Simulation Effect of Water and Nitrogen Transport under Wide Ridge and Furrow Irrigation in Winter Wheat Using HYDRUS-2D

Abstract

An experiment was conducted to create a science-based program of irrigation and fertilizer application for two-year winter wheat under wide ridge and furrow irrigation in the Yellow River irrigation area. The study was performed in a test field located in Zhengzhou, Henan Province, China. A numerical model of soil water and nitrogen transport for winter wheat under wide ridge and furrow irrigation was created using HYDRUS-2D. The behavior of soil water and nitrogen was predicted for different irrigation water and nitrogen treatments and analyzed to identify pathways of nitrogen transport and transformation. The nitrogen balance was calculated for the different water and nitrogen treatments. The coefficients of determination for measured and predicted values of soil water content, nitrate nitrogen, and ammonium nitrogen in both horizontal and vertical directions were all >0.68; the mean absolute error was <0.06; and the root mean square error was <0.1. These values indicate the feasibility of using a numerical model of nitrogen transport for wide ridge and furrow irrigation. The correlation coefficient R² between simulated values of nitrogen uptake and measured values of total crop nitrogen content was 0.88, the RMSE value was 10.58 kg/ha, and the MAE value was 5.9 kg/ha. Nitrogen loss was primarily caused by denitrification, and the quantity of gaseous nitrogen loss was 7.05–38.2% of the nitrogen form. The total quantity of ammonium nitrogen absorbed by winter wheat plant roots in each treatment was 7.6–15.1% of the total amount of nitrate nitrogen absorbed. The maximum nitrogen uptake was 155.53 kg/ha with a yield of 6888.67 kg/ha at a nitrogen application rate of 220 kg/ha and irrigating to 70% field capacity. The UE of the 220 kg/ha and irrigating to 70% field capacity treatment was relatively high, the PFP of the 120 kg/ha and irrigating to 80% field capacity treatment was relatively high, and the nitrogen use efficiency of the 320 kg/ha and irrigating to 60% field capacity treatment was the lowest overall. This study provides a basis for investigating soil water and nitrogen transport mechanisms of winter wheat under wide ridge and furrow irrigation in the Yellow River irrigation area.

1. Introduction

Water and nitrogen are critical plant growth factors that can be controlled to influence crop development [1]. Excessive irrigation and chemical fertilizer application to obtain high yield have become the norm in agricultural production and have resulted in non-point source pollution that has deteriorated water and soil environments [2] and led to groundwater nitrate concentrations that exceed standards [3]. Much research has been conducted into water and nitrogen transport using indoor soil containers with different irrigation methods in conjunction with numerical models [4,5,6,7,8,9] in order to accurately simulate water and nitrogen transport and to develop efficient water and fertilizer application systems. Similar field-based research into water and fertilizer application has also been conducted [10,11]. Although an indoor experiment can reveal the regularities and mechanisms of soil water and fertilizer movement, it necessarily excludes key crop growth and weather factors and, therefore, any model built depending on it has defects. A field experiment will provide realistic experimental data, but it is extremely time and energy-consuming to conduct such experiments, and experimental conclusions often lack generality. Li et al. optimized water and nitrogen management measures for winter wheat and studied the effects of controlled-release fertilizers with different release periods and their water and fertilizer dosages on the yield of winter wheat [12]. Gu et al. investigated the effects of different bed sizes and fertilizer application timings on the distribution pattern of soil nitrate-N and on the yield of winter wheat [13]. Li et al. used summer maize-winter wheat crop rotation in North China as a study object to explore irrigation and fertilization methods that can reduce nitrous oxide emissions while ensuring the grain yield [14].

Present research is mainly directed towards combining experimentally measured data with a numerical model to create an appropriate numerical model [15,16,17,18]. However, the paradigm for most current field water transport models is one-dimensional vertical infiltration, and there has been little research into the development of water and nitrogen transport models for two-dimensional ridge and furrow irrigation of winter wheat. Differences in water and fertilizer application methods result in differences in the soil distribution of water and nitrogen, thus changing the physical and chemical environment of the root zone and influencing the nitrification, mineralization, and denitrification occurring in the soil and ultimately causing differences in the total nitrogen absorption of the crop. The crop modeled in this study is winter wheat [19]. More needs to be reported on the high-accuracy model of two-dimensional water movement, nitrogen transport and transformation, and nitrogen uptake and utilization of winter wheat in the Yellow River irrigation area. In order to develop a suitable water and fertilizer application treatment that takes account of local conditions, it is necessary to build a water and nitrogen transport model for winter wheat growth that will predict the distribution of water and nitrogen in the soil and the nitrogen uptake and accumulation of plants in response to water and fertilizer treatments.

The objectives of the current study were as follows. Comparative field experiments were conducted on two-year winter wheat under wide ridge and furrow irrigation. Field-measured data were used in creating a water and nitrogen transport model for winter wheat under wide ridge and furrow irrigation. The case was used to predict the synergistic response of plants to different water and nitrogen distributions in the soil and the total nitrogen accumulation of plants in response to different experimental treatments. The water and fertilizer treatment that produced the greatest nitrogen accumulation in plants was identified, and the nitrogen use efficiencies of different treatments were compared. This study provides scientific support for water and chemical fertilizer management that will reduce agricultural non-point source pollution during the growth period of winter wheat in the middle and lower reaches of the Yellow River.

