Assessment of solute fluxes beneath an orchard irrigated with treated sewage water: A numerical study

Authors

  • David Russo,

    Corresponding author
    • Department of Environmental Physics and Irrigation, Institute of Soils, Water and Environmental Sciences, Agricultural Research Organization, Bet Dagan, Israel
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  • Asher Laufer,

    1. Department of Environmental Physics and Irrigation, Institute of Soils, Water and Environmental Sciences, Agricultural Research Organization, Bet Dagan, Israel
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  • Roi H. Shapira,

    1. Department of Environmental Physics and Irrigation, Institute of Soils, Water and Environmental Sciences, Agricultural Research Organization, Bet Dagan, Israel
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  • Daniel Kurtzman

    1. Department of Environmental Physics and Irrigation, Institute of Soils, Water and Environmental Sciences, Agricultural Research Organization, Bet Dagan, Israel
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Corresponding author: D. Russo, Department of Environmental Physics and Irrigation, Institute of Soils, Water and Environmental Sciences, Agricultural Research Organization, Bet Dagan 50250, Israel. (vwrosd@agri.gov.il)

Abstract

[1] Detailed numerical simulations were used to analyze water flow and transport of nitrate, chloride, and a tracer solute in a 3-D, spatially heterogeneous, variably saturated soil, originating from a citrus orchard irrigated with treated sewage water (TSW) considering realistic features of the soil-water-plant-atmosphere system. Results of this study suggest that under long-term irrigation with TSW, because of nitrate uptake by the tree roots and nitrogen transformations, the vadose zone may provide more capacity for the attenuation of the nitrate load in the groundwater than for the chloride load in the groundwater. Results of the 3-D simulations were used to assess their counterparts based on a simplified, deterministic, 1-D vertical simulation and on limited soil monitoring. Results of the analyses suggest that the information that may be gained from a single sampling point (located close to the area active in water uptake by the tree roots) or from the results of the 1-D simulation is insufficient for a quantitative description of the response of the complicated, 3-D flow system. Both might considerably underestimate the movement and spreading of a pulse of a tracer solute and also the groundwater contamination hazard posed by nitrate and particularly by chloride moving through the vadose zone. This stems mainly from the rain that drove water through the flow system away from the rooted area and could not be represented by the 1-D model or by the single sampling point. It was shown, however, that an additional sampling point, located outside the area active in water uptake, may substantially improve the quantitative description of the response of the complicated, 3-D flow system.

1. Introduction

[2] The shortage in water resources and rain in the semiarid and arid zones and the need of fresh water resources for the use of an increasing urban sector necessitate the use of treated sewage water (TSW) for irrigation. Inasmuch as TSW may contain substantial concentrations of soluble salts, its long-term use for irrigation may contaminate water resources underneath the irrigated regions. This is particularly so in orchards irrigated during many years and in the same spatial configuration. Quantitative descriptions of field-scale transport of chemicals in the vadose zone, therefore, are essential for a better understanding of the transport of TSW in near-surface formations and for the prediction of the future spread of TSW in these formations. Furthermore, they are essential for the reliable assessment of the threat posed by the extensive use of TSW for irrigation to the underlying water resources.

[3] The traditional approach for modeling chemical transport in the unsaturated zone has been to model flow and transport by using macroscopic physical and chemical soil properties that obey physical and chemical laws, expressed in the form of 1-D, vertical partial differential equations and vary spatially in a deterministic manner [e.g., Kurtzman and Scanlon, 2011]. Considering irrigation with TSW, at least three subsystems should be taken into account in the modeling effort: (1) the N-C-O subsystem describing the cycling of nitrogen and carbon compounds in the unsaturated zone; (2) the major ion subsystem (Cl, SO4, HCO3, Ca, Mg, Na, and K) contributing to salinity; and (3) phosphate, boron, and trace metals.

[4] In reality, the soil properties relevant to flow and transport are spatially variable [e.g., Nielsen et al., 1973; Russo and Bresler, 1981; Jones and Wagenet, 1984; Russo and Bouton, 1992; Russo et al., 1997; Khaleel and Relyea, 2001; Botros et al., 2009]. The spatial variability in the soil properties occurs on a scale that generally is not captured by soil sampling and in turn may have a substantial effect on flow and transport. This effect has been observed in field experiments [e.g., Butters et al., 1989; Ellsworth et al., 1991; Roth et al., 1991; Flury et al., 1994; Forrer et al., 1999; Schulin et al., 2002; Onsoy et al., 2005] and has been demonstrated by numerical simulations [e.g., Russo, 1991; Russo et al., 1994, 1998, 2001, 2006; Tseng and Jury, 1994; Harter and Yeh, 1996; Roth and Hammel, 1996; Foussereau et al., 2001; Botros et al., 2012]. Furthermore, additional features of realistic flow systems, such as the plant roots, also vary spatially; in addition, the flow system may be subject to spatially nonuniform water and solute fluxes, imposed on the soil surface. Consequently, a 3-D approach is required in order to describe quantitatively the water flow and solute transport in the realistic, near-surface soil-water-plant-atmosphere flow systems.

[5] In addition to chloride, which is the main source for salinity load in groundwater, because of its mobility and persistence, nitrate is also considered as a primary groundwater pollutant [U.S. Environmental Protection Agency, 1990; Bransby et al., 1998]. In Israel, the main reason for the closure of drinking-water wells in the coastal aquifer is the presence of excessive nitrate concentrations in the wells [Elhanany, 2009]. For these reasons, the focus in this study is on the transport of chloride and nitrate. Consequently, in the N-C-O subsystem, only ammonium, nitrate, and their transformations are considered, while in the major ions subsystem, only chloride is considered. Sodium/calcium exchange and the effect of these ions on the soil hydraulic properties [Russo et al., 2004], the interaction between the two subsystems, chloride uptake by plant roots [Moya et al., 2003], the antagonism between nitrate and chloride uptake [Cerezo et al., 1997], the inhibition of nitrate uptake by ammonium or by the products of its assimilation [Serna et al., 1992], and the fate of other contaminants such as phosphate, boron, and trace metals are not considered in the present study.

[6] Although a considerable amount of research has been applied to study the nitrogen mass balance in the root zone [e.g., Stenger et al., 2002], the effect of the nitrogen transport and transformation processes in the deep vadose zone below the root zone on nitrate leaching to groundwater, however, is still not adequately quantified [Botros et al., 2012]. The common idea is that the vadose zone below the root zone may act as a limited buffer zone in which nitrate is attenuated by the denitrification process, before reaching the groundwater. In the spatially heterogeneous soils, however, nonuniform flows, and particularly preferential flow paths which might occur, may accelerate nitrate leaching in the deep vadose zone and its arrival to the groundwater [Onsoy et al., 2005; Baran et al., 2007].

[7] The general objective of the present study is threefold: (1) to investigate the field-scale transport of nitrate, chloride, and a tracer solute, originating from an orchard irrigated with TSW, in a 3-D, spatially heterogeneous, variably saturated soil; (2) to compare the results of the 3-D simulations with the results of simplified analyses, based on the deterministic, 1-D vertical simulations and on limited soil monitoring; and (3) to make use of the results of (1) and (2) in order to further investigate the sampling strategy for monitoring the fate of the contaminants in the unsaturated zone.

[8] The approach adopted here to pursue the aforementioned objectives is a stochastic-mechanistic approach. The approach combines the efficient numerical schemes to solve the partial differential equations governing the water flow and solute transport in the 3-D, spatially heterogeneous, variably saturated soils (in which both very steep head-gradients and saturated regions might develop) under cropped conditions with statistical generation methods to produce realizations of the heterogeneous soil properties in sufficient resolution.

[9] This approach, viewed as a “numerical experiment,” is a competent tool to study the processes' mechanisms and to evaluate the response of the relatively complicated flow systems to different, credible scenarios [Russo et al., 2006]. The approach may circumvent most of the stringent assumptions of analytical studies on the one hand and may facilitate the analyses of simplified, yet realistic, situations, on the other hand. Furthermore, the approach may facilitate better physical experiment design and consequently better use of resources. The approach, however, cannot serve as a substitution for field experiments.

