A Non-Uniform Broadcast Fertilization Method and Its Performance Analysis under Basin Irrigation

The broadcast fertilization method is widely used under basin irrigation in China. A reasonable broadcast fertilization method can effectively improve application performance of fertilization and reduce pollution from non-point agricultural sources. In this study, firstly, a non-uniform broadcast fertilization method and a non-uniform application coefficient were proposed. The value of non-uniform application coefficient is defined in this paper. It represents the ratio of the difference between the maximum and the average fertilization amount of fertilizer applied on the basin surface to the average fertilization amount of fertilizer applied on the basin surface. Secondly, field experiments were conducted to study the movement characteristics of fertilizer under non-uniform broadcast fertilization for basin irrigation. Field experiment results showed that under the condition of basin irrigation, the non-uniform broadcast fertilization method could weaken the non-uniform distribution of fertilizer due to erosion and transport capacity of solid fertilizer by irrigation water flow, which could significantly improve the uniformity of soil solute content. Thirdly, the solute transport model for broadcast fertilization was corroborated by the field experiment results. The variation rule of fertilization performance with non-uniform application coefficient under different basin length and inflow rate was achieved by simulation. The simulation results showed that fertilization uniformity and fertilization storage efficiency increased first and then decreased with the increase of non-uniform application coefficient. In order to be practically applicable, suitable irrigation programs of non-uniform application coefficient under different basin length and inflow rate conditions were proposed by numerical simulation.


Introduction
Irrigation and fertilization are two important factors in agricultural production management. Suitable irrigation and fertilization methods can improve the application efficiency of water and fertilizer. At present, surface irrigation is currently the predominant irrigation method worldwide [1,2]. In China, it is currently practiced on about 90% of irrigated land, and application efficiency ranging from 39% to 91% (average, 60%) [3]. Under surface irrigation, broadcast fertilization is the most widely used fertilization method. Generally, practices such as large-scale application of nitrogen fertilizer and unreasonable irrigation and fertilization management result in excessive irrigation and fertilization, and other issues that does not meet the requirements of crop development [4][5][6][7]. The management mode of large water and large fertilizer not only restricts good growth in grain yield, water-use efficiency (WUE), and fertilizer-use efficiency (NUE), but also causes a series of environmental problems, such as process, which induced "backward warping" phenomenon and resulted in the non-uniform distribution of fertilizer in the soil. Therefore, we envisage a non-uniform broadcast fertilization method. Before irrigation, from the basin head to the basin tail gradually reduced fertilizer was applied on the basin surface. After irrigation, the fertilizer from the head to the tail of the basin will be more uniform, and this method is relatively simple in practical application.
As shown in Figure 1, the basin was divided into several sections along its length, and fertilizer was non-uniformly applied in a broadcast manner to all sections. When the section number is small, the amount of fertilizer shows an obvious ladder distribution. As the section number increases, the distribution of fertilizer along the basin length tends to be linear distribution [34].
Water 2020, 12, x 3 of 19 uniform distribution of fertilizer in the soil. Therefore, we envisage a non-uniform broadcast fertilization method. Before irrigation, from the basin head to the basin tail gradually reduced fertilizer was applied on the basin surface. After irrigation, the fertilizer from the head to the tail of the basin will be more uniform, and this method is relatively simple in practical application. As shown in Figure 1, the basin was divided into several sections along its length, and fertilizer was non-uniformly applied in a broadcast manner to all sections. When the section number is small, the amount of fertilizer shows an obvious ladder distribution. As the section number increases, the distribution of fertilizer along the basin length tends to be linear distribution [34]. Figure 2A-C shows the process of gradual change from non-uniform to uniform broadcast fertilization. In order to ensure a non-uniform application coefficient values is 0 when uniform broadcast fertilization is adopted. The non-uniform application coefficient USN is defined as following:  (1) where Nmax is the maximum amount of fertilizer application on the basin surface; Nave is the average amount of fertilizer application on the basin surface.   (1), it can be seen that the non-uniform application coefficients values USN corresponding to Figure 2A-C are 1.5, 1 and 0 respectively. It can be seen that USN = 0 represents the uniform application of fertilizer, which is the currently used common practice. The non-uniformity increases as the USN values increase. In theory, USN is no less than zero and tends to increase toward infinity, i.e., 0 ≤ USN < ∞. In practical applications, however, 0 ≤ USN < finite values. Figure 2A-C shows the process of gradual change from non-uniform to uniform broadcast fertilization. In order to ensure a non-uniform application coefficient values is 0 when uniform broadcast fertilization is adopted. The non-uniform application coefficient U SN is defined as following: (1) where N max is the maximum amount of fertilizer application on the basin surface; N ave is the average amount of fertilizer application on the basin surface.
Water 2020, 12, x 3 of 19 uniform distribution of fertilizer in the soil. Therefore, we envisage a non-uniform broadcast fertilization method. Before irrigation, from the basin head to the basin tail gradually reduced fertilizer was applied on the basin surface. After irrigation, the fertilizer from the head to the tail of the basin will be more uniform, and this method is relatively simple in practical application. As shown in Figure 1, the basin was divided into several sections along its length, and fertilizer was non-uniformly applied in a broadcast manner to all sections. When the section number is small, the amount of fertilizer shows an obvious ladder distribution. As the section number increases, the distribution of fertilizer along the basin length tends to be linear distribution [34]. Figure 2A-C shows the process of gradual change from non-uniform to uniform broadcast fertilization. In order to ensure a non-uniform application coefficient values is 0 when uniform broadcast fertilization is adopted. The non-uniform application coefficient USN is defined as following: where Nmax is the maximum amount of fertilizer application on the basin surface; Nave is the average amount of fertilizer application on the basin surface. Figure 2. Different non-uniform broadcast fertilization modes, Nmax is the applied fertilizer maximum quantity at upstream end and Nave is the applied fertilizer average quantity along field plot: (A) Nmax = 2.5 Nave; (B) Nmax = 2.0 Nave; (C) Nmax = 1.0 Nave. The total amount of fertilizer applied was the same in all three cases. Figure 2A-C are the non-uniform broadcast fertilization methods selected in this paper. Through the calculation of Equation (1), it can be seen that the non-uniform application coefficients values USN corresponding to Figure 2A-C are 1.5, 1 and 0 respectively. It can be seen that USN = 0 represents the uniform application of fertilizer, which is the currently used common practice. The non-uniformity increases as the USN values increase. In theory, USN is no less than zero and tends to increase toward infinity, i.e., 0 ≤ USN < ∞. In practical applications, however, 0 ≤ USN < finite values. . Different non-uniform broadcast fertilization modes, N max is the applied fertilizer maximum quantity at upstream end and Nave is the applied fertilizer average quantity along field plot: The total amount of fertilizer applied was the same in all three cases. Figure 2A-C are the non-uniform broadcast fertilization methods selected in this paper. Through the calculation of Equation (1), it can be seen that the non-uniform application coefficients values U SN corresponding to Figure 2A-C are 1.5, 1 and 0 respectively. It can be seen that U SN = 0 represents the uniform application of fertilizer, which is the currently used common practice. The non-uniformity increases as the U SN values increase. In theory, U SN is no less than zero and tends to increase toward infinity, i.e., 0 ≤ U SN < ∞. In practical applications, however, 0 ≤ U SN < finite values.