2. Materials and Methods

2.1. Soil Conditions and Experiment Design

2.1.1. Overview of the Study Area and Soil Characteristics

The experiment was conducted in the experimental field of the Agricultural High Efficiency Water Use Test Field of North China University of Water Resources and Hydropower in Zhengzhou from October 2020 to June 2022. The ditch length in a single test area was 50 m, the ridge width was 0.7 m, and the total ditch width on each side of the ridge was 0.8 m. The geographical coordinates of the field are 34°50′ N, 113°48′ E. During the experiment, average temperature in the area was 13.56 °C, and average daily sunshine was 4.82 h. The location of the test area is shown in Figure 1. In the winter wheat growth period, the temperature during the overwintering period was <0 °C, and the soil was subjected to freeze–thaw cycles. During this period, soil water did not flow, but the HYDRUS-2D case does not accommodate freeze–thaw cycles, so the soil moisture and solute transport process module did not model water and nitrogen treatment in the early stage of winter wheat growth. Therefore, this paper simulates the changes in soil water content, ammonium nitrogen concentration, and nitrate nitrogen concentration from 1 March to 25 May 2021 and 24 February to 20 May 2022. Before the test, the particle size distribution of the test soil at different depths was determined by a BT-9300ST laser particle size analyzer, and the basic physical and chemical properties of the soil were determined. The basic physical properties and physicochemical parameters of the soil in the test site are shown in

Table 1. Basic physical properties and physicochemical parameters of soil.

Soil Depth (cm)	Soil Type	Soil Characteristic Parameters				Particle Size Composition (%)			Physicochemical Parameters of the Tested Soil
		Dry Bulk Density of Soil (g/cm3)	Field Capacity (%)	Soil Organic Matter (%)	Average Total Nitrogen Content (%)	<0.002	0.002–0.02	0.02–2	Ammonium Nitrogen (mg/kg)	Nitrate Nitrogen (mg/kg)
0–20	Loam	1.45	34	0.87	0.05	7	43	53	9.48	8.62
20–40	Silty loam	1.47	32	0.86	0.05	7	44	49	8.24	4.67
40–60	Silty loam	1.48	30	0.83	0.04	6	45	49	11.65	6.05
60–80	Silty loam	1.5	29	0.78	0.04	6	43	51	7.74	4.81
80–100	Silty loam	1.46	28	0.56	0.03	2	12	86	9.57	8.18

Note: water content in the table is by volume.

.

2.1.2. Experiment Design

The experimental variety of winter wheat was Jimai 22, which were sown on 12 October 2020 and 15 October 2021, and harvested on 25 May 2021 and 20 May 2022. The irrigation method was wide ridge and furrow irrigation [20]; irrigation timing depended on the lower limit of soil moisture content. According to local planting practices in Henan Province, and in conjunction with the goals of this study, the nitrogen application range for winter wheat was determined based on existing research results [21,22]. We combined three nitrogen application rates (120 kg/ha (F₁), 220 kg/ha (F₂), and 320 kg/ha (F₃)) and three soil moisture controls (irrigation to the lower limits of 60% field water capacity (W₁), 70% field water capacity (W₂), and 80% field water capacity (W₃)) to give nine experimental water and nitrogen application treatments. Fertilizer application timing, irrigation water, fertilizer amount, and upper and lower limits of irrigation for the nine treatments are detailed in

Table 2. Different water and fertilizer treatments for winter wheat.

Treatment	Irrigation Lower Limit	Irrigation Water (mm)	Number of Top Dressing Applications	Nitrogen Application Rate (kg/ha)
				Ground Fertilizer	Jointing Stage	Date of Ear Emergence	Grand Total
W1F1	60% θfield	90	2	55	32.5	32.5	120
W1F2					82.5	82.5	220
W1F3					132.5	132.5	320
W2F1	70% θfield	180			32.5	32.5	120
W2F2					82.5	82.5	220
W2F3					132.5	132.5	320
W3F1	80% θfield	240			32.5	32.5	120
W3F2					82.5	82.5	220
W3F3					132.5	132.5	320

Note: water content in the table is by volume.

. Rainfall after the regreening period is shown in Figure 2. The field was plowed immediately after base fertilizer (compound fertilizer of potassium sulfate, N/15%, P/15%, and K/15%) application. The top dressing was incorporated with water and fertilizer (urea, N/46.3%) and applied by irrigation.

2.2. Determination Items and Methods

2.2.1. Soil Moisture Measurement

Soil moisture content was measured by a Trime-PICO-IPH (time domain reflectometry) every 2–3 d during the wheat growth period. Before wheat planting, after harvest, and during the key growth period, a 0–100 cm soil depth probe was drilled into the soil; every 20 cm was considered to be a layer. Soil moisture content was measured by drying to calibrate the soil moisture content measured by the Trime-PICO-IPH.

2.2.2. Determination of Soil Nitrogen Content

Before winter wheat planting, after harvest and during key growth periods, and 5 d after fertilization treatment, soil samples were taken with a soil auger, treating every 20 cm as a distinct soil layer for a total of 5 layers. The soil samples were extracted by a KCl solution, and the contents of ammonium nitrogen and nitrate nitrogen in the solution were measured by ultraviolet spectrophotometry. In order to model the soil nitrogen transformation process accurately, the dry soil nitrogen content was converted into concentration in a soil solution.

$$C_w=\frac{C_s\cdot \rho }{1000\cdot \theta }$$

(1)

where: C_w is the soil nitrogen content in soil solution, mg/cm³; C_s is the dry soil nitrogen content, mg/kg; ρ is soil bulk density, g/cm³; and θ is the soil volumetric water content, cm³/cm³.

2.2.3. Fertilizer Agronomic Efficiency, Fertilizer Physiological Efficiency, Fertilizer Utilization Efficiency, and Partial Factor Productivity of Fertilizer

Fertilizer agronomic efficiency (AE, kg/kg):

$$AE=\frac{Y_N-Y_{CK}}{T_N}$$

(2)

where: Y_N is the yield of winter wheat, kg/hm²; Y_CK is the yield of the control, kg/hm²; and T_N is the amount of nitrogen applied, kg/hm².

