuous 222Rn measurement techniques in TSZs(e.g., Gilfedder et al. 2013) as well as the increasing useof 222Rn as a residence time tracer in TSZs (Bourke et al.2014; Cranswick et al. 2014) requires further developmentof robust 222Rn modeling techniques.

In this paper, we use a combination of point andcontinuous 222Rn measurements and explicit modeling of222Rn via advection-dispersion-reaction in a fully couplednumerical computer code (HydroGeoSphere, HGS). Theaim is to (1) to demonstrate how HGS can be usedto model 222Rn tracer data during steady and dynamicflow, (2) understand how processes such as dispersionaffecting 222Rn transport and apparent ages in 2D TSZs,and (3) show 222Rn can be used to calibrate complexprocess-based models at short residence times. While it isbased on specific field examples, the methods and resultspresented in this study have broad general applicabilityand will improve the understanding of processes in TSZsin riverine ecosystems.

Research Methods222Rn as a Residence Time and Water Flux Tracer in TSZs

222Rn is a radioactive (t0.5 = 3.81 days) noble gasin the 238U decay chain. It is produced by the decay of226Ra in rocks and sediments and accumulates in aquiferpore water, with activities in excess of 100,000 Bq/m3

locally recorded (Cecil and Green 2000). 222Rn activitiesat secular equilibrium depend on aquifer mineralogy, withthe highest activities recorded in granitic sediments andthe lowest in beach sands. Secular equilibrium (steadystate between decay and emanation) is reached after fivetimes the half-life which is approximately 21 days. Surfacewater generally has very low 222Rn activities (less than1000 Bq/m3) due to loss to the atmosphere and radioactivedecay. This contrast in activities is commonly exploited tomap and quantify the influx of groundwater to lakes andrivers as well as calculate τ app. in the subsurface (Cook2012; Kluge et al. 2012; Gilfedder et al. 2015).

As surface water infiltrates into a TSZ and flowsalong a hypothetical idealized stream tube the 222Rnactivities increase with time due to emanation from theaquifer matrix (called ingrowth) according to:

d222Rnτ

dτ= γ

θ− λ222Rnτ (1)

where 222Rnτ [Bq/L3] is the 222Rn activity in TSZ porewater at apparent age τ app. [T], γ is the emanation ratefrom the sediments [Bq/L3/T], λ [per T] is the decayconstant (0.18 per day), and � [−] is the sedimentporosity. γ is related to 222Rn at secular equilibriumby 222Rnτ → ∞ = dRn/dt = 0 = γ /�λ. Equation 1 may besolved analytically for τ app. (Hoehn and von Gunten

NGWA.org B.S. Gilfedder et al. Groundwater 57, no. 1: 36–47 37

1989). Including the river water 222Rn concentration(Cranswick et al. 2014; Pittroff et al. 2017) results in:

τapp = 1

λln

[ 222Rn∞ − 222RnR

222Rn∞−222Rnτ

](2)

where 222RnR [Bq/L3] is the 222Rn activity in the riverwater endmember. Apparent flow velocities through theTSZ are then calculated by dividing the flowpath lengthby τ app (Hoehn and von Gunten 1989; Bertin and Bourg1994). The maximum τ app. measurable is about 20 days(depending on detector precision) after which secularequilibrium is reached with the TSZ matrix. The primaryassumptions associated with this approach are (1) thattransport is dominated by advective flow, (2) no mixingbetween streamlines or with the regional groundwateroccur, (3) emanation is a constant in space and time, and(4) the stream water endmember is time invariant.

