Aquifer Vulnerability Assessment Based on Sequence Stratigraphic and 39 Ar Transport Modeling

Aquifer Vulnerability Assessment Based onSequence Stratigraphic and 39Ar TransportModelingby Torben O. Sonnenborg1, Peter B. Scharling2,3, Klaus Hinsby2, Erik S. Rasmussen2, and Peter Engesgaard4

AbstractA large-scale groundwater flow and transport model is developed for a deep-seated (100 to 300 m below ground surface)

sedimentary aquifer system. The model is based on a three-dimensional (3D) hydrostratigraphic model, building on a sequencestratigraphic approach. The flow model is calibrated against observations of hydraulic head and stream discharge while the credibilityof the transport model is evaluated against measurements of 39Ar from deep wells using alternative parameterizations of dispersivityand effective porosity. The directly simulated 3D mean age distributions and vertical fluxes are used to visualize the two-dimensional(2D)/3D age and flux distribution along transects and at the top plane of individual aquifers. The simulation results are used toassess the vulnerability of the aquifer system that generally has been assumed to be protected by thick overlaying clayey units andtherefore proposed as future reservoirs for drinking water supply. The results indicate that on a regional scale these deep-seatedaquifers are not as protected from modern surface water contamination as expected because significant leakage to the deeperaquifers occurs. The complex distribution of local and intermediate groundwater flow systems controlled by the distribution of theriver network as well as the topographical variation (Toth 1963) provides the possibility for modern water to be found in even thedeepest aquifers.

IntroductionWorldwide, many shallow aquifers are polluted by

infiltrating nitrate from agriculture (e.g., Zhang et al.2009; Hansen et al. 2011; Liao et al. 2012). Hence, thereis a need for locating new and unpolluted aquifers,and, not the least, procedures for doing so. Age datingof groundwater is one way. Environmental tracers andisotopes in complex sedimentary aquifer systems locatedseveral hundred meters below surface have indicated thatages within the aquifers can be highly variable rangingfrom nearly modern waters to water several thousandyears old (Chen et al. 2005; Hinsby and Rasmussen

1Corresponding author: Department of Hydrology, GeologicalSurvey of Denmark and Greenland (GEUS), Øster Voldgade 10, DK-1350 København K, Denmark; +45 91333635; fax: +45 38142050;[email protected]

2Department of Hydrology, Geological Survey of Denmarkand Greenland (GEUS), Øster Voldgade 10, DK-1350 København K,Denmark.

3Currently at COWI A/S, Parallelvej 2, DK-2800 KongensLyngby, Denmark.

4Department of Geosciences and Natural Resource Manage-ment, University of Copenhagen, Øster Voldgade 10, DK-1350København K, Denmark.

Received February 2014, accepted April 2015.© 2015, National Ground Water Association.doi: 10.1111/gwat.12345

2008; Scharling 2011). This is in good agreement withthe theoretical description of groundwater flow systemsoriginally introduced by Toth (1963) and Freeze andWitherspoon (1967), later by Winter (1998), and recentlyby Jiang et al. (2012) and Gomez and Wilson (2013),which shows that groundwater flow can be subdivided intoa complex distribution of local, intermediate, and regionalflow systems having very different ages. The flow systemsare controlled by (1) the relief of the land surface, (2)position of surface water bodies, and (3) the depth of theunderlying aquifer system.

To test the conceptual understanding of the flowregime as well as the degree of protection from intrusionof modern water into the deep aquifer systems, anumerical fully three-dimensional (3D) flow and transportmodel can be an option. Groundwater flow models haveoften been used solely for this purpose, but they maysuffer from the lack of unique solutions because they arecalibrated entirely on hydraulic heads and river discharge.This was demonstrated by Seifert et al. (2008) whodeveloped a local-scale groundwater model representingdeep-seated aquifers with thick overlying clayey unitsand a coarse grained buried valley that short circuit theotherwise isolated aquifers. Calibration was carried outbased on hydraulic head and river discharge for twomodel setups, with and without inclusion of the buried

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valley, and it turned out that the calibration was notimproved by implementing the valley structure. Particletracking showed, however, that the infiltration area andresidence time of the groundwater were affected bythe deeply incised valley. Castro and Goblet (2003)and Troldborg et al. (2007) showed that calibration ofa regional groundwater flow model with very differentgeological model inputs did not change the calibrationresults significantly. However, they were able to constrainthe number of plausible geological models by applyingadditional information regarding groundwater age fromtracer data. Flow models can therefore benefit from theinformation provided by concentration data based onsampled environmental/isotope tracer data in order tofurther constrain the model results. Simulating advectiveages thus has the possibility for providing additionalinsight into the conceptual model by improving the fitbetween simulated and measured tracer ages. Troldborget al. (2008) simulated breakthrough concentrations ofchloro-fluoro-carbons (CFCs) in a shallow aquifer systemby a convolution approach using the simulated particleage distributions at well screens and the measuredconcentrations in precipitation. Sanford et al. (2004) usedparticle tracking and 14C to estimate recharge rates. Sheetset al. (1998) used tracer data directly as calibration targetsagainst simulated particle ages for constraining the finalparameter values.

Direct simulation of tracer transport provides anextra dimension to the investigation of groundwatersystems. For example, Engesgaard et al. (1996) simulatedtritium concentrations in order to investigate large-scaledispersion in a sandy aquifer. Weissmann et al. (2002)modeled the distribution of groundwater and CFC agesin a shallow heterogeneous aquifer and found thatgroundwater spanned a wide range of ages even overshort screened intervals. With minor modifications of thetransport equation it is also possible to simulate the meanage or “age mass” directly (Goode 1996; Engesgaard andMolson 1998). It can, however, be argued that even thoughthe directly simulated mean age provides a very intuitivetool for presenting age distribution of groundwater, itusually does not provide information on the dispersionmechanisms (Sanford 2010). The method gives the steady-state age or concentration within the model domain butno information regarding the mixing of waters that formthe resulting age or concentration. Sater and Levenspiel(1966) solved this problem by performing a momentanalysis on a breakthrough curve where the spreading ofthe concentration or age of groundwater can be calculatedwithin any of the model cells. This method has laterbeen applied by, for example, Goltz and Roberts (1987),Neuman (1993), Butera and Tanda (1999), and Varni andCarrera (1998). Even though numerous methods exist totake advantage of tracer information when constructiongroundwater models, Zuber et al. (2010) point out thateven though an acceptable match to the tracer data isobtained, there is still no guarantee that the solution isthe most adequate representation of the system. Unknownheterogeneity in the form of clay or sand lenses at

decameter scale within larger sandy or clayey unitsis another factor that has a significant impact on thedispersion and transport of solutes and groundwater age(Weissmann et al. 2002; Eaton 2006). Even if sufficientdata exist to describe the heterogeneity and to adequatelysimulate groundwater age and concentration distributions,limitations in present day computer power will, however,prevent implementation in regional-scale models (Sanfordand Pope 2010).

