Optimizing Fertilizer Management Practices in Summer Maize Fields in the Yellow River Basin

: This study aims to examine the impact of combined irrigation and fertilizer control on the summer maize yield, nitrogen use efﬁciency (NE), and nitrogen leaching (NL) in the Yellow River Basin. Based on the measured data from the ﬁeld summer maize experiment in 2021 and 2022, a water-nitrogen movement model was constructed for ‘Zhengdan 958’ maize under two irrigation methods (wide furrow irrigation (G) and border irrigation (Q)), three fertilizer rates (120 kg/ha (N1), 220 kg/ha (N2), and 320 kg/ha (N3)), and three fertilizer frequencies (1 (T1), 2 (T2), and 3 (T3)), yielding 18 total treatments. Calculation of nitrogen leaching was based on water nitrogen transport modeling. The study then analyzed the factors and their combined effects. A multi-objective optimization genetic algorithm (NSGA-II) was established to evaluate maize yield, nitrogen use efﬁciency, and nitrogen leaching. The results indicate that the determination coefﬁcients between simulated and measured water, nitrogen values exceeded 0.74. The rate optimized HYDRUS model effectively simulated the soil solute movement. The interaction of the irrigation method, fertilizer rate, and fertilizer application frequency did not signiﬁcantly affect yield and nitrogen leaching, but did signiﬁcantly impact nitrogen use efﬁciency ( p < 0.05). Nitrogen leaching increased gradually as nitrogen application increased. The yield under wide furrow irrigation was 6.26% higher than that under border irrigation. The optimal coupling scheme of water and fertilizer was obtained using the genetic algorithm multi-objective optimization method, where the combined GN2T2 treatment was the optimal management model, the summer maize yield reached 14,077 kg/ha, nitrogen use efﬁciency and nitrogen leaching were reduced to 30.21 kg · kg − 1 and 17.64 kg/ha, respectively. These ﬁndings can guide summer maize cultivation in the Yellow River Basin and assist in reducing nitrogen surface source pollution.