2. Theoretical Considerations

2.1. Physical Domain

[10] The case under consideration is a citrus orchard irrigated with TSW using micro-sprinklers. The orchard is planted on a Hamra Red Mediterranean soil (Rhodoxeralf) in the Bnei-Dror site, located in the coastal region of Israel, north of Tel Aviv. This region is characterized by a distinct rainy period during the winter (with mean precipitation of 570 mm) and a relatively long dry season, requiring irrigations. Consider a subplot of this orchard (see the schematic presentation of its horizontal layout, depicted in Figure 1), consisting of a 3-D, spatially heterogeneous, variably saturated flow domain that extends over several meters in both the vertical and horizontal directions. The investigation focuses on the transport of nonconservative, reactive solutes (nitrate and ammonium) and on the transport of conservative, nonreactive solutes (a tracer solute and chloride). Realistic features of the flow domain, taken into account in the investigation, include the irrigation water quantity and quality, the spatial pattern of the irrigation system at the soil surface, the spatial variability in the relevant soil properties, the spatial pattern of the plant roots, and the atmospheric forcing conditions imposed on the soil surface.

Figure 1.

A scheme of the field plot showing the locations of the citrus trees (open triangles), the micro-sprinklers (open circles), the first sampling point (closed circle), and the second sampling points (half closed circles), estimated by minimizing equation (8). The inner rectangular area bounded by the dashed line denotes the averaging domain.

2.2. Governing Partial Differential Equations

[11] A Cartesian coordinate system (x1, x2, x3), where x1 is directed vertically downward, is considered here. It is assumed that this coordinate system coincides with the principal axes associated with the principal components of the hydraulic conductivity tensor K. Considering water uptake by the plant roots, the Richards equation that governs water flow in a rigid, 3-D, variably saturated flow domain is

display math(1)

where t is the time; θ=θ(x,t) is the volumetric water content; ψ=ψ(x,t) is the pressure head; Kii=Kii(ψ,x) (i=1, 2, 3) are the principal components of K, taken as a symmetrical tensor of rank two with zero off-diagonal components; and Sw=Sw(x,t) is a sink term, representing water uptake by plant roots. Assuming local isotropy, the principal components of the hydraulic conductivity tensor in equation (1) are given by the scalar K(ψ,x).

[12] Neglecting chloride uptake by the plant roots, assuming that the effects of salinity stress and water stress on the plants are additive, the macroscopic sink term in equation (1) is given [Nimah and Hanks, 1973a, 1973b; Feddes et al., 1974; Bresler, 1987] as

display math(2)

where ψr(t) is the pressure head at the root-soil interface; ψt(x,t)=ψ(x,t)+π(x,t) and π(x,t) are the total water pressure head and the osmotic pressure head of the soil solution, respectively; Re(x,t)=Rz(x1)Rk(x2,x3) is the root effectiveness function; Rz(x1) is a normalized root depth-distribution function; and Rk(x2,x3) is a time-invariant, bivariate normal distribution function [Coelho and Or, 1996], accounting for the lateral distribution of the roots associated with a given tree; for more details, see Russo et al. [2006].

[13] Considering solute uptake by the plant roots, assuming a linear and reversible adsorption isotherm for the partitioning of the solute between the solid and liquid phases and that the partition of the solute between the liquid and gaseous phases obey Henry's law, the advection-dispersion equation that governs the transport of the kth nonconservative, reactive, solute species in a 3-D, variably saturated flow domain is

display math(3)

where ck=ck(x,t) is the resident aqueous solute concentration of the kth solute species, expressed as mass per unit volume of soil solution; Kd is the liquid/solid partitioning coefficient; ρb is the soil bulk density; KH is a dimensionless form of Henry's constant; Ssk=Ssk(x,t) is a macroscopic sink/source term, representing solute uptake by plant roots and solute transformations; ui (i=1, 2, 3) are the components of the Eulerian velocity vector; and Dij (i, j=1, 2, 3) are the components of the pore-scale dispersion tensor. Neglecting molecular diffusion, Dij are given [Bear, 1972] as

display math(4)

where λL and λT are the longitudinal and transverse pore-scale dispersivities; δij is the Kronecker delta (i.e., δij=1, if i=j, and δij=0 if ij); and math formula=(u12+u22+u32)1/2.

[14] It is further assumed here [e.g., Lotse et al., 1992] that the nitrate and the ammonium ions are changed by a series of first-order reactions. Assuming that the concentration of nitrite is negligibly small as compared with those of ammonium and nitrate, the transformations of the latter are represented by the following first-order kinetic expressions:

display math(5a)
display math(5b)

where c1 and c2 are the resident aqueous concentrations of ammonium and nitrate, respectively; and K1 and K2 are the apparent first-order rate constants for the processes of nitrification and denitrification, respectively.

[15] The latter processes involve mirobially mediated reactions, which, in turn, may depend on many environmental variables. To simplify the analyses, however, it is assumed here that the nitrification and denitrification processes are controlled by abiotic response functions, involving soil water content and soil temperature [Johnsson et al., 1987], i.e., K1=em1etK1 and K2=em2etK2, where em1=em1(x,t) and em2=em2(x,t) and et=et(x,t) are soil moisture and soil temperature factors, respectively, and K1 and K2 are the first-order rate constants for the nitrification and the denitrification processes, respectively. Note, however, that because isothermal conditions were assumed here, et is considered as a constant. In addition, unlike nitrate, ammonium is adsorbed to the soil and may be lost to the atmosphere by ammonia volatilization.

[16] Pertaining to the regulation of root N uptake, there is a general agreement on the hypothesis that feedback repression exerted by the nitrogen nutritional status of the plant is involved in the control of root ammonium and nitrate uptake systems [Cerezo et al., 2007]. Furthermore, root nitrate uptake may be inhibited by ammonium or by the products of its assimilation [Serna et al., 1992], while chloride may affect root nitrate uptake due to the antagonism between nitrate and chloride uptake [Cerezo et al., 1997]. To simplify the analyses, however, the last two processes were not considered in the present study. It is assumed here that root ammonium and nitrate uptake Nuk (k=1, 2), respectively, depend on both plant internal factors related to the N demand of the plant and on nitrate and ammonium availability in the soil solution and may be represented by the following expression:

display math(6)

where Kuk(t) (k=1, 2) are the time-dependent, plant-specific, root uptake coefficients for ammonium and nitrate, respectively, related to the N demand of the plant; ck(x,t) (k=1, 2) are the ammonium and nitrate resident concentrations in the soil solution, respectively; θ(x,t) is the volumetric soil water content; and Re(x,t), considered here as time-invariant, is the root effectiveness function (equation (2)) proportional to the specific area of the soil-root interface and inversely proportional to the impedance of the soil-root interface.

[17] Note that for the nitrate, chloride, and the tracer solute, KH=0, and, neglecting anion exclusion, Kd=0; furthermore, for the chloride (k=3) and the tracer (k=4), assuming that their uptake by the plant roots is negligibly small, Ssk(x,t)=0.

2.3. Numerical Approach

[18] The 3-D simulation model of Russo et al. [2001], modified to account for nitrogen transformations in the soil-plant-water-atmosphere system, was employed here in order to simulate the flow and transport in a 3-D, heterogeneous, variably saturated, flow domain. Details of the numerical methods used to approximate the partial differential equations governing water flow and solute transport in the 3-D, spatially heterogeneous, variably saturated formations are given by Russo et al. [1998, 2001, 2006]. For the solute transport, the numerical scheme [Russo et al., 2001] employed here is similar to the third-order total-variation-diminishing (TVD) scheme implemented in the MT3D code [Zheng and Wang, 1999]. Note that similar to the TVD scheme, the numerical scheme employed here [Russo et al., 2001] is designed to minimize the numerical dispersion for advection-dominated transport problems. Therefore, this scheme can be utilized even in the purely advective case (Pe → ∞), where Pe is the grid Peclet number, introducing some limited numerical dispersion that smears sharp concentration front (e.g., c=1 to c=0 step) over approximately three numerical cells in the 1-D case.

