For the three aforementioned crop types, representative fields were selected for deep sampling in the Hamra soils of the Sharon region: potato and strawberry fields representing the vegetable land use; a persimmon plantation representing the deciduous crop, and data from an orange orchard reported in Kurtzman et al. (2013) representing citrus. In each field, data of irrigation and fertilization regimes (quantities and timing in daily resolutions) were collected from the farmers. Data on irrigation water quality (nitrate and chloride concentrations) were collected from the Israel Water Authority. The potato field was irrigated by sprinklers, with an average irrigation depth of 480 mm yr-1, and fertilized with 450 kg N ha-1 yr-1. The strawberry field was irrigated by micro-sprinklers (at the early stage of growing) and drip irrigation afterwards to an average depth of 1000 mm yr-1 and fertilized with 450 kg N ha-1 yr-1. Strawberries were grown under plastic tunnels and the field was completely covered with a plastic sheet during the winter; hence, precipitation was not counted in the water balance for this field. The persimmon orchard was irrigated by micro-sprinklers to an average depth of 850 mm yr-1, and fertilized with 200 kg N ha-1 yr-1. The nitrogen forms of the applied fertilization were ammonium–nitrate solution in the irrigation water (persimmon and strawberry) and dry scattering of urea (potato). Nitrogen in the compost was accounted for in the strawberry and potato fields where this organic amendment was applied. The farmers in all representative fields reported that the same crop was cultivated for at least 15 years before sampling (with minor exceptions for the potato field). Time series of daily precipitation and reference evapotranspiration (Penman–Monteith equation; Allen et al., 1998) for each field were collected from nearby automated meteorological stations operated by the Israel Ministry of Agriculture.

In each of the three fields (persimmon, strawberry, and potato), three sampling core holes were drilled using the direct push technique, and a continuous core was obtained from 0 to 10 m depth (Fig. 3). The core holes were drilled at a distance of 50–200 m from each other. Soil (and sediment) cores were cut into 30 cm segments. Drilling was done in June 2012. Core segments were sealed with caps and tape and kept in a cooler until reaching the laboratory, where the core segments were analyzed for the following variables: gravimetric water content (105 ∘C), bulk density (core dry mass per volume), gravimetric particle-size distribution (hydrometer method), chloride concentration of a 1 : 2 soil-to-water extract (with Sherwood 926 chloridometer), nitrate and ammonium concentrations in a 1 M KCl 1 : 5 soil-to-water solution extract (Kachurina et al., 2000, with QuikChem 8000 autoanalyzer, Lachat Instruments, Loveland, CO). The soil samples that were used for extraction were ground and sieved to 2 mm after drying (40 ∘C for 3 days).

Average fluxes of water and nitrate–nitrogen toward the groundwater under the fields were calculated in a steady-state approximation with the chloride mass balance (Allison and Hughes, 1983; Scanlon et al., 2007): R=P⋅ClP+I⋅ClI∫z=10mz=2mθzdz∫z=10mz=2mθz⋅ClPWzdz, where R (L T-1) is the mean annual groundwater recharge flux, P (L T-1) is the mean annual precipitation flux, I (L T-1) is the mean annual irrigation application, Cl (M L-3) is the steady-state approximation of the chloride concentration with subscripts P, I, and PW referring to precipitation, irrigation water, and unsaturated-zone pore water, respectively, and θ (L3 L-3) is the volumetric water content. The interval of integration for calculating deep unsaturated-zone averages was from z= 2 m (below the root zone) to z= 10 m depth (deepest available data). The steady-state approximation of nitrate flux to the groundwater was obtained by multiplying the water flux (R, Eq. 1) by the depth- and θ-weighted average of nitrate–nitrogen concentrations below the root zone: FNO3=R∫z=10mz=2mθz⋅NO3-NPW(z)dz∫z=10mz=2mθzdz, where FNO3 (M L-2 T-1) is the mean annual flux of nitrate–nitrogen to the groundwater and NO3-NPW (M L-3) is the nitrate–nitrogen concentration in the deep vadose-zone pore water.

