Journal of Contaminant Hydrology 149 (2013) 27–45

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Journal of Contaminant Hydrology

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Simulating variably-saturated reactive transport of seleniumand nitrogen in agricultural groundwater systems

Ryan T. Bailey a,⁎, Timothy K. Gates a, Ardell D. Halvorson b

a Department of Civil and Environmental Engineering, Colorado State University, 1372 Campus Delivery, Fort Collins, CO 80523-1372, United Statesb USDA-ARS, 2150 Centre Ave, Bldg. D, Ste 100, Fort Collins, CO 80526-8119, United States

a r t i c l e i n f o

⁎ Corresponding author. Tel.: +1 970 491 5387; faxE-mail addresses: rtbailey@engr.colostate.edu (R.T

tkg@engr.colostate.edu (T.K. Gates), ardell.halvorson@(A.D. Halvorson).

0169-7722/$ – see front matter © 2013 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.jconhyd.2013.03.001

a b s t r a c t

Article history:Received 17 September 2012Received in revised form 28 January 2013Accepted 6 March 2013Available online 13 March 2013

Selenium (Se) contamination in environmental systems has become a major issue in manyregions world-wide during the previous decades, with both elevated and deficient Seconcentrations in groundwater, surface water, soils and associated cultivated crops reported.To provide a tool that can assess baseline conditions and explore remediation strategies, thispaper presents a numerical model capable of simulating the reactive transport of Se species inlarge-scale variably-saturated groundwater systems influenced by agricultural practices.Developed by incorporating a Se reaction module into the multi-species, variably-saturatedreactive transport model UZF-RT3D, model features include near-surface Se cycling due toagricultural practices, oxidation–reduction reactions, and the inclusion of a nitrogen (N) cycleand reaction module due to the dependence of Se transformation and speciation on thepresence of nitrate (NO3). Although the primarymotivation is applying themodel to large-scalesystems, this paper presents applications to agricultural soil profile systems to corroborate thenear-surface module processes that are vital in estimating mass loadings to the saturated zonein large-scale fate and transport studies. The first application jointly tests the Se and Nmodulesfor corn test plots receiving varying loadings of fertilizer, whereas the second application teststhe N module for fertilized and unfertilized test plots. Results indicate that the model issuccessful in reproducing observedmeasurements of Se and NO3 concentrations, particularly inlower soil layers and hence in regards to leaching. For the first application, the EnsembleKalman Filter (EnKF) is used to condition model parameters, demonstrating the usefulness ofthe EnKF in real-world reactive transport systems.

© 2013 Elsevier B.V. All rights reserved.

Keywords:SeleniumSubsurface nutrient transportGroundwater modelingEnsemble Kalman Filter

1. Introduction

Selenium (Se) is an element that naturally occurs as a traceconstituent in geologic formations and associated soils, crops,and water bodies. Although an essential micro-nutrient forhumans and animals (Aro et al., 1998; Combs et al., 1986)elevated concentrations and bio-accumulation have provendetrimental to human and animal health (Aro et al., 1998;Flury et al., 1997; Schwarz and Foltz, 1957). The narrow range

: +1 970 491 7727.. Bailey),ars.usda.gov

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between dietary deficiency (b40 μg day−1) and toxic levels(>400 μg day−1) (Levander and Burk, 2006) for humans hasled to Se being termed the “double-edged sword element”(Fernández-Martínez and Charlet, 2009) and an “essentialtoxin” (Stolz et al., 2002).

During the last half-century, the presence of elevated Seconcentrations in groundwater, surface waters, and associatedcrops has emerged as a serious concern in the United States(Gates et al., 2009; Hudak, 2010; Seiler, 1995), the Middle East(Afzal et al., 2000; Kuisi and Abdel-Fattah, 2010), and East Asia(Mizutani et al., 2001; Zhang et al., 2008). Deformities anddeathamong water fowl and fish populations have been caused bytoxic concentrations of Se in surfacewaters fed by contaminatedaquifer systems (Flury et al., 1997; Hamilton, 1998; Skorupa,

28 R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

1998), with the specific negative biological effects includingnervous system defects, inhibition of tissue breathing, anddecrease in enzyme activity (Kishchak, 1998). In several regionsof the world, however, Se deficiency in soils and associatedcultivated crops has been reported to be linked with diseasesaffecting both animal (Aro et al., 1998; Kishchak, 1998) andhuman (Alfthan et al., 1995; Peng et al., 1995; Schwarz andFoltz, 1957; Wang and Gao, 2001) populations.

Regardless of the nature of concern regarding Se, there is abasic need for tools that allow the processes governing Se fateand transport in agricultural groundwater systems to besimulated in assessing baseline conditions and exploringremediation schemes. Due to the complex dynamics of Setransformation processes, the dependence of transformationprocesses on other chemical species such as dissolved oxygen(O2) and nitrate (NO3) (e.g., Weres et al., 1990; White et al.,1991) and the numerous time-dependent sources and sinks ofSe in an agricultural system, the use of numerical reactivetransportmodels is an appealing approach for the developmentof such tools. Numerical modeling studies involving Se fate andtransport thus far have been limited to one-dimensional (1D)soil profile models (Alemi et al., 1988, 1991; Fio et al., 1991;Guo et al., 1999; Liu and Narasimhan, 1994; Mirbagheri et al.,2008) and a small-scale two-dimensional (2D) vertical profilemodel (Tayfur et al., 2010). For the majority of the studies, Setransport in saturated or unsaturated conditions is subject tosorption processes, redox reactions, or both in a 1D soil columnin a laboratory setting, and forcing terms such as inflow rateand concentration of influent have been kept very basic. Nonehave taken into account the influence of other chemical species.

More recently, Mirbagheri et al. (2008) incorporated a morecomplete suite of the processes involving Se species in theunsaturated zone for a 1Dmodel, including advective–dispersivetransport, sorption, redox reactions, volatilization, mineraliza-tion and immobilization, and plant uptake of Se. In a similarstudy, Tayfur et al. (2010) employed a small-scale (3-m soilprofiles) 2D vertical cross-section finite element model tosimulate Se transport in both saturated and unsaturated soilzones, considering the same processes as Mirbagheri et al.(2008). For both studies, reactions were simulated using simplefirst-order kinetics, without taking into account the requirementof organic carbon (OC), the influence of other chemical species,and the redox reactions governing the release of Se frommarineshale. Furthermore, the cycling of Se through input of cropresidue and fertilizer and the general decomposition of organicSe in soil organic matter was not simulated.

The objective of this study is to present the developmentand application of a numerical reactive transportmodel capableof simulating the fate and transport of Se in multi-dimensionalvariably-saturated groundwater systems. The model is devel-oped by incorporating a Se cycling and reactionmodule into therecently-developed multi-species, reactive transport modelUZF-RT3D (Bailey et al., 2012c) that includes 1D downwardflow in the unsaturated zone and 3D flow in the saturated zone.The Se module includes all pertinent components for applica-tions to agricultural groundwater systems, including Se cycling,accompanying carbon (C) and nitrogen (N) cycling to includethe influence of OC and NO3, Monod and dual-Monodformulation of redox reactions, and system sources and sinkssuch as fertilizer, irrigation water, and canal seepage. C and Ncycling is adopted fromexisting simulationmodels (Birkinshaw

and Ewen, 2000; Gusman and Mariño, 1999; Johnsson et al.,1987), andMonod kinetics and the dependence of reactions onhigher-redox species are simulated as specified by publishedreactive transport groundwater models (Kindred and Celia,1989; Kinzelbach et al., 1991; Widdowson et al., 1988).

Although the intended use of themodel is for regional-scaleaquifer systems, which will be demonstrated in a forthcomingwork, the application of themodel in this study is limited to 1Dsoil systems to corroborate the cycling processes, redoxreactions, and system sources/sinks that have been includedin the model. Specifically, the model is tested against Se andNO3 concentrations along soil profiles, with soil samplescollected from multiple test plots at the Colorado StateUniversity Arkansas Valley Research Center (AVRC) in RockyFord, CO (southeastern Colorado), a problem area for Secontamination (Gates et al., 2009). Parameter estimation isaccomplished using the Ensemble Kalman Filter (EnKF)(Evensen, 1994), a Monte Carlo Bayesian-based data assimila-tionmethod that to date has been used only in synthetic aquifersettings to estimate reactive transport parameters in soil andgroundwater systems (Bailey and Baù, 2011; Bailey et al.,2012b). In addition, a time-series of observed NO3 concentra-tions in soil water underlying a cultivated field (Johnsson et al.,1987) is used to provide further testing of the N module, withresults shown in Supplementary Data.

