# Using Desalinated Water for Irrigation: Its Effect on Field Scale Water Flow and Contaminant Transport under Cropped Conditions

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## Abstract

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## 1. Introduction

^{8}in 2015 to 1.7 × 10

^{9}in 2050 [1], or in relative numbers: 7.5% of the world population in 2015 to a projected 18% in 2050. Global production capacity of desalinated seawater is predicted to double between 2011 and 2040 [2]. In Israel, five large desalination plants were built on the Mediterranean coast between 2005 and 2015 (production ≥ 90 × 10

^{6}m

^{3}/yr per plant; total 585 × 10

^{6}m

^{3}/yr [3]), bringing the desalinated seawater from close to 0 at 2004 to ~40% of the total Israeli freshwater consumption in 2017 [4].

^{6}m

^{3}/yr by 2024, and to 1100 × 10

^{6}m

^{3}/yr by 2030 [5], and dominate potable water production in this Mediterranean-climate country. With respect to irrigation with desalinated seawater in Israel between 2015–2017, we estimate it at 200 × 10

^{6}m

^{3}/yr, which is about 40% of the national freshwater irrigation consumption [4,6].

## 2. Materials and Methods

#### 2.1. The Physical Domain and its Parametrization

_{1}, x

_{2}, x

_{3}), where x

_{1}directed downwards, a subplot of this orchard consisting of a 3-D spatially heterogeneous and variably saturated flow domain which extended over L

_{1}= 5 m, L

_{2}= 15 m, and L

_{3}= 10 m along the x

_{1}, x

_{2}, and x

_{3}axes, respectively, was considered for this study. The subplot included two adjacent tree rows, located 6 m apart, with four trees, located 4 m apart, along each row.

_{s}, shape parameters α and n, as well as the saturated, θ

_{s}, and residual, θ

_{r}, values of water content, θ), was implemented here for the local description of the constitutive relationships for unsaturated flow. Based on previous studies [18,19], it was assumed that each of the VG parameters was a second-order stationary, statistically anisotropic, random space function, characterized by a constant mean and a two-point covariance. Parameters of the latter, the variance, and the correlation length scales were adopted from [19]. Mean values of the VG parameters were estimated using the soil texture-based procedure suggested by [21]. Details of the generation of the 3-D cross-correlated realizations of the spatially heterogeneous VG parameters are given in [22]. Mean values and coefficients of variation (CV) of the resultant VG parameters are given in [23].

_{0}= 5.4 × 10

^{−5}m

^{2}/d, dimensionless Henry’s constant, K

_{H}= 0.2, and pore-scale dispersion tensor (with longitudinal dispersivity, λ

_{L}= 2 × 10

^{−3}m, and transverse dispersivity, λ

_{T}= 1 × 10

^{−4}m, [24]) were considered in the simulations. First-order rate constants for nitrification and denitrification, K

_{1}and K

_{2}, respectively, and liquid–solid partitioning coefficient for ammonium, K

_{d1}, were taken into account as depth-dependent implementing values within the range suggested by [25]. Estimates of the root uptake coefficients for ammonium and nitrate, K

_{u1}and K

_{u2}, respectively, were calculated by extending the method of [26]; for more details, see [27].

#### 2.2. The Flow and Transport Scenarios and their Implementation

_{FNO3}= C

_{NO3}/ [K

_{m1}(1 + C

_{Cl}/ K

_{m2}) + C

_{NO3}],

_{FNO3}is the relative nitrate uptake flux, C

_{Cl}and C

_{NO3}are the soil solution concentrations of chloride and nitrate, respectively, and K

_{m1}and K

_{m2}are the Michaelis–Menten constants accounting for the affinity of nitrate and chloride to the uptake site, respectively. Note that for C

_{NO3}> 0, R

_{FNO3}→ 1 when C

_{Cl}→ 0, whereas R

_{FNO3}→ 0 when C

_{NO3}→ 0.

_{NITC}, and the chloride concentration, namely,

_{NITC}= min {[1 − (K

_{Cl}× C

_{Cl}/ C

_{NO3})],1},

_{Cl}is a coefficient accounting for the effect of chloride to reduce the nitrification rate. Note that for C

_{NO3}> 0, R

_{NITC}→ 1 when C

_{Cl}→ 0.