Introduction
The Yellow River Basin, home to 11,933,300 square hectares of arable land (12.4% of China's total), plays a critical role in China's agricultural development [1].However, due to issues like outdated irrigation technology, poor ecological conditions, water scarcity, unfit soil and water resources, and irrational fertilizer application, sustainable agriculture faces challenges such as water shortages in irrigation areas, soil nitrogen pollution, and low crop economic efficiency [2,3].As such, clarifying the nitrogen control mechanism for agricultural fields in the Yellow River Basin is of paramount importance for promoting ecological protection and high-quality development in the area.
Irrigation and nitrogen fertilization are key management strategies that significantly enhance maize yields [4].Fertilizer application not only boosts crop yield but also improves drought resistance [5].However, an excessive application of nitrogen fertilizer can lead to low nitrogen use efficiency, substantial nitrogen losses, and harmful environmental effects, such as greenhouse gas emissions [6], water pollution [7], soil degradation [8], and nitrate accumulation in deep soil [9].Hence, reducing soil nitrate leaching from agroecosystems and enhancing crop yield and nitrogen use efficiency through effective nitrogen management are crucial for sustainable agriculture [10].Research by Piazzoli et al. [11] demonstrated the impacts of nitrogen fertilizer application and density on the agronomic performance of maize, observing the effects of density and application on factors such as plant thickness, plant height, ear height, and seed yield under high-altitude conditions.Jia et al. [12] noted that nitrogen leaching in maize-wheat rotation systems primarily occurred during the maize growing season.Other studies, such as that by Pan et al. [13], assessed the effect of in-season nitrogen fertilizer management (INM) on post-spat nitrogen application and its physiological impacts on maize yield.Han et al. [14] conducted a twoyear field trial to investigate the effects of the separation of nitrogen fertilizer and water with alternating furrow irrigation (SNWAFI) and conventional irrigation and fertilizer (CIF) in maize (Zea mays L.) production systems.The study assessed the impacts of irrigation and fertilizer application on soil profile water, nitrogen use, volatile soil ammonia, nitrate nitrogen leaching, and nitrate nitrogen transfer.To understand how maize yield responds to water and nitrogen regulation in different salinity levels, Xu et al. [15] conducted field experiments on three types of saline farmlands with three irrigation and nitrogen application levels, supplementing these with model simulations.Similarly, Zhao et al. [16] examined the response of physiological, ecological indicators, and summer maize yield to different urea spray concentrations, using surface irrigation and urea spreading treatments as controls.Fuentes et al. [17] studied the agronomic traits and nitrogen recovery of maize with varied nitrogen applications in both autumn-winter (off-season) and spring-summer crop seasons.
Despite their significance, separate field trials are time-consuming, require considerable effort, and lack repeatability due to field environment constraints [18].Therefore, most researchers supplement field trials with the HYDRUS model, which is widely employed for numerically simulating water movement, nitrogen migration and transformation, and crop root water uptake in agricultural fields.This approach reduces the pressure of field trials while ensuring a high degree of accuracy.Bai et al. [19] investigated the changes in transport fluxes of nitrate-nitrogen over increasing movement distances and identified the relationship between these fluxes and water diffusion coefficients.Fronczyk et al. [20] evaluated the parameters controlling the migration of nitrogen compounds through selected fine and sandy soils, factors that may affect the groundwater quality in agricultural areas.Pan et al. [21] examined the effect of water content and temperature on nitrate conversion, while Ali et al. [22] assessesd the impacts of alkaline water irrigation on soil.Mekala et al. [23] studied the transformation of nitrogen transport under various soil water content conditions.Miguel et al. [24] analyzed water flow and nitrate transport using HYDRUS-1D and explored the effect of organic matter and hydrogel on nitrate leaching.
Liu et al. [25] probed into the effects of nitrogen application and fertilizer application frequency on dry matter accumulation and nitrogen utilization in drip-irrigated summer maize.It was found that an increase in the fertilizer application frequency significantly enhanced the aboveground dry matter accumulation in summer maize and improved both the agronomic efficiency of nitrogen fertilizer and the nitrogen partial productivity of maize plants.Wang et al. [26] explored the impact of fertilizer chasing measures on summer maize yield and concluded that there was no significant effect on changes in plant height and leaf area index.Xiao et al. [27] studied the effect of urea follow-up on nitrogen volatilization and leaching during winter wheat and summer maize seasons, and observed that urea follow-up substantially reduced the ammonia volatilization and leaching losses of followup nitrogen.Ding et al. [28] investigated the recovery supply of supplementary fertilizer on the growth and yield of flooded maize, and found that the supplementary application of nitrogen fertilizer significantly enhanced the recovery effect on growth and yield.
In conclusion, substantial research on the multifaceted aspects of irrigation methods and the interaction of water and nitrogen in maize has been conducted.However, less focus has been directed towards the combined effects of irrigation methods and fertilizer schedules in the irrigated areas of the Yellow River Basin.Various irrigation methods and fertilizer control measures may have differing coupling effects on maize growth, yield, and nitrogen utilization.The mechanism of fertilizer regulation in summer maize in the Yellow River Basin has yet to be explored, and there is a conspicuous lack of precise models for water and nitrogen movement in summer maize.Wide furrow irrigation and border irrigation, two main methods used in the Yellow River Basin's irrigation areas, are noted for their simplicity of operation and minimal cost expenditure.The study examined the fusion of varying irrigation methods, differing fertilizer frequencies, and three distinct nitrogen application rates-high, medium, and low.A two-year comparative field experiment was conducted on summer maize to optimize water and nitrogen movement parameters, based on the data acquired from the 2021 summer maize field, which was validated against the measured values from the 2022 trial.The HYDRUS model was constructed under two irrigation methods to examine the synergistic response mechanism of nitrogen leaching, nitrogen use efficiency and nitrogen leaching to the different experimental schemes.The goal was to propose an appropriate irrigation and fertilizer control system for summer maize in the Yellow River Basin.This research is intended to provide a technical reference for fertilizer management in the main summer maize production areas.