N fertilizer physiological efficiency (PE, kg/kg):

$$PE=\frac{Y_N-Y_{CK}}{U_N-U_{CK}}$$

(3)

where: U_N is the amount of nitrogen absorbed by the crop, kg/hm²; and U_CK is the amount of nitrogen absorbed by the control crop, kg/hm².

N fertilizer utilization efficiency (UE, kg/kg):

$$UE=\frac{U_N-U_{CK}}{T_N}$$

(4)

Partial factor productivity of fertilizer (PFP, kg/kg):

$$PFP=\frac{Y_N}{T_N}$$

(5)

2.3. Mathematical Model

The mean absolute error (MAE), root mean square error (RMSE) and coefficient of determination (R²) were used to evaluate the accuracy of the model.

2.3.1. Water Movement Equation

The basic equation of unsaturated soil water movement [23] and the Van Genuchten–Mualem (VG-M) model were used to calculate K(θ):

$$\frac{\partial \theta }{\partial t}=\frac{\partial }{\partial x}\left[D(\theta )\frac{\partial \theta }{\partial x}\right]+\frac{\partial }{\partial z}\left[D(\theta )\frac{\partial \theta }{\partial z}\right]+\frac{\partial K(\theta )}{\partial z}-S(x,z,h)$$

(6)

$$K(\theta )=\{\begin{array}{ll}{K}_s{S}_e^l{\left[1-{(1-S_e^{1/m})}^m\right]}^2& h<0\\ K_s& h\ge 0\end{array}$$

(7)

$$S_e=\{\begin{array}{ll}\frac{\theta -{\theta }_r}{{\theta }_s-{\theta }_r}=\frac{l}{{(1+{\left|\alpha h\right|}^n)}^m}& h<0\\ 1& h\ge 0\end{array}$$

(8)

where: θ is the soil volumetric water content, cm³/cm³; t is the infiltration time, min; r and z are the spatial coordinates, with z downward as the positive direction, cm; K(θ) is the soil unsaturated hydraulic conductivity, cm³/min; D(θ) is the moisture diffusivity, cm³/min; S(x,z,h) is the crop root water uptake; S_e is the relative soil saturation; K_s is the soil saturated hydraulic conductivity, cm/min; α is the reciprocal of the air-entry suction value, cm⁻¹; m and n are the shape coefficients, with m = 1 − 1/n; and l is the soil hydraulic characteristic curve fitting coefficient, 0.5.

2.3.2. Solute Transport Equation

The convection–dispersion governing partial differential equations for unsaturated nitrogen transport and transformation in winter wheat [24] are:

Urea nitrogen:

$$\begin{array}{l}\frac{\partial \left(\theta ·C_{urea}\right)}{\partial t}=\frac{\partial }{\partial x}\left(\theta D_{xx}\frac{\partial C_{urea}}{\partial x_x}+\theta D_{xz}\frac{\partial C_{urea}}{\partial z}\right)+\frac{1}{x}\left(\theta D_{xx}\frac{\partial C_{urea}}{\partial x_x}+\theta D_{xz}\frac{\partial C_{urea}}{\partial z}\right)+\\ \frac{\partial }{\partial z}\left(\theta D_{xx}\frac{\partial C_{urea}}{\partial x_x}+\theta D_{xz}\frac{\partial C_{urea}}{\partial z}\right)-\left(\frac{\partial q_x{C}_{urea}}{\partial x}+\frac{\partial q_x{C}_{urea}}{x}+\frac{\partial q_z{C}_{urea}}{z}\right)-{\mu }_{w,urea}^{\prime }\theta C_{urea} \end{array}$$

(9)

Ammonium nitrogen (volatilization, nitrification, mineralization, and biological immobilization):

$$\begin{array}{l}\frac{\partial (\theta C_{N{H}_4^{+}})}{\partial t}+\rho \frac{\partial s_{N{H}_4^{+}}}{\partial t}=\frac{\partial }{\partial x}(\theta D_{xx}\frac{\partial C_{N{H}_4^{+}}}{\partial x}+\theta D_{xz}\frac{\partial C_{N{H}_4^{+}}}{\partial z})+\frac{1}{x}(\theta D_{xx}\frac{\partial C_{N{H}_4^{+}}}{\partial x}+\theta D_{xz}\frac{\partial C_{N{H}_4^{+}}}{\partial z})+\\ \frac{\partial }{\partial z}(\theta D_{zz}\frac{\partial C_{N{H}_4^{+}}}{\partial x}+\theta D_{xz}\frac{\partial C_{N{H}_4^{+}}}{\partial z})-(\frac{\partial q{C}_{N{H}_4^{+}}}{\partial x}+\frac{q{C}_{N{H}_4^{+}}}{x}+\frac{\partial q{C}_{N{H}_4^{+}}}{\partial z})+{\mu }_{w,urea}^{\prime }\theta C_{urea}-\\ \left({\mu }_{w,N{H}_4^{+}}^{\prime }\theta C_{N{H}_4^{+}}+{\mu }_{s,N{H}_4^{+}}^{\prime }\rho S_{N{H}_4^{+}}\right)-{\mu }_{w,N{H}_4^{+}}\theta C_{N{H}_4^{+}}+{\gamma }_{w,N{H}_4^{+}}\theta +{\gamma }_{\mathrm{s},N{H}_4^{+}}\rho -S{C}_{N{H}_4^{+}}\end{array}$$

(10)