_{m1}, K

_{m2}, and Kcl were determined by an optimization procedure that ensures that the selected values minimize the effect of the chloride on nitrogen uptake and nitrification when the chloride concentration approaches its concentration in the desalinated seawater (DSW). Based on this criterion, the values of K

_{m1}= 0.0036 mg/L, K

_{m2}= 0.0023 mg/L, and Kcl = 0.012 were employed in the present study.

_{p}(t) = ετ

_{p}(t)) was adopted here, where ετ

_{p}(t) and τ

_{p}(t) are the potential evapotranspiration and transpiration rates, respectively. The maximization iterative (MI) approach proposed by [30], and applied to 3-D spatially heterogeneous flow domains by [31], was adopted here in order to calculate water uptake by the plant roots, and, concurrently, actual transpiration rate, τ

_{a}(t). Uptake of nitrate and ammonium by the plants’ roots was also calculated by an MI approach described in [27].

_{i}, was selected as spatially uniform, ψ

_{i}(x) = −3m; spatially uniform initial solute concentrations of ammonium, nitrate, and chloride, c

_{ik}(x), k=1 to 3, respectively, were selected as c

_{ik}(x) = 5, 50, and 300 mg/L, for k = 1 to 3, respectively; for the tracer (bromide, k = 4), c

_{ik}= 0. For the flow, a second-type upper boundary condition was imposed on the top boundary (x

_{1}=0) with flux that was determined by the time-dependent irrigation and rainfall fluxes, associated with entry zone whose size varied between the irrigation and the rainfall seasons. A unit-head-gradient boundary was specified at the bottom boundary (x

_{1}= L

_{1}).

_{0k}, k = 1 to 4, that varied between the irrigation and the rainfall seasons. A zero-gradient boundary was specified at the bottom boundary.

_{NH4}= 10 and C

_{NO3}= 70 ppm, respectively, and three different chloride concentrations (Ccl = Ciw = 50, 300, and 640 ppm, for the scenarios of desalinated (D), fresh (F) and saline (S) waters, corresponding to D, F, and S, respectively, in the figures), were considered here. Chloride concentration in the rainfall water was 15 ppm, whereas ammonium and nitrate were absent. A tracer (bromide with concentration, C

_{bro}= 10 ppm) was applied as pulse during the first irrigation event.

## 3. Results

#### 3.1. Water Uptake by the Trees’ Roots

_{2p},x

_{3p},Zup;t) and Vz(x

_{2p},x

_{3p},Zup;t) over the four trees in the inner core of the flow domain, are depicted as functions of time in Figure 2. Here, x

_{2p}and x

_{3p}(p = 1 to Np), are the coordinate locations of the p-th tree at the soil surface, and Np=4. This figure clearly demonstrates the effect of Ciw on the temporal variations of both water content and the vertical velocity in the most active part of the root zone.

#### 3.2. Movement, Spread, and Breakthrough of a Pulse of a Solute Tracer

_{1},R

_{2},R

_{3}) is the coordinate of the centroid of the tracer plume, and S’

_{ij}(t) (i,j = 1,2,3) are second spatial moments, proportional to the moments of inertia of the tracer plume.

_{1}(t), and the spread about it in the vertical direction, S

_{11}(t) = S’

_{11}(t) − S’

_{11}(0), as functions of time, for the same cases presented in the previous figures. Note that the first derivatives of R

_{1}and S

_{11}with respect to time provide estimates of the effective time-dependent longitudinal components of the solute velocity vector, Ve, and the macrodispersion tensor, De, respectively.

_{11}with time, t, faster than linearly in t, associated with scenarios F and S, suggest that in these cases the transport is essentially a convection-dominated process, controlled by the disparity between regions of different velocities. On the other hand, in the case of scenario D, S

_{11}tends to evolve at a linear rate, suggesting that in this case the transport is essentially a convection–dispersion process. This is also shown in Figure 6, which depicts scaled travel time probability density functions (PDFs), f(τ;L), derived from temporal changes of the mean flux-averaged concentration, c

_{f}(t;L), of the tracer, averaged over a horizontal control plane (CP) located at vertical distance, L = 1m. Figure 5 and Figure 6 suggest that the reduction in water content caused by irrigation with desalinated water (scenario D) essentially damps out the extremely fast travel times, slows down the longitudinal spreading of the tracer’s plume, and, consequently, promotes mixing between regions of differing convection, leading to a Fickian behavior.