The results from flow and age transport simulationsmay be used to evaluate the vulnerability of the groundwa-ter system to surface contaminations. Frind et al. (2006)defined the intrinsic aquifer vulnerability as the protec-tive effect of layers overlying a drinking water aquifer,where the term intrinsic relates to the physical parame-ters (hydraulic conductivity, porosity, dispersivity, etc.).Direct simulation of mean ages can be used to assess theintrinsic vulnerability of aquifers as demonstrated by Mol-son and Frind (2012). Based on a 3D flow and transportmodel they evaluated the vulnerability of a layered aquifersystem using information on the age distribution whereareas with young water were considered vulnerable andlocations with old waters were assumed to be protected.

The objective of this work is to demonstrate anapproach, whereby a reliable groundwater model can beconstructed on the basis of sequence stratigraphical inter-pretation of the geological architecture on a regionalscale within deep-seated sedimentary aquifers and thatthe resulting model can be used to assess the vulnera-bility of the aquifers that are assumed to be protected bythick overlying clayey units. The applied method is basedon a combination of using environmental tracer data, 39Ar(Scharling 2011), and simulation methodologies from flowand transport modeling. The 3D flow model is calibratedagainst an extensive data set on hydraulic head measure-ments and river fluxes. Transport parameters are estimatedby comparing modeled 39Ar concentrations against sam-pled 39Ar concentrations. This approach has not beentested before for a system where only regional geolog-ical variations can be implemented and heterogeneity ondecameter and even 100-m scale generally must be dis-regarded. The vulnerability of the deep-seated aquifers isevaluated based on flow paths, vertical fluxes, and ground-water age distributions.

Study CatchmentThe study catchment is situated on the peninsula

of Jutland in western Denmark, Figure 1, where deep-seated Miocene aquifers have received increasing focusover the past 15 years (e.g., Rasmussen 1996; Rasmussen2004a; Rasmussen and Dybkjær 2005; Scharling et al.2009). Valuable geological information has been obtainedregarding the location and distribution of major aquifersystems located 100 to 300 m below ground surface. Thegeneral conceptual understanding of the flow systems isthat modern water recharges the Miocene aquifers towardeast, where they are close to the ground surface, andgroundwater progressively gets older toward west.

2 T.O. Sonnenborg et al. Groundwater NGWA.org

Figure 1. Study area in central Jutland, Denmark. The equipotential lines are interpolated based on hydraulic head datafrom screens at depths from 70 to 150 m representing the regional Burdigalian aquifer system. Sampling for tracer data isdone in wells along transects A and B (Figure 2).

Climate and HydrologyThe study catchment covers an area of more than

5500 km2 (Figure 1). The area includes the subcatchmentsto the Skjern and Varde river systems both flowing towardwest with discharge for the Skjern river system intothe Ringkøbing Fjord and for the Varde river systeminto the North Sea via Ho Bay. The climate is atypical maritime regime dominated by westerly windscarrying precipitation from the North Sea. Precipitationand actual evapotranspiration are approximately 1000 and600 mm/year, respectively (Stisen et al. 2011). Land useis dominated by agriculture.

GeologyThe geology is controlled by the development of the

North Sea basin (Ziegler 1990; Rasmussen 2004a, 2004b).During Miocene, the coastline propagated south of thestudy area three times during the three stages Aquitanian,Burdigalian, and Langhian, resulting in deposits rangingfrom exclusively marine clays to sandy deposits such asnear-shore sands, delta lobe deposits, lagoon deposits,brackish water deposits, to terrestrial deposits. Duringperiods where the coastline was situated north and eastof the study area and marine conditions prevailed, it maybe assumed that coherent units of marine clays were

deposited throughout the model area. The entire Miocenesuccession was tilted toward west and deformed duringQuaternary. Border moraine deposits that are visible asa range of north-south striking heights through centralJutland define the maximum extent of the Weichelianglaciation. Quaternary sediments are present throughoutthe area with highly variable thicknesses ranging froma few meters to more than 300 m at buried valleylocations (Houmark-Nielsen and Kjær 2003; Sandersenand Jørgensen 2003; Jørgensen and Sandersen 2006). Theburied valleys often have a high sand content comparedto the surroundings (Jørgensen et al. 2003a,b; Sandersenand Jørgensen 2003) and are found to cross-cut the deepMiocene aquifers that otherwise are protected by thickoverlying clayey units (Scharling et al. 2009). The buriedvalleys therefore significantly affect the vulnerability ofdeep-seated aquifers by intrusion of modern water (Seifertet al. 2008).

Based on seismic profiles, gamma-ray logs, sedimentdescriptions, and palynological analysis of boreholesamples Scharling et al. (2009) carried out a sequencestratigraphic interpretation of the Miocene units. Thelaterally extensive clay units are expected to be of majorimportance when groundwater flow and transport are to beestimated because they may act as barriers to flow between

NGWA.org T.O. Sonnenborg et al. Groundwater 3

the surface and underlying aquifers. In this work, themultiaquifer systems are referred to as originating fromthe Aquitanian, Burdigalian, or Langhian progradation(Figure 2). The description of the Quaternary geology isbased on Henriksen et al. (2003) where the distribution ofsand and clay was interpreted from borehole logs.