Nitrate nitrogen (denitrification and biological fixation):

$$\begin{array}{l}\frac{\partial (\theta C_{N{O}_3^{-}})}{\partial t}=\frac{\partial }{\partial x_i}(\theta D_{xx}\frac{\partial C_{N{O}_3^{-}}}{\partial x}+\theta D_{xz}\frac{\partial C_{N{O}_3^{-}}}{\partial z})+\frac{1}{x}(\theta D_{xx}\frac{\partial C_{N{O}_3^{-}}}{\partial x}+\theta D_{xz}\frac{\partial C_{N{O}_3^{-}}}{\partial z})+\\ \frac{\partial }{\partial z}(\theta D_{xx}\frac{\partial C_{N{O}_3^{-}}}{\partial x}+\theta D_{xz}\frac{\partial C_{N{O}_3^{-}}}{\partial z})-(\frac{\partial q{C}_{N{O}_3^{-}}}{\partial x}+\frac{q{C}_{N{O}_3^{-}}}{x}+\frac{\partial q{C}_{N{O}_3^{-}}}{\partial z})+\\ \left({\mu }_{w,N{H}_4^{+}}^{\prime }\theta C_{N{H}_4^{+}}+{\mu }_{s,N{H}_4^{+}}^{\prime }\rho S_{N{H}_4^{+}}\right)-({\mu }_{w,N{O}_3^{-}}+{\mu }_{s,N{O}_3^{-}})\theta {\mathrm{C}}_{N{O}_3^{-}}-S{C}_{N{O}_3^{-}}\end{array}$$

(11)

Altogether:

$$\theta D_{xx}=D_L\frac{q_x^2}{\left|q\right|}+D_T\frac{q_z^2}{\left|q\right|}+\theta D_w\tau$$

(12)

$$\theta D_{zz}=D_L\frac{q_z^2}{\left|q\right|}+D_T\frac{q_x^2}{\left|q\right|}+\theta D_w\tau$$

(13)

$$\theta D_{xz}=\left(D_L-D_T\right)\frac{q_x{q}_z}{\left|q\right|}$$

(14)

$$\tau ={\theta }^{7/3}/{\theta }_s^2$$

(15)

where $C_{urea}$ is urea liquid concentration, $C_{N{H}_4^{+}}$ is ammonium nitrogen liquid concentration, $S_{N{H}_4^{+}}$ is ammonium nitrogen solid concentration, and $C_{N{O}_3^{-}}$ is nitrate nitrogen liquid concentration, all in mg/cm³; $q_i$ is water flow rate, cm/min; $D_{ij}$ is the liquid dispersion coefficient, cm²/min; ${\mu }_{w,urea}^{\prime }$ is the first-order kinetic reaction coefficient for urea hydrolysis,/day; ${\mu }_{w,N{H}_4^{+}}$ is the liquid phase first-order kinetic reaction coefficient for ammonium nitrogen,/day; ${\mu }_{w,N{H}_4^{+}}^{\prime }$ and ${\mu }_{s,N{H}_4^{+}}^{\prime }$ are, respectively, the second-order kinetic reaction coefficients of ammonium nitrogen liquid and solid phases involved in nitrogen nitrification,/day; ${\gamma }_{w,N{H}_4^{+}},{\gamma }_{\mathrm{s},N{H}_4^{+}}$ are, respectively, the zero-order kinetic reaction coefficients of nitrogen transformation (mineralization and biological immobilization),/day; and ${\mu }_{w,N{O}_3^{-}}$ and ${\mu }_{s,N{O}_3^{-}}$ are, respectively, the denitrification reaction coefficients of liquid and solid nitrate nitrogen (a first-order reaction).

Assuming that ammonium ions are adsorbed by soil in a solid phase, the isothermal adsorption relationship between liquid ammonium ions and solid ammonium ions is described by the linear equation:

$$S_{N{H}_4^{+}}=K_d{C}_{N{H}_4^{+}}$$

(16)

where K_d is the adsorption constant of ammonium nitrogen, 0.0035 cm³/mg [25].

2.3.3. Root Water Absorption Equation and Root Growth

Winter wheat roots were mainly distributed in the 0–60 cm soil depth. The water absorption equation for wheat roots uses the Feddes generalized root water absorption model in HYDRUS-2D software, and the user can quantitatively specify the water consumption of the roots as volume per unit time. The equation for root water absorption using the HYDRUS-2D, specific parameters are detailed in

Table 3. Water absorption parameters of winter wheat roots.

Parameter Name	P0 (cm)	P0Pt (cm)	P2H (cm/day)	P2L (cm)	P3 (cm)	r2h (cm/day)	r2L (cm/day)
Numerical value	0	−1	−500	−900	−16,000	0.5	0.1

, built-in wheat parameters is:

$$S_{(x,z,h)}=\alpha (x,z,h)b(x,z)T_{P}L$$

(17)

where α(x,z,h) is the dimensionless water stress response function of root water uptake; b(x,z) is the root water uptake distribution function (L/day); T_P is the crop potential transpiration rate, cm/day; and L is the maximum width of root zone distribution with a field-measured value of 3 cm.

The actual transpiration rate of winter wheat is calculated by the equation:

$$E{T}_a={\displaystyle \underset{L_R}{\int }S(h,z,t)}dz=T_p(t){\displaystyle \underset{L_R}{\int }\alpha (h)}\beta (z,t)dz$$

(18)

The root distribution area is described by the root growth model of HYDRUS-2D:

$$L_R(t)=L_m{f}_r(t)$$

(19)

where: L_m is the maximum root depth, cm; and f_r(t) is the dimensionless root growth coefficient, estimated by the Verhulst–Pearl logistic growth function.

$$f_r(t)=\frac{L_0}{L_0+(L_m-L_0)e^{-rt}}$$

(20)

where: r is the root growth rate, day⁻¹; the L_m of each treatment was measured by destructive sampling in the range of 40–80 cm during the critical fertility period of winter wheat and varied with the water and nitrogen regulation deficit; 𝐿₀ is the initial value of root length in the simulation stage of winter wheat, cm.

