**3. Results and discussion**

#### **3.1 Water flow simulation**

Simulated soil water content in the soil profile are shown in **Figure 1**. However, the results in this section are presented to have an idea about the water regime in the soil profile with respect to the day of planting and harvesting the tomato. There were several rainfall events during the simulation period; however, more rainfall events were registered in the first part of the simulation period. As a result, the soil water content showed at all depths fluctuated more frequently in the first part of the simulation compared to the second and third part.

HYDRUS 1-D was also compared to the water content from field data collected from each treatment (by TDR) and simulated data for the soil profile over the growing season. The following observations are based on visual assessment of model fit compared with observed values of moisture contents of soil. The simulated and measured water contents at 20, 40, 60 and 100 cm are shown in **Figure 2A** and **B**, **Figure 3C** and **Figure 4D**, respectively. The predicted water

*Numerical Modeling of Soil Water Flow and Nitrogen Dynamics in a Tomato Field… DOI: http://dx.doi.org/10.5772/intechopen.98487*

#### **Figure 1.**

*Recent Advances in Numerical Simulations*

The average error is defined as:

mean square error are calculated as outlined in [33]:

The Root Mean Square Error is defined as:

The Nash-Sutcliffe Efficiency is defined as:

**3. Results and discussion**

**3.1 Water flow simulation**

CRM criteria are 0, 0, 1, and 0, respectively. Positive values of CRM indicate that the model underestimates the measurements and negative values for CRM indicate a tendency to overestimate them. If EF is less than zero, the models' predicted values are worse than simply using the observed mean. The average error and root

*Average error AE =*

( ) (∑ ) *<sup>n</sup>*

*Root mean square error RMSE =* (6)

( ) ( ) <sup>=</sup>

*S O*

*O O*

( ) ( )

*O*

*S*

*i i i*

*i i i*

=

=

∑ ∑ **1**

=

Where n is the number of observations, Oi is the average of the observed values

Simulated soil water content in the soil profile are shown in **Figure 1**. However, the results in this section are presented to have an idea about the water regime in the soil profile with respect to the day of planting and harvesting the tomato. There were several rainfall events during the simulation period; however, more rainfall events were registered in the first part of the simulation period. As a result, the soil water content showed at all depths fluctuated more frequently in the first part of

HYDRUS 1-D was also compared to the water content from field data collected from each treatment (by TDR) and simulated data for the soil profile over the growing season. The following observations are based on visual assessment of model fit compared with observed values of moisture contents of soil. The simulated and measured water contents at 20, 40, 60 and 100 cm are shown in **Figure 2A** and **B**, **Figure 3C** and **Figure 4D**, respectively. The predicted water

**1**

 <sup>−</sup> <sup>=</sup> 

*Q <sup>n</sup> i i i n i i*

*n*

*n*

**1**

∑ ∑

**1**

*EF*

The coefficient of residual mass (CRM) is defined as:

the simulation compared to the second and third part.

*CRM*

and Si and Oi are the simulated and measured values, respectively [34].

<sup>−</sup> = −

**1**

<sup>−</sup>

*i i i=1S -Q*

(5)

(7)

(8)

*n*

( ) ( )

**2**

**2**

1 *n i i <sup>i</sup> S Q n*

<sup>=</sup> ∑ <sup>−</sup>

2

**138**

*Simulated soil water content at different times of the experiment in the soil profile. With (T0=50 days, T1=150 days, T2=200 days, T3= 240 days, T4=300 days and T5=339 days)..*

contents at 20 cm depth agree well with the measured values during growing season. The simulation closely match the measured moisture dynamics, except in the (wet) spring and winter of 2010 when the model at times underestimates the soil water content in the top soil. The simulated water contents did not agree well with the measured data at 40, 60 and 100 cm depths, the response of the model was lower than measured, especially deeper in the soil profile. At all depths, a close agreement between the measured and simulated data was registered during (wet) winter period. The difference between simulated and measured water contents varied with depth from −0.045 to 0.152 cm3 cm−3. For the deeper positions (40, 60 and 100 cm), the model systematically underestimates the measured water content by 0.04 to 0.110 cm3 /cm3 over the entire growing season at deeper depths, potentially due to under-estimation in the amount of free drainage and an over-estimation of the soil porosity, although the dynamics (water depletion in summer, replenishment in winter) is well simulated. Given that the underestimation is not just limited to the growing season, but is also evident in winter periods when there is little evapotranspiration and the entire soil profile is draining suggests that the problem is not with the crop parameters or evapotranspiration, but rather with the soil hydraulic properties of the deeper soil horizons: the parameters of the van Genuchten-Mualem K-h-θ relationship control the equilibrium water contents in winter ('field capacity').