Experimental Area Overview
Basin irrigation experiments using different non-uniform broadcast fertilization methods were performed in Daxing Experimental Station, Beijing, China in 2016. The station is in the Beijing southern suburbs. The station experiences a semi-arid temperate continental monsoon climate, and an annual precipitation of 540 mm.
Corn is continually cropped in the summer (mid-June to the end of September). Winter wheat is cropped in the remaining months (early October to mid-June).
The experimental crop used was JiMai 22 Chinese wheat. The wheat was sowed on 18 October, and will harvest on 14 June next year. The soil in the experimental area had mainly a sandy loam texture with some clay in the soil layer from 20 cm to 40 cm, as shown in Table 1. The irrigation method used was basin irrigation. The water source during basin irrigation was confined groundwater. Taking the impact of microtopography on irrigation into account, two days before sowing, the laser-controlled land level was implemented, and the average slope was 0.3% after leveling.

Field Experimental Design
As shown in Table 2, the non-uniform application coefficients and inflow rate were selected as design factors in basin irrigation with fertilization. The non-uniform application coefficients were 0, 1 and 1.5. The inflow rate were 2 and 6 L/(s·m), respectively. For a complete experimental design, six types of experimental treatments were included, namely, U SN = 0 with small discharge (I (q2-s0)), U SN = 1 with small discharge (II (q2-s1)), U SN = 1.5 with small discharge (III (q2-s1.5)), U SN = 0 with large discharge (IV (q6-s0)), U SN = 1 with large discharge (V (q6-s1)), U SN = 1.5 with large discharge (VI (q6-s1.5)). In order to easy the analysis of the fertilizer distribution in surface water and soil under six types of experimental treatments, easily soluble ammonium sulfate was used as the nitrogen fertilizer for this experiment. The selection of ammonium sulfate fertilizer in this paper is mainly based on the following considerations 1. Ammonium sulfate is a soluble fertilizer. The distribution of solute in surface water flow can be measured in the experiment, which is convenient for the subsequent model simulation to provide data support. 2. The results of the experiment in 2015 showed that t there was a high linear correlation (correlation coefficient: 0.93) between increments of SO 2− 4 concentration and the increment of NO − 3 -N and NH + 4 -N concentration in soil after irrigation, so it is feasible to use the uniformity and efficiency of SO 2− 4 in soil to characterize the uniformity and efficiency of fertilization. This characterize approach could reduce the costs of testing. To avoid errors caused by instability of nitrogen in the fertilizer, SO 2− 4 was used to measure fertilization performance. Each experimental treatment was replicated three times. Therefore, a total of 18 basins were prepared. The layout is shown in Figure 3. Each basin had a length of 100 m, a width of 1.7 m, and a slope of 3/10,000. An empty area is 0.8 m wide between every basin was set up to facilitate data observation and prevent interaction between basins.   6 1 VI (q6-s1.5) 6 1.5 Basin irrigation experiments with fertilization were carried out on 6 April in 2016, during the winter wheat returning green stage. Six treatments were simultaneously selected for the experiment.
For each irrigation, the time when the flow advanced to the basin tail was used as the actual irrigation time to ensure that irrigation water covers the whole basin. The inflow rate was monitored in real-time using an Ultrasonic Flowmeter (1010 P/WP, America CONTROLOTRON) installed on the basin irrigation pipeline. When inflow rate were 2 and 6 L/(s⋅m), the average irrigation amount for each basin is approximately 103 mm. The amount of conventional nitrogen applied by the local farmers in Daxing was approximately 200 kg/hm 2 in spring irrigation [35]. Therefore, the amount of applied nitrogen in this spring irrigation experiment was 200 kg/hm 2 . The nitrogen concentration of the ammonium sulfate was 21%, so the application amount of ammonium sulfate is 952.4 kg/hm 2 .
In this experiment, the non-uniform application coefficients were 0, 1 and 1.5. The basin was divided into ten sections to spread the fertilizer on the basin surface according to the set non-uniform application coefficients. The length of each part was 10 m. Corresponding to non-uniform application coefficients 0, 1 and 1.5. The fertilization amount in each part was calculated, which was shown in Table 3. Basin irrigation experiments with fertilization were carried out on 6 April in 2016, during the winter wheat returning green stage. Six treatments were simultaneously selected for the experiment.
For each irrigation, the time when the flow advanced to the basin tail was used as the actual irrigation time to ensure that irrigation water covers the whole basin. The inflow rate was monitored in real-time using an Ultrasonic Flowmeter (1010 P/WP, America CONTROLOTRON) installed on the basin irrigation pipeline. When inflow rate were 2 and 6 L/(s·m), the average irrigation amount for each basin is approximately 103 mm. The amount of conventional nitrogen applied by the local farmers in Daxing was approximately 200 kg/hm 2 in spring irrigation [35]. Therefore, the amount of applied nitrogen in this spring irrigation experiment was 200 kg/hm 2 . The nitrogen concentration of the ammonium sulfate was 21%, so the application amount of ammonium sulfate is 952.4 kg/hm 2 .
In this experiment, the non-uniform application coefficients were 0, 1 and 1.5. The basin was divided into ten sections to spread the fertilizer on the basin surface according to the set non-uniform application coefficients. The length of each part was 10 m. Corresponding to non-uniform application coefficients 0, 1 and 1.5. The fertilization amount in each part was calculated, which was shown in Table 3.

Experimental Observation and Test Methods
Five stations were set up along the basin length. The observation points from upstream were 10, 30, 50, 70, and 90 m (Figure 4). At every observation point, soil samples were obtained with an auger in 20 cm depth increments down to 80 cm. The soil samples were collected 2 days before and after irrigation for all experimental treatments (18 basins), the total number of soil samples was 720, and each sample was approximately 100 g; sample were placed into the valve bag to measure SO 2− 4 concentration.

Experimental Observation and Test Methods
Five stations were set up along the basin length. The observation points from upstream were 10, 30, 50, 70, and 90 m (Figure 4). At every observation point, soil samples were obtained with an auger in 20 cm depth increments down to 80 cm. The soil samples were collected 2 days before and after irrigation for all experimental treatments (18 basins), the total number of soil samples was 720, and each sample was approximately 100 g; sample were placed into the valve bag to measure SO

