*Article* **Modeling of Fertilizer Transport for Various Fertigation Scenarios under Drip Irrigation**

#### **Romysaa Elasbah <sup>1</sup> , Tarek Selim 1,\* , Ahmed Mirdan <sup>1</sup> and Ronny Berndtsson 2,3**


Received: 1 April 2019; Accepted: 20 April 2019; Published: 28 April 2019

**Abstract:** Frequent application of nitrogen fertilizers through irrigation is likely to increase the concentration of nitrate in groundwater. In this study, the HYDRUS-2D/3D model was used to simulate fertilizer movement through the soil under surface (DI) and subsurface drip irrigation (SDI) with 10 and 20 cm emitter depths for tomato growing in three different typical and representative Egyptian soil types, namely sand, loamy sand, and sandy loam. Ammonium, nitrate, phosphorus, and potassium fertilizers were considered during simulation. Laboratory experiments were conducted to estimate the soils' adsorption behavior. The impact of soil hydraulic properties and fertigation strategies on fertilizer distribution and use efficiency were investigated. Results showed that for DI, the percentage of nitrogen accumulated below the zone of maximum root density was 33%, 28%, and 24% for sand, loamy sand, and sandy loam soil, respectively. For SDI with 10 and 20 cm emitter depths, it was 34%, 29%, and 26%, and 44%, 37%, and 35%, respectively. Results showed that shallow emitter depth produced maximum nitrogen use efficiency varying from 27 to 37%, regardless of fertigation strategy. Therefore, subsurface drip irrigation with a shallow emitter depth is recommended for medium-textured soils. Moreover, the study showed that to reduce potential fertilizer leaching, fertilizers should be added at the beginning of irrigation events for SDI and at the end of irrigation events for DI. As nitrate uptake rate and leaching are affected by soil's adsorption, it is important to determine the adsorption coefficient for nitrate before planting, as it will help to precisely assign application rates. This will lead to improve nutrient uptake and minimize potential leaching.

**Keywords:** drip irrigation; fertilizer transport; fertigation strategy; adsorption coefficient; HYDRUS-2D/3D

#### **1. Introduction**

Fertilization practice includes application of nitrogen, phosphate, and potassium before planting. For this purpose, manual broadcasting and mechanical spreading or spraying are used. Fertigation can be defined as the process of mixing irrigation water with fertilizers. Fertigation promotes overall root activity, improves nutrient mobility and uptake, as well as mitigating pollution of surface water and groundwater [1,2]. In Egypt, fertigation is practiced on only 13% of agricultural lands [3]. The fertigation technique is mainly used with nitrogen (N) and potassium (K) fertilizers [4].

For Egyptian agricultural conditions, nitrogen is considered one of the most important factors in crop production. Due to its excessive application by farmers, combined with poor surface irrigation management, N concentration is, on average, 1.50 ppm in the Nile Delta drains [3]. Therefore, sustainable agricultural management should be adopted. This management must include water saving

irrigation methods (e.g., drip irrigation) along with precise estimation of fertilizer application rates to mitigate harmful effects of excessive use of fertilizers on the surrounding environment.

The most common N fertilizers used in Egypt are nitrate (NO<sup>3</sup> <sup>−</sup>), ammonium (NH<sup>4</sup> <sup>+</sup>), and urea. Nitrate and ammonium are absorbed and used by crops, while urea is hydrolyzed to ammonium by heterotrophic bacteria, then nitrified to nitrite and nitrate by autotrophic bacteria [5]. Nitrate is highly mobile and easily leaches, due to its negative charge. Thus, excessive application of N might lead to nitrate contamination of surface water and groundwater [6]. Potassium, also adsorbs weakly to soil particles. Therefore, intensive use of fertilizers may increase N and K concentrations in groundwater [7,8]. Phosphorus leaching and runoff are insignificant, because phosphorus is usually adsorbed to particles, and is thus considered almost immobile [9].

Irrigation methods, soil hydraulic properties, management practices, climatic parameters, crop type, and crop rotation are major factors affecting risk for fertilizer leaching [10–12]. To achieve maximum fertilizer use efficiency, a proper fertigation strategy associated with modern irrigation technology should be implemented. Drip irrigation is considered a modern irrigation system that provides a great degree of control for both irrigation water and fertigation, allowing accurate application in accordance with crop water requirements and thereby reducing fertilizer leaching. Moreover, it allows for a controlled placement of nutrients near the plant roots, limits fertilizer losses, and reduces fertilizer leaching to the groundwater. Full understanding of water and fertilizer distribution patterns in the root zone and fertilizer leaching below the root zone are required for proper design of drip fertigation systems, regarding application rate and duration [13]. Considering all these parameters through large-scale field experiments is labor-, time-, and cost-consuming. Numerical simulations, on the other hand, are an inexpensive alternative which can help in assessing either existing or proposed fertigation practices.