Field Site 1: Steady-State Hyporheic Exchange RoterMain River Germany

The field site 1 is used here as an exampleof estimating τ app. during steady-state hyporheic flow.As part of a previous study on hyporheic residencetimes 222Rn (as well as other chemical parameters) wasmeasured in samples from 5 to 45 cm sediment depth atthe beginning (downwelling zone) of a riffle section in theRoter Main River, NE Bavaria, Germany (Pittroff et al.2017). The Roter Main River is a forth order river witha mean discharge of approximately 4 m3/s and base flowdischarge of about 1 m3/s. It flows from the FichtelgebirgeMountains toward the north-west where it joins the MainRiver system and eventually the Rheine River at Mainz.The Roter Main mostly meanders through low intensityagricultural areas with Bayreuth (pop. 72,000) being thelargest urban center. Other than being heavily channelizedin the city area and about five wears over its 40 km lengththe river is relatively undisturbed, with well-developedriffle pool sequences, and sand bars prominent aroundmeander bends. The few existing hydraulic conductivityvalues (∼10−6 m/s) reflect the mix of sandy and sandy-clay sediment in the riparian and floodplain areas. Tenvertical samples were extracted on July 1, 2014 fromthe hyporheic zone using a multiport minipiezometerconstructed of 10 individual screened polyurethane tubes.The distance between each sampling port was 5 cmand slightly off-set from the above sampling tube tominimize mixing between samples. This is similar to thehyporheic sampling device employed by Boulton (1993)and Lamontagne and Cook (2007) for sampling hyporheicpore water for chemical and biological measurements.The groundwater endmember was sampled by hammeringa stainless steel push-point piezometer (screen length10 cm) to 1 m depth in the streambed. 222Rn activitieswere measured from 80 to 100 mL of sample using aRAD7 device as described by Lee and Kim (2006).Shortly, each sample was connected to a closed circuitair loop with the RAD7 instrument (relative humidity

less than 10%). The sample was then purged for 5 minand counted for 60 min. Replicate counting of the samesample gave relative standard deviation errors of lessthan 10% and better than 5% when activities were above10,000 Bq/m3. Further details of the site, sampling andmeasurement procedures can be found in Pittroff et al.(2017).

Field Site 2: Transient Hydrological Conditions and BankStorage Avon River Australia

The Avon River (Victoria, Australia) example isused to study transient effects on calculating τ app. duringbank storage. The Avon River is 122 km long and liesin the central part of the Gippsland Basin. It drainssouthwards from Mt. Wellington (664 m a.s.l.) into LakeWellington, which is connected to the Southern Oceanthrough the Gippsland Lakes system. About 30% ofthe catchment consists of the mountainous headwaters,while the remaining 70% comprises lowland plains withundulating hills. A pronounced flood regime has led tothe development of a wide gravel, and in some placesbraided, river channel in the lowland section (Cartwrightand Hofmann 2016). During most of the year the riveronly occupies a small portion of the channel and meandersthrough depressions in the gravel beds scoured duringhigh flow events. The Pearces Lane site is located in themiddle section of the Avon River, approximately 30 kmupstream from where it enters Lake Wellington and 20 kmfrom the township of Stratford. Pearces Lane is typicalfor the majority of the lowland sections of the river withextensive highly conductive (Ksat ∼10−3 m/s) gravel bedseither side of the main channel. A transect of 5 bores weredrilled perpendicular to the river at distances between3 (bore 5) and 55 (bores 1 and 2) meters from theriver (Figure 1B). The continuous 222Rn measurementspresented here were conducted in bore 5, a 5.5 m deepbore located directly on the river bank (Figure 1B). Thecontinuous 222Rn measurements were conducted using theOctoRad instrument described by Gilfedder et al. (2013).An OctoRad comprises eight 1.5 m long gas-permeablesilicone membrane tubes strung vertically between twohollow end pieces which allow air to cycle through thetubes. It is placed in the screened section of a bore andconnected in closed circuit with a 222Rn detector situatedat the top of the bore using PVC tubing. 222Rn in thegroundwater diffuses through the gas-permeable siliconetubes into the air loop and is then measured by a 222Rndetector at the top of the bore. We employed a Geigercounter system (AWARE Electronics Corp, Wilmington,Delaware.) for 222Rn detection as discussed in Gilfedderet al. (2013). 222Rn activities in the water were calculatedfrom the 222Rn activities in the air loop using theOstwald solubility coefficient α (RnGW = Rnair*α). Alphais calculated by α = 0.105 + 0.405e−0.0502t , where t isthe water temperature in ◦C (Meyer and Schweidler1916; Weigel 1978). Errors are on the order of lessthan 20%, except when approaching the detection limitof 1000 Bq/m3, where they can be larger. Measurementswere made from October 29 to November 11, 2012. In