2. Se fate and transport in agricultural groundwater systems

Se is present in nature primarily in the four oxidation statesof +VI (selenate SeO4

2−), +IV (selenite SeO32−), 0 (elemental

seleniumSe0), and−II (selenide Se2−). Selenide occurs inmanyforms, such as organic selenomethionine (−II) (SeMet), gaseousDimethylselenide (CH3)2Se (− II) (DMSe, a product of thevolatilization of SeMet), and solid Se found in geologicformations in the form of seleno-pyrite (−II) (FeSexS2 − x), inwhich Se substitutes for S in pyrite (FeS2) (Bye and Lund, 1982)or as other Se-bearing species (Ryser et al., 2005). Soluble speciesof Se include SeO4, a weak sorbent (Ahlrichs and Hossner, 1987)andone of themost toxic of the Se species; SeO3, a strong sorbent(Balistrieri and Chao, 1987); and SeMet; whereas Se0 and otherforms of Se2− are insoluble and hence immobile unlesssuspended. In oxygenated agricultural waters, SeO4 has beenreported to account for 90% to 95% of soluble Se (Gates et al.,2009; Gerla et al., 2011; Masscheleyn et al., 1989) and henceis the principal target in Se contamination remediation.

Se, as a trace constituent in all igneous rocks, is present inall soils (Byers, 1937), particularly in irrigated agriculturalaquifer systems underlain by or adjacent to shale formationscontaining seleno-pyrite (Gates et al., 2009; Seiler, 1995,1997)wherein SeO4 can be released via autotrophic reductionof O2 or NO3 (Stillings and Amacher, 2010; Wright, 1999):

2FeSexS2−x þ 7O2 þ 2H2O→2Fe2þ þ 2xSeO2−4 þ 4−2xð ÞSO2−

4 þ 4Hþ ð1aÞ

5FeSexS2−x þ 14NO−3 þ 4Hþ→5Fe2þ þ 5xSeO2−

4 þ 10−5xð ÞSO2−4 þ 7N2 þ 2H2O:

ð1bÞReleased SeO4 then can be transported through aquifer

systems to either shallow soil zones or surface water dischargepoints, with transport tempered by possible sorption andchemical reduction processes that lead to immobilized and/or

29R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

precipitated forms of Se. These processes, however, are inhibitedby the presence of oxygenated groundwater species such asdissolved oxygen (O2) and nitrate (NO3) (Oremland et al., 1989;Weres et al., 1990; White et al., 1991; Zhang and Moore, 1997).Once accumulated in the shallow soil and root zone inagricultural regions, due to either transport through theaquifer or deposited within irrigation water, Se is subject tocycling in the plant–soil system similar to other nutrients suchas nitrogen (N), phosphorus (P), and sulfur (S) (Shrift, 1954;Stolz et al., 2002).

Microbially-mediated (Oremland et al., 1990) chemicalreduction reactions reduce SeO4 to SeO3 (Eq. (2a)) and SeO3

to either immobile Se0 (Eq. (2b)) ormobile SeMet (see Ellis andSalt (2003) for detailed description):

CH2Oþ 2SeO2−4 →CO2 þ 2SeO2−

3 þH2O ð2aÞ

CH2Oþ SeO2−3 þ 2Hþ→CO2 þ Se0 þ 2H2O ð2bÞ

where CH2O represents a generic OC compound. SeMet canthen be volatilized to non-toxic DMSe (Calderone et al., 1990;Frankenberger and Arshad, 2001). The system requirements forSe reduction to proceed include (i) the presence of microbialpopulations possessing the appropriate metabolic capacity, (ii)the presence of e− donors such as OC, and (iii) the restrictedavailability of O2 and NO3 due to the succession of terminal e−

-acceptor processes. Possible mitigation pathways of SeO4

remediation, all of which include reduction to SeO3, Se0, orSeMet, are inhibited by the presence of O2 and NO3. However,Oremland et al. (1990), Gates et al. (2009), and Bailey et al.(2012a) each suggested a concentration of NO3 at which NO3

reduction and SeO4 reduction can occur simultaneously.Similar to other nutrients, Se is taken up by crop rooting

systems (e.g., Ajwa et al., 1998; Bisbjerg and Gissel-Nielsen,1969; Johnsson, 1991; Logan et al., 1987), distributed throughout

Fig. 1. Conceptual model of fate and transport of selenium, organic carbon, and nitrand groundwater system. Species' mass enters the system via fertilizer, irrigation winclude organic matter decomposition, mineralization/immobilization, heterotroph

the plant structure, and then deposited back to the soil eitherthrough decaying root mass or above-ground crop material(i.e., stover) not removed at harvest. The decaying crop mass,as a part of the soil organic matter pool, can be mineralized toinorganic species of Se (i.e., SeO4 or SeO3) (Bañuelos andMeek,1990; Bujdos et al., 2000; Dhillon et al., 2007; Stavridou et al.,2011), which then are either sorbed, chemically reduced,leached through the soil profile, or taken up by the crop duringthe next growing season. Immobilization, whereby themicrobesconvert inorganic Se to organic Se to satisfy cellular Se re-quirements, has also been reported (Ajwa et al., 1998). SeO4 andSeO3 are the predominant species taken up by crops, althoughSeMet also can be used by crops (Abrams et al., 1990; Sager,2006;Williams andMayland, 1992). In general, SeO4 is taken upat higher rates than SeO3 (Sors et al., 2005), with Bisbjerg andGissel-Nielsen (1969) and Sager (2006), respectively, reportingthat SeO4 is taken up from soil by plants up to 8 and 10 timesmore effectively than SeO3. Overall, the rate of Se uptake isaffected principally by concentration of Se in the soil water (Wanet al., 1988).

Including appropriate system sources and sinks, the concep-tualmodel of Se fate and transport in an irrigated agricultural soiland groundwater system is presented in Fig. 1. All redoxreactions as discussed previously in this section are shown,including the following reactions that describe the chemicalreduction of O2 and NO3:

CH2Oþ O2→CO2 þH2O ð3aÞ

3CH2Oþ 2NO3→3CO2 þ 3H2Oþ N2: ð3bÞ

Nitrification and volatilization of ammonium (NH4) alsoare included. Cycling of C, N, and Se are based on conceptualmodels of C and N cycling as presented by Johnsson et al.(1987) and Birkinshaw and Ewen (2000). For C, N, and Se, the

ogen solid-phase and dissolved-phase species in an irrigated agricultural soilater, and aquifer-stream exchange (e.g., canal seepage). Chemical reactionsic and autotrophic chemical reduction, volatilization, and sorption.

30 R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

model includes three immobile, solid-phase species thatcontribute to the composition of soil organic matter [litter L(fast-decomposing), humus H (slow-decomposing), manureM], with C species included due to the dependence of N masstransfer on C mass transfer, with the dependence governed byC/N ratios of soil organic matter and microbial populations. Atharvest the dead root mass is incorporated into the litter pool,and at plowing the remaining rootmass and after-harvest stoveris incorporated into the litter pool, uponwhich decomposition ofthe organic matter occurs with associated production of CO2

used as an indicator of the availability of OC as e− donors forredox reactions to proceed. Mineralization of organic matterto inorganic species and immobilization of inorganic speciesto organic matter also occurs.

The conceptual model also includes six mobile, dissolved-phase species: O2, NH4-N, NO3-N, SeO4-Se, SeO3-Se, and SeMet,of which NH4, SeO4, and SeO3 can sorb. For simplicity ofnotation, NH4-N, NO3-N, SeO4-Se, SeO3-Se will be written asNH4, NO3, SeO4, and SeO3 throughout the remainder of thispaper. Redox reactions are dependent on species concentration,concentration of e− donors, soil temperature, soil moisture, andpresence of higher-redox species. Uptake of the mobile speciesoccurs throughout the growing season. System sources includeSe and N in root and stover mass (which are dependent onthe amount taken up during the previous growing season),fertilizer, irrigation water, precipitation, and canal seepage, andSe in the aquifer solids. Species mass reaching the base of theroot zone undergoes leaching through the underlying soilprofile, and upon reaching the water table is transportedthrough the aquifer via advection and further influenced bysorption and redox reactions.

