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Agricultural Water Management 180 (2017) 35–49

Contents lists available at ScienceDirect

Agricultural Water Management

journa l homepage: www.e lsev ier .com/ locate /agwat

evelopment and application of a fully integrated model fornsaturated-saturated nitrogen reactive transport

an Zhu a, Jinzhong Yang a, Ming Ye b, Huaiwei Sun c, Liangsheng Shi a,∗

State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, Hubei 430072, ChinaDepartment of Scientific Computing, Florida State University, Tallahassee, FL 32306, USASchool of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

r t i c l e i n f o

rticle history:eceived 13 January 2016eceived in revised form 4 October 2016ccepted 19 October 2016vailable online 1 November 2016

eywords:ntegrated nitrogen modelitrogen transformationeptic tanksacksonvillensaturated-saturated zone

a b s t r a c t

This paper presents a fully integrated model to simulate coupled unsaturated-saturated flow and reac-tive transport of ammonium and nitrate, the two major nitrogen species. Based on our previous work ofdeveloping a coupled model of unsaturated-saturated flow and solute transport of a single species, thekey contribution of this study is to develop a new mathematical model and the new computer code fora comprehensive list of biogeochemical reactions, which are necessary for simulating nitrogen reactivetransport. The computer code is verified by comparing its simulated results with those obtained usinganother model for a synthetic case. Model calibration and validation are conducted for two real-worldcases to simulate nitrogen reactive transport. The two cases are at the experimental plot scale withthe sewage water irrigation and at the field scale with the septic tank effluent infiltration, respectively.Quantitative evaluation of the numerical modeling results indicates that the new model and computercode can accurately simulate field observations of moisture content, water table elevation, and nitro-

gen concentration. For example, the root mean square error for simulating moisture content can be assmall as 0.01. The code is computationally efficient to capture spatial and temporal trends of nitrogenconcentrations at the field scale with a large number of computational nodes and time steps. The fullyintegrated model is a promising tool for large-scale modeling of water flow and nitrogen transformationand transport under complex conditions in agricultural and urban environments.

© 2016 Elsevier B.V. All rights reserved.

. Introduction

As nitrogen is an essential nutrient for crop growth, applyingitrogen fertilizer is necessary to replenish soil nitrogen deficiencynd to increase crop yield. However, excessive use of nitrogen fer-ilizer has caused high nitrogen concentration in crop soils androundwater aquifers (Brady and Weil, 2008; Gastal and Lemaire,002). Nitrogen pollution in crop soils and/or groundwater has aumber of adverse impacts on human health and environmentaluality (Jalali et al., 2008; Muyen et al., 2011; Valipour, 2014a).or example, high nitrate concentration in drinking water is car-inogenic, and may also cause blue baby syndrome (Wolfe andatz, 2002). Environmental regulations have been established for

onitoring nitrate concentration in drinking water for human

onsumption (USEPA, 2012). In order to improve nitrogen manage-ent in agricultural areas and to minimize nitrogen pollution risks,

∗ Corresponding author.E-mail address: liangshs@whu.edu.cn (L. Shi).

ttp://dx.doi.org/10.1016/j.agwat.2016.10.017378-3774/© 2016 Elsevier B.V. All rights reserved.

it is important to estimate nitrogen contributions from various con-tamination sources to the subsurface and surface environments.This entails quantitative simulation of transformation and trans-port of nitrogen in soil zones and groundwater aquifers.

A large amount of efforts have been spent to characterize andsimulate physical, chemical, and biological processes that controlnitrogen transformation and transport among different nitro-gen pools in soil zones and groundwater aquifers. The processesand their interactions are complicated, including mineralization,immobilization, nitrification, denitrification, and volatilization (Xuet al., 2012; Canion et al., 2014). In addition, these processesare heavily influenced by human activities, soil water dynamics,groundwater recharges, and soil vegetation systems (Huang andHuang, 2009). To comprehensively investigate the processes froma system perspective, modeling approaches have been widely usedto provide quantitative estimates of soil water flow and nitro-

gen reactive transport especially at field scales (Wriedt and Rode,2006). During the past several decades, a number of nitrogenreactive transport models have been developed, such as DAISY(Hansen et al., 1991), ANIMO (Groenendijk and Kroes, 1999), RISK-

3 ter Ma

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uouettgLwg(2amwrtcdcissihiiatrug

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6 Y. Zhu et al. / Agricultural Wa

(Oyarzun et al., 2007) and ArcNLET (Rios et al., 2013; Wangt al., 2013; Zhu et al., 2016). These models have different lev-ls of complexity for simulating nitrogen reactive transport inoth unsaturated and saturated zones. While the models usually

nclude a module for simulating complex soil nitrogen trans-ormation, they are inadequate to simulate three-dimensional3-D) groundwater flow and nitrogen transformation in ground-ater aquifers, which limits their applications to complex regional

omains with both soil and groundwater flow. Therefore, a fully 3- unsaturated-saturated model is necessary for nitrogen reactive

ransport modeling (Wang et al., 2003). However, the computa-ional cost of such a model may not be practically affordable due toigh non-linearity of unsaturated flow.

In order to reduce the computational burden, couplednsaturated-saturated models have been developed by explicitlyr implicitly linking an unsaturated soil nitrogen model with a sat-rated groundwater nitrogen model (Stenemo et al., 2005; Ajdaryt al., 2007; Rahil and Antonopoulos, 2007; Bonton et al., 2012). Inhe explicit coupling method, unsaturated water flow and nitrogenransformation processes are simulated using soil-water and nitro-en models, such as EPIC (Williams, 1995), Agriflux (Banton andarocque, 1997) and mRISK-N (Wriedt and Rode, 2006); ground-ater flow and nitrogen transport processes are simulated using

roundwater models, such as RT3D (Clement, 1997), MT3DMSZheng and Wang, 1999), and HydroGeoSphere (Therrien et al.,006). The soil and groundwater models are executed separately,nd water and nitrogen fluxes computed by the soil nitrogenodels are used as the upper boundary condition of the ground-ater nitrogen models. The explicit coupling methods usually

equire a fixed water table, which may limit feedbacks betweenhe linked models (Wriedt and Rode, 2006). In practice, the explicitoupling methods are unsuitable under dynamic water flow con-itions, since soil water and groundwater hydraulic conditionshange substantially due to climate conditions and human activ-ties. Therefore, the implicit coupling methods are necessary toimultaneously simulate flow and nitrogen reactive transport inoil and groundwater systems. Following Gärdenäs et al. (2005),mplicitly coupled models are referred to as integrated modelsereinafter. However, it happens often that the nitrogen reactions

n either soil or groundwater system are oversimplified in existingntegrated models, which hampers the model compatibility anddaptability to general hydrological and nitrogen transport condi-ions (Lee et al., 2006; Bonton et al., 2012). This problem can beesolved by developing an integrated model that adequately sim-lates nitrogen reactive transport processes in both soil zones androundwater aquifers.