Overview and Soil Characteristics of the Study Area
The trial took place at the experimental field of the North China University of Water Resources and Electric Power in Zhengzhou.Before the trial commenced, the particle size composition of the soil at different depths was determined using a laser particle size distribution instrument.The basic physicochemical properties of the soil were also evaluated.The specific soil properties are presented in Table 1, and the experimental location is depicted in Figure 1.

Experimental Design
The variety of summer maize selected for this study was 'Zhengdan 958'.Planting was conducted on 9 June 2021, and 8 June 2022, with harvest taking place upon maturation on 30 September 2021, and 17 September 2022, respectively.Given the optimal range for N application to summer maize in the Yellow River Basin and prevalent irrigation methods, an experimental irrigation and N application program was developed [29,30].A split-plot design was employed, with the primary plot focusing on the irrigation method, the secondary plot on the amount of nitrogen applied, and the secondary sub-plot on the fertilizer frequencies.The primary plot included wide furrow irrigation and border irrigation, while the secondary plot was designed with low nitrogen (120 kg/ha, N1), medium nitrogen (220 kg/ha, N2), and high nitrogen (320 kg/ha, N3).The secondary sub-plot was divided into 1 (T1), 2 (T2), and 3 (T3) fertilizer application frequency.The base fertilizer was a compound fertilizer (N-15, P-15, K-15) and the topdressing fertilizer was urea with a nitrogen mass fraction of 46%.Each treatment maintained soil water control at 70% of the field capacity (θ field ).A control group (CK) was established without irrigation and fertilizer treatment.The trial design is detailed in Table 2, and Figure 2 shows the variation in rainfall during the trial.Drainage ditches were installed in the field to drain water from the field ditches.

Experimental Design
The variety of summer maize selected for this study was 'Zhengdan 958'.Planting was conducted on 9 June 2021, and 8 June 2022, with harvest taking place upon maturation on 30 September 2021, and 17 September 2022, respectively.Given the optimal range for N application to summer maize in the Yellow River Basin and prevalent irrigation methods, an experimental irrigation and N application program was developed [29,30].A splitplot design was employed, with the primary plot focusing on the irrigation method, the secondary plot on the amount of nitrogen applied, and the secondary sub-plot on the fertilizer frequencies.The primary plot included wide furrow irrigation and border irrigation, while the secondary plot was designed with low nitrogen (120 kg/ha, N1), medium nitrogen (220 kg/ha, N2), and high nitrogen (320 kg/ha, N3).The secondary sub-plot was divided into 1 (T1), 2 (T2), and 3 (T3) fertilizer treatments.The base fertilizer was a compound fertilizer (N-15, P-15, K-15) and the topdressing fertilizer was urea with a nitrogen mass fraction of 46%.Each treatment maintained soil water control at 70% of the field capacity (θfield).A control group (CK) was established without irrigation and fertilizer treatment.The trial design is detailed in Table 2, and Figure 2 shows the variation in rainfall during the trial.Drainage ditches were installed in the field to drain water from the field ditches.

Soil Nitrogen Determination
Nitrate nitrogen and ammonium nitrogen levels in the soil were assessed using a UV

Soil Nitrogen Determination
Soil was sampled using soil augers at a depth of 0-1 m in layers of 20 cm, for a total of 5 layers.Nitrate nitrogen and ammonium nitrogen levels in the soil were assessed using a UV spectrophotometer at critical points in the reproductive phase, both before and after fertilizer application.

Maize Yield
In each plot, a 1 m 2 area of summer maize was randomly selected, and the relevant yield indicators, such as thousand kernel mass, were measured.The total mass was weighed after drying to calculate the yield per unit area.

