Journal of Hydrology 529 (2015) 35–48
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Journal of Hydrology
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Modeling watershed-scale solute transport using an integrated, process-based hydrologic model with applications to bacterial fate and transport ⇑ Jie Niu a,b, Mantha S. Phanikumar a, a Department of Civil & Environmental Engineering, Michigan State University, East Lansing, MI, United States b Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, United States article info summary
Article history: Distributed hydrologic models that simulate fate and transport processes at sub-daily timescales are use- Received 1 January 2015 ful tools for estimating pollutant loads exported from watersheds to lakes and oceans downstream. There Received in revised form 4 July 2015 has been considerable interest in the application of integrated process-based hydrologic models in recent Accepted 7 July 2015 years. While the models have been applied to address questions of water quantity and to better under- Available online 11 July 2015 stand linkages between hydrology and land surface processes, routine applications of these models to This manuscript was handled by Geoff Syme, Editor-in-Chief, with the assistance of address water quality issues are currently limited. In this paper, we first describe a general John W. Nicklow, Associate Editor process-based watershed-scale solute transport modeling framework, based on an operator splitting strategy and a Lagrangian particle transport method combined with dispersion and reactions. The trans- Keywords: port and the hydrologic modules are tightly coupled and the interactions among different hydrologic Solute transport components are explicitly modeled. We test transport modules using data from plot-scale experiments Particle tracking and available analytical solutions for different hydrologic domains. The numerical solutions are also com- Distributed hydrologic models pared with an analytical solution for groundwater transit times with interactions between surface and Surface–subsurface coupling subsurface flows. Finally, we demonstrate the application of the model to simulate bacterial fate and Bacterial transport transport in the Red Cedar River watershed in Michigan and test hypotheses about sources and transport Groundwater–surface water interactions pathways. The watershed bacterial fate and transport model is expected to be useful for making near real-time predictions at marine and freshwater beaches. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction insights into the fundamental transport processes at the watershed scale. A number of such watershed models have been developed in The ability to quantify fluxes of nutrients, bacteria, viruses and the last few decades including, for example, CATHY (Weill et al., other contaminants exported from watersheds to downstream 2011), InHM (VanderKwaak, 1999), OpenGeoSys (Kolditz et al., receiving water bodies such as lakes and oceans is important for 2012), ParFlow (Kollet and Maxwell, 2006), PAWS (Shen and managing coastal resources (e.g., to generate timely predictions Phanikumar, 2010), tRIBS (Ivanov et al., 2004) and Wash123 (Yeh of water quality for beach closures, e.g., Ge et al., 2012a,b) and to et al., 2011). Although a majority of these models have the ability understand and assess threats to human and ecosystem health. to simulate transport processes, the routine application of In the Great Lakes region of North America, for example, increased process-based hydrologic models to address water quality issues beach closures due to microbiological pollution, eutrophication is currently still limited. and harmful algal blooms and drinking water related issues con- The assessment and management of non-point sources of pollu- tinue to be causes for concern highlighting the need for tion (e.g., microbial pollution) is an issue of great interest. well-tested and reliable transport models. Integrated Escherichia coli (E. coli) is a commonly used fecal indicator organ- process-based hydrologic models, which are based on the conser- ism in freshwaters. Prior research has shown that E. coli densities vation principles of mass, momentum and energy, are useful tools are correlated with swimming-associated gastroenteritis (Prüss, for making accurate predictions and have the potential to offer 1998). Models such as MWASTE (Moore et al., 1989), COLI (Walker et al., 1990) and SEDMOD (Fraser et al., 1998) have been developed to simulate landscape microbial pollution processes. ⇑ Corresponding author. These models successfully simulate the manure-borne bacteria E-mail addresses: [email protected] (J. Niu), [email protected] (M.S. Phanikumar). http://dx.doi.org/10.1016/j.jhydrol.2015.07.013 0022-1694/Ó 2015 Elsevier B.V. All rights reserved. 36 J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48 releasing process and the transport of bacteria through runoff; equation for overland flow can be expressed in a conservative form however, the die-off due to solar radiation and other environmen- in terms of the solute flux (Deng et al., 2006) as: tal factors was not considered, and there was no interaction among @ðCohÞ @ðCouhÞ @ðCovhÞ @ @Co @ @Co different hydrologic components in these models. There are mod- þ þ ¼ hDx þ hDy els incorporating both landscape and in-stream microbial pro- @t @x @y @x @x @y @y cesses, for example, the Soil and Water Assessment Tool (SWAT) þ rDmðCs CoÞ kCoh ð2Þ (Frey et al., 2013), a watershed model developed by Tian et al. (2002), a modified SWAT model (Cho et al., 2012), which consid- where the subscript o denotes overland flow, Co is the 3 ered solar radiation associated bacterial die-off, and a coastal cross-sectionally averaged solute concentration [ML ] or the mass watershed fecal coliform fate and transport model based on HSPF of solute per unit volume of runoff; CS represents the solute concen- 1 (Hydrologic Simulation Program Fortran, Rolle et al., 2012). These tration in the soil mixing zone; r is a mass transfer coefficient [T ]; models tend to use conceptual representations of the groundwater Dm is the mixing zone thickness [L] which is proportional to flow 1 and vadose zone compartments, ignoring the complexity of the depth; k is the decay coefficient [T ]; Dx and Dy are the x- and 2 1 flow in the subsurface domain. The subsurface flow is an integral y-direction diffusion coefficients [L T ]. Eq. (2) can be fully component of the hydrologic cycle and in shallow water table con- expanded and rearranged as below: ditions groundwater controls soil moisture and provides sources of @h @ðuhÞ @ðvhÞ @Co @Co @Co Co þ þ þ h þ u þ v water for evapotranspiration (ET) (Shen and Phanikumar, 2010). @t @x @y @t @x @y Therefore, the subsurface flow domain should be fully considered ! 