Methods

Model CodesThe 3D steady-state groundwater flow model is

based on MODFLOW 2000 (Harbaugh et al. 2000). Thegeological model is based on the work of Scharlinget al. (2009). The hydrostratigraphic model surfaces wereimported into the hydraulic unit flow (HUF) package ofMODFLOW 2000. The HUF package has the advantagethat the hydrostratigraphic layers are independent of thenumerical grid, which allows application of very complexgeological models without the need for having the samelayer structure in the numerical grid. The flow modelis calibrated using the PEST optimization tool (Doherty2004).

Transport simulation of the 39Ar distribution is carriedout using MT3DMS (Zheng 1990) using the third-ordertotal variation diminishing (TVD) scheme as solver. The39Ar concentration is set to 100% for the constant inputconcentration that enters the system with recharge andthereafter starts decaying with a half-life of 269 years. Themodel was run for 10,000 years; however, based on mass-balance budgets, steady-state conditions are achievedwithin 2000 years. The flow solution used as basis forthe transport simulations was generated with groundwaterextraction set to 0. Significant groundwater extraction hasonly taken place during the last 50 years and the long-term flow and transport is therefore dominated by pristineconditions.

Direct simulation of the mean groundwater age iscarried out using the RT3D code (Clement 1997), whichessentially is the same as MT3DMS but allow usermodifications of the reaction part of the code. The methodis based on a modified steady-state advection-dispersiontransport equation with a zero-order rate term of unity(+1) added to account for the aging of groundwater withone second per one second elapsed time (Goode 1996)

∇·D· ∇A − ∇·Aq

ø+ 1 = 0 (1)

where ø is the effective porosity, q is the specificdischarge vector (m/s), D is the hydrodynamic dispersiontensor (m2/s), and A is the mean age (s). The method wasalso used with success by Engesgaard and Molson (1998)to model apparent ages determined from tritium.

Model Setup

DiscretizationThe hydrostratigraphic units were originally con-

structed by individual two-dimensional surfaces with a

grid resolution of 100 × 100 m, each representing thetop of a geological surface (Scharling et al. 2009). Themodeled geological structures have lateral extents on thescale of kilometers and are therefore reproduced with anacceptable accuracy using this resolution. The ground-water model is constructed with uniform horizontal griddimensions of 500 × 500 m in the modeling software GMS(Figure 3). As the resolved hydrostratigraphic units havea horizontal extent on the scale of kilometers, the 500 mdiscretization is assumed sufficient to represent these.

The numerical layers do not follow the hydrostrati-graphic layers because there are many pinch-outs thatcomplicate the setup of a flow model where the numericallayers follow the hydrostratigraphical layers. The numeri-cal grid therefore consists of a top layer that extends fromthe soil surface to approximately 3 m below the ground-water table and 21 additional layers that are distributedevenly between the top layer and the bottom of the model.The total model thickness generally varies between 100and 300 m where the largest thicknesses are found towardthe very western part of the area. However, the Mioceneaquifers of interest are generally not extending that farwest. A vertical discretization of 5 to 12 m for the numer-ical grid is therefore considered sufficient for resolvingthe hydrogeological structures of interest.

External Boundary ConditionsThe model catchment is surrounded by no-flow

boundaries toward North, South, and East (Figure 3).The Eastern border coincides with the Mid Jutland highsthat also represent the regional north-south trendinggroundwater divide of Jutland. Lagoons and the sea inthe western part of the catchment are specified as constanthead boundaries with a hydraulic head of 0 m. The modelextends 1 km into the North Sea in order to accountfor upward flowing water from the aquifers to the sea.Considering that the Miocene aquifers terminate far fromthe west coast, this representation is considered to besatisfactory for this study.

Net recharge is applied as a specified distributedflux to the groundwater table based on an average ofthe time period 1991 to 2010. The data originate fromthe National Water Resources Model (Henriksen et al.2003). The spatially distributed recharge has a mean of480 mm/year with a standard deviation of 100 mm/year.For pragmatic reasons, this recharge estimate is assumedto be valid for the 2000 year long age simulation.

Internal Boundary ConditionsThe rivers are represented by the River package

in MODFLOW, where the river stage and the riverbottom are placed 1 and 2 m below surface, respectively.Only major rivers that are assumed active throughoutthe year are included (Figure 3) similar to that proposedby Henriksen et al. (2003). A “specific” conductance of0.003 m2/s/m was used for the river bed, and the riverconductance for the entire cell (in m2/s) was calculatedaccording to the total length of the river segments withinthe cell. Additionally, tile drains and/or ditches have


(a)

(b)

Figure 2. (a) Transect A along the sample wells A-O. (b) Transect B along the sample wells P-Z (see Figure 1 for locationof transects). The geological units are based on the hydrostratigraphical model of Scharling et al. (2009) and the lithologicallogs are binary presentations of geological logs from the national geological well database.

been installed in the agricultural fields. To representthe combined effect of tile drains, ditches, and smallerstreams, drains are placed in all other cells at a depthof 0.5 m below ground surface using the Drain package.Where the surface is close to the sea level, the drain depthsare reduced in order to prevent drains from being locatedbelow sea level. The drains are assigned a very highconductance of 20 m2/s to ensure that the groundwaterlevel do not increase significantly above the drain level.

Groundwater exploitation can be divided into twomajor consumers; drinking water supply and farm-ing/industry. A total of 1264 extraction wells witha mean groundwater extraction (1991 to 2010) of34.7 × 106 m3/year have been identified in the nationalJupiter database. Information regarding irrigation of farm-land and water for industrial purposes is also a part of thedatabase but is not as updated compared to informationon drinking water supply. Each irrigation well is assignedan estimated pumping rate based on combined informa-tion about pumping permissions as obtained from Jupiter(year 2000) and knowledge about the actual crops grownin the area (Henriksen et al. 2003). The total mean extrac-tion rate for irrigation was estimated to 2.0 × 106 m3/year.Because of the limited resolution of the geological model,

especially in the vertical direction, the screens of somepumping wells may be partially located within model lay-ers with clay. The extraction from these wells has beenset to 0.