The objective of this study is to develop a fully integrated modelf nitrogen reactive transport for simulating nitrogen contaminantransport in soil and groundwater systems. This development isased on the existing integrated model developed in our previousork for simulating unsaturated-saturated flow and solute trans-

ort (Zhu et al., 2012, 2013). The previous model only considersransport of a single species, and cannot be used for simulat-ng reactive transport of multiple nitrogen species. The models extended in this study by including the transport and trans-ormation processes of multiple nitrogen species. In the existingntegrated flow and transport model, one-dimensional (1-D) aver-ge vertical unsaturated flow and nitrogen reactive transport areimulated in the soil zone, and 3-D groundwater flow and nitro-en reactive transport are simulated in the groundwater system. Inhis study, the unsaturated and saturated zones are integrated as ahole to couple flow components, solute transport, and nitrogen

eactions with their specific characteristics in the unsaturated-aturated zones. The model accuracy and computational efficiencyre evaluated in three cases, including a hypothetical 1-D case, aeld case with treated sewage water irrigation, and a 3-D case

nagement 180 (2017) 35–49

with point nitrogen sources from septic systems. The integratedmodel is in spirit similar to TOUGHTREACT-N (Gu and Riley, 2010;Finsterle et al., 2012) in that the latter one is also based on an inte-grated model that simulates coupled processes of advective anddiffusive nutrient transport in soil and groundwater. However, ourmodel solves the partial differential equations of groundwater flowand saturated solute transport in a different way, using the finitevolume method and a hybrid method of finite element and finitedifference. Our numerical methods have the advantages of keep-ing mass balance and obtaining accurate solution near irregulardomain boundaries (Zhu et al., 2012, 2013). Furthermore, our modelis more computationally efficient, because the unsaturated domainis divided into a number of sub-areas and the unsaturated flow andtransport in each sub-area is simplified to be one dimension. Thisreduces the number of computational nodes to save computationalcost for large-scale nitrogen reactive modeling.

2. Methodology

The model presented in this paper is an extension of our pre-vious model of integrated unsaturated-saturated flow and solutetransport (Zhu et al., 2012, 2013) by including a comprehensive listof biogeochemical reactions involved in nitrogen reactive trans-port. The major nitrogen transformations in the unsaturated andsaturated zones considered in the model are shown in Fig. 1.The soil nitrogen includes both organic and inorganic nitrogen.The organic nitrogen is in two major pools: (1) the litter poolcomposed of crop residuals, dead roots, and microbial biomasses,and (2) the humus pool composed of stabilized decompositionproducts. The inorganic nitrogen are ammonium and nitrate. Allthe soil nitrogen transformation processes depicted in Fig. 1 (i.e.,mineralization/immobilization, nitrification, denitrification, andvolatilization) are simulated in the integrated model. Denitrifica-tion in groundwater aquifers is designed in the model as a useroption. When the temperature is suitable and sufficient organiccarbon exists, the denitrifying bacteria can survive in this anaero-bic environment and denitrification occurs (Soares, 2000; Hantushand Marino, 2001). Otherwise, users do not activate the denitri-fication function of the model. Nitrification of ammonium is alsokept in the model as a user option, and it is activated if nitri-fication is observed in laboratory and field studies (Smith et al.,2006).

Fig. 2 shows the flowchart of the nitrogen reactive transportmodeling. Within each time step, the simulation starts with solv-ing the water flow equations. Subsequently, the transformationprocesses related to ammonium (i.e., volatilization, mineraliza-tion/immobilization, and nitrification) are simulated as sourceterms of the ammonium transport equations. After obtaining theammonium concentration, the model starts to simulate the nitratetransformation processes by solving the transport equations. The1-D and 3-D advection-dispersion equations (ADEs) are used todescribe nitrogen transport in soil and groundwater, respectively.The equations are discretized and solved instantaneously by assem-bling a unified matrix with linking mass fluxes (Zhu et al., 2013).The details of reactive nitrogen transport modeling are given inSections 3.2 and 3.3.

3. Model development

3.1. Unsaturated-saturated water flow dynamics

The integrated flow model is used as the flow module of theintegrated model. This module is described briefly here to makethe paper self-contained, and more details are referred to Zhu et al.

Y. Zhu et al. / Agricultural Water Management 180 (2017) 35–49 37

F transr are al

(t

wucstGa

V

wvflsmhw

ez

q

wtpt

ig. 1. Nitrogen transformation processes in soil and groundwater systems. Theespectively. The transformation between the organic and inorganic nitrogen pools

2012). The soil water flow is governed by the 1-D Richards’ equa-ion,

∂∂t

= ∂∂z

[K

(∂h∂z

− 1

)]− S, (1)

here is the volumetric water content (volume of water per vol-me of soil) [−]; t is the time [T]; K(h) is the unsaturated hydrauliconductivity as a function of pressure head [L T−1]; h is the pres-ure head [L], and the relationship between the soil moisture andhe pressure head is calculated by the van Genuchten model (vanenuchten, 1980); z is the elevation in the vertical direction [L];nd S is the root uptake term, or other source/sink term [T−1].

The saturated flow equation is

H

t= QH + QV + QS, (2)

here is the elastic storage coefficient [L−1]; V is the contrololume [L3]; H is the hydraulic head [L]; QH is the net lateralux [L3 T−1]; QV is the vertical flow flux [L3 T−1]; and QS is theource/sink terms [L3 T−1]. Eq. (2) is solved by the finite volumeethod, which is particularly accurate when simulating hydraulic

ead along irregular boundaries and also preserves mass balanceell (Zhu et al., 2012).

The two equations of Eqs. (1) and (2) are coupled by thexchange flux, qex [L T−1], between the unsaturated and saturatedones via,

ex = −K × H − (h + z)L

, (3)

here L is the distance between the unsaturated node adjacento the water table and the node at the water table [L]. The cou-ling scheme of the two equations and formulating procedure ofhe global stiffness matrix are referred to Zhu et al. (2012).

formation processes are characterized in the soil zone and groundwater systemso marked in details.

3.2. Soil nitrogen reactive transport

The transport of the soil nitrate and ammonium are governedby the conventional advection-dispersion equations (ADEs),

∂cSW3

∂t= ∂∂z

(Dzz

∂cSW3

∂z

)− ∂qzcSW3

∂z+ RS3, (4)

∂cSW4

∂t+ ∂SSW4

∂t= ∂∂z

(Dzz

∂cSW4

∂z

)− ∂qzcSW4

∂z+ RS4, (5)

where cSW 3 and cSW 4 are the soil nitrate and ammonium concen-trations [M L−3], respectively; Dzz is the hydrodynamic dispersioncoefficient [L2 T−1]; qz is the vertical Darcy flux [L T−1]; is the soilbulk density [M L−3]; SSW 4 is the adsorbed concentration of ammo-nium on soil particles, which is evaluated by the linear isothermalmodel by multiplying the adsorption coefficient Kd with aquoussolute concentration [M L−3]; RS3 and RS4 are the source and sinkterms related to nitrate and ammonium [M L−3 T−1], respectively.The source/sink terms are expressed as,

RS3 = Rm3 + Rn − Rdn − Rp3, (6)

RS4 = Rm4 − Rn − Rv − Rp4, (7)

where Rm3 is the net immobilization from nitrate [M L−3 T−1];Rn is the nitrification term [M L−3 T−1]; Rdn is the denitrificationterm [M L−3 T−1]; Rp3 and Rp4 are the root uptake of nitrate andammonium [M L−3 T−1], respectively; Rm4 is the net mineraliza-tion/immobilization to/from ammonium [M L−3 T−1]; and Rv is thevolatilization term of ammonium [M L−3 T−1].