The statistical criteria of quantitative model evaluation between simulated and measured soil water content are summarized in **Table 6**. Overall, the values calculated demonstrate a good correlation of the model to field data. The results of the simulations may be affected by the value of the saturated hydraulic conductivity (Ks). Therefore, optimizing this parameter for all the three layers using inverse modeling of the Hydrus-1D, would slightly improve the simulation results. So the predicted water contents at −40, −60 and -100 cm are indeed much closer to the measured value, and this parameter change does not affect the (good) match observed for -20 cm. For further improvement, other hydraulic parameters (e.g. θs and α) also should be optimized. In addition, changing the matric pressure head may lead to good results.

#### **Figure 2.**

*Daily rainfall (solid bars, A) [cm], and measured (circles) and simulated (lines) soil water contents at 20 cm (A), 40 cm (B), 60 cm (C) and 100 cm (D) depths.*

#### **Figure 3.**

*Variation of concentration Urea, Ammonium and Nitate in different observational nodes of experiment in the soil profile. With (N1=20cm , N2=40cm, N3=60cm, N4=100cm and N5=120cm).*

**141**

**Figure 4.**

**3.2 Fate of nitrogen sources**

We determined the effects of different sources of nitrogen on the soil distribution of urea, ammonium, and nitrate during of growing season tomato field.

*Variation of concentration urea, ammonium and Nitate with depths for different times and depths of experiment for different treatment. With (T0=50 days, T1=150 days, T2=200 days, T3= 240 days , T4=300 days and T5=339 days).*

*Numerical Modeling of Soil Water Flow and Nitrogen Dynamics in a Tomato Field…*

*DOI: http://dx.doi.org/10.5772/intechopen.98487*

*Numerical Modeling of Soil Water Flow and Nitrogen Dynamics in a Tomato Field… DOI: http://dx.doi.org/10.5772/intechopen.98487*

#### **Figure 4.**

*Recent Advances in Numerical Simulations*

**140**

**Figure 3.**

**Figure 2.**

*(A), 40 cm (B), 60 cm (C) and 100 cm (D) depths.*

*Variation of concentration Urea, Ammonium and Nitate in different observational nodes of experiment in the* 

*Daily rainfall (solid bars, A) [cm], and measured (circles) and simulated (lines) soil water contents at 20 cm* 

*soil profile. With (N1=20cm , N2=40cm, N3=60cm, N4=100cm and N5=120cm).*

*Variation of concentration urea, ammonium and Nitate with depths for different times and depths of experiment for different treatment. With (T0=50 days, T1=150 days, T2=200 days, T3= 240 days , T4=300 days and T5=339 days).*

#### **3.2 Fate of nitrogen sources**

We determined the effects of different sources of nitrogen on the soil distribution of urea, ammonium, and nitrate during of growing season tomato field.


*Note: n = number of measurements, AE = average error, RMSE = relative root mean square error, EF = modeling efficient and CRM= coefficient of residual mass.*

#### **Table 6.**

*Statistical criteria for the simulated and measured soil water content.*


#### **Table 7.**

*Components of nitrogen balance at the end of simulation period in kg N ha−1 for a soil depth of 150 cm.*

To evaluate the Hydrus model performance with respect to nitrogen transport and transformations, the simulated nitrogen concentrations (NH4-N and NO3-N) are compared for different treatments at different depths of soil profile, (7.5, 22.5, 37.5, 52.5 and 120 cm from soil surface). **Figure 3 (A**–**C)** gives the daily variations in the simulated Urea-N, NH4-N and NO3-N concentrations respectively. It takes about 4 days to convert 90% of urea into ammonium and it takes about 70 days to convert 90% of ammonium into nitrate. Urea fertilizer is easily dissolved in water and transferred to the soil. After fertilization, urea is hydrolysed in the soil a urea concentration decreased over time between irrigations and ammonium is formed and then, during the nitration process by bacteria in the soil, convert ammonium to nitrite and then to nitrate. Immediately after fertigation, at 3.73 days, the urea was concentrated near the soil surface.

For all treatments ammonium accumulated in the topsoil immediately (**Figure 4**). Because of soil adsorption and subsequent fast nitrification and/or root uptake, there was only a slight movement of ammonium in the soil profile. The results obtained in this study indicated that nitrate moved continuously downwards during the 28-day of growing season simulation. Also, nitrate is easily exposed to leaching due to its high mobility and is not adsorbed to the soil, therefore denitrification was assumed negligible.