Model Introduction
Significant vertical solute transport in the application of broadcast fertilization. The fullhydrodynamic broadcast fertilization model based on the assumption of uniform vertical flow velocity is obviously difficult to provide a physical mechanism for the migration of nitrogen fertilizer [36]. Zhang based on the full hydrodynamic basin irrigation model and continuity equation of incompressible fluid mechanics [37], combined with the convection-diffusion equation which can describe the concentration field along the basin length and vertical non-uniform distribution, constructed the solute transport model of surface water flow for basin irrigation.
The expression is as follows: where c is the non-uniform solute concentration in the surface water flow along the basin length and in any vertical section, mg/L; ux and uy are non-uniformly distributed velocity fields along basin During the basin irrigation experiment, surface flow samples were obtained at each station. 200 mL water for each sample was collected in plastic vials and sealed for analysis. The first sampling was performed when the water flow first reached each station. The second sampling was performed when the water flow reached the last observed point. The third and fourth samplings were performed when the water flow reached the basin tail and reached the basin tail 15 min later when the water flow diffusion in all directions had almost stopped, respectively. The number of water samples was 342, and concentrations of SO 2− 4 was measured. The measurement of SO 2− 4 concentration in the soil and water samples was based on SO 2− 4 concentration in the soil using series standards in NY/T 1121 "soil detection".

Model Introduction
Significant vertical solute transport in the application of broadcast fertilization. The full-hydrodynamic broadcast fertilization model based on the assumption of uniform vertical flow velocity is obviously difficult to provide a physical mechanism for the migration of nitrogen fertilizer [36]. Zhang based on the full hydrodynamic basin irrigation model and continuity equation of incompressible fluid mechanics [37], combined with the convection-diffusion equation which can describe the concentration field along the basin length and vertical non-uniform distribution, constructed the solute transport model of surface water flow for basin irrigation.
The expression is as follows: where c is the non-uniform solute concentration in the surface water flow along the basin length and in any vertical section, mg/L; u x and u y are non-uniformly distributed velocity fields along basin length and vertical direction respectively, m/s; d xx , d zz , d xz and d zx are the non-uniform tensor solute diffusion coefficients of surface solute along the length and vertical direction, respectively, m 2 /s.
where u τ is the frictional velocity along the basin surface, m/s; z + is the dimensionless distance vertically upward with the basin surface as the reference point, and z + =|u τ | z/υ, κ is a Karman constant with a value of 0.41; υ is the viscosity coefficient of surface water movement with a value of 1.31 × 10 −6 m 2 /s; C const is a constant to be determined. Using surface water infiltration flux i c as the boundary condition of the surface velocity field, in the dynamic free surface boundary space from the surface of the water depth h, based on the constructed flow velocity u x , the incompressible hydrodynamic continuity Equations (2) and (3) is used to solve the flow velocity u z in the z direction.

Boundary Conditions
(1) Surface boundary conditions of basin: Based on the initial condition Equation (5), the dissolution process of surface fertilizers in the basin is described by the first-order dynamic equation [38].
where C s is the solute concentration at the interface, C eq is the solute concentration in equilibrium with the solid and k d is the local reaction rate constant, 1/s; T s is the time when the fertilizer applied at any point on the surface of the basin are dissolved and completely transported to the surface water flow and infiltrated into the soil, s. Within the unit area of the basin surface, the total amount of solutes transported upward to surface water and downward to soil was marked with C up and C down respectively.
According to the physical meaning of Equations (6) and (7), Ts should satisfy the following formula: (2) The boundary condition of free surface is zero concentration gradient, which can be expressed as follows: (3) The boundary of the impervious check ridge is also the condition that the concentration gradient is zero.

Simulation Conditions and Boundary Selection
During the irrigation time, the inflow boundary condition is a given flow rate of a single width and no solute flux. When the irrigation is stopped, the boundary condition of the basin head is that the inflow and solute flux are equal to zero at the same time. In the whole irrigation process, the zero flux of water flow and solute is taken as the boundary condition of the basin tail. The upper boundary is a free water surface, and the corresponding boundary condition is zero flux of solute. The infiltration flux of surface water flow and solute is used as the lower boundary condition.
According to the local multi-point test results of double-loop permeameter [39], Kostiakov empirical formula was used to characterize the infiltration performance of soil.
The Schmidt coefficient of surface turbulent movement S t = 1.59 [40]. According to the solubility of ammonium sulfate and other physical properties [41]. And the temperature of surface soil and groundwater, the local reaction kinetics constants k d and the correction coefficient α c were calculated. The field microtopography was set to S d = 2 cm.

Numerical Simulation Experimental Design
Numerical simulation was carried out to understand the response law of fertilization performance to the non-uniform application coefficient for non-uniform broadcast fertilization method under different basin irrigation conditions. The basin length, inflow rate, and non-uniform application coefficient were set at 3 (60, 100 and 150 m), 3 (2, 4 and 6 L/(m·s)) and 16 (0 to 1.5, interval 0.1) types for the numerical simulation, respectively.