[19] The approach adopted in this study is the “single realization” approach, extensively used in the past [e.g., Ababou, 1988; Russo, 1991; Polmann et al., 1991; Russo et al., 1998, 2001, 2006; Tseng and Jury, 1994]. Using the “single realization” approach, two issues must be considered in the design of the numerical simulations. To satisfy ergodicity requirements [Dagan, 1989], the flow domain must span a sufficient number of the correlation length-scales of the relevant soil properties in the vertical and horizontal directions, Iv and Ih, respectively. In addition, to preserve details of the spatial structure of the relevant soil properties [Ababou, 1988], the size of the numerical cells must be small as compared with Iv and Ih.

2.3.1. Flow, Transport, and Crop Parameters

[20] The five-parameter van Genuchten [1980] (VG) model was adopted here for the local description of the K(ψ;x) and the θ(ψ;x) relationships. The soil parameters of the VG model, each viewed as a realization of a second-order, stationary random space function, include the saturated conductivity Ks, the soil pore size distribution parameters α and n, and the saturated θs and the residual θr volumetric water contents. Following Russo et al. [1998], it was assumed here that the correlation length-scales of the various VG parameters are equal to those of log Ks, i.e., Iph=Ih=0.8 m and Ipv=Iv=0.2 m, for the horizontal and vertical directions, respectively [Russo et al., 1997], and that the spatial two-point covariance of these parameters is given by a 3-D, exponential model.

[21] The flow domain under consideration spans a distance L1=12 m in the vertical x1 axis and distances L2=15 m and L3=10 m in the horizontal x2 and x3 axes, respectively. This provides a flow domain spanning 60, 18, and 12 correlation length-scales of log Ks in the respective directions. The flow domain was subdivided into uniform numerical cells ω measuring 1=0.05 m in the vertical direction and 2=3=0.20 m in the horizontal directions. This provides four nodes per the correlation length-scale of log Ks, in agreement with the constraint suggested by Ababou [1988].

[22] Taking into account the statistics of the VG parameters and the respective linear cross-correlation coefficients among these parameters [Russo and Bouton, 1992], the 3-D, cross-correlated realizations of the VG parameters were generated by the turning bands method [Tompson et al., 1989] in combination with the multivariate normal distribution function method [Mood and Graybill, 1963].

[23] Using the procedure suggested by Mishra et al. [1989], depth variations of each of the VG parameters and the soil bulk density, ρb, were estimated from soil texture data measured to a soil depth of 9 m in one location at the Bnei-Dror site (see Figure 1). The estimated, depth-dependent soil parameters, in turn, were superimposed on the zero mean, unit standard deviation-generated realizations of the VG parameters. Profiles of the horizontally averaged mean and standard deviations of the resultant VG parameters are depicted in Figure 2. Note that the increase in the mean values and the standard deviations of θs and θr and the decrease in the mean values and the standard deviations of Ks, α, and n, below the 7 m depth, are due to an increase in the clay fraction of the soil below this soil depth.

Figure 2.

Profiles of the (a) horizontally averaged mean values and (b) standard deviations of the soil parameters of the VG model.

[24] In addition, a deterministic dimensionless Henry's constant KH=0.2 and a deterministic pore-scale dispersion tensor (with longitudinal dispersivity λL=2 × 10−3 m and transverse dispersivity λT=1 × 10−4 m) [Perkins and Johnston, 1963], were considered in the simulations. Note that the grid Peclet numbers for the longitudinal and the transverse pore-scale dispersion are 25 and 2000, respectively. In other words, the use of equation (4) in our 3-D transport model [Russo et al., 2001] might introduce some limited numerical dispersion, only in the transverse direction. The liquid-solid partitioning coefficient for ammonium Kd and the first-order rate constants for nitrification and denitrification, K1 and K2, respectively, were considered as depth-dependent with values within the range suggested by Lotse et al. [1992]. Estimates of the time-dependent, root uptake coefficients for ammonium and nitrate, Ku1 and Ku2, respectively, were calculated by a maximization iterative (MI) approach described in section 2.3.3. Root distribution data, adopted from Mantell and Goell [1972], were employed in order to construct the time-invariant, normalized root depth-distribution function Rz(x1) characterized by rooting depth of 1.5 m and a centroid located at a soil depth of 0.6 m [see Russo et al., 1998, Figure 1a].

2.3.2. Flow and Transport Scenarios and Boundary and Initial Conditions

[25] Transport of solutes in a flow domain with initial pressure head ψi(x) corresponding to a given initial water content θi(x) and with initial solute concentrations cik(x) (k=1–3) for the tracer solute (k=4), cik(x)=0, was considered here. The flow domain is a subplot of a citrus orchard, which consists of two double rows of trees aligned parallel to the x2 axis (Figure 1). Each double row is irrigated with TSW, using a single line lateral located between the double rows, with micro-sprinklers spaced 4 m apart (Figure 1). Inasmuch as the water table in the Bnei-Dror site is quite deep (>20 m), the simulations in the present study were restricted to the upper part of the vadose zone, yet, much deeper than the depth of the main root zone.

[26] During the irrigation season, water and solutes are applied spatially nonuniformly to the soil by a set of micro-sprinklers, which, in turn, cover only a portion of the soil surface of the subplot. In addition, at the beginning of the first irrigation season, a one-time pulse t0 of a tracer solute is injected into the flow domain via the irrigation system. During the subsequent rain season, only water and chloride are added to the flow system by a series of rain events imposed on the entire soil surface of the subplot.

[27] No-flow conditions were assumed for the vertical planes of the flow domain located at the x2=0 and x2=L2 and the x3=0 and x3=L3 boundaries, while unit head-gradient was assumed for the lower horizontal plane located at the x1=L1 boundary. No-solute flux conditions were assumed for the horizontal plane located at the x1=0 boundary, outside the planar sources, and for the vertical planes located at the x2=0 and x2=L2 and the x3=0 and x3=L3 boundaries. A zero-solute gradient-boundary was specified for the lower horizontal plane located at the x1=L1 boundary.

2.3.3. Implementation

[28] Time-dependent quantity and quality of the TSW and irrigation rate and frequency were taken as those actually used in the Bnei-Dror site, i.e., irrigation every 3 days, using a micro-sprinkler system with a discharge of 75 L/h, a mean spraying diameter of 2 m, and a spatially nonuniform distribution of the water application rates. Nearby weather station provided data of rainfall rates and amounts and daily amounts of reference evapotranspiration ET0(t) [Allen et al., 1998]. Potential evapotranspiration rate ETp(t) was estimated from the ET0(t) data using the time-dependent crop coefficients actually used in the Bnei-Dror site, which vary with time within the range 0.32–0.9. It was assumed that in the area wetted by the micro-sprinklers in the proximity of the trees (where the tree canopy completely covers the soil surface), as compared to the potential transpiration Tp(t), the potential soil evaporation Ep(t) is small enough to be excluded from the analyses; consequently, Tp(t) is equal to ETp(t).

[29] The MI approach suggested by Neuman et al. [1975] and implemented in the 3-D, spatially heterogeneous flow domains by Russo et al. [1998] was used to implement water uptake by the tree roots; the latter, in turn, determines the actual transpiration Ta(t). For the area outside the area wetted by the micro-sprinklers in the proximity of the trees, assuming that Tp(t) is negligibly small, i.e., Ep(t)=ETp(t), actual water loss by evaporation Ea(t) was implemented by a similar MI approach. For more details, see Fiori and Russo [2008].

[30] Uptake of ammonium and nitrate by the tree roots was also implemented by a MI approach, in which the solute uptake rate per unit area of the soil surface at time t given by Uak(t)=∫ΩNuk(x,t) dx (k=1, 2) is maximized by adjusting the time-dependent, root uptake coefficients Kuk (k=1, 2) subject to three constraints: (1) the sum of the actual uptake rates of ammonium and nitrate Uak(t) (k=1, 2), respectively, cannot exceed the sum of their potential rates Upk (k=1,2), which, in turn, is determined by the prescribed N demand of the plant; (2) the concentrations ck(x,t) (k=1, 2) cannot decrease below the critical prescribed values cckl (k=1, 2); and (3) the concentrations ck(x,t) (k=1, 2) cannot increase above the critical prescribed values cckh (k=1, 2). Values of cc1l=cc2l=0 and based on the experimental evidence (D. Kurtzman, personal communication, 2012) values of cc1h+cc2h=30 g/m3 were employed in the present study.