The HYDRUS-2D/3D model [14] can efficiently simulate two or three dimensional water flow and fertilizer (e.g., urea–ammonium–nitrate, phosphorus, and potassium) transport in partially saturated porous media. In addition, it can simulate root water extraction and root nutrient uptake. Many researchers have shown that HYDRUS-2D/3D is a suitable software with which to simulate water flow and solute transport under different irrigation systems and fertigation scenarios (e.g., References [5,15–24]). Cote et al. [15] used HYDRUS-2D/3D to simulate water and fertilizer movement under subsurface trickle irrigation, considering different fertigation strategies for bare soil. They found that fertigation at the beginning of irrigation cycles can reduce nitrogen leaching. Gardenas et al. [16] evaluated nitrate leaching for various fertigation scenarios under micro irrigation systems, considering different soil types (sandy loam, loam, silt, and clay), assuming that the adsorption coefficient for nitrate was set equal to zero based on the assumption that the soils were free from positive charges, as nitrate is negatively charged, and, if soil is free from positive charges, nitrate will not adsorb to soil particles (i.e., adsorption coefficient for nitrate = 0). This also assumes that no other processes occur that affect the retention or release of soil chemical or biological nitrate content. They demonstrated that seasonal leaching was highest for coarse-textured soil, and that it increased when applying fertilizers at the beginning of the irrigation cycle, as compared to fertigation at the end of irrigation cycle. They showed that nitrate uptake by plant roots is smaller for micro-sprinkler irrigation, as compared to drip irrigation systems. The N use efficiency varied from 20 to 30% in micro-sprinkler irrigation. However, it reached 40 to 60% in drip irrigation. Hanson et al. [5] studied N uptake and leaching using urea–ammonium–nitrate fertilizers for surface drip (DI) and subsurface drip irrigation (SDI) systems. They ignored the adsorption behavior for urea and nitrate. They found that N use efficiency was about 50 to 65% for DI and 44 to 47% for SDI. Ajdari et al. [17] used HYDRUS-2D/3D to investigate nitrate leaching for an experimental onion field under DI, considering different emitter discharges. They found that as the emitter discharge increases, the amount of nitrogen leaching out from the root zone increases. The same conclusion was reached by Shekofteh et al. [25]. In addition, they found that simulation of nitrate movement using HYDRUS 2D/3D was close to the measured results in field soils.

As a result of the lack of irrigation water, some of Egypt's agricultural land suffers from chemical contamination due to illegal practices such as use of untreated drainage water from industry and agriculture for irrigation purposes. Examples of sources of contaminants are organic phosphorus pesticides, chlorinated hydrocarbon pesticides, rodenticides, and a variety of other pesticides including lead arsenate, calcium arsenate, copper oxides, and mercury [26]. Therefore, it is necessary to investigate the effects of soil composition and charge, especially for land areas suffering from chemical contamination, on nitrate adsorption behavior that affect leaching rates and N use efficiency. Nitrate can be adsorbed to soil particles if they contain positive charges. Iron and aluminum oxide concentrations in soil, organic matter content, and soil texture affect the nitrate adsorption rates to soil particles.

The present study introduces DI and SDI as alternatives to traditional irrigation methods (flood and furrow irrigattion) in order to overcome the problems associated with water shortage and to protect the environment from excessive application of nitrogen fertilizers using surface irrigation methods. Consequently, the HYDRUS-2D/3D model was used to investigate fertilizer distribution (i.e., ammonium, nitrate, phosphorus, and potassium) under DI and SDI, considering different fertigation strategies and soil types cultivated with tomato crops. The effect of fertilizer adsorption on the fertilizer uptake rates and fertilizers' leaching was also investigated.

#### **2. Materials and Methods**

The HYDRUS-2D/3D model (version 2.04, PC-Progress, Prague, Czech Republic) was used to simulate fertilizer movement under DI and SDI of tomatoes growing in three different soil types (sand, loamy sand, and sandy loam) representing typical Egyptian soils (Typic Xeropsamments to Typic Psammiaquents). Ammonium, nitrate, phosphorus, and potassium fertilizers were considered during simulations. Moreover, the impact of soil hydraulic properties, fertigation strategy, and fertilizer adsorption behavior, such as fertilizer distribution and losses, were investigated. HYDRUS-2D/3D is a computer software package used to simulate water, solute (i.e., chemicals), and heat transport in two or three dimensional variably saturated porous media. The HYDRUS-2D/3D model uses the Galerkin finite element method to solve the modified form of Richards' equation, which includes a sink term to consider water uptake by plant roots for simulating water flow. The model solves the Fickian-based advection–dispersion equation for solute transport (e.g., [27]). The transport equations contain terms for nonlinear non-equilibrium reactions between the solid and liquid phases and two first-order degradation reactions. For more details of the HYDRUS code and its application, see Reference [14].