Calibration of Flow Model

Calibration DataThe 3D flow model was calibrated in steady-state

mode using mean values of both hydraulic heads and riverdischarges. Head measurements from 5183 screens andriver discharge from 30 discharge stations are available.Both data types are distributed fairly homogeneously inthe model area (Scharling 2011). Potentiometric head datawere selected from the same time span as used to calculatethe averaged recharge input (1991 to 2010). Each screenis assigned to a specific hydrogeological unit to laterinterpret model performance with respect to simulatingthe head distribution within different hydrostratigraphicunits. Based on time series data from 28 screens, atrend analysis revealed that the assumption of stationarityis not violated. Therefore, it is assumed that all datameasured in the period 1991 to 2010 can be used forcalibration.


Figure 3. Discretization and boundary conditions for the top layer of the groundwater model. See Figure 1 for location ofthe model area. Cross-section B-B′ is shown in Figure 7.

The observation data are assigned an observationweight that is used when calculating the objectivefunction. Highest weights are given to the deep Mioceneunits and lowest weights are assigned the observationpoints in the Quaternary units. This is done to compensatethe uneven number of observations in the hydrogeologicalunits as the number of head observations is very limitedwith depth. For example, only 23 observations areavailable in the deepest aquifer system (Aquitanian),whereas 1410 observations are available for the mostshallow Miocene aquifer system (Langhian), and 3440observations for the Quaternary aquifers. Based onsubjective criteria, the weights assigned for the Aquitanianand Burdigalian are twice as high as for the Langhianobservations and eight times as high compared to theQuaternary observations.

River discharge data from the 30 discharge stationsare represented by the median minimum runoff valuethat is found as the median of annual minimum dailydischarge (Ovesen et al. 2000). It is assumed that thesimulated discharge to the river system represents baseflow in the same way as the median minimum runoffdata (Sonnenborg et al. 2003), as net recharge is assigneddirectly to the groundwater table and the water generatedby the drains that are defined throughout the model areais not routed to the rivers.

Weights are assigned to the group of discharge datato ensure that 10% of the total error calculated by theobjective function originates from the match to riverdischarge data and the last 90% from the hydraulic headdata. These weights are not constant but changed during

the calibration to ensure a constant contribution of 10%from the rivers because the error from the two data setschange for every set of calibrated parameters.

To evaluate the fit of the model to observedpotentiometric head and river discharge data, the meanerror (ME) is used to indicate if the model generallyoverestimate or underestimate the observed values, whilethe root mean square (RMS) error is used to represent thescatter in the difference between the model results and theactual measurements.

ParameterizationThe Miocene is divided into six regional sequence

stratigraphical units deposited mainly during the Aqui-tanian, Burdigalian, and Langhian stages, where eachstage contains two depositional sequences. Each sequenceis subsequently subdivided into system tracts (up tofour types), see Scharling et al. (2009). To convert thestratigraphical model into a hydrostratigraphical model, aregional sediment analysis is carried out where the systemtracts are disintegrated into clays and sands. The resultinghydrogeological model consists of 22 Miocene hydros-tratigraphical clay and sand units (Scharling et al. 2009)and two Quaternary hydrofacies based on the work ofHenriksen et al. (2003). Not all are present throughoutthe area so the number of hydrostratigraphic units can besmaller in a particular area. Hence, even though a binarysystem is used to describe the distribution of hydraulicproperties within a particular sequence, the distribution offacies is fairly complex (Figure 2). It is assumed that thehydraulic properties of the sand and clay facies within


each system tract are uniform and therefore the hetero-geneity within the hydrofacies is not explicitly taken intoaccount. Based on a sensitivity analysis and an evaluationof how well the model parameters are known (includ-ing recharge rate, boundary conditions, anisotropy ratio,hydraulic conductivity) it was decided to carry out cal-ibration on the hydraulic conductivities of the Mioceneand the Quaternary hydrostratigraphic units. The cali-brated parameters are not constrained by upper and lowerbounds. Horizontal and vertical hydraulic conductivitiesare tied together through an anisotropy factor. Hydraulicproperties are assigned directly to individual materialsthat are assigned to the HUF package units. The mate-rial properties are thereafter assigned to one or morehydrostratigraphic unit. The calibration was carried outon successive model setups starting with a homogeneousmodel where the hydrofacies of all stages were assumed tohave identical hydraulic properties. Increasing complex-ity was added for each following model setup where thecalibration result of the former model was used as ini-tial conditions for the calibration of the subsequent model(Scharling 2011). Results from step four using six hydro-facies for the Miocene are presented here. This representsan intermediate step where the estimated parameters arephysically plausible and close to the values estimated inthe previous step. Additionally, the estimated parame-ter uncertainties are relatively low. The low parameteruncertainty indicates high sensitivity and the low num-ber of parameters minimize nonuniqueness problems (Hill1998).

Solute Transport

Tracer DataThe calibrated model is tested against 10 39Ar data

points sampled in 2008. Transect A is sampled for 39Arin well A, C, E, F, and J; and transect B is sampled inwell Q, R, S, T, and V (Figure 2). The average screenlength is 11 m with a minimum of 1 m and a maximumof 25 m. For a detailed description of the samplingprocedures and analysis, see Scharling (2011). The screensare located in the eastern part of the Burdigalian sand unitsbecause it was originally assumed that the ages in thedeepest Aquitanian sand units in the western part of thetransects would be far older than the dating range of 39Ar(∼100 to 1000 year). This assumption was later foundto be incorrect. The measured 39Ar concentrations arecorrected for interlayer diffusion (Sanford 1997; Scharling2011) before comparison with model results. Correctingfor diffusion is important because the geological modelused here does not include the heterogeneity withinthe individual formations (e.g., Burdigalian sand). Onlyconcentrations that indicate ages higher than 320 yearsare corrected for diffusion, see discussion by Scharling(2011).

ParameterizationAlternative parameter values for the dispersion

parameters, effective porosity, and diffusion coefficient

are evaluated by comparing model predictions and obser-vations of 39Ar concentration along transects A and B(Figures 1 and 2). The set of most likely parameter valuesare then used as input for subsequent age simulations.