Variation Index
Variability analysis was performed using standard deviation (STD) and coefficient of variation (C v ), STD and C v are calculated as, where n is the total number of observation points; x i is the solute concentration of the i-th observation point; x i is the average value of solute concentration at all observation points.

Fertilization Performance Indexes
The soluble fertilizer had four performance indices, namely, nitrogen distribution uniformity, nitrogen efficiency, nitrogen adequacy, and nitrogen loss [42]. In this study, the more stable sulfate was used as the representative, and the fertilization uniformity and efficiency were used to measure the performance of basin irrigation with ammonium sulfate applications quantitatively.
The fertilization uniformity UCC was used to measure the difference between the actual fertilizer amount at every observation point and the average fertilizer amount from the entire basin, where 14) where N ave is the average amount of applied fertilizer in basin, g/m; N i is the amount of applied fertilizer in basin section [x i−1 x i ], g/m; L is the basin length, m; and M is the sampling number in basin. The fertilization storage efficiency index is used to measure the proportion of crop absorption and utilization of the actual amount of fertilizer applied to the crop in the effective rooting depth. Because the root system of plants is the primary site of nutrient uptake [43], estimates of effective rooting depth are necessary for the efficient management of surface fertigation systems. Based on the change and distribution of root mass density of winter wheat crops with the depth of soil [44], the effective root depth of the crops in the returning green stage was 0-40 cm. where where N T is the incremental fertilizer in the soil, mg; and N rz is the incremental fertilizer in the effective rooting depth, mg.

Numerical Simulation Metrics
The mean absolute relative error (ARE) [45] is used to evaluate the simulation effect of solute transport in surface water flow between the measured solute concentration and the simulated value. ARE is calculated as,