38 B.S. Gilfedder et al. Groundwater 57, no. 1: 36–47 NGWA.org

Figure 1. Conceptual models for the two case studies Roter Main and Avon River with applied boundary conditions.

addition to 222Rn we also measured river stage, EC andgroundwater level using an Aqua Troll 200 (In-situ Inc.,Fort Collins, Colorado) in bore 5 and groundwater levelin bore 2 (Rugged Troll, In-situ Inc.).

Virtual Experiments: Explicit Simulation of 222Rn DuringSteady and Transient Conditions

The process-based hydrological model HGS wasused to model 222Rn transport and behavior at the twofield sites. HGS (Aquanty Inc. 2015) provides a fullyintegrated 3D solution for variably saturated subsurfaceflow (Richards equation) and a 2D depth-averagedsolution for surface flow based on the diffusive waveapproximation to the St. Venant equations (Aquanty Inc.2015). HGS is being increasingly used for the simulationof coupled surface-subsurface hydrologic systems (e.g.,Brookfield et al., 2009; Jones et al., 2006). The two HGSmodels include (1) a 2D cross section located alongthe thalweg, representing a typical riffle structure forthe Roter Main River (Figure 1A) and (2) a 2D crosssection of the Avon River bank based on the field sitedescribed above (Figure 1B). HGS was used in order torepresent the hydrological conditions for the field sites andthe migration of 222Rn in porous media which involvesadvective and dispersive transport, 222Rn-emanation and-decay according to Equation 3:

− ∇ (q222Rn − �sD∇222Rn

) − �sλ222Rn + γ

= ∂(�s

222Rn)

∂t(3)

In Equation 3, q [L/T] represents the subsurface fluidflux derived from solving 3D Richards and surface flowequations, �s [−] the saturated water content, D [L2/T]the hydrodynamic dispersion tensor and γ [Bq/L3/T] a

Table 1HGS Parameters for the Avon River and Roter

Main Model

Avon RiverModel

RoterMain Model

γ (Bq/m3/day) 540 1468λ (per day) 0.18 0.18C stream (Bq/m3) 100 188K sat (m/s) (calibrated) 8.4 × 10−3 3.4 × 10−3

αL (m) (calibrated) 1.78 × 10−2 2.13 × 10−2

αT (m) (calibrated) 1.25 × 10−2 1.14 × 10−2

� 0.4 0.34

zero-order source term representing emanation of 222Rnfrom the sediments. Both models are rather generic innature, falling into the category of virtual experiments(Weiler and McDonnell 2004), and are not meant toactually represent the full complexity of the two field sites.For both models we use simplified boundary conditionsand a loose calibration to 222Rn field data with the purposeof capturing a realistic range of 222Rn activities. Bothmodels were calibrated using the automated calibrationsoftware PEST (Doherty and Hunt 2010) based onmeasured steady state 222Rn depth profiles (Roter MainRiver) and a 12 day time-series of continuous 222Rndata measured in bore 5 on the Avon River. Parametersthat were subject to calibration are longitudinal αL [L]and transverse αT [L] dispersivities which are part ofthe hydrodynamic dispersion tensor D and values forthe saturated hydraulic conductivities K sat [L/T]. Modelsettings and final calibrated parameters are listed inTable 1.