Dispersion at this scale is associated with a highdegree of uncertainty. Various model runs are thereforecarried out with different dispersivity values in order totest which set of values provides the best fit betweenobserved and simulated 39Ar concentrations. The literaturesuggests that dispersivity is scale-dependent, in the orderof 1% to 10% of the transport distance in the directionof flow (Gelhar et al. 1992; Xu and Eckstein 1995).The maximum distance in the direction of flow isapproximately 90 km long (from east to west), however,as transport is dominated by local and intermediateflow systems (see below) the average transport distanceis considerably shorter. In this work, model runs areperformed with longitudinal dispersivity values of 0,0.05, 0.5, 5, 10, 50, 100, and 500 m in order to testthe sensitivity of dispersion on the simulation results.Transverse dispersivities of 1/10 and 1/100 of thelongitudinal dispersivity for the horizontal and verticaldirections relative to flow, respectively, are used.

The effective porosity is assigned to the hydrostrati-graphic units. For sandy units, values between 0.15 and0.30 are tested while values between 0.05 and 0.30 areused for clayey units. The diffusion coefficient cannot beassigned directly to the hydrostratigraphic units but onlyto numerical layers (that do not follow the units). It istherefore not possible to apply a similar method as forthe effective porosity. An effective diffusion coefficientof 6.16 × 10−10 m2/s was calculated based on the size ofthe argon atom and an average tortuosity of the sediments(Scharling 2011). The influence of diffusion is tested bycomparing with a simulation where the effective diffusioncoefficient equals 0 (see below).

Model Calibration and Evaluation

Calibration of Flow ModelThe calibrated parameters and 95% confidence inter-

vals are presented in Table 1. In the final model presentedhere, the Kv/Kh ratios were fixed to 0.1 for both sandy andclayey units for pragmatic reasons as these are not known.Two mass transport simulations studies in the vicinity ofthe study area have tried to estimate this ratio by compar-ing simulation results with observations. Engesgaard et al.(1996) report on a large-scale transport simulation studyand found that an anisotropy ratio of 0.5 matches observedtritium profiles measured in a sandy outwash aquifer. Ina similar sedimentary environment, Karan et al. (2014)argued that a ratio of 0.02 to 0.1 was needed to matchboth the measured discharge of groundwater to a lake andan observed nitrate plume beneath the lake bed. The useof a ratio of 0.1 is therefore not unrealistic.

As expected, there is a significant contrast betweenthe hydraulic conductivities for the sandy and clayeyMiocene units. With respect to the Quaternary unit, the


Table 1Results of Model Optimization Including Estimates of Horizontal Hydraulic Conductivities for the SandyUnits, Vertical Hydraulic Conductivities for the Clayey Units, and 95% Linear Confidence Intervals (Hill

1998). Anisotropy Factors of 10 Are Used for Both the Sandy and the Clayey Units

Parameter Estimate (m/s) 95% CI (m/s) Description

Kh_Qua_S 3.45 × 10−5 2.88 × 10−5 to 4.14 × 10−5 Horizontal K for Quaternary sand unitKv_Qua_C 2.04 × 10−6 1.05 × 10−6 to 3.96 × 10−6 Vertical K for Quaternary clay unitKh_Lan_S 1.24 × 10−4 9.53 × 10−5 to 1.62 × 10−4 Horizontal K for Langhian sand unitKv_Lan_C 2.31 × 10−7 7.90 × 10−8 to 6.74 × 10−7 Vertical K for Langhian clay unitKh_Bur_S 3.84 × 10−4 3.51 × 10−4 to 4.21 × 10−4 Horizontal K for Burdigalian sand unitKv_Bur_C 9.30 × 10−7 8.42 × 10−7 to 1.03 × 10−6 Vertical K for Burdigalian clay unitKh_Aqu_S 2.84 × 10−4 2.38 × 10−4 to 3.39 × 10−4 Horizontal K for Aquitanian sand unitKv_Aqu_C 3.16 × 10−7 2.21 × 10−7 to 4.52 × 10−7 Vertical K for Aquitanian clay unit

vertical hydraulic conductivity for clay is, however, onlya factor of 17 lower than the horizontal conductivity ofsand. This indicates that the Quaternary units are relativelyheterogeneous. The estimated hydraulic conductivities forthe sandy Miocene units are in the order of 10−4 m/s. Thisis within the same range as the hydraulic conductivitiesfound by Sonnenborg et al. (2003) and it is thereforeassumed that the calibration result is acceptable. Still,the hydraulic conductivities of the clayey units are inthe high end of what is expected when dealing withthick marine deposits, for example, with a value of9.3 × 10−7 m/s for the Burdigalian clay unit. However, asdocumented by Scharling (2011), the hydrostratigraphicunits are heterogeneous, which affects the estimatedeffective hydraulic conductivity. The relatively highvalues of vertical hydraulic conductivity of Quaternaryclay and horizontal conductivity of the top Mioceneaquifer (Langhian sand) indicate that there is a highpotential for intrusion of modern water to the Mioceneformations.

The uncertainties on the estimated parameters,expressed through the 95% linear confidence interval (Hill1998), are generally low. The highest uncertainty is foundfor the vertical conductivity for the Burdigalian clay unit,where the confidence interval spans almost an order ofmagnitude. A test was done to examine if each of thesix Miocene units could be further subdivided accordingto the sequence stratigraphical model by Scharling et al.(2009). However, the resulting estimation uncertainty wasfound to be too high with coefficients of variation signif-icantly higher than one for most units (Scharling 2011).Hence, to minimize nonuniqueness the version with sixunits was preferred.

With respect to performance statistics, the ME wasfound to be −0.58 m while an RMS value of 4.71 m wascalculated for the model as a whole. Compared to therange in observed heads of approximately 100 m, the MEis found to be acceptable. In Figure 4, plots of observedvs. simulated head for the Quaternary, the Langhian,and the Burdigalian and Aquitanian units are presented.The data points fall relatively symmetrically around thesymmetry line indicating an acceptable calibration with

negligible bias. An exception is found for a relative smallgroup of observations from the Quaternary with highhydraulic heads that are underestimated by the model.Decreasing RMS values are found with depth belowsurface, with values of 4.88, 4.67, and 3.75 m for the threeunits referred above. This is partially explained by theintroduced weighing where measurements from the deeperaquifers are given higher weights than measurements frommore shallow screens, see Section “Calibration Data.”Additionally, the Quaternary sediments are dominated bymoraine deposits that are expected to exhibit a higherdegree of heterogeneity than the Miocene deposits, whichcould result in a higher RMS value. Calibration of anothersteady-state model within approximately the same areawas done by Sonnenborg et al. (2003) and it was estimatedthat the uncertainty of the head measurements expressedas standard deviation was in the range of 3 m. Consideringthe scale of model, the result is therefore satisfactorily.This is supported by an evaluation of the error distributionamong the different hydrogeological units (not shown)that displays a high degree of randomness in the locationof screens with positive and negative errors.