Transient vertical 1-D numerical models of water flow and nitrogen transport were calibrated to data of one drill hole in each field: potato, strawberry, and persimmon. The numerical code HYDRUS-1D was used for the calibration and simulations (Šimůnek et al., 2009). The 1-D vertical Richards equation with a root water-uptake sink was used for modeling flow in the unsaturated zone: ∂θ(h)∂t=∂∂zKh⋅∂h∂z+1-Sh, where t (T) is the time, z (L) is the vertical coordinate, h=h(z,t) (L) is the pressure head, θ(h) is the volumetric water content, K(h) (L T-1) is the unsaturated hydraulic conductivity, and S(h) (T-1) is a root water-uptake sink term which is non-zero in a transpiring root zone. The van Genuchten–Mualem model (Mualem, 1976; van Genuchten, 1980) was used for the θ(h) and K(h) relationships of the different sediment layers, and Feddes et al.'s (1978) functions, fitted to each crop, were used for S(h) (Šimůnek et al., 2009).

One dimensional advection–dispersion equations representing chain reactions of the nitrogen system are presented in Eqs. (4–6). Only ammonium is accounted for in the solid phase. Sink/source terms for root uptake of ammonium and nitrate, urea/compost mineralization, ammonium volatilization, ammonium nitrification, and nitrate denitrification complete the right-hand side of this equation system. ∂θCUr∂t=∂∂zθD∂CUr∂z-∂qCUr∂z-μminθCUr,∂θCNH4∂t+∂ρKdCNH4∂t=∂∂zθD∂CNH4∂z-∂qCNH4∂z-fNH4SCNH4+μminθCUr-μnitθCNH4-μvolθCNH4,∂θCNO3∂t=∂∂zθD∂CNO3∂z-∂qCNO3∂z-fNO3S⋅CNO3+μnitθCNH4-μdnitθCNO3, where CUr, CNH4, and CNO3 (M L-3) are concentrations of the nitrogen species (urea, ammonium, and nitrate, respectively) in the porewater solution, ρ (M L-3) is the soil's bulk density, θ (L3 L-3) is volumetric water content, D (L2 T-1) is the hydrodynamic dispersion coefficient, q (L T-1) is the water flux, fNH4SCNH4 and fNO3SCNO3 (M T-1 L-3) are the root ammonium–nitrogen- and nitrate–nitrogen-uptake sinks, respectively, where fNH4 and fNO3 are user-defined functions relating solute uptake to the water uptake S and solute concentrations; μmin (T-1) is a first-order urea/compost mineralization rate (sink term in Eq. 4 and source term in Eq. 5), μnit (T-1) is a first-order nitrification rate (sink term in Eq. 5 and source term in Eq. 6), μvol (T-1) is a first-order ammonium–nitrogen volatilization rate, μdnit (T-1) is a first-order denitrification rate, and kd (L3 M-1) is the ammonium–nitrogen partition coefficient. Application of compost (strawberry) was treated with Eqs. (4–6) as follows: farmers' reports of annual application of compost (m3 ha-1) were converted to mineralized nitrogen (Eq. 4) according to 15 and 5 % nitrogen by mass mineralized in the first and second years after application, respectively (Eghball et al., 2002). A dry compost density of 600 kg m-3 with 2 % of the dry mass consisting of nitrogen was used (Ben Hagai et al., 2011).

A total of 50 years (1962–2012) of daily precipitation, reference evapotranspiration (approximated from pan evaporation before 2002), irrigation water (with appropriate chloride and nitrate concentrations), and nitrogen fertilization was set as the upper boundary condition. A “free drainage” boundary (pressure gradient of 0) was used as the bottom boundary condition throughout. The calibration was aimed at fitting the measured profiles on the day of sampling, which was the last day of the 50 years of model runs, under the assumption of steady crop and the same agricultural practice during the 50 years.

Rosetta pedotransfer functions (Schaap et al., 2001) were used with particle-size distribution and bulk-density data to obtain initial values of the parameters of the hydraulic function θ(h) and K(h) for the model layers in the top 10 m (which were sampled and analyzed). These initial values were slightly changed (i.e., only KS within the same order of magnitude) during the calibration of the flow model in which the error between measured and modeled water contents was minimized. Dispersion coefficients of the soil/sediment layers were calibrated in the transport models with the unsaturated-zone chloride observations. Nitrate–nitrogen data were used for calibrating the nitrate, mostly by changing the function of nitrate uptake, fNO3 (Eq. 6). All calibrations were performed manually by trial-and-error runs.

