**2.5 Soil hydraulic properties**

In this model, soil hydraulic properties, concerning soil moisture retention characteristics, θ(h), and saturated hydraulic conductivity, Ksat, were measured in the field. The parameters of the [23] model were evaluated by fitting on θ(h) data using the Curve RETC code. The average values of Van Genuchten parameters for study at different soil depths are given in **Table 5**.

### **2.6 Parameter values**

Initial soil water contents for tomato in different soil depths were 0.20– 0.30 cm3 cm−3 (giving a mean value of 0.27 cm3 cm−3). Transport parameters were the model inputs. They were modified to calibrate the model. The modified longitudinal dispersivity and molecular diffusion coefficients of NO3–N in free water (Do) were used as/set at 1.0 cm and 1.65 cm2 d−1), respectively. Urea and NO3− were assumed to be present only in the dissolved phase (i.e., Kd = 0 cm3 g−1) soil. The first-order decay coefficient, μ, for urea, representing hydrolysis, was set at 0.38 day−1. Again, similar values were used in the literature, for example by [24] and

**137**

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

**Depth θ<sup>r</sup> θ<sup>s</sup> a n m Ksat**

 0.067 0.412 0.0073 1.86 0.414 3.896 0.095 0.375 0.0075 1.317 0.5310 2.160 0.185 0.421 0.0068 1.657 0.3916 0.131 0.048 0.473 0.0298 1.751 0.4259 18.922

by [25] who all considered hydrolysis to be in the range of 0.36 or 0.38 to 0.56 day−1.

which represents the center of the range of values reported in the literature, e.g., 0.2 day−1 ([24, 26], 0.02–0.5 day−1 [27], 0.226–0.432 day−1 [28], 0.15–0.25 day−1 [25], and 0.24–0.72 day−1 [29]. It is further assumed that the maximum rooting depth increases logistically with time (increases from 2 cm at germination at 60 cm at harvest), and that there is an exponential root distribution with depth. Uptake of nitrate and ammonium is by passive uptake only. That means that, e.g. NO3-N uptake at a given time and depth is equal to the water uptake multiply nitrate concentration in neglected. But assume that the maximum allowed concentration for solute is

*<sup>h</sup>* <sup>=</sup> *r sr* <sup>+</sup> <sup>−</sup> /1 || <sup>+</sup> *a h , m = 1–1/n.*

*Parameters of Van Genuchten equation for the soil moisture retention characteristics and the hydraulic* 

The model was evaluated by comparing measured and simulated values over time and depth using both qualitative and quantitative procedures. The qualitative procedures consisted of visually comparison between measured and simulated values over time and depth. For quantitative procedures, statistical analysis were used to calculate the average error (AE), the root mean square error (RMSE), the coefficient of residual mass (CRM), and the modeling efficiency (EF) between the measured and simulated values of water content in the soil during the study period [30–32]. The (AE) is the average difference between the simulated and the measured values. The AE with a positive or negative sign indicates whether the model tends to overestimate or underestimate the measured values. The RMSE statistical index shows the mean difference between simulated and observational data. The RMSE coefficient is equal to the variance of the remaining error and the lower the value, the higher the accuracy of the model. In the Nash-Sutcliffe criterion (EF), the numerical value of one indicates the complete conformity of the simulated and observational data. The CRM also shows the difference between experimental and estimated values. Positive CRM values indicate that the proposed model estimates the values less than its actual value, and vice versa. In the most optimal case, the RMSE and CRM values are equal to zero, in which case the proposed model estimates the values with the highest possible accuracy. Wilmott agreement statistical index (d) with a value it is between zero and one that the value of one indicates the best fit. The value of Willmott's index (*d*) reflects the degree of agreement, and *d* = 1 indicates perfect agreement between the measured and simulated values.