[31] Starting with the irrigation season (1 April), simulations of flow and transport proceeded for a sequence of 6 successive years. During the irrigation seasons, concentrations c0k of ammonium (k=1) and nitrate (k=2), varied between 10 and 80 g/m3 and between 5 and 75 g/m3, respectively, and were negligibly small during the rain seasons; chloride concentrations c03 were 200 and 15 g/m3 during the irrigation and the rain seasons, respectively. For the tracer solute, values of c04=10 g/m3 and t0=0.05 days were employed in the simulations. The estimated cumulative potential evapotranspiration and the total rainfall for the 6 years were 773, 800, 795, 795, 805, and 780 mm and 510, 590, 580, 580, 625, and 550 mm, respectively; the respective cumulative amounts of TSW used for irrigation were 620, 640, 610, 610, 615, and 580 mm. In agreement with previous studies [Dasberg, 1987; Alva et al., 2005, 2007], the potential annual consumption use of nitrogen (i.e., nitrate+ammonium) by the trees, employed for each of the 6 years, was 25 g/m2. For the period of 6 years, both the actual simulated transpiration and the actual simulated consumption use of nitrogen by the trees approached their prescribed potential values. These results indicate full root-zone availability for both water uptake and nitrogen uptake by the trees.

[32] Appropriate initial conditions for the present analyses were created by considering measured water content and solute concentration profiles obtained from a single, 9 m long soil core obtained by using a direct-push rig (D. Kurtzman et al., Considering agricultural nitrogen application in light of nitrate concentration in ground water: Observation-based model in an effluent irrigated area overlying the coastal aquifer [in Hebrew], Final Research Report, pp. 1–18, submitted to the Chief Scientist of the Ministry of Agriculture, Israel, 2012); see Figure 1 for the location of the sampling point in the horizontal plane of the Bnei-Dror site. The core was cut to depth intervals of 0.3 m. All depth intervals were analyzed in the top 3 m, and every second depth interval was analyzed between 3 and 9 m soil depth. Bulk density (core dry mass per volume) and gravimetric water content were obtained for each interval. Chloride concentration of soil water extracts (1:5) was analyzed with a chloride meter. Nitrate and ammonium ions in 1:5 soil extractions with a KCl solution (1 M) were analyzed using an autoanalyzer [Kachurina et al., 2000].

[33] The measured flow-controlled attributes at the soil depth of 9 m were adopted for the deeper soil layer extending to a depth of 12 m. The resultant water content and solute concentration profiles were used as estimates for the horizontally uniform initial water content θi(x1;x2,x3) and solute concentrations cik(x1;x2,x3) (k=1–3), respectively; flow and transport were simulated for 2 successive years subject to the appropriate boundary and initial conditions. The spatial distributions of the final pressure head and solute concentrations obtained from this set of simulations, in turn, were used as initial conditions for the actual simulations of flow and transport, which proceeded for 6 successive years. The results of the latter simulations, in turn, provided the foundation for the analyses presented in this paper. Profiles of the horizontally averaged mean values and standard deviations of the water content and the concentrations of chloride and nitrate, used as initial conditions for the actual simulations, are depicted in Figure 3.

Figure 3.

Profiles of the horizontally averaged mean values and standard deviations of the initial concentrations of (a) chloride and (b) nitrate, and (the inset in (b)) the initial water content.

3. Results and Discussion

3.1. Solute Concentration Distributions

[34] In the following analyses, we exclude the ammonium, inasmuch as its concentrations in the flow domain are small as compared with the nitrate concentrations. Spreading patterns of the tracer, chloride, and nitrate, obtained from the solution of equations (1) and (3) subject to the appropriate boundary and initial conditions, at the end of the rain season of the third consecutive year, are depicted in Figures 4, 5, and 6, respectively. Figures 4-6 represent contours of the solute concentrations in the proximity of the six inner trees (see Figure 1), in the vertical x1x2 plane (at x3=5 m), perpendicular to the direction of the tree rows (top), and in the vertical x1x3 plane (at x2=6 m), parallel to the direction of the tree rows (bottom).

Figure 4.

Contours of the simulated tracer concentration (in g/m3) (top) in the vertical x1x2 plane, at x3=5 m, across the orchard rows and (bottom) in the vertical x1x3 plane, at x2=6 m, along the first row of the orchard. Results are depicted for the end of the rain season of the third consecutive year.

Figure 5.

Contours of the simulated chloride concentration (in g/m3) (top) in the vertical x1x2 plane, at x3=5 m, across the orchard rows and (bottom) in the vertical x1x3 plane, at x2=6 m, along the first row of the orchard. Results are depicted for the end of the rain season of the third consecutive year.

Figure 6.

Contours of the simulated nitrate concentration (in g/m3) (top) in the vertical x1x2 plane, at x3=5 m, across the orchard rows and (bottom) in the vertical x1x3 plane, at x2=6 m, along the first row of the orchard. Results are depicted for the end of the rain season of the third consecutive year.

[35] The solute plumes depicted in Figures 4-6 exhibit an irregular spatial pattern, attributed to the small-scale variability in the soil hydraulic properties. Figures 4-6 reveal that because of the repeated cycles of irrigation season followed by a rain season, the solute spread after the rain season of the third consecutive year is still affected by the spatially nonuniform pattern of the water and the solute fluxes imposed on the soil surface during the irrigation season, as well as by the spatially nonuniform pattern of the tree roots. This behavior persists for the entire simulation period (6 years). Figure 4 reveals that at the end of the rain season there is only a slight overlap between the tracer plumes originating from the adjacent sources, associated with the two different tree rows (top) and a substantial overlap between the tracer plumes originating from adjacent sources along a tree row (bottom). This behavior attributes to the areal configuration of the solute sources at the soil surface.

[36] Figures 5 and 6 suggest that at the end of the rain season, chloride and nitrate are leached from the upper soil layer close to the soil surface. Note that the plumes of both the chloride (Figure 5), which is not extracted by the tree roots (but is added to the soil also during the rain season with lower concentration c03), and the nitrate (Figure 6), which is extracted by the tree roots and is subject to nitrification-denitrification processes (but is not added to the soil during the rain season), exhibit different patterns. Generally, the chloride exhibits more lateral spreading than the nitrate, in particular, along the tree row. Figures 5 and 6 suggest a slight overlap between the chloride plumes and even less overlap between the nitrate plumes, originating from the adjacent sources associated with the two different tree rows (top), patterns that persist for a substantial soil depth, the extent of which increases as the elapsed time further increases. To the contrary, a substantial overlap exists between the chloride plumes (Figure 5, bottom), while only a slight overlap exists between the nitrate plumes, originating from adjacent sources along a tree row (Figure 6, bottom).These patterns persist during the simulation period (6 years).

[37] Spreading patterns of the chloride and nitrate concentrations over the shallower control plane (CP; located at soil depth of 2 m, below the root zone), at the end of the rain season of the sixth consecutive year, depicted in Figure 7, clearly demonstrate the difference between the lateral spreading of the conservative (top) and reactive (bottom) solutes. This, difference, however, decreases with increasing soil depth. The increase in the overlap between the solute plumes with increasing soil depth stems from the lateral solute spreading, driven by the velocity variations, which promotes lateral mixing of the solute and consequently decreases the lateral variations in the solute concentrations with increasing soil depth. This behavior is demonstrated in Figure 8, which depicts the cumulative distribution plots of the chloride and nitrate resident concentrations over the horizontal CPs located at different soil depths, at the end of the rain season of the sixth consecutive year.

Figure 7.