Nitrogen Use Efficiency and Nitrogen Leaching
Nitrogen use efficiency (NE, kg•kg −1 ): where U N is the amount of nitrogen absorbed by the crop, kg/hm 2 ; and U CK is the amount of nitrogen absorbed by the control crop, kg/hm 2 , and T N is the amount of nitrogen applied.Calculation of Nitrogen leaching (NL, kg/ha): In this study, NL was defined as the cumulative changes in nitrate nitrogen in the soil layer ranging from 60 to 100 cm.Soil nitrate nitrogen residues were determined using the equal mass method [31].
where NL i represents the cumulative amount of nitrate nitrogen in the equivalent mass of soil, kg/ha; P i denotes the soil volume of layer i, g/cm 3 ; H i signifies the thickness of layer i, cm; and M i is the nitrate nitrogen content of layer i, mg/kg.

NSGA-II
The Multi-objective Optimisation Genetic Algorithm (NSGA-II) is an evolutionary algorithm for solving multi-objective optimisation problems.It is based on the principle of genetic algorithm to find the optimal set of solutions to the problem by simulating the process of biological evolution.A general mathematical model of a multi-objective optimization problem can be expressed as follows: where V-max is vector maximization, x denotes a factor, n stands for the number of objective functions, s represents the initial number of individuals, t signifies the maximum number of genetic generations, X symbolizes the coupling treatment, and m is the number of factors.This paper employs a genetic algorithm's parallel selection method to solve the Pareto solution for the multi-objective function [32].

HYDRUS Models
The model's accuracy was appraised employing mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R 2 ).The wide furrow irrigation approach encompassed five observation points horizontally and five vertically, totaling 10, whereas border irrigation involved five observation points only in the vertical direction.

Water and Nitrogen Transport Equations
The water and nitrogen transport equations using the fundamental equation for unsaturated soil water movement and the convective dispersion equation.The van Genuchten-Mualem (VG-M) model [33] was utilized to calculate K(θ).
where Ks is the soil saturated hydraulic conductivity, cm/min; α is the reciprocal of the air-entry suction value, /cm; m and n are shape coefficients, with m = 1 − 1/n; and l is the soil hydraulic characteristic curve fitting coefficient, 0.5; c is the mass concentration of soil solution, g/cm 3 ; D w ij is the dispersion coefficient, cm 2 /d.

Root System Water Uptake Equation
Field measurements indicate that the roots of summer maize were primarily distributed in the soil from 0 to 60 cm in depth.Thus, the Feddes model was used to represent the water uptake equation for summer maize [34].
where α(x, y, z, h) represents the water stress response function, b(x, z) denotes the root water uptake distribution function, 1•d −1 ; T P symbolizes the potential crop transpiration rate, cm•d −1 ; and L T signifies the soil surface width during transpiration, cm.

Crop Transpiration Rate
The potential evapotranspiration (PET) is calculated employing the single crop coefficient technique.The reference crop evapotranspiration (E T0 ) is calculated using the Penman-Monteith equation, reliant on meteorological data from proximate weather stations in the experimental vicinity.Then, the PET of the crop is subsequently calculated using the single crop coefficient method, followed by using the Beer's law to separate the potential evaporation and potential transpiration components [35].
The PET is calculated as follows: where E T is the potential evapotranspiration, mm; K C is the combined crop coefficient, using the FAO recommendations.Beer's law calculates the potential evapotranspiration equation: where T P is the potential transpiration, mm; K is the extinction coefficient dimensionless, usually 0.4 for maize; and L is the leaf area index dimensionless.The actual transpiration is calculated as follows: where T is the actual transpiration, mm/d; Ω is the root zone area, cm 2 ; α is the water stress factor; w is the soil water potential, cm; w φ is the percolation head, cm; and b is the root distribution function.