3.2.1. Denitrification, nitrification, and volatilizationThe nitrification, denitrification and volatilization processes in

Eqs. (6) and (7) can be simulated as a kinetic equation. Three kindsof kinetic equations are used in this study, and they are the zero-

38 Y. Zhu et al. / Agricultural Water Management 180 (2017) 35–49

F ter flos d trant

o2

wtapm[

nf

ig. 2. Flow chart of the ammonium and nitrate modeling. The model starts from waubsequently. The red dot line marks the ammonium and nitrate transformation anhe reader is referred to the web version of this article.)

rder, first-order, and Michaelis-Menten kinetics as follows (Lu,004; Yang et al., 2008),

∂cN∂t

= −K0 × ( + Kd) × f (, T), (8)

∂cN∂t

= −K1 × ( + Kd) × f (, T) × cN, (9)

∂cN∂t

= −Km × f (, T) × ( + Kd)cN( + Kd)cN + Kc

, (10)

here cN is the nitrogen species concentration in the soil solu-ion [M L−3]; K0 is the zero-order rate coefficient [M L−3 T−1]; f(,T)re the response functions from the soil water moisture and tem-erature [−]; K1 is the first-order rate coefficient [T−1]; Km is theaximum rate constant [M L−3 T−1]; Kc is the saturation coefficient

M L−3].While there is a lack of consensus on the kinetics for the soil

itrogen transformation processes, the first-order kinetics is pre-erred in this study to calculate the nitrification and volatilization

w module, then turns to calculate the ammonium module, with the nitrate modulesport modules. (For interpretation of the references to colour in this figure legend,

processes. The Michaelis-Menten kinetics is usually chosen to cal-culate the denitrification process. When site-specific values of theparameters in Eqs. (8)–(10) are not available, one can use literaturevalues (Zhu et al., 2009).

3.2.2. Immobilization and mineralizationThree assumptions are made to simulate the immobiliza-

tion/mineralization process: (1) ammonium is the only reactionproduct from the organic nitrogen pools; (2) both nitrate andammonium can be immobilized to the litter nitrogen pool, andammonium immobilization occurs before nitrate immobilization;(3) the C/N ratio in the humus pool is a constant value. The transfor-mation processes between the organic nitrogen pool and inorganicnitrogen pool can be found in Fig. 1, which helps to calculate the

immobilization/mineralization process (Jansson, 1991; Lu, 2004).In Fig. 1, qc is the carbon decomposition rate in the litter pool; rland r0 is the C/N ratio in the litter and humus pools, respectively;fe is the synthesis efficiency constant, representing the portion of

ter Ma

ctlr

wlis

c

(

d

(

iot

wmv

t

wf[

pitrapla

C

C

C

wttCi

Y. Zhu et al. / Agricultural Wa

arbon transformation from litters to the biomass and humus; fh ishe humification fraction. The decomposition rate of nitrogen in theitter pool is calculated from the C/N ratio and the decompositionate of carbon via

∂cN,l∂t

= 1rl

∂cC,l∂t

= −Klfl(, T)cC,lrl

, (11)

here cC,l and cN,l are the carbon and nitrogen concentrations in theitter pool [M L−3], respectively; Kl is the first-order rate coefficientn litter pool [T−1]; and fl(, T) are the response functions from theoil water moisture and soil temperature [−].

The change rate of nitrogen concentration from the internalycling in the litter pool is governed by

RNl )l→l = − (1 − fh)fer0

∂cC,l∂t

. (12)

The change rate of nitrogen concentration in the humus poolue to humification from the litter pool is governed by

RNh )l→h = − fhfe

r0

∂cC,l∂t

. (13)

The net decomposition rate of nitrogen from the litter pool tonorganic form is calculated from the balance of the decompositionf nitrogen in the litter pool, the internal cycling nitrogen rate tohe litter pool, and the humification rate as follows,

Nl= −[

1rl

∂cC,l∂t

− (1 − fh)fer0

∂cC,l∂t

− fhfer0

∂cC,l∂t

]= −

[1rl

− fer0

] ∂cC,l∂t

,

(14)

here Nl is the inorganic nitrogen concentration change due toineralization/immobilization in litter pool [M L−3 T−1]. NegativeNl values indicate occurrence of immobilization, and positive Nl

alues indicates occurrence of mineralization.The decomposition rate of nitrogen from the humus pool into

he soil solution (ammonium) is calculated by,

Nh = −Khfh(, T, pH)cN,h (15)

here Kh is the first-order rate coefficient in humus pool [T−1];h(,T,pH) are the response functions from , T, and soil pH value−]; and cN,h is the nitrogen content in the humus pool [M L−3].

In the model presented in this paper, the advection and dis-ersion processes of organic carbon and organic nitrogen are

gnored. The soil organic carbon and organic nitrogen concen-rations in the litter or humus pools in each time step aree-calculated by subtracting/adding the mass loss/load of miner-lization/immobilization processes, as shown above. We directlyrovide the equations to calculate the soil organic carbon in the

itter pool and the organic nitrogen in the litter and humus poolss follows,

C,l,i+1 = CC,l,i exp [−Klflti] − (1 − fh)feCC,l,i [exp(−Klflti) − 1] ,

(16)

N,l,i+1 = CN,l,i +[

1rl

− (1 − fh)fer0

]CC,l,i, (17)

N,h,i+1 =(CN,h,i+1 + (− fefh

r0CC,l,i)

)exp(−Khfhti), (18)

CC,l,i = CC,l,i [exp(−Klflti) − 1] , (19)

here i and i + 1 means the previous and present time; ti is the

ime step; CC ,l,i+1, CC ,l,i is the soil organic carbon concentration inhe litter pool in the current and previous time [M L−3]; CN ,l,i + 1 andN ,l,i are the soil organic nitrogen concentration in the litter pool

n the current and previous time [M L−3], respectively; and, CN ,h,i+1

nagement 180 (2017) 35–49 39

and CN ,h,i are soil organic nitrogen concentration in the humus poolin the current and previous time [M L−3], respectively.