2 2 while developing a general framework for the solute transport @ Co @ Co @h @Co @h @Co ¼ hDx þ Dy þ Dx þ Dy problem even if the subsurface contribution is not important for @x2 @y2 @x @x @y @y certain types of pollutants. þ rDmðCs CoÞ kCoh ð3Þ A process-based, watershed-scale reactive transport modeling framework is developed in this work to quantify the fluxes of con- Using the kinematic wave approximation which ignores the servative and reactive solutes exported from watersheds. The dis- pressure gradient terms, we have oh/ox = 0 and oh/oy =0. tributed hydrologic model PAWS (Process-based Adaptive Substituting Eqs. (1) into (3) and dividing both sides of the above equation by the flow depth h gives the following equation: Watershed Simulator, Shen and Phanikumar, 2010; Shen et al., 2013; Niu et al., 2014) was used to simulate integrated hydrology, 2 2 @Co @Co @Co @ Co @ Co rDm S þ u þ v ¼ Dx þ Dy þ ðCs CoÞ þ k Co including flows in channel networks, overland flow, and subsurface @t @x @y @x2 @y2 h h flows and interactions between different domains. The computa- ð4Þ tional efficiency of the PAWS model allows for long-term, large-scale simulations and makes it possible to simulate transport in large watersheds. An operator-splitting strategy (e.g., 2.2. Channel flow, the river network and river junctions Phanikumar and McGuire, 2004) combined with a Lagrangian par- ticle transport modeling approach (e.g., de Rooij et al., 2013) with The one-dimensional channel transport equation used in the reactions to describe transport in different hydrologic units was present work appears as shown below (see, for example, Gunduz, applied. Due to the complexity of the processes involved, extensive 2004): model testing against analytical solutions for different hydrologic domains is a necessary first step before the performance of the @ðCrAÞ @ @ @Cr þ ðvACrÞ ADL þ kCrA qLCL integrated model can be fully evaluated. Such detailed testing pro- @t @x @x @x vides a way to ascertain the sources of error when model Cg Cr þ nsedDsed wr qoCo ¼ 0 ð5Þ inter-comparison exercises are conducted (e.g., Maxwell et al., mr 2014). In the present paper, the algorithms were tested using avail- able analytical solutions and data from plot-scale experiments where Cr is the solute concentration within the river channel, CL and before applying the bacterial fate and transport model to describe Co are concentrations associated with lateral seepage and overland monitoring data from the Red Cedar River watershed in the Great flows respectively, qL and qo are lateral seepage and overland flows per channel length [L3T 1L 1] (considered positive for inflow), A is Lakes region. Future papers will describe additional model testing 2 (especially interactions between the groundwater and surface the cross-sectional flow area [L ], DL is the longitudinal dispersion 2 1 water domains) as well as the development and application of coefficient in the channel [L T ], Dsed is vertical dispersion coeffi- 2 1 additional transport modules (e.g., carbon, nitrogen and phospho- cient [L T ] in the sediment layer, nsed is porosity of the sediment rus cycles). layer (dimensionless), Cg is solute concentration associated with groundwater flow, mr is thickness of the sediment layer [L], and wr is river wetted perimeter [L]. 2. Methods Initial solute concentrations need to be specified along the
one-dimensional channel domain: Cr(x,0)=Cr0(x), where Cr0 is 2.1. 2D overland flow transport the initial concentration distribution along the channel network. Concentration boundary conditions in the form of Dirichlet, A commonly accepted approximation of the St. Venant equa- Neumann or mixed type can be specified at the external ends of tions for overland flow is the kinematic wave equation (Singh, the domain depending on whether a specified concentration or dif- 1996) which can be expressed as: fusional or total mass flux is being specified. @h @ðuhÞ @ðvhÞ In addition, internal boundary conditions may need to be spec- þ þ ¼ S ð1Þ @t @x @y ified when two or more channels join to form a junction. While handling river junctions, the change in mass storage within a junc- where h is the overland flow water depth [L], u, v are the x- and tion is assumed to be negligible compared to the change in mass y-direction water velocities [LT 1], S is either a source term to rep- within the channel. Furthermore, the continuity of concentration resent precipitation or exfiltration from the subsurface, or a sink at junctions guarantees that all the concentrations must be equal term to represent infiltration or evaporation. The solute transport at 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 later vxvy Dxy ¼ Dyx ¼ðaL aT Þ ð11Þ section, and an implicit step is used for dispersion and reactions. jvj The details of this operator splitting method including the method 2 2 of characteristics used for handling the river junctions are available vy v D ¼ a þ a x ð12Þ in Gunduz (2004). yy L jvj T jvj
2.3. Transport in the vadose zone aL is the longitudinal dispersivity, aT is the transverseqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dispersivity, 2 2 qx |v| is the magnitude of the seepage velocity, v ¼ vx þ vy , vx ¼ h
Solute transport within the soil profile below the land surface is qy and vy ¼ . The general source/sink term qsCs can represent solute controlled by both infiltration and diffusion. In PAWS, the h exchange between soil vadose zone and the first layer of the one-dimensional Richards equation is used to describe soil mois- groundwater, the solute exchange with groundwater at the bed of ture in the vadose zone and lateral moisture diffusion is ignored. river channels, or solute exchange between confined and uncon- Consistent with this description, the vertical transport of a linearly fined aquifers. More layers can be added to the current model sorbing solute was modeled by the following 1D advection–disper framework to simulate (quasi-) 3D groundwater transport. sion-reaction equation (e.g., Dong and Wang, 2013; van Genuchten and Wagenet, 1989): 2.5. Particle tracking scheme and mass balance @aCs @ @Cs ¼ Ds ICs kCs ð6Þ @t @z @z Most numerical methods for solving the advection–dispersion where z is the vertical coordinate [L], CS is the solute concentration equation can be classified as Eulerian, Lagrangian, or mixed in the soil water below the mixing layer, a = qbkp + h (dimension- Eulerian–Lagrangian (Neuman, 1984). Eulerian methods offer the 3 less), qb is the dry soil bulk density [ML ], and kp is a partition coef- advantage and convenience of a fixed grid, are generally mass con- ficient [L3M 1]. For non-adsorbing chemicals, a is equal to the soil servative, and handle dispersion-dominated problems accurately moisture h [L3L 3]. I denotes the infiltration rate [LT 1] in the soil, and efficiently. However, for advection-dominated problems that 2 1 DS is the dispersion coefficient [L T ] in the soil and is taken as exist in many natural systems, an Eulerian method is susceptible the sum of the effective molecular diffusion coefficient and the to excessive numerical dispersion or artificial oscillations mechanical dispersion coefficient (Ahuja, 1990; Bear and Bachmat, (Anderson and Cherry, 1979; Pinder and Gray, 1977). Lagrangian 1990; Bresler, 1973). methods, on the other hand, provide an accurate and efficient solu- tion to advection-dominated problems by essentially eliminating 0 c 0 Ds ¼ a jvj þ D s 7 false numerical dispersion (Tompson and Gelhar, 1990). 0 bh ð Þ Ds ¼ D0ae However, the velocity interpolation needed in particle tracking can also result in local mass-balance errors (LaBolle et al., 1996). where a and b are empirical coefficients, with typical values of When Eulerian methods are used, the time-step restriction associ- a = 0.005, b =10(Olson and Kemper, 1961). D is the diffusion coef- 0 ated with the advection step tends to be fairly restrictive. This lim- ficient of the solute in free water, c is a constant (equal to unity), v is itation can be overcome using a Lagrangian method; therefore we the velocity in soil pores, and a0 is the dispersivity parameter [L]. used a Lagrangian method for the advection step in this work since The initial condition of Eq. (6) is: our primary interest is in solute transport in large watersheds. The Csðz; 0Þ¼Cs0 ð8Þ details of the particle tracking method can be found in (Zheng and Bennett, 2002). A fourth-order Runge–Kutta method was used in where CS0 is the solute concentration in the soil when rainfall the present work. begins. Transport in the vadose zone is treated differently from transport in other hydrologic domains and the derivation and dis- 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 (Zheng cretization of the vadose zone transport equation are presented in and Bennett, 2002): Appendix A.