The Variability of Fertilizer Concentration in the Surface Water Flow
The supply of water and fertilizer was combined in irrigation, i.e., the fertilizer was broadcasted onto the basin surface in advance, the water flowed onto the field, and fertilizer was dissolved and infiltrated into the soil as the flow advances. Under the broadcast fertilization method, the surface water flow carried fertilizer and closely related to the distribution of fertilizer in the soil. The temporal and spatial distribution of fertilizer in the surface water flow would affect the distribution of fertilizer in the root zone of the soil. Therefore, distribution migration characteristics of ions in the surface water flow could better reflect the influence of the diffusion of water under basin irrigation on the distribution of fertilizer. Figure 5 shows      Under the non-uniform broadcast fertilization (Figure 5b,c,e,f), the SO 2− 4 concentration decreased gradually along the basin length at the first sampling time. As the result of interaction between the non-uniform broadcast fertilization and the increased solute concentration at the flow front, the effect of the non-uniform broadcast fertilization was the opposite of the increased solute concentration at the flow front. Additionally, the effect of the non-uniform application coefficient on SO 2− 4 concentration was higher than that of the flow advance under the experimental condition, which resulted in that the SO 2− 4 concentration decreased along the basin length when the flow reached the observation point under the condition of the non-uniform broadcast fertilization, indicated that the non-uniform application coefficient had a significant effect on SO 2− 4 concentration at the first sampling time for each observation point.
For all experimental treatments, the general trend of change in SO 2− 4 concentration in the surface water flow over time was that the value decreased sharply and then stabilized after the water advanced to the observation points. The corresponding statistical characteristics of the spatial distribution of SO 2− 4 concentration along the basin length are given in Table 4. At the first sampling time, the difference in SO 2− 4 concentration in the surface water between observation points was not obvious under the different experimental treatments; the coefficient of variation C v was between 0.12 and 0.42. At the second, third and fourth sampling time, when the inflow rate was the same, the C v decreased with the increases in the non-uniform application coefficient, indicated that the SO 2− 4 distribution in the surface water flow was non-uniform under the condition of uniform broadcast fertilization; moreover, the uniformity of the SO 2− 4 distribution in the surface water flow increased with the increase of the non-uniform application coefficient.  Figure 6 shows the spatial distribution of the average increment of SO 2− 4 concentration in the 0~80 cm soil layers under different fertilization treatments 2 days after irrigation, and SO 2− 4 concentration was the average value from the three repetitions. Under different fertilization treatments, the increment of SO 2− 4 concentration in the soil decreased with the increase of soil depth, and this process was affected by the soil moisture in the effective root layer of the crop. The increment of SO 2− 4 concentration in the soil was larger in the 0~40 cm soil layer, and the increments were both smaller and had little differences in the 40~60 cm and 60~80 cm soil layers. At treatment I and treatment IV, the increment of SO 2− 4 concentration in the soil at the basin tail (80~100 m) was higher than that at the beginning of the basin. At treatment III and treatment VI, the increment of SO 2− 4 concentration in the soil from 0~60 m of the basin beginning was higher than that at the basin tail. At treatment II and treatment V, the difference in the increment of SO 2− 4 concentration in the effective root layer (0~40 cm) of crops was small along the basin length for each observation point and reached a relatively uniform state, which was related to the SO 2− 4 distribution in the surface water flow. The uniform distribution of the SO 2− 4 concentration in the surface water flow was good along the basin length, and the uniformity of the average increment of SO 2− 4 concentration in the soil was high. The results in Table 5 also show that in the same soil layer, especially in the effective root depth, the variation coefficient C v values of treatment II and V are smaller than those of other treatments. The results showed that non-uniform broadcast fertilization could effectively improve the non-uniform situation of fertilizer distribution caused by "backward warping" in relation to solutes in the soil at the basin tail.   Table 6 shows the fertilization performance under different fertilization treatments for winter wheat in the returning green stage. In conclusion, non-uniform application coefficient and inflow rate had effects on fertilization uniformity and fertilization storage efficiency, especially significant for fertilization uniformity. Under the condition of uniform broadcast fertilization (under treatment I and treatment IV), the smaller inflow rate was higher than the larger inflow rate in the uniformity of SO 2− 4 distribution and its fertilization storage efficiency, and its values were increased by 5.1% and 5.2%, respectively. The results showed that under uniform application coefficient, the smaller inflow rate had higher fertilization performance.  Table 6 shows the fertilization performance under different fertilization treatments for winter wheat in the returning green stage.  In conclusion, non-uniform application coefficient and inflow rate had effects on fertilization uniformity and fertilization storage efficiency, especially significant for fertilization uniformity. Under the condition of uniform broadcast fertilization (under treatment I and treatment IV), the smaller inflow rate was higher than the larger inflow rate in the uniformity of SO 2− 4 distribution and its fertilization storage efficiency, and its values were increased by 5.1% and 5.2%, respectively. The results showed that under uniform application coefficient, the smaller inflow rate had higher fertilization performance. The results of the field evaluation of the fertilization performance showed that non-uniform broadcast fertilization could improve effectively the fertilization uniformity and fertilization storage efficiency. Under the non-uniform broadcast fertilization method, with non-uniform application coefficient increased, the SO 2− 4 fertilization uniformity and fertilization storage efficiency first increased and then declined. When the inflow rate was 2 L/(m·s), fertilization uniformity increased from 69.8% to 76%, and fertilization storage efficiency increased from 55.5% to 62.5%, increased by 6.2% and 7%, respectively. The results showed that non-uniform broadcast fertilization could improve effectively the fertilization uniformity and fertilization storage efficiency under smaller inflow rate. When the inflow rate was 6 L/(m·s), the fertilization uniformity increased from 64.7% to 85.3%, and fertilization storage efficiency increased from 50.3% to 71.4%, increased by 20.6% and 21.1%, respectively. The results showed that under larger inflow rate non-uniform broadcast fertilization could improve effectively the fertilization performance. When the non-uniform application coefficient is the same, fertilization performance of the larger flow rate is better.

The Evaluation of the Fertilization Performance
From six treatments of experimental designed, the best combination of fertilization performance was q6-s1. Its fertilization uniformity and fertilization storage efficiency were 85.3% and 79.4%, respectively. The above results showed that the reasonable combination of non-uniform application coefficient and inflow rate was beneficial to improve the fertilization performance. In practical applications, it was possible to obtain a better fertilization effect by selecting an appropriate non-uniform application coefficient in combination with the actual inflow rate.