3. Model development

3.1. Multi-species reactive transport in variably-saturated flowsystems

The base reactive transport model for the Se and Nmodulesis UZF-RT3D (Bailey et al., 2012c), which was developed bylinking a version of RT3D (Clement, 1997; Clement et al., 1998),modified to handle variably-saturated transport, with theUnsaturated-Zone Flow (UZF1) package (Niswonger et al.,2006) developed for MODFLOW-NWT (Niswonger et al., 2011),a Newton formulation for MODFLOW-2005 (Harbaugh, 2005).UZF1 assumes vertical heterogeneity of the unsaturated zoneand neglects the diffusive term in the Richards equation, hencerequiring less computational effort than models that solve thefull Richards equation and providing an attractive approach tosimulating variably-saturated flow and transport in large-scaleaquifer systems. Using 1D downward flow in the unsaturatedzone, 3D flow in the saturated zone, and flow sources and sinksprovided by MODFLOW-UZF1, UZF-RT3D solves the followingsystem of advection–dispersion–reaction (ADR) equations fordissolved-phase and solid-phase species using the operator-splitstrategy (Bailey et al., 2012c; Clement, 1997; Yeh and Tripathi,1989):

∂ Ckθð Þ∂t Rk ¼ − ∂

∂xiθviCkð Þ þ ∂

∂xiθDij

∂Ck

∂xj

!þ qf Cf k

þ θrf k ¼ 1;2;…;m ð4aÞ

∂ Clεð Þ∂t ¼ αlPs þ εrs l ¼ 1;2;…;n ð4bÞ

where m and n are the total number of dissolved-phase andsolid-phase species, respectively; Ck and Cl are the concentrationof the kth dissolved-phase species [MfLf−3] and lth solid-phasespecies [MsLs−3], respectively, where f denotes the fluid phaseand s denotes the solid phase; and is equal to 1−ϕ; Dij is thehydrodynamic dispersion coefficient [L2T−1]; v is the porevelocity [LbT−1] provided by MODFLOW-UZF1 with b denotingthe bulk phase; ϕ is the soil porosity [Lf3Lb−3] θ is thevolumetric water content [Lf3Lb−3]; ε is the volumetric solidcontent [Ls3Lb−3] qf is the volumetric flux ofwater representingsources and sinks [Lf3T−1Lb−3]; Cf k

is the concentration of thesource or sink for the kth dissolved-phase species [MfLf−3]; Psrepresents the mass application rate of all solid-phase massinputs for the lth solid-phase species [MsLb−3] with αl thefraction of Ps attributed to species l [−]; rf and rs represent therate of all reactions that occur in the dissolved-phase andsolid-phase for the kth species [MfLf3T−1] and lth species[MsLs3T−1]; and Rk is the retardation factor for the kthdissolved-phase species, equal to 1 + (ρb Kdk

)/θ, where ρb isthe bulk density of the porous media [MbLb−3] and Kdk is thepartitioning coefficient for the kth species [Lf−3Mb].

3.2. Selenium and nitrogen modules

Using the form of the ADR equation in Eq. (4a) and theconceptual model in Fig. 1, the following equations are writtenfor the Se dissolved-phase species:

∂ CSeO4θ

� �∂t RSeO4

¼ − ∂∂xi

θviCSeO4

� �þ ∂∂xi

θDij

∂CSeO4

∂xj

!þ qf Cf SeO4

þ FSeO4−USeO4

þ ε rmins;Se−rimm

s;Se

� �þ θ rautof ;SeO4

−rhetf ;SeO4

� � ð5aÞ

∂ CSeO3θ

� �∂t RSeO3

¼ − ∂∂xi

θviCSeO3

� �þ ∂∂xi

θDij

∂CSeO3

∂xj

!þ qf Cf SeO3

þ FSeO3−USeO3

þ θ rhetf ;SeO4−rhet Sesð Þ

f ;SeO3−rhet SeMetð Þ

f ;SeO3

� �ð5bÞ

∂ CSeMetθð Þ∂t ¼ − ∂

∂xiθviCSeMetð Þ þ ∂

∂xiθDij

∂CSeMet

∂xj

!þ qf Cf SeMet

−USeMet

þ θ rhet SeMetð Þf ;SeO3

−rhetf ;SeMet

� �ð5cÞ

where the volumetric flow rate for each of the MODFLOW-UZF1sources/sinks (e.g., aquifer-stream exchange, pumping, infiltrat-ing water at the ground surface) and the accompanying speciesconcentration for each of the sources/sinks are contained inthe terms qf and Cf, respectively; F is the inorganic fertilizerapplication [MfLb3T−1]; U is the potential uptake rate [MfLb3T−1];min and imm signify mineralization and immobilization, respec-tively; and auto and het represent autotrophic and heterotrophicchemical reduction, respectively. A glossary for all modelparameters is included at the end of the paper for ease ofreference. Mathematical expressions for terms are presented inSection 3.3. Similar equations are written for NH4, NO3, and O2:

∂ CNH4θ

� �∂t RNH4

¼ − ∂∂xi

θviCNH4

� �þ ∂∂xi

θDij

∂CNH4

∂xj

!þ qf Cf NH4

þ FNH4−UNH4

þ ε rmins;N −rimm

s;N

� �þ θ −rnitf −rvolf

� � ð6aÞ

31R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

∂ CNO3θ

� �∂t ¼ − ∂

∂xiθviCNO3

� �þ ∂∂xi

θDij

∂CNO3

∂xj

!þ qf Cf NO3

þ FNO3−UNO3

þ θ rnitf −rhetf ;NO3−rautof ;NO3

� � ð6bÞ

∂ CO2θ

� �∂t ¼ − ∂

∂xiθviCO2

� �þ ∂∂xi

θDij

∂CO2

∂xj

!þ qf Cf O2

þ θ −rhetf ;O2−rautof ;O2

� �: ð7Þ

Following the pattern established for C and N cycling in soilsystems (e.g., Birkinshaw and Ewen, 2000), the followingequations are written in the form of Eq. (4b) for the Se solid-phase LSe, HSe, and MSe, with similar equations (not shown)implemented for C and N cycling:

∂ CLSeε

� �∂t ¼ αRt;SePRt þ αSt;SePSt þ ε rdecs;Se H→Lð Þ þ rdecs;Se M→Lð Þ þ rdecs;Se L→Lð Þ−rdecs;Se Lð Þ

� �

þ ε rimms;Se Lð Þ−rmin

s;Se Lð Þ� � ð8aÞ

∂ CHSeε

� �∂t ¼ ε rdecs;Se L→Hð Þ−rdecs;Se Hð Þ

� �þ ε rimm

s;Se Hð Þ−rmins;Se Hð Þ

� �ð8bÞ

∂ CMSeε

� �∂t ¼ MSe−εrdecs;Se Mð Þ þ rimm

s;Se Mð Þ−rmins;Se Mð Þ

� �ð8cÞ

where PRt and PSt are the application rates of root and after-harvest stover mass, respectively; αRt,Se and αSt,Se are theportions of the root and stover mass attributed to Se; decsignifies organic matter decomposition; and L, H, and Mrepresent the litter, humus, and manure pool, with the arrowrepresenting the direction of mass flow.

3.3. Definition of mass-balance terms

3.3.1. Selenium and nitrogen sources and sinksAdditions of Se and N mass include inorganic fertilizer

application F, organic fertilizer (manure) application M, incor-poration of root mass PRt into the litter pool at harvest andplowing events, and incorporation of stover mass PSt into thelitter pool (within the specified plowing depth dpw) at plowingevents at the end of the growing season. Se and N mass alsoenter/leave the system via infiltrating water, aquifer-streamexchange, groundwater pumping, and drainage. Fertilizerloadings are applied to the top soil layers and can be splitbetween application times. As with other N cycling models(Gusman and Mariño, 1999; Hansen et al., 1995; Shaffer et al.,1991), urea [CO(NH2)2] applied as N fertilizer is assumed tohydrolyze to NH4 instantaneously. For perennial crops, thenumber of years of application during the perennial cycle isspecified. For incorporation of dead rootmass, the fraction of liveroots at harvest (i.e., the fraction that is incorporated at plowing)is specified.

As the rate of Se uptake is affected principally by concentra-tion of Se in the soilwater (Wanet al., 1988), it is simulatedusingfirst-order kinetics:

USeO4¼ λup;SeCSeO4

USeO3¼ λup;Se

γupCSeO3

USeMet ¼ λup;SeCSeMet

ð9Þ

where λup,Se is the Se uptake first-order rate constant [T−1] andγup is the SeO4–SeO3 uptake ratio and signifies the effectivenessof the crop to take up SeO4 as opposed to SeO3 [−]. For N, dailyuptake is calculated using a logistic equation (Johnsson et al.,1987) that accounts for the relative rate of uptake during stagesof the growing season, with the daily uptake divided betweenNH4 and NO3 according to the relative concentration of each.

