Journal of Hydrologyphani/JH_Niu.pdf · stand linkages between hydrology and land surface processes, routine applications of these models to address water quality issues are currently

Journal of Hydrology 529 (2015) 35–48

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Journal of Hydrology

journal homepage: www.elsevier .com/ locate / jhydrol

Modeling watershed-scale solute transport using an integrated,process-based hydrologic model with applications to bacterialfate and transport

http://dx.doi.org/10.1016/j.jhydrol.2015.07.0130022-1694/� 2015 Elsevier B.V. All rights reserved.

⇑ Corresponding author.E-mail addresses: [email protected] (J. Niu), [email protected] (M.S. Phanikumar).

Jie Niu a,b, Mantha S. Phanikumar a,⇑a Department of Civil & Environmental Engineering, Michigan State University, East Lansing, MI, United Statesb Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, United States

a r t i c l e i n f o s u m m a r y

Article history:Received 1 January 2015Received in revised form 4 July 2015Accepted 7 July 2015Available online 11 July 2015This manuscript was handled by GeoffSyme, Editor-in-Chief, with the assistance ofJohn W. Nicklow, Associate Editor

Keywords:Solute transportParticle trackingDistributed hydrologic modelsSurface–subsurface couplingBacterial transportGroundwater–surface water interactions

Distributed hydrologic models that simulate fate and transport processes at sub-daily timescales are use-ful tools for estimating pollutant loads exported from watersheds to lakes and oceans downstream. Therehas been considerable interest in the application of integrated process-based hydrologic models in recentyears. While the models have been applied to address questions of water quantity and to better under-stand linkages between hydrology and land surface processes, routine applications of these models toaddress water quality issues are currently limited. In this paper, we first describe a generalprocess-based watershed-scale solute transport modeling framework, based on an operator splittingstrategy and a Lagrangian particle transport method combined with dispersion and reactions. The trans-port and the hydrologic modules are tightly coupled and the interactions among different hydrologiccomponents are explicitly modeled. We test transport modules using data from plot-scale experimentsand available analytical solutions for different hydrologic domains. The numerical solutions are also com-pared with an analytical solution for groundwater transit times with interactions between surface andsubsurface flows. Finally, we demonstrate the application of the model to simulate bacterial fate andtransport in the Red Cedar River watershed in Michigan and test hypotheses about sources and transportpathways. The watershed bacterial fate and transport model is expected to be useful for making nearreal-time predictions at marine and freshwater beaches.

� 2015 Elsevier B.V. All rights reserved.

1. Introduction

The ability to quantify fluxes of nutrients, bacteria, viruses andother contaminants exported from watersheds to downstreamreceiving water bodies such as lakes and oceans is important formanaging coastal resources (e.g., to generate timely predictionsof water quality for beach closures, e.g., Ge et al., 2012a,b) and tounderstand and assess threats to human and ecosystem health.In the Great Lakes region of North America, for example, increasedbeach closures due to microbiological pollution, eutrophicationand harmful algal blooms and drinking water related issues con-tinue to be causes for concern highlighting the need forwell-tested and reliable transport models. Integratedprocess-based hydrologic models, which are based on the conser-vation principles of mass, momentum and energy, are useful toolsfor making accurate predictions and have the potential to offer

insights into the fundamental transport processes at the watershedscale. A number of such watershed models have been developed inthe last few decades including, for example, CATHY (Weill et al.,2011), InHM (VanderKwaak, 1999), OpenGeoSys (Kolditz et al.,2012), ParFlow (Kollet and Maxwell, 2006), PAWS (Shen andPhanikumar, 2010), tRIBS (Ivanov et al., 2004) and Wash123 (Yehet al., 2011). Although a majority of these models have the abilityto simulate transport processes, the routine application ofprocess-based hydrologic models to address water quality issuesis currently still limited.

The assessment and management of non-point sources of pollu-tion (e.g., microbial pollution) is an issue of great interest.Escherichia coli (E. coli) is a commonly used fecal indicator organ-ism in freshwaters. Prior research has shown that E. coli densitiesare correlated with swimming-associated gastroenteritis (Prüss,1998). Models such as MWASTE (Moore et al., 1989), COLI(Walker et al., 1990) and SEDMOD (Fraser et al., 1998) have beendeveloped to simulate landscape microbial pollution processes.These models successfully simulate the manure-borne bacteria

36 J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48

releasing process and the transport of bacteria through runoff;however, the die-off due to solar radiation and other environmen-tal factors was not considered, and there was no interaction amongdifferent hydrologic components in these models. There are mod-els incorporating both landscape and in-stream microbial pro-cesses, for example, the Soil and Water Assessment Tool (SWAT)(Frey et al., 2013), a watershed model developed by Tian et al.(2002), a modified SWAT model (Cho et al., 2012), which consid-ered solar radiation associated bacterial die-off, and a coastalwatershed fecal coliform fate and transport model based on HSPF(Hydrologic Simulation Program Fortran, Rolle et al., 2012). Thesemodels tend to use conceptual representations of the groundwaterand vadose zone compartments, ignoring the complexity of theflow in the subsurface domain. The subsurface flow is an integralcomponent of the hydrologic cycle and in shallow water table con-ditions groundwater controls soil moisture and provides sources ofwater for evapotranspiration (ET) (Shen and Phanikumar, 2010).Therefore, the subsurface flow domain should be fully consideredwhile developing a general framework for the solute transportproblem even if the subsurface contribution is not important forcertain types of pollutants.

A process-based, watershed-scale reactive transport modelingframework is developed in this work to quantify the fluxes of con-servative and reactive solutes exported from watersheds. The dis-

tributed hydrologic model PAWS (Process-based Adaptive

Watershed Simulator, Shen and Phanikumar, 2010; Shen et al.,2013; Niu et al., 2014) was used to simulate integrated hydrology,including flows in channel networks, overland flow, and subsurfaceflows and interactions between different domains. The computa-tional efficiency of the PAWS model allows for long-term,large-scale simulations and makes it possible to simulate transportin large watersheds. An operator-splitting strategy (e.g.,Phanikumar and McGuire, 2004) combined with a Lagrangian par-ticle transport modeling approach (e.g., de Rooij et al., 2013) withreactions to describe transport in different hydrologic units wasapplied. Due to the complexity of the processes involved, extensivemodel testing against analytical solutions for different hydrologicdomains is a necessary first step before the performance of theintegrated model can be fully evaluated. Such detailed testing pro-vides a way to ascertain the sources of error when modelinter-comparison exercises are conducted (e.g., Maxwell et al.,2014). In the present paper, the algorithms were tested using avail-able analytical solutions and data from plot-scale experimentsbefore applying the bacterial fate and transport model to describemonitoring data from the Red Cedar River watershed in the GreatLakes region. Future papers will describe additional model testing(especially interactions between the groundwater and surfacewater domains) as well as the development and application ofadditional transport modules (e.g., carbon, nitrogen and phospho-rus cycles).