Model Validation
Before model validation, the model parameters are determined. Firstly, the field double-loop experiment was carried out to obtain the infiltration parameters. Secondly, the model parameters were calibrated according to the experimental results of treatment I, II, IV and V. Finally, the model was validated according to the experimental results of treatment III and VI. Figure 7 shows the dynamic time change process of simulated and measured surface SO 2− 4 concentration at different observation points, and Table 7 shows the corresponding ARE values. It can be seen that the initial value of SO 2− 4 concentration in surface water is relatively high due to the thin surface water layer at the beginning of sampling. As the irrigation water flows downstream, the surface water depth increases, and the SO 2− 4 concentration in both simulated and measured surface water showed a trend of gradual decline. The ARE values under different inflow rates are between 6.94%~13.91% and 6.60%~9.74%, respectively. This showed that the model can better simulate the change process of SO 2− 4 concentration.
Water 2020, 12, x 13 of 19 The results of the field evaluation of the fertilization performance showed that non-uniform broadcast fertilization could improve effectively the fertilization uniformity and fertilization storage efficiency. Under the non-uniform broadcast fertilization method, with non-uniform application coefficient increased, the SO 2− 4 fertilization uniformity and fertilization storage efficiency first increased and then declined. When the inflow rate was 2 L/(m·s), fertilization uniformity increased from 69.8% to 76%, and fertilization storage efficiency increased from 55.5% to 62.5%, increased by 6.2% and 7%, respectively. The results showed that non-uniform broadcast fertilization could improve effectively the fertilization uniformity and fertilization storage efficiency under smaller inflow rate. When the inflow rate was 6 L/(m·s), the fertilization uniformity increased from 64.7% to 85.3%, and fertilization storage efficiency increased from 50.3% to 71.4%, increased by 20.6% and 21.1%, respectively. The results showed that under larger inflow rate non-uniform broadcast fertilization could improve effectively the fertilization performance. When the non-uniform application coefficient is the same, fertilization performance of the larger flow rate is better.
From six treatments of experimental designed, the best combination of fertilization performance was q6-s1. Its fertilization uniformity and fertilization storage efficiency were 85.3% and 79.4%, respectively. The above results showed that the reasonable combination of non-uniform application coefficient and inflow rate was beneficial to improve the fertilization performance. In practical applications, it was possible to obtain a better fertilization effect by selecting an appropriate nonuniform application coefficient in combination with the actual inflow rate.

Model Validation
Before model validation, the model parameters are determined. Firstly, the field double-loop experiment was carried out to obtain the infiltration parameters. Secondly, the model parameters were calibrated according to the experimental results of treatment I, II, IV and V. Finally, the model was validated according to the experimental results of treatment III and VI. Figure 7 shows the dynamic time change process of simulated and measured surface SO 2− 4 concentration at different observation points, and Table 7 shows the corresponding ARE values. It can be seen that the initial value of SO 2− 4 concentration in surface water is relatively high due to the thin surface water layer at the beginning of sampling. As the irrigation water flows downstream, the surface water depth increases, and the SO 2− 4 concentration in both simulated and measured surface water showed a trend of gradual decline. The ARE values under different inflow rates are between 6.94%~13.91% and 6.60%~9.74%, respectively. This showed that the model can better simulate the change process of SO     Figure 8 shows the variation trend of fertilization uniformity and fertilization storage efficiency under different basin lengths, inflow rate and non-uniform application coefficient. In general, fertilization uniformity and fertilization storage efficiency have similar laws, that is, the combination with higher fertilization uniformity has higher fertilization storage efficiency, and vice versa. Therefore, the non-uniform broadcast fertilization method has the dual effect of improving fertilization uniformity and fertilization storage efficiency. With the increase of non-uniform application coefficient, the fertilization uniformity and storage efficiency increased first and then decreased. The simulation results were consistent with the experimental results. This phenomenon can be explained as follows: when the non-uniform application coefficient is 0, the larger fertilizer concentration at the basin tail will reduce the uniformity and storage efficiency of fertilization; when the non-uniform application coefficient is 1.5, the amount of fertilizer applied at the basin head will increase, and the driving effect of irrigation water is limited; when the irrigation is over, the fertilizer concentration at the basin head will reduce the uniformity and storage efficiency of fertilization.   Figure 8 shows the variation trend of fertilization uniformity and fertilization storage efficiency under different basin lengths, inflow rate and non-uniform application coefficient. In general, fertilization uniformity and fertilization storage efficiency have similar laws, that is, the combination with higher fertilization uniformity has higher fertilization storage efficiency, and vice versa. Therefore, the non-uniform broadcast fertilization method has the dual effect of improving fertilization uniformity and fertilization storage efficiency. With the increase of non-uniform application coefficient, the fertilization uniformity and storage efficiency increased first and then decreased. The simulation results were consistent with the experimental results. This phenomenon can be explained as follows: when the non-uniform application coefficient is 0, the larger fertilizer concentration at the basin tail will reduce the uniformity and storage efficiency of fertilization; when the non-uniform application coefficient is 1.5, the amount of fertilizer applied at the basin head will increase, and the driving effect of irrigation water is limited; when the irrigation is over, the fertilizer concentration at the basin head will reduce the uniformity and storage efficiency of fertilization. Therefore, choosing appropriate non-uniform application coefficient can effectively improve the performance of fertilization. Therefore, choosing appropriate non-uniform application coefficient can effectively improve the performance of fertilization. For the same basin length, when the non-uniform application coefficient is 0, the fertilization performance decreases with the increase of the inflow rate. The simulation results were consistent with the experimental result. With the increase of non-uniform application coefficient, the highest fertilization performance can be obtained, and the corresponding optimal non-uniform application coefficient increases with the increase of inflow rate. Under the optimal non-uniform application coefficient, the highest fertilization performance increases with the increase of inflow rate, which For the same basin length, when the non-uniform application coefficient is 0, the fertilization performance decreases with the increase of the inflow rate. The simulation results were consistent with the experimental result. With the increase of non-uniform application coefficient, the highest fertilization performance can be obtained, and the corresponding optimal non-uniform application coefficient increases with the increase of inflow rate. Under the optimal non-uniform application coefficient, the highest fertilization performance increases with the increase of inflow rate, which indicates that for non-uniform broadcast fertilization method the higher inflow rate had a greater potential to improve fertilization performance.
For different basin length, when the non-uniform application coefficient is 0, the fertilization performance tends to decrease with the increase of the basin length, which indicates that with the increase of the basin length, the effect of water flow on the accumulation of fertilizer in the basin tail is more significant. With the increase of the non-uniform application coefficient, the highest fertilization performance can be obtained, and the corresponding optimal non-uniform application coefficient increases with the increase of basin length, which indicates that a longer basin length requires a larger non-uniform application coefficient to achieve better fertilization performance.
According to the highest fertilization performance in Figure 8, Table 8 gives the non-uniform application coefficient under different conditions, which are convenient for practical production. When the theoretical maximum fertilization performance is reached, the fertilization uniformity of different schemes is above 82.5% and the fertilization storage efficiency is above 70%. Therefore, the non-uniform broadcast fertilization method has great application value.