The closer the calculated values are to zero, the better the approximation of the simulated data to the field data [33]. The optimum values of AE, RMSE, EF and

(50 ppm N 550 mgN/L). Assume the soil profile is initially solute free.

was modeled using the rate coefficient of 0.2 day−1,

 *with Se = (θ - θr)/(θs - θr), θs and θr are saturated and residual water content,* 

 **cm−3) cm−1 — — cm hr.−1**

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

 **cm−3) (cm3**

*respectively, Ksat is saturated hydraulic conductivity, a and n empirical parameters***.**

Nitrification from NO4

*conductivity function.*

*K(h) = KsatSe1/2[1-(1-Se1/m)m]*

**Table 5.**

**(cm) (cm3**

**2.7 Model testing**

+ to NO3 −

*Note: Van Genuchten model:* ( ) ( ) ( ) *<sup>m</sup> <sup>n</sup>* θ θ θθ

*2*

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


*Note: Van Genuchten model:* ( ) ( ) ( ) *<sup>m</sup> <sup>n</sup>* θ θ θθ*<sup>h</sup>* <sup>=</sup> *r sr* <sup>+</sup> <sup>−</sup> /1 || <sup>+</sup> *a h , m = 1–1/n.*

*K(h) = KsatSe1/2[1-(1-Se1/m)m] 2 with Se = (θ - θr)/(θs - θr), θs and θr are saturated and residual water content, respectively, Ksat is saturated hydraulic conductivity, a and n empirical parameters***.**

#### **Table 5.**

*Recent Advances in Numerical Simulations*

during the growing season.

*Chemical analyses of animal manure.*

**Table 4.**

**2.4 Boundary conditions**

BC and zero concentration gradient.

study at different soil depths are given in **Table 5**.

cm−3 (giving a mean value of 0.27 cm3

water (Do) were used as/set at 1.0 cm and 1.65 cm2

**2.5 Soil hydraulic properties**

**2.6 Parameter values**

**2.3 Model selection: HYDRUS 1D**

simulation, the model was calibrated with field data.

for chemical fertilizer, 50% N and total P fertilizers were applied to the sowing seeds. Tomato was seeded on first week of May of each year in the plots at a plant spacing of 75 cm; Weed, diseases and insect control were uniformly managed during the growing season. After planting, irrigation was applied as required with well water until green stage and then treatments and irrigation applied as required

— ds/m−1 % — Mgkg−1

**pH EC N P K OC C:N Fe Mn Cu Zn**

7.73 13.6 2.4 1.02 0.81 61 25.4 1611 72 4 54

The HYDRUS-1D software package uses numerical methods to solve the Richards' equation for saturated–unsaturated water flow and the convection–dispersion equation for solute transport [20]. In this study, we used HYDRUS-1D to analyze water flow and nitrogen transport through tomato field irrigated with wastewater and soil surface management strategies. The measured data used are taken from completed research projects in field study. The data measurements were realized by [3, 21, 22] and were combined with additional measurements. Before

As the all the plots were at field capacity during the transplantation, therefore, the initial condition for volumetric soil water content was between 0.2–0.3 cm3

for all simulations. The upper boundary soil condition was the atmospheric boundary with a surface layer at which rainfall and evaporation occurred. The upper and lower soil boundary conditions (BC) for solute transport were considered as flux

In this model, soil hydraulic properties, concerning soil moisture retention characteristics, θ(h), and saturated hydraulic conductivity, Ksat, were measured in the field. The parameters of the [23] model were evaluated by fitting on θ(h) data using the Curve RETC code. The average values of Van Genuchten parameters for

Initial soil water contents for tomato in different soil depths were 0.20–

were the model inputs. They were modified to calibrate the model. The modified longitudinal dispersivity and molecular diffusion coefficients of NO3–N in free

were assumed to be present only in the dissolved phase (i.e., Kd = 0 cm3

soil. The first-order decay coefficient, μ, for urea, representing hydrolysis, was set at 0.38 day−1. Again, similar values were used in the literature, for example by [24] and

cm−3). Transport parameters

d−1), respectively. Urea and

cm−3

g−1)