3.2.3. Root uptakeThe root uptake of ammonium and nitrate is estimated by using

the following equations (Yang et al., 2008),

Rp4 = max(csw4 × fR × S, cmax 4 × fR × S), (20)

Rp3 = max(csw3 × fR × S, cmax 3 × fR × S), (21)

where fR is the root uptake coefficient ranging from 1.0 to 1.25[−]; cmax4 and cmax3 are the maximum root uptake concentrationof ammonium and nitrate [M L−3]; S is defined as (Feddes et al.,1978),

S = ˛(h)Sp, (22)

(h) being a pressure response function of root uptake [−], and Spbeing the potential water uptake by plant [T−1].

3.3. Groundwater nitrogen reactive transport

The transformation and transport of nitrate and ammonium inthe groundwater are governed by the following 3-D ADEs,

∂cGW3

∂t= ∂∂xi

(Dij

∂cGW3

∂xj

)− ∂qicGW3

∂xi+ RG3, (23)

∂cGW4

∂t+ ∂SGW4

∂t= ∂∂xi

(Dij

∂cGW4

∂xj

)− ∂qicGW4

∂xi+ RG4, (24)

where cGW 3 and cGW 4 are nitrate and ammonium concentrations inthe groundwater [M L−3], respectively; SGW 4 is the adsorbed con-centration of ammonium on solid particles in the groundwater [−];RG3 and RG4 are the source and/or sink terms of groundwater nitrateand ammonium, [M L−3 T−1], respectively. The sink/source termsare evaluated as,

RG3 = (RGW )dn + (RGW )n, (25)

RG4 = (RGW )n, (26)

where (RGW )dn and (RGW )n are the denitrification and nitrificationrate in the groundwater system [M L−3 T−1], respectively, calcu-lated by the kinetics equations shown in Eqs. (9) and (10) withtheir specified parameters. Dij is the dispersion coefficient [L2T−1]calculated by (Bear, 1972),

Dij = DT |q|ıij + (DL − DT )qiqj|q| + Ddıij, (27)

where DL and DT are the longitudinal and transverse dispersivity,respectively [L]; ıij is the Kronecker delta function [−]; |q| is theabsolute value of the Darcian fluid flux density [L T−1]; Dd is theionic or molecular diffusion coefficient in free water [L2 T−1], and is the tortuosity factor [−].

Both the 3-D nitrate and ammonium transport equations canbe dispersed by the vertical/horizontal splitting concept into thedepth averaged 2-D equation and the vertical variation 1-D equa-tion. Then the spatial discretization is carried out in the horizontaland vertical directions respectively by the hybrid finite elementmethod (FEM) and finite difference method (FDM). The details ofthe numerical methods can be found in Zhu et al. (2013).

3.4. Integration of the unsaturated and saturated nitrogentransport

Fig. 3(a) illustrates a fully coupled unsaturated-saturated systemwith one saturated layer and one unsaturated sub-area. Fig. 3(b)shows the connection nodes (node i in the unsaturated zone and

40 Y. Zhu et al. / Agricultural Water Management 180 (2017) 35–49

F line ws ratedl

nzraflo

(

w

tat

4

bacdri(aiwadaI(u

M

R

wY

ig. 3. (a) The illustrative example and (b) the integration nodes. The vertical solidolid nodes above the water table and (m’-m) nodes below the water table. The satuocation.

ode M at the water table) between the unsaturated and saturatedones. The 1-D equations of unsaturated ammonium and nitrateeactive transport are coupled with the 3-D equations of saturatedmmonium and nitrate reactive transport by their exchange massuxes, (Rex)p (p = 4, 3), which can be calculated by concentrationsf the two nodes above and below water table via,

Rex)p = −Dzz(cM)j+1

p − (ci)j+1p

L+ qz

(cM)j+1p + (ci)

j+1p

2, (28)

here subscript p = 3 and 4 are for nitrate and ammonium, respec-

ively; superscript j + 1 is the present time; Dzzis the geometricverage dispersion coefficient of the two nodes [L2 T−1]; and qzishe geometric average flow velocity of the two nodes [L T−1].

. Model evaluation and application

Three cases are carried out to test model validity and applica-ility in different conditions. Since different transport equationsre coupled together in the soil zone and groundwater, a syntheticase (case 1) is needed to test the mathematical coupling methodescribed in Section 3.4. The evaluation is done by comparing theesults of this study with those obtained using Nitrogen2D, whichs a well-calibrated variable unsaturated-saturated nitrogen modelWang, 2007; Yang et al., 2008). Case 2 is designed to test the modelbility in agricultural conditions, in which the model of this studys used to simulate the nitrogen dynamics in vertical soil profiles

ith crop growth and sewage water irrigation. To test the consider-tion of spatial variability with multiple 1-D soil columns, Case 3 isesigned to simulate 3-D water flow and nitrogen transformationnd transport from septic systems to soil zone and groundwater.n these test cases, mean error (ME) and root mean square errorRMSE) are used to quantitatively evaluate the misfit between sim-lated and observed data. ME and RMSE can be calculated as

E = 1n

n∑i=1

(Yimod − Yiobs), (29)

MSE =

√√√√1n∑

(Yimod − Yiobs)2, (30)

ni=1

here n is the sample number; Yimod is the simulated value, andiobs is the observed value.

ith m’ nodes means the special dicretization of the 1-D soil column, with m black zone is discretized by 2n nodes. The grey interface means the transient water table

4.1. Case 1: code verification in comparison with nitrogen2D

This synthetic case considers 1-D water flow and nitrogen trans-formation and transport. The size of the simulated soil column isset as 0.1m*0.1m* 3 m and the initial water table is 2.9 m. A con-stant pressure head 0.1 m is applied to the soil bottom. The dailyinfiltration rate and evaporation/transpiration rates used in case 2are applied to the soil surface (shown in Fig. 7, from the first dayto the 150th day). The ammonium and nitrate concentration in theirrigation water are 25.0 mg L−1 and 1.5 mg L−1. The no-flow bound-ary condition is prescribed around the column. The soil hydraulicproperties are described by the van Genuchten model. The corre-sponding five parameters are as follows: the residual water contentr is 0.095; the saturated water content s is 0.35; the coefficientin the soil water retention function is 1.9 m−1; the exponentin the soil water retention function n is 1.31; and the saturatedhydraulic conductivity Ks is 0.6 m d−1. The nitrogen reactive trans-port parameters are listed in Table 1, which are selected accordingto the parameter ranges (also listed in Table 1) compiled by Zhuet al. (2009).

Fig. 4 shows the simulated values of soil moisture, nitrate andammonium concentrations by the model of this study and Nitro-gen2D at the two different soil depths. A good agreement betweenthe two sets of simulations is observed. This not surprising, becausethe two models use the same kinetics to represent the trans-formation processes. The deviations between the simulations areattributed to the fact that the model of this study specifies the waterflow and nitrogen reactions in the unsaturated and saturated zonesseparately, while Nitrogen2D considers the overall water flow andnitrogen reactions in the unsaturated-saturated zone. Based onthe simulated results, the ammonium and nitrate concentrationsin the top soil layer increase during irrigation, and have positiverelation with the nitrogen concentration in the irrigated water.However, due to the adsorption in the soil and nitrification process,the ammonium concentration decreases with depth. In contrast,the nitrate concentration slightly increases with depth.