#### *2.1. System Description*

In the DI setup, the spacing between drip lines was set to 140 cm (one drip line per plant row), and the spacing between emitters was set to 35 cm with an emitter flow rate of 1 L h−<sup>1</sup> . The simulation domain used was rectangular with a 100 cm soil depth and a 70 cm width, with a tomato plant located at the upper left corner of the simulation domain. The SDI system was arranged to have the same characteristics as the DI system with emitter depths of 10 and 20 cm below the soil surface (Figure 1). Unstructured triangular mesh with 21,086 and 21,896 2D elements was used to spatially discretize the flow domain for the DI and SDI, respectively, with smaller size mesh elements at the surface and close to the emitter.

**Figure 1.** Simulation domain for the investigated drip irrigation (DI) and subsurface drip irrigation **Figure 1.** Simulation domain for the investigated drip irrigation (DI) and subsurface drip irrigation (SDI) systems.

#### Soil Parameters

(SDI) systems.

Soil Parameters. Three different soil types (sand, loamy sand, and sandy loam) representing three typical and representative agricultural soil types in Egypt were considered. Table 1 shows the physical properties of the three different soil types. Three different soil types (sand, loamy sand, and sandy loam) representing three typical and representative agricultural soil types in Egypt were considered. Table 1 shows the physical properties of the three different soil types.

**Table 1.** Physical properties for the different soil types used in the simulations (Typic Xeropsamments to Typic Psammiaquents). **Table 1.** Physical properties for the different soil types used in the simulations (Typic Xeropsamments to Typic Psammiaquents).


considered in the present study. Table 2 shows the soil hydraulic parameters used during model simulation, and Table 3 summarizes observed chemical parameters for the simulated soil types. Table 3 shows that all simulated soils have positive charges, due to the existence of heavy metals and other contaminants. These positive charges will affect the adsorption behavior of nitrate and other fertilizers. Soil hydraulic parameters were taken according to Abou Lila et al. [28], as the same fields were considered in the present study. Table 2 shows the soil hydraulic parameters used during model simulation, and Table 3 summarizes observed chemical parameters for the simulated soil types. Table 3 shows that all simulated soils have positive charges, due to the existence of heavy metals and other contaminants. These positive charges will affect the adsorption behavior of nitrate and other fertilizers.

> **Table 2.** Hydraulic parameters for the different soil types used in the simulations**. Soil Type** *θr* **(m3 m−3)** *θs* **(m3 m−3)** *α n Ks* **(cm day−1)** *l*

Soil hydraulic parameters were taken according to Abou Lila et al. [28], as the same fields were


**Table 2.** Hydraulic parameters for the different soil types used in the simulations.

θ*r* : residual water content. θ*<sup>s</sup>* : saturated water content. *K<sup>s</sup>* : saturated hydraulic conductivity. α: inverse of the air-entry value. *n*: pore size distribution index, *l*: pore connectivity parameter.

**Table 3.** Observed chemical characteristics for soil types used in the simulations.


#### *2.2. Solute Parameters*

Molecular diffusion coefficient (*Dw*), first-order decay coefficients (µ*w*, µ*s*), and adsorption isotherm coefficient (*Kd*) for each type of fertilizer were required for simulation implementation. Longitudinal and lateral dispersivities (ε*<sup>L</sup>* and ε*<sup>t</sup>* , respectively) were also required. Thus, ε*<sup>L</sup>* was set = 0.1 m (i.e., one tenth of the simulation domain [29,30], while ε*<sup>t</sup>* was set = 0.1 × ε*<sup>L</sup>* [30]. Molecular diffusion was set equal to 1.957 <sup>×</sup> <sup>10</sup>−<sup>5</sup> cm<sup>2</sup> s −1 for NH<sup>4</sup> <sup>+</sup> and K<sup>+</sup> [31], and 1.902 <sup>×</sup> <sup>10</sup>−<sup>5</sup> cm<sup>2</sup> s −1 for NO<sup>3</sup> − [25,31].

The rate coefficients of nitrification from ammonium to nitrate (µ*w*, µ*s*) were set equal to 0.2 day−<sup>1</sup> [32,33].