XNPm
2.4. Transport in the groundwater domain CmðtÞ¼ f p ð13Þ p¼1
A general two-dimensional solute transport equation for the 3 where fp is the mass fraction [ML ] represented by the pth particle. fully saturated groundwater domain, considering advection, dis- Transport equations for all hydrologic domains, with the excep- persion, fluid sinks/sources is as follows (Zheng and Bennett, tion of the vadose zone, used the mixed Eulerian–Lagrangian 2002): method. To combine the advantages of both classes of methods, a @Cg @ @ Lagrangian (particle tracking) solution of the advection equation hR þ qxCg þ ðqyCg Þ @t @x @y was combined with solutions of the dispersion and reaction equa- @ @C @ @C @ @C tions based on the Eulerian approach. The diffusion term was dis- ¼ hD g þ hD g þ hD g xx xy yy cretized using the central differencing scheme and solved @x @x @x @y @y @y @ @C implicitly using the Generalized Conjugate Gradient method þ hD g q C kC ð9Þ @y yx @x s s g (Zheng and Bennett, 2002). Some commonly used mixed Eulerian–Lagrangian procedures, such as the method of character- where R is the retardation factor (dimensionless); C is the dissolved g istics (MOC), do not guarantee mass conservation. Many mixed concentration; q and q are Darcy velocities [LT 1]; q is flow rate of x y s Eulerian–Lagrangian methods may be generally characterized as a fluid source or sink per unit aquifer volume [T 1]; C is the concen- s the forward-tracking MOC, the backward-tracking modified MOC tration associated with a fluid source or sink and h is porosity (MMOC) and a combination of these two methods which tracks (dimensionless). D , D , D , D are the elements of the dispersion xx xy yy yx mass associated with fluid volumes to conserve mass locally and tensor [L2T 1] described below: globally, depending on the use of different Lagrangian techniques 2 2 to approximate the advection term. The comparisons between v vy D ¼ a x þ a ð10Þ xx L jvj T jvj numerical 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- the overland flow domain to the river cell as M and noting that cate that the numerical schemes used in our current model frame- Mim denotes the exchange from the river to the land, the exchange work conserve mass very well. of solutes can be simply calculated as: We used dynamic particle allocation based on the plume loca- M tion and the evolution of the concentration field with time as this q C ¼ C ; from land to channel ð14Þ o o L o method uses less number of particles and increases the efficiency c of the MOC with little loss of accuracy. The MOC has the advantage or that it is almost free of numerical dispersion. However, MOC is not Mim computationally efficient, especially when a large number of mov- q Co ¼ Cr; from channel to land ð15Þ o L ing particles need to be tracked. Unlike the MOC which tracks a c large number of moving particles as well as associated concentra- where Lc is the length of the channel segment that overlaps with the tion and position of each particle forward in time, MMOC is more land cell [L]. computationally efficient and much less memory-intensive because (1) the MMOC places only one particle at the nodal point 2.6.2. Interaction between the land surface and the vadose zone of the fixed grid at each new time level; (2) the particle is tracked A mass balance equation for the surface ponding layer is solved backward to find its position at the old time level; and (3) the con- simultaneously with the soil water pressure head as described in centration associated with that position is used to approximate the Shen and Phanikumar (2010). The solute in the ponded water on concentration at the intermediate time level. land surface can percolate through the soil column by infiltration The MOC solves the advection term using the moving particles and/or diffusion. The coupling of solute transport between over- dynamically distributed around each cell when sharp concentra- land flow and soil water in the vadose zone is simulated via a tion fronts are present, while away from such fronts the advection boundary condition, which at the underlying soil surface for Eq. term is solved by an MMOC technique. In this adaptive procedure (6) is related to two stages during rainfall–runoff (Dong and the MOC and the MMOC are combined, which can provide accurate Wang, 2013): solutions with virtually no numerical dispersion by selecting an d½hð0; tÞC ðtÞ Jð0; tÞ IC ð0; tÞ appropriate criterion for controlling the switch between the MOC o ¼ s 0 t t dt D P and MMOC schemes. In the present work a combination of MOC m ð16Þ and MMOC methods (called the Hybrid MOC or HMOC, Zheng d½hð0; tÞCoðtÞ Jð0; tÞ ICsð0; tÞþICoðtÞ ¼ tP t and Bennett, 2002) was used. dt Dm
where t is the time [T] from the start of rainfall to when runoff 2.6. Interactions among domains P takes place, Co is the solute concentration in the runoff on top of the soil column, C is the solute concentration in the soil water The fluxes in one domain are connected to those in other S below the mixing layer, D is the mixing zone thickness, h is soil domains in a fully integrated hydrologic system. The flow coupling m moisture, and J is the diffusion flux of the solute from the soil below was described in Shen and Phanikumar (2010), and in this section the mixing layer, which is described by Fick’s law: we describe the coupling schemes used for the transport equations across different domains. @C J ¼ D s ð17Þ s @z 2.6.1. Interaction between the land surface and channel The exchange volumes between the land and the channel are computed using the framework for a wide rectangular weir and 2.6.3. Interaction between the vadose zone and groundwater details are described in Shen and Phanikumar (2010). The logic PAWS uses a coupling scheme to reduce the fully for computing the direction (land to channel or vice versa) and three-dimensional Richards equation for the unsaturated vadose magnitude of exchange volumes is summarized in Fig. 5 in Shen zone to a series of one dimensional equations for soil columns with and Phanikumar (2010). Briefly, if the flow is from the land to the unconfined aquifer underneath. The coupling between vadose the river cell and there is water on the land, we compute the zone and the groundwater domain is via the source/sink term qSCS in Eq. (9), where CS is the solute concentration in the bottom exchange (Mex) explicitly using the diffusive wave equation. This volume, however, cannot exceed the amount of water currently cell of the soil column linked to the unconfined aquifer and qS is the recharge rate calculated in PAWS using an iterative scheme. available on the land cell and this provides an upper bound (Ma). In addition, we can identify an equilibrium state in which the river When qS < 0, the value of CS becomes the same as the solute con- stage is equal to the land free surface elevation. The exchange vol- centration in the unconfined aquifer, Cg, and the term qSCg will be added to the right hand side of the solute transport equation ume (ME) that leads to this equilibrium state can be computed based on the current channel stage and the equilibrium stage when in the vadose zone (Eq. (6)). the channel stage and land surface elevations are equal. Thus the exchange mass will be the minimum among these three volumes 2.6.4. Interaction between groundwater and channel The seepage flux between the groundwater domain and the (Mex, Ma, ME). A fourth condition corresponds to flooding, which would occur if the river stage rises above the land free surface ele- river channel, qL in the 1D channel flow Eq. (5), is accumulated vation (and also the bank elevation, condition 3 in Shen and as groundwater contribution (to the channel) and subtracted from Phanikumar (2010)). The exchange volume corresponding to this the source/sink term in the groundwater flow equation in PAWS using the conductance/leakance concept and solved by an operator case (Mim) is computed using the diffusive wave formulation and by solving two ordinary differential equations presented in Shen splitting method (Gunduz and Aral, 2005; Shen and Phanikumar, and Phanikumar (2010). To enhance stability, a backward Euler 2010). Then the associated solute concentration in the seepage term is: implicit approach is used to solve for the exchange mass Mim. Once the direction and magnitude of exchange volumes are Cr; q < 0 determined, it is fairly straightforward to compute the exchange C ¼ L ð18Þ L C ; q > 0 mass of solutes. Denoting the exchange volume of water from g L 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- (Bicknell et al., 1997). The release of microorganisms depends on tion of the seepage flux such that when the groundwater head is the time of runoff yield, the processes of which are more complex larger than the river stage, the seepage is positive and flows from than the model descriptions of linear or exponential release (Guber the groundwater toward the river channel via the river bed, and et al., 2006). However, they were successfully simulated with two the value takes the associated concentration coming from the models according to Vadas et al. (2004) and Bradford and Schijven groundwater (i.e., Cg) and vice versa. (2002). The exponential release model of HSPF (Bicknell et al., 1997) was used in the current work: 2.7. Parameter estimation
DMR ¼ MS½1 expð bDQÞ ð19Þ A few parameters with uncertainty were estimated in the plot-scale transport simulations and to simulate the hydrology of where DMR is the count of bacteria (CFU) released during a time the watershed. The calibration parameters for hydrology, described interval Dt during the runoff event; MS is the count of bacteria in Shen et al. (2013), included hydraulic conductivities, the van (CFU) in the manure storage layer of soil at the beginning of the Genuchten soil parameters, river bed leakances etc. The parameter interval Dt; DQ is the runoff yield [L] during the interval; b is the optimization followed the procedure described in Niu et al. (2014) release rate parameter [L 1] (see Table 2). which involved minimizing an objective function that included The total loss rate for bacteria is represented as (Chapra, 2008): contributions from both surface water and groundwater domains.