Fig. 5 shows that the accumulated nitrogen masses due tomineralization, denitrification, nitrification, and root uptake sim-ulated by the model of this study and by Nitrogen2D. The twosets of simulations are again similar. The absolute errors of theaccumulated nitrogen masses between the two models over the

entire simulation domain (0.03 m3) are 0.1 g, 0.4 g, 0.041 g, 0.2 g and0.02 g for the mineralization, denitrification, nitrification, nitrateand ammonium root uptake processes, respectively. The nitrogen

Y. Zhu et al. / Agricultural Water Management 180 (2017) 35–49 41

Table 1The nitrogen transformation and transport parameters of Case 1. The value range is from the information collection work of Zhu et al. (2009).

Parameter Unit Value range Value

The first order rate coefficient in humus pool Kh (d−1) 0.0000027–0.00034 0.00008The synthesis efficiency constant fe (−) 0.2–0.9 0.5The humification fraction fh (−) 0.1–0.9 0.2The first order rate coefficient in litter pool Kl (d−1) 0.001–0.07 0.035The maximum rate constant of denitrification Km (d−1) 0–0.3 0.027The saturation coefficient Kc (kg m−3) 0–10 10First-order rate coefficient of nitrification Kn (d−1) 0.00207–1.2 0.025The vertical dispersivity in the unsaturated zone (m) 0–1.0 1.0Longitudinal dispersivity DL (m) 0–1.0 1.0Transverse dispersivity DT (m) 0–0.5 0.5Constant of linear equilibrium interactions between solution concentration and adsorbed solute Kd (m3 kg−1) 0.326–5.71 4.0 (ammonium)

0.15

0.2

0.25

0.3

0.35

0.4

0 50 100 150

θ

t (d)

Depth=0.2m, The proposed model Depth=0.2m, Nitrogen2DDepth=1.5m, The prop osed model Depth=1.5m, Nitrogen2D

(a)

102030405060708090

100

0 50 100 150

Nitr

ate

conc

entra

tion

(mg

L-1)

t (d)

Depth=0.2m, The propo sed mod el Depth=0.2m, Nit rog en2 DDepth=1.5m, The propo sed mod el Depth=1.5m, Nit rog en2 D

(b)

00.5

11.5

22.5

33.5

4

0 50 100 150

Am

mon

ium

con

cent

ratio

n (m

g L-1

)

t (d)

Depth=0.2m, The prop osed model Depth=0.2m, Nitrogen2DDepth=1.5m, The prop osed model Depth=1.5m, Nitrogen2D

(c)

F D at tc

man7

ig. 4. The transient simulated results from the proposed model and Nitrogen2oncentration, (c) ammonium concentration.

ass balance is also analyzed in this case. The absolute error of

mmonium mass is 0.1069 g, and the relative error is 11.3%. Foritrate, the absolute mass error is 0.12 g, and the relative error is.1%. The errors are acceptable for both masses.

wo different soil depths from the ground surface, (a) soil moisture, (b) nitrate

Fig. 6 shows the dynamics of flux exchange of ammonium and

nitrate between the unsaturated and saturated zones. This is afeature not available in Nitrogen2D. The model of this study cansimulate the flux exchange, because the model simulate the unsat-

42 Y. Zhu et al. / Agricultural Water Management 180 (2017) 35–49

(4.60)

(3.60)

(2.60)

(1.60)

(0.60)

0.40

1.40

0 20 40 60 80 100 120 140

Acc

umul

ated

nitr

ogen

reac

tion

mas

s (g

)

t (d)

Mineralization (the proposed model) Mineralization (Nitrogen2D)Denit rificati on (The proposed mod el) Denit rification (Nit rogen2 D)Nit rificati on (The p roposed model) Nit rificati on (Nit rogen2D)Roo t uptake (The p roposed mod el) Root uptake (Nit rog en2 D)

Fig. 5. The accumulated nitrogen mass of the reaction processes from the proposed modemodel, and the different widths of solid line mean the results from Nitrogen2D.

-0.2

0

0.2

0.4

0.6

0.8

1

0 50 100 150

Exch

ange

flux

(g d

-1m

-2)

t (d)

NitrateAmmonium

Fz

umwt

4

tICtfiT(JmhutA0so0

oee(Vire(c

ig. 6. The transient exchange fluxes of nitrate and ammonium between the soilone and groundwater system.

rated and saturated zones separately. This advantage enables theodel to estimate the nitrate load or extraction to/from ground-ater. This figure demonstrates the unique feature of the model of

his study.

.2. Case 2: lysimeter experiments with sewage water irrigation

The lysimeter experiment was conducted from November 2003o June 2004 during the growing season of winter wheat at therrigation and Drainage Experimental Station in Wuhan University,hina (Wang, 2007). Three experiment plots were constructed inhree drainage lysimeters (each with the size of 2m × 2m × 3m)lled by repacked soil and irrigated with treated sewage water.he three plots are numbered as Plot 1 (P1), Plot 2 (P2), and Plot 3P3). The initial water table is 1.7 m below the soil surface. Beforeanuary 7, 2004, the experiment site was subject to natural cli-

ate conditions. Afterward, a waterproof sheet was placed at theeight of 4 m over the experiment site to isolate the site from nat-ral precipitation. Treated sewage irrigation water was appliedo the plots four times on January 7, January 9, March 10, andpril 21, 2004, with the irrigation water amount 0.28 m3, 0.105 m3,.42 m3, and 0.42 m3, respectively. The major nitrogen forms in theewage water are ammonium and nitrate with the concentrationsf 30 mg L−1 and 0.17 mg L−1, respectively. The organic nitrogen is.83 mg L−1.

The climate information is downloaded from the China Mete-rological Data Sharing Service System. The reference cropvapotranspiration rate is calculated by the Penman-Monteithquation, which is well evaluated and applied worldwideDoorenbos and Pruitt, 1977; Valipour and Eslamian, 2014;alipour, 2014b, 2015a, 2015b, 2015c). The real evapotranspiration

s calculated by multiplying the reference crop evapotranspiration

ate with crop coefficient 0.87. The crop transpiration rate over soilvaporation rate is assumed to be 3:1 in the crop growing seasonWang, 2007). Fig. 7 plots the data of precipitation/irrigation rate,rop transpiration rate, and soil evaporation rate, which are the

l and Nitrogen2D. The different types of dot line mean the results from the proposed

input information at the upper boundary. The ammonium, nitrate,and total nitrogen concentrations were measured by taking 14 soilsamples at different depths (0.05 m, 0.15 m, 0.25 m, 0.35 m, 0.45 m,0.55 m, 0.65 m, 0.75 m, 0.85 m, 0.95 m, 1.15 m, 1.35 m, 1.75 m, and1.95 m) and using ultraviolet spectrophotometer (three measure-ments were taken for each sample). During the experiment, fieldmeasurements were taken four times on 2 November 2003 (theinitial condition), 8 March 2004, 21 April 2004, and 1 June 2004(the final condition). Soil moisture content and pressure head weremeasured at 10 depths (from 0.10 m to 1.9 m with the incrementof 0.2 m) using TDR and tension-meters during the experiment.