2.3.4. Crop Transpiration Rate

Bell’s law divides the actual transpiration of winter wheat into soil surface evaporation and plant evapotranspiration:

$$Evap=ETa(1-SCF)$$

(21)

$$Transp=ETa\times SCF$$

(22)

$$SCF=1-\exp (-rExtinct\times LAI)$$

(23)

where: LAI is the wheat leaf area index for the growth period, which is determined by data fitting using the winter wheat leaf area index–time equation; SCF is the crop light transmission coefficient; ETa is the actual evapotranspiration of winter wheat and rExtinct is obtained using a plant canopy analyzer and the supporting analysis system:

$$rExtinct=-\ln \left(\frac{TPAR}{PAR}\right)LAI$$

(24)

where: TPAR is instantaneous photosynthetically active radiation below the canopy, µmol/m²/s; and PAR is instantaneous photosynthetically active radiation above the canopy, µmol/m²/s.

2.4. Boundary Conditions

Initial conditions:

The measured values from the field experiment of the moisture content of each soil layer and the soil ammonium nitrogen and nitrate nitrogen contents were input into the HYDRUS-2D case as initial conditions. The model assumption is that the initial soil water and nitrogen contents of each layer are evenly distributed in the horizontal and vertical directions:

$$\{\begin{array}{l}{\theta }_i(x,z)={\theta }_{0i}(0\le x\le X,z_{id}\le z\le z_{iu},t=0)\\ c_i(x,z)=c_{0i}(0\le x\le X,z_{id}\le z\le z_{iu},t=0)\end{array}$$

(25)

where i is the number of the soil layer; θ_i is the soil moisture content of layer i; $c_i$ is the mass concentration of soil $N{H}_4^{+}-N$ or $N{O}_3^{-}-N$ for layer i, mg/cm³; ${\theta }_{0i}$ is the initial value of ${\theta }_i$; $c_{0i}$ is the initial value of $c_i$; $z_{iu}$ represents the vertical coordinates of the upper boundary of soil layer i, cm; and $z_{id}$ represents the vertical coordinates of the upper boundary of soil layer i, cm.

A constant flow boundary was used for the irrigation ditch; change in the width of the saturated zone over time during an irrigation event was ignored due to the long simulation period. It was assumed that the horizontal width of the saturated zone was fixed with value w, and the value taken for the field experiment was the value at 15 cm from the center of the ditch. The saturated zone was treated as a constant flow boundary that did not change with time during irrigation events and an atmospheric flux boundary at other times. The remainder of the upper boundary was the atmospheric boundary. The flow and solute concentration boundary conditions in the saturation region were:

$$\{\begin{array}{l}-K(h)\frac{\partial h}{\partial z}-K(h)=\sigma (t)(0\le x\le w,z=80,0<t<T)\\ -(\theta D_{xx}\frac{\partial c_1}{{\partial }_x}+\theta D_{xz}\frac{\partial c_1}{{\partial }_x})+q_x{c}_1=q_x{c}_a(0\le x\le w,z=80,0<t<T)\\ -(\theta D_{zz}\frac{\partial c_1}{{\partial }_z}+\theta D_{xz}\frac{\partial c_1}{{\partial }_x})+q_z{c}_1=q_x{c}_a(0\le x\le w,z=80,0<t<T)\end{array}$$

(26)

where C_a is the urea nitrogen mass concentration of the fertilizer solution, mg/m³, T is the time of water flow recession in the furrow, h; σ(t) is the constant flow boundary flux at irrigation points during irrigation, 3 cm/day. The left and right sides of the model area were zero flux boundaries, and the lower part of the model was the free drainage boundary, as shown in Figure 3.

2.5. Parameter Inversion and Model Calibration

The parameters of the Van Genuchten–Mualem (VG-M) were inverted by the measured water content from the field experiment using the built-in HYDRUS-2D inversion module, and the parameters of solute transport and transformation were calibrated using the ammonium nitrogen and nitrate nitrogen concentrations. The sensitivity of the 5 parameters of the V-G model was analyzed using HYDRUS-2D. We found that residual water content θ_r had the least influence on the results [26]. Based on existing laboratory research [27], θ_r was given the fixed value 0.0324 cm³/cm³. The experimentally measured diffusion coefficients of nitrate nitrogen and ammonium nitrogen were 1.64 cm²/day and 1.52 cm²/day. Based on references [28,29,30], the solute longitudinal dispersion (D_L) of nitrogen transport was taken to be 10 cm, equal to 10% of the simulation area. Transverse dispersion (D_T) was taken to be 5% of longitudinal dispersion. After parameter inversion, the parameters for volumetric water content, nitrate nitrogen content, and ammonium nitrogen content in different soil depths for treatments W₂F₁, W₂F₂, and W₃F₃ were determined for the regreening stage to the mature stage in 2021. The results are shown in

Table 4. Parameters of the V-G model under the fertilizer (NH₄NO₃) infiltration.