Discussion
The concept of non-uniform broadcast fertilization method was proposed in this paper, and the solute transport model for broadcast fertilization was verified and validated with field experiments, and used it for numerical simulation. The research is still in the preliminary stage of exploration with the following problems to be resolved: The Kostiakov empirical infiltration formula is used to describe the infiltration process of the solute transport model. The Kostiakov infiltration formula considers the interaction coupling effect between soil water and surface water, which can precisely describe the infiltration process of surface water in irrigation process but hard to simulate the continuous movement process of soil water after irrigation. Therefore, in order to describe the process of surface irrigation water and solute transport more reasonably, it is necessary to extend the content of solute transport model.
In this paper, the experiment and numerical simulation of soluble nitrogen fertilizer-ammonium sulfate were carried out with sufficiently good results obtained. However, whether other soluble and insoluble fertilizers can obtain the same results, which need further study. The purpose of fertilization is to increase crop yields.
The non-uniform broadcast fertilization method proposed in this paper can effectively improve the uniformity and efficiency of one-time fertilization. However, during the growth period of winter wheat, in addition to apply the bottom fertilizer, there will be several top dressings. High crop yields are the results of several efficient fertilization processes.
Additionally, in order to make the experimental results clearer, the basin was divided into ten equal-length sections to spread the fertilizer on the basin surface according to the set non-uniform application coefficients. In practice, workload increases significantly with increasing number of sub-sections. Therefore, finding the balance between the appropriate number of sections and fertilization performance is also the next step of the study.

Conclusions
In this paper, field experiments were conducted to understand the movement characteristics of fertilizers in surface water under non-uniform broadcast fertilization for basin irrigation. The spatial distribution of SO 2− 4 concentration in the soil was studied under six fertilization treatments after irrigation, and the fertilization performance was evaluated to discuss the suitable operation fertilization treatments. The solute transport model for broadcast fertilization was validated by the field experiment results, and the model was used for the numerical simulation to obtain a set of optimum non-uniform application coefficients for different basin length and inflow rate. The conclusions are as the following: (1) The non-uniform broadcast fertilization method could weaken the "backward warping ", which was caused by the accumulation of fertilizer in the tail of the basin caused by the advance of irrigation water and the solid fertilizer migration, and could effectively improve fertilization uniformity and fertilization efficiency. Under the six treatments of the designed experiments, the most effective combination of non-uniform application coefficient and inflow rate increased its fertilization uniformity and fertilization storage efficiency by 20.6% and 21.1%, compared with uniform broadcast fertilization. (2) The numerical simulation results successfully showed the effects of basin length, inflow rate and non-uniform application coefficient on fertilization uniformity and storage efficiency. With the increase of non-uniform application coefficient, the fertilization uniformity and storage efficiency increased first and then decreased. And for different basin length and inflow rate the optimum non-uniform application coefficient is different. The results showed that the higher basin length and inflow rate had greater potential to fertilization performance improvement by adopting non-uniform broadcast fertilization method. In order to be practically applicable, this paper presents a combination of the basin length, inflow rate, and non-uniform application coefficient with highest fertilization performance. In addition, in areas where it is not convenient to use the non-uniform broadcast fertilization method, smaller basin length and inflow rate will also improve the uniformity and storage efficiency of fertilization.