For the plot-scale transport simulation (reported in Section 3.2), k ¼ kb1 þ kbi þ kbs ð20Þ seven parameters are estimated, including the parameters in the van Genucheten formulation (Eq. (18) in Shen and Phanikumar, 1 1 where k is the total loss rate (d ), kb1 = base mortality rate (d ), 2010), saturated and residual soil moistures, initial water table 1 kbi = loss rate due to solar radiation (d ), kbs = settling loss rate depth and saturated soil conductivity, by minimizing the root (d 1) (not considered in the present study). There is no confusion mean square error of simulated and measured accumulated runoff. between the total loss rate k for bacteria in Eq. (20) and the symbol The parameter optimization code used for this case is the Shuffled k which is also used to denote a general reaction rate (loss or gain Complex Evolution algorithm (Duan et al., 1992), which was mod- term) in the transport equations for different domains. If the equa- ified to run on multiple cores in parallel. For the watershed-scale tions are written for E. coli, then k denotes an E. coli loss rate. transport simulation (Section 3.3), all parameters used were based The following equation was used to calculate a base mortality on literature values and no parameter estimation was conducted. rate for bacteria (Mancini, 1978; Thomann and Mueller, 1997):
T 20 2.8. Application: Microorganism release and loss rate kb1 ¼ð0:8 þ 0:006PsÞ1:07 ð21Þ
1 where Ps = percent seawater. A freshwater loss rate of 0.8 d was One of the major sources of bacteria is animal manure used in the present work ignoring the temperature correction fac- (Jamieson et al., 2004). In watersheds where Concentrated tor. The bacteria loss due to the effects of sunlight was modeled Animal Feeding Operation (CAFO) centers are located, it is impor- as (Thomann and Mueller, 1997): tant to quantify the production rate of bacteria associated with ani- mal manure (Dorner et al., 2006). Manure production rates for kbi ¼ dI ð22Þ different animal categories are available as standard data (American Society of Agricultural Engineers; ASAE Standards, where d = a proportionality constant, I = average light intensity 1 2003). To estimate the bacteria shedding intensity in log number (ly h ). Based on earlier data, Thomann and Mueller (1997) con- of bacteria per gram of fresh manure, the daily manure production cluded that d is approximately unity. In the vadose zone and rate was first generated randomly following a normal distribution groundwater flow domains the bacteria loss due to solar radiation (with mean and variance for a given animal category from the was neglected. ASAE data). The E. coli load was then directly estimated by multi- The fate and transport of bacteria at the watershed-scale were plying the manure production rate by standard mean fecal coliform modeled using the above formulations for bacterial die-off com- shedding numbers (also from ASAE and using a factor to convert bined with mechanistic routing methods in different domains fecal coliform numbers to E. coli). Then given the number of ani- including overland flow, channel flow and the vadose zone. In what mals in the CAFO/region, using daily manure production rates, follows, we present a systematic evaluation of the transport mod- the daily bacteria production was calculated by summing the num- els in different domains before applying the bacterial fate and ber of bacteria shed by all animals in a given category. The total transport model to the Red Cedar River watershed in Michigan. daily bacteria production rate was obtained by summing the daily bacteria production from all individual animal categories. 3. Results and discussion Significant uncertainty is associated with confined animal feed- ing operations including the storage and application of manure on 3.1. Comparison with analytical solutions land. Technical guidelines (e.g., EPA, 2012) to minimize the chances of runoff are usually followed for land application of man- 3.1.1. One-dimensional channel transport ure and these guidelines were implemented in our modeling. In The one-dimensional channel transport model was tested Michigan, CAFO waste is not applied during rain events, when land against available analytical solutions within a single channel is flooded, saturated, or frozen or rainfall exceeding 0.5 in. is fore- framework. The commonly used one-dimensional advection dis- casted. In addition to the EPA guidelines and based on available persion equation with first order decay can be written as: information, we also assumed that manure is applied only during @C @C @2C the growing season and that only 2/3 of the manure generated is r r r þ v DL 2 þ kCr ¼ 0 ð23Þ applied on land and that the remaining 1/3 is composted (and @t @x @x not applied). which is a simplified version of Eq. (5). The analytical solution for