			θr (cm3/cm3)	θs (cm3/cm3)	α (cm−1)	n	Ks (cm/day)	R2
Initial value	Treatment	Soil depth	0.0324	0.3785	0.0253	1.4793	33.2	0.92
				0.3815	0.0246	1.4376	25.3	0.98
				0.3927	0.0231	1.4563	29.4	0.97
				0.3721	0.0158	1.5239	36.6	0.94
				0.3865	0.0193	1.6271	25.4	0.93
Optimized value	W2F1	0–20	–	0.3785	0.0153	1.3293	36.2	0.95
		20–40		0.3815	0.0146	1.2376	26.6	0.93
		40–60		0.3927	0.0151	1.4563	30.7	0.94
		60–80		0.3721	0.0158	1.3239	35.4	0.92
		80–100		0.3865	0.0163	1.2271	24.6	0.9
	W2F2	0–20	–	0.3832	0.0143	1.3531	37.7	0.94
		20–40		0.3895	0.0134	1.2786	29.8	0.92
		40–60		0.4032	0.0139	1.4957	32.1	0.91
		60–80		0.3837	0.0147	1.3854	33.9	0.9
		80–100		0.3843	0.0139	1.1295	23.2	0.9
	W2F3	0–20	–	0.3891	0.0135	1.3835	39.7	0.92
		20–40		0.3937	0.0127	1.3145	31.5	0.93
		40–60		0.4154	0.0131	1.5054	33.8	0.93
		60–80		0.3774	0.0149	1.3067	29.4	0.89
		80–100		0.3835	0.0158	1.2174	31.8	0.91

and

Table 5. Parameters of the V-G model with fertilizer (NH₄NO₃) infiltration.

	Treatment		Soil Depth (cm)	DL (cm)	${\mathit{\mu }}_{\mathit{w},\mathit{u}\mathit{r}\mathit{e}\mathit{a}}^{\prime }$ (/day)	Kd (cm3/mg)	${\mathit{\mu }}_{\mathit{w},\mathit{N}{\mathit{H}}_4^{+}}$ (/day)	${\mathit{\mu }}_{{}_{\mathit{w},\mathit{N}{\mathit{H}}_4^{+}}}^{\prime }$ (/day)	${\mathit{\mu }}_{{}_{\mathbf{s},\mathit{N}{\mathit{H}}_4^{+}}}^{\prime }$ (/day)	${\mathit{\mu }}_{\mathit{w},\mathit{N}{\mathit{O}}_3^{-}}$ (/day)	${\mathit{\mu }}_{\mathbf{s},\mathit{N}{\mathit{O}}_3^{-}}$ (/day)	${\mathit{\gamma }}_{\mathit{w},\mathit{N}{\mathit{H}}_4^{+}}$ (mg/cm3/day)	${\mathit{\gamma }}_{\mathit{s},\mathit{N}{\mathit{H}}_4^{+}}$ (mg/cm3/day)
Initial value		–	20	10	0.56	0.0032	0.02	0.2	0.2	0.04	0.04	3 × 10−5	3 × 10−5
			40	10	0.55	0.0035	0.025	0.3	0.3	0.03	0.03	7 × 10−5	7 × 10−5
			60	10	0.54	0.0035	0.03	0.26	0.26	0.03	0.03	5 × 10−6	5 × 10−6
			80	10	0.58	0.0032	0.028	0.27	0.27	0.04	0.04	4 × 10−6	4 × 10−6
			100	10	0.57	0.0037	0.37	0.36	0.36	0.05	0.05	3 × 10−6	3 × 10−6
Value ranges		–	0–100	–	0.3–0.8	0.003–0.004	0.02–0.05	0.01–0.68	0.02–0.72	0.01–0.24	0.02–0.24	1 × 10−6–8 × 10−5	1 × 10−6–8 × 10−5
Optimized value		W2F1	0–20	–	0.47	0.0032	0.03	0.26	0.26	0.02	0.02	1 × 10−5	1 × 10−5
			20–40		0.43	0.0035	0.025	0.34	0.34	0.03	0.03	1 × 10−5	1 × 10−5
			40–60		0.49	0.0036	0.033	0.27	0.27	0.02	0.02	1 × 10−5	1 × 10−5
			60–80		0.48	0.0036	0.038	0.37	0.37	0.02	0.02	4 × 10−6	4 × 10−6
			80–100		0.47	0.0035	0.37	0.26	0.26	0.01	0.01	8 × 10−6	8 × 10−6
		W2F2	0–20	–	0.56	0.0032	0.023	0.25	0.25	0.04	0.04	7 × 10−6	7 × 10−6
			2–40		0.55	0.0035	0.027	0.33	0.33	0.05	0.05	6 × 10−6	6 × 10−6
			40–60		0.54	0.0035	0.035	0.36	0.36	0.03	0.03	2 × 10−6	2 × 10−6
			60–80		0.58	0.0031	0.038	0.26	0.26	0.01	0.01	1 × 10−6	1 × 10−6
			80–100		0.57	0.0032	0.033	0.31	0.31	0.01	0.01	2 × 10−6	2 × 10−6
		W2F3	0–20	–	0.58	0.0032	0.026	0.24	0.24	0.05	0.05	3 × 10−6	3 × 10−6
			20–40		0.60	0.0035	0.029	0.32	0.32	0.07	0.07	2 × 10−6	2 × 10−6
			40–60		0.62/	0.0033	0.031	0.3	0.3	0.04	0.04	1 × 10−6	1 × 10−6
			60–80		0.58	0.0032	0.029	0.28	0.28	0.02	0.02	1 × 10−5	1 × 10−6
			80–100		0.57	0.0037	0.034	0.34	0.34	0.03	0.03	1 × 10−6	1 × 10−6

.

3. Results

3.1. Model Verification

In 2022, model calculations were carried out for field experiment treatments W₃F₁, W₃F₂, and W₃F₃ in the field experiment in order to verify the modified soil hydraulic characteristic parameters (Table 4) and solute transport and transformation parameters (Table 5). Figure 4 and Figure 5 show for comparison the measured and predicted values of soil moisture content, ammonium nitrogen, and nitrate nitrogen in the vertical and horizontal directions in different periods from the regreening stage to the maturity stage of winter wheat. It can be seen that the modified soil hydraulic parameters and solute transport and transformation parameters were highly accurate. The specific error values are shown in

Table 6. Error analysis of the measured and predicted values of soil volumetric water content, ammonium nitrogen, and nitrate nitrogen.