To account for the actual unsaturated-zone thickness in each cell of the groundwater model, the unsaturated models were extended/shortened to fit steady-state approximations of the actual unsaturated thickness (4–50 m below the ground, at 1 m resolution; Fig. 4). This extension was also applied to the citrus orchard model from Kurtzman et al. (2013). Another model was constructed for water flow and nitrogen transport (10 kg ha-1 yr-1 nitrogen applied on ground surface) in the unsaturated zone below uncultivated areas using the hydraulic properties of the citrus orchard drill holes (this sampling point is at the center of the modeled area).

Thus, we created a “data library” of transient water and nitrate fluxes at the water table beneath the four land uses (posteriorly, the potato model was used for the vegetable land use because the strawberry deep fluxes were similar and the potato field covered a greater area).

A water flow and nitrate transport numerical model in the groundwater below the agricultural area in the Sharon region was developed. The model was constructed with GMS 8.2 software (AQUAVEO, 2012), the MODFLOW model for water flow (McDonald and Harbaugh, 1988), and the MT3D model for transport (Zheng, 1990). The model solves the water flow and advection–dispersion equations in the groundwater numerically (Eqs. 7 and 8): SS⋅∂h∂t=∂∂xKxx∂h∂x+∂∂yKyy∂h∂y+∂∂zKzz∂h∂z+R-P,∂C∂t=∂∂xDx∂C∂x-∂vxC∂x+∂∂yDy∂C∂y-∂vyC∂y+∂∂zDz∂C∂z-∂vzC∂z+R⋅Cduzn-P⋅Cn, where SS (L-1) is the specific storage, h (L) is the hydraulic head, t (T) is the time, x, y, z (L) are the three-dimensional coordinates, Kxx, Kyy, and Kzz (L T-1) are the hydraulic conductivities along the x, y, z axes, P and R (T-1) are volumetric fluxes per unit volume that represent sinks of water pumping in wells (P) and sources of water from recharge (R). C (M L-3) is nitrate concentration in the aquifer, Dx, Dy, and Dz (L2 T-1) are hydrodynamic dispersion coefficients, vx, vy, and vz (L T-1) are the velocities, n is porosity, and Cduz (M L-3) is the nitrate concentration in the deep unsaturated zone (in the recharge flux). The last term on the right in Eq. (8) is the nitrate sink due to pumping.

The modeled area was a polygon of 13.3 km2 of agricultural land in the Sharon region of Israel. There has been no significant residential land use in this area in the last 60 years and all nitrate fluxes from the ground surface were assumed to be from agricultural sources. The boundary conditions were transient hydraulic heads and nitrate concentrations based on data from wells near the model boundaries. Model calibration was based on transient measured data in wells inside the polygon (Fig. 5a). Time series of well heads and nitrate concentrations for the boundary conditions and calibration were obtained from the Israel Water Authority.

The area was discretized to cells of 150 : 150 m. Vertically, the model consists of 13 layers with thicknesses set according to the wells' perforations (Fig. 5b and c). Each cell in the top layer is fed with specific transient fluxes of water and nitrate from the unsaturated zone, according to the unsaturated-zone land-use model and its thickness (Fig. 4).

The groundwater model was run for 20 years (1992–2012). The input source/sink fluxes and boundary conditions were inserted into the model as monthly values (stress period of 1 month). By choosing this period, we ensured that the fluxes from the unsaturated zone (model runs start in 1962) represent the land use and not an artifact of initial conditions of the unsaturated-zone models. Moreover, during the years 1992–2012, the average water level in the model regions was relatively stable (Israel Water Authority data), supporting the steady-state approximation of the unsaturated-zone thickness.