For both Se andN, the calculated rate of uptake is distributedacross a profile of grid cells according to the depth and massdistribution of the root system using the depth–distributionfunction of Neitsch et al. (2005), with the time-dependentrooting depth calculated using a logistic equation similar to theone used in calculating daily N uptake. Maximum seasonaluptake values Seup andNup [MLb−2] are specified, with seasonaldeficits tracked and subtracted from the amount of Se and Nplaced back into the soil through root and stover material inorder to maintain mass balance (Wriedt and Rode, 2006). Foreach crop type included, the planting day, harvest day, plowingday, fertilizer loading and timing, potential seasonal uptake,maximum rooting depth drt,max [L], mass of roots and stover,and constants defining the root growth and daily uptake rateare specified. For perennial crops, incorporation of root andstover mass occurs only at the end of the perennial cycle.

3.3.2. Selenium and nitrogen transformation processesRates of decomposition, mineralization, immobilization, and

redox reactions are tempered according to soil moisture and soiltemperature (T) through the inclusion of an environmentalreduction factor E [−] that has the form E = Eθ ET, where Eθ andET are the normalized microbial activities [−] as a function of θand soil temperature (T), respectively. Values of Eθ for nitrifica-tion, mineralization, and denitrification for varying degrees ofsaturation are based on the work of Brady and Weil (1996) andthe values found in Birkinshaw and Ewen (2000). For all otherreactions the Eθ values for nitrification are adopted, which aresimilar to those in Birkinshaw and Ewen (2000) for genericreactions. Values of ET at a given depth z below the groundsurface are calculated as (Johnsson et al., 1987):

ET zð Þ ¼ Q10ð ÞTZ−TBð Þ

10 ð10Þ

where Tz [°C] is the soil T at a depth z below the groundsurface, Q10 [−] is the factor change in rate for a 10-degreechange in soil T, and TB [°C] is the base soil T at which ET = 1,and hence has no effect on the reaction rates. Values of Tz arecalculated using the approach of Wriedt and Rode (2006)where Tz in the top (0–50 cm depth), middle (50–250 cmdepth), and deep soil layers (below250 cmdepth) is influencedby damped daily air temperatures (average of preceding3 days), damped annual cycle (average of preceding 60 days),and the mean annual temperature (average of preceding365 days), respectively.

Mathematical expressions for organic matter decompo-sition reactions can be written using first-order kinetics(Birkinshaw and Ewen, 2000; van Veen and Paul, 1981).Such expressions for decomposition of LC, HC, MC, LN, HN, andMN are contained elsewhere (e.g., Birkinshaw and Ewen, 2000),and only expressions for LSe,HSe,MSewill be presented.Microbialpopulations are assumed to reside only in the litter pool

Table 1Summary of 9 irrigation events during the 2009 growing season for the corn testplots, showing the infiltrated depths (0.089 m for all events), and concentrationof SeO4, NH4, NO3, and O2 in the irrigation water.

Irrigation event Date CSeO4a

μg mf−3

CNH4

g mf−3

CNO3

g mf−3

CO2a

g mf−3

1 6/17/2009 8.10 0.098 1.31 8.742 6/23/2009 8.10 0.065 0.94 8.743 6/29/2009 8.10 0.052 1.00 8.744 7/04/2009 8.10 0.063 1.14 8.745 7/10/2009 7.31 0.072 1.18 7.566 7/17/2009 7.31 0.060 1.50 7.567 7/20/2009 7.31 0.039 1.34 7.568 7/31/2009 7.31 0.075 1.61 7.569 8/10/2009 7.31 0.065 1.61 7.56Applied (m) 0.094TW fraction 0.05Infiltrated (m) 0.089

a Sampled from nearby Rocky Ford Canal.

32 R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

(Johnsson et al., 1987). A final assumption is that decomposedmass is transferred via three pathways: to the pool of destination,to the microbial mass within the litter pool, and to CO2 thatis used for microbial energy. Rate expressions defining thedecomposition of LSe, HSe, MSe and inter-pool mass transfersare:

rdecs;Se Hð Þ ¼ λHCHSeE

rdecs;Se H→Lð Þ ¼ λH CHSe=HC=Se

� �f eE

rdecs;Se Mð Þ ¼ λMCMSeE

rdecs;Se M→Lð Þ ¼ λM CMSe=BC=Se

� �E

rdecs;Se Lð Þ ¼ λLCLSeE

rdecs;Se L→Hð Þ ¼ λL CLSe=BC=Se

� �f ef hE

rdecs;Se L→Lð Þ ¼ λL CLSe=BC=Se

� �f e 1−f hð ÞE

ð11Þ

where λL, λH, λM are the first-order rate constants for litter,humus, and manure decomposition [T−1], respectively; fe isthe synthesis efficiency constant (Johnsson et al., 1987) anddefines the fraction of decomposed mass that reaches thedestination pool [−], or in other words the fraction (1−fe)converted to CO2; fh is the humification factor [−] andrepresents the portion of decomposed mass transferred tothe humus pool, and HC/Se and BC/Se are humus andmicrobialpopulation C/Se ratios, similar to the C/N ratios used inBirkinshaw and Ewen (2000). The process of LSe decomposi-tion includes an internal cycle, since Se incorporated intomicrobial biomass stays in LSe under the assumption thatmicrobes reside only in LSe.

Decomposed Se mass is transferred to HSe, LSe throughincorporation of microbial biomass, or, if there is any remaining,to SeO4 through mineralization. However, if the requirement ofSe for microbial growth is not satisfied through the decompo-sition of available organic Se, than SeO4 mass is immobilized toorganic Se. The difference between the total Se mass transferred

and the Semass incorporated intoHSe and themicrobial biomassdefine mineralization and immobilization, with these processesoccurring if the amount is positive and negative, respectively:

λLE CLSe−

CLSe f ef hHC=Se

−CLSe f eBC=Se

!(> 0 ¼ rmin

s;Se Lð Þb 0 ¼ rimm

s;Se Lð Þ

λME 1− f eBC=Se

!(> 0 ¼ rmin

s;Se Mð Þb 0 ¼ rimm

s;Se Mð Þ

λHCHSeE

1HC=Se

− f eBC=Se

!> 0 ¼ rmin

s;Se Hð Þb 0 ¼ rimm

s;Se Hð Þ:

(ð12Þ

Similar equations are included for N (Birkinshaw and Ewen,2000).

The rate law expressions for heterotrophic reduction of O2,NO3, SeO4, SeO3, and SeMet using Monod terms are written as:

rhetf ;O2¼ λhet

O2CO2

CO2

KO2þ CO2

!CO2;prod

KCO2þ CO2;prod

!E ð13aÞ

rhetf ;NO3¼ λhet

NO3CNO3

CNO3

KNO3þ CNO3

!CO2;prod

KCO2þ CO2;prod

!IO2

IO2þ CO2

!E ð13bÞ

rhetf ;SeO4¼ λhet

SeO4CSeO4

CO2;prod

KCO2þ CO2;prod

!IO2

IO2þ CO2

!INO3

INO3þ CNO3

!E ð13cÞ

rhet Sesð Þf ;SeO3

¼ λhet Sesð ÞSeO3

CSeO3

CO2;prod

KCO2þ CO2;prod

!IO2

IO2þ CO2

!INO3

INO3þ CNO3

!E ð13dÞ

rhet SeMetð Þf ;SeO3

¼ λhet SeMetð ÞSeO3

CSeO3

CO2;prod

KCO2þ CO2;prod

!IO2

IO2þ CO2

!INO3

INO3þ CNO3

!E

ð13eÞrhetf ;SeMet ¼ λhet

SeMetCSeMetCO2;prod

KCO2þ CO2;prod

!IO2

IO2þ CO2

!INO3

INO3þ CNO3

!E ð13fÞ

where Kj is the Monod half-saturation constant for species j[MfLf−3]; IO2

and INO3are the O2 and NO3 inhibition constants

[MfLf−3] signifying the species concentration at which lower-redox species can undergo appreciable rates of reduction; andCO2,prod is the total amount of CO2 produced during decompo-sition of LC,HC,MC and is used as an indicator of available OC formicrobial consumption (Birkinshaw and Ewen, 2000). It iscalculated as:

CO2;prod ¼ λLCLC1−f eð Þ þ λHCHC

1−f eð Þ þ λMCMC1−f eð Þ

h iE:

ð14Þ

Assuming that FeS2 is in limitless supply in any adjacent shalematerial, the rate law expressions for autotrophic reduction of O2

and NO3 are:

rautof ;O2¼ λauto

O2CO2

CO2

KO2þ CO2

!ð15aÞ

rautof ;NO3¼ λauto

NO3CNO3

CNO3

KNO3þ CNO3

!IO2

IO2þ CO2

!: ð15bÞ

The mass of Se released during these two reactions isdependent on the portion of autotrophically-reducedO2 or NO3

Table 2Agricultural management, crop, and chemical reaction parameter symbols,units, and values for the model application. For parameters that are perturbedduring the predicted ensemble simulations, the coefficient of variation (CV)value also is shown.