Direction	Treatment	Classification	MAE	RMSE	R2
Perpendicular	W3F1	Moisture content	0.007	0.007	0.811
		Ammonium nitrogen	0.003	0.003	0.7084
		Nitrate nitrogen	0.011	0.012	0.7577
	W3F2	Moisture content	0.01	0.009	0.8147
		Ammonium nitrogen	0.007	0.009	0.7245
		Nitrate nitrogen	0.051	0.054	0.744
	W3F3	Moisture content	0.006	0.005	0.8377
		Ammonium nitrogen	0.008	0.023	0.6818
		Nitrate nitrogen	0.052	0.064	0.7718
Level	W3F1	Moisture content	0.011	0.0106	0.832
		Ammonium nitrogen	0.007	0.025	0.6918
		Nitrate nitrogen	0.008	0.018	0.7353
	W3F2	Moisture content	0.012	0.011	0.8681
		Ammonium nitrogen	0.009	0.034	0.7125
		Nitrate nitrogen	0.035	0.052	0.7871
	W3F3	Moisture content	0.008	0.008	0.8377
		Ammonium nitrogen	0.021	0.049	0.6889
		Nitrate nitrogen	0.06	0.097	0.7844

. Model accuracy was greatest for soil volumetric water content, with R² in the horizontal direction > 0.83 and R² in the vertical direction > 0.81. The MAE for predicted ammonium nitrogen compared with the measured value was 0.007–0.021 in the horizontal direction and 0.003–0.008 in the vertical direction. The RMSE was 0.025–0.049 in the horizontal direction and 0.003–0.023 in the vertical direction. However, R² was >0.68 due to the low concentration of ammonium nitrogen; only the ammonium nitrogen content had changed in surface samples, and the number of samples was small. The MAE for nitrate nitrogen content ranged from 0.008 to 0.06 in the horizontal direction and from 0.011 to 0.052 in the vertical direction. The RMSE ranged from 0.018 to 0.097 in the horizontal direction.

3.2. Model of Soil Nitrogen Balance

In order to study the nitrogen balance of winter wheat planting soil under wide ridge and furrow irrigation, the nitrogen balance of winter wheat planting soil in 2022 was calculated based on the HYDRUS-2D case.

Table 7. HYDRUS-2D case predictions of nitrogen balance and measured yield.

Water–Fertilizer Treatment	W1F1	W1F2	W1F3	W2F1	W2F2	W2F3	W3F1	W3F2	W3F3
Ammonium nitrogen (kg/ha)
Nitrogen application rate	65.00	165.00	265.00	65.00	165.00	265.00	65.00	165.00	265.00
Urea nitrogen hydrolysis	43.03	114.62	209.63	38.62	124.72	208.35	42.74	112.09	207.59
Mineralization reaction and biological fixation	59.49	46.27	13.22	69.41	62.64	33.05	66.10	46.27	33.05
Ammonia volatilization	0.83	3.05	5.57	0.86	2.77	6.39	0.93	2.87	6.28
Nitration	89.75	134.31	188.81	93.25	163.96	217.10	100.78	136.78	213.97
Root absorption amount	8.91	17.70	15.09	10.84	13.65	17.59	6.78	16.22	14.01
Soil accumulation	3.03	5.82	13.38	3.07	6.99	0.33	0.34	2.49	6.38
Nitrate nitrogen (kg/ha)
Denitrification reaction	6.33	15.61	63.20	7.69	20.40	75.14	7.07	26.26	81.74
Root absorption amount	81.59	118.58	107.67	83.93	141.88	136.22	92.59	107.02	127.07
Soil accumulation	1.83	0.13	17.94	1.64	1.67	5.74	1.12	3.50	5.16
Total nitrogen uptake	90.50	136.28	122.76	94.76	155.53	153.80	99.37	123.25	141.08
Total nitrogen (g/ha)	56.2	101.24	78.62	66.93	145.09	128.59	65.44	116.8	126.31
Yield (kg/ha)	5860.67	6070.33	5953.00	6121.33	6888.67	6431.00	5876.67	6361.33	6590.00

shows accumulated nitrogen balances predicted by the HYDRUS-2D case for winter wheat after the overwintering period. Ammonium nitrogen produced by mineralization reactions and biological immobilization decreased as the field nitrogen concentration increased. Ammonia volatilization ranged from 0.83 to 6.39 kg/ha and increased as urea application increased. An increase in nitrogen application did not significantly increase crop absorption and utilization of nitrogen. In the medium water–medium fertilizer treatment W₂F₂, the maximum total nitrogen absorption by crops was 155.53 kg/ha. The total quantity of ammonium nitrogen absorbed by winter wheat roots in each treatment was only 7.6–15.1% of the total quantity of nitrate nitrogen absorbed. When the nitrogen application rate and irrigation quantity increased, the nitrification of ammonium nitrogen significantly increased, and the nitrate nitrogen content significantly increased to 89.75–217.1 kg/ha. The rate of denitrification of nitrate nitrogen increased, and the generated N₂ and N₂O were diffused into the air as gases. The denitrification quantity for each treatment accounted for 7.01–38.2% of the nitrification quantity.

Analysis of the nitrogen uptake of winter wheat from HYDRUS simulations with the measured values of total nitrogen was conducted. The correlation coefficient R² was 0.88, the RMSE value was 10.58 kg/hm², and the MAE value was 5.9 kg/hm², indicating that the model simulation was effective. The results of the nitrogen use efficiency calculation using the total nitrogen uptake of winter wheat (Table 7) and the measured values of winter wheat yield are shown in Figure 6. The UE of the W₂F₂ treatment was relatively high, the PFP of the W₃F₁ treatment was relatively high, and the nitrogen use efficiency of the W₁F₃ treatment was the lowest overall.