Simulated concentration distributions of (top) chloride and (bottom) nitrate in the horizontal x2x3 plane, at x1=2 m. Results are depicted for the end of the rain season of the sixth consecutive year. Tree rows are oriented parallel to the x3 axis.

Figure 8.

Cumulative distribution plots of (top) the chloride and (bottom) the nitrate resident concentrations and (inset) the longitudinal component of the Eulerian velocity vector, in horizontal CPs located at different soil depths. Results are depicted for the end of the rain season of the sixth consecutive year.

[38] Figure 8 demonstrates the considerable range of nitrate concentrations, and particularly of chloride concentrations, that might occur on a field plot, whose characteristic horizontal length-scales are in the order of 10–15 m. This considerable variability is consistent with the substantial variations of the longitudinal (vertical) component of the Eulerian velocity vector, u1 (see the inset in Figure 8) over the horizontal CPs, and decreases with increasing depth. At the shallower CP, located at L=2 m, the concentrations range from 34.8 to 990.5 mg/L and from 5.1 to 107.9 mg/L for the chloride and the nitrate-nitrogen (NO3-N, referred to nitrate hereafter), respectively. The mean values and standard deviations for the shallower CP are 678.1 and 184.6 mg/L and 65.1 and 23.6 mg/L for the chloride and the nitrate, respectively. At the deeper CP, located at L=8 m, the concentrations range from 156 to 792 mg/L and from 13 to 60 mg/L for the chloride and the nitrate, respectively. The mean values and standard deviations for the deeper CP are 585.8 and 142.1 mg/L and 44.8 and 7.9 mg/L for the chloride and the nitrate, respectively.

[39] Note that unlike u1 which, for a given soil depth, is approximately lognormally distributed in the horizontal plane, the distribution of the concentrations of the nonreactive conservative solute (chloride) is essentially bimodal with peaks at the lower and the higher range of its concentrations. The bimodal pattern of the distribution of the chloride concentrations in the horizontal plane persists with soil depth. On the other hand, the distribution of the concentrations of the nonconservative, reactive solute (nitrate) is essentially lognormal with a tail (associated with high concentrations), whose extent decreases with increasing soil depth. Note that the second peak of the distribution of the chloride concentration, associated with high concentrations, stems from the substantial overlap between the chloride plumes originating from the adjacent sources along the tree row (Figures 5 (bottom) and 7 (top)).

[40] We would like to emphasize that our 3-D simulations may not capture the considerable range of measured concentrations that might be observed on the field scale [e.g., Onsoy et al., 2005]. For the Bnei-Dror area, additional eight 9 m long soil cores from neighboring orchards sampled within a radius of 1 km provided (for the deep soil layer ranging from 7 to 9 m) measured chloride and nitrate concentrations ranging from 175 to 1204 mg/L and from 3.6 to 108 mg/L, respectively [Shapira, 2012]. This range of measured concentrations is not substantially greater than the respective ranges of the simulated concentrations, obtained for a field plot whose characteristic horizontal length-scales are in the order of 10–15 m.

[41] In addition, it should be emphasized that for the deeper CP (located at L=8 m), the range of our simulated nitrate concentrations (13–60 mg/L) is similar to the range of simulated nitrate concentrations reported by Botros et al. [2012] (3.9–42 mg/L) for the deep unsaturated zone. The latter results are based on the 2-D and 3-D simulations of nitrate transport in a deep alluvial vadose zone, beneath a nectarine orchard, irrigated by flooding and fertilized by ammonium-nitrate fertilizer, in a field site located at the eastern San Joaquin Valley in California.

3.2. Water Content and Solute Concentration Profiles

[42] Figures 9, 10, and 11 depict the simulated profiles of water content, chloride concentration, and nitrate concentration, respectively, “sampled” at different locations (spaced 2 m apart) between adjacent tree rows (top) and along a tree row (bottom), at the end of the irrigation season of the third consecutive year. Figures 9-11 demonstrate the sensitivity of the “sampled” profiles of water content and particularly solute concentrations to their position in the horizontal plane of a relatively small-scale field plot. Simulated profiles of water content, chloride concentration, and nitrate concentration, at the fixed horizontal position, used for the soil coring (see Figure 1) and their counterparts associated with the deterministic, 1-D vertical simulations are also depicted in Figures 9-11. Note that along the approach generally employed in stochastic subsurface analyses [e.g., Fiori and Russo, 2007], the geometric mean of Ks and the mean values of the other soil parameters were adopted as constants in the deterministic, 1-D simulations.

Figure 9.

Simulated profiles of the water content at the end of the irrigation season of the third consecutive year. Results are depicted for different locations (spaced 2 m apart) (a) along a line perpendicular to the orchard rows and (b) along a line parallel to the first row of the orchard. Thick solid and dashed lines denote the simulated profiles associated with the sampling point (Figure 1) and the simplified, 1-D simulation, respectively.

Figure 10.

Simulated profiles of the chloride concentration at the end of the irrigation season of the third consecutive year. Results are depicted for different locations (spaced 2 m apart) (a) along a line perpendicular to the orchard rows and (b) along a line parallel to the first row of the orchard. Thick solid and dashed lines denote the simulated profiles associated with the sampling point (Figure 1) and the simplified, 1-D simulation, respectively.

Figure 11.

Simulated profiles of the nitrate concentration at the end of the irrigation season of the third consecutive year. Results are depicted for different locations (spaced 2 m apart) (a) along a line perpendicular to the orchard rows and (b) along a line parallel to the first row of the orchard. Thick solid and dashed lines denote the simulated profiles associated with the sampling point (Figure 1) and the simplified, 1-D simulation, respectively.

[43] The “sampled” water content profiles (Figure 9) exhibit a substantial spatial variability attributed to the spatial locations of the sampling points, the water sources, and the water sinks and to the small-scale heterogeneity in the soil hydraulic properties. It should be emphasized that the “sampled” water content profiles at the end of the rain season (not shown here) behave similarly with the exception that water content increases in the upper part of the soil profile due to the increase in the net applied water during the rain season.

[44] The “sampled” concentration profiles (Figures 9 and 10) exhibit a considerable spatial variability, much larger than that of the “sampled” water content profiles. As in the case of water content, the spatial variability of the solute concentrations is attributed to the spatial locations of the sampling points, the water and the solute sources at the soil surface, and the trees (which extract water and nitrate) and to the small-scale heterogeneity in the soil hydraulic properties. The “sampled” concentration profiles at the end of the rain season (not shown here) behave similarly with the exception that because of the increase in the net applied water and the decrease in the concentrations c0k (k=2, 3) during the rain season, both chloride and nitrate concentrations decrease in the upper part of the soil profile.

[45] The larger variability in the solute concentration profiles (Figures 10 and 11) than in the water content profiles (Figure 9) may be explained as follows. Solute mass flux in the heterogeneous soils is dominated by its advective component, which, in turn, depends on water content and solute concentration and on the Eulerian velocity vector related to the hydraulic conductivity through Darcy's law. The latter varies spatially considerably due to its linear dependence on the spatially variable saturated conductivity and due to its highly nonlinear dependence on water content. Consequently, even moderate spatial variability in water content may lead to a considerable spatial variability in the solute concentration. As compared with a homogeneous flow domain, the spatial variability in the soil properties generally retards solute movement in the longitudinal (vertical) direction and enhances solute spread in both the longitudinal and transverse directions.

[46] Figures 9, 10 clearly show that the information which may be gained from the results of the simplified, deterministic, 1-D vertical simulations or from a single sampling point located at a given horizontal position in the field is insufficient to quantitatively describe the response of the complicated, 3-D flow domain considered here.

3.3. Water Drainage and Solute Leaching

[47] Important attributes, related to groundwater contamination, are the longitudinal (vertical) components of the water volumetric flux and the solute mass flux vectors, qw1(x,t) and qs1(x,t), respectively, monitored at a given horizontal CP located at a given vertical distance from the soil surface. Mean water volumetric flux Qw1(t) and mean solute mass flux Qs1(t) at different horizontal CPs are depicted in the insets in Figures 12-14. The latter were determined by averaging the longitudinal components of the water volumetric flux and the solute mass flux vectors, respectively, over the horizontal CPs.