The water flow model was calibrated against measured water levels in the wells (1992–2012). The model was run with some zonation of horizontal hydraulic conductivity and a constant value of the storage coefficient until the mean absolute error (MAE) between measured and calculated water levels over the years was less than 0.5 m, and the mean error (bias) was close to zero. Recharge fluxes from the unsaturated-zone models were strictly kept. In the first calibration stage of the nitrate transport model, dispersivity was fitted. Further steps in the calibration of this model were strongly related to the results and are elaborated upon in Sect. 3.

An approximation based on the unsaturated modeling results reported by Kurtzman et al. (2013) was used to estimate the nitrate fluxes at the water table under different fertilization scenarios: a decrease of 25 % in the nitrogen-fertilization mass results in a decrease of 50 % nitrate–nitrogen flux at the water table, whereas a reduction of 50 % in nitrogen fertilization results in a 72 % reduction in nitrate–nitrogen at the water table. Time series of nitrate–nitrogen fluxes at the water table were constructed using these ratios and the previously mentioned unsaturated flow and transport models (fitted to land uses and depth of the unsaturated zone). Three scenarios were tested: “business as usual”, and 25 and 50 % reduction in nitrogen application for the years 2012–2052. In these scenarios, it was assumed that land use would not change and that the precipitation and potential evapotranspiration would be the same as that of 1972 to 2012. In the groundwater transport model, the initial condition was the measured nitrate concentration in 2012. The transient nitrate-concentration boundary conditions were modified to account for similar reductions in nitrogen fertilization outside of the model domain. This was done in two steps: (1) running the model to the future with constant nitrate-concentration boundary conditions and looking at the trends of the nitrate concentration of the wells inside the model domain; (2) adjusting these trends to the boundary condition and running the model to the future again with transient nitrate-concentration boundary conditions.

Some spatial variability within the plot of each land use was observed, with one extremely different nitrate profile under the persimmon orchard (Fig. 6). Steady-state recharge and nitrate–nitrogen fluxes (Eqs. 1 and 2) were calculated for the data from each core hole. The spatial variability seen in the profiles (Fig. 6) was reflected by the variable deep fluxes within the plots (Table 1). Transient models were constructed for one core hole in each field. Nitrate–nitrogen fluxes under the strawberry and potato fields were relatively similar (∼ 210 kg N ha-1 yr-1); hence, the transient potato model that was calibrated to profile C was used for all areas of vegetable land use. The transient model representing the deciduous land use was Persimmon C (Table 1, Fig. 4). Hydraulically significant lithologic data of the sediment profiles as gravimetric percentage of the clay texture (< 0.002 mm) are displayed in Table 2.

Table 2a–c present the hydraulic, transport, and reaction model parameters that were calibrated to the observed unsaturated-zone data. The partition coefficient for ammonium, kd-NH4= 3.5 L kg-1, was used in all layers, and the first-order mineralization rate was set to μmin= 0.56 day-1 (Hanson et al., 2006). The relation of nitrate–nitrogen uptake to root-zone concentration and water uptake (fNO3SCNO3) was of the form used by Kurtzman et al. (2013) with limiting nitrate–nitrogen concentrations of 45, 35, and 20 mg L-1 for potato, strawberry, and persimmon, respectively. Limitation of the nitrogen reactions to the top layers of the soil was based on previous work in which nitrification potential was analyzed in orchard soils from this region (Kurtzman et al., 2013). Water and nitrogen balances resulting from the calibrated models showed significant recharge and deep nitrate–nitrogen leaching (40–55 % of total nitrogen input) under the investigated agricultural land (Table 3a and b). The yearly average (for 2002–2012) water and nitrate–nitrogen fluxes toward the water table calculated by the numerical models and those calculated by the steady-state approximation (chloride mass balance) matched well (Table 3a and b). The maximal difference between the two methods was 24 mm yr-1 (6.5 %) and 20 kg ha-1 yr-1 (7 %) for the water and nitrate–nitrogen fluxes, respectively. The average flux of nitrate–nitrogen toward the water table in citrus orchards in this area was found to be 30 % of the total nitrogen input (Kurtzman et al. 2013), lower than the leaching fraction under the vegetable and deciduous areas investigated here.