The 213-day experiment was simulated using the model. Theupper boundary condition is set as the atmospheric condition withdata shown in Fig. 7. The lateral boundary is set as the no-flowboundary, and the bottom boundary condition is set as the constanthead of 0.1m. The observed pressure head and moisture contentdata along the soil profile are used to fit the soil water character-istic curves to obtain the five parameters of the van Genuchtenmodel. The parameter values for the three plots are listed inTable 2. The parameters of nitrogen transformation and transportare obtained by calibrating the simulation results against the cor-responding measurements. The measurements of P1 are used forthe calibration, which is conducted manually in a trial-and-errormanner.

Fig. 8(a) plots the vertical profiles of the simulated and observedmoisture content and ammonium and nitrate concentrations at theend of the experiment (June 1, 2004) at P1. The agreement betweenthe simulations and observations is the worst at the end of theexperiment because of simulation error accumulation with time.However, the simulated moisture content in the soil profile is ina good agreement with the measurements with ME = 0.001 andRMSE = 0.01. Fig. 8(a) also shows the comparison of the simulatedand measured ammonium and nitrate concentrations in the soilprofile. Although the RMSE values of ammonium and nitrate arerelatively large (1.18 mg L−1 and 40 mg L−1, respectively), the MEvalues of ammonium and nitrate are 0.01 mg L−1 and 6.85 mg L−1,respectively. It indicates that the average differences of ammoniumand nitrate are small and that the simulation results are accurateto maintain nitrogen balance in the whole domain. The nitrogentransformation and transport parameters obtained in the calibra-tion are listed in Table 3, and they are used to predict the nitrogendynamics of P2 and P3.

Fig. 8(b) and (c) show the simulated and measured profiles ofsoil moisture content and ammonium and nitrate concentrationsfor plots P2 and P3 by using the calibrated parameters listed inTables 2 and 3. The figures show good agreements between the

simulated and measured moisture content. The ME and RMSE val-ues of the moisture content at P2 are 0.001 and 0.02, respectively,while the values are 0.008 and 0.01 for P3. As shown in Fig. 8(b), themodel of this paper captures the ammonium concentrations in the

Y. Zhu et al. / Agricultural Water Management 180 (2017) 35–49 43

Fig. 7. The upper boundary conditions. (a) Daily crop transpiration rate, (b) daily evaporation rate, and (c) daily precipitation and irrigation rate.

Table 2Soil water characteristic parameters of Case 2.

No. Depth (m) r (−) s (−) (m−1) n (−) Ks (m d−1)

P1 0–0.4 0.067 0.39 2.0 1.41 0.60.4–1.8 0.067 0.39 2.0 1.31 0.41.8–3.0 0.095 0.39 2.0 1.41 0.01

P2 0–0.3 0.095 0.40 1.9 1.31 0.40.3–1.8 0.095 0.36 1.9 1.31 0.41.8–3.0 0.095 0.35 1.9 1.31 0.2

P3 0–0.2 0.1 0.38 2.0 1.41 0.60.2–1.8 0.1 0.38 2.0 1.23 0.41.8–3.0 0.1 0.37 1.5 1.23 0.3

Note: r is the residual water content. s is the saturated water content. is the coefficienfunction. Ks is the saturated hydraulic conductivity.

Table 3The calibrated nitrogen transformation and transport parameters of Case 2.

Parameter Unit Value

The first order rate coefficient in humus pool Kh (d−1) 0.0001The synthesis efficiency constant fe (−) 0.5The humification fraction fh (−) 0.2The first order rate coefficient in litter pool Kl (d−1) 0.035The maximum rate constant of denitrification Km (d−1) 0.007The saturation coefficient Kc (kg m−3) 10First-order rate coefficient of nitrification Kn (d−1) 0.025First-order rate coefficient of volatilization Kv (d−1) 0.002The vertical dispersivity in the unsaturated zone (m) 0.1Longitudinal dispersivity DL (m) 0.1Transverse dispersivity DT (m) 0.05Constant of linear equilibrium interactions (m3 kg−1) 2.0 (ammonium)

swltcoafvPmeo

between solution concentration and adsorbedsolute Kd

oil profile except the underestimated ammonium concentrationsithin the depth of 0.2 m to 0.5 m. The ME value between the simu-

ated and measured ammonium concentrations is 0.02 mg L−1, andhe RMSE value is 0.55 mg L−1. For the comparison of nitrate con-entrations, Fig. 8(b) shows the underestimation above the depthf 0.5 m but the overestimation within the depth between 0.8 mnd 1.3 m. Since the measured nitrate concentration near the sur-ace is significantly larger than the simulated one, the ME and RMSEalues are large, being −5.3 mg L−1 and 136 mg L−1, respectively. At

3, the simulated ammonium concentrations agree well with theeasurements above the depth of 1 m. However, the model under-

stimates the ammonium concentration from 1 m to 1.5 m, whileverestimates it from 1.5 m to 2.0m. The ME value is 0.02 mg L−1,

t in the soil water retention function. n is the exponent in the soil water retention

and the RMSE value is 0.99 mg L−1. The model again underestimatesthe nitrate concentrations at P3, with the ME and RMSE values being13.6 mg L−1 and 46.6 mg L−1, respectively.

Overall, the model obtains reasonable moisture content with thecalibrated parameter values. The deviation between the simulatedand measured ammonium concentration is significantly smallerthan that for nitrate concentration. The worst agreement betweenthe simulated and measured nitrate concentrations occurred in thetop soil within the depth of 0.2 m, where the simulated values aresignificantly smaller than the measured ones. This may be caused bythe constant C/N ratio used in the simulation, which can influencethe mineralization/immobilization significantly. In particular, het-erogeneity of nitrogen transformation parameters is not consideredin this simulation.