NGWA.org B.S. Gilfedder et al. Groundwater 57, no. 1: 36–47 39

The steady state Roter Main River TSZ model is20 m long and has an average thickness of around0.6 m, and represents the hyporheic area below the river(Figure 1A). The vertical and horizontal grid resolution ofthe model domain varies between 2 and 10 cm. Althoughvertical groundwater inflow is common for the Roter MainRiver, we applied no flow boundaries for the lateral andlower boundaries of the model (Figure 1A). As our mainintention is to highlight the potential of combining in-situ Rn measurements and numerical modeling and not torepresent a specific field site as realistically as possible, weuse no flow boundaries as simplifying assumptions. Theupper model boundary represents the streambed interfacewith a spatially varying bed form topography that wasmeasured using a theodolite during the field survey.Variations of surface heads along the streambed interface,which are an important control on hyporheic exchangeprocesses, are explicitly simulated in HGS by solving thediffusive wave approximation to the St. Venant equations.The representation of surface heads in the model onlyaccounts for hydrostatic pressure and gravitation butnot for dynamical pressure components which wouldrequire a separate computational fluid dynamics (CFD)simulation. Dynamic pressure components were reportedto be important especially for small-scale in-streambedforms at the centimeter-scale such as rippled bedforms(Kessler et al. 2012; Azizian et al. 2015) but only play asubordinate role for structures at larger scales with a lesspronounced bedform amplitude (Tonina and Buffington2007) such as the presented pool-riffle section of the RoterMain. The exchange of water between the surface andsubsurface flow domain utilizes the conductance conceptthat is implemented within HGS (Aquanty Inc. 2015).Under fully saturated conditions the exchange betweenthe surface and subsurface flow domain o [L/T] isrepresented according to Equation 4. In Equation 4 Kz[L/T] is the vertical saturated hydraulic conductivity,h − ho [L] is the head difference between subsurface andsurface and l exch [L] is the user defined coupling length.

o = Kz

(h − h0)

lexch(4)

For the surface flow domain, lateral boundaries in theRoter Main model are implemented using constant headboundaries with a head difference of 0.1 m producingflow from left to right in the model (Figures 1A and 3A).For all computational nodes representing the streambedinterface, 222Rn concentrations were fixed to the measured222Rn in-stream activity (∼200 Bq/m3). Initially, Rnactivities for all nodes in the subsurface were set to thecorresponding 222Rn activities in the river and simulationswere carried out using a homogenous 222Rn emanationterm γ (see Table 1). For the given set of transport andflow boundary conditions, the model was run until steadystate was reached.

The model of the Avon River banks is 1000 m longand represents the transition from the stream channel(40 m) to the floodplain (Figure 1B). The vertical and

horizontal grid resolution of the model domain variesbetween 25 cm close to the streambed interface and4 m for the hinterland areas (Figure 1). In the model,the boundary located at x = 1000 m is a constant headboundary with an assigned constant head of 15.41 m(Figure 1B). This represents the long-term head gradientat the site. The lower no flow boundary conditioncorresponds to a basal clay layer that was found 24 mbelow the surface (Figure 1B). The effect of a variablygaining and loosing stream (bank storage) was representedin the model by applying a transient head boundary forthe stream nodes (Figure 1B) based on a measured 12-day head record. To represent low 222Rn activities ofinfiltrating stream water, the river nodes were fixed to aconstant value of 100 Bq/m3 during the entire simulation.This is similar to the values measured in the Avonriver by Cartwright and Hofmann (2016). In the model,222Rn emanation γ in the subsurface is constant (seeTable 1) and initial conditions for head potentials and222Rn concentrations result from a spin-up simulation thatwas run until the model reached steady-state base flowconditions.

For both models the mean water age distributionof subsurface water was simulated by using the traveltime probability method implemented within HGS. Thismethod estimates the mean age since infiltration for eachelement from the first moment form of an correspondingAdvection-Dispersion-type equation (Aquanty Inc. 2015):

− ∇q A + ∇θD∇ A − qo A + θ = 0 (5)

Here, 〈A〉 [T] represents the mean age of water sinceinfiltration, q [L/T] and qo [L/T] is the subsurface fluidflux and the exchange flux with the surface flow domainand � [−] is the sediment porosity. The mean water age isrelative to a starting location, where the age signature iszero. The starting location here is where surface waterinfiltrates into the sediments which in the case of theRoter Main takes place across the streambed interface(Figure 1A) and for the Avon along the wetter perimeterof the river (Figure 1B). The mean age simulations forboth models were performed based on the calibratedvalues listed in Table 1.