2. Methods

2.1. 2D overland flow transport

A commonly accepted approximation of the St. Venant equa-tions for overland flow is the kinematic wave equation (Singh,1996) which can be expressed as:

@h@tþ @ðuhÞ

@xþ @ðvhÞ

@y¼ S ð1Þ

where h is the overland flow water depth [L], u, v are the x- andy-direction water velocities [LT�1], S is either a source term to rep-resent precipitation or exfiltration from the subsurface, or a sinkterm to represent infiltration or evaporation. The solute transport

equation for overland flow can be expressed in a conservative formin terms of the solute flux (Deng et al., 2006) as:

@ðCohÞ@t

þ @ðCouhÞ@x

þ @ðCovhÞ@y

¼ @

@xhDx

@Co

@x

� �þ @

@yhDy

@Co

@y

� �þ rDmðCs � CoÞ � kCoh ð2Þ

where the subscript o denotes overland flow, Co is thecross-sectionally averaged solute concentration [ML�3] or the massof solute per unit volume of runoff; CS represents the solute concen-tration in the soil mixing zone; r is a mass transfer coefficient [T�1];Dm is the mixing zone thickness [L] which is proportional to flowdepth; k is the decay coefficient [T�1]; Dx and Dy are the x- andy-direction diffusion coefficients [L2T�1]. Eq. (2) can be fullyexpanded and rearranged as below:

Co@h@tþ @ðuhÞ

@xþ @ðvhÞ

@y

� �þ h

@Co

@tþ u

@Co

@xþ v @Co

@y

� �

¼ h Dx@2Co

@x2 þ Dy@2Co

@y2

!þ Dx

@h@x

@Co

@xþ Dy

@h@y

@Co

@y

þ rDmðCs � CoÞ � kCoh ð3Þ

Using the kinematic wave approximation which ignores thepressure gradient terms, we have oh/ox = 0 and oh/oy = 0.Substituting Eqs. (1) into (3) and dividing both sides of the aboveequation by the flow depth h gives the following equation:

@Co

@tþu

@Co

@xþv @Co

@y¼Dx

@2Co

@x2 þDy@2Co

@y2 þrDm

hðCs�CoÞ�

Shþk

� �Co

ð4Þ

2.2. Channel flow, the river network and river junctions

The one-dimensional channel transport equation used in thepresent work appears as shown below (see, for example, Gunduz,2004):

@ðCrAÞ@t

þ @

@xðvACrÞ �

@

@xADL

@Cr

@x

� �þ kCrA� qLCL

þ nsedDsedCg � Cr

mrwr � qoCo ¼ 0 ð5Þ

where Cr is the solute concentration within the river channel, CL andCo are concentrations associated with lateral seepage and overlandflows respectively, qL and qo are lateral seepage and overland flowsper channel length [L3T�1L�1] (considered positive for inflow), A isthe cross-sectional flow area [L2], DL is the longitudinal dispersioncoefficient in the channel [L2T�1], Dsed is vertical dispersion coeffi-cient [L2T�1] in the sediment layer, nsed is porosity of the sedimentlayer (dimensionless), Cg is solute concentration associated withgroundwater flow, mr is thickness of the sediment layer [L], andwr is river wetted perimeter [L].

Initial solute concentrations need to be specified along theone-dimensional channel domain: Cr(x, 0) = Cr0(x), where Cr0 isthe initial concentration distribution along the channel network.Concentration boundary conditions in the form of Dirichlet,Neumann or mixed type can be specified at the external ends ofthe domain depending on whether a specified concentration or dif-fusional or total mass flux is being specified.

In addition, internal boundary conditions may need to be spec-ified when two or more channels join to form a junction. Whilehandling river junctions, the change in mass storage within a junc-tion is assumed to be negligible compared to the change in masswithin the channel. Furthermore, the continuity of concentrationat junctions guarantees that all the concentrations must be equalat junctions. Eq. (5) is first solved by an advection step using

J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48 37

Lagrangian particle tracking scheme, which is described in a latersection, and an implicit step is used for dispersion and reactions.The details of this operator splitting method including the methodof characteristics used for handling the river junctions are availablein Gunduz (2004).

2.3. Transport in the vadose zone

Solute transport within the soil profile below the land surface iscontrolled by both infiltration and diffusion. In PAWS, theone-dimensional Richards equation is used to describe soil mois-ture in the vadose zone and lateral moisture diffusion is ignored.Consistent with this description, the vertical transport of a linearlysorbing solute was modeled by the following 1D advection–dispersion-reaction equation (e.g., Dong and Wang, 2013; van Genuchtenand Wagenet, 1989):@aCs

@t¼ @

@zDs@Cs

@z� ICs

� �� kCs ð6Þ

where z is the vertical coordinate [L], CS is the solute concentrationin the soil water below the mixing layer, a = qbkp + h (dimension-less), qb is the dry soil bulk density [ML�3], and kp is a partition coef-ficient [L3M�1]. For non-adsorbing chemicals, a is equal to the soilmoisture h [L3L�3]. I denotes the infiltration rate [LT�1] in the soil,DS is the dispersion coefficient [L2T�1] in the soil and is taken asthe sum of the effective molecular diffusion coefficient and themechanical dispersion coefficient (Ahuja, 1990; Bear and Bachmat,1990; Bresler, 1973).

Ds ¼ a0jv jc þ D0sD0s ¼ D0aebh

ð7Þ

where a and b are empirical coefficients, with typical values ofa = 0.005, b = 10 (Olson and Kemper, 1961). D0 is the diffusion coef-ficient of the solute in free water, c is a constant (equal to unity), v isthe velocity in soil pores, and a0 is the dispersivity parameter [L].

The initial condition of Eq. (6) is:

Csðz;0Þ ¼ Cs0 ð8Þ

where CS0 is the solute concentration in the soil when rainfallbegins. Transport in the vadose zone is treated differently fromtransport in other hydrologic domains and the derivation and dis-cretization of the vadose zone transport equation are presented inAppendix A.

2.4. Transport in the groundwater domain

A general two-dimensional solute transport equation for thefully saturated groundwater domain, considering advection, dis-persion, fluid sinks/sources is as follows (Zheng and Bennett,2002):

hR@Cg

@tþ @

@xqxCg� �

þ @

@yðqyCgÞ

¼ @

@xhDxx

@Cg

@x

� �þ @

@xhDxy

@Cg

@y

� �þ @

@yhDyy

@Cg

@y

� �

þ @

@yhDyx

@Cg

@x

� �� qsCs � kCg ð9Þ

where R is the retardation factor (dimensionless); Cg is the dissolvedconcentration; qx and qy are Darcy velocities [LT�1]; qs is flow rate ofa fluid source or sink per unit aquifer volume [T�1]; Cs is the concen-tration associated with a fluid source or sink and h is porosity(dimensionless). Dxx, Dxy, Dyy, Dyx are the elements of the dispersiontensor [L2T�1] described below:

Dxx ¼ aLv2

x

jv j þ aTv2

y

jv j ð10Þ

Dxy ¼ Dyx ¼ ðaL � aTÞvxvy

jv j ð11Þ

Dyy ¼ aLv2

y

jvj þ aTv2

x

jv j ð12Þ

aL is the longitudinal dispersivity, aT is the transverse dispersivity,

|v| is the magnitude of the seepage velocity, v ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiv2

x þ v2y

q, vx ¼ qx

h

and vy ¼qy

h . The general source/sink term qsCs can represent soluteexchange between soil vadose zone and the first layer of thegroundwater, the solute exchange with groundwater at the bed ofriver channels, or solute exchange between confined and uncon-fined aquifers. More layers can be added to the current modelframework to simulate (quasi-) 3D groundwater transport.