4.3. Case 3: nitrogen transport from septic systems togroundwater

The modeling site of 7000 m2 in area is located in the City of Jack-sonville in northeast Florida, USA. Nitrate load from septic systemsis considered as a significant contamination source to groundwa-ter and surface water bodies (Wang et al., 2013). As shown in Fig. 9,the site includes 56 septic systems, and is surrounded by ditchesin the north and west boundaries and by the Red Bay Branch inthe east. In order to monitor groundwater quality, two monitoring

wells were installed by the St. Johns Water Management District(Leggette, Brashears, and Graham, Inc., 2004), and water table ele-vation and concentration of ammonium and nitrate were measuredfrom March 8, 2005 to October 12, 2006. Data from two monitor-

44 Y. Zhu et al. / Agricultural Water Management 180 (2017) 35–49

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6

Dep

th (m

)

θ (-)

0

0.5

1

1.5

2

2.5

3

0 500 1000

Nitrate concentration(mg L-1)

P1

Simulation s

Mea surements

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8

Ammonium concentrati on (mg L-1)

(a)

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4

Dep

th (m

)

θ (-)

0

0.5

1

1.5

2

2.5

3

0 200 400 600

Nitrate concentration(mg L-1)

P2

Simulati ons

Measurements

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8

Ammonium concentration (mg L-1)

(b)

0

0.5

1

1.5

2

2.5

3

0 0.2 0. 4

Dep

th (m

)

θ (-)

0

0.5

1

1.5

2

2.5

3

0 500

Nitrate conce ntration(mg L-1)

P3

Simulations

Mea surements

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8

Amm onium con centration (mg L-1)

(c)

F nd nit(

iAlAtdi

ig. 8. Vertical profiles of simulated and observed moisture content, ammonium aa) P1, (b) P2 and (c) P3.

ng wells were compared to model simulations in this study. WellM-MW-1 is located near the Red Bay Branch, and has very shal-

ow water table, which leads to an incomplete nitrification process.s the result, ammonium concentration is high but nitrate concen-

ration is low at the well. At AM-MW-2, because the water table iseeper, ammonium concentration is low but nitrate concentration

s high. The data of water table and nitrogen concentration at the

rate concentrations at the end of the experiment (June 1, 2004) at the three plots,

two wells represent the flow and nitrogen transport processes atthe site.

The precipitation data of the site is downloaded from thewebsite of http://climatecenter.fsu.edu/, and the actual evapotran-

spiration data at a nearby weather station is downloaded fromhttp://waterdata.usgs.gov/fl/nwis. The data are shown in Fig. 10,and they are used for setting the upper boundary condition. The

Y. Zhu et al. / Agricultural Water Management 180 (2017) 35–49 45

Fig. 9. The digital elevation model (DEM) of the simulation domain, with the dot representing the septic tanks, the red triangles representing the monitoring wells, andthe polygon shape representing the water bodies. The different color of DEM shows the topographic conditions. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

of evapotranspiration and precipitation rates.

aaTdwt

opuenm0atsorwaionuf

Table 4The calibrated nitrogen transformation and transport parameters of Case 3.

Parameter Unit Value

The first order rate coefficient in humus pool Kh (d−1) 0.000001The synthesis efficiency constant fe (−) 0.5The humification fraction fh (−) 0.2The first order rate coefficient in litter pool Kl (d−1) 0.0001The maximum rate constant of denitrification Km (d−1) 0.0027The saturation coefficient Kc (kg m−3) 10First-order rate coefficient of nitrification Kn (d−1) 0.27The vertical dispersivity in the unsaturated zone (m) 1.0Longitudinal dispersivity DL (m) 10.0Transverse dispersivity DT (m) 1.0Constant of linear equilibrium interactions (m3 kg−1) 2.0 (ammonium)

Fig. 10. The upper boundary conditions

mmonium and nitrate concentrations in each septic system are sets constant values of 60 mg L−1 and 1 mg L−1 (McCray et al., 2005).he soil type is loamy sand and the porosity is 0.40 from the SSURGOatabase. A total of 13 1-D soil columns are used to represent theater flow and solute transport in the vadose zone according to the

opography conditions and nitrogen source conditions at the site.The observed data of 2005 is used for model calibration. The

bservations of water table are used to calibrate the soil hydraulicarameters, and the ammonium and nitrate concentrations aresed to calibrate the nitrogen transformation and transport param-ters. Fig. 11 plots the measured and simulated water table anditrate and ammonium concentrations. The coefficient of deter-ination (R2) between the measurements and simulations are

.6793, 0.9377, and 0.9111 for water table, nitrate concentration,nd ammonium concentration, respectively. The R2 value of waterable is low due to the large difference between the measured andimulated values at AM-MW-2 on 8/10/2005. The sudden increasef the observed water table is not well captured by the model. Afteremoving this measurement, the R2 is 0.967. The RMSE value ofater table is 0.66 m (n = 29). When removing the measured data

t AM-MW-2 on 8/10/2005 from the RMSE calculation, the RMSEs 0.15 m. Overall, the simulated water table agrees well with thebserved data. The calibrated soil hydraulic parameter values are

r = 0.095, s = 0.4, =1.9 m−1, n = 1.3, and Ks = 6.9 m d−1. For theitrogen concentrations, Fig. 11(b) and (c) show that the RMSE val-es are 0.35 mg L−1 (n = 29) for ammonium and 1.8 mg L−1 (n = 29)

or nitrate. The calibrated parameters of nitrogen reactive transport

between solution concentration and adsorbedsolute Kd

are listed in Table 4. Due to the high absorption and low mobility ofammonium in the groundwater system, the simulated ammoniumconcentration stays relatively stable as shown in Fig. 11(b).

The calibrated parameter values are used to simulate the watertable and nitrogen concertation measured in 2006. Fig. 12 showsthe observed and simulated water table and ammonium andnitrate concentrations at the two monitoring wells. The RMSE val-

ues for the cross-validation period are 0.24 m (n = 22) for watertable, 1.2 mg L−1 for nitrate concentration, and 0.35 mg L−1 forammonium concentration. These values indicate a good agree-ment between the observed and simulated data, suggesting that

46 Y. Zhu et al. / Agricultural Water Management 180 (2017) 35–49

y = 0.660 9x + 1.88 46R² = 0.679 3

RMSE=0.66 m

4

5

6

7

8

9

4 5 6 7 8 9 10

Sim

ulat

ed w

ater

tabl

e (m

)

Measured water table (m)

y = 0.9376x + 0.1108R² = 0.9111

RMSE=0.35 mg L-1

0

4

0 1 2 3 4

Sim

ulat

ed a

mm

oniu

m c

once

ntra

tion

(mg

L-1)

Measured ammon ium concentration(mg L-1)

(a) (b)

y = 0.926 5x + 0.821 6R² = 0.93 77

RMSE=1.8 mg L-1

0

5

10

15

20

25

0 10 20 30Sim

ulat

ed n

itrat

e co

ncen

tratio

n (m

g L-1

)

Measured Nitrate con centration (mg L-1)

(c)

F ium aa

tssttawdAs

tsitwtots

uiittp

bst

ig. 11. The linear regression of the simulated and measured water table, ammonmmonium concentration, and (c) nitrate concentration.

he calibrated parameter values are reasonable. The observed andimulated water table away from the water bodies show relativelytable trend even with the variable climate upper boundary condi-ions, while the water table near the water bodies changes alonghe climate information due to the shallow water table depth. Themmonium concentration in well AM-MW-1 change slightly withater table variation, and the increased water table results in the

ecrease of ammonium concentration. The nitrate concentration inM-MW-2 does not appear to change with water table, and remainstable during the simulation period.