Results

Steady-State TSZs: Hyporheic Flow Roter Main RiverThe Roter Main River discharge at the time of mea-

surement was 1 m3/s, which is below the yearly average,but about equal to the average base flow discharge. Flowhad been steady for 3 weeks prior to sampling, with thelast high discharge event on the 11th of June. 222Rn activ-ities increased from approximately 200 Bq/m3 in the riverwater to 8700 Bq/m3 at 45 cm depth in the hyporheic zone(Figure 2). Insufficient sample could be removed from50 cm depth for 222Rn measurements. The groundwaterendmember assumed to be representative at 1 m belowthe streambed, had a 222Rn activity of 24,000 Bq/m3 and

40 B.S. Gilfedder et al. Groundwater 57, no. 1: 36–47 NGWA.org

Figure 2. Measured and modeled 222Rn activities in thehyporheic zone of the Roter Main River, Bayreuth.

is assumed to be in secular equilibrium with the hyporheicsediments.

The HGS model of the riffle-pool sequence wascalibrated using PEST to the measured 222Rn profile usingonly the first five sampling points (to a depth of 25 cm)as we have found previously (Pittroff et al. 2017) thatthe deeper samples are influenced by upwelling regionalgroundwater which is neglected in our simulations.This can be seen by the rapid increase in 222Rnactivities below 30 cm depth, as well as in otherchemical parameters such as Cl−. The optimized hydraulicconductivity (K sat.) was 3.4 × 10−3 m/s and longitudinaland transverse dispersivities 2.13 × 10−2 and 1.14 × 10−2

m, respectively, which is on the lower side but consistentwith a sandy aquifer with a length scales of 0.5–1 m(Table 1) (Schulze-Makuch 2005).

The HGS model reproduced the upper part of themeasured 222Rn profile well (r = 0.91), with both thegeneral trend of increasing 222Rn with depth and theabsolute concentrations in the sediments being capturedin the simulation (Figure 2). The modeled 222Rn activitiesin the 2D riffle-pool sequence show clearly the down- andupwelling zones within the hyporheic zone (Figure 3B),with young low 222Rn water in the downwelling areasand old, 222Rn rich water where upwelling dominates(Figure 3C). This is also reflected in the mean agecalculated by HGS, with a range 0–5 days (Figure 3D).There is considerable heterogeneity in modeled 222Rnactivities and water ages over the 20 m sequence,reflecting the complex flowpath response to the surfaceheads (Figure 3A). It also can be seen that the 2Dsimulation has areas with large contrasting activities dueto the local up- and downwelling flow cells caused bythe spatial variation of surface heads along the streambedinterface. Such concentration gradients are unlikely toarise in a 1D model, but are an important part of dispersivemixing in 2D and 3D flow in the hyporheic zone (Hester

et al. 2017). The modeled sequences also show featuressuch as the “chimney effect” (Azizian et al. 2015) wheredeep old upwelling hyporheic water enters the streamwith little interaction with shallow flow cells (at e.g.,∼5 and 10 m). Chimney features are usually associatedwith pressure variations on the surface of the streambedinterface, causing deeper water in the hyporheic zoneto flow upwards and exfiltrate into the stream. Theywere reported for small-scale in-stream ripples (cm scale)Kessler et al. 2012 and (Azizian et al. 2015) as well as forriffle-pool structures at the meter scale (Frei et al. 2018).