2.5. Particle tracking scheme and mass balance

Most numerical methods for solving the advection–dispersionequation can be classified as Eulerian, Lagrangian, or mixedEulerian–Lagrangian (Neuman, 1984). Eulerian methods offer theadvantage and convenience of a fixed grid, are generally mass con-servative, and handle dispersion-dominated problems accuratelyand efficiently. However, for advection-dominated problems thatexist in many natural systems, an Eulerian method is susceptibleto excessive numerical dispersion or artificial oscillations(Anderson and Cherry, 1979; Pinder and Gray, 1977). Lagrangianmethods, on the other hand, provide an accurate and efficient solu-tion to advection-dominated problems by essentially eliminatingfalse numerical dispersion (Tompson and Gelhar, 1990).However, the velocity interpolation needed in particle trackingcan also result in local mass-balance errors (LaBolle et al., 1996).When Eulerian methods are used, the time-step restriction associ-ated with the advection step tends to be fairly restrictive. This lim-itation can be overcome using a Lagrangian method; therefore weused a Lagrangian method for the advection step in this work sinceour primary interest is in solute transport in large watersheds. Thedetails of the particle tracking method can be found in (Zheng andBennett, 2002). A fourth-order Runge–Kutta method was used inthe present work.

Assuming that the number of particles in cell m at time t is NPm,the concentration for the cell at time t can be estimated as (Zhengand Bennett, 2002):

CmðtÞ ¼XNPm

p¼1

f p ð13Þ

where fp is the mass fraction [ML�3] represented by the pth particle.Transport equations for all hydrologic domains, with the excep-

tion of the vadose zone, used the mixed Eulerian–Lagrangianmethod. To combine the advantages of both classes of methods, aLagrangian (particle tracking) solution of the advection equationwas combined with solutions of the dispersion and reaction equa-tions based on the Eulerian approach. The diffusion term was dis-cretized using the central differencing scheme and solvedimplicitly using the Generalized Conjugate Gradient method(Zheng and Bennett, 2002). Some commonly used mixedEulerian–Lagrangian procedures, such as the method of character-istics (MOC), do not guarantee mass conservation. Many mixedEulerian–Lagrangian methods may be generally characterized asthe forward-tracking MOC, the backward-tracking modified MOC(MMOC) and a combination of these two methods which tracksmass associated with fluid volumes to conserve mass locally andglobally, depending on the use of different Lagrangian techniquesto approximate the advection term. The comparisons betweennumerical and analytical solutions of different advection diffusion

38 J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48

equations (ADE) in different domains shown in later sections indi-cate that the numerical schemes used in our current model frame-work conserve mass very well.

We used dynamic particle allocation based on the plume loca-tion and the evolution of the concentration field with time as thismethod uses less number of particles and increases the efficiencyof the MOC with little loss of accuracy. The MOC has the advantagethat it is almost free of numerical dispersion. However, MOC is notcomputationally efficient, especially when a large number of mov-ing particles need to be tracked. Unlike the MOC which tracks alarge number of moving particles as well as associated concentra-tion and position of each particle forward in time, MMOC is morecomputationally efficient and much less memory-intensivebecause (1) the MMOC places only one particle at the nodal pointof the fixed grid at each new time level; (2) the particle is trackedbackward to find its position at the old time level; and (3) the con-centration associated with that position is used to approximate theconcentration at the intermediate time level.

The MOC solves the advection term using the moving particlesdynamically distributed around each cell when sharp concentra-tion fronts are present, while away from such fronts the advectionterm is solved by an MMOC technique. In this adaptive procedurethe MOC and the MMOC are combined, which can provide accuratesolutions with virtually no numerical dispersion by selecting anappropriate criterion for controlling the switch between the MOCand MMOC schemes. In the present work a combination of MOCand MMOC methods (called the Hybrid MOC or HMOC, Zhengand Bennett, 2002) was used.

2.6. Interactions among domains

The fluxes in one domain are connected to those in otherdomains in a fully integrated hydrologic system. The flow couplingwas described in Shen and Phanikumar (2010), and in this sectionwe describe the coupling schemes used for the transport equationsacross different domains.

2.6.1. Interaction between the land surface and channelThe exchange volumes between the land and the channel are

computed using the framework for a wide rectangular weir anddetails are described in Shen and Phanikumar (2010). The logicfor computing the direction (land to channel or vice versa) andmagnitude of exchange volumes is summarized in Fig. 5 in Shenand Phanikumar (2010). Briefly, if the flow is from the land tothe river cell and there is water on the land, we compute theexchange (Mex) explicitly using the diffusive wave equation. Thisvolume, however, cannot exceed the amount of water currentlyavailable on the land cell and this provides an upper bound (Ma).In addition, we can identify an equilibrium state in which the riverstage is equal to the land free surface elevation. The exchange vol-ume (ME) that leads to this equilibrium state can be computedbased on the current channel stage and the equilibrium stage whenthe channel stage and land surface elevations are equal. Thus theexchange mass will be the minimum among these three volumes(Mex, Ma, ME). A fourth condition corresponds to flooding, whichwould occur if the river stage rises above the land free surface ele-vation (and also the bank elevation, condition 3 in Shen andPhanikumar (2010)). The exchange volume corresponding to thiscase (Mim) is computed using the diffusive wave formulation andby solving two ordinary differential equations presented in Shenand Phanikumar (2010). To enhance stability, a backward Eulerimplicit approach is used to solve for the exchange mass Mim.

Once the direction and magnitude of exchange volumes aredetermined, it is fairly straightforward to compute the exchangemass of solutes. Denoting the exchange volume of water from

the overland flow domain to the river cell as M and noting thatMim denotes the exchange from the river to the land, the exchangeof solutes can be simply calculated as:

qoCo ¼MLc

Co; from land to channel ð14Þ

or

qoCo ¼Mim

LcCr ; from channel to land ð15Þ

where Lc is the length of the channel segment that overlaps with theland cell [L].

2.6.2. Interaction between the land surface and the vadose zoneA mass balance equation for the surface ponding layer is solved

simultaneously with the soil water pressure head as described inShen and Phanikumar (2010). The solute in the ponded water onland surface can percolate through the soil column by infiltrationand/or diffusion. The coupling of solute transport between over-land flow and soil water in the vadose zone is simulated via aboundary condition, which at the underlying soil surface for Eq.(6) is related to two stages during rainfall–runoff (Dong andWang, 2013):

d½hð0; tÞCoðtÞ�dt

¼ Jð0; tÞ � ICsð0; tÞDm

0 � t � tP

d½hð0; tÞCoðtÞ�dt

¼ Jð0; tÞ � ICsð0; tÞ þ ICoðtÞDm

tP � tð16Þ

where tP is the time [T] from the start of rainfall to when runofftakes place, Co is the solute concentration in the runoff on top ofthe soil column, CS is the solute concentration in the soil waterbelow the mixing layer, Dm is the mixing zone thickness, h is soilmoisture, and J is the diffusion flux of the solute from the soil belowthe mixing layer, which is described by Fick’s law:

J ¼ �Ds@Cs

@zð17Þ

2.6.3. Interaction between the vadose zone and groundwaterPAWS uses a coupling scheme to reduce the fully

three-dimensional Richards equation for the unsaturated vadosezone to a series of one dimensional equations for soil columns withthe unconfined aquifer underneath. The coupling between vadosezone and the groundwater domain is via the source/sink termqSCS in Eq. (9), where CS is the solute concentration in the bottomcell of the soil column linked to the unconfined aquifer and qS isthe recharge rate calculated in PAWS using an iterative scheme.When qS < 0, the value of CS becomes the same as the solute con-centration in the unconfined aquifer, Cg, and the term qSCg willbe added to the right hand side of the solute transport equationin the vadose zone (Eq. (6)).