Figure 12.

(insets) Mean volumetric water flux at different horizontal CPs, and cumulative water volume fraction that drain below the CPs as functions of time. Results are depicted for (top) the spatially heterogeneous, 3-D and (bottom) the deterministic, 1-D flow domains.

[48] The results depicted in the insets in Figure 12 suggest that in both the fully, 3-D, realistic (top) and the simplified, 1-D (bottom) flow domains, the capability of the flow (which acts like a low-pass filter that filters out high-frequency signals) to attenuate the effect of the upper-boundary flux temporal variability, increases with increasing vertical distance. The insets in Figure 12 clearly demonstrate that the 1-D approximation (which disregard both the horizontal patterns of the irrigation system and the tree root distribution and the spatial variability in the soil properties) considerably underestimates both the magnitude of the time-averaged mean water flux and the magnitude of its periodic fluctuation at different soil depths below the root zone.

[49] Figure 12 depicts the cumulative water volume fractions drained below the different horizontal CPs, QD/QT, as functions of time. Here QD is the cumulative water discharge at a given CP, QT=QA+QIQE, QA is the cumulative volume of water applied at the surface, QI is the initial water volume stored from the soil surface to the CP, and QE is the cumulative volume of water extracted by the tree roots. Figure 12 suggests that as expected (see the water fluxes in the insets in Figure 12, and because the initial storage QI increases with increasing soil depth), for both the 3-D (top) and the 1-D (bottom) flow domains, QD/QT decreases with increasing soil depth. Figure 12, however, demonstrates that the 1-D approximation may underestimate the water volume fraction drained below a given horizontal CP by 50%.

[50] The results depicted in the insets in Figures 13 and 14 suggest that as in the case of the water flux (Figure 12) for both chloride and nitrate, respectively, the capability of the flow to attenuate the effect of the temporal variability of the solute mass flux imposed on the soil surface increases with increasing vertical distance. This is true for both the fully, 3-D, realistic (top) and simplified, 1-D (bottom) flow systems. The insets in Figures 13 and 14 demonstrate, however, that the 1-D approximation considerably underestimates the solute fluxes, particularly at the deeper soil depths, and for a period that increases with increasing soil depth. This stems from the substantial solute concentrations that initially reside in the deeper part of the flow system, combined with substantially larger water fluxes in the 3-D case as compared with the 1-D case (Figure 12). The mean flux-averaged concentrations Cf of chloride and nitrate that cross the deeper CP, obtained by averaging the longitudinal components of the water flux and the solute flux vectors over the pertinent horizontal CP, decrease with time faster in the 3-D flow domain than in the 1-D flow domain. After a period of 6 years, the formers fluctuate with time within the range of 300–360 and 20–25 g/m3, respectively, as compared their counterparts associated with the 1-D flow domain, 450 and 23 g/m3, respectively.

Figure 13.

(insets) Mean chloride mass flux at different horizontal CPs, and cumulative mass fraction of chloride that leached below the CPs as functions of time. Results are depicted for (top) the spatially heterogeneous, 3-D and (bottom) the deterministic, 1-D flow domains.

Figure 14.

(insets) Mean nitrate mass flux at different horizontal CPs, and cumulative mass fraction of chloride that leached below the CPs as functions of time. Results are depicted for (top) the spatially heterogeneous, 3-D and (bottom) the deterministic, 1-D flow domains.

[51] Figures 13 and 14 depict the cumulative mass fractions ML/MT of the chloride and the nitrate, respectively, that crossed the different horizontal CPs, as functions of time. Here ML is the cumulative solute mass leached through a given CP, MT=MA+MIME, MA is the cumulative mass of solute applied at the soil surface, MI is the initial solute mass stored from the soil surface to the soil depth L, and ME is the cumulative mass of solute leaving the system due to solute extraction by tree roots and solute transformations. The results for the chloride (Figure 13), for which ME=0 suggest that as expected (see the solute fluxes in the insets in Figure 13, and because the initial storage MI increases with increasing soil depth) for both the 3-D (top) and 1-D (bottom) flow domains, ML/MT decreases with increasing soil depth. Figure 13 demonstrates that the 1-D approximation considerably underestimates the cumulative mass fraction of chloride leached through a given horizontal CP, particularly through the CP located at the deeper soil depth (by 37%).

[52] The results for the nitrate (Figure 14), for which ME>0, suggest that as expected (see the solute fluxes in the insets in Figure 14, and because the initial storage MI increases with increasing soil depth) for both the 3-D (top) and 1-D (bottom) flow domains, for a considerable period of time, ML/MT increases with increasing soil depth. Figure 14 demonstrates that the 1-D vertical approximation considerably underestimates the cumulative mass fraction of nitrate leached through a given horizontal CP, particularly through the CP located at the shallower soil depth (45%, as compared with 28% for the CP located at the larger soil depth).

[53] A comparison between the cumulative solute mass fractions ML/MT, depicted in Figures 13 and 14, suggests that the vadose zone may provide more capacity for the attenuation of the nitrate load in the groundwater than for the chloride load in the groundwater. For example, consider the 3-D flow domain. For the CP located at L=8 m, and for t=2200 days, ML/MT=0.67 and ML/MT=0.52 for the chloride and the nitrate, respectively. This difference between the solute mass fractions leached below the CP, in turn, is attributed to nitrate uptake by the tree roots and to nitrogen transformations in the vadose zone.

[54] Figures 12-14 suggest that in the case of an orchard irrigated by micro-sprinklers, a fully 3-D, heterogeneous modeling approach is needed to properly characterize the long-term field-scale water drainage and solute leaching to the groundwater. In this case, during the irrigation season, water and solute fluxes into the flow system occur only through a portion of the soil surface, in the proximity of the trees. During the rain season, however, water flux into the flow system occurs over the entire soil surface. Consequently, regions far from the trees associated with negligibly small water (and solute) uptake are more affected by the local high-conductance, preferential flow paths in the heterogeneous soil and thus may enhance the water flow and solute transport below the root-zone depth.

[55] It was shown [Russo et al., 1998] that the combination of spatially heterogeneous soil hydraulic properties and a periodic flux imposed on the surface with substantial redistribution periods between successive water applications may create a 3-D velocity fluctuation field with significant transverse components. The resultant velocity fluctuation field promotes lateral mixing of the solute and increases its transverse spreading. Furthermore, it was shown [Russo et al., 2006] that in the case of multiple planar sources, similar to case considered here, the partial wetting of the soil surface associated with significant lateral head-gradients further enhances transverse solute spreading. The lateral spreading, induced by soil heterogeneity, periodic influx, and source geometry, may lead to significant solute concentrations in the regions of the flow domain outside the area wetted by the micro-sprinklers in the vicinity of the trees (see Figures 4-7) and in combination with the enhanced longitudinal spreading may significantly contribute to the solute fluxes below the root zone during the rain periods. A deterministic, 1-D vertical modeling approach cannot account for this complicated flow and transport mechanism and consequently underestimates the amount of water drained and the amount of solutes leached to groundwater, in comparison to the heterogeneous 3-D simulations.

[56] From water volume and solute mass balance considerations, the enhanced drainage and leaching to the groundwater, associated with the heterogeneous 3-D simulation, should lead to smaller amounts of water and solutes stored in the soil, as compared with the simplified, 1-D simulations. The relative volume of water Vst(t)/Vst(0) and the relative mass of chloride and nitrate Mst(t)/Mst(0) stored in the soil as functions of time depicted in Figure 15 clearly demonstrate this tendency. Note that runoff was negligibly small in the simulations, while chloride uptake by plant roots was excluded in the simulations. The remaining components of the water volume balance and the solute mass balances that might affect water and solute storage in the soil, i.e., evapotranspiration and nitrate and ammonium uptake by plant roots, nitrification-denitrification process, and ammonia volatilization, associated with the 3-D and 1-D simulations, were also analyzed.

Figure 15.