HGS calculates the mean water age based on theadvection-dispersion equation (Equation 5), while the222Rn τ app. model (Equation 2) is conceptually similar tothe piston flow model. If the mean water age is treatedas the reference age, we can test how well the simpleτ app. ingrowth model approximates water ages at steadystate and systemically investigate how processes suchas dispersion influence τ app.. Figures 3 and 4 show that(1) there is considerable scatter between the mean waterages calculated by HGS and 222Rn τ app. both above andbelow the 1:1 line, and (2) the τ app. tend to be shorter(below the 1:1 line) than the reference mean water ages.The ratio between the τ app. and the mean water age ofthe base case scenario ranged between 0.1 and 8.4, witha mean of 0.76 ± 0.1 and median of 0.78. Deviationslying above the 1:1 line (Figure 4) are located close tothe upper and right model boundaries (red and blankedareas in Figure 3). Values greater than one are physicallyimpossible and can be considered as model artifacts thatarise from the fact that different boundary conditionsfor the 222 Rn (fixed concentration) and mean age (fluxboundary) simulation were used. Two extra runs wereconducted with identical conditions except for one runwith 5× the base case dispersion (5×D) and the other withhalf the base case value (0.5×D). This shows clearly thatthe higher dispersion values increase the off-set from the1:1 line to lower τ app., an observation that has also beenmade using other apparent age tracers (Weissmann et al.2002). What was unexpected is that the lower dispersionvalues (0.5×D) lead to more scatter between HGS agesand τ app. than the highest dispersion values (Figure 4).In this case it appears that dispersive mixing reduces theconcentration gradients in the TSZ and thus the scatter inthe data.

Transient Conditions: Bank Storage at the Avon RiverDuring the deployment of the OctoRad there was a

single rain event of 30 mm in the Avon River catchment.This caused the river stage at Pearces Lane to riseby almost 1 m (Figure 5). The rise in stage caused aclear increase in groundwater heads close to the river.The head in bore 5 rapidly increased on the rising limband decreased on the falling limb while the heads in bore2, located 55 m from the river, rise less rapidly and fallmore slowly than in bore 5 as expected for bank storage(Gerecht et al. 2011; Fovet et al. 2015). 222Rn activitiesdecreased from around 5000 Bq/m3 prior to the eventto below the instrument detection limit over about 12 h.

NGWA.org B.S. Gilfedder et al. Groundwater 57, no. 1: 36–47 41

Figure 3. HGS modeling of the Roter Main River. (A) Simulated water depth above the streambed. (B) Simulated headdistribution in the hyporheic zone; surface flow occurs from the left to the right (C) modeled 222Rn activities in the hyporheiczone. (D) Mean water age calculated by HGS. (E) Comparison of 222Rn ages with HGS ages. In panel (E) the upper boundary(ratio less than 0.3), as well as extremely high values at the right hand boundary (ratios more than 1.2) have been removedto limit boundary effects.

As head levels declined, the 222Rn activities increasedrapidly over approximately 3 days and then increasedmore slowly for the remainder of the measurement period.222Rn activities had only reached 4000 Bq/m3 when themeasurements were ceased on eighth of November, 9 daysafter the start of the event.

Modeling Bank StorageThe HGS model of bank storage on the Avon was

calibrated using the 222Rn activities as the advectivefront of the infiltrating flood wave passed through bore5 (Figure 1B). The correlation coefficient for the bestfit model was r = 0.89, with K sat. = 8.4 × 10−3 m/s,αL = 1.78 × 10−2 m and αT = 1.25 × 10−2 m. This issimilar to the K sat. values measured by slug tests at thesite (0.5–5 × 10−3 m/s). The model was able to captureboth the decrease in 222Rn activities as the advectivefront passed through the bore, and the increase of 222Rnactivities to near-background activities on the receding

limb of the event as water flowed back toward theriver.

There were some differences between modeled andmeasured 222Rn activities during bank return flow, withthe measured values being generally higher than modeled(Figure 5). It was also not possible to capture theflattening of measured 222Rn activities 4 days into thereceding limb. This may be due to modeled dispersionbeing too low so that mixing with the high 222Rnregional groundwater was underestimated, heterogeneityin K sat. in the bank, or perhaps the most likely scenariois that the three dimensional flow fields in the gravelbeds were not fully captured in the two dimensionalsimulation. Heterogeneity in the emanation rate withinthe gravel beds may also have contributed to the morerapid increase in measured 222Rn values during bankreturn flow compared to modeled values. This is suggestedby 222Rn measurements from bores 2 and 3 being upto 15,000 Bq/m3. It would possible to construct a 3D

42 B.S. Gilfedder et al. Groundwater 57, no. 1: 36–47 NGWA.org

Figure 4. Comparison of HGS mean water ages with 222Rnτ app. calculated using the ingrowth method. The differentpoints in the figure show the relation between the apparentage estimated with the 222Rn method and the simulated meanwater age (HGS) at every node of the computational grid.Nodal values above the 1:1 line arise from boundary effectsand values above 1:1.1 have been removed.