2.6.4. Interaction between groundwater and channelThe seepage flux between the groundwater domain and the

river channel, qL in the 1D channel flow Eq. (5), is accumulatedas groundwater contribution (to the channel) and subtracted fromthe source/sink term in the groundwater flow equation in PAWSusing the conductance/leakance concept and solved by an operatorsplitting method (Gunduz and Aral, 2005; Shen and Phanikumar,2010). Then the associated solute concentration in the seepageterm is:

CL ¼Cr ; qL < 0Cg ; qL > 0

�ð18Þ

J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48 39

This means that the value of CL changes according to the direc-tion of the seepage flux such that when the groundwater head islarger than the river stage, the seepage is positive and flows fromthe groundwater toward the river channel via the river bed, andthe value takes the associated concentration coming from thegroundwater (i.e., Cg) and vice versa.

2.7. Parameter estimation

A few parameters with uncertainty were estimated in theplot-scale transport simulations and to simulate the hydrology ofthe watershed. The calibration parameters for hydrology, describedin Shen et al. (2013), included hydraulic conductivities, the vanGenuchten soil parameters, river bed leakances etc. The parameteroptimization followed the procedure described in Niu et al. (2014)which involved minimizing an objective function that includedcontributions from both surface water and groundwater domains.

For the plot-scale transport simulation (reported in Section 3.2),seven parameters are estimated, including the parameters in thevan Genucheten formulation (Eq. (18) in Shen and Phanikumar,2010), saturated and residual soil moistures, initial water tabledepth and saturated soil conductivity, by minimizing the rootmean square error of simulated and measured accumulated runoff.The parameter optimization code used for this case is the ShuffledComplex Evolution algorithm (Duan et al., 1992), which was mod-ified to run on multiple cores in parallel. For the watershed-scaletransport simulation (Section 3.3), all parameters used were basedon literature values and no parameter estimation was conducted.

2.8. Application: Microorganism release and loss rate

One of the major sources of bacteria is animal manure(Jamieson et al., 2004). In watersheds where ConcentratedAnimal Feeding Operation (CAFO) centers are located, it is impor-tant to quantify the production rate of bacteria associated with ani-mal manure (Dorner et al., 2006). Manure production rates fordifferent animal categories are available as standard data(American Society of Agricultural Engineers; ASAE Standards,2003). To estimate the bacteria shedding intensity in log numberof bacteria per gram of fresh manure, the daily manure productionrate was first generated randomly following a normal distribution(with mean and variance for a given animal category from theASAE data). The E. coli load was then directly estimated by multi-plying the manure production rate by standard mean fecal coliformshedding numbers (also from ASAE and using a factor to convertfecal coliform numbers to E. coli). Then given the number of ani-mals in the CAFO/region, using daily manure production rates,the daily bacteria production was calculated by summing the num-ber of bacteria shed by all animals in a given category. The totaldaily bacteria production rate was obtained by summing the dailybacteria production from all individual animal categories.

Significant uncertainty is associated with confined animal feed-ing operations including the storage and application of manure onland. Technical guidelines (e.g., EPA, 2012) to minimize thechances of runoff are usually followed for land application of man-ure and these guidelines were implemented in our modeling. InMichigan, CAFO waste is not applied during rain events, when landis flooded, saturated, or frozen or rainfall exceeding 0.5 in. is fore-casted. In addition to the EPA guidelines and based on availableinformation, we also assumed that manure is applied only duringthe growing season and that only 2/3 of the manure generated isapplied on land and that the remaining 1/3 is composted (andnot applied).

To simulate the release of manure-borne microorganisms theassumptions of the linear or exponential release are frequentlyused in watershed scale models such as SWAT and HSPF

(Bicknell et al., 1997). The release of microorganisms depends onthe time of runoff yield, the processes of which are more complexthan the model descriptions of linear or exponential release (Guberet al., 2006). However, they were successfully simulated with twomodels according to Vadas et al. (2004) and Bradford and Schijven(2002). The exponential release model of HSPF (Bicknell et al.,1997) was used in the current work:

DMR ¼ MS½1� expð�bDQÞ� ð19Þ

where DMR is the count of bacteria (CFU) released during a timeinterval Dt during the runoff event; MS is the count of bacteria(CFU) in the manure storage layer of soil at the beginning of theinterval Dt; DQ is the runoff yield [L] during the interval; b is therelease rate parameter [L�1] (see Table 2).

The total loss rate for bacteria is represented as (Chapra, 2008):

k ¼ kb1 þ kbi þ kbs ð20Þ

where k is the total loss rate (d�1), kb1 = base mortality rate (d�1),kbi = loss rate due to solar radiation (d�1), kbs = settling loss rate(d�1) (not considered in the present study). There is no confusionbetween the total loss rate k for bacteria in Eq. (20) and the symbolk which is also used to denote a general reaction rate (loss or gainterm) in the transport equations for different domains. If the equa-tions are written for E. coli, then k denotes an E. coli loss rate.

The following equation was used to calculate a base mortalityrate for bacteria (Mancini, 1978; Thomann and Mueller, 1997):

kb1 ¼ ð0:8þ 0:006PsÞ1:07T�20 ð21Þ

where Ps = percent seawater. A freshwater loss rate of 0.8 d�1 wasused in the present work ignoring the temperature correction fac-tor. The bacteria loss due to the effects of sunlight was modeledas (Thomann and Mueller, 1997):

kbi ¼ dI ð22Þ

where d = a proportionality constant, I = average light intensity(ly h�1). Based on earlier data, Thomann and Mueller (1997) con-cluded that d is approximately unity. In the vadose zone andgroundwater flow domains the bacteria loss due to solar radiationwas neglected.

The fate and transport of bacteria at the watershed-scale weremodeled using the above formulations for bacterial die-off com-bined with mechanistic routing methods in different domainsincluding overland flow, channel flow and the vadose zone. In whatfollows, we present a systematic evaluation of the transport mod-els in different domains before applying the bacterial fate andtransport model to the Red Cedar River watershed in Michigan.

3. Results and discussion

3.1. Comparison with analytical solutions

3.1.1. One-dimensional channel transportThe one-dimensional channel transport model was tested

against available analytical solutions within a single channelframework. The commonly used one-dimensional advection dis-persion equation with first order decay can be written as:

@Cr

@tþ v @Cr

@x� DL

@2Cr

@x2 þ kCr ¼ 0 ð23Þ

which is a simplified version of Eq. (5). The analytical solution forinitial and boundary conditions Cr(x, 0) = 0, Cr(0, t) = C0 and withconstant coefficients can be expressed as (O’Loughlin andBowmer, 1975; Chapra, 2008):

0

0.2

0.4

0.6

0.8

1 1800s Analytical1800s model3600s Analytical3600s model7200s Analytical7200s model

0

0.2

0.4

0.6

0.8

1

Con

cent

ratio

n (m

g/L)

0 2000 4000 6000 8000 10000

0

0.2

0.4

0.6

0.8

1

Channel Position (m)

(a) DL = 1.0E-8 m2/s

(b) DL = 30 m2/s

(c) DL = 100 m2/s

Fig. 1. Comparison between numerical and analytical results for 1-D channeltransport. (a) ‘Pure’ advection case with negligible longitudinal dispersion, (b)moderate dispersion with DL = 30 m2/s, and (c) large dispersion coefficient case(DL = 100 m2/s). The solid lines are the analytical results while the symbolsrepresent the numerical solution. Different colors represent solutions at differenttimes. (For interpretation of the references to color in this figure legend, the readeris referred to the web version of this article.)