^{2}/d, and effective macrodispersivity, λe = De/Ve = 0.075, 0.146 and 0.180 m, for scenarios D, F, and S, respectively.

_{1}(t) and the S

_{11}(t) curves depicted in Figure 5 yield Ve = dR

_{1}/dt = 0.0045, 0.0090, and 0.0110 m/d, De = (1/2) dS

_{11}/dt = 0.00052, 0.0016, and 0.0020 m

^{2}/d, and λe = De/Ve = 0.116, 0.178, and 0.182 m, for scenarios D, F, and S, respectively.

#### 3.3. Nitrogen Uptake by the Trees’ Roots

#### 3.4. Nitrification, Denitrification, and Volatilization

#### 3.5. Contaminant Leaching

## 4. Discussion

## 5. Summary and Concluding Remarks

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Profiles of the horizontally averaged root’s water uptake rate for the three different irrigation scenarios (D, Ccl = 50 ppm, F, Ccl = 300 ppm, and S, Ccl = 640 ppm); in all cases, C

_{NH4}= 10 ppm and C

_{NO3}= 70 ppm. Results are depicted for t = 455 d (ninety days after the start of the irrigation season of the second year). D, desalinated; F, fresh; S, saline.

**Figure 2.**(

**a**)Temporal variations of the simulated soil water content, θ, and (

**b**) vertical component of the velocity vector, Vz, at soil depth x

_{1}= Zup, representing the vertical position of the centroid of the soil volume active in water uptake, for the different scenarios examined. Results are depicted for the irrigation season of the second year.

**Figure 3.**Profiles of the (

**a**) horizontally averaged mean and (

**b**) SD of the water content for the different scenarios examined. Results are depicted for the irrigation season of the second year.

**Figure 4.**Profiles of the (

**a**) horizontally averaged mean and (

**b**) SD of the vertical component of the velocity vector for the different scenarios examined. Results are depicted for the irrigation season of the second year.

**Figure 5.**(

**a**) Vertical position of the centroid of the tracer mass, Zc, and (

**b**) the spread about it in the vertical direction, S

_{11}, as functions of time, for the different scenarios examined.

**Figure 6.**Scaled travel time at a horizontal control plane (CP) located at soil depth, L = 1 m, for the different scenarios examined.

**Figure 7.**Cumulative mass of N extracted by the trees’ roots as a function of time, for the different scenarios examined. Top panel—the effect of the competition between nitrate and chloride on N uptake was disregarded.

**Figure 8.**Cumulative mass of nitrate gained by nitrification, as a function of time, for the different scenarios examined. Top panel—the effect of the chloride on nitrification was disregarded.

**Figure 9.**Cumulative mass fluxes of chloride crossing a horizontal CP located at soil depth, L = 4 m, for the different scenarios examined. Top panel—the effect of the chloride on N uptake and nitrification was disregarded.

**Figure 10.**Cumulative mass fluxes of nitrate crossing a horizontal CP located at soil depth, L = 4 m, for the different scenarios examined. Top panel—the effect of the chloride on N uptake and nitrification was disregarded.

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**MDPI and ACS Style**

Russo, D.; Kurtzman, D.
Using Desalinated Water for Irrigation: Its Effect on Field Scale Water Flow and Contaminant Transport under Cropped Conditions. *Water* **2019**, *11*, 687.
https://doi.org/10.3390/w11040687

**AMA Style**

Russo D, Kurtzman D.
Using Desalinated Water for Irrigation: Its Effect on Field Scale Water Flow and Contaminant Transport under Cropped Conditions. *Water*. 2019; 11(4):687.
https://doi.org/10.3390/w11040687

**Chicago/Turabian Style**

Russo, David, and Daniel Kurtzman.
2019. "Using Desalinated Water for Irrigation: Its Effect on Field Scale Water Flow and Contaminant Transport under Cropped Conditions" *Water* 11, no. 4: 687.
https://doi.org/10.3390/w11040687