Parameter Units Mean value(predicted Ensemble)

CV

Agricultural management & parametersPlanting day – 27-Apr –

Harvest day – 10-Oct –

Plowing day – 7-Nov –

dpw m 1.0 0.2FNH4 kg ha−1 56.2/280.8a –

FNO3 kg ha−1 0 –

PRt kg ha−1 500 0.2αRt,Se – 2.2 × 10−6 0.2αRt,N – 0.016 –

PSt kg ha−1 5616 0.2αSt,Se – 1.3 × 10−6 0.2αSt,N – 0.008 –

Crop parametersSeup g ha−1 10.8 0.1Nup kg ha−1 225 0.2λup,Se d−1 0.01 0.1γup – 10 –

drt,max m 1.22 0.2

Chemical reaction parametersGeneralQ10 – 2.5 –

TB0C 20.0 –

Kd;NH4 – 7.0 0.2

Organic matter decompositionλH d−1 0.003 0.5λL d−1 0.25 0.5fe – 0.5fh – 0.2HC/Se – 1.23 × 105

BC/Se – 1.75 × 105

HC/N – 12BC/N – 8

Oxidation–reductionλhetSeO4

d−1 0.04 0.5λhet Sesð ÞSeO3

d−1 0.08 0.5λhet SeMetð ÞSeO3

d−1 0.08 0.5λSeMethet d−1 0.02 –

ξ – 3000 –

λnit d−1 0.2 0.5λvol d−1 0.1 –

λhetNO3

d−1 0.3 0.5KNO3 g mf

−3 10 –

INO3 g mf−3 0.5 –

λhetO2

d−1 5.0 0.2IO2 g mf

−3 1.0 –

KO2 g mf−3 1.0 –

KCO2 g mf−3 0.75 –

a Treatment N1 = 56.2, Treatment N2 = 280.8.

Fig. 2. Measured daily precipitation, daily corn crop coefficients, and calculateddaily evapotranspiration (using the American Society of Civil Engineersstandardized reference evapotranspiration equation) using alfalfa as a referencecrop and the corn crop coefficients.

33R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

that contributes to the production of SeO4, and is dependent onthe stoichiometry of Eq. (1a) and the ratio of S to Se in the shalematerial:

rautof ;SeO4¼ rautof ;O2

1ξ

� �YSe:O2

þ rautof ;NO3

1ξ

� �YSe:NO3

ð16Þ

where YSe:O2is the mass of Se produced for O2 consumed in

Eq. (1a),YSe:NO3is themass of Se produced for NO3 consumed in

Eq. (1b), and ξ is the ratio of S to Se in the shale material. Thislast term is included since autotrophic reduction of O2 and NO3

release both S and Se from shale. Referring to Eq. (1a), YSe:O2is

equal to 1.41 (315.84 g/224.0 g) and YSe:NO3is equal to 4.03

(789.6 g/196.0 g).

3.4. Parameter estimation and model evaluation

Parameter estimation for the 1D soil profile system isaccomplished using the EnKF methodology, which uses a set(i.e., ensemble) of Monte Carlo simulations and the EnKFstatistical update routine to provide improved estimates ofparameter values. An initial ensemble of Monte Carlo simula-tions is used to define the prior probability density function(pdf) and to establish statistical correlations between param-eters and model-simulated variables; whereupon observedvariables from the actual system are assimilated into theensemble results within the EnKF update routine and usedto provide a posterior pdf of the system and to condition(i.e., correct) the parameter values. The conditioned param-eter values are then used to re-run the ensemble of MonteCarlo simulations, with simulation results expected to providea better match with the observed data values. The termspredicted and corrected are used commonly to represent thepre-conditioning and post-conditioning simulation ensemblesfor data assimilation studies, and are retained in this paper.

The predicted ensemble of simulations, in which initialconditions, forcing terms, and parameters are stochasticallyvaried using the best available data, establishes the system stateXtp [n × nmc] at a given time t, where p indicates predicted, n is

the number of computational points (e.g., grid cells), and nmc isthe number of realizations, or simulations, in the ensemble. Inthe correction step, m field-observed values from the truesystem are assimilated into Xt

p to obtain the corrected systemstate Xt

c via the following update algorithm:

Xct ¼ Xp

t þPptH

T

HPptH

T þ RtDt−HXp

t

� � ð17Þ

where Dt [m × nmc] holds the measurement data, with databeing perturbed if incorporation of measurement error isdesired; H [m × n] contains binary constants (0 or 1) resulting

Fig. 3. Seasonal variation of (A) carbon litter LC concentration, (B) nitrogen litter LN concentration, and (C) selenium litter LSe concentration during 10-yearspin-up period for the top five layers in the model grid, demonstrating the achievement of steady seasonal variations.

34 R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

Fig. 4. Daily mass transfer of selected mass-balance terms for (A) selenium and (B) nitrogen. Mass balance terms for selenium are shown in μg, whereas those fornitrogen are shown in g. For selenium, the process of root uptake is the dominant process of mass transfer, where nitrification is the dominant process for nitrogen.

35R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

in the matrix product HXtp holding model results at measure-

ment locations; and Ptp [n × n] andRt [m × m] are the prediction

error covariance and measurement error covariance matrices,respectively. Correction to the predicted values are governed bythe residual between themodel values andmeasurement data aswell as the relative error associated with each, contained in Pt

fc

and Rt. Any information from the model system (e.g., parame-ters, forcing terms) can be included in Xt

p, and if significantcorrelation exists with the measurement data, can be condi-tioned to reflect a system that produces the measurement data(Bailey and Baù, 2011). In the present study, observed CSeO4

and

CNO3in soil profiles are used to condition system parameters and

forcing terms in the model.Simulation results are evaluated using the mean absolute

error (MAE) and coefficient of efficiency (CE) “goodness-of-fit”measures, which are defined as:

MAE ¼ N−1XNi¼1

Oi−Pij j CEj ¼ 1:0−

XNi¼1

Oi−Pij jj

XNi¼1

Oi−O�� ��j ð18Þ

Fig. 5. Plot of theCNO3 vs.CSeO4 relationship for (A) layer 4 and (B) layer 7 in themodel grid.

Fig. 6. Simulated fluctuation of species concentration in the top layer of the soil profile fopredicted ensemble of CSeO4 , and (D) the corrected ensemble of CSeO4 . The corrected enscheme. For each plot the member simulations of the ensemble are depicted by lightsampling (October 19, 2009) is indicated on each plot, and corresponds to the soil profileshown on the sampling day with circle points.

36 R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

where N is the number of observation points, O and P are theobserved and predicted values, respectively, the overbar de-notes the mean, and j denotes an arbitrary power (e.g., 1 or 2).Whereas MAE describes the difference between the observedand predicted values in the units of the variable, CE describesthe relative magnitude of the variance of the residualscompared to the variance of the measured data (Nash andSutcliffe, 1970), i.e., how well a plot of simulated vs. observeddata fits the 1:1 line. CE ranges between −∞ and 1.0, with 1.0being the optimal value and 0.0 indicating that the model is asgood a predictor as the observed mean (Legates and McCabe,1999). Generally, values between approximately 0.0 and 1.0 areviewed as acceptable values (Moriasi et al., 2007). The CE1measure, which uses absolute values and hence is not inflated bysquared values, has been recommended for hydrologic modelevaluations (Legates and McCabe, 1999), and is used in thisstudy. As correlation-based measures are deemed inappropriateto evaluate the goodness-of-fit of model simulations dueto insensitivities in differences of observed and model-simulated means and variances (Legates and McCabe,1999), the coefficient of determination (R2) is not used toevaluate model results in this study.