40 J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48

Crðx;tÞ¼C0

2e

vx2DLð1�CÞerfc

x�vtC2ffiffiffiffiffiffiffiDLtp

� �þe

vx2DLð1þCÞerfc

xþvtC2ffiffiffiffiffiffiffiDLtp

� �� ð24Þ

where C ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 4g

p, g ¼ kDL

v2 .To test the model with the analytical solution given above, a

constant velocity of 1 m/s was prescribed in a 10-km-long channel.Initially, the solute concentration was assumed to be zero in thechannel. A constant unit concentration was then injected at theupstream boundary of the channel. Decay coefficient k was set tozero. We performed three different tests with three different dis-persion coefficients: DL = 1.0 � 10�8 m2/s for an essentially pureadvection case, DL = 30 m2/s and DL = 100 m2/s. The numericaland analytical solutions are compared in Fig. 1(a–c). It can be seenthat for the pure advection case the shape and position of the sharpfront are accurately captured by the numerical method at three dif-ferent times. The simulations based on the particle trackingscheme are almost free of numerical dispersion. For the second testcase with moderate dispersion, the simulated results are very closeto the analytical solution. In the third test case the dispersion coef-ficient is so high that the plume shows a large deviation from itscenter. Similar to the previous two test cases, an excellent agree-ment is obtained between the numerical and analytical solutions.

3.1.2. Two-dimensional overland flow transportFor this test case, we consider two-dimensional transport from

a line source in a unidirectional flow field assuming that the x- axisis aligned with the direction of the velocity (v), and that there areno reaction or source/sink terms. The simplified form of the gov-erning transport equation for this test case can be written as:

@Co

@t¼ Dx

@2Co

@x2 þ Dy@2Co

@y2 � v @Co

@xð25Þ

with the initial condition

Coðx; y;0Þ ¼ 0

and the following boundary conditions:

Coð0; y; tÞ ¼C0ðtÞ �y0 < y < y0

0 otherwise

�left boundary;

Coð1; y; tÞ ¼ 0 right boundary;Coðx;1; tÞ ¼ 0 upper boundary;and Coðx;�1; tÞ ¼ 0 lower boundary

The analytical solution is (Zheng and Bennett, 2002):

Coðx; y; tÞ ¼x

4ffiffiffiffiffiffiffiffiffipDxp

Z t

0C0ðt � nÞ 1

n3=2 exp �ðx� vnÞ2

4Dxn

" #

� erfcy� y0

2ffiffiffiffiffiffiffiffiDyn

p !

� erfcyþ y0

2ffiffiffiffiffiffiffiffiDyn

p !" #

dn ð26Þ

where C0ðtÞ ¼ Coðx ¼ 0; tÞ is the inflow concentration at the leftboundary within the patch extending from �y0 to y0.

The following coefficient values are used: v = 1 m/s, Dx = 1 m2/s,Dy = 0.1 m2/s and C0 = 1 g/mL. To compare the numerical and ana-lytical solutions, we plot the concentration profiles in two differentways: First, in Fig. 2a, the longitudinal concentration distributionof the normalized concentration (Co/C0) at different times (t = 10,20, 30 s) are shown from the center of the patch source (y = 0 m);Second, in Fig. 2b, we show the breakthrough curves at differentdownstream locations (d = 5, 10, 20 m) from the center of the patchsource (y = 0 m). At the downstream location d = 5 m, the concen-tration breakthrough curve reaches a plateau after a certain timesince we assume a constant concentration C0 at the source. Thesame trends are noted at different downstream locations(d = 10 m and d = 20 m), but the further the downstream location

from the patch source, the smaller the maximum concentrationand the later the equilibrium state reached due to the dispersionand travel time of the solute transport. Good overall agreementis noted between the numerical and analytical solutions. Fornon-adsorbed solutes, transport in the vadose zone follows thesimple ADE form if the soil moisture h and infiltration rate I areconstant. We compared the model results with an analytical solu-tion from van Genuchten and Alves (1982), also described inWarrick (2003). The equations and the results are available inNiu (2013).

3.1.3. Groundwater transit time simulationWe consider a vertical section through a saturated flow system

within an unconfined aquifer underlain by an impervious bound-ary (Chesnaux et al., 2005) as shown in Fig. 3. A uniform positiveinfiltration, W [LT�1], representing net recharge, is applied overthe entire upper boundary of the aquifer. The left-hand boundaryis impermeable and flow discharges through the right-handfixed-head boundary (hL). Flow is also assumed to be at steadystate, which implies that (1) the numerical model converges tothe state that (2) the downstream discharge equals the groundwater recharge and that (3) the water table position does not

0 5 10 15 20 25 30 35 40 45 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance (m)

Con

cent

ratio

n ( C

/C0

)

10s Analytical10s model20s Analytical20s model30s Analytical30s model

0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time (s)

5 m Analytical5 m model10m Analytical10m model20m Analytical20m model

(a)

(b)

Fig. 2. Comparison between numerical and analytical results for 2-D overland flowtransport at (a) different times and (b) different downstream locations. The solidlines with different colors show the analytical solutions at different times orlocations, while symbols with the same colors represent the correspondingnumerical solutions. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

hmax

yRecharge, W

qx = 0

0 xi Impermeable

hL

Lake, Riveror Drain

L x

Water Table

Fig. 3. Conceptual diagram for a test case from Chesnaux et al. (2005) involvinggroundwater transit time simulations between an arbitrary location xi and the exitboundary at x = L. Figure shows an unconfined aquifer receiving uniform recharge,an impermeable boundary on the left and a fixed-head boundary on the right.

J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48 41

change with time. The hydraulic head solution follows the Dupuit–Forchheimer ellipse (Bear, 1972). The analytical solution for thetravel time from an arbitrary point xi at the water table to the rightexit boundary is given by (Chesnaux et al., 2005):

tðxiÞ¼ne

ffiffiffiffiffiffiffiffiffik

KW

rL

ffiffiffiffiffiffiffiffiffiffiffiffiffi1L2�

1k

s�xi

ffiffiffiffiffiffiffiffiffiffiffiffiffi1x2

i

�1k

sþ ln

ffiffikp

xiþ

ffiffiffiffiffiffiffiffiffiffiffik

x2i�1

qffiffikp

L þffiffiffiffiffiffiffiffiffiffiffik

x2i�1

q0B@

1CA

264

375 ð27Þ

where ne is porosity, k ¼ L2 þ Kh2L=W , K is hydraulic conductivity

[LT�1] and L is the aquifer length [L]. For this test case, the 2Dgroundwater equation can be simplified as:

@

@xKxx

@h@x

� �þ @

@yKyy

@h@y

� �þW ¼ 0 ð28Þ

where Kxx and Kyy are the horizontal and vertical components of thehydraulic conductivity. To determine the travel time, we also makeuse of the stream function solution. Streamlines represented byconstant stream function are tangent to the velocity field. For a fluidparticle to travel a distance s within a stream tube defined bystream function interval Dw [L2T�1], following the stream functionsolution the transit time t can be calculated as:

t ¼ ne

Dw

Zs

DpðsÞds ð29Þ

where Dp is the width of the stream tube [L]. The integral in theabove equation is the area of the chosen stream tube along s. Thisarea was computed by interpolating the nodal stream function val-ues along the finite difference mesh. For this test case, the area inte-grations were computed based on a stream function interval of8 � 10�8 m2/s (equivalent to 100 stream tubes).