Figure 5. Measured and modeled 222Rn activities in bore 5together with the river stage during a high flow event on theAvon River, Australia. AHD is Australian Height Datum.

HGS model that is likely to better capture such effects,but it would require a distributed network of 222Rn andhead measurements within the gravel beds to sufficientlycalibrate the model.

Once calibrated the 2D model was used to visualizethe bank storage processes, quantify mean water agesand fluxes within the bank. On the rising limb, low222Rn activity water from the river displaced and dilutedthe bank water by the combination of advection anddispersion, respectively. The largest water fluxes to thebanks occurred at the flood peak (36 m3/day), where afterthe gradient reversed and the water in storage drained

back toward the river. The flood water penetrated to amaximum of 7 m into the river bank. Exfiltration wasslow, however, with 98% of the newly infiltrated riverwater remaining in the bank at the end of the simulation.In total, 81.5 m3 of river water per meter river length wasstored in the bank during the event.

Comparing the HGS mean water ages with τ app. fromthe 222Rn ingrowth model gives a more complex picturethan the Roter Main steady state simulation (Figure 6).The most obvious effect is the systematic underestimationof τ app. compared to the HGS mean ages. This occursalong the advective front (Figure 7B and 7C) wherehigh 222Rn regional groundwater and young low 222Rnriver water mix within the bank (points far off the 1:1line in Figure 7A), increasing activities above ingrowthalone. This effect has been well described for other agetracers such as 14C where very old water from aquitardsmixes with aquifer water (Bethke and Johnson 2002). Thedifference between linear mixing and exponential decay oringrowth processes leads to a large deviation of apparentages from mean water age. Away from the advectivefront toward the stream, there is a very good agreementbetween the water ages estimated from the two models,with values lying very close to the 1:1 line (Figure 7A).Within the mixing zone between stream and groundwater(Figure 7B and 7C) there are some spatially limited areaslocated close to the model boundaries that show a ratiobetween τ app and the HGS mean age above 1 (red areas inFigure 7). In Figure 7A, these points lie above the 1:1 lineand as described previously for the Roter Main modelcan be explained by model artifacts that arise due to thedifferent boundary conditions applied for the 222Rn andmean age simulations.

DiscussionFor the two test cases, Roter Main and Avon River,

we have demonstrated how the combination of in-situ222Rn measurements and numerical modeling can beused to mechanistically understand TSZ’s under steadystate and transient flow conditions. In the steady stateexample from the hyporheic zone we noticed a systematicunderestimation of water ages using the apparent agemodel. This was related to dispersive effects and increasedfrom 0.5×D to 5×D. Similar effects on radioactive tracertransport and dating have also been observed for 3H insimple 1D systems, but over much larger time scalesdue to 3H’s longer half-life. One important differencebetween 222Rn and these previous studies is that the inputof 222Rn is constant whereas more conventional tracershave defined input shapes such as the bomb pulse for 3Hor exponential increase for SF6 and CFCs (Schlosser et al.1989; Weissmann et al. 2002). The effect of dispersionwill be dependent on the length scale as well as theconcentration gradient, and thus it is conceivable that theerror incurred by using the apparent age model increaseswith flowpath length. The error incurred by the apparentage model will also be exacerbated where water of highlydifferent concentrations are in close proximity. This is

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Figure 6. HGS simulation of mean water ages and 222Rn activities in the Avon floodplain. (A-E) Time series of water age and222Rn activities during a bank storage event on the Avon River. Red numbers indicate contour lines for mean water age.

likely the reason that the deviation between HGS meanwater ages and the apparent age model ages are largestat the edges of the upwelling zones. Such effects wouldbe increased during parafluvial flow or bank storagewhere flow paths tend to be tens of meters in length andwhere TSZ water abuts regional groundwater with high222Rn activities. This can be seen during bank storageon the Avon River where the HGS model computed asystematic underestimation of apparent ages, with theunderestimation at the advective front being particularlylarge. The incorporation of 222Rn into HGS allows forcomplex flow processes to be captured and evaluated andthus is a useful tool for interpreting 222Rn tracer data. Forexample, it is possible extend the model to 3D flow fields,or to model saturated-unsaturated flow processes, whichare important during over bank and return flow processes.