#### *2.3. Batch Experiments*

Batch experiments were carried out to estimate fertilizer adsorption isotherm parameters for the different soil types. The batch experiments were conducted for each type of fertilizer and repeated for each type of soil, as described by Flury and Fluhler [34]. Soil samples were sieved through a 2 mm sieve and dried over one day at 105 ◦C. Solutions with initial concentrations (*Co*) of 124, 60, 46.5, and 132.3 ppm of potassium, phosphorus, ammonium, and nitrate were prepared using potassium sulfate, phosphoric acid, ammonium sulfate, and calcium nitrate, respectively. A 25 mL of the prepared solution of each fertilizer was mixed with 25 g soil and shaken in an inert Teflon flask for 3 h at 20 ◦C. After that, soil and solution were separated by 30 min centrifugation and the concentration of fertilizers in the supernatant solution was measured. Flame photometer was used to measure potassium concentration, while spectrophotometer at a wavelength of 660 nm was used to estimate phosphorus concentration and Kjeldahl to measure nitrogen concentration. The adsorbed mass of fertilizer (*Ca*; mg kg−<sup>1</sup> ) was calculated based on mass balance (the difference compared to the total mass of fertilizers). The mass found in the liquid phase at equilibrium (*C<sup>l</sup>* ; g m−<sup>3</sup> ) was assumed to be adsorbed by the soil. The experiments were made in duplicate.

Adsorption isotherm parameters were calculated using linear Freundlich isotherm equations ((Equation (1)).

$$\mathbb{C}\_d = \mathbb{K}\_d \mathbb{C}\_l \tag{1}$$

where *K<sup>d</sup>* is the distribution coefficient (dm<sup>3</sup> kg−<sup>1</sup> ). Values of the distribution coefficient for different types of fertilizer in the different soil types used in the model simulations are presented in Table 4.


**Table 4.** Distribution coefficient for fertilizers in the different soil types (cm<sup>3</sup> g −1 ).

In contrast to most previous research that assumed *K<sup>d</sup>* for nitrate to be equal to zero, the batch experiments gave an input for the *K<sup>d</sup>* for all collected soil samples. Most previous research (e.g., [5,16]) has assumed that nitrate is not adsorbed to soil particles with negative charge. However, in our case, the chemical analyses of collected soil samples (Table 3) revealed the presence of heavy metals and other contaminants that have positive charges. It is worth mentioning that the collected soil samples for this study were taken from the El-Salam Canal region. The El-Salam Canal water is considered brackish, as it is a mixture of Nile water and salty agricultural drainage water. It may also contain industrial waste water.

The volatilization of ammonium and subsequent ammonium transport by gaseous diffusion were neglected during simulations.

#### *2.4. Initial Conditions*

The initial soil water content (θ*<sup>i</sup>* ) in soil was assumed to be uniform in the entire flow domain. The effective saturation (θ*e*) was set equal to 0.25 m<sup>3</sup> m−<sup>3</sup> for all soil types, in order to determine θ*<sup>i</sup>* according to:

$$
\theta\_{\ell} = \frac{\theta - \theta\_r}{\theta\_s - \theta\_r} \tag{2}
$$

where θ is the volumetric water content equal to θ*<sup>i</sup>* at *t* = 0. The resulting θ*<sup>i</sup>* values were equal to 0.13, 0.15, and 0.169 m<sup>3</sup> m−<sup>3</sup> for sand, sandy loam, and loamy sand, respectively. The simulation domain was assumed to be free of fertilizers at the beginning of simulations.

#### *2.5. Boundary Conditions*

Figure 1 shows the imposed boundary conditions (B.C.) assumed during simulation of DI and SDI. No flux B.C. was set along vertical sides of the simulation domain. The left side was set as zero flux B.C. due to symmetry, and as the result of using a large flow domain the right boundary was set to zero flux B.C. as well. The bottom boundary was assigned as free drainage B.C., as the groundwater table is situated 1.50 m below the soil surface. In SDI, the top boundary was set as the atmospheric B.C. that allows for crop evapotranspiration (ETc) along the whole length of the upper boundary of the simulation domain. In DI, the location of the emitter was set as variable flux B.C., and the remaining part of the top boundary was assigned as atmospheric B.C. The ET<sup>c</sup> value was taken as a constant (0.75 cm day−<sup>1</sup> ), as calculated by Selim et al. [35] using the same study area. Although the HYDRUS-2D/3D model required partitioning of ET<sup>c</sup> to evaporation (E) and transpiration (T), T was set equal to ETc, while E was assumed to be zero during the simulation period. T was set equal to ETc, as the simulation was conducted only during the mid-growth season of the tomato crop, for which the surface area of land was approximately covered by tomato leaves (i.e., crop canopy). A constant flux (q) of 68.57 and 109.14 cm day−<sup>1</sup> was used at the emitter location during irrigation events in the case of DI (Equation (3)) and SDI (Equation (4)), respectively. When irrigation was terminated, these fluxes were converted to no flux boundary condition.