Initial and Boundary Conditions
Initial conditions: the initial water content and the ammonium and nitrate nitrogen content of each soil layer, as per field trial measurements, were input into the HYDRUS-2D module in layers.This simulation assumed that the initial water and nitrogen content of each soil layer was uniformly distributed in both horizontal and vertical directions.
where i is the number of soil layers; θ i represents the soil water content of layer i; c i denotes the mass concentration of ammonium or nitrate nitrogen of layer i, mg•cm −3 ; θ 0i stands for the initial value of θ i ; c 0i is the initial value of c i ; z iu represents the vertical coordinate of the upper boundary of layer i, cm; z id denotes the vertical coordinate of the lower boundary of layer i, cm.The upper and lower boundaries of the wide furrow and border irrigation models were set at 0 mm above the model surface and 100 mm below the soil depth of the field, respectively.The upper boundary is set to the atmospheric boundary, the boundary conditions change daily with time, and the corresponding daily meteorological data are entered during the test simulation period.

Parameter Selection
The optimized rates for the V-G model parameters and nitrogen kinematics parameters were determined based on the measured soil water content and nitrogen values for the summer maize treatments in the 2021 field, using the integrated inversion module of the HYDRUS-2D(3.x)software (see Table 3).

Model Validation
The treatments of the 2022 field trial were numerically simulated based on the adjusted water and nitrogen transport parameters in Table 3, and compared with the actual measurements from the field.Figures 3 and 4 display a comparison between the measured and simulated values of soil water content, ammonium nitrogen, and nitrate nitrogen during the reproductive period of summer maize with wide furrow and border irrigation (N2T1-N2T3).As illustrated in Figures 3 and 4, the developed model, using adjusted soil hydraulic property parameters and solute transport transformation parameters, demonstrated a high degree of accuracy.A detailed analysis of the water and nitrogen errors can be found in Table 4.The coefficients of determination for the simulated and measured values of water content exceeded 0.8, with both MAE and RMSE below 0.02.The coefficients of determination for the simulated and measured ammonium nitrogen values exceeded 0.74, with both MAE and RMSE under 0.0012.Finally, the coefficients of determination for the simulated and measured nitrogen values surpassed 0.77, with both MAE and RMSE less than 0.003.

Effect of Different Irrigation and Fertilizer Treatments on Maize Yield
To evaluate the impacts of irrigation and fertilizer management strategies on summer maize yield, NE, and NL, both ANOVA and multiple comparisons were performed (see Table 5).As demonstrated in Table 5, the fertilizer application frequency, irrigation method, and fertilizer rate significantly influenced summer maize yield (p < 0.01).Moreover, the interaction between the fertilizer application frequency and fertilizer rate exhibited a highly significant effect on yield (p < 0.01).However, the interaction effect of these three factors did not significantly affect on yield (p > 0.05).Among these, the influence of fertilizer rate on yield was more pronounced than fertilizer application frequency and irrigation method.To assess the effect of various fertilizer management measures on yield improvement, a control group without any fertilizer treatment was used.This is depicted in Figure 5.As observed in Figure 5, for T1 and T2 treatments, the yield initially increased and then decreased with a rise in the nitrogen application frequency, under both irrigation methods.The yield peaked at the N2T2 treatment, reaching 13969.5 kg/ha and 14077.36kg/ha, respectively.On average, the yield under wide furrow irrigation was 6.26% higher than that under border irrigation.In the case of the N3 treatment, multiple fertilizer treatments boosted the summer maize yield to 12277.64 kg/ha (for GN3T3), which was an increase of 124.8% compared to GN3T1, and to 12023.16kg/ha (for QN3T3), marking a 129.56% yield increase compared to QN3T1.