**136**

NO3−

0.30 cm3

*Parameters of Van Genuchten equation for the soil moisture retention characteristics and the hydraulic conductivity function.*

by [25] who all considered hydrolysis to be in the range of 0.36 or 0.38 to 0.56 day−1. Nitrification from NO4 + to NO3 − was modeled using the rate coefficient of 0.2 day−1, which represents the center of the range of values reported in the literature, e.g., 0.2 day−1 ([24, 26], 0.02–0.5 day−1 [27], 0.226–0.432 day−1 [28], 0.15–0.25 day−1 [25], and 0.24–0.72 day−1 [29]. It is further assumed that the maximum rooting depth increases logistically with time (increases from 2 cm at germination at 60 cm at harvest), and that there is an exponential root distribution with depth. Uptake of nitrate and ammonium is by passive uptake only. That means that, e.g. NO3-N uptake at a given time and depth is equal to the water uptake multiply nitrate concentration in neglected. But assume that the maximum allowed concentration for solute is (50 ppm N 550 mgN/L). Assume the soil profile is initially solute free.

#### **2.7 Model testing**

The model was evaluated by comparing measured and simulated values over time and depth using both qualitative and quantitative procedures. The qualitative procedures consisted of visually comparison between measured and simulated values over time and depth. For quantitative procedures, statistical analysis were used to calculate the average error (AE), the root mean square error (RMSE), the coefficient of residual mass (CRM), and the modeling efficiency (EF) between the measured and simulated values of water content in the soil during the study period [30–32].

The (AE) is the average difference between the simulated and the measured values. The AE with a positive or negative sign indicates whether the model tends to overestimate or underestimate the measured values. The RMSE statistical index shows the mean difference between simulated and observational data. The RMSE coefficient is equal to the variance of the remaining error and the lower the value, the higher the accuracy of the model. In the Nash-Sutcliffe criterion (EF), the numerical value of one indicates the complete conformity of the simulated and observational data. The CRM also shows the difference between experimental and estimated values. Positive CRM values indicate that the proposed model estimates the values less than its actual value, and vice versa. In the most optimal case, the RMSE and CRM values are equal to zero, in which case the proposed model estimates the values with the highest possible accuracy. Wilmott agreement statistical index (d) with a value it is between zero and one that the value of one indicates the best fit. The value of Willmott's index (*d*) reflects the degree of agreement, and *d* = 1 indicates perfect agreement between the measured and simulated values.

The closer the calculated values are to zero, the better the approximation of the simulated data to the field data [33]. The optimum values of AE, RMSE, EF and

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

The average error is defined as:

$$Average\ error\ (AE) = \frac{\left(\sum\_{i=1}^{n} \mathbf{S}\_i \cdot \mathbf{Q}\_i\right)}{n} \tag{5}$$

The Root Mean Square Error is defined as:

$$\text{Root mean square error} \left( \text{RMSE} \right) = \sqrt{\frac{\left( \sum\_{i=1}^{n} S\_i - Q\_i \right)^2}{n}} \tag{6}$$

The Nash-Sutcliffe Efficiency is defined as:

$$EF = \left[ 1 - \frac{\sum\_{i=1}^{n} \left( \mathbf{S}\_i - \mathbf{O}\_i \right)^2}{\sum\_{i=1}^{n} \left( \mathbf{O}\_i - \overline{\mathbf{O}\_i} \right)^2} \right] \tag{7}$$

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

$$\mathbf{CRM} = \left[ \frac{\sum\_{i=1}^{n} (Q\_i - \mathbf{S}\_i)}{\sum\_{i=1}^{n} (\mathbf{O}\_i)} \right] \tag{8}$$

**139**

**Figure 1.**

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

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

*Simulated soil water content at different times of the experiment in the soil profile. With (T0=50 days, T1=150* 

positions (40, 60 and 100 cm), the model systematically underestimates the

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

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.

control the equilibrium water contents in winter ('field capacity').

/cm3

cm−3. For the deeper

over the entire growing season

water contents varied with depth from −0.045 to 0.152 cm3

measured water content by 0.04 to 0.110 cm3

*days, T2=200 days, T3= 240 days, T4=300 days and T5=339 days)..*

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

Where n is the number of observations, Oi is the average of the observed values and Si and Oi are the simulated and measured values, respectively [34].