4. Model testing: application to soil profiles

This section describes the application of the Se–N transportmodel to soil profile systems underlying cultivated fields at the

r (A) thepredicted ensemble ofCNO3 , (B) the corrected ensemble ofCNO3 , (C) thesembles use parameters estimated from observation data and the EnKF updategray lines and the ensemble mean is depicted by a solid black line. The day ovalues shown in Figs. 7 and 8. The observed values for the two test plots also are

f

Fig. 7. Simulated concentration in the soil profile after 292 days with accompanying observation data for the fields receiving the N1 fertilizer treatment level(56.2 kg ha−1) for (A) the predicted ensemble of CNO3 (B) the corrected ensemble of CNO3 (C) the predicted ensemble of CSeO4 , and (D) the corrected ensemble ofCSeO4 . The observation data from the first and second test plots are shown in dashed and dotted lines, respectively, and the ensemble mean of each simulatedensemble is shown in black with +/− σ error bars.

37R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

AVRC. After a description of the test site and field data collection(Section 4.1), model prediction (Section 4.2), parameter estima-tion (Section 4.3), and model correction (Section 4.4) isdescribed and presented. Section 4.4 also provides a generaldiscussion of results.

4.1. Site description and data collection

Soil samples were collected from recently-harvested corntest plots at the AVRC in October 2009. The test plots hadreceived varying rates of urea N fertilizer loading, with fertilizerapplied seven days before planting (April 27, 2009). Irrigationfrom a nearby canal was applied 9 times from June 17 to August10, with an average applied depth of 9.5 cm. Tail water fraction,which represents the portion of irrigation water that does notinfiltrate and runs off the end of the field, was approximately0.05 (5%), representative of the regional trend (Gates et al.,2012) and the typically higher efficiencies of irrigation applica-tion at the AVRC.

Irrigation water was sampled and analyzed for CNH4 andCNO3 using a continuous flow analyzer QuickChem (LachatQuickchem FIA+8000 Series, Lachat Instruments) usingmethods QuickChem Method 12-107-06-3-B for NH4 andQuickChem Method 12-107-04-1-B for NO3, with an extracting

solution made up with deionized water. CSeO4 and CO2 were notmeasured directly in the irrigationwater at each irrigation event,but rather were estimated from samples taken from the nearbyRocky Ford Canal. Samples forCSeO4 analysiswere collected usinga peristaltic pump, filtered through disposable in-line 0.45 μmcapsule filters, placed in 0.12 L bottles, acidified, stored on iceand sent to the Olson Biochemistry Laboratories at South DakotaState University in Brookings, SD (USEPA certified) for analysisusing Official Methods of Analysis of AOAC International, 17thEdition, test number 996.16 Selenium in Feeds and Premixes,Fluorometric Method. Analysis of CO2 was made just beforesample collection using a decontaminated and calibrated YSI600QS Multiparameter Sampling System. Timing of irrigationevents and values of CSeO4 , CNH4 , CNO3 , and CO2 in the irrigationwater for each event are shown in Table 1.

Soil was sampled at 7 depths (0.15 m, 0.30 m, 0.61 m,0.91 m, 1.22 m, 1.52 m, and 1.83 m) on October 19, 2009 fromfour plots, two receiving a fertilizer loading of 56.2 kg ha−1

(Treatment N1) and the other two a loading of 280.8 kg ha−1

(Treatment N2). Soil was sampled using a hand auger, placedon ice, and transported to the Agricultural Research Service(ARS) laboratories at the USDA Natural Resources ResearchCenter in Fort Collins, CO. CSeO4 in the soil water was analyzedusing saturated paste extracts: soil samples were air-dried,

Fig. 8. Simulated concentration in the soil profile after 292 days with accompanying observation data for the fields receiving the N2 fertilizer treatment level(280.8 kg ha−1) for (A) the predicted ensemble ofCNO3 (B) the corrected ensemble ofCNO3 (C) the predicted ensemble ofCSeO4 , and (D) the corrected ensemble ofCSeO4 . The observation data from the first and second test plots are shown in dashed and dotted lines, respectively, and the ensemble mean of each simulatedensemble is shown in black with +/− σ error bars.

38 R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

ground to pass through a 2-mmsieve, andbrought to saturationto create a saturated paste, upon which a 80 kPa vacuum wasapplied to extract the soil water. The extracted soil water wassent to the Olson Laboratories for analysis using the samemethod as for the irrigation water samples. CNO3 in the soilwater was analyzed using the QuickChem analysis with a 1 MKCl extracting solution. Results are shown in Section 4.2 alongwith model results.

Table 3Mean Absolute Error (MAE) of the simulated CNO3 and CSeO4 values for eachlayer of the soil profiles.

CNO3 CSeO4

TreatmentN1

TreatmentN2

TreatmentN1

TreatmentN2

Layer Depth(m)

Pred. Corr. Pred. Corr. Pred. Corr. Pred. Corr.

1 0.15 20.1 17.3 19.5 1.5 30.5 26.6 6.3 2.92 0.30 11.2 11.1 9.8 0.2 11.1 4.4 9.9 5.73 0.61 5.0 3.8 6.5 1.4 4.2 4.5 8.1 6.74 0.91 3.2 1.7 10.0 1.6 1.8 12.3 7.1 7.95 1.22 4.3 1.7 6.7 0.2 9.4 4.3 7.6 7.26 1.52 1.9 0.7 12.5 4.1 6.8 1.6 3.2 3.77 1.83 2.6 0.2 15.1 5.5 12.4 7.2 0.5 0.1

It should be noted that air-drying and sieving may alter thespeciation of Se in the soil through redox reactions andvolatization (Fio et al., 1991), although soil samples wereunsaturated and hence the changes in Se speciation areprobably negligible (Fio et al., 1991). In general, measurementsof solute concentration using saturated paste extracts shouldbe treated cautiously, with moderate values of coefficient ofvariation (CV) reported for solution extract methodologies(Kleinman et al., 2001).

Depth towater table, asmeasured from an observationwelllocated approximately 200 to 300 m from the test plots, was4.26 m, thus excluding the occurrence of significant capillaryupflux from the water table to the unsaturated zone. Averagewater table depth over 143measurements at this location fromMarch 2000 to October 2009 is 4.18 m with a CV of 0.13.

4.2. Model set-up and predicted model ensemble

The 1D profile finite-difference grid was constructed toinclude one cell for each depth of sampling (i.e., 7 cells) to easilycompare model results with observed data. The ensembleincluded 300 flow-reactive transport simulations, with eachsimulation run for 9 years (using the 2009 data) to establishsteady seasonal variation in species concentration andunbiased

Table 4Average Mean Absolute Error (MAE) and coefficient of efficiency (CE1) of the simulated CSeO4 and CNO3 values, for each soil profile.

CNO3 CSeO4

Measure Treatment N1 Treatment N2 Treatment N1 Treatment N2

Pred. Corr. Pred. Corr. Pred. Corr. Pred. Corr.

MAE 6.91 5.21 11.45 2.09 10.89 8.69 6.09 4.88CE1 −0.48 −0.12 −1.74 0.50 −0.90 −0.52 −0.11 0.11

39R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

initial conditions,whereupon the final yearwas run to establishthe fluctuation of species concentration during 2009. Daily timesteps were used. Since no apparent differences exist betweenthe forcing terms and parameters between the plots receivingthe same fertilizer loading, only one ensemble was run for eachof the two fertilizer treatment levels.

Themodel parameter values for the Se andNmodules for thepredicted ensemble are presented in Table 2, with valuesgathered either from the literature or provided by Dr. MichaelBartolo at the AVRC (personal communication, June 2010).Forcing terms and parameters for the flow regime consisted ofdaily precipitation, infiltrated irrigation water from the 9irrigation events, daily evapotranspiration (ET), soil porosity ϕ(0.45), saturated hydraulic conductivity (0.15 m day−1), resid-ual water content θr (0.20), Brooks–Corey exponent ε [−] (5.0),and the ET extinction depth (1.22 m). ET was calculated usingthe ASCE standardized Penman–Monteith reference ET equation(Allen et al., 2005) with climate data measured at the AVRCweather station located within 150–200 m from the test plots.Alfalfawas used as the reference crop,with corn crop coefficientssupplied by Allen and Wright (2002). Daily precipitation, dailyET, and daily values for the corn crop coefficient are shown inFig. 2. Average measured air temperature for 2009 was 10.7 °C,with aminimumof−18.1 °C (9 Dec) and amaximumof 27.1 °C(7Aug),whichwere used in the ET calculations aswell as the soiltemperature and associated daily ET values, as described inSection 3.3.2.