Effect of Different Irrigation and Fertilizer Control Methods on NE
As indicated in Table 5, the combined effects of the irrigation method, fertilizer application frequency, and fertilizer rate on NE were significant (p < 0.05).Also, the interaction effects between any two of these three factors on NE were significant (p < 0.05).Individually, all of these factors had a highly significant influence on NE (p < 0.01).Moreover, the impacts of fertilizer application frequency, fertilizer rate, and irrigation method on NE, followed the order: fertilizer rate > fertilizer application frequency > irrigation method.From Figure 6, at the same N application rate, NE showed a trend of increasing

Effect of Different Irrigation and Fertilizer Control Methods on NE
As indicated in Table 5, the combined effects of the irrigation method, fertilizer application frequency, and fertilizer rate on NE were significant (p < 0.05).Also, the interaction effects between any two of these three factors on NE were significant (p < 0.05).Individually, all of these factors had a highly significant influence on NE (p < 0.01).Moreover, the impacts of fertilizer application frequency, fertilizer rate, and irrigation method on NE, followed the order: fertilizer rate > fertilizer application frequency > irrigation method.From Figure 6, at the same N application rate, NE showed a trend of increasing and then decreasing when one or two fertilizer treatments were carried out, and consistently increasing at three fertilizer treatments.The wide furrow irrigation treatment significantly increased NE, reaching the maximum (30.21 kg•kg −1 ) for the N2T2 treatment with wide furrow irrigation and the minimum (13.84 kg•kg −1 ) for the N3T1 treatment with border irrigation.

Effect of Different Irrigation and Fertilizer Control Methods on NL
In this study, NL was defined as the cumulative changes in ammonium and nitrate nitrogen in the soil layer ranging from 60 to 100 cm.The HYDRUS water, which simulates water and nitrogen transport for summer maize in the Yellow River Basin, was constructed based on field measurements from 2021 to 2022.It was used to simulate soil water and fertilizer transport transformations, as well as the main patterns of change under rainfall conditions.NL was determined based on the dynamic changes in soil nitrogen content at a depth of 60 to 100 cm.As per Table 5, the interaction effects of irrigation method, fertilizer application frequency, and fertilizer rate on NL was insignificant (p > 0.05).The two-by-two interaction effect between factors and the effect of a single factor on NL was highly significant.Figure 7 illustrates the nitrogen leaching in each treatment.As seen from Figure 7, NL was generally higher in the broad furrow irrigation than in the border irrigation.NL was at its peak in the N3T1 treatment.Compared with the CK treatment, NL increased by 515.32% and 457.11% in the N3T1 treatment with wide furrow and border irrigation.Given the same nitrogen treatment, NL significantly reduced with an increase in the fertilizer application frequency.From QN3T1 to QN3T3, NL decreased by 19.42% and 44.30% for QN3T2 and QN3T3, respectively, in comparison with the QN3T1 treatment.NL was significantly increased by increasing the amount of nitrogen applied at a given number of fertilizer treatments.From QN1T1 to QN3T1, the NL decreased by 27.65% and 66.11% for QN2T1 and QN3T1, respectively, in comparison with the QN3T1 treatment.

Effect of Different Irrigation and Fertilizer Control Methods on NL
In this study, NL was defined as the cumulative changes in ammonium and nitrate nitrogen in the soil layer ranging from 60 to 100 cm.The HYDRUS water, which simulates water and nitrogen transport for summer maize in the Yellow River Basin, was constructed based on field measurements from 2021 to 2022.It was used to simulate soil water and fertilizer transport transformations, as well as the main patterns of change under rainfall conditions.NL was determined based on the dynamic changes in soil nitrogen content at a depth of 60 to 100 cm.As per Table 5, the interaction effects of irrigation method, fertilizer application frequency, and fertilizer rate on NL was insignificant (p > 0.05).The two-by-two interaction effect between factors and the effect of a single factor on NL was highly significant.Figure 7 illustrates the nitrogen leaching in each treatment.As seen from Figure 7, NL was generally higher in the broad furrow irrigation than in the border irrigation.NL was at its peak in the N3T1 treatment.Compared with the CK treatment, NL increased by 515.32% and 457.11% in the N3T1 treatment with wide furrow and border irrigation.Given the same nitrogen treatment, NL significantly reduced with an increase in the fertilizer application frequency.From QN3T1 to QN3T3, NL decreased by 19.42% and 44.30% for QN3T2 and QN3T3, respectively, in comparison with the QN3T1 treatment.NL was significantly increased by increasing the amount of nitrogen applied at a given number of fertilizer treatments.From QN1T1 to QN3T1, the NL decreased by 27.65% and 66.11% for QN2T1 and QN3T1, respectively, in comparison with the QN3T1 treatment.
The R 2 for these three regression equations were verified to be 0.947, 0.98, and 0.987, respectively, signifying that the regression relationships were significant.The multi-objective optimization problem was then modeled using Equations ( 15)-(17).
The multi-objective optimal genetic algorithm was solved using Matlab 2019a.We set the initial number of individuals to 2000, the maximum number of genetic generations to 300, the binary number of variables to 20, the crossover probability to 0.7, and the generation gap to 0.9.This produced an optimal yield of 14,077 kg/ha, an optimal NE of 30.21 kg•kg −1 , and optimal NL of 17.64 kg/ha.The treatment was determined to be GN2T2 when the optimal solution was reached.