4. Discussion

4.1. Inversion of Water Transport Parameters and Physicochemical Solute Parameters

Based on the experimental data of 2021, the numerical simulation of water and nitrogen transport in winter wheat in 2022 was constructed using HYDRUS-2D. The coefficients of determination for model verification of soil moisture content, nitrate nitrogen, and ammonium nitrogen were, respectively, >0.81, >0.73, and >0.68. Previous studies have found that the error between predicted and measured soil water content was <10% [31], and the error between predicted and measured nitrogen content was <25% [32,33]. This is because environmental conditions have a great influence on nitrate nitrogen and ammonium nitrogen content. Moisture content, temperature, and soil oxygen content change soil nitrogen distribution in different ways. In the 0–60 cm soil depth, the soil water movement parameters θ_s, n, and K showed an increasing trend as the concentration of fertilizer in solution increased, but a showed a decreasing trend.

In the 60–100 cm soil depth, soil water movement parameters did not change significantly; this result is consistent with existing research [34]. The principal reason was that the irrigation amount of 30 mm during irrigation and fertilization was inadequate to transport urea to deeper soil, and urea nitrogen was rapidly converted into ammonium nitrogen. Ammonium nitrogen is strongly adsorbent [25] and adsorbs with anions on the surfaces of soil colloids. Soil colloids gradually agglomerate to form soil aggregates because of the attraction between positive and negative charges. Aggregate formation changes soil surface structure, increases soil porosity, and changes soil water conductivity. However, water does not easily transport ammonium nitrogen because of the strong adsorption to soil particles, and so ammonium nitrogen affects pore structure in the 0–20 cm soil layer. However, nitrate nitrogen produced by the nitrification of ammonium nitrogen is readily transported by water, and so many pores become closed as water infiltrates. This explanation shows that fertilizer–irrigation affects the physical and chemical properties of the soil only in the 0–60 cm layer.

4.2. Nitrogen Balance

Variations in fertilizer application will cause differences in root growth, alter soil pore structure, and change soil water storage capacity [35]. Different water and fertilizer treatments, therefore, have different effects on the crop and will affect the total nitrogen accumulation of wheat. Certain levels of water and fertilizer will promote wheat growth, but levels above some thresholds will adversely affect wheat growth [22,36]. The total nitrogen uptake for the low water–high fertilizer treatment (W₁F₃) decreased by 26.69% and for the high water–high fertilizer treatment (W₃F₃) decreased by 10.24% when compared with the medium water–high fertilizer treatment W₂F₃; obvious nitrogen stress was observed. Excessive nitrogen application led to poor root growth and did not supply the required nutrients and water to the aboveground part of the plants. Nitrogen uptake and accumulation by wheat in high water treatments was greater than in wheat in low fertilizer treatments because frequent irrigation resulted in water infiltrating easily transportable nitrate nitrogen into deep soil [37], which reduced soil nitrogen content in the wheat root zone.

In the low and medium fertilizer treatments, overirrigation or underirrigation does not promote increased nitrogen accumulation in wheat. Underirrigation causes drought effects, which constrain crop root growth and cause crop roots to wither easily [38]. Overirrigation greatly decreases soil air and reduces the activity of aerobic soil microorganisms, and resultant root damage reduces root growth and absorption [39]. We found that ammonium nitrogen absorption by winter wheat roots accounted for 8–13% of the total root nitrogen absorption. In a paddy field experiment [40], ammonium nitrogen absorption accounted for 60% of total root nitrogen absorption due to the high soil water content in the paddy field. In a plastic film mulch with a hole irrigation experiment [41], ammonium nitrogen absorption accounted for >47% of total root nitrogen absorption. The plastic mulch was in contact with the soil surface and inhibited oxygen in the air from entering the soil. In turn, less oxygen in the soil inhibits the nitrification of ammonium nitrogen. Wide ridge furrow irrigation, as used in our experiment, is a form of furrow irrigation in which the ridge soil layer is loose, and atmospheric oxygen can, therefore, easily enter the soil. In low water treatments, an appropriate nitrogen application quantity promotes wheat root growth, increases root area available for absorption, fosters root activity, reduces damage to cell membranes, and alleviates the adverse effects of water deficit. We found that excessive nitrogen application slightly affected drought resistance, and it has been found to have negative effects [42,43].

5. Conclusions

(1) The coefficients of determination for model verification of soil moisture content, ammonium nitrogen, and nitrate nitrogen were, respectively, >0.81, >0.68, and >0.73. The calibrated HYDRUS-2D model can be used to accurately simulate soil water and nitrogen transport. Parameter accuracy met the study requirements, and the model calibration and verification results were acceptable.

(2) The rate-determined HYDRUS case can better simulate the nitrogen balance of winter wheat during the whole reproductive period. Analysis of nitrogen balance showed that denitrification was the main pathway of nitrogen loss in winter wheat; gaseous loss for each treatment accounted for 7.01–38.2% of its nitrogen form. The total amount of ammonium nitrogen absorbed by winter wheat roots for each treatment was only 7.6–15.1% of the total amount of nitrate nitrogen absorbed. The maximum nitrogen uptake was 155.53 kg/ha with a yield of 6888.67 kg/ha in the medium water–fertilizer treatment W₂F₂. Both water and N application and the interaction between them had highly significant effects on AE, PE, UE, and PFP in winter wheat. The UE of the W₂F₂ treatment was relatively high, the PFP of the W₃F₁ treatment was relatively high, and the nitrogen use efficiency of the W₁F₃ treatment was the lowest overall.