To simulate the release of manure-borne microorganisms the initial and boundary conditions Cr(x,0)=0,Cr(0, t)=C0 and with assumptions of the linear or exponential release are frequently constant coefficients can be expressed as (O’Loughlin and used in watershed scale models such as SWAT and HSPF Bowmer, 1975; Chapra, 2008): 40 J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48 C vx 1 C x tC vx 1 C xþ tC 2 0 2D ð Þ v 2D ð þ Þ v (a) D = 1.0E-8 m /s Crðx;tÞ¼ e L erfc pffiffiffiffiffiffiffi þ e L erfc pffiffiffiffiffiffiffi ð24Þ L 2 2 DLt 2 DLt pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1800s Analytical where C ¼ 1 þ 4g, g ¼ kDL. 1800s model v2 0.8 3600s Analytical To test the model with the analytical solution given above, a 3600s model constant velocity of 1 m/s was prescribed in a 10-km-long channel. 0.6 7200s Analytical 7200s model Initially, the solute concentration was assumed to be zero in the 0.4 channel. A constant unit concentration was then injected at the 0.2 upstream boundary of the channel. Decay coefficient k was set to zero. We performed three different tests with three different dis- 0 8 2 persion coefficients: DL = 1.0 10 m /s for an essentially pure 2 2 (b) D = 30 m2/s advection case, DL =30m /s and DL = 100 m /s. The numerical L and analytical solutions are compared in Fig. 1(a–c). It can be seen 1 that for the pure advection case the shape and position of the sharp front are accurately captured by the numerical method at three dif- 0.8 ferent times. The simulations based on the particle tracking 0.6 scheme are almost free of numerical dispersion. For the second test case with moderate dispersion, the simulated results are very close 0.4 to the analytical solution. In the third test case the dispersion coef- ficient is so high that the plume shows a large deviation from its 0.2 Concentration (mg/L) center. Similar to the previous two test cases, an excellent agree- 0 ment is obtained between the numerical and analytical solutions. (c) D = 100 m2/s L 3.1.2. Two-dimensional overland flow transport For this test case, we consider two-dimensional transport from 1 a line source in a unidirectional flow field assuming that the x- axis 0.8 is aligned with the direction of the velocity (v), and that there are no reaction or source/sink terms. The simplified form of the gov- 0.6 erning transport equation for this test case can be written as: 0.4 2 2 @Co @ Co @ Co @Co ¼ Dx þ Dy v ð25Þ 0.2 @t @x2 @y2 @x 0 with the initial condition 0 2000 4000 6000 8000 10000 Coðx; y; 0Þ¼0 Channel Position (m) and the following boundary conditions: Fig. 1. Comparison between numerical and analytical results for 1-D channel C0ðtÞ y0 < y < y0 transport. (a) ‘Pure’ advection case with negligible longitudinal dispersion, (b) Coð0; y; tÞ¼ left boundary; 2 moderate dispersion with DL =30m /s, and (c) large dispersion coefficient case 0 otherwise 2 (DL = 100 m /s). The solid lines are the analytical results while the symbols Coð1; y; tÞ¼0 right boundary; represent the numerical solution. Different colors represent solutions at different times. (For interpretation of the references to color in this figure legend, the reader Coðx; 1; tÞ¼0 upper boundary; is referred to the web version of this article.) and Coðx; 1; tÞ¼0 lower boundary
The analytical solution is (Zheng and Bennett, 2002): from the patch source, the smaller the maximum concentration Z "# t 2 and the later the equilibrium state reached due to the dispersion xffiffiffiffiffiffiffiffiffi 1 ðx vnÞ Coðx; y; tÞ¼ p C0ðt nÞ 3=2 exp and travel time of the solute transport. Good overall agreement 4 pD 0 n 4Dxn "#x ! ! is noted between the numerical and analytical solutions. For y y y þ y non-adsorbed solutes, transport in the vadose zone follows the erfc pffiffiffiffiffiffiffiffi0 erfc pffiffiffiffiffiffiffiffi0 dn 26 ð Þ simple ADE form if the soil moisture h and infiltration rate I are 2 Dyn 2 Dyn constant. We compared the model results with an analytical solu- where C0ðtÞ¼Coðx ¼ 0; tÞ is the inflow concentration at the left tion from van Genuchten and Alves (1982), also described in boundary within the patch extending from y0 to y0. Warrick (2003). The equations and the results are available in 2 The following coefficient values are used: v = 1 m/s, Dx =1m /s, Niu (2013). 2 Dy = 0.1 m /s and C0 = 1 g/mL. To compare the numerical and ana- lytical solutions, we plot the concentration profiles in two different 3.1.3. Groundwater transit time simulation ways: First, in Fig. 2a, the longitudinal concentration distribution We consider a vertical section through a saturated flow system of the normalized concentration (Co/C0) at different times (t=10, within an unconfined aquifer underlain by an impervious bound- 20, 30 s) are shown from the center of the patch source (y = 0 m); ary (Chesnaux et al., 2005) as shown in Fig. 3. A uniform positive Second, in Fig. 2b, we show the breakthrough curves at different infiltration, W [LT 1], representing net recharge, is applied over downstream locations (d = 5, 10, 20 m) from the center of the patch the entire upper boundary of the aquifer. The left-hand boundary source (y = 0 m). At the downstream location d = 5 m, the concen- is impermeable and flow discharges through the right-hand tration breakthrough curve reaches a plateau after a certain time fixed-head boundary (hL). Flow is also assumed to be at steady since we assume a constant concentration C0 at the source. The state, which implies that (1) the numerical model converges to same trends are noted at different downstream locations the state that (2) the downstream discharge equals the ground (d = 10 m and d = 20 m), but the further the downstream location water recharge and that (3) the water table position does not J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48 41
1 Recharge, W 0.9 (a) 10s Analytical 10s model y 0.8 20s Analytical 20s model h 0.7 30s Analytical max 30s model 0.6 Water Table 0.5 Lake, River 0.4 q = 0 or Drain x 0.3 h L
) 0.2 0 0.1 0 0x Impermeable L x 0 5 10 15 20 25 30 35 40 45 50 i
Distance (m) Fig. 3. Conceptual diagram for a test case from Chesnaux et al. (2005) involving 0.8 groundwater transit time simulations between an arbitrary location xi and the exit boundary at x = L. Figure shows an unconfined aquifer receiving uniform recharge, (b) an impermeable boundary on the left and a fixed-head boundary on the right.