Relative volume of water and relative mass of chloride and nitrate stored in the soil as functions of time. Relative cumulative volume of water loss due to evapotranspiration (E), relative cumulative mass of nitrate loss due to uptake (U) and denitrification (D), nitrate gain due to nitrification (N), and ammonium loss due to ammonia volatilization (V) are depicted in the insets. Results are depicted for the 3-D and 1-D flow domains.

[57] Results of these analyses, expressed in relative terms (i.e., ETa(t)/Vst(0), MU(t)/Mst(0), MN(t)/Mst(0), MD(t)/Mst(0), and MV(t)/Mst(0), where MU and MD are the cumulative mass of nitrate loss due to uptake and denitrification, respectively; MN is the cumulative mass of nitrate gain due to nitrification; and MV is the cumulative mass of ammonium loss due to ammonia volatilization) are depicted in the insets of Figure 15. The results depicted in the insets of Figure 15 suggest that the aforementioned components of the water and the solute balances associated with the 1-D simulations are slightly larger than their counterparts associated with the 3-D simulations and therefore cannot explain the reduced storage of water and solutes in the soil, associated with the 3-D simulations. In other words, the considerable difference in relative water storage and solute storage between the heterogeneous 3-D and homogeneous 1-D simulations is mainly due to the differences in the respective vertical fluxes below the root zone (see the insets in Figures 12-14).

3.4. Tracer Solute Breakthrough Curves

[58] The breakthrough curve (BTC) of a tracer solute, monitored at a horizontal CP located at a given vertical distance from the soil surface, L, is an important characteristic of the solute transport. On the field scale, the mean solute BTC corresponding to a narrow-pulse input of the solute can be used as an approximation of the solute travel time probability density function (PDF) f(τ;L). In the derivation of a general shape for f(τ;L), an effective entity is the flux-averaged concentration [Kreft and Zuber, 1978], cf(t;L)=qs1(t;L)/qw1(t;L). Note that since qs1(t;L) and qw1(t;L) are positively cross-correlated, cf(t;L) partially filters out the temporal variability in qs1(t;L) [Russo et al., 1994, 1998, 2001].

[59] The travel time PDF f(τ;L) is analyzed here, considering the scaled flux-averaged concentration CfQm/M0 as a function of the scaled cumulative water volume W(t;L)/Qm [see, e.g., Rodhe et al., 1996; Fiori and Russo, 2008; Russo, 2011]. Here W(t;L)=0tQw(t′;L) dt′, Qw is the water discharge through the horizontal CP located at x1=L, Qm is the mean annual net applied water discharge, M0 is the total tracer solute mass injected, and Cf(t;L) is the mean flux-averaged concentration of the tracer solute at the CP, obtained by averaging cf(x2,x3;L,t) over the horizontal CP.

[60] Figure 16 depicts the scaled travel time probability density f(τ;L)τ0 as functions of the scaled travel time τ/τ0, where τ0=∫f(τ;L)τ dτ is the mean travel time, for both the 3-D (top) and simplified, 1-D (bottom) flow domains. Unlike the smooth, quite narrow, approximately lognormally distributed dimensionless travel time PDFs in the 1-D case, their counterparts in the 3-D case exhibit erratic-like, highly skewed pattern, with an apparent bimodality, which, in turn, attenuates with increasing distance to the horizontal CP. The pattern of the latter travel time PDF stems from the sequences of an irrigation season followed by a rain season, from the spatially and temporally nonuniform water uptake by the tree roots and from the small-scale variability in the soil hydraulic properties.

Figure 16.

Dimensionless travel time PDFs of the tracer solute at different horizontal CPs. Results are depicted for (a) the spatially heterogeneous, 3-D and (b) the deterministic, 1-D flow domains; the respective mean travel times τ0 are depicted in this figure.

3.5. Applications

[61] Results of the analyses presented in the previous sections demonstrate that the information which may be obtain from a single sampling or monitoring point located at a given horizontal position in the field is insufficient to quantitatively describe the response of the complicated, 3-D flow domain considered here. A practical problem, therefore, is how to improve the quantification of the response of the complicated flow system by an appropriate, yet, feasible sampling scheme. This problem was addressed by Russo et al. [2006], with an objective being formulated as: “how many sampling points are needed and where to locate them spatially in the horizontal x2x3 plane of the field in order to obtain a reasonable estimate of a given flow-controlled attribute.”

[62] In this section, the methodology of Russo et al. [2006] is applied to the Bnei-Dror site, focusing on water flow and transport of both passive and interactive solutes. Consider a data set available at soil depth x1=L, containing a record of qw1(pi,tj;L) and qs1(pi,tj;L) (i=1 to n, j=1 to m), where pi=pi(x2,x3) is the position of the sampling point in the horizontal x2x3 plane, tj is the sampling time, and qw1 and qs1 are the longitudinal (vertical) components of the water flux and solute flux vectors, respectively, This data set is averaged over the n sampling points to produce the horizontal averages of the cumulative volume of water drained, QD, the cumulative mass of chloride and nitrate leached, ML, and the tracer solute BTC through the horizontal CP located at L, given as

display math(7a)
display math(7b)

and

display math(7c)

respectively, where Δtj=tjtj−1.

[63] Following Russo et al. [2006], the rectangular area in Figure 1 was subdivided into a sampling network of a 1 m × 1 m rectangular grid (Np=121). An overall effective measure of accuracy of an estimate of a given flow-controlled attribute Φ(tj) (Φ=QD, ML, or Cf), associated with the two-grid points (g,g), =1–Np, ′=1–Np, ′, i.e., φ(g,g;tj) (φ=⟨QD⟩, ⟨ML⟩, or ⟨Cf⟩), is provided by the square root of the mean-square error (MSE), given as

display math(8)

[64] Unlike Russo et al. [2006] who searched for the location of the first sampling point, in this study, we considered the location of the single sampling point in Figure 1, psp, as the location for the first sampling point, i.e., p1=psp, and we searched for the location for the second sampling point p2. Following Russo et al. [2006], a search was conducted in order to find the grid point g that along with the first sampling point minimizes (equation (8)). This point, in turn, was selected as the location for the second sampling point p2. Using gmin1=p1 and employing the Np−1 pairs of grid points (g,gmin1) (ggmin1, =1 to Np−1), ⟨QD(tj,L)⟩, ⟨ML(tj,L)⟩, and ⟨Cf(tj,L)⟩ were calculated from equations (7a), (7b), and (7c), respectively; using n=2, p1=gmin1, p2=g (=1 to Np−1), Δtj=1 day, and L=2 m, in turn, were used to calculate MSE(g,gmin1) (=1 to Np−1) using equation (8). The grid point that comprised the pair of grid points (g,gmin1) which yielded a minimum of MSE(g,gmin1) ((=1,Np−1), ggmin1, i.e., gmin2) was selected as the second sampling point, i.e., p2=gmin2. Note that the procedure can be repeated for additional sampling points; for more details, see Russo et al. [2006].

[65] Tracer mean flux-averaged concentration Cf at a horizontal CP located at soil depth of L=2 m, cumulative volume of water drained QD(t), and cumulative chloride and nitrate mass leached ML(t) through this CP, based on the first sampling point p1, are compared in Figure 17 with their counterparts, based a pair of sampling points p1 and p2, and with their “true” counterparts, based on averaging over the entire horizontal extent of the flow domain.

Figure 17.

(a) Mean flux-averaged concentration Cf of the tracer solute at a horizontal CP located at L=2 m, (b) cumulative water volume flux that drains below this CP QD, and (c) cumulative mass fluxes ML of chloride and (inset) nitrate that leached below this CP as functions of time. Solid, dashed, and dashed-dotted lines represent mean values, one-point estimate, and two-point estimate, respectively.

[66] Figure 17 demonstrates that the analyses based on a single sampling point may considerably underestimate the movement and spreading of a pulse of a tracer solute and the skewing of its BTC and may considerably underestimate the groundwater contamination hazard posed by nitrate and chloride moving through the vadose zone. The remarkably good agreement between Cf(t), QD(t), and ML(t), based on the minimum-error pair of points and their “true” counterparts, depicted in Figure 17, however, suggests that the selected pair of sampling points may provide relatively good estimates for the mean values of the examined flow-controlled attributes.