The travel time can also be computed by using the particletracking scheme in our model. We released particles at differentpositions along the water table. The particles will finally flow tothe right-hand exit boundary as shown in Fig. 3. We compare theanalytical solution (Eq. (27)), the numerical solution using streamfunction (Eq. (29)), and the numerical solution using particle track-ing scheme for one value of the hydraulic conductivity K in Fig. 4.Additional comparisons can be found in Niu (2013). The analyticalsolution matches the two numerical solutions well. This test caseshows that the particle tracking scheme can accurately estimategroundwater transit times and is even more accurate than thenumerical method derived from the commonly used stream func-tion method. Hence we conclude that the particle-tracking schemeis suitable for groundwater transport problems, especially withinteractions between the soil and the groundwater domains.

3.2. Plot-scale simulations of manure-borne fecal coliforms

For this test case described in Guber et al. (2009), the data werecollected from overland flow experiments with manure-bornefecal coliforms (FC) and the experiments were performed inOctober 2003 on a two-sided lysimeter 21.34 m long and 13.2 mwide located at the Patuxent Wildlife Research Refuge inBeltsville, MD. The slope of the lysimeter surface was 20%. Theaverage simulated rainfall rate measured was 5.8 ± 1.9 cm h�1

applied to the area. The manure slurry was uniformly applied ontop of the plots in a 30-cm-wide strip at the rate of 11.7 L m�2.Irrigation was started immediately after manure application.Rainfall was simulated for 1 h after the initiation of runoff.Runoff volume and fecal coliform concentrations were measuredat the bottom of the lysimeter. More details about the experimentcan be found in Guber et al. (2009). The hydrologic model was cal-ibrated by minimizing the root mean square error of the measuredand simulated accumulated runoff time series. The governingequations for overland transport and release of bacteria are pre-sented in Guber et al. (2009). The boundary condition of h = 0 atx = 0 was used for the overland flow, where h is the depth of

0

5

10

15

20

25(a) Transit time from water table to exit boundary ( K = 10−4m/s )

Trav

el T

ime

(yea

rs)

0

2

4

6

8

10

Elev

atio

n (m

)

(b) Streamfunction ( ∆ψ = 5×10 −7 m2 /s )

0 50 100 150 200 250 300 350 400 450 5000

2

4

6

8

10

Distance (m)

Elev

atio

n (m

)

(c) Velocity field

Numerical solution (Eq. 29)Analytical solution (Eq. 27)Numerical solution usingparticle tracking

Fig. 4. Comparison of numerical and analytical solutions for groundwater transit time simulations. (a) Results of two numerical approaches and an analytical solution, (b) thestream function solution, and (c) the velocity vectors.

42 J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48

ponding and x is distance measured along the slope. The Manningroughness coefficient n was set to 0.035. The best values of the sat-urated hydraulic conductivity (K), and other parameters in the vanGenuchten formulation related to the soil properties were esti-mated by fitting the simulated runoff to the experimental data.To calculate the concentration of released bacteria from manure(boundary condition for overland flow transport), an equation fromBradford and Schijven (2002) (Eq. (7) in Guber et al. (2009)) wasused together with parameters from Guber et al. (2006).Additional details can be found in Guber et al. (2009). The runoffsimulation result after calibration is shown in Fig. 5a. The perfor-mance of the calibrated transport model is shown in Fig. 5b.Flow and transport results are found to be in good agreement withobservations.

3.3. Modeling E. coli fate and transport in the Red Cedar Riverwatershed

The transport model was applied to simulate the fate and trans-port of E. coli in the Red Cedar River watershed (RCR). Although theterm solute is used in the title and throughout the paper, bacteriaare suspended particles. However, both dissolved and suspendedparticles can be adequately described using the advection–dispersion–reaction equation and its variants with similar sets of param-eters (Shen et al., 2008). Monitoring data for E. coli were obtainedfrom Michigan DEQ (Department of Environmental Quality) andobserved solar radiation data were used for the light-based bacte-rial die-off formula. The total area of the RCR watershed is

1169 km2 (Fig. 6). The watershed has a relatively low relief withthe maximum elevation recorded as 324 m and a minimum of249 m. 30 m resolution National Elevation dataset (NED) fromthe USGS was used for slope and surface runoff calculations.Land use and land cover (LULC) data were based on the 30 m res-olution IFMAP (Integrated Forest Monitoring Assessment andPrescription) datasets from the Michigan Department of NaturalResources (MDNR, 2010). Depending on the grid size, a cell maypossess a mixture of land use/land cover types in the PAWS model.LULC data were re-classified into model classes, which are repre-sented by several generic plant types (called the representativeor functional plant types). Meteorological data including precipita-tion, air temperature, relative humidity and wind speed wereobtained from several National Climatic Data center (NCDC,2010) and MAWN (Michigan Automated Weather Network)(Enviro-weather, 2010) stations within the watershed. The SoilSurvey Geographic (SSURGO) (Soil Survey Staff) database fromthe U.S. Department of Agriculture, Natural ResourcesConservation Service was used for soil classification and for calcu-lating the parameters associated with soil properties. The NationalHydrography dataset (NHD) from USGS was used for channel net-work and for routing and flow computations. The stream flow andgroundwater head data for comparison were obtained from a num-ber of USGS gaging stations within the watershed. Hydraulic con-ductivity data were obtained by processing the information inthe MDEQ Wellogic database for the groundwater model to esti-mate local hydraulic conductivities, groundwater heads and thick-nesses of the glacial drift layer. Spatial fields were obtained bykriging after removing noise in the data (Simard, 2007).

0

1

2

3

4

5

6C

umul

ativ

e R

unof

f (10

-2m

)(a) Runoff

SimulatedObserved

0 1/6 1/3 1/2 2/3 5/6 110−3

10−2

10−1

(b) Bacteria breakthrough

Time (hr)

C/C

0

Fig. 5. Comparison between model results and measured data from plot-scalerunoff experiments with manure-borne fecal coliform release (a) surface runoffresults and (b) concentration time series for manure-borne fecal coliforms. Solidlines represent the model simulation and symbols denote the field observations.

84˚30’0”W 84˚20’0”W 84˚10’0”W 84˚0’0”W

42˚40’0”N

42˚30’0”N

42˚20’0”N

WWTPE. coli monitoring sitesCAFONCDC Weather StationsUSGS GaugesNHD streamsRCR watershed

Elevation (m):326

249

0 2 4 8 12

km

Kubiak

Mar Jo Lo

MSU 12

34

N

Fig. 6. Map of the Red Cedar River watershed. Elevation is shown using the colormap. National Hydrography Dataset (NHD) streams, U.S. Geological Survey (USGS)gauges, National Climatic Data Center (NCDC) weather stations, Waste WaterTreatment Plants (WWTPs), Concentrated Animal Feeding Operation (CAFO) centersand E. coli monitoring sites are shown on the map. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthis article.)

Table 1Coordinates of the E. coli Monitoring sites and sources.