Concentration ( C/C 0.7 Z n 0.6 t ¼ e DpðsÞds ð29Þ Dw s 0.5 where Dp is the width of the stream tube [L]. The integral in the above equation is the area of the chosen stream tube along s. This 0.4 area was computed by interpolating the nodal stream function val- ues along the finite difference mesh. For this test case, the area inte- 0.3 grations were computed based on a stream function interval of 8 10 8 m2/s (equivalent to 100 stream tubes). 0.2 5 m Analytical The travel time can also be computed by using the particle 5 m model 10m Analytical tracking scheme in our model. We released particles at different 0.1 10m model 20m Analytical positions along the water table. The particles will finally flow to 20m model the right-hand exit boundary as shown in Fig. 3. We compare the 0 analytical solution (Eq. (27)), the numerical solution using stream 0 5 10 15 20 25 30 function (Eq. (29)), and the numerical solution using particle track- Time (s) ing scheme for one value of the hydraulic conductivity K in Fig. 4. Additional comparisons can be found in Niu (2013). The analytical Fig. 2. Comparison between numerical and analytical results for 2-D overland flow solution matches the two numerical solutions well. This test case transport at (a) different times and (b) different downstream locations. The solid lines with different colors show the analytical solutions at different times or shows that the particle tracking scheme can accurately estimate locations, while symbols with the same colors represent the corresponding groundwater transit times and is even more accurate than the numerical solutions. (For interpretation of the references to color in this figure numerical method derived from the commonly used stream func- legend, the reader is referred to the web version of this article.) tion method. Hence we conclude that the particle-tracking scheme is suitable for groundwater transport problems, especially with change with time. The hydraulic head solution follows the Dupuit– interactions between the soil and the groundwater domains. Forchheimer ellipse (Bear, 1972). The analytical solution for the travel time from an arbitrary point xi at the water table to the right exit boundary is given by (Chesnaux et al., 2005): 3.2. Plot-scale simulations of manure-borne fecal coliforms 2 0 ffiffi qffiffiffiffiffiffiffiffiffiffiffi13 rffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffi p For this test case described in Guber et al. (2009), the data were k k 1 x þ x2 k 6 1 1 1 1 B i i C7 collected from overland flow experiments with manure-borne tðxiÞ¼ne 4L xi þln@pffiffi qffiffiffiffiffiffiffiffiffiffiffiA5 ð27Þ KW L2 k x2 k k k 1 fecal coliforms (FC) and the experiments were performed in i L þ x2 i October 2003 on a two-sided lysimeter 21.34 m long and 13.2 m wide located at the Patuxent Wildlife Research Refuge in 2 2 Beltsville, MD. The slope of the lysimeter surface was 20%. The where ne is porosity, k ¼ L þ Kh =W, K is hydraulic conductivity L 1 [LT 1] and L is the aquifer length [L]. For this test case, the 2D average simulated rainfall rate measured was 5.8 ± 1.9 cm h groundwater equation can be simplified as: applied to the area. The manure slurry was uniformly applied on top of the plots in a 30-cm-wide strip at the rate of 11.7 L m 2. @ @h @ @h Irrigation was started immediately after manure application. K þ K þ W ¼ 0 ð28Þ @x xx @x @y yy @y Rainfall was simulated for 1 h after the initiation of runoff. Runoff volume and fecal coliform concentrations were measured where Kxx and Kyy are the horizontal and vertical components of the at the bottom of the lysimeter. More details about the experiment hydraulic conductivity. To determine the travel time, we also make can be found in Guber et al. (2009). The hydrologic model was cal- use of the stream function solution. Streamlines represented by ibrated by minimizing the root mean square error of the measured constant stream function are tangent to the velocity field. For a fluid and simulated accumulated runoff time series. The governing particle to travel a distance s within a stream tube defined by equations for overland transport and release of bacteria are pre- stream function interval Dw [L2T 1], following the stream function sented in Guber et al. (2009). The boundary condition of h =0 at solution the transit time t can be calculated as: x = 0 was used for the overland flow, where h is the depth of 42 J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48
−4 (a) Transit time from water table to exit boundary ( K = 10 m/s ) 25 Numerical solution (Eq. 29) 20 Analytical solution (Eq. 27) Numerical solution using 15 particle tracking
10
5
Travel Time (years) 0
(b) Streamfunction ( ∆ψ = 5×10 −7 m2 /s ) 10
8
6
4
Elevation (m) 2
0
(c) Velocity field 10
8
6
4
Elevation (m) 2
0 0 50 100 150 200 250 300 350 400 450 500 Distance (m)
Fig. 4. Comparison of numerical and analytical solutions for groundwater transit time simulations. (a) Results of two numerical approaches and an analytical solution, (b) the stream function solution, and (c) the velocity vectors.
ponding and x is distance measured along the slope. The Manning 1169 km2 (Fig. 6). The watershed has a relatively low relief with roughness coefficient n was set to 0.035. The best values of the sat- the maximum elevation recorded as 324 m and a minimum of urated hydraulic conductivity (K), and other parameters in the van 249 m. 30 m resolution National Elevation dataset (NED) from Genuchten formulation related to the soil properties were esti- the USGS was used for slope and surface runoff calculations. mated by fitting the simulated runoff to the experimental data. Land use and land cover (LULC) data were based on the 30 m res- To calculate the concentration of released bacteria from manure olution IFMAP (Integrated Forest Monitoring Assessment and (boundary condition for overland flow transport), an equation from Prescription) datasets from the Michigan Department of Natural Bradford and Schijven (2002) (Eq. (7) in Guber et al. (2009)) was Resources (MDNR, 2010). Depending on the grid size, a cell may used together with parameters from Guber et al. (2006). possess a mixture of land use/land cover types in the PAWS model. Additional details can be found in Guber et al. (2009). The runoff LULC data were re-classified into model classes, which are repre- simulation result after calibration is shown in Fig. 5a. The perfor- sented by several generic plant types (called the representative mance of the calibrated transport model is shown in Fig. 5b. or functional plant types). Meteorological data including precipita- Flow and transport results are found to be in good agreement with tion, air temperature, relative humidity and wind speed were observations. obtained from several National Climatic Data center (NCDC, 2010) and MAWN (Michigan Automated Weather Network) (Enviro-weather, 2010) stations within the watershed. The Soil 3.3. Modeling E. coli fate and transport in the Red Cedar River Survey Geographic (SSURGO) (Soil Survey Staff) database from watershed the U.S. Department of Agriculture, Natural Resources Conservation Service was used for soil classification and for calcu- The transport model was applied to simulate the fate and trans- lating the parameters associated with soil properties. The National port of E. coli in the Red Cedar River watershed (RCR). Although the Hydrography dataset (NHD) from USGS was used for channel net- term solute is used in the title and throughout the paper, bacteria work and for routing and flow computations. The stream flow and are suspended particles. However, both dissolved and suspended groundwater head data for comparison were obtained from a num- particles can be adequately described using the advection–disper ber of USGS gaging stations within the watershed. Hydraulic con- sion–reaction equation and its variants with similar sets of param- ductivity data were obtained by processing the information in eters (Shen et al., 2008). Monitoring data for E. coli were obtained the MDEQ Wellogic database for the groundwater model to esti- from Michigan DEQ (Department of Environmental Quality) and mate local hydraulic conductivities, groundwater heads and thick- observed solar radiation data were used for the light-based bacte- nesses of the glacial drift layer. Spatial fields were obtained by rial die-off formula. The total area of the RCR watershed is kriging after removing noise in the data (Simard, 2007). J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48 43
(a) Runoff Table 1 6 Coordinates of the E. coli Monitoring sites and sources.