Genetic Algorithm-Based Optimization of Yield, NE, and NL Combinations
Experimental data for yield, NE, and NL were analyzed using a ternary quadratic fit.This resulted in a regression model for summer maize yield (Y), NE, and NL based on the coded values of the fertilizer application frequency (x 1 ), fertilizer rate (x 2 ), and irrigation method (x 3 ).The R 2 for these three regression equations were verified to be 0.947, 0.98, and 0.987, respectively, signifying that the regression relationships were significant.The multi-objective optimization problem was then modeled using Equations ( 15)- (17).
The multi-objective optimal genetic algorithm was solved using Matlab 2019a.We set the initial number of individuals to 2000, the maximum number of genetic generations to 300, the binary number of variables to 20, the crossover probability to 0.7, and the generation gap to 0.9.This produced an optimal yield of 14,077 kg/ha, an optimal NE of 30.21 kg•kg −1 , and optimal NL of 17.64 kg/ha.The treatment was determined to be GN2T2 when the optimal solution was reached.

Discussion
The rate optimized HYDRUS model demonstrated an improved capacity to simulate soil solute movement.This aligns with the findings of previous studies [36].Although the simulation of ammonium nitrogen was not as accurate as that of nitrate nitrogen, it was still better than previous simulations.This could be attributed to maintaining the soil water content at 70% of the field water holding rate throughout the whole growth period.This condition ensured a higher soil moisture level, facilitating faster water movement.Consequently, ammonium nitrogen was transported to deeper soil layers, thus reducing its accumulation in surface soil colloids due to sorption [37].The coefficients of determination for both the simulated and measured nitrogen values exceeded 0.74, indicating that HYDRUS could be successfully utilized for NL pollution studies in agricultural fields.
Water and nitrogen play a pivotal role in crop yield, with a proper supply of both significantly enhancing crop growth and yield [38]. Yield serves as a key indicator for evaluating the growth of summer maize [39].Given a fixed nitrogen application, the yield of summer maize rose with the fertilizer application frequency.However, when applying fertilizer only once, the yield showed a parabolic pattern, increasing first and then decreasing with an increase in nitrogen application.This is attributed to the surplus nitrogen application, leading to excess residual soil nitrate nitrogen, which tends to be carried deeper into the soil with the mid-loam flow [40,41].This surplus is challenging for maize to reabsorb and use, thereby elevating the risk of nitrogen pollution in the deeper soil.An application of a single fertilizer rate of 265 kg/ha resulted in soil solution concentrations higher than the concentration in the root cytosol, causing cell dehydration, cytoplasmic and wall separation, and wilting of stems and leaves, particularly during the seedling stage of summer maize.At this stage, cytosol concentration was even lower, making the seedlings more susceptible to damage from excessive fertilizer concentrations.Zhao et al. [16] found that the maximum maize yield was achieved with a total nitrogen application rate of 215 kg/ha, which aligns with the nitrogen application rate employed in this study to achieve maximum yield.Nitrate leaching from soil is a major route for fertilizer NL [42,43], and increasing the fertilizer application frequency can effectively mitigate NL issues.Lowering fertilizer application enhanced NE and nitrogen physiological efficiency and reduced NL, but significantly reduced maize yield, which is in accordance with Liu et al.'s study [44].
Yield, NE, and NL are essential indicators for green summer maize production [45].However, the evaluation results of a single objective often encompass a certain degree of uncertainty, complicating the realization of high crop yield while reducing NL.We employed a multi-objective optimal genetic algorithm to seek the optimal solution.The efficacy and reliability of the genetic algorithm juxtaposition selection method in solving the issue of optimal crop water and fertilizer ratios have been validated by Zhang et al. [30].However, in their study, the optimal yield was obtained with a nitrogen application of 270 kg/ha, slightly higher than the nitrogen application of 220 kg/ha in our findings.This difference was due to the trial being conducted with multiple fertilizers in summer to prevent NL caused by heavy rainfall and to minimize nitrogen losses.This study utilized this method to find the optimal solution for yield, NE, and NL for different irrigation methods combined with fertilizer regulation.The solution takes into account yield, NE, and NL, rendering it more widely applicable than previous comprehensive analysis methods that generate uncertainties.