ID Description Latitude Longitude

Monitoringsites

1 Webberville-A 42.68 �84.172 Webberville-B 42.68 �84.193 Williamston 42.72 �84.524 East Lansing 42.73 �84.51

WWTPa East Lansing 42.73 �84.50Williamston 42.69 �84.29

CAFOb Kubiak Farm Primary Species:Diary

42.71 �84.17

Mar Jo LoFarm

Primary Species:Diary

42.63 �84.36

MSU Primary Species:Mixed

42.70 �84.48

a Waste Water Treatment Plant.b Concentrated Animal Feeding Operation Centers.

Table 2List of parameters used for the E. coli simulation.

Longitudinal dispersion coefficient, DL Deng et al. (2001)a

Freshwater loss rate, kb1 0.8 day�1

Coefficient of loss rate due to sunlight, d in Eq. (22) 1.0b in Eq. (19) 0.69 cm�1

a Empirical equations and data from Shen et al. (2010).

Date (mm/dd/yy)06/02/04 12/19/04 07/07/05 01/23/06 08/11/06

Dis

char

ge (c

ms)

0102030405060708090

100

ObservedSimulated

USGS 04112500 NSE = 0.7

Fig. 7. Comparison between observed (USGS) and PAWS-simulated stream flowsfor USGS Gage # 04112500 (Red Cedar River at East Lansing). NSE is the Nash–Sutcliffe model efficiency coefficient.

J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48 43

Numerous sources within the watershed contribute E. coli to theriver. While some sources are well characterized (discharge andconcentration reported as a function of time), no data were avail-able for many other sources. There are three concentrated animalfeeding operation (CAFO) centers located in the watershed thatare known sources of E. coli from livestock and two wastewatertreatment plants (WWTP) are located on the RCR that are consid-ered to be significant sources of E. coli to the river (Table 1).Therefore, instead of attempting to include all sources in this initialapplication of the transport model, we wanted to use the model totest the hypothesis that the CAFOs and WWTPs are the majorsources impacting bacterial levels within the RCR. AlthoughPAWS is an integrated hydrologic model, we did not have sufficientinformation about subsurface sources contributing E. coli withinthe watershed, therefore only overland and channel flows are con-sidered for simulating E. coli fate and transport with the assump-tion that overland transport is advection-dominated (Abbasiet al., 2003; Deng et al., 2005; Kim et al., 2013). However,

02/23/04 09/10/04 03/29/05 10/15/05 05/03/06 11/19/06 06/07/07

simobs

sim CAFO only

Date (mm/dd/yy)

100

101

102

103

104

105

106

Monitoring Station # 2RMSE = 0.59

Lo

g10

(E

. co

li )

(CF

U /

100

mL

)

Fig. 8. Comparison between model simulations and field observations for E. coli at monitoring site #2 in the Red Cedar River watershed.

1 For interpretation of color in Figs. 8 and 9, the reader is referred to the webversion of this article.

44 J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48

interactions among all domains including vadose zone and thegroundwater domain are taken into account while simulating thehydrology of the watershed. The parameters used in the E. colimodel are listed in Table 2. Based on the number and type of ani-mals in the CAFOs, the manure production and bacterial sheddingrates were estimated as described earlier. The reported animalmanure in the MSU CAFO is 9145 tons per year, while the esti-mated average and maximum amounts are 9460 and 10,814 tonsper year based on the animal types and numbers reported fromMSU CAFO, and the average daily manure production rate for eachanimal category from ASAE. The estimated and reported values are24,032 and 32,020 tons per year for the Kubiak CAFO respectively.The numbers are 14,496 and 5500 tons per year for the Mar Jo LoCAFO. The mismatches in the estimated and the reported manureamounts can be attributed to incorrect estimates for collectedmanure, unaccounted manure loss during the collection process,or inaccurate animal numbers reported. Also, according to ASAEdata, the standard deviation in the average daily manure produc-tion is quite large. The daily discharge and fecal coliform bacteriaconcentration time series data for East Lansing and WilliamstonWWTP were also provided as model inputs. For the WWTP onlyfecal coliform data were available (obtained from MDEQ), asE. coli were not measured. A ratio of 0.6 was used to calculatethe E. coli concentrations from fecal coliform measurements basedon literature values (Rasmussen and Ziegler, 2003). However, theratio is known to be highly variable introducing an additionalsource of uncertainty into the modeling. In addition to the CAFOsand WWTPs, we assumed that wildlife from different land use/landcovers contribute different background E. coli levels based on avail-able information in the literature. The assumed background levelsare 960, 5000, 440 and 2200 CFU/100 mL for forested, urban, rowcrop and forage crop land uses respectively (Ouattara et al., 2012).

In Fig. 6, the monitoring sites (triangles) and the USGS gauges(circles) are all on the Red Cedar River. The flow is from east towest. The monitoring site 1 near Webberville is the most upstreammonitoring site. We did not have any information about sourcesupstream of site 1 therefore a decision had to be made aboutapproximating the behavior of these unknown sources. We firstran the model to see if the background values associated with dif-ferent land uses alone can explain the observed data at site 1. Sincewe were unable to capture the upstream source effects using thebackground values for different LULC (figure not shown), theobserved time series data (at site 1) were used as an upstreamboundary condition in our simulations.

An 880 m � 880 m grid was used for the simulations asdescribed in Shen and Phanikumar (2010). PAWS uses adaptivetime stepping and has the ability to use different time steps for

different domains. A typical time step for surface flow componentsis about 10 min although this value can change dynamicallydepending on local conditions to maintain numerical stability. Acomparison between observed (USGS) and simulated streamflowsis first presented in Fig. 7. The observed streamflows are generallysimulated well by the model.

A comparison between observed and simulated E. coli concen-trations at monitoring sites 2–4 is shown in Figs. 8 and 9. In thesefigures the red lines are the simulation results using all sourcesincluding WWTP and CAFO inputs, the background values for dif-ferent LULC and the observed time series data at site 1 to capturethe upstream effects. The blue1 lines represent simulation resultsusing CAFO inputs as well as the background values for differentLULC (labeled as ‘‘CAFO only’’ in the figures). Since the monitoringsite 2 is immediately downstream of the site 1 (used as a boundarycondition), the simulations match well with observed data at site 2in Fig. 8. The difference between the red and blue lines in Fig. 8comes from the upstream E. coli concentrations that were includedin one simulation (red line) but not the other (blue lines). As wemove downstream, the signal becomes more complex and the com-parisons (especially, with the low background values of E. coli)become relatively worse (Fig. 9). In Figs. 8 and 9 the RMSE valuesare based on log-transformed concentrations. Since sites 3 and 4are far from the Kubiak CAFO, which has the largest reported annualmanure production, the simulated E. coli concentrations at these twosites were dominated by effluents from the East Lansing andWilliamston WWTPs. On the other hand, at site 2 which is close tothe Kubiak CAFO, most of the peaks were contributed by CAFOinputs (Fig. 8).