Sensitivity Analysis of the Transport ModelThe model is used to investigate the impact of alterna-

tive values of effective porosity, diffusion, and dispersioncoefficients on the simulated 39Ar concentrations alongtransects A and B. The following reference parame-ters were specified: αL = 5 m, αTH = 0.5 m, αTV = 0.05 m,ø s = 0.25, ø c = 0.25, Deff = 6.16 · 10−10 m2/s, where α

denotes dispersivity, and subscripts L, TH, and TV arethe longitudinal, transverse horizontal, and transverse ver-tical, respectively. ø is porosity and subscript s denotessand and c denotes clay. In Figure 5, ME and RMS valuesare presented to show the effect of changing αL from 0to 500 m and the impact of changing the effective poros-ity between 0.15 and 0.3 (same value for sand and clay).For αL values lower than 0.5 m, the effect on both MEand RMS is small. The reason for the lack of sensitiv-ity may be that numerical dispersion dominates for thegrid size used, as discussed by Sanford (2010). As αL

is increased beyond 0.5 m, ME approaches 0 while RMS


(a)

(c)

(b)

(d)

Figure 4. Plots for observed vs. simulated head for the Quaternary, Langhian, the Burdigalian, and Aquitanian aquifers.Also shown is observed vs. simulated river discharge (lower right).

decreases. The optimal αL seems to be a value of approx-imately 50 m where the minimum ME is found. If αL

is increased to 500 m, ME gets significantly worse whilethe RMS value is only affected moderately. The data pre-sented by Gelhar et al. (1992) show that αL in the orderof 10 to 100 m are found at transport distances of 103

to 104 m. Using the regression lines estimated by Xu andEckstein (1995), values for αL in the range of 12 to 31 mwere found at a transport distance of 103 m while valuesbetween 24 and 72 m were found for a distance of 104 m.Results from particle tracking revealed that the travel dis-tances to the 10 filters where 39Ar are measured generallyvary from 1 × 103 to 1.5 × 104 m. Hence, the αL foundhere complies well with observations from other sites.

The model shows a stronger sensitivity to theeffective porosity than to dispersion, see Figure 5(right panel). When the porosity is increased, the flowvelocity decreases resulting in longer travel times andtherefore higher degradation of 39Ar. Hence, the 39Arconcentrations decrease when the porosity is increased.The results show that an optimal ME is found at aneffective porosity value of 0.25 to 0.30. With respect toRMS, the minimum is located at an effective porosity of

0.25. Additional simulations were carried out to determinethe impact of using different clay and sand porosities. Theresults (not shown) demonstrate that the effective porosityof the sandy units is more important for the simulatedconcentrations than the value used for the clayey units.The optimal solution was found for effective porositiesof sand and clay of 0.3 and 0.2, respectively. In Table 2,the simulated 39Ar concentrations using the optimal flowand transport parameters are listed next to the observed(diffusion corrected) values. Considering the relativelyhigh uncertainty on the observed values, the simulatedresults are found to be acceptable for both transects.

Diffusion has very little effect on the modeled con-centrations (changing concentrations up to 0.3%), proba-bly a result of relatively high numerical dispersion. How-ever, diffusion is activated in the subsequent simulationsof direct mean ages.

ResultsIn the following, results on the flux and the mean age

of the water arriving at the boundaries to the Mioceneaquifers are presented. Additionally, the distribution of


(a) (b)

(c) (d)

Figure 5. Mean error (ME) and root mean squared (RMS) error between observed and simulated 39Ar concentration as afunction of longitudinal dispersivity (left) and porosity (right), respectively.

Table 2Observed vs. Simulated 39Ar Concentration at the10 Sampled Wells. Wells A, C, E, F, and J Belongto Transect A While Wells Q, R, S, T, and V Are

Located on Transect B

Well No.Screen

Depth (m)Observed 39Ar

(%)Simulated 39Ar

(%)

A 115 to 127 51 78C 104 to 115 89 73E 120 to 130 59 38F 103.5 to 104.5 58 48J 100 to 115 45 41Q 125.2 to 140.2 57 62R 121.5 to 127.5 85 70S 84 to 88 67 76T 75 to 87 45 70V 116.5 to 128.5 63 72

mean age in the two sampled cross sections (Figure 1) isillustrated.

Water Flux in Sand UnitsFigure 6 shows the vertical groundwater flux to

the top of the Burdigalian and Aquitanian sand units.Both positive (downward) and negative (upward) fluxesare present. The fluxes are highly controlled by therivers with upward fluxes below the rivers, whereas the

highest downward fluxes are found in between the rivers,especially in areas with the highest surface elevations atthe upstream parts of the catchment. In Figure 7, theflow vectors in an east-west cross section through thecentral part of the catchment display a complex patternof local flow from one river to the next and intermediateflow where major zones with primarily horizontal flowtakes place from east toward west within the Mioceneaquifers, which later discharges to a river. The overalldistribution of flow can be explained by the theory oflocal, intermediate, and regional flow systems (Toth 1963;Freeze and Witherspoon 1967). Flow within the catchmentseems to be dominated by local and intermediate flowsystems and not by regional flow as first anticipated. Thisis further supported by results from backward particletracking from the well screens to the groundwater table.In transect A, mean travel distances between 850 m and15 km are found with an average of 6.2 km. For transectB, mean travel distances between 750 m and 7.5 km areestimated with an average of 4 km. These travel distancesare considerably smaller than the distance to the rechargeareas near the Mid Jutland highs indicating that flow isnot characterized by regional flow systems.

Major geological features like Quaternary valleys thatpenetrate the Miocene units often result in an increaseddownward flux. Examples are encircled with black inFigures 6a, 6b, and 7. In a few and very local partsof these areas, the flux to the Burdigalian sand units iseven higher than the recharge to the groundwater table


(a) (b)

Figure 6. Vertical flux presented at (a) the top of Burdigalian aquifers and (b) the top of Aquitanian aquifers. (c) Flux vectorsat cross-section A-A´ in Figure 6a where the flux to the Burdigalian sands below the river is higher than recharge to thegroundwater table.