The flow model was calibrated by assigning different horizontal hydraulic conductivities, in the range of Kxx= Kyy= 4.5–30 m d-1, to five subregions, where the higher values are in the western part of the modeled area. These hydraulic conductivity values are similar to previous studies in the Sharon region of the Israel coastal aquifer (Bachmat et al., 2003; Lutsky and Shalev, 2010). The calibrated anisotropy was Kxx Kzz-1= 5 and the specific yield was Sy = 0.12.

The goodness-of-fit parameters between calculated and observed heads were the MAE and the mean error (the bias), calculated for each observation well (Table 4) and for all observations. The improvement in the calibration ceased when the target weighted-average MAE less than 0.5 m and bias less than 0.1 for all observations were achieved (Table 4, Fig. 7).

The nitrate transport model was calibrated by changing the dispersivity value, starting with a value in line with Neuman's (1990) formula. The final transport parameters used in the calibrated model were dispersivity of 500 m, ratio between longitudinal and transverse dispersivities of 10, and effective porosity of 0.12. This first stage of the calibration resulted in a good fit between observed and modeled mean nitrate concentration for the entire modeled area (i.e., spatially weighted average with weights for each well calculated by the Thiessen polygon method; Thiessen, 1911). However, the model showed poor fits between observed and calculated nitrate concentrations at each well separately (Table 5, Fig. 8a). This means that the model reconstructed well the entire mass of nitrate in the aquifer but it failed to describe nitrate's spatial variability (bottom two lines in Table 5a vs. observed, average, and standard deviations). To test whether the nitrate inputs from the unsaturated-zone model are significant in comparison to nitrate flowing from the boundaries (variable-concentration boundary condition), the model was run with zero nitrate flux from the unsaturated zone. The overall average nitrate concentration was 0.66 of the observed concentration (bottom two lines in Table 5b vs. observed, averages, and standard deviations). These results led to the understanding that although the unsaturated model produces good values for overall nitrate flux, the contaminated wells cannot be modeled with fluxes resulting from “normal” agricultural practice. The meaning of this is that nitrate spatial variability cannot be explained only by physical process of agricultural practice and land-use variability on surface. Other factors, that are local and arbitrary, significantly affect nitrate concentration in some wells and therefore the measured spatial variability of nitrate in the aquifer. These factors were introduced into the numerical model as will be explained hereafter.

Simulations showed that observed nitrate concentrations above 100 mg L-1 cannot be simulated with the nitrate fluxes produced by the calibrated unsaturated-zone model (Table 3b). Multiplication of fluxes by up to a factor of 10 was needed to produce high concentrations in the wells. On the other hand, we had to maintain the overall flux of nitrate over the entire model domain. Therefore, in the second stage of the calibration, nitrate fluxes that were calculated by the unsaturated-zone model were multiplied by factors as follows: 1 % of the area – factor of 10 (near the most contaminated wells); 3 % of the area – factor of 5; 4 % – factor of 2.8; 55 % – factor of 1; 19 % – factor of 0.6, and in 18 % of the area, the fluxes were multiplied by a factor of 0.1. The reasoning and some physical explanations for these extreme fluxes in small areas surrounding some wells will be discussed later (in Sect. 4). These local multipliers resulted in a reasonable fit between observed and modeled nitrate concentrations for each well separately and the overall nitrate average and standard deviation (bottom two lines in Table 5c vs. observed).

The calibrated model was run to 40 years in the future (2012–2052) under three scenarios: (i) business as usual; (ii) application of 75 % of the currently applied nitrogen fertilization; (iii) application of 50 % of the currently applied nitrogen fertilization. The simulation results showed that (i) the average concentration in all wells in the simulated area will continue to increase in the business as usual scenario, reaching 106 mg L-1 in 2052 (vs. 87 mg L-1 in 2012); (ii) reducing the fertilization to 75 % will approximately maintain the present concentrations; (iii) reducing the fertilization to 50 % will lead to a trend of declining nitrate concentration to less than 70 mg L-1 (Israel's drinking water standard for nitrate) as an average for all wells in the modeled area (Fig. 9 and Table 6). Even in this case about half of the wells will still exceed the standard concentration.