Closer examination of the comparisons in Fig. 9 (see panels b, c,e and f) shows that although the weekly sampling is not adequateto resolve all the peaks, the model was able to capture the peakswhere data are available. The log-RMSE values (that is, RMSE val-ues based on log-transformed concentrations) for the three moni-toring sites in Figs. 8 and 9 ranged from 0.59 to 1.00. These valuesare comparable to the numbers reported in the literature for E. colimodeling. For example, Desai et al. (2011) examined a number ofsources contributing to the observed E. coli in a 288-km2 urbanwatershed in Texas including sediment-associated bacteria. TheirHSPF model for E. coli fate and transport was calibrated for atwo-year period producing log-RMSE values in the range 0.67 to0.96. While distributed hydrologic models tend to perform wellin simulating watershed hydrology, the models have not met witha similar level of success in simulating the fate and transport of

02/23/04 09/10/04 03/29/05 10/15/05 05/03/06 11/19/06 06/07/07

Monitoring Station # 3. RMSE = 0.97

100

101

102

103

104

Lo

g10

(E

. co

li )

(CF

U /

100

mL

)

05/28/05 07/07/05 08/16/05 09/25/05 11/04/05

1000

2000

3000

4000

5000

6000

7000

04/28/07 06/07/07 07/17/07 08/26/07 10/05/07

2000

4000

6000

8000

10000

12000

14000

16000

E. c

oli

(CF

U /

100

mL

)

E. c

oli

(CF

U /

100

mL

)

Date (mm/dd/yy)

Date (mm/dd/yy)Date (mm/dd/yy)

simobssim CAFO only

02/23/04 09/10/04 03/29/05 10/15/05 05/03/06 11/19/06 06/07/07

Monitoring Station # 4. RMSE = 1.00

100

101

102

103

104

105

Lo

g10

(E

. co

li )

(CF

U /

100

mL

)

05/08/05 06/17/05 07/27/05 09/05/05 10/15/05

1000

2000

3000

4000

5000

05/03/06 06/22/06 08/11/06 09/30/06

0.5

1

1.5

2

2.5

3

3.5

x 104

E. c

oli (

CFU

/ 10

0 m

L)

E. c

oli (

CFU

/ 10

0 m

L)

Date (mm/dd/yy) Date (mm/dd/yy)

Date (mm/dd/yy)

(a)

(b) (c)

(d)

(e) (f)

Fig. 9. Comparison between model simulations and field observations for E. coli at monitoring sites #3 and #4 in the Red Cedar River watershed.

J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48 45

bacteria and pathogens at the watershed scale (Baffaut andSadeghi, 2010; Frey et al., 2013). Considering the uncertainties inthe modeling and the weekly sampling, we conclude that, overall,

a reasonable agreement was obtained between observations andmodel results. The model results also indicate that the CAFOsand the WWTPs are the primary sources impacting bacterial levels

46 J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48

within the river. As expected, the relative importance of CAFOs andWWTPs changed depending the sampling location. The back-ground concentrations of E. coli (values around and less than100) are difficult to simulate accurately as several sources (unac-counted for in the modeling) could potentially contribute to thesebackground values and their temporal variation. One of theassumptions in our modeling was that the primary transportmechanism for E. coli is overland transport and that channel flowbecomes important once bacteria enter the streams. However,the RCR watershed within and around the MSU campus has a net-work of pipes draining the landscape. Flow and transport withinthis network was not simulated in the modeling. Once flow entersthe pipe network, travel times are expected to be generally shorterand this effect can be seen in the timing associated with someE. coli peaks (see Fig. 9f). Haydon and Deletic (2006), who foundmismatches in the timing of their simulated E. coli peaks, indicatethat small errors in timing are generally of little consequence froma management perspective.

Finally a few words on the limitations of the current transportmodeling maybe appropriate. Consistent with the descriptions usedin the PAWS hydrology modules, lateral diffusion of soil moistureand the associated solute transport are assumed to be negligible.Therefore, in situations where lateral transport of contaminants inthe vadose zone is important, we can expect the PAWS transportmodule to introduce errors. Although the bacterial transport modeldescribed in this paper used mechanistic routing procedures, theprocesses of release of bacteria from the soil and their attachmentto and detachment from soil particles are extremely complex pro-cesses and large uncertainties are associated with them. Our futurework will attempt to further refine the modeling by usinghigh-resolution datasets based on daily/sub-daily sampling, param-eter sensitivity analyses and detailed source characterization.

4. Conclusions

A watershed-scale transport model based on a process-baseddistributed hydrologic model was developed. The model used anoperator-splitting strategy that combined a Lagrangian particletransport modeling approach for advection with an Eulerianapproach for dispersion and reactions. The transport model wastested using available analytical solutions and data fromplot-scale experiments. The coupled hydrologic/transport modelwas applied to the Red Cedar River watershed to simulate bacterial(E. coli) fate and transport. Standard manure production data andstatistical methods were used to estimate the release ofmanure-borne bacteria at the CAFO sites. The transport modelwas found to be useful in testing hypotheses related to the relativecontributions of various sources. Future papers will describe addi-tional model testing and extensions to the current transport mod-eling framework.

Acknowledgements

This project was funded by a NOAA Grant to the last author. Wethank Ruth Kline-Robach, Leroy Smith and Catherine Garnham forproviding the E. coli monitoring data and the fecal coliform dis-charge data from the wastewater treatment plant. We thankChaopeng Shen, Pennsylvania State University for his contributionsto this research and Andrey Guber, MSU for providing the data forthe plot-scale experiment.

Appendix A. Solution of the vadose zone transport equation

The vadose zone transport equation (Eq. (6)) can be expandedand rearranged as:

a@CS

@t¼ � @a

@tþ @I@zþ k

� �CS þ

@DS

@z� I

� �@CS

@zþ DS

@2CS

@z2 ðA1Þ

Using subscripts (i � 1, i, i + 1) to denote space and superscripts(n, n + 1) to denote old and new time levels, Eq. (A1) is discretizedas shown below:

aCnþ1

Si� Cn

Si

Dt¼ � @a

@tþ @I@zþ k

� �Cnþ1

Siþ @DS

@z� I

� �Cnþ1Siþ1� Cnþ1

Si�1

2Dz

þ DS

Cnþ1Siþ1� 2Cnþ1

Siþ Cnþ1

Si�1

Dz2 ðA2Þ

Let A0 ¼ aDt

, B0 ¼ � @a@tþ @I@zþ k

� �, C0 ¼

ð@DS@z � IÞ2Dz

, D0 ¼ DS

Dz2,

then Eq. (A2) can be written as:

ð�C0 þ D0ÞCsnþ1i�1 þ ð�A0 þ B0 � 2D0ÞCsnþ1

i þ ðC 0 þ D0ÞCsnþ1iþ1 ¼ �A0Csn

i

ðA3Þ

The coefficients of the unknown concentrations on the left handside of Eq. (A3) are in the tridiagonal matrix form, which is solvedusing the Thomas algorithm (Press et al., 2007). The term @a

@t in coef-ficient B0 is calculated as:

@a@t¼ @ðqbkP þ hÞ

@t¼ @h@t¼ hnþ1

i � hni

DtðA4Þ

The term @DS@z in coefficients C0 is calculated as:

@DS

@z¼ @ða

0jtjc þ D0SÞ@z

ðA5Þ

Note that D0S ¼ D0aebh and a0 is constant (Ahuja, 1990; Bear andBachmat, 1990; Bresler, 1973) thus Eq. (A5) is calculated as:

@DS

@z¼ a0

@jtjc

@zþ D0abebh @h

@z

¼ a0jtnþ1

iþ1 jc � jtnþ1

i�1 jc

2Dzþ D0abðebÞh

nþ1i

hnþ1iþ1 � hnþ1

i�1

2DzðA6Þ

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