(encircled with broken lines, Figure 6a). It is seen as anarrow band right next to a river where the Quaternarypenetrates the Burdigalian sand units. A cross sectionthrough one of those areas is shown in Figure 6c. Thehigh flux is generated by focused flow from a larger areato a point beneath the river from where a strong upwardflux takes place. Generally, the Quaternary valleys havethe opposite effect toward the western part of the modelarea where the Miocene sand aquifers terminate. Here,groundwater discharges from the deep-seated aquifers tothe surface and rivers (Figure 7, toward west).

Figures 6 and 7 show that fluxes in general are highlyreduced with depth and toward west in the thick Mioceneclay units. The recharge to the Burdigalian sand units isin some areas close to 100% of the net recharge to thegroundwater table. At some locations the recharge to thedeep Aquitanian aquifer system is also high with valuesexceeding 50% of the net groundwater recharge; however,generally values between 50 to 100 mm/year are predicted.Hence, as extraction of a high fraction of the naturalrecharge may result in groundwater quality problems(Henriksen et al. 2008), the sustainable groundwater

resource is considerable smaller for the Aquitanian aquifercompared to the overlying Burdigalian aquifers.

General Age DistributionExisting conceptual geological models from this area

(e.g., Rasmussen and Dybkjær 2005; Scharling et al.2009) and similar aquifer systems in Jutland (Hinsby et al.2001) suggest that groundwater in the multiaquifer systemis increasingly older from east toward west because of thedistance from the topographic highs, where the top aquiferreaches the surface, and because the depth to all threemain aquifers increases toward west. It was therefore apriori assumed that the majority of the recharge of newgroundwater (age 0) to the aquifers occurs in the east witha clear age evolution from east to west.

Figure 8 shows the directly simulated mean age atthe top of the three aquifer systems. Notice that allthree aquifer systems are not present throughout thewhole catchment. The uppermost Miocene aquifer system,Langhian, is strongly eroded by Quaternary sediments andis therefore presented as the top of pre-Quaternary. Inall aquifers, the age is indeed found to increase from


Figure 7. An east-west cross section through the central part of the numerical model setup, see Figure 3. Flow vectors aredisplaying the direction of flow and the color of the vectors indicates the flux. The ellipse represents a Quaternary valley alsomarked on Figures 6a and 6b.

east to west. At the top of pre-Quaternary, the mean ageincreases from less than 50 years to approximately 100years. At the top of the middle aquifer (Burdigalian),the mean age increases from less than 50 years toapproximately 300 years, and at the top of the loweraquifer (Aquitanian) the mean age increases from around100 years to approximately 700 years. The distribution ofgroundwater age within the aquifers is, however, to a highdegree controlled by the fluxes to and between the aquifersthroughout the catchment as discussed in Section “WaterFlux in Sand Units.” The Skjern and Varde river systemshave a dramatic effect on the age distribution with mucholder groundwater mixing with younger groundwater inthe vicinity of the rivers because the governing flowsystems is regarded as local or intermediate types andnot regional (Toth 1963). Heterogeneity is also thoughtto play an important role in mixing of groundwater ofdifferent ages (Weissmann et al. 2002; Scharling 2011)but cannot be resolved at the level of the Miocenegeological units defined by the sequences stratigraphicanalysis. To compensate for the lack of heterogeneitywithin the units of the geological model, a relatively largelongitudinal dispersivity is used to ensure a relatively highdegree of mixing.

The directly simulated mean age is visualized alongtransects A and B in Figure 9. No clear age evolutionis observed from east to west in either transects. Rather,the simulation results show that the age distribution evenat great depth is to a large extent controlled by therivers because older groundwater discharges to the riversfrom great depths. Upwelling of old water also occursin depressions where rivers are not represented by thegroundwater model. This is a clear indication of theimportance of the topography in controlling groundwaterflow patterns even at depths exceeding 100 m as also

proposed by Toth (1963), Freeze and Witherspoon (1967)and recently by Jiang et al. (2012). This circulation patternis also found in Figure 7, as indicated by the flux vectors.The age distribution is, however, more complex thanwhat is predicted from a Toth basin as also demonstratedby Jiang et al. (2012), which is due to the irregulartopography and, in our case, the complex geologicalarchitecture and the fact that groundwater is allowed toflow in all three dimensions. From Figures 8 and 9, itcan be seen that the clay layers do not seem to have highconfining effects against recharge of young groundwaterto the Burdigalian and Aquitanian aquifers. This can beexplained by the large heterogeneity within the clayeyunits as documented by Scharling (2011) and capturedin the calibration of the hydraulic conductivities as well.The groundwater age generally increases toward west(Figure 8), but it should be noticed that the depth from thesoil surface to the pre-Quaternary surface and the Mioceneaquifers also increases toward west. The relatively shorttravel distance between the recharge areas and the screens,generally less than 10 km, suggests that the increase in ageto a large extent is controlled primarily by the depth tothe screen and to a lesser degree by an aging within theaquifer caused by horizontal flow from east toward west.

Assessment of VulnerabilityBased on Figure 8, the age of groundwater recharg-

ing the upper Miocene formations is generally so lowthat these aquifers must be considered as vulnerable tosurface contamination. The vulnerability of the primaryaquifers from Burdigalian is highly variable. In dischargeareas, primarily beneath the river valleys where ground-water discharges to the surface water bodies, relativelyold water representing low vulnerability is found. How-ever, in the upstream areas, especially in the northwestern


(a) (b)

(c)

Figure 8. Direct age of groundwater presented at the top of the pre-Quaternary (a) and the top of the Burdigalian (b) andAquitanian (c) aquifer systems. It should be noticed that different time scales are used in the three illustrations.