Nitrogen is applied to the soil solution by fertilizer application, treated wastewater irrigation and animal manure.

**143**

*Numerical Modeling of Soil Water Flow and Nitrogen Dynamics in a Tomato Field…*

Ammonium is usually ionically exchanged and stabilized in the surface of clay minerals. It is found in small amounts in soil solution and can be retained by the negative charges of clay mineral particles and organic particles. Therefore, the mobility of ammonium ions is lower than that of nitrate ions. The NH4-N then transformed to nitrate by the nitrification process, which is the most soluble form

**Table 7** shows the different components of nitrogen balance during the simulation period. Slightly smaller leaching percentages were computed for the urea– ammonium–nitrate wastewater compared to the nitrate- fertilizer and manure. Fertilizer use efficiency ranged from 54% (treatmentT4) to 84.9% (treatment T1). The results reported from nitrogen balance components show that nitrate leaching losses (0%, 23% and 25%) in treatments T1, T3, T4 respectively, and mainly occurred during the winter period. The reduced level of leaching is explained by low amount of drainage water, low nitrogen concentration of irrigation wastewater and excessive nitrogen uptake by the crop. Since the nitrate transport through the soil profile and out into field drains or deep groundwater, is usually controlled by water movement. The effect of irrigating different on the grain yield of tomato was also significant (P < 5%) (**Table 7**). The results showed an increase in the mean of fresh and dry forage yield (8.25% fresh forage and 23.14% of dry forage) (**Table 7**). Because treated wastewater is an important source of plant nutrients and can be

The HYDRUS-1D software was performed to simulated water flow and nitrogen transport in tomato crop soil for wastewater irrigation and fertilization. Based on the study carried out in the field, the ability of the model to predict the moisture in the soil at various depths is accurate. This can be due to an acceptable method in the

The results reported from nitrogen balance components show that nitrate leaching losses (0%, 23% and 25%) in treatments T1, T3, T4 respectively and mainly occurred during the winter period. The reduced level of leaching is explained by low amount of drainage water, and excessive nitrogen uptake by the crop. Since the nitrate transport through the soil profile and out into field drains or deep groundwater, is usually controlled by water movement. It was fund that the slightly smaller leaching percentages for the urea–ammonium–nitrate wastewater compared to the nitrate- fertilizer and manure. Fertilizer use efficiency ranged from 54% (treatment T4) to 84.9% (treatment T1). Based on these results we conclude that nitrogen from wastewater has smaller nitrate leaching compared to nitrogen from animal manure and commonly fertilizer. Nevertheless, our simulation results provide guidance on

the appropriate fertigation strategy for use of waste water in irrigation.

*DOI: http://dx.doi.org/10.5772/intechopen.98487*

of nitrogen in the soil for uptake by crops.

reused for irrigation to increase forage crop production.

**4. Conclusions**

simulation model.

*Numerical Modeling of Soil Water Flow and Nitrogen Dynamics in a Tomato Field… DOI: http://dx.doi.org/10.5772/intechopen.98487*

Ammonium is usually ionically exchanged and stabilized in the surface of clay minerals. It is found in small amounts in soil solution and can be retained by the negative charges of clay mineral particles and organic particles. Therefore, the mobility of ammonium ions is lower than that of nitrate ions. The NH4-N then transformed to nitrate by the nitrification process, which is the most soluble form of nitrogen in the soil for uptake by crops.

**Table 7** shows the different components of nitrogen balance during the simulation period. Slightly smaller leaching percentages were computed for the urea– ammonium–nitrate wastewater compared to the nitrate- fertilizer and manure. Fertilizer use efficiency ranged from 54% (treatmentT4) to 84.9% (treatment T1). The results reported from nitrogen balance components show that nitrate leaching losses (0%, 23% and 25%) in treatments T1, T3, T4 respectively, and mainly occurred during the winter period. The reduced level of leaching is explained by low amount of drainage water, low nitrogen concentration of irrigation wastewater and excessive nitrogen uptake by the crop. Since the nitrate transport through the soil profile and out into field drains or deep groundwater, is usually controlled by water movement. The effect of irrigating different on the grain yield of tomato was also significant (P < 5%) (**Table 7**). The results showed an increase in the mean of fresh and dry forage yield (8.25% fresh forage and 23.14% of dry forage) (**Table 7**). Because treated wastewater is an important source of plant nutrients and can be reused for irrigation to increase forage crop production.