ID Description Latitude Longitude
5 Monitoring 1 Webberville-A 42.68 84.17 m)
-2 sites 2 Webberville-B 42.68 84.19 3 Williamston 42.72 84.52 4 4 East Lansing 42.73 84.51 WWTPa East Lansing 42.73 84.50 3 Williamston 42.69 84.29 CAFOb Kubiak Farm Primary Species: 42.71 84.17 Diary 2 Mar Jo Lo Primary Species: 42.63 84.36 Farm Diary
Cumulative Runoff (10 MSU Primary Species: 42.70 84.48 1 Simulated Mixed Observed a Waste Water Treatment Plant. 0 b Concentrated Animal Feeding Operation Centers. (b) Bacteria breakthrough
Table 2 −1 10 List of parameters used for the E. coli simulation.
a Longitudinal dispersion coefficient, DL Deng et al. (2001) 1 Freshwater loss rate, kb1 0.8 day Coefficient of loss rate due to sunlight, d in Eq. (22) 1.0 b in Eq. (19) 0.69 cm 1 0 −2 10 a Empirical equations and data from Shen et al. (2010). C/C
100 90 USGS 04112500 −3 Observed 10 NSE = 0.7 Simulated 0 1/6 1/3 1/2 2/3 5/6 1 80 Time (hr) 70 60 Fig. 5. Comparison between model results and measured data from plot-scale runoff experiments with manure-borne fecal coliform release (a) surface runoff 50 results and (b) concentration time series for manure-borne fecal coliforms. Solid lines represent the model simulation and symbols denote the field observations. 40
Discharge (cms) 30 20 10 0 N 06/02/04 12/19/04 07/07/05 01/23/06 08/11/06 Date (mm/dd/yy) 3 4 Kubiak Fig. 7. Comparison between observed (USGS) and PAWS-simulated stream flows MSU for USGS Gage # 04112500 (Red Cedar River at East Lansing). NSE is the Nash– 2 1 42˚40’0”N Sutcliffe model efficiency coefficient.
Mar Jo Lo Numerous sources within the watershed contribute E. coli to the river. While some sources are well characterized (discharge and concentration reported as a function of time), no data were avail- 42˚30’0”N able for many other sources. There are three concentrated animal WWTP feeding operation (CAFO) centers located in the watershed that E. coli monitoring sites are known sources of E. coli from livestock and two wastewater CAFO Elevation (m): treatment plants (WWTP) are located on the RCR that are consid- NCDC Weather Stations 0 2 4 8 12 326 ered to be significant sources of E. coli to the river (Table 1). USGS Gauges km NHD streams Therefore, instead of attempting to include all sources in this initial 249 42˚20’0”N RCR watershed application of the transport model, we wanted to use the model to test the hypothesis that the CAFOs and WWTPs are the major 84˚30’0”W 84˚20’0”W 84˚10’0”W 84˚0’0”W sources impacting bacterial levels within the RCR. Although Fig. 6. Map of the Red Cedar River watershed. Elevation is shown using the color PAWS is an integrated hydrologic model, we did not have sufficient map. National Hydrography Dataset (NHD) streams, U.S. Geological Survey (USGS) information about subsurface sources contributing E. coli within gauges, National Climatic Data Center (NCDC) weather stations, Waste Water the watershed, therefore only overland and channel flows are con- Treatment Plants (WWTPs), Concentrated Animal Feeding Operation (CAFO) centers sidered for simulating E. coli fate and transport with the assump- and E. coli monitoring sites are shown on the map. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of tion that overland transport is advection-dominated (Abbasi this article.) et al., 2003; Deng et al., 2005; Kim et al., 2013). However, 44 J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48
106 sim Monitoring Station # 2 obs RMSE = 0.59 sim CAFO only 105
104
3
) (CFU / 100 mL) 10
102 E. coli ( 10 101 Log
0 10 02/23/04 09/10/04 03/29/05 10/15/05 05/03/06 11/19/06 06/07/07 Date (mm/dd/yy)
Fig. 8. Comparison between model simulations and field observations for E. coli at monitoring site #2 in the Red Cedar River watershed. interactions among all domains including vadose zone and the different domains. A typical time step for surface flow components groundwater domain are taken into account while simulating the is about 10 min although this value can change dynamically hydrology of the watershed. The parameters used in the E. coli depending on local conditions to maintain numerical stability. A model are listed in Table 2. Based on the number and type of ani- comparison between observed (USGS) and simulated streamflows mals in the CAFOs, the manure production and bacterial shedding is first presented in Fig. 7. The observed streamflows are generally rates were estimated as described earlier. The reported animal simulated well by the model. manure in the MSU CAFO is 9145 tons per year, while the esti- A comparison between observed and simulated E. coli concen- mated average and maximum amounts are 9460 and 10,814 tons trations at monitoring sites 2–4 is shown in Figs. 8 and 9. In these per year based on the animal types and numbers reported from figures the red lines are the simulation results using all sources MSU CAFO, and the average daily manure production rate for each including WWTP and CAFO inputs, the background values for dif- animal category from ASAE. The estimated and reported values are ferent LULC and the observed time series data at site 1 to capture 24,032 and 32,020 tons per year for the Kubiak CAFO respectively. the upstream effects. The blue1 lines represent simulation results The numbers are 14,496 and 5500 tons per year for the Mar Jo Lo using CAFO inputs as well as the background values for different CAFO. The mismatches in the estimated and the reported manure LULC (labeled as ‘‘CAFO only’’ in the figures). Since the monitoring amounts can be attributed to incorrect estimates for collected site 2 is immediately downstream of the site 1 (used as a boundary manure, unaccounted manure loss during the collection process, condition), the simulations match well with observed data at site 2 or inaccurate animal numbers reported. Also, according to ASAE in Fig. 8. The difference between the red and blue lines in Fig. 8 data, the standard deviation in the average daily manure produc- comes from the upstream E. coli concentrations that were included tion is quite large. The daily discharge and fecal coliform bacteria in one simulation (red line) but not the other (blue lines). As we concentration time series data for East Lansing and Williamston move downstream, the signal becomes more complex and the com- WWTP were also provided as model inputs. For the WWTP only parisons (especially, with the low background values of E. coli) fecal coliform data were available (obtained from MDEQ), as become relatively worse (Fig. 9). In Figs. 8 and 9 the RMSE values E. coli were not measured. A ratio of 0.6 was used to calculate are based on log-transformed concentrations. Since sites 3 and 4 the E. coli concentrations from fecal coliform measurements based are far from the Kubiak CAFO, which has the largest reported annual on literature values (Rasmussen and Ziegler, 2003). However, the manure production, the simulated E. coli concentrations at these two ratio is known to be highly variable introducing an additional sites were dominated by effluents from the East Lansing and source of uncertainty into the modeling. In addition to the CAFOs Williamston WWTPs. On the other hand, at site 2 which is close to and WWTPs, we assumed that wildlife from different land use/land the Kubiak CAFO, most of the peaks were contributed by CAFO covers contribute different background E. coli levels based on avail- inputs (Fig. 8). able information in the literature. The assumed background levels Closer examination of the comparisons