The contours of simulated nitrate concentration at the waterable depth at three different times (100, 160, and 200 days) arehown in Fig. 13 to understand the temporal evolution of nitrogennfiltration to groundwater. The figure shows that the spatial pat-ern of nitrate concentration has small temporal variation. If oneants to further reduce the computational cost, it is reasonable to

reat the soil system as steady state. Fig. 13 shows the transportf nitrate to the Red Bay Branch (the east boundary), indicatinghat septic tanks are important nitrogen contamination sources tourface water bodies.

The numerical simulation uses 7640 saturated nodes, 1040nsaturated nodes, and 3650 time steps. The total simulation time

s 1,200s, which is considered to be acceptable and fast. This numer-cal study demonstrates that our integrated model can simulateemporal distribution of nitrogen concentration under complexopographic and hydrological conditions with relative low com-utational cost.

While quantification and reduction of predictive uncertainty is

eyond the scope of this study, they will be investigated in a futuretudy for improving accuracy of model predictions. The predic-ive uncertainty may be caused by uncertainty in model structures

nd nitrate concentration of the two monitoring wells in 2005, (a) water table (b)

and parameters. Ajami and Gu (2010) presented an example ofmodel uncertainty that there may exist multiple plausible modelsfor simulating nitrogen reactive transport. The model uncertaintymay be quantified using the method of multi-model analysis (alsoknown as model averaging) by first considering multiple modelsand then selecting the best models for predictive analysis (Ye et al.,2004, 2008; Lu et al., 2013, 2015). The parametric uncertainty canbe substantially reduced by calibrating the models against fieldobservations. Due to nonlinearity of reactive transport models, theMarkov chain Monte Carlo (MCMC) methods may be more suitablethan nonlinear regression methods, as shown in Shi et al. (2014)and Lu et al. (2014). Since model calibration is computationallyexpensive, a sensitivity analysis may be needed to select impor-tant parameters so that model calibration is applied only to theimportant parameters, as shown in Wang et al. (2013). For the twofield applications presented in this example, since a relatively largenumber of model parameters are involved, a sensitivity analysis isthe first step toward reducing predictive uncertainty.

5. Conclusions

This paper presents a fully integrated model for simulatingunsaturated and saturated flow and nitrogen transformation andtransport. The key contribution of the recently developed modelis to incorporate the transport of multiple nitrogen species anda comprehensive list of biogeochemical reactions of nitrogentransformation. The incorporation is non-trivial, as it requires a

substantial effort of not only developing numerical formulation forthe unsaturated and saturated systems, but also developing com-puter code for implementing the formulation. The fully integratedmodel and associated computer code developed in this study is a

Y. Zhu et al. / Agricultural Water Management 180 (2017) 35–49 47

4

5

6

7

8

0 50 100 150 200 25 0 300 35 0 400

Wat

er ta

ble

(m)

t (d)

AM-MW-1 Mea surements AM-MW-1 SimulationsAM-MW-2 Mea surements AM-MW-2 Simulations

(a)

00.5

11.5

22.5

33.5

44.5

5

0 50 100 150 200 250 300 350 400

Am

mon

ium

con

cent

ratio

n (m

g L-1

)

t (d)

AM-MW-1 Mea surementsAM-MW-1 Simulation sAM-MW-2 Mea surementsAM-MW-2 Simulation s

(b)

02468

101214161820

0 50 100 150 200 250 300 350 400

Nitr

ate

conc

entra

tion

(mg

L-1)

t (d)

AM-MW-1 Measurements AM-MW-1 SimulationsAM-MW-2 Measurements AM-MW-2 Simulations

(c)

F (a) wJ

vp

(

(

ig. 12. The simulated and measured results at the two monitoring wells in 2006,anuary, 1, 2006.

ital alternative to the existing models of nitrogen reactive trans-ort modeling.

The major conclusions of this study are as follows:

1) The fully integrated model considers a large number of nitrogentransformation processes and transport mechanisms occurringin soils and groundwater aquifers. The numerical evaluationdemonstrates the accuracy of the integration method of cou-pling unsaturated and saturated nitrogen transformation andtransport. This enables the model to comprehensively includethe nitrogen reaction and transport processes in the entireunsaturated-saturated system, which makes it suitable for gen-eral and complex field conditions.

2) Building on our previous fully integrated unsaturated-saturated flow and solute transport model, the integrated

nitrogen reactive transport model presented in this study iscomputational efficient due to the numerical methods used inthe numerical modeling and to the simplification of the verticalwater flow and reactive transport in the unsaturated zone.

ater table, (b) ammonium concentration, (c) nitrate concentration. The first day is

(3) Practical applications of the model and computer code to the1-D and 3-D problems demonstrate the model flexibility torepresent major nitrogen transformation processes and to sim-ulate nitrogen reactive transport under complex geological andhydrological conditions such as agricultural irrigation and spa-tial topography.

It should be noted that, due to the use of the 1-D vertical soilcolumns for the soil zone, our model may not accurately simulatenitrogen transport in highly heterogeneous soils where lateral flowcannot be ignored. In addition, the current model does not considerreactive transport of other species (e.g., carbon) and crop growththat are also important to nitrogen reactive transport in agriculturalareas. Further model development to incorporate other biogeo-

chemical reactions and crop growing processes is warranted. Inaddition, the impacts of temperature and organic carbon on denitri-fication in the groundwater system will be estimated in the futuredevelopment.

48 Y. Zhu et al. / Agricultural Water Management 180 (2017) 35–49

x (m)

y(m)

0 100 200 300 4000

50

100

150119.586.553.520.5

Unit: mg L-1

(a)

x (m)

y(m)

0 100 200 300 4000

50

100

150 10.99.78.57.36.14.93.72.51.30.1

Unit: mg L-1

(b)

x (m)

y(m)

0 100 200 300 4000

50

100

150 9.28.27.26.25.24.23.22.21.20.2

Unit: mg L-1

(c)

es in

A

d5PdpF

References

Fig. 13. The nitrate distributions in the groundwater system at different tim

cknowledgements

The study was supported by National Natural Science Foun-ation of China through Grants (51409192, 41272270, 51479143,1479144, and 51328902), Natural Science Foundation of Hubeirovince (2016CFB576), and the China Postdoctoral Science Foun-ation Award (2014M560627). The third author was supported inart by the NSF-EAR grant 1552329 and contract WQ005 with the

lorida Department of Environmental Protection.

2006, (a) t = 100d, (b) t = 160d, (c) t = 200d. The first day is January 1, 2006.

Appendix A. Supplementary data

Supplementary data associated with this article can be found,in the online version, at http://dx.doi.org/10.1016/j.agwat.2016.10.017.

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L

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