Selected parameters and forcing terms for the Se–Nmodulesare perturbed stochastically using the corresponding CV values,also shown in Table 2. The depth of infiltrated water perirrigation event, the daily reference ET rates, and the cropcoefficient also were perturbed, using a CV of 0.20. Values forCSeO4 and CO2 in the irrigation water (CSeO4 ;irrig and CO2 ;irrig) areperturbed (CV = 0.20) since they are taken from a nearbycanal and hence not known with certainty for the irrigationwater supplied on the test plots, whereas CNH4 and CNO3 weremeasured in the applied irrigation water and hence are treateddeterministically. Ranges of each perturbed parameter orforcing terms associated with the CV values were determinedeither from literature or provided by Dr. Bartolo at the AVRC(personal communication, June 2010). Parameter value meanand CV values for the predicted ensemble were the same foreach of the four test plots.

Results from a representative simulation of the predictedensemble are shown in Figs. 3, 4, and 5. Fig. 3 shows the achievedsteady seasonal variation during the combined 10-year periodfor LC, LN, and LSe. Fig. 4 shows simulateddailymass-balance termvalues, in μg and g for Se and N, respectively, and Fig. 5 presentsscatter-plots of the CNO3–CSeO4 relationship at layers 4 and 7 inthe soil profile (depths of 0.91 m and 1.83 m, respectively).

Relationships (R2 values of 0.65 and 0.39, respectively) aresimilar to the relationship found by Gates et al. (2009) forgroundwater samples in the region surrounding the AVRC,indicating the model is correctly capturing the dependence ofCSeO4 on CNO3 and the associated correlation.

Fig. 6A and C show the predicted ensemble and ensemblemean (average value of the simulations) for CNO3 and CSeO4 forthe entire 365-day period of 2009 for layer 1, respectively forTreatment N2. The observed values for the two test plots alsoare shown. For CNO3 , replenishment of N mass occurs at thebeginning of the growing season due to nitrification of theapplied NH4 fertilizer. For CSeO4 , Se mass does not enter thesystem via fertilizer application, and replenishment of Se massoccurs at a later period due to Semass supplied in the irrigationwater.

Fig. 7A and C show the predicted ensemble and ensemblemean for CSeO4 and CNO3 for each sample depth on the samplingday (day 292) and the observed values for the two N1 plots.Fig. 8A and C show results for the N2 plots. Note that the valuesof observedCSeO4 vary significantly between the two test plots foreach fertilizer treatment level, whereas the values of observedCNO3 between plots are more comparable. As mentionedpreviously, this likely is due to the use of the saturated pasteextract method for CSeO4 analysis and the associated error, withCV values reported to range between 0.11 and 0.70 (Kleinman etal., 2001). Therefore, these plots should be analyzed with theknowledge that the measured data have error. For the ensemblemean of model results, +/− σ error bars, where σ signifiesstandard deviation, are included to show the spread of theensemble at each sampling depth. The values ofMAE ofCSeO4 andCNO3 for each layer of the soil profile is shown in Table 3, and theoverall values of MAE and CE1 for each soil profile are shown inTable 4. Comparisons between simulated and observed valueswere calculated using the average of the two test plots for eachsoil profile layer. This was considered necessary since no systemforcing (e.g., fertilizer, climate, irrigation, land management)variations are known to have occurred between the two testplots, and hence could not be included in the model.

For the N1 treatment, the ensemble simulations generallyunder-predict CNO3 (Fig. 7A), although the MAE is reduceddrastically between the upper layer (20.1 g mf

−3) and lowerlayer (2.6 g mf

−3). For CSeO4 , under-prediction occurs for theupper and lower layers (Fig. 7C, Table 3), with good agreementfor layer 4 (MAE = 1.8 μg mf

−3). Overall MAE values for CNO3

andCSeO4 for the N1 treatment are 6.9 g mf−3 and 10.9 μg mf

−3,respectively. These results also are summarized by the CE1measure, with values of −0.48 and −0.90 for CNO3 and CSeO4 ,respectively, indicating that the pre-calibrated model is not asgood a predictor of the system as the observedmean. For the N2treatment, the ensemble generally over-predicts CNO3 (Fig. 8A),

40 R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

summarized by the overall MAE and CE1 values of 11.5 g mf−3

and−1.74, respectively. ForCSeO4 , themodel performs better forthe N2 treatment than for the N1 treatment, with overall MAEandCE1values of 6.1 μg mf

−3 and−0.11. This also canbe seen inFig. 8C.

Fig. 9. Selected scatter-plot relationships between CNO3 and (A) λnit, (B) Nup, (C) PSt,using the ensemble of model predicted simulations. Such plots are used to determhence which parameters are conditioned in the EnKF update scheme using the obs

4.3. Sensitivity analysis and parameter estimation

Influential parameters and forcing terms that could beconditioned using the EnKF update algorithm were identifiedusing scatter-plot analysis. Fig. 9 shows scatter-plots and fitted

(D) λden and between CSeO4 and (E) λSeO4 , (F) Seup, (G), Sert, and (H) CSeO4 ;irrig

ine which parameters are most influential on simulated CSeO4 and CNO3 , andervation data.

Table 5Parameter values used in the predicted ensemble and the corrected ensemble,with corrected values obtained using the observed data and the EnKF updateroutine.

Mean value (corrected ensemble)

Parameter Treatment N1 Treatment N2

CSeO4 ;irrig – 9.77αRt,Se – 1.5 × 10−6

PSt 5855 5478Seup 10.47 10.5Nup – 245drt,max 1.17 1.28Kd;NH4

10.9 –

λSeO4 0.023 0.023λnit 1.04 0.08

41R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

regression relationships between CSeO4 , CNO3 , and selectedparameters for the Treatment N2 ensemble. For CNO3 , theprincipal governing parameters are λnit for layer 1 (R2 = 0.77,positive correlation), and Nup for layer 3 (R2 = 0.46, negativecorrelation), with negligible influence from drt,max for layer 3(R2 = 0.05, negative correlation, not shown) and PSt for layer 4(R2 = 0.03, positive correlation). For CSeO4 , CSeO4 ;irrig has thestrongest influence (R2 = 0.71, positive correlation), withinfluences also from λhet

SeO4in layer 3 (R2 = 0.19, negative

correlation), and from Seup in layer 4 (R2 = 0.05, negativecorrelation). A similar procedure was used to identifysensitive parameters for the Treatment N1 ensemble.

Using these results, observed values of CSeO4 and CNO3 wereassimilated into the model results of the predicted ensembleusing the EnKF update algorithm Eq. (17) to condition λnit, Nup,drt,max, PSt, CSeO4 ;irrig , λ

hetSeO4

, and Seup. The ensemble mean of the

Fig. 10. Predicted and corrected frequency distribution for the ensemble of parameinfluence of conditioning the parameters using the observed values of CSeO4 and CN

updated parameter values are shown in Table 5. It should benoted that the observed values assimilated in the EnKF schemewere the average of the two test plots receiving the samefertilizer treatment. If the parameter value is assumed to be thesame for the fields of both treatment N1 and N2, then only onecorrected value is obtained (e.g., for CSeO4 ;irrig). If, on the otherhand, the parameter value is assumed to vary between thefields, then a corrected value is obtained for both treatmentlevels (N1 and N2). Fig. 10 shows the frequency distribution forthe ensemble of predicted and corrected values for λnit, Nup,λhetSeO4

, and CSeO4 ;irrig . Notice that only a slight change occurs forNup andλ

hetSeO4

, with a large change occurring forλnit andCSeO4 ;irrig .

4.4. Corrected model ensemble and discussion

Using the corrected ensemble of parameter values andforcing term values, the model simulation ensembles for bothN1 and N2 treatments were re-run to establish the correctedensemble. The corrected ensemble for CNO3 is shown in Figs. 6B,7B, and 8B, and the corrected ensemble for CSeO4 is shown inFigs. 6D, 7D, and 8D. The ensemble spread of the correctedensemble for CNO3 is much smaller (Fig. 6B) than for thepredicted ensemble (Fig. 6A), with a similar yet smallerdecrease in ensemble spread occurring for CSeO4 (Fig. 6D). Thedecrease in ensemble spread is due to the decrease in ensemblespread of the sensitive parameters (see Fig. 10).

The general improvement of the model results along thesoil profiles is seen in Figs. 7B and 8B for CNO3 and in Figs. 7Dand 8D for CSeO4 . For the N1 treatment, CNO3 values for layers4–7 are approximately equal to the average of the observedplot values (Fig. 7B); for theN2 treatment,CNO3 values track theobserved values very well, and the ensemble spread is much

ter values for (A) λnit, (B) Nup, (C) λSeO4 , and (D) CSeO4 ;irrig , demonstrating theO3 .