part, relatively young water is found and the Burdigalianaquifers may be vulnerable at these locations. Buried Qua-ternary valleys are shown to alter the flow paths furtherby enhancing downward or upward flow in the upstreamand downstream parts of the catchment, respectively. Thesignificance of these buried valleys on transporting pol-lution to deep-seated aquifers is demonstrated by theobservation of nitrate concentrations of 5.1 mg/L in wellN with a screen 128 to 134 m below surface (Schar-ling 2011). Higher ages and therefore lower vulnerabilityare found in the southwestern part of the area, however,the thickness of the sandy Miocene formations generally

decreases toward southwest (Figure 7) and the potentialfor groundwater extraction is therefore relatively low.Hence, the most optimal locations of groundwater extrac-tion with low vulnerability and high aquifer transmissivityare in the central parts of the catchment, close to the majorriver branches. With ages above 100 years, the Aquitanianaquifers are estimated to exhibit low vulnerability andwould be an attractive groundwater reservoir. However,as the natural recharge to this aquifer is relatively low,the quantity of water that can be abstracted sustainableis probably lower than from the Burdigalian formations.It should be noticed that the assessment of vulnerability


(a)

(b)

Figure 9. Directly simulated mean ages along (a) transect A and (b) transect B (see Figure 1 for location of transects).

carried out here is based on results on mean age. Basedon a moment analysis, Scharling (2011) demonstrateda significant spread on the mean age with coefficientsof variation of 0.29 and 0.36 for transects A and B,respectively, illustrating that water collected at the wellsrepresents a mixture of residence times with a wide rangeof ages. Hence, even though the mean age exceeds 100years the youngest waters may represent periods wheresignificant pollution with, for example, nitrate or pesti-cides took place at the ground surface after the SecondWorld War.

UncertaintiesThe results on flow patterns and groundwater ages

are affected by a number of uncertainties. The simulationof flow paths are expected to be particularly sensitive tothe conceptual geological model (Seifert et al. 2012). Thegeological model for the Miocene formations is based ona limited number of seismic lines and deep boreholes

(Scharling et al. 2009) and especially in data sparseareas the uncertainty on the local flow patterns can berelatively high. However, additional local information onthe geological architecture is not expected to change theobservations regarding local, intermediate, and regionalflow systems. Steady-state flow boundary conditions,including groundwater recharge and sea level during thetime required to reach a steady-state age distribution(∼2000 years) could be another factor with an impacton not just the overall flow regime, but also the agedistribution. According to Lambeck et al. (1990, 1998),the sea level in the North Sea has been relativelyconstant within this period and sea level changes aretherefore not expected to be a major uncertainty factor.Groundwater recharge to the model is estimated fromclimate data representing the period 1991 to 2010. Whiletemperature has been relatively constant in Denmarkduring late Holocene (Brown et al. 2011), significantchanges in precipitation might be expected both during the


period where historical data on precipitation are available(Karlsson et al. 2014) and preceding periods whererecords of periods with relative wet and dry signals havebeen reconstructed based on analysis of plant macrofossils(Barber et al. 2004). Such transient conditions mayenhance mixing and affect the age distributions in theaquifers, however, with more stable responses in thedeeper parts of the system (Gomez and Wilson 2013).Additionally, anthropogenic changes (land use, drainage,irrigation, etc.) may affect the magnitude and the spatialdistribution of groundwater recharge, which have beenshown to affect the mean age distribution in shallowand local flow systems (Gomez and Wilson 2013). Thesehistorical variations are unfortunately difficult to quantify.Parameter uncertainty could also play a significant roleboth on flow patterns and groundwater age. The flowpatterns are sensitive to, for example, the magnitudeof the hydraulic conductivity of the clay layers. Ifsignificant lower clay conductivities were used in themodel, the flow patterns would shift from local andintermediate to more regional systems. However, theparameter uncertainties obtained from the autocalibrationare relatively low, Table 1, implying that the resultingeffects of this uncertainty on flow and transport iscomparatively low. Despite the uncertainties listed here,the mean age simulations provide a valuable way ofassessing the vulnerability of deep-seated aquifers.

Summary and ConclusionsRegional flow and transport within large aquifers

systems in the Miocene succession, Jutland, Denmarkhave been investigated. Based on a regional-scalesequence stratigraphical interpretation of the geology,the architecture of the deep-seated sedimentary aquiferswas delineated. The resulting geological model wasshown to provide a credible basis for flow and transportsimulations, even though the defined geological unitsinclude a high degree of geological heterogeneity, whichwas not described explicitly by the model. During thecalibration process, it was necessary to merge units fromdifferent depositional environments such that each stage(Aquitanian, Burdigalian, and Langhian) was describedby only effective sand and clay hydraulic conductivities.As a result of the inherent heterogeneity not explicitlyresolved by the geological model, a relatively large macrodispersion was found, characterized by a longitudinaldispersivity of 50 m, in order to capture the mixingcaused by geological heterogeneity. However, theobserved hydraulic heads and groundwater ages at thewells sampled for 39Ar were both predicted satisfactorily.

Based on a combination of flow and direct agemodeling, valuable insight regarding groundwater agedistribution and the vulnerability of the aquifers has beenobtained. This study emphasizes also the advantages orpotential of isotope or environmental tracer methods fortesting and evaluation of numerical flow models. Theresults indicate that on a regional scale, deep-seatedaquifers like these are not protected from modern surface

water contamination even when they apparently areoverlain by thick clayey units. The flow pattern generallyfollow the theory of Toth (1963), where it was shownthat local and intermediate groundwater flow paths arecontrolled by rivers. Even at depth exceeding 100 m, thesurface topography and distribution of the river networkcontrols the groundwater flow paths where old wateris upwelling beneath rivers and young water infiltratesin between the rivers. The geological heterogeneity ondecameter and even 100-m scale is not resolved explicitlyby this regional model. However, relatively high valuesof effective vertical hydraulic conductivity of the clayformations are estimated that is shown to have significantregional impact on aquifer vulnerability even though it isoften neglected when vulnerability estimates are carriedout on regional scale. The model results can probablynot be used directly for local-scale studies but additionalinterpretation of the hydrostratigraphy is needed togetherwith recalibration of the hydraulic conductivities and arefinement of the numerical grid.

AcknowledgmentThe authors would like to acknowledge Geocenter

Denmark for funding the study. We also appreciate thecareful evaluation and constructive comments from threeanonymous reviewers.

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Aquifer Vulnerability Assessment Based on Sequence Stratigraphic and 39 Ar Transport Modeling

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