Galser et al. (2016) suggests that we still lackapproaches that include spatially distributed data in theevaluation of physically based models that are supposedto represent spatiotemporal processes ranging from afew centimeters up to the scale of entire catchments.Although both the cases here only represent generic casesof real world conditions, including 222Rn measurements

into model calibration shows a high potential to furtherconstrain the nonuniqueness of hydrological modelsand to get an improved mechanistic understanding ofhydrological systems on time scales of hours to days.222Rn is unique compared to other tracers as it is emittedfrom the aquifer matrix, and as a radioactive isotope, hasan explicit and well-defined time scale for emanation anddecay. However, it is also clear from previous studiesthat calibration to a single field measurement type leadsto significant uncertainty in model parameter uniqueness.The more field parameters that can be incorporated intothe calibration and validation process the lower theuncertainty in the model results and more unique theindividual parameters will be (Sanford 2010). 222Rn offersa new and powerful tracer that can be used explicitlywithin the model calibration process, but this should notbe to the exclusion of other calibration data that canbe measured in the field, such as hydraulic conductivity,pressure head, and other chemical and radioactive tracers.

Representation of 222Rn in subsurface hydrologicalsystems requires a model that is capable of representingadvective and dispersive transport processes as well as222Rn-decay and -emanation in the subsurface. Many

44 B.S. Gilfedder et al. Groundwater 57, no. 1: 36–47 NGWA.org

Figure 7. (A) Comparison of 222Rn ages calculated using theingrowth method and the HGS mean water ages duringthe bank storage event. The different points in the figureshow the relation between the apparent age estimated withthe Rn method and the simulated mean water age (HGS)for different times (different colors) at every node of thecomputational grid. (B and C) Spatial distribution of theratio between the 222Rn ages and the HGS mean water agefor the mixing zone between stream water and groundwaterfor days 8 and 12.

numerical hydrological models are capable of representingreactive solute transport with simple first order reactionkinetics. However, the inclusion of a constant sourceterm that can be used to account for 222Rn-emanationis not often the case. Schilling et al. 2017 have recentlyused HGS to understand and incorporate geochemical dataincluding 222Rn into the model calibration processes whensimulating bank filtration. While a novel approach, theseauthors have not modeled the tracers explicitly (i.e., viathe advection-dispersion-reaction equation), instead usingthe dynamic mixing cell approach and then (in the caseof 222Rn) the apparent age method to quantify water ages.This will likely have led to errors where dispersion is animportant part of the mixing process, especially if thereis a component of regional groundwater in the samples

or where concentration gradients exist as water of variousages converge on the pumping well. The zero-order sourceterm, that is implemented in HGS and used to accountfor 222Rn-emanation, could also be extended to otherradioactive tracers that are emitted from the aquifer matrixsuch as 4He and 37Ar (Schilling et al. 2017). In evaluatinghydrological models that are capable of solving surfaceand subsurface flow processes simultaneously a majorchallenge is still to extend 222Rn-transport to the surfaceflow domain. In surface flow 222Rn is lost not only byradioactive decay, but additionally is subject to degassingto the atmosphere which represents a major sink in surfacewater bodies. Contrary to emanation, degassing cannot berepresented by a simple constant sink term as it highlydepends on the characteristic of surface flow such as thedegree of turbulence. This point remains to be addressedin future model developments.

AcknowledgmentsThis work was funded using the internal funds of the

Limnological Research Station, University of Bayreuthas well as the National Centre for Groundwater Researchand Training (NCGRT). Three reviewers and the editorare thanked for improving previous versions of themanuscript.

Authors’ NoteThe authors do not have any conflicts of interest or

financial disclosures to report.

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