42 R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

smaller for each layer (Fig. 8B). These results are reflected inthe goodness-of-fit values (Tables 3 and 4). The overall MAEvalue is equal to 5.2 g mf

−3 and 2.1 g mf−3 for treatments N1

and N2 (Table 4), an improvement of 25% and 82%, respective-ly, from the predicted ensemble. The overall CE1 value is equal−0.12 and 0.50 for treatments N1 and N2, an improvement of24% and 71% from the predicted ensemble. The improvementfrom the predicted ensemble to the corrected ensemble is seenfurther in Fig. 11A, which shows a frequency distribution ofpredicted and corrected simulatedCNO3 values for layer 1 of theN2 treatmentmodel. For the corrected ensemble, the ensemblespread is much smaller and the ensemble values approach theobserved values of the two test plots.

The corrected ensemble for CSeO4 also is improved from thepredicted ensemble, although not to the same degree as for theCNO3 values. An example of improvement is seen in Fig. 11B forlayer 1 of the N2 treatment model, with the corrected ensemblecloser in value to the average of the observed values than thepredicted ensemble. However, as seen in Fig. 8D, improvementin the ensemble in the soil profile occurs only in the upper layerswhereCSeO4 ;irrig has a strong influence, although improvement inthe lower layers could not be expected since the forecastensemble already captures the approximate pattern of the twotest plots (Fig. 8D). The overallMAE value is equal to 8.7 μg mf

−3

and 4.9 μg mf−3 for treatments N1 and N2 (Table 4), an

improvement of 20% from the predicted ensemble for bothtreatments, and the CE1 value is −0.52 and 0.11, also animprovement of 20%.

Fig. 11. Frequency distribution of the predicted and corrected ensemble ofsimulation results in the top layer of the soil profile for (A) CNO3 and (B) CSeO4 .The observed values ofCNO3 andCSeO4 in the top layer are shown in dashed anddotted lines for the first and second test plots. Results are shown for the twoplots receiving the N2 fertilizer treatment level.

The CE1 value for treatment N2 for both CNO3 and CSeO4 (0.50and 0.11) indicate that the model is an excellent predictor ofthe system, whereas the value for treatment N1 approaches 0.0(−0.12 and −0.52), indicating that for the N1 test plots themodel is not quite as good a predictor as the observed mean.This is especially true for the top layer, with MAE values of17.3 g mf

−3 and 26.6 μg mf−3 for CNO3 and CSeO4 , respectively

(Table 3). This is expected, since a lower fertilizer loading(56.2 kg ha−1) provided to the model produces much lowervalues of CNO3 in the upper layers than for the N2 treatment. Theobserved CNO3 values are in fact opposite of what is expected inthe field, with higher values of CNO3 in the N1 treatment plots,and hence were affected by factors not included in the model.However, the model performs well under conditions of typicalfertilizer loading (treatment N2). Furthermore, it should benoted that improved parameter conditioningwould be achievedif separate predicted ensembles were run for each set ofobserved data, rather than conditioning one ensemble to theaverage of the observed data. Overall, and particularly for the N2treatment plots, themodel fits seem to be better forCNO3 than forCSeO4 .

In general, the results are encouraging in regards to theimproved match between model-calculated and observedvalues of CSeO4 and CNO3 for the four test plots using thecorrected ensembles, especially when considering (i) the errorassociated with establishing the observed data through fieldsampling and laboratory analysis and (ii) the lack of agreementbetween observed CSeO4 for plots receiving the same fertilizertreatment. In regards to a fundamental objective of this study,i.e. to determine if the Se and Nmodules for UZF-RT3D are ableto provide accurate estimates of species leaching to thesaturated zone for regional-scale reactive transport simula-tions, of utmost importance is the concentration values at thebase of the soil profiles. For CNO3 , the MAE value in layer 7(Table 3) for treatments N1 and N2 is 0.2 g mf

−3 and5.5 g mf

−3, improvements of 92% and 64% from the predictedensemble, and for CSeO4 theMAE value in layer 7 for treatmentsN1 and N2 is 7.2 μg mf

−3 and 0.1 μg mf−3, improvements of

42% and 80% from the predicted ensemble. This agreementoccurs even for soil profiles wherematches between simulatedand observed values are somewhat poor in the upper soil layers(see Figs. 7B, D, and 8D).

5. Summary and conclusions

A numerical reactive transport model capable of simulatingthe fate and transport of Se in multi-dimensional variably-saturated groundwater systems is presented in this study.The model was constructed through the development of aselenium cycling and reaction module for the recently-developed UZF-RT3D model, and includes an accompanyingnitrogen cycling and reactionmodule due to the dependence ofSe transformation and speciation on the presence of NO3. Allrelevant sources and sinks (fertilizer, species mass in irrigationwater, root mass, after-harvest stover mass, crop uptake) andchemical reactions (organic matter decomposition, minerali-zation/immobilization, nitrification, volatilization, heterotro-phic chemical reduction, autotrophic chemical reduction) areincluded.

The model was applied to 1D agricultural soil profilesystems underlain by a groundwater table to corroborate

43R.T. Bailey et al. / Journal of Contaminant Hydrology 149 (2013) 27–45

the correctness of the incorporated processes and toexplore the ability of the near-surface cycling and chemicalreactions to provide accurate estimates of leaching tothe saturated zone when the model is employed in alarge-scale agriculturally-influenced aquifer setting. In afirst application, the selenium and nitrogen modules weretested against observed concentrations of SeO4 and NO3

with depth for soil profiles in four corn test plots insoutheastern Colorado. Using the Ensemble Kalman Filter(EnKF) methodology to condition parameters and forcingterms, the corrected parameter values were able to producean ensemble with mean values that matched the observedconcentration values to a reasonable degree. Identified sensi-tive parameters include the rate of chemical reduction of SeO4,seasonal uptake of SeO4, concentration of SeO4 in the irrigationwater, rate of nitrification, maximum rooting depth, andseasonal uptake of N. Model-calculated and observed valuesmatched particularly well in the deepest soil layer (1.83 m),indicating that leaching to the underlying shallow groundwa-ter table is accurately depicted and hence the Se andNmodulesfor UZF-RT3D can be applied with confidence to agriculturalsettings. Results demonstrate also the applicability of the EnKFin conditioning reaction rates and other parameters insubsurface reactive transport systems. In a second application,shown in the Supplementary Data, the nitrogen module wasable to accurately reproduce a 3-year time series of NO3

concentration in the near-surface soil water for unfertilizedand fertilized plots.

6. Glossary of terms

General terms

Agricultural parameters and inputs

Litter pool

L Solute conc. of x in irrigationwater

Cx,irrig

Humus pool

H Maximum rooting depth drt,max

Manure pool

M Plowing depth dpw Mineralization min Nitrogen seasonal crop

uptake

Nup

Immobilization

imm Selenium uptake rate λup,Se

Organic matterdecomposition

dec

SeO4–SeO3 uptake ratio γup

Autotrophic chemicalreduction

auto

Inorganic fertilizer loadingrate

F

Heterotrophic chemicalreduction

het

Solid-phase source rate P

Nitrification

nit Fraction of solid-phase masssource

α

NH4 volatilization

vol Organic matter decomposition Root mass Rt Synthesis efficiency fe After-harvest stovermass

St

Humification factor fh

Soil parameters andvariables

Humus mass ratio

H

Soil porosity

ϕ Microbial mass ratio B Water content θ Oxidation-reduction reactions Solid content ε First-order kinetic rate

constant

λ

Soil bulk density

ρb Monod half-saturation constant K Solute concentration C Chemical reduction inhibition

term

I

Partitioning coefficient

Kd S:Se shale mass ratio ξ Environmental reductionfactor

E

Soil temp. factor change

Q10

Base soil temperature

TB

Acknowledgments

This work has been made possible by grants from theColorado Agricultural Experiment Station and the NonpointSource Programof the ColoradoDepartment of PublicHealth andEnvironment. We appreciate Dr. Michael Bartolo for providingthe opportunity to sample soil from theArkansasValleyResearchCenter and for providing ranges of values for parameter andsystem forcing terms. We thank also Dr. William Hunter ofUSDA-ARS at the Natural Resources Research Center in FortCollins, CO for providing laboratory space to conduct soil analysisand to Robin Montenieri for expert technical assistance. Wewould like to acknowledge two anonymous reviewers for theirhelpful comments and suggestions in improving the content ofthis paper.

Appendix A. Supplementary data

Supplementary data to this article can be found online athttp://dx.doi.org/10.1016/j.jconhyd.2013.03.001.

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