Conclusions
(1) The rate optimized HYDRUS model demonstrates enhanced capabilities in simulating soil water solute movement, thus qualifying the HYDRUS model for NL simulations.(2) The irrigation method, fertilizer application frequency, and fertilizer rate significantly impact yield, NE, and NL.However, the combined effects of these three factors were found to be insignificant for yield and NL, and significant for NE.Notably, the increment in the fertilizer application frequency significantly diminishes NL.

Figure 1 .
Figure 1.Schematic diagram of the experimental location.

Figure 3 .
Figure 3.Comparison of simulated and measured values of water content, ammonium nitrogen, and nitrate nitrogen in wide furrow irrigation.

Figure 4 .
Figure 4. Comparison of simulated and measured values of water content, ammonium nitrogen, and nitrate nitrogen in border irrigation.

Figure 4 .
Figure 4. Comparison of simulated and measured values of water content, ammonium nitrogen, and nitrate nitrogen in border irrigation.

Figure 5 .
Figure 5.Effect of irrigation method and fertilizer treatments on yield.a, b, c, d…… whether the differences between groups are significant or not by comparing them with each other, same figure below.

Figure 5 .
Figure 5.Effect of irrigation method and fertilizer treatments on yield.a, b, c, d. ... . .whether the differences between groups are significant or not by comparing them with each other.

1 Figure 6 .
Figure 6.Effect of irrigation method and fertilizer treatments on NE.

Figure 6 .
Figure 6.Effect of irrigation method and fertilizer treatments on NE. a, b, c, d. ... . .whether the differences between groups are significant or not by comparing them with each other.

− 1 Figure 7 .
Figure 7. Effect of irrigation method and fertilizer control measures on NL.

Figure 7 .
Figure 7. Effect of irrigation method and fertilizer control measures on NL.

Table 1 .
Basic physicochemical parameters of the soil.

Table 2 .
Different water and fertilizer treatment options for summer maize.

Table 2 .
Different water and fertilizer treatment options for summer maize.

Table 3 .
Optimization of model water-nitrogen transport parameters.

Table 4 .
Error analysis of measured and simulated values of soil volumetric water content, ammonium nitrogen, and nitrate nitrogen.
Figure 3.Comparison of simulated and measured values of water content, ammonium nitrogen, and nitrate nitrogen in wide furrow irrigation.

Table 4 .
Error analysis of measured and simulated values of soil volumetric water content, ammonium nitrogen, and nitrate nitrogen.

Table 5 .
Effect of different treatments on summer maize yield, NE, and NL.
Note: * indicates significant correlation at the 0.05 level.** indicates highly significant correlation at the 0.01 level, same table below Agronomy 2023, 13, x FOR PEER REVIEW 13 of 19