in Fig. 9 (see panels b, c, are 960, 5000, 440 and 2200 CFU/100 mL for forested, urban, row e and f) shows that although the weekly sampling is not adequate crop and forage crop land uses respectively (Ouattara et al., 2012). to resolve all the peaks, the model was able to capture the peaks In Fig. 6, the monitoring sites (triangles) and the USGS gauges where data are available. The log-RMSE values (that is, RMSE val- (circles) are all on the Red Cedar River. The flow is from east to ues based on log-transformed concentrations) for the three moni- west. The monitoring site 1 near Webberville is the most upstream toring sites in Figs. 8 and 9 ranged from 0.59 to 1.00. These values monitoring site. We did not have any information about sources are comparable to the numbers reported in the literature for E. coli upstream of site 1 therefore a decision had to be made about modeling. For example, Desai et al. (2011) examined a number of approximating the behavior of these unknown sources. We first sources contributing to the observed E. coli in a 288-km2 urban ran the model to see if the background values associated with dif- watershed in Texas including sediment-associated bacteria. Their ferent land uses alone can explain the observed data at site 1. Since HSPF model for E. coli fate and transport was calibrated for a we were unable to capture the upstream source effects using the two-year period producing log-RMSE values in the range 0.67 to background values for different LULC (figure not shown), the 0.96. While distributed hydrologic models tend to perform well observed time series data (at site 1) were used as an upstream in simulating watershed hydrology, the models have not met with boundary condition in our simulations. a similar level of success in simulating the fate and transport of An 880 m 880 m grid was used for the simulations as described in Shen and Phanikumar (2010). PAWS uses adaptive 1 For interpretation of color in Figs. 8 and 9, the reader is referred to the web time stepping and has the ability to use different time steps for version of this article. J. Niu, M.S. Phanikumar / Journal of Hydrology 529 (2015) 35–48 45
Monitoring Station # 3. RMSE = 0.97
(a)
104 sim obs sim CAFO only
103 ) (CFU / 100 mL)
102 E. coli ( 10
1
Log 10
100 02/23/04 09/10/04 03/29/05 10/15/05 05/03/06 11/19/06 06/07/07 Date (mm/dd/yy)
7000 (b)16000 (c) 6000 14000 5000 12000 4000 10000 8000 3000 (CFU / 100 mL) (CFU / 100 mL) 6000 2000 4000
E. coli 1000 E. coli 2000
05/28/05 07/07/05 08/16/05 09/25/05 11/04/05 04/28/07 06/07/07 07/17/07 08/26/07 10/05/07 Date (mm/dd/yy) Date (mm/dd/yy) Monitoring Station # 4. RMSE = 1.00
(d) 105
104
103 ) (CFU / 100 mL)
102 E. coli ( 10 101 Log
0 10 02/23/04 09/10/04 03/29/05 10/15/05 05/03/06 11/19/06 06/07/07 Date (mm/dd/yy) x 104
3.5 5000 (e) (f) 3 4000 2.5 3000 2 1.5 (CFU / 100 mL)
2000 (CFU / 100 mL) 1 1000 0.5 E. coli E. coli
05/08/05 06/17/05 07/27/05 09/05/05 10/15/05 05/03/06 06/22/06 08/11/06 09/30/06 Date (mm/dd/yy) Date (mm/dd/yy)
Fig. 9. Comparison between model simulations and field observations for E. coli at monitoring sites #3 and #4 in the Red Cedar River watershed. bacteria and pathogens at the watershed scale (Baffaut and a reasonable agreement was obtained between observations and Sadeghi, 2010; Frey et al., 2013). Considering the uncertainties in model results. The model results also indicate that the CAFOs the modeling and the weekly sampling, we conclude that, overall, and 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 and @C @a @I @D @C @2C a S ¼ þ þ k C þ S I S þ D S ðA1Þ WWTPs changed depending the sampling location. The back- @t @t @z S @z @z S @z2 ground concentrations of E. coli (values around and less than 100) are difficult to simulate accurately as several sources (unac- Using subscripts (i 1, i, i + 1) to denote space and superscripts counted for in the modeling) could potentially contribute to these (n, n + 1) to denote old and new time levels, Eq. (A1) is discretized background values and their temporal variation. One of the as shown below: assumptions in our modeling was that the primary transport nþ1 n nþ1 nþ1 C C @a @I @D CS CS mechanism for E. coli is overland transport and that channel flow a Si Si ¼ þ þ k Cnþ1 þ S I iþ1 i 1 Dt @t @z Si @z 2Dz becomes important once bacteria enter the streams. However, nþ1 nþ1 nþ1 the RCR watershed within and around the MSU campus has a net- CS 2CS þ CS þ D iþ1 i i 1 ðA2Þ work of pipes draining the landscape. Flow and transport within S Dz2 this network was not simulated in the modeling. Once flow enters a @a @I ð@DS IÞ D the pipe network, travel times are expected to be generally shorter Let A0 ¼ , B0 ¼ þ þ k , C0 ¼ @z , D0 ¼ S , and this effect can be seen in the timing associated with some Dt @t @z 2Dz Dz2 E. coli peaks (see Fig. 9f). Haydon and Deletic (2006), who found then Eq. (A2) can be written as: mismatches in the timing of their simulated E. coli peaks, indicate ð C0 þ D0ÞCsnþ1 þð A0 þ B0 2D0ÞCsnþ1 þðC0 þ D0ÞCsnþ1 ¼ A0Csn that small errors in timing are generally of little consequence from i 1 i iþ1 i a management perspective. ðA3Þ Finally a few words on the limitations of the current transport The coefficients of the unknown concentrations on the left hand modeling maybe appropriate. Consistent with the descriptions used side of Eq. (A3) are in the tridiagonal matrix form, which is solved in the PAWS hydrology modules, lateral diffusion of soil moisture using the Thomas algorithm (Press et al., 2007). The term @a in coef- and the associated solute transport are assumed to be negligible. @t ficient B0 is calculated as: Therefore, in situations where lateral transport of contaminants in the vadose zone is important, we can expect the PAWS transport @a @ðq k þ hÞ @h hnþ1 hn ¼ b P ¼ ¼ i i ðA4Þ module to introduce errors. Although the bacterial transport model @t @t @t Dt described in this paper used mechanistic routing procedures, the The term @DS in coefficients C0 is calculated as: processes of release of bacteria from the soil and their attachment @z to and detachment from soil particles are extremely complex pro- @D @ða0jtjc þ D0 Þ S ¼ S ðA5Þ cesses and large uncertainties are associated with them. Our future @z @z work will attempt to further refine the modeling by using 0 bh 0 high-resolution datasets based on daily/sub-daily sampling, param- Note that DS ¼ D0ae and a is constant (Ahuja, 1990; Bear and eter sensitivity analyses and detailed source characterization. Bachmat, 1990; Bresler, 1973) thus Eq. (A5) is calculated as: @D @jtjc @h S ¼ a0 þ D abebh 4. Conclusions @z @z 0 @z nþ1 c nþ1 c nþ1 nþ1 jt j jt j hnþ1 h h ¼ a0 iþ1 i 1 þ D abðebÞ i iþ1 i 1 ðA6Þ A watershed-scale transport model based on a process-based 2Dz 0 2Dz distributed hydrologic model was developed. The model used an operator-splitting strategy that combined a Lagrangian particle transport modeling approach for advection with an Eulerian References approach for dispersion and reactions. The transport model was Abbasi, F., Simunek, J., van Genuchten, M., Feyen, J., Adamsen, F., Hunsaker, D., tested using available analytical solutions and data from Strelkoff, T., Shouse, P., 2003. Overland water flow and solute transport: Model plot-scale experiments. The coupled hydrologic/transport model development and field-data analysis. J. Irrig. Drain Eng. 129 (2), 71–81. was applied to the Red Cedar River watershed to simulate bacterial Ahuja, L.R., 1990. 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