$$q = \frac{\text{Emitter discharge flow rate}}{\text{Drip tubing surface area}} = \frac{1 \times 1000 \times 24}{10 \times 35} = 68.57 \text{ cm day}^{-1} \tag{3}$$

where the flux diameter (10 cm) was assumed to be equal to the wetted diameter to avoid numerical simulation instability.

$$q = \frac{\text{Emitter discharge flow rate}}{\text{Drip tubing surface area}} = \frac{Q}{2\pi \, r \, \text{S}} = \frac{1 \times 1000 \times 24}{2 \times \pi \times 1 \times 35} = 109.14 \, \text{cm day}^{-1} \tag{4}$$

where *Q* is the emitter discharge (L<sup>3</sup> T −1 ), *r* is the emitter radius (L), and *S* is the distance between emitters (L).

As fertilizers were assumed to be applied with irrigation water, third-type Cauchy B.C. was set at the top edge of the simulation domain and along the emitter location for both DI and SDI.

#### *2.6. Fertilizer Application*

Fertilizers were added to the tomato crop with irrigation water according to the agricultural bulletin for tomato issued by the Egyptian Ministry of Agriculture. Four fertigation strategies were assumed in this study. The irrigation event period was divided into three equal intervals. In the first fertigation strategy (strategy B), fertilizers were applied at the beginning of the irrigation period (i.e., during the first third of irrigation). In the second and third fertigation strategies (strategies M and E, respectively), fertilizers were applied at the middle and at the end of the irrigation event period, respectively. In fertigation strategy C, fertilizers were applied during the whole period of the irrigation event. The total amounts of fertilizers added in the entire simulation period were 300.0, 21.4, 128.6, and 200.0 kg/ha for potassium, phosphorus, ammonium, and nitrate, respectively. Phosphorus was only added during the first 21 days, while other fertilizers were added during the entire simulation period. Potassium and phosphorus were added three times a week, while ammonium and nitrate were added twice a week.

#### *2.7. Root Parameters*

As the HYDRUS-2D/3D model version 2.04 does not consider root growth, and as a result of the lack of information about the root distribution through the entire growing season of the tomato crop, only simulation of the mid-growth season of tomato crop was executed. The growing stage was selected as the leaf area index for tomato crop is relatively constant, which leads to a constant root-to-shoot ratio [36]. The Vrugt et al. [37] model was used to describe root parameters. The following parameters of Vrugt's model were used as input for the HYDRUS-2D/3D model: *Z<sup>m</sup>* = 100 cm, *X<sup>m</sup>* = 70 cm, *z*\* = 25 cm, *x*\* = 0, *P<sup>z</sup>* = 1, and *P<sup>x</sup>* = 1 [5]. The effect of water stress on root water uptake was considered using a threshold water stress response function presented by Feddes et al. [38] with the following parameters: *<sup>P</sup><sup>o</sup>* <sup>=</sup> <sup>−</sup>1 cm, *<sup>P</sup>opt* <sup>=</sup> <sup>−</sup>2 cm, *<sup>P</sup>2H* <sup>=</sup> <sup>−</sup>800 cm, *<sup>P</sup>2L*<sup>=</sup> <sup>−</sup>1500 cm, *<sup>P</sup><sup>3</sup>* <sup>=</sup> <sup>−</sup>8000, *<sup>r</sup>2H* <sup>=</sup> 0.10 cm day−<sup>1</sup> , and *r2L* = 0.10 cm day−<sup>1</sup> .

#### *2.8. Simulation Scenarios*

Simulations were conducted to investigate the effect of irrigation method, soil hydraulic properties, fertilizers' adsorption behavior, and fertigation strategy on fertilizer transport when growing tomato crops. Surface and subsurface drip irrigation with emitters at depths 10 and 20 cm below soil surface were considered in the simulation. The simulations were conducted for sand, loamy sand, and sandy loam during a 40 day period representing the mid-growth stage of tomato crop, and irrigation was applied every alternate day with a duration of 7.35 h for each irrigation event. Four different fertilizer types, namely ammonium, nitrate, phosphorus, and potassium, were considered during the current work. Four fertigation strategies were investigated. Strategies B, M, and E lasted 2.45 h, and strategy C lasted 7.35 h. This led to 36 simulation scenarios.