[67] Note that the first sampling point is located in the area active in water uptake in the proximity of the tree rows, while the second sampling point obtained by minimizing equation (8) is located relatively far from the tree rows outside the area active in water uptake and in the vicinity of the border of the area wetted by the micro-sprinklers (Figure 1). Furthermore, the location of the selected sampling point (x2=3 m, x3=3 m) is the same for QD(t) and for QL(t) (for both the chloride and the nitrate) and is different from the location of the selected sampling point associated with Cf(t) (x2=9 m, x3=3 m). The two selected sampling points, however, are located at the same relative configuration, with respect to the first and second tree rows.

[68] These results are in agreement with the results of the analyses of Russo et al. [2006], which considered mean soil properties, water application rate spatial distribution, and tree spatial configuration, different from their counterparts addressed in the present study. Furthermore, in the present study we considered additional flow-controlled attributes, i.e., cumulative volume of water drained, and cumulative chloride and nitrate mass leached through a horizontal CP located at L=2 m, for a considerable time (6 years), much larger than the time considered by Russo et al. [2006] (1 year). It should be emphasized, however, that the results presented in Figure 17 are pertinent to the unrealistic situation in which the expected values of the examined flow-controlled attributes Φ(t) are known a priori. Nevertheless, the results of the “worst case” scenario, analyzed by Russo et al. [2006] (which is equivalent to the practical situation in which prior information on Φ(t) is absent), support the conclusions of Russo et al. [2006] regarding the sampling strategy in cases in which the soil surface is partially wetted during the irrigation season. These conclusions are further strengthening by the results of the present analyses.

4. Summary and Concluding Remarks

[69] This study focused on the analyses of solute fluxes beneath a citrus orchard irrigated with TSW using micro-sprinklers. Water flow and transport of nitrate, chloride, and a tracer solute in the 3-D, spatially heterogeneous, variably saturated soil were analyzed numerically, considering realistic features of the soil-water-plant-atmosphere system. The results of the 3-D simulations, in turn, were used to assess their counterparts based on a simplified, deterministic, 1-D vertical simulation and on limited soil monitoring. The main findings of the present study summarized as follows:

[70] Under conditions of long-term irrigation with TSW because of nitrate uptake by the tree roots and nitrogen transformations, the vadose zone may provide more capacity for the attenuation of the nitrate load in the groundwater than for the chloride load in the groundwater.

[71] The information which may be gained from a single sampling point (located close to the area active in water uptake by the tree roots) or from the results of the simplified, deterministic, 1-D vertical simulations cannot describe quantitatively the response of the complicated, 3-D flow system considered in this study. Both substantially underestimate the movement and spreading of a pulse of a tracer solute and the skewing of its BTC through a given horizontal CP; furthermore, they may considerably underestimate the groundwater contamination hazard posed by nitrate and particularly by chloride moving through the vadose zone. The aforementioned underestimates stem from the rain that drove water through the flow system away from the rooted area, which could not be represented by the 1-D model or by the single sampling point.

[72] The use of a pair of sampling points, rather than a single sampling point, may considerably improve the quantitative description of the response of the complicated, 3-D flow system. This may occur if one of the sampling point is located in the area active in water uptake in the proximity of the tree rows, while the second sampling point is located outside the area active in water uptake, relatively far from the tree rows.

[73] Finding 1 is in qualitative agreement with previous analyses of the consequences of irrigation with TSW based on the deterministic, 1-D analyses [e.g., Russo, 1995]. This finding has both agricultural and environmental implications. It suggests further minimization of irrigation water (for a given amount of irrigation water) to the amount of nitrate consumed by the relevant crop. Furthermore, finding 1 implies that the only practical way to minimize the salt load in the groundwater is to reduce its concentration in the irrigation water, for example, by a desalinization procedure applied at the source of the TSW. The control of the chloride mass flux below the root zone, by using water quality-water quantity substitutions, was analyzed numerically by Russo et al. [2009] for corn irrigated with surface drip irrigation system; further analysis of this issue is beyond the limited scope of the present study.

[74] Finding 2 stems from the fact that the response of the soil-water-plant-atmosphere flow system considered here is characterized by a rather complicated spatial pattern of water content and solute concentrations with substantial lateral variations, which, in turn, cannot be reconstructed by a simplified, deterministic, 1-D vertical analysis. The complicated spatial pattern of the response of the 3-D flow system, in turn, is attributed to the spatial and the temporal variability in the sources and sinks of the water and the solutes and to the small-scale variability in the soil hydraulic properties.

[75] Finding 3 is in agreement with the results of the study of Russo et al. [2006] regarding the sampling strategy in cases in which the soil surface is partially wetted during the irrigation season. In this case, during the irrigation season, water and solute fluxes into the flow system occur only through a portion of the soil surface, in the proximity of the trees. During the rain season, however, water flux into the flow system occurs over the entire soil surface; consequently, regions far from the trees associated with negligibly small water (and solute) uptake play a major role in water flow and solute transport below the root-zone depth. Consequently, the additional sampling point, located relatively far from the trees, adds essential information that substantially improve the quantitative description of the response of the complicated, 3-D flow system.

[76] It should be emphasized that the numerical experiments conducted in the present study provide detailed information (that generally is not attainable in practice from field-scale physical experiments) on the consequences of soil, crop, irrigation, and meteorological characteristics for water flow and transport of conservative and reactive solutes on the field scale under relatively realistic conditions. We would like to stress, however, that detailed analyses of the complicated chemical and physiological processes that might occur in the soil-root interface are beyond the limited scope of the present study. These analyses require quantification of the entire chemical composition of the soil solution and the plant tissues as well as quantification of the regulatory mechanism of root solute uptake that operates at the whole plant level. The chloride and nitrate in this study, therefore, should be considered as conservative and reactive numerical tracers of groundwater, respectively, and not as the actual ions that may undergo complicated processes, which were not considered in the present study.

[77] Because of the simplifying assumptions employed in the present study, its conclusions should be considered with caution. Furthermore, the general validity of the results obtained in this study is limited by the “single realization” approach adopted here. Results of previous analyses of solute transport in a similar flow system using additional independent realizations of the input soil properties and the applied weather pattern [Russo et al., 2006] suggest, however, that the response of the investigated flow system is quite robust.

[78] In addition, we would like to emphasize that the findings of this study are restricted to a particular site-specific application with given characteristics of soil, crop, weather, and the irrigation system. Furthermore, because the response of the flow system under consideration depends on many input parameters, it is difficult to generalize the results of this study and to express them in terms of measurable input parameters. We believe, however, that the scope of this paper is of broad interest and is relevant to environmental safety issues related to the interaction between irrigation water quality and groundwater contamination in the semiarid zones.

[79] Finally, we would like to emphasize that we do not claim that our 3-D simulations necessarily capture the considerable range of measured concentrations that one might observed on the field scale. The agreement between the range of measured concentrations, based on the limited data set from the Bnei-Dror area, and the range of our simulated concentrations, however, are encouraging. This is in contrast to the considerable discrepancy between the simulated nitrate concentration distributions [Botros et al., 2012] and their measured counterparts [Onsoy et al., 2005]. This discrepancy (i.e., much larger simulated nitrate concentrations with a considerably less spreading) led Botros et al. [2012] to conclude that the presence of a significant immobile domain within the deep vadose zone should be considered in simulating nitrate transport under conditions of cyclical infiltration. Our results do not support this conclusion. Inasmuch as characteristics of the climate and particularly of the soil, the irrigation method, and the nitrate application method relevant to our study, are substantially different from their counterparts relevant to the study of Botros et al. [2012], we believe that their conclusion should be restricted to their particular site-specific application.

Acknowledgments

[80] This is contribution 101/12 from the Institute of Soils, Water and Environmental Sciences, the Agricultural Research Organization, Israel. This research was supported in part by a grant from the United States-Israel Bi-National Agricultural Research and Development Fund (BARD), by a grant from the Israel Water Authority, and by a grant from the Chief Scientist of the Israeli